%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW376+1 : TPTP v8.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n025.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Jun 24 18:08:47 EDT 2024 % Result : Theorem 178.07s 177.92s % Output : CNFRefutation 178.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SWW376+1 : TPTP v8.2.0. Released v5.2.0. % 0.12/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.35 % Computer : n025.cluster.edu % 0.12/0.35 % Model : x86_64 x86_64 % 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.35 % Memory : 8042.1875MB % 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.35 % CPULimit : 300 % 0.12/0.35 % WCLimit : 300 % 0.12/0.35 % DateTime : Wed Jun 19 07:15:39 EDT 2024 % 0.12/0.35 % CPUTime : % 0.53/0.59 start to proof:theBenchmark % 177.61/177.75 %------------------------------------------- % 177.61/177.75 % File :CSE---1.7 % 177.61/177.75 % Problem :theBenchmark % 177.61/177.75 % Transform :cnf % 177.61/177.75 % Format :tptp:raw % 177.61/177.75 % Command :java -jar mcs_scs.jar %d %s % 177.61/177.75 % 177.61/177.75 % Result :Theorem 163.680000s % 177.61/177.75 % Output :CNFRefutation 163.680000s % 177.61/177.75 %------------------------------------------- % 177.61/177.75 %------------------------------------------------------------------------------ % 177.61/177.75 % File : SWW376+1 : TPTP v8.2.0. Released v5.2.0. % 177.61/177.75 % Domain : Software Verification % 177.61/177.75 % Problem : Hoare's Logic with Procedures 435545, 5000 axioms selected % 177.61/177.75 % Version : Especial. % 177.61/177.75 % English : % 177.61/177.75 % 177.61/177.75 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 177.61/177.75 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 177.61/177.75 % Source : [Bla11] % 177.61/177.75 % Names : hoare_435545.5000.p [Bla11] % 177.61/177.75 % 177.61/177.75 % Status : ContradictoryAxioms % 177.61/177.75 % Rating : 0.83 v8.2.0, 0.78 v8.1.0, 0.81 v7.4.0, 0.90 v7.3.0, 0.86 v7.1.0, 0.87 v7.0.0, 0.90 v6.4.0, 0.88 v6.3.0, 0.83 v6.2.0, 0.92 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.96 v5.3.0, 1.00 v5.2.0 % 177.61/177.75 % Syntax : Number of formulae : 5243 (1736 unt; 0 def) % 177.61/177.75 % Number of atoms : 12595 (4516 equ) % 177.61/177.75 % Maximal formula atoms : 13 ( 2 avg) % 177.61/177.75 % Number of connectives : 8368 (1016 ~; 154 |; 715 &) % 177.61/177.75 % ( 895 <=>;5588 =>; 0 <=; 0 <~>) % 177.61/177.75 % Maximal formula depth : 22 ( 6 avg) % 177.61/177.75 % Maximal term depth : 19 ( 2 avg) % 177.61/177.75 % Number of predicates : 144 ( 143 usr; 2 prp; 0-6 aty) % 177.61/177.75 % Number of functors : 384 ( 384 usr; 56 con; 0-7 aty) % 177.61/177.75 % Number of variables : 16657 (16512 !; 145 ?) % 177.61/177.75 % SPC : FOF_CAX_RFO_SEQ % 177.61/177.75 % 177.61/177.75 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 177.61/177.75 % 2011-03-01 12:49:52 % 177.61/177.75 %------------------------------------------------------------------------------ % 177.61/177.75 %----Relevant facts (4986) % 177.61/177.75 fof(fact_ext,axiom, % 177.61/177.75 ! [V_g_2,V_f_2] : % 177.61/177.75 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 177.61/177.75 => V_f_2 = V_g_2 ) ). % 177.61/177.75 % 177.61/177.75 fof(fact_image__image,axiom, % 177.61/177.75 ! [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) ). % 177.61/177.75 % 177.61/177.75 fof(fact_image__ident,axiom, % 177.61/177.75 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 177.61/177.75 % 177.61/177.75 fof(fact_com_Osimps_I6_J,axiom, % 177.61/177.75 ! [V_pname_H_2,V_pname_2] : % 177.61/177.75 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2) % 177.61/177.75 <=> V_pname_2 = V_pname_H_2 ) ). % 177.61/177.75 % 177.61/177.75 fof(fact_WT__bodiesD,axiom, % 177.61/177.75 ! [V_b,V_pn] : % 177.61/177.75 ( c_Com_OWT__bodies % 177.61/177.75 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) % 177.61/177.75 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ). % 177.61/177.75 % 177.61/177.75 fof(fact_finite__dom__body,axiom, % 177.61/177.75 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ). % 177.61/177.75 % 177.61/177.75 fof(fact_WT_OBody,axiom, % 177.61/177.76 ! [V_pn] : % 177.61/177.76 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom) % 177.61/177.76 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_WT_Oequations_I7_J,axiom, % 177.61/177.76 ! [V_a_2] : % 177.61/177.76 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2))) % 177.61/177.76 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_state__not__singleton__def,axiom, % 177.61/177.76 ( c_Hoare__Mirabelle_Ostate__not__singleton % 177.61/177.76 <=> ? [B_s,B_t] : B_s != B_t ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_single__stateE,axiom, % 177.61/177.76 ( c_Hoare__Mirabelle_Ostate__not__singleton % 177.61/177.76 => ! [B_t] : % 177.61/177.76 ~ ! [B_s] : B_s = B_t ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_MGF__lemma1,axiom, % 177.61/177.76 ! [V_ca_2,V_G_2] : % 177.61/177.76 ( c_Hoare__Mirabelle_Ostate__not__singleton % 177.61/177.76 => ( ! [B_x] : % 177.61/177.76 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) % 177.61/177.76 => 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)))) ) % 177.61/177.76 => ( hBOOL(hAPP(c_Com_OWT,V_ca_2)) % 177.61/177.76 => 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)))) ) ) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_WTs__elim__cases_I8_J,axiom, % 177.61/177.76 ! [V_a_2,V_P_2,V_X_2] : % 177.61/177.76 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2))) % 177.61/177.76 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P_2))) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_WT_Oequations_I8_J,axiom, % 177.61/177.76 ! [V_a3_2,V_a1_2,V_a2_2] : % 177.61/177.76 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2))) % 177.61/177.76 <=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_empty__not__insert,axiom, % 177.61/177.76 ! [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) ). % 177.61/177.76 % 177.61/177.76 fof(fact_insert__not__empty,axiom, % 177.61/177.76 ! [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)) ). % 177.61/177.76 % 177.61/177.76 fof(fact_empty,axiom, % 177.61/177.76 ! [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))) ). % 177.61/177.76 % 177.61/177.76 fof(fact_hoare__derivs_Oequations_I1_J,axiom, % 177.61/177.76 ! [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))) ). % 177.61/177.76 % 177.61/177.76 fof(fact_insert__absorb2,axiom, % 177.61/177.76 ! [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) ). % 177.61/177.76 % 177.61/177.76 fof(fact_insert__commute,axiom, % 177.61/177.76 ! [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)) ). % 177.61/177.76 % 177.61/177.76 fof(fact_doubleton__eq__iff,axiom, % 177.61/177.76 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 177.61/177.76 ( 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)))) % 177.61/177.76 <=> ( ( V_a_2 = V_ca_2 % 177.61/177.76 & V_b_2 = V_d_2 ) % 177.61/177.76 | ( V_a_2 = V_d_2 % 177.61/177.76 & V_b_2 = V_ca_2 ) ) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_com_Osimps_I7_J,axiom, % 177.61/177.76 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] : % 177.61/177.76 ( 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) % 177.61/177.76 <=> ( V_vname_2 = V_vname_H_2 % 177.61/177.76 & V_pname_2 = V_pname_H_2 % 177.61/177.76 & V_fun_2 = V_fun_H_2 ) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_insert__code,axiom, % 177.61/177.76 ! [V_x_2,V_A_2,V_y_2,T_a] : % 177.61/177.76 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2),V_x_2)) % 177.61/177.76 <=> ( V_y_2 = V_x_2 % 177.61/177.76 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_cut,axiom, % 177.61/177.76 ! [V_G_2,V_ts_2,V_G_H_2,T_a] : % 177.61/177.76 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 177.61/177.76 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_G_H_2) % 177.61/177.76 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_hoare__derivs_Oinsert,axiom, % 177.61/177.76 ! [V_ts_2,V_t_2,V_G_2,T_a] : % 177.61/177.76 ( 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)))) % 177.61/177.76 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) % 177.61/177.76 => 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)) ) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_derivs__insertD,axiom, % 177.61/177.76 ! [V_ts_2,V_t_2,V_G_2,T_a] : % 177.61/177.76 ( 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)) % 177.61/177.76 => ( 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)))) % 177.61/177.76 & c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_singleton__inject,axiom, % 177.61/177.76 ! [V_b_2,V_a_2,T_a] : % 177.61/177.76 ( 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))) % 177.61/177.76 => V_a_2 = V_b_2 ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_image__constant__conv,axiom, % 177.61/177.76 ! [V_ca_2,T_b,T_a,V_A_2] : % 177.61/177.76 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.61/177.76 => 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)) ) % 177.61/177.76 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.61/177.76 => 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))) ) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_image__insert,axiom, % 177.61/177.76 ! [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)) ). % 177.61/177.76 % 177.61/177.76 fof(fact_image__is__empty,axiom, % 177.61/177.76 ! [V_A_2,V_f_2,T_a,T_b] : % 177.61/177.76 ( 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)) % 177.61/177.76 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_image__empty,axiom, % 177.61/177.76 ! [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)) ). % 177.61/177.76 % 177.61/177.76 fof(fact_empty__is__image,axiom, % 177.61/177.76 ! [V_A_2,V_f_2,T_b,T_a] : % 177.61/177.76 ( 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) % 177.61/177.76 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_com_Osimps_I63_J,axiom, % 177.61/177.76 ! [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) ). % 177.61/177.76 % 177.61/177.76 fof(fact_com_Osimps_I62_J,axiom, % 177.61/177.76 ! [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) ). % 177.61/177.76 % 177.61/177.76 fof(fact_WT_OCall,axiom, % 177.61/177.76 ! [V_a_2,V_X_2,V_pn_2] : % 177.61/177.76 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn_2))) % 177.61/177.76 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2))) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_finite__imageI,axiom, % 177.61/177.76 ! [V_h_2,T_b,V_F_2,T_a] : % 177.61/177.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 177.61/177.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_F_2))) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_finite_OinsertI,axiom, % 177.61/177.76 ! [V_a_2,V_A_2,T_a] : % 177.61/177.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.61/177.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_finite_OemptyI,axiom, % 177.61/177.76 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 177.61/177.76 % 177.61/177.76 fof(fact_dom__eq__empty__conv,axiom, % 177.61/177.76 ! [V_f_2,T_b,T_a] : % 177.61/177.76 ( c_Map_Odom(T_a,T_b,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.61/177.76 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_dom__empty,axiom, % 177.61/177.76 ! [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)) ). % 177.61/177.76 % 177.61/177.76 fof(fact_insert__dom,axiom, % 177.61/177.76 ! [T_b,V_y_2,T_a,V_x_2,V_f_2] : % 177.61/177.76 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 177.61/177.76 => 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) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_MGT__BodyN,axiom, % 177.61/177.76 ! [V_G_2,V_pn_2] : % 177.61/177.76 ( 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)))) % 177.61/177.76 => 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)))) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_the__elem__eq,axiom, % 177.61/177.76 ! [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 ). % 177.61/177.76 % 177.61/177.76 fof(fact_WTs__elim__cases_I7_J,axiom, % 177.61/177.76 ! [V_P] : % 177.61/177.76 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P))) % 177.61/177.76 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_bot__fun__def,axiom, % 177.61/177.76 ! [V_x_2,T_b,T_a] : % 177.61/177.76 ( class_Orderings_Obot(T_a) % 177.61/177.76 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_option_Osimps_I2_J,axiom, % 177.61/177.76 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ). % 177.61/177.76 % 177.61/177.76 fof(fact_option_Osimps_I3_J,axiom, % 177.61/177.76 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ). % 177.61/177.76 % 177.61/177.76 fof(fact_the_Osimps,axiom, % 177.61/177.76 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ). % 177.61/177.76 % 177.61/177.76 fof(fact_finite__code,axiom, % 177.61/177.76 ! [V_A_2,T_a] : % 177.61/177.76 ( class_Finite__Set_Ofinite(T_a) % 177.61/177.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_finite,axiom, % 177.61/177.76 ! [V_A_2,T_a] : % 177.61/177.76 ( class_Finite__Set_Ofinite(T_a) % 177.61/177.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_option_Oinject,axiom, % 177.61/177.76 ! [V_a_H_2,V_a_2,T_a] : % 177.61/177.76 ( hAPP(c_Option_Ooption_OSome(T_a),V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_a_H_2) % 177.61/177.76 <=> V_a_2 = V_a_H_2 ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_bot__apply,axiom, % 177.61/177.76 ! [V_x_2,T_b,T_a] : % 177.61/177.76 ( class_Orderings_Obot(T_a) % 177.61/177.76 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_finite_Oequations_I1_J,axiom, % 177.61/177.76 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 177.61/177.76 % 177.61/177.76 fof(fact_finite__insert,axiom, % 177.61/177.76 ! [V_A_2,V_a_2,T_a] : % 177.61/177.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) % 177.61/177.76 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_not__None__eq,axiom, % 177.61/177.76 ! [T_a,V_x_2] : % 177.61/177.76 ( V_x_2 != c_Option_Ooption_ONone(T_a) % 177.61/177.76 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_a),B_y) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_not__Some__eq,axiom, % 177.61/177.76 ! [T_a,V_x_2] : % 177.61/177.76 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_a),B_y) % 177.61/177.76 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_Option_Oset_Osimps_I2_J,axiom, % 177.61/177.76 ! [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))) ). % 177.61/177.76 % 177.61/177.76 fof(fact_weak__Body,axiom, % 177.61/177.76 ! [V_Q_2,V_pn_2,V_P_2,V_G_2,T_a] : % 177.61/177.76 ( 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)))) % 177.61/177.76 => 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)))) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_BodyN,axiom, % 177.61/177.76 ! [V_G_2,V_Q_2,V_pn_2,V_P_2,T_a] : % 177.61/177.76 ( 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)))) % 177.61/177.76 => 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)))) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_folding__one__idem_Oinsert__idem,axiom, % 177.61/177.76 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 177.61/177.76 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 177.61/177.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.61/177.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.61/177.76 => 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)) ) ) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_the__elem__def,axiom, % 177.61/177.76 ! [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))))) ). % 177.61/177.76 % 177.61/177.76 fof(fact_dom__eq__singleton__conv,axiom, % 177.61/177.76 ! [V_x_2,V_f_2,T_b,T_a] : % 177.61/177.76 ( 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))) % 177.61/177.76 <=> ? [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)) ) ). % 177.61/177.76 % 177.61/177.76 fof(fact_set__empty__eq,axiom, % 177.69/177.76 ! [V_xo_2,T_a] : % 177.69/177.76 ( c_Option_Oset(T_a,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.69/177.76 <=> V_xo_2 = c_Option_Ooption_ONone(T_a) ) ). % 177.69/177.76 % 177.69/177.76 fof(fact_Option_Oset_Osimps_I1_J,axiom, % 177.69/177.76 ! [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)) ). % 177.69/177.76 % 177.69/177.76 fof(fact_ran__empty,axiom, % 177.69/177.76 ! [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)) ). % 177.69/177.76 % 177.69/177.76 fof(fact_option_Osimps_I5_J,axiom, % 177.69/177.76 ! [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) ). % 177.69/177.76 % 177.69/177.76 fof(fact_option_Orecs_I2_J,axiom, % 177.69/177.76 ! [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) ). % 177.69/177.76 % 177.69/177.76 fof(fact_option_Osimps_I4_J,axiom, % 177.69/177.76 ! [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 ). % 177.69/177.76 % 177.69/177.76 fof(fact_fun__upd__triv,axiom, % 177.69/177.76 ! [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 ). % 177.69/177.76 % 177.69/177.76 fof(fact_triple_Oinject,axiom, % 177.69/177.76 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_a] : % 177.69/177.76 ( 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) % 177.69/177.76 <=> ( V_fun1_2 = V_fun1_H_2 % 177.69/177.76 & V_com_2 = V_com_H_2 % 177.69/177.76 & V_fun2_2 = V_fun2_H_2 ) ) ). % 177.69/177.76 % 177.69/177.76 fof(fact_fun__upd__idem,axiom, % 177.69/177.76 ! [T_a,T_b,V_y_2,V_x_2,V_f_2] : % 177.69/177.76 ( hAPP(V_f_2,V_x_2) = V_y_2 % 177.69/177.76 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2) = V_f_2 ) ). % 177.69/177.76 % 177.69/177.76 fof(fact_fun__upd__other,axiom, % 177.69/177.76 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 177.69/177.76 ( V_z_2 != V_x_2 % 177.69/177.76 => 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) ) ). % 177.69/177.76 % 177.69/177.76 fof(fact_fun__upd__twist,axiom, % 177.69/177.76 ! [V_d_2,V_b_2,V_m_2,T_b,T_a,V_ca_2,V_a_2] : % 177.69/177.76 ( V_a_2 != V_ca_2 % 177.69/177.76 => 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) ) ). % 177.69/177.76 % 177.69/177.76 fof(fact_fun__upd__apply,axiom, % 177.69/177.76 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 177.69/177.76 ( ( V_z_2 = V_x_2 % 177.69/177.76 => 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 ) % 177.69/177.76 & ( V_z_2 != V_x_2 % 177.69/177.76 => 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) ) ) ). % 177.69/177.76 % 177.69/177.76 fof(fact_fun__upd__same,axiom, % 177.69/177.76 ! [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 ). % 177.69/177.76 % 177.69/177.76 fof(fact_fun__upd__upd,axiom, % 177.69/177.76 ! [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) ). % 177.69/177.76 % 177.69/177.76 fof(fact_fun__upd__idem__iff,axiom, % 177.69/177.76 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 177.69/177.76 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 % 177.69/177.76 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ). % 177.69/177.76 % 177.69/177.76 fof(fact_folding__one__idem_Oidem,axiom, % 177.69/177.76 ! [V_x_2,V_F_2,V_f_2,T_a] : % 177.69/177.76 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 177.69/177.76 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 177.69/177.76 % 177.69/177.76 fof(fact_fun__upd__def,axiom, % 177.69/177.76 ! [V_b_2,V_f_2,T_b,T_a,V_a_2,V_x_2] : % 177.69/177.76 ( ( V_x_2 = V_a_2 % 177.69/177.76 => 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 ) % 177.69/177.76 & ( V_x_2 != V_a_2 % 177.69/177.76 => 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) ) ) ). % 177.69/177.76 % 177.69/177.76 fof(fact_map__upd__Some__unfold,axiom, % 177.69/177.76 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_a,T_b] : % 177.69/177.76 ( 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) % 177.69/177.76 <=> ( ( V_x_2 = V_a_2 % 177.69/177.76 & V_b_2 = V_y_2 ) % 177.69/177.76 | ( V_x_2 != V_a_2 % 177.69/177.76 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ) ). % 177.69/177.76 % 177.69/177.76 fof(fact_map__upd__triv,axiom, % 177.69/177.76 ! [T_b,V_x_2,T_a,V_k_2,V_t_2] : % 177.69/177.76 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 177.69/177.76 => 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 ) ). % 177.69/177.76 % 177.69/177.76 fof(fact_map__upd__eqD1,axiom, % 177.69/177.76 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_b,T_a] : % 177.69/177.76 ( 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)) % 177.69/177.76 => V_x_2 = V_y_2 ) ). % 177.69/177.76 % 177.69/177.76 fof(fact_empty__upd__none,axiom, % 177.69/177.77 ! [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) ). % 177.69/177.77 % 177.69/177.77 fof(fact_ran__map__upd,axiom, % 177.69/177.77 ! [V_b_2,T_b,T_a,V_a_2,V_m_2] : % 177.69/177.77 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_a) % 177.69/177.77 => 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)) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_map__upd__nonempty,axiom, % 177.69/177.77 ! [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)) ). % 177.69/177.77 % 177.69/177.77 fof(fact_option_Orecs_I1_J,axiom, % 177.69/177.77 ! [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 ). % 177.69/177.77 % 177.69/177.77 fof(fact_MGF__complete,axiom, % 177.69/177.77 ! [V_Q_2,V_P_2,V_ca_2] : % 177.69/177.77 ( 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)))) % 177.69/177.77 => ( 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)))) % 177.69/177.77 => 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)))) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_finite__pointwise,axiom, % 177.69/177.77 ! [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] : % 177.69/177.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_U_2)) % 177.69/177.77 => ( ! [B_p] : % 177.69/177.77 ( 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)))) % 177.69/177.77 => 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)))) ) % 177.69/177.77 => ( 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)) % 177.69/177.77 => 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)) ) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_triple_Orecs,axiom, % 177.69/177.77 ! [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) ). % 177.69/177.77 % 177.69/177.77 fof(fact_triple_Osimps_I2_J,axiom, % 177.69/177.77 ! [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) ). % 177.69/177.77 % 177.69/177.77 fof(fact_hoare__derivs_OBody,axiom, % 177.69/177.77 ! [V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] : % 177.69/177.77 ( 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)) % 177.69/177.77 => 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)) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_escape,axiom, % 177.69/177.77 ! [V_Q_2,V_ca_2,V_G_2,T_a,V_P_2] : % 177.69/177.77 ( ! [B_Z,B_s] : % 177.69/177.77 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 177.69/177.77 => 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)))) ) % 177.69/177.77 => 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)))) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_hoare__derivs_OSkip,axiom, % 177.69/177.77 ! [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)))) ). % 177.69/177.77 % 177.69/177.77 fof(fact_hoare__derivs_Oequations_I7_J,axiom, % 177.69/177.77 ! [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)))) ). % 177.69/177.77 % 177.69/177.77 fof(fact_conseq2,axiom, % 177.69/177.77 ! [V_Q_2,V_Q_H_2,V_ca_2,V_P_2,V_G_2,T_a] : % 177.69/177.77 ( 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)))) % 177.69/177.77 => ( ! [B_Z,B_s] : % 177.69/177.77 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s)) % 177.69/177.77 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) ) % 177.69/177.77 => 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)))) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_conseq1,axiom, % 177.69/177.77 ! [V_P_2,V_Q_2,V_ca_2,V_P_H_2,V_G_2,T_a] : % 177.69/177.77 ( 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)))) % 177.69/177.77 => ( ! [B_Z,B_s] : % 177.69/177.77 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 177.69/177.77 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) ) % 177.69/177.77 => 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)))) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_folding__one__idem_Ohom__commute,axiom, % 177.69/177.77 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_a] : % 177.69/177.77 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 177.69/177.77 => ( ! [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)) % 177.69/177.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 177.69/177.77 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.69/177.77 => 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)) ) ) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_Comp,axiom, % 177.69/177.77 ! [V_R_2,V_d_2,V_Q_2,V_ca_2,V_P_2,V_G_2,T_a] : % 177.69/177.77 ( 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)))) % 177.69/177.77 => ( 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)))) % 177.69/177.77 => 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)))) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_WTs__elim__cases_I4_J,axiom, % 177.69/177.77 ! [V_c2,V_c1] : % 177.69/177.77 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2))) % 177.69/177.77 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 177.69/177.77 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_com_Osimps_I12_J,axiom, % 177.69/177.77 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ). % 177.69/177.77 % 177.69/177.77 fof(fact_com_Osimps_I13_J,axiom, % 177.69/177.77 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ). % 177.69/177.77 % 177.69/177.77 fof(fact_Un__absorb,axiom, % 177.69/177.77 ! [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 ). % 177.69/177.77 % 177.69/177.77 fof(fact_Un__commute,axiom, % 177.69/177.77 ! [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) ). % 177.69/177.77 % 177.69/177.77 fof(fact_Un__left__absorb,axiom, % 177.69/177.77 ! [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) ). % 177.69/177.77 % 177.69/177.77 fof(fact_Un__left__commute,axiom, % 177.69/177.77 ! [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)) ). % 177.69/177.77 % 177.69/177.77 fof(fact_Un__assoc,axiom, % 177.69/177.77 ! [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)) ). % 177.69/177.77 % 177.69/177.77 fof(fact_bex__Un,axiom, % 177.69/177.77 ! [V_P_2,V_B_2,V_A_2,T_a] : % 177.69/177.77 ( ? [B_x] : % 177.69/177.77 ( 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))) % 177.69/177.77 & hBOOL(hAPP(V_P_2,B_x)) ) % 177.69/177.77 <=> ( ? [B_x] : % 177.69/177.77 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.69/177.77 & hBOOL(hAPP(V_P_2,B_x)) ) % 177.69/177.77 | ? [B_x] : % 177.69/177.77 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 177.69/177.77 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_ball__Un,axiom, % 177.69/177.77 ! [V_P_2,V_B_2,V_A_2,T_a] : % 177.69/177.77 ( ! [B_x] : % 177.69/177.77 ( 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))) % 177.69/177.77 => hBOOL(hAPP(V_P_2,B_x)) ) % 177.69/177.77 <=> ( ! [B_x] : % 177.69/177.77 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.69/177.77 => hBOOL(hAPP(V_P_2,B_x)) ) % 177.69/177.77 & ! [B_x] : % 177.69/177.77 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 177.69/177.77 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_com_Osimps_I3_J,axiom, % 177.69/177.77 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] : % 177.69/177.77 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) % 177.69/177.77 <=> ( V_com1_2 = V_com1_H_2 % 177.69/177.77 & V_com2_2 = V_com2_H_2 ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_Un__empty,axiom, % 177.69/177.77 ! [V_B_2,V_A_2,T_a] : % 177.69/177.77 ( 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)) % 177.69/177.77 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.69/177.77 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_Un__empty__right,axiom, % 177.69/177.77 ! [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 ). % 177.69/177.77 % 177.69/177.77 fof(fact_Un__empty__left,axiom, % 177.69/177.77 ! [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 ). % 177.69/177.77 % 177.69/177.77 fof(fact_finite__UnI,axiom, % 177.69/177.77 ! [V_G_2,V_F_2,T_a] : % 177.69/177.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 177.69/177.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) % 177.69/177.77 => 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))) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_finite__Un,axiom, % 177.69/177.77 ! [V_G_2,V_F_2,T_a] : % 177.69/177.77 ( 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))) % 177.69/177.77 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 177.69/177.77 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_Un__insert__left,axiom, % 177.69/177.77 ! [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)) ). % 177.69/177.77 % 177.69/177.77 fof(fact_Un__insert__right,axiom, % 177.69/177.77 ! [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)) ). % 177.69/177.77 % 177.69/177.77 fof(fact_image__Un,axiom, % 177.69/177.77 ! [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)) ). % 177.69/177.77 % 177.69/177.77 fof(fact_com_Osimps_I49_J,axiom, % 177.69/177.77 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ). % 177.69/177.77 % 177.69/177.77 fof(fact_com_Osimps_I48_J,axiom, % 177.69/177.77 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 177.69/177.77 % 177.69/177.77 fof(fact_WT_Oequations_I4_J,axiom, % 177.69/177.77 ! [V_a2_2,V_a1_2] : % 177.69/177.77 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2))) % 177.69/177.77 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 177.69/177.77 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_WT_OSemi,axiom, % 177.69/177.77 ! [V_c1,V_c0] : % 177.69/177.77 ( hBOOL(hAPP(c_Com_OWT,V_c0)) % 177.69/177.77 => ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 177.69/177.77 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_com_Osimps_I51_J,axiom, % 177.69/177.77 ! [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) ). % 177.69/177.77 % 177.69/177.77 fof(fact_com_Osimps_I50_J,axiom, % 177.69/177.77 ! [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) ). % 177.69/177.77 % 177.69/177.77 fof(fact_WT_OSkip,axiom, % 177.69/177.77 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 177.69/177.77 % 177.69/177.77 fof(fact_com_Osimps_I18_J,axiom, % 177.69/177.77 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 177.69/177.77 % 177.69/177.77 fof(fact_com_Osimps_I19_J,axiom, % 177.69/177.77 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ). % 177.69/177.77 % 177.69/177.77 fof(fact_WT_Oequations_I1_J,axiom, % 177.69/177.77 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 177.69/177.77 % 177.69/177.77 fof(fact_com_Osimps_I21_J,axiom, % 177.69/177.77 ! [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 ). % 177.69/177.77 % 177.69/177.77 fof(fact_com_Osimps_I20_J,axiom, % 177.69/177.77 ! [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) ). % 177.69/177.77 % 177.69/177.77 fof(fact_insert__is__Un,axiom, % 177.69/177.77 ! [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) ). % 177.69/177.77 % 177.69/177.77 fof(fact_hoare__sound,axiom, % 177.69/177.77 ! [V_ts_2,V_G_2,T_a] : % 177.69/177.77 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) % 177.69/177.77 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,V_ts_2) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_folding__one__idem_Ounion__idem,axiom, % 177.69/177.77 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 177.69/177.77 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 177.69/177.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.69/177.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.69/177.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.69/177.77 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.69/177.77 => 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)) ) ) ) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_Body__sound__lemma,axiom, % 177.69/177.77 ! [V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] : % 177.69/177.77 ( 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)) % 177.69/177.77 => 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)) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_Body1,axiom, % 177.69/177.77 ! [V_pn_2,V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] : % 177.69/177.77 ( 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)) % 177.69/177.77 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procs_2)) % 177.69/177.77 => 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)))) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_sup1CI,axiom, % 177.69/177.77 ! [T_a,V_A_2,V_x_2,V_B_2] : % 177.69/177.77 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2)) % 177.69/177.77 => hBOOL(hAPP(V_A_2,V_x_2)) ) % 177.69/177.77 => 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)) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_sup1E,axiom, % 177.69/177.77 ! [V_x_2,V_B_2,V_A_2,T_a] : % 177.69/177.77 ( 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)) % 177.69/177.77 => ( ~ hBOOL(hAPP(V_A_2,V_x_2)) % 177.69/177.77 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_sup__fun__def,axiom, % 177.69/177.77 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 177.69/177.77 ( class_Lattices_Olattice(T_a) % 177.69/177.77 => 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)) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_sup__apply,axiom, % 177.69/177.77 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 177.69/177.77 ( class_Lattices_Olattice(T_a) % 177.69/177.77 => 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)) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_sup__eq__bot__iff,axiom, % 177.69/177.77 ! [V_y_2,V_x_2,T_a] : % 177.69/177.77 ( class_Lattices_Obounded__lattice__bot(T_a) % 177.69/177.77 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_a) % 177.69/177.77 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_a) % 177.69/177.77 & V_y_2 = c_Orderings_Obot__class_Obot(T_a) ) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_sup__bot__right,axiom, % 177.69/177.77 ! [V_x,T_a] : % 177.69/177.77 ( class_Lattices_Obounded__lattice__bot(T_a) % 177.69/177.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_sup__bot__left,axiom, % 177.69/177.77 ! [V_x,T_a] : % 177.69/177.77 ( class_Lattices_Obounded__lattice__bot(T_a) % 177.69/177.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_the__eq__trivial,axiom, % 177.69/177.77 ! [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 ). % 177.69/177.77 % 177.69/177.77 fof(fact_the__sym__eq__trivial,axiom, % 177.69/177.77 ! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 177.69/177.77 % 177.69/177.77 fof(fact_LoopF,axiom, % 177.69/177.77 ! [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)))) ). % 177.69/177.77 % 177.69/177.77 fof(fact_equalityCE,axiom, % 177.69/177.77 ! [V_ca_2,T_a,V_B_2,V_A_2] : % 177.69/177.77 ( V_A_2 = V_B_2 % 177.69/177.77 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 177.69/177.77 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) % 177.69/177.77 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 177.69/177.77 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_emptyE,axiom, % 177.69/177.77 ! [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)))) ). % 177.69/177.77 % 177.69/177.77 fof(fact_insertE,axiom, % 177.69/177.77 ! [V_A_2,V_b_2,V_a_2,T_a] : % 177.69/177.77 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 177.69/177.77 => ( V_a_2 != V_b_2 % 177.69/177.77 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_insertCI,axiom, % 177.69/177.77 ! [V_b_2,V_B_2,V_a_2,T_a] : % 177.69/177.77 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 177.69/177.77 => V_a_2 = V_b_2 ) % 177.69/177.77 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_image__eqI,axiom, % 177.69/177.77 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_b_2] : % 177.69/177.77 ( V_b_2 = hAPP(V_f_2,V_x_2) % 177.69/177.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 177.69/177.77 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ). % 177.69/177.77 % 177.69/177.77 fof(fact_UnCI,axiom, % 177.69/177.77 ! [V_A_2,V_B_2,V_ca_2,T_a] : % 177.69/177.77 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 177.69/177.77 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) % 177.69/177.77 => 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))) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_UnE,axiom, % 177.69/177.78 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 177.69/177.78 ( 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))) % 177.69/177.78 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 177.69/177.78 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_WTs__elim__cases_I6_J,axiom, % 177.69/177.78 ! [V_ca_2,V_b_2] : % 177.69/177.78 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_ca_2))) % 177.69/177.78 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_eq__mem,axiom, % 177.69/177.78 ! [V_y_2,V_x_2,T_a] : % 177.69/177.78 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2))) % 177.69/177.78 <=> V_x_2 = V_y_2 ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_pred__equals__eq,axiom, % 177.69/177.78 ! [V_S_2,V_R_2,T_a] : % 177.69/177.78 ( 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) % 177.69/177.78 <=> V_R_2 = V_S_2 ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_eq__mem__trans,axiom, % 177.69/177.78 ! [V_A_2,T_a,V_b_2,V_a_2] : % 177.69/177.78 ( V_a_2 = V_b_2 % 177.69/177.78 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 177.69/177.78 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_eqelem__imp__iff,axiom, % 177.69/177.78 ! [V_A_2,T_a,V_y_2,V_x_2] : % 177.69/177.78 ( V_x_2 = V_y_2 % 177.69/177.78 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.69/177.78 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_eqset__imp__iff,axiom, % 177.69/177.78 ! [V_x_2,T_a,V_B_2,V_A_2] : % 177.69/177.78 ( V_A_2 = V_B_2 % 177.69/177.78 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.69/177.78 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_com_Osimps_I5_J,axiom, % 177.69/177.78 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] : % 177.69/177.78 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) % 177.69/177.78 <=> ( V_fun_2 = V_fun_H_2 % 177.69/177.78 & V_com_2 = V_com_H_2 ) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_mem__def,axiom, % 177.69/177.78 ! [V_A_2,V_x_2,T_a] : % 177.69/177.78 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.69/177.78 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_bot__empty__eq,axiom, % 177.69/177.78 ! [V_x_2,T_a] : % 177.69/177.78 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) % 177.69/177.78 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_sup__Un__eq,axiom, % 177.69/177.78 ! [V_x_2,V_S_2,V_R_2,T_a] : % 177.69/177.78 ( 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)) % 177.69/177.78 <=> 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))) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_all__not__in__conv,axiom, % 177.69/177.78 ! [V_A_2,T_a] : % 177.69/177.78 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.69/177.78 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_ex__in__conv,axiom, % 177.69/177.78 ! [V_A_2,T_a] : % 177.69/177.78 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.69/177.78 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_empty__iff,axiom, % 177.69/177.78 ! [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)))) ). % 177.69/177.78 % 177.69/177.78 fof(fact_equals0D,axiom, % 177.69/177.78 ! [V_a_2,T_a,V_A_2] : % 177.69/177.78 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.69/177.78 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_insertI1,axiom, % 177.69/177.78 ! [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))) ). % 177.69/177.78 % 177.69/177.78 fof(fact_insert__iff,axiom, % 177.69/177.78 ! [V_A_2,V_b_2,V_a_2,T_a] : % 177.69/177.78 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 177.69/177.78 <=> ( V_a_2 = V_b_2 % 177.69/177.78 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_insert__ident,axiom, % 177.69/177.78 ! [V_B_2,V_A_2,V_x_2,T_a] : % 177.69/177.78 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.69/177.78 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 177.69/177.78 => ( 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) % 177.69/177.78 <=> V_A_2 = V_B_2 ) ) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_insertI2,axiom, % 177.69/177.78 ! [V_b_2,V_B_2,V_a_2,T_a] : % 177.69/177.78 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 177.69/177.78 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_insert__absorb,axiom, % 177.69/177.78 ! [V_A_2,V_a_2,T_a] : % 177.69/177.78 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.69/177.78 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = V_A_2 ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_rev__image__eqI,axiom, % 177.69/177.78 ! [T_b,V_f_2,V_b_2,V_A_2,V_x_2,T_a] : % 177.69/177.78 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.69/177.78 => ( V_b_2 = hAPP(V_f_2,V_x_2) % 177.69/177.78 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_imageI,axiom, % 177.69/177.78 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 177.69/177.78 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.69/177.78 => 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))) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_image__iff,axiom, % 177.69/177.78 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] : % 177.69/177.78 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 177.69/177.78 <=> ? [B_x] : % 177.69/177.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 177.69/177.78 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_UnI2,axiom, % 177.69/177.78 ! [V_A_2,V_B_2,V_ca_2,T_a] : % 177.69/177.78 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 177.69/177.78 => 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))) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_UnI1,axiom, % 177.69/177.78 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 177.69/177.78 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 177.69/177.78 => 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))) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_Un__iff,axiom, % 177.69/177.78 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 177.69/177.78 ( 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))) % 177.69/177.78 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 177.69/177.78 | hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_While,axiom, % 177.69/177.78 ! [V_b_2,V_ca_2] : % 177.69/177.78 ( hBOOL(hAPP(c_Com_OWT,V_ca_2)) % 177.69/177.78 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_ca_2))) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_WT_Oequations_I6_J,axiom, % 177.69/177.78 ! [V_a1_2,V_a2_2] : % 177.69/177.78 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2))) % 177.69/177.78 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_com_Osimps_I58_J,axiom, % 177.69/177.78 ! [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) ). % 177.69/177.78 % 177.69/177.78 fof(fact_com_Osimps_I59_J,axiom, % 177.69/177.78 ! [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) ). % 177.69/177.78 % 177.69/177.78 fof(fact_com_Osimps_I60_J,axiom, % 177.69/177.78 ! [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) ). % 177.69/177.78 % 177.69/177.78 fof(fact_com_Osimps_I61_J,axiom, % 177.69/177.78 ! [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) ). % 177.69/177.78 % 177.69/177.78 fof(fact_com_Osimps_I47_J,axiom, % 177.69/177.78 ! [V_com2_2,V_com1_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ). % 177.69/177.78 % 177.69/177.78 fof(fact_com_Osimps_I46_J,axiom, % 177.69/177.78 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 177.69/177.78 % 177.69/177.78 fof(fact_com_Osimps_I17_J,axiom, % 177.69/177.78 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 177.69/177.78 % 177.69/177.78 fof(fact_com_Osimps_I16_J,axiom, % 177.69/177.78 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 177.69/177.78 % 177.69/177.78 fof(fact_singleton__iff,axiom, % 177.69/177.78 ! [V_a_2,V_b_2,T_a] : % 177.69/177.78 ( 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))))) % 177.69/177.78 <=> V_b_2 = V_a_2 ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_singletonE,axiom, % 177.69/177.78 ! [V_a_2,V_b_2,T_a] : % 177.69/177.78 ( 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))))) % 177.69/177.78 => V_b_2 = V_a_2 ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_insert__image,axiom, % 177.69/177.78 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 177.69/177.78 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.69/177.78 => 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) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_domIff,axiom, % 177.69/177.78 ! [V_m_2,T_b,V_a_2,T_a] : % 177.69/177.78 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2))) % 177.69/177.78 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_b) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_domI,axiom, % 177.69/177.78 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] : % 177.69/177.78 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2) % 177.69/177.78 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2))) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_image__map__upd,axiom, % 177.69/177.78 ! [V_y_2,V_m_2,T_b,V_A_2,V_x_2,T_a] : % 177.69/177.78 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.69/177.78 => 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) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_folding__one__idem_Oin__idem,axiom, % 177.69/177.78 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 177.69/177.78 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 177.69/177.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.69/177.78 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.69/177.78 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_ranI,axiom, % 177.69/177.78 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] : % 177.69/177.78 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2) % 177.69/177.78 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2))) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_elem__set,axiom, % 177.69/177.78 ! [V_xo_2,V_x_2,T_a] : % 177.69/177.78 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Option_Oset(T_a,V_xo_2))) % 177.69/177.78 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_sup_Oidem,axiom, % 177.69/177.78 ! [V_a,T_a] : % 177.69/177.78 ( class_Lattices_Osemilattice__sup(T_a) % 177.69/177.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_sup__idem,axiom, % 177.69/177.78 ! [V_x,T_a] : % 177.69/177.78 ( class_Lattices_Osemilattice__sup(T_a) % 177.69/177.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_sup_Ocommute,axiom, % 177.69/177.78 ! [V_b,V_a,T_a] : % 177.69/177.78 ( class_Lattices_Osemilattice__sup(T_a) % 177.69/177.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_a) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_inf__sup__aci_I5_J,axiom, % 177.69/177.78 ! [V_y,V_x,T_a] : % 177.69/177.78 ( class_Lattices_Olattice(T_a) % 177.69/177.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_sup__commute,axiom, % 177.69/177.78 ! [V_y,V_x,T_a] : % 177.69/177.78 ( class_Lattices_Osemilattice__sup(T_a) % 177.69/177.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_sup_Oleft__idem,axiom, % 177.69/177.78 ! [V_b,V_a,T_a] : % 177.69/177.78 ( class_Lattices_Osemilattice__sup(T_a) % 177.69/177.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_inf__sup__aci_I8_J,axiom, % 177.69/177.78 ! [V_y,V_x,T_a] : % 177.69/177.78 ( class_Lattices_Olattice(T_a) % 177.69/177.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_sup__left__idem,axiom, % 177.69/177.78 ! [V_y,V_x,T_a] : % 177.69/177.78 ( class_Lattices_Osemilattice__sup(T_a) % 177.69/177.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_sup_Oleft__commute,axiom, % 177.69/177.78 ! [V_c,V_a,V_b,T_a] : % 177.69/177.78 ( class_Lattices_Osemilattice__sup(T_a) % 177.69/177.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_inf__sup__aci_I7_J,axiom, % 177.69/177.78 ! [V_z,V_y,V_x,T_a] : % 177.69/177.78 ( class_Lattices_Olattice(T_a) % 177.69/177.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_sup__left__commute,axiom, % 177.69/177.78 ! [V_z,V_y,V_x,T_a] : % 177.69/177.78 ( class_Lattices_Osemilattice__sup(T_a) % 177.69/177.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_sup_Oassoc,axiom, % 177.69/177.78 ! [V_c,V_b,V_a,T_a] : % 177.69/177.78 ( class_Lattices_Osemilattice__sup(T_a) % 177.69/177.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_inf__sup__aci_I6_J,axiom, % 177.69/177.78 ! [V_z,V_y,V_x,T_a] : % 177.69/177.78 ( class_Lattices_Olattice(T_a) % 177.69/177.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_sup__assoc,axiom, % 177.69/177.78 ! [V_z,V_y,V_x,T_a] : % 177.69/177.78 ( class_Lattices_Osemilattice__sup(T_a) % 177.69/177.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_sup1I1,axiom, % 177.69/177.78 ! [V_B_2,T_a,V_x_2,V_A_2] : % 177.69/177.78 ( hBOOL(hAPP(V_A_2,V_x_2)) % 177.69/177.78 => 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)) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_sup1I2,axiom, % 177.69/177.78 ! [V_A_2,T_a,V_x_2,V_B_2] : % 177.69/177.78 ( hBOOL(hAPP(V_B_2,V_x_2)) % 177.69/177.78 => 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)) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_image__constant,axiom, % 177.69/177.78 ! [V_ca_2,T_b,V_A_2,V_x_2,T_a] : % 177.69/177.78 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.69/177.78 => 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))) ) ). % 177.69/177.78 % 177.69/177.78 fof(fact_folding__one_Oinsert,axiom, % 177.74/177.78 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 177.74/177.78 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 177.74/177.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.78 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.78 => 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)) ) ) ) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_folding__image__simple_Oinsert,axiom, % 177.74/177.78 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 177.74/177.78 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 177.74/177.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 177.74/177.78 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 177.74/177.78 => 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)) ) ) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_dom__fun__upd,axiom, % 177.74/177.78 ! [V_x_2,V_f_2,T_b,T_a,V_y_2] : % 177.74/177.78 ( ( V_y_2 = c_Option_Ooption_ONone(T_a) % 177.74/177.78 => 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)))) ) % 177.74/177.78 & ( V_y_2 != c_Option_Ooption_ONone(T_a) % 177.74/177.78 => 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)) ) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_folding__image__simple__idem_Ounion__idem,axiom, % 177.74/177.78 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 177.74/177.78 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 177.74/177.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 177.74/177.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 177.74/177.78 => 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)) ) ) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_fun__upd__image,axiom, % 177.74/177.78 ! [V_y_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 177.74/177.78 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.78 => 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)))))) ) % 177.74/177.78 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.78 => 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) ) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 177.74/177.78 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 177.74/177.78 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 177.74/177.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 177.74/177.78 => 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)) ) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_map__add__upd__left,axiom, % 177.74/177.78 ! [V_u1_2,V_e1_2,V_e2_2,T_b,V_m_2,T_a] : % 177.74/177.78 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_e2_2))) % 177.74/177.78 => 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)) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_finite__induct,axiom, % 177.74/177.78 ! [V_P_2,V_F_2,T_a] : % 177.74/177.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 177.74/177.78 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 177.74/177.78 => ( ! [B_x,B_F] : % 177.74/177.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 177.74/177.78 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_F)) % 177.74/177.78 => ( hBOOL(hAPP(V_P_2,B_F)) % 177.74/177.78 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_x),B_F))) ) ) ) % 177.74/177.78 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 177.74/177.78 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 177.74/177.78 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 177.74/177.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 177.74/177.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 177.74/177.78 => hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_map__comp__None__iff,axiom, % 177.74/177.78 ! [V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] : % 177.74/177.78 ( 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) % 177.74/177.78 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 177.74/177.78 | ? [B_k_H] : % 177.74/177.78 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) % 177.74/177.78 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_a) ) ) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_MGT__alternD,axiom, % 177.74/177.78 ! [V_ca_2,V_G_2] : % 177.74/177.78 ( c_Hoare__Mirabelle_Ostate__not__singleton % 177.74/177.78 => ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),c_Natural_Oevalc(V_ca_2))))),c_fequal))),V_ca_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 177.74/177.78 => 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)))) ) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_DiffI,axiom, % 177.74/177.78 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 177.74/177.78 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 177.74/177.78 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 177.74/177.78 => 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))) ) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_DiffE,axiom, % 177.74/177.78 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 177.74/177.78 ( 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))) % 177.74/177.78 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 177.74/177.78 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_finite__Diff,axiom, % 177.74/177.78 ! [V_B_2,V_A_2,T_a] : % 177.74/177.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.78 => 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))) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_fun__diff__def,axiom, % 177.74/177.78 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 177.74/177.78 ( class_Groups_Ominus(T_a) % 177.74/177.78 => 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)) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_minus__apply,axiom, % 177.74/177.78 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 177.74/177.78 ( class_Groups_Ominus(T_a) % 177.74/177.78 => 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)) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_Diff__idemp,axiom, % 177.74/177.78 ! [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) ). % 177.74/177.78 % 177.74/177.78 fof(fact_map__add__assoc,axiom, % 177.74/177.78 ! [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) ). % 177.74/177.78 % 177.74/177.78 fof(fact_folding__image__simple__idem_Oidem,axiom, % 177.74/177.78 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 177.74/177.78 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 177.74/177.78 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_Diff__iff,axiom, % 177.74/177.78 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 177.74/177.78 ( 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))) % 177.74/177.78 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 177.74/177.78 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_DiffD1,axiom, % 177.74/177.78 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 177.74/177.78 ( 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))) % 177.74/177.78 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_DiffD2,axiom, % 177.74/177.78 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 177.74/177.78 ( 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))) % 177.74/177.78 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_Diff__cancel,axiom, % 177.74/177.78 ! [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)) ). % 177.74/177.78 % 177.74/177.78 fof(fact_Diff__empty,axiom, % 177.74/177.78 ! [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 ). % 177.74/177.78 % 177.74/177.78 fof(fact_empty__Diff,axiom, % 177.74/177.78 ! [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)) ). % 177.74/177.78 % 177.74/177.78 fof(fact_finite__Diff2,axiom, % 177.74/177.78 ! [V_A_2,V_B_2,T_a] : % 177.74/177.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.74/177.78 => ( 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))) % 177.74/177.78 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_Un__Diff__cancel,axiom, % 177.74/177.78 ! [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) ). % 177.74/177.78 % 177.74/177.78 fof(fact_Un__Diff__cancel2,axiom, % 177.74/177.78 ! [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) ). % 177.74/177.78 % 177.74/177.78 fof(fact_Un__Diff,axiom, % 177.74/177.78 ! [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)) ). % 177.74/177.78 % 177.74/177.78 fof(fact_map__add__None,axiom, % 177.74/177.78 ! [V_k_2,V_n_2,V_m_2,T_a,T_b] : % 177.74/177.78 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_a) % 177.74/177.78 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 177.74/177.78 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_a) ) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_map__add__find__right,axiom, % 177.74/177.78 ! [V_m_2,T_b,V_xx_2,T_a,V_k_2,V_n_2] : % 177.74/177.78 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2) % 177.74/177.78 => 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) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_empty__map__add,axiom, % 177.74/177.78 ! [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 ). % 177.74/177.78 % 177.74/177.78 fof(fact_map__add__empty,axiom, % 177.74/177.78 ! [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 ). % 177.74/177.78 % 177.74/177.78 fof(fact_map__add__def,axiom, % 177.74/177.78 ! [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)) ). % 177.74/177.78 % 177.74/177.78 fof(fact_folding__image__simple_Oinsert__remove,axiom, % 177.74/177.78 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 177.74/177.78 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 177.74/177.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 177.74/177.78 => 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)))))) ) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_folding__one_Oinsert__remove,axiom, % 177.74/177.78 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 177.74/177.78 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 177.74/177.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.78 => ( ( 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)) % 177.74/177.78 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 177.74/177.78 & ( 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)) % 177.74/177.78 => 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)))))) ) ) ) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_insert__Diff1,axiom, % 177.74/177.78 ! [V_A_2,V_B_2,V_x_2,T_a] : % 177.74/177.78 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 177.74/177.78 => 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) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_insert__Diff__if,axiom, % 177.74/177.78 ! [V_A_2,V_B_2,V_x_2,T_a] : % 177.74/177.78 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 177.74/177.78 => 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) ) % 177.74/177.78 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 177.74/177.78 => 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)) ) ) ). % 177.74/177.78 % 177.74/177.78 fof(fact_insert__Diff__single,axiom, % 177.74/177.78 ! [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) ). % 177.74/177.78 % 177.74/177.78 fof(fact_Diff__insert2,axiom, % 177.74/177.78 ! [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) ). % 177.74/177.78 % 177.74/177.78 fof(fact_Diff__insert,axiom, % 177.74/177.78 ! [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)))) ). % 177.74/177.78 % 177.74/177.78 fof(fact_finite__Diff__insert,axiom, % 177.74/177.78 ! [V_B_2,V_a_2,V_A_2,T_a] : % 177.74/177.78 ( 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)))) % 177.74/177.79 <=> 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))) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_folding__image__simple_Oempty,axiom, % 177.74/177.79 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 177.74/177.79 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 177.74/177.79 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_folding__image__simple_Oremove,axiom, % 177.74/177.79 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 177.74/177.79 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 177.74/177.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 177.74/177.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 177.74/177.79 => 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)))))) ) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_folding__one_Oremove,axiom, % 177.74/177.79 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 177.74/177.79 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 177.74/177.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.79 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.79 => ( ( 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)) % 177.74/177.79 => hAPP(V_F_2,V_A_2) = V_x_2 ) % 177.74/177.79 & ( 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)) % 177.74/177.79 => 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)))))) ) ) ) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_map__add__dom__app__simps_I1_J,axiom, % 177.74/177.79 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) % 177.74/177.79 => 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) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_map__add__dom__app__simps_I3_J,axiom, % 177.74/177.79 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] : % 177.74/177.79 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) % 177.74/177.79 => 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) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_map__add__dom__app__simps_I2_J,axiom, % 177.74/177.79 ! [V_l2_2,V_l1_2,T_b,V_m_2,T_a] : % 177.74/177.79 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l1_2))) % 177.74/177.79 => 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) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_map__comp__simps_I1_J,axiom, % 177.74/177.79 ! [V_m1_2,T_b,T_c,T_a,V_k_2,V_m2_2] : % 177.74/177.79 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 177.74/177.79 => 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) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_map__comp__simps_I2_J,axiom, % 177.74/177.79 ! [V_m1_2,T_b,T_c,V_k_H_2,T_a,V_k_2,V_m2_2] : % 177.74/177.79 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_k_H_2) % 177.74/177.79 => 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) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_map__comp__Some__iff,axiom, % 177.74/177.79 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] : % 177.74/177.79 ( 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) % 177.74/177.79 <=> ? [B_k_H] : % 177.74/177.79 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) % 177.74/177.79 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_map__add__SomeD,axiom, % 177.74/177.79 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] : % 177.74/177.79 ( 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) % 177.74/177.79 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 177.74/177.79 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 177.74/177.79 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_map__add__Some__iff,axiom, % 177.74/177.79 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] : % 177.74/177.79 ( 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) % 177.74/177.79 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 177.74/177.79 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 177.74/177.79 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_dom__map__add,axiom, % 177.74/177.79 ! [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)) ). % 177.74/177.79 % 177.74/177.79 fof(fact_map__add__upd,axiom, % 177.74/177.79 ! [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)) ). % 177.74/177.79 % 177.74/177.79 fof(fact_insert__Diff,axiom, % 177.74/177.79 ! [V_A_2,V_a_2,T_a] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.74/177.79 => 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 ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_Diff__insert__absorb,axiom, % 177.74/177.79 ! [V_A_2,V_x_2,T_a] : % 177.74/177.79 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.79 => 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 ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_dom__minus,axiom, % 177.74/177.79 ! [V_A_2,T_b,T_a,V_x_2,V_f_2] : % 177.74/177.79 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_a) % 177.74/177.79 => 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) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_map__comp__empty_I2_J,axiom, % 177.74/177.79 ! [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) ). % 177.74/177.79 % 177.74/177.79 fof(fact_map__comp__empty_I1_J,axiom, % 177.74/177.79 ! [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) ). % 177.74/177.79 % 177.74/177.79 fof(fact_map__comp__def,axiom, % 177.74/177.79 ! [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)) ). % 177.74/177.79 % 177.74/177.79 fof(fact_MGT__def,axiom, % 177.74/177.79 ! [V_ca_2] : hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),V_ca_2),c_Natural_Oevalc(V_ca_2)) ). % 177.74/177.79 % 177.74/177.79 fof(fact_MGT__alternI,axiom, % 177.74/177.79 ! [V_ca_2,V_G_2] : % 177.74/177.79 ( 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)))) % 177.74/177.79 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),c_Natural_Oevalc(V_ca_2))))),c_fequal))),V_ca_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_folding__one_Osingleton,axiom, % 177.74/177.79 ! [V_x_2,V_F_2,V_f_2,T_a] : % 177.74/177.79 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 177.74/177.79 => 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 ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_evalc__elim__cases_I6_J,axiom, % 177.74/177.79 ! [V_s1,V_s,V_P] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1)) % 177.74/177.79 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_evalc_OBody,axiom, % 177.74/177.79 ! [V_s1,V_s0,V_pn] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1)) % 177.74/177.79 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_evalc__elim__cases_I1_J,axiom, % 177.74/177.79 ! [V_t,V_s] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t)) % 177.74/177.79 => V_t = V_s ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_evalc_OSkip,axiom, % 177.74/177.79 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ). % 177.74/177.79 % 177.74/177.79 fof(fact_evalc_OSemi,axiom, % 177.74/177.79 ! [V_s2,V_c1,V_s1,V_s0,V_c0] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1)) % 177.74/177.79 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2)) % 177.74/177.79 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_evalc_OWhileTrue,axiom, % 177.74/177.79 ! [V_s2_2,V_s1_2,V_ca_2,V_s0_2,V_b_2] : % 177.74/177.79 ( hBOOL(hAPP(V_b_2,V_s0_2)) % 177.74/177.79 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s0_2),V_s1_2)) % 177.74/177.79 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s1_2),V_s2_2)) % 177.74/177.79 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s0_2),V_s2_2)) ) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_evalc_OWhileFalse,axiom, % 177.74/177.79 ! [V_ca_2,V_s_2,V_b_2] : % 177.74/177.79 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 177.74/177.79 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_s_2)) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_evalc_Oequations_I9_J,axiom, % 177.74/177.79 ! [V_a3_2,V_a2_2,V_a1_2] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2)) % 177.74/177.79 <=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2))),V_a2_2),V_a3_2)) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_evalc_Oequations_I1_J,axiom, % 177.74/177.79 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ). % 177.74/177.79 % 177.74/177.79 fof(fact_evalc_Oequations_I4_J,axiom, % 177.74/177.79 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2)) % 177.74/177.79 <=> ? [B_s1] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1)) % 177.74/177.79 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_evalc_Oequations_I8_J,axiom, % 177.74/177.79 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2)) % 177.74/177.79 <=> ( ( V_a5_2 = V_a2_2 % 177.74/177.79 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 177.74/177.79 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 177.74/177.79 & ? [B_s1] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) % 177.74/177.79 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_com__det,axiom, % 177.74/177.79 ! [V_u,V_t,V_s,V_c] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) % 177.74/177.79 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u)) % 177.74/177.79 => V_u = V_t ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_evalc_Oequations_I7_J,axiom, % 177.74/177.79 ! [V_a2_2,V_a3_2,V_a1_2] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2)) % 177.74/177.79 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 177.74/177.79 => ? [B_s1] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) % 177.74/177.79 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_fun__upd__None__restrict,axiom, % 177.74/177.79 ! [V_m_2,T_b,V_D_2,V_x_2,T_a] : % 177.74/177.79 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 177.74/177.79 => 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))))) ) % 177.74/177.79 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 177.74/177.79 => 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) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_folding__one_Oclosed,axiom, % 177.74/177.79 ! [V_A_2,V_F_2,V_f_2,T_a] : % 177.74/177.79 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 177.74/177.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.79 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.79 => ( ! [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)))))) % 177.74/177.79 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_,axiom, % 177.74/177.79 ! [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) ). % 177.74/177.79 % 177.74/177.79 fof(fact_fun__upd__restrict__conv,axiom, % 177.74/177.79 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 177.74/177.79 => 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) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_restrict__fun__upd,axiom, % 177.74/177.79 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] : % 177.74/177.79 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 177.74/177.79 => 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) ) % 177.74/177.79 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 177.74/177.79 => 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) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_finite__empty__induct,axiom, % 177.74/177.79 ! [V_P_2,V_A_2,T_a] : % 177.74/177.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.79 => ( hBOOL(hAPP(V_P_2,V_A_2)) % 177.74/177.79 => ( ! [B_a,B_A] : % 177.74/177.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A)) % 177.74/177.79 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) % 177.74/177.79 => ( hBOOL(hAPP(V_P_2,B_A)) % 177.74/177.79 => 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)))))) ) ) ) % 177.74/177.79 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_Option_Omap__def,axiom, % 177.74/177.79 ! [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)) ). % 177.74/177.79 % 177.74/177.79 fof(fact_fun__left__comm__idem__remove,axiom, % 177.74/177.79 ! [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))))) ). % 177.74/177.79 % 177.74/177.79 fof(fact_fun__upd__restrict,axiom, % 177.74/177.79 ! [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) ). % 177.74/177.79 % 177.74/177.79 fof(fact_fold__graph_H_Ointros_I2_J,axiom, % 177.74/177.79 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.79 => ( 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) % 177.74/177.79 => 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)) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom, % 177.74/177.79 ! [V_z_2,V_x_2,V_f_2,T_b,T_a] : % 177.74/177.79 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 177.74/177.79 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) = hAPP(hAPP(V_f_2,V_x_2),V_z_2) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom, % 177.74/177.79 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 177.74/177.79 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 177.74/177.79 => 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)) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_fold__graph_H_Ointros_I1_J,axiom, % 177.74/177.79 ! [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) ). % 177.74/177.79 % 177.74/177.79 fof(fact_fold__graph_H_Oequations_I1_J,axiom, % 177.74/177.79 ! [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) ). % 177.74/177.79 % 177.74/177.79 fof(fact_restrict__in,axiom, % 177.74/177.79 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.79 => 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) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_option__map__is__None,axiom, % 177.74/177.79 ! [V_opt_2,V_f_2,T_a,T_b] : % 177.74/177.79 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_a) % 177.74/177.79 <=> V_opt_2 = c_Option_Ooption_ONone(T_b) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_option__map__None,axiom, % 177.74/177.79 ! [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) ). % 177.74/177.79 % 177.74/177.79 fof(fact_option__map__eq__Some,axiom, % 177.74/177.79 ! [V_y_2,V_xo_2,V_f_2,T_a,T_b] : % 177.74/177.79 ( 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) % 177.74/177.79 <=> ? [B_z] : % 177.74/177.79 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),B_z) % 177.74/177.79 & hAPP(V_f_2,B_z) = V_y_2 ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_option__map__Some,axiom, % 177.74/177.79 ! [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)) ). % 177.74/177.79 % 177.74/177.79 fof(fact_fun__left__comm__idem__insert,axiom, % 177.74/177.79 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)) ). % 177.74/177.79 % 177.74/177.79 fof(fact_restrict__map__empty,axiom, % 177.74/177.79 ! [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) ). % 177.74/177.79 % 177.74/177.79 fof(fact_fun__left__comm__idem__sup,axiom, % 177.74/177.79 ! [T_a] : % 177.74/177.79 ( class_Lattices_Osemilattice__sup(T_a) % 177.74/177.79 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_dom__option__map,axiom, % 177.74/177.79 ! [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) ). % 177.74/177.79 % 177.74/177.79 fof(fact_restrict__out,axiom, % 177.74/177.79 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 177.74/177.79 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.79 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_restrict__map__insert,axiom, % 177.74/177.79 ! [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)) ). % 177.74/177.79 % 177.74/177.79 fof(fact_restrict__map__def,axiom, % 177.74/177.79 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 177.74/177.79 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.79 => 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) ) % 177.74/177.79 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.79 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_restrict__map__to__empty,axiom, % 177.74/177.79 ! [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) ). % 177.74/177.79 % 177.74/177.79 fof(fact_fold__graph_H_Oequations_I2_J,axiom, % 177.74/177.79 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a] : % 177.74/177.79 ( 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)) % 177.74/177.79 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.79 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 ) % 177.74/177.79 | ? [B_x,B_y] : % 177.74/177.79 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) % 177.74/177.79 & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a2_2)) % 177.74/177.79 & 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) ) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_ran__restrictD,axiom, % 177.74/177.79 ! [V_A_2,V_m_2,T_b,V_y_2,T_a] : % 177.74/177.79 ( 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)))) % 177.74/177.79 => ? [B_x] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 177.74/177.79 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_restrict__upd__same,axiom, % 177.74/177.79 ! [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))))) ). % 177.74/177.79 % 177.74/177.79 fof(fact_restrict__complement__singleton__eq,axiom, % 177.74/177.79 ! [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)) ). % 177.74/177.79 % 177.74/177.79 fof(fact_Sup__fin_Oremove,axiom, % 177.74/177.79 ! [V_x_2,V_A_2,T_a] : % 177.74/177.79 ( class_Lattices_Olattice(T_a) % 177.74/177.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.79 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.79 => ( ( 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)) % 177.74/177.79 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = V_x_2 ) % 177.74/177.79 & ( 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)) % 177.74/177.79 => 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)))))) ) ) ) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_Diff1__fold__graph,axiom, % 177.74/177.79 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 177.74/177.79 ( 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)) % 177.74/177.79 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.79 => 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))) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inj__on__insert,axiom, % 177.74/177.79 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 177.74/177.79 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) % 177.74/177.79 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.74/177.79 & ~ 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))))))) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_folding__image__simple_Ounion__disjoint,axiom, % 177.74/177.79 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 177.74/177.79 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 177.74/177.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 177.74/177.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 177.74/177.79 => ( 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)) % 177.74/177.79 => 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)) ) ) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_folding__one_Ounion__disjoint,axiom, % 177.74/177.79 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 177.74/177.79 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 177.74/177.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.79 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.74/177.79 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.79 => ( 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)) % 177.74/177.79 => 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)) ) ) ) ) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_folding__one_Ounion__inter,axiom, % 177.74/177.79 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 177.74/177.79 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 177.74/177.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.74/177.79 => ( 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)) % 177.74/177.79 => 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)) ) ) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf1E,axiom, % 177.74/177.79 ! [V_x_2,V_B_2,V_A_2,T_a] : % 177.74/177.79 ( 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)) % 177.74/177.79 => ~ ( hBOOL(hAPP(V_A_2,V_x_2)) % 177.74/177.79 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf1I,axiom, % 177.74/177.79 ! [T_a,V_B_2,V_x_2,V_A_2] : % 177.74/177.79 ( hBOOL(hAPP(V_A_2,V_x_2)) % 177.74/177.79 => ( hBOOL(hAPP(V_B_2,V_x_2)) % 177.74/177.79 => 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)) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_IntE,axiom, % 177.74/177.79 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 177.74/177.79 ( 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))) % 177.74/177.79 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 177.74/177.79 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_IntI,axiom, % 177.74/177.79 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 177.74/177.79 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 177.74/177.79 => 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))) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_finite__Int,axiom, % 177.74/177.79 ! [V_G_2,V_F_2,T_a] : % 177.74/177.79 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 177.74/177.79 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) ) % 177.74/177.79 => 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))) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inj__on__empty,axiom, % 177.74/177.79 ! [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))) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inj__uminus,axiom, % 177.74/177.79 ! [V_A_2,T_a] : % 177.74/177.79 ( class_Groups_Oordered__ab__group__add(T_a) % 177.74/177.79 => c_Fun_Oinj__on(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a),V_A_2) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_ComplI,axiom, % 177.74/177.79 ! [V_A_2,V_ca_2,T_a] : % 177.74/177.79 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 177.74/177.79 => 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))) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_fun__Compl__def,axiom, % 177.74/177.79 ! [V_x_2,V_A_2,T_b,T_a] : % 177.74/177.79 ( class_Groups_Ouminus(T_a) % 177.74/177.79 => 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)) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf__fun__def,axiom, % 177.74/177.79 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 177.74/177.79 ( class_Lattices_Olattice(T_a) % 177.74/177.79 => 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)) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_compl__inf__bot,axiom, % 177.74/177.79 ! [V_x,T_a] : % 177.74/177.79 ( class_Lattices_Oboolean__algebra(T_a) % 177.74/177.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf__compl__bot,axiom, % 177.74/177.79 ! [V_x,T_a] : % 177.74/177.79 ( class_Lattices_Oboolean__algebra(T_a) % 177.74/177.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_Inf__fin_Oidem,axiom, % 177.74/177.79 ! [V_x,T_a] : % 177.74/177.79 ( class_Lattices_Olattice(T_a) % 177.74/177.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inj__on__Int,axiom, % 177.74/177.79 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.79 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.74/177.79 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 177.74/177.79 => 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)) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_Int__assoc,axiom, % 177.74/177.79 ! [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)) ). % 177.74/177.79 % 177.74/177.79 fof(fact_Compl__eq__Compl__iff,axiom, % 177.74/177.79 ! [V_B_2,V_A_2,T_a] : % 177.74/177.79 ( 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) % 177.74/177.79 <=> V_A_2 = V_B_2 ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_Int__left__commute,axiom, % 177.74/177.79 ! [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)) ). % 177.74/177.79 % 177.74/177.79 fof(fact_Int__left__absorb,axiom, % 177.74/177.79 ! [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) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inj__on__def,axiom, % 177.74/177.79 ! [V_A_2,V_f_2,T_b,T_a] : % 177.74/177.79 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.74/177.79 <=> ! [B_x] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.74/177.79 => ! [B_xa] : % 177.74/177.79 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 177.74/177.79 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 177.74/177.79 => B_x = B_xa ) ) ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_Int__commute,axiom, % 177.74/177.79 ! [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) ). % 177.74/177.79 % 177.74/177.79 fof(fact_Int__absorb,axiom, % 177.74/177.79 ! [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 ). % 177.74/177.79 % 177.74/177.79 fof(fact_double__complement,axiom, % 177.74/177.79 ! [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 ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf1D2,axiom, % 177.74/177.79 ! [V_x_2,V_B_2,V_A_2,T_a] : % 177.74/177.79 ( 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)) % 177.74/177.79 => hBOOL(hAPP(V_B_2,V_x_2)) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf1D1,axiom, % 177.74/177.79 ! [V_x_2,V_B_2,V_A_2,T_a] : % 177.74/177.79 ( 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)) % 177.74/177.79 => hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf__apply,axiom, % 177.74/177.79 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 177.74/177.79 ( class_Lattices_Olattice(T_a) % 177.74/177.79 => 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)) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf__assoc,axiom, % 177.74/177.79 ! [V_z,V_y,V_x,T_a] : % 177.74/177.79 ( class_Lattices_Osemilattice__inf(T_a) % 177.74/177.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf__sup__aci_I2_J,axiom, % 177.74/177.79 ! [V_z,V_y,V_x,T_a] : % 177.74/177.79 ( class_Lattices_Olattice(T_a) % 177.74/177.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf_Oassoc,axiom, % 177.74/177.79 ! [V_c,V_b,V_a,T_a] : % 177.74/177.79 ( class_Lattices_Osemilattice__inf(T_a) % 177.74/177.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_compl__eq__compl__iff,axiom, % 177.74/177.79 ! [V_y_2,V_x_2,T_a] : % 177.74/177.79 ( class_Lattices_Oboolean__algebra(T_a) % 177.74/177.79 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2) % 177.74/177.79 <=> V_x_2 = V_y_2 ) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf__left__commute,axiom, % 177.74/177.79 ! [V_z,V_y,V_x,T_a] : % 177.74/177.79 ( class_Lattices_Osemilattice__inf(T_a) % 177.74/177.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf__sup__aci_I3_J,axiom, % 177.74/177.79 ! [V_z,V_y,V_x,T_a] : % 177.74/177.79 ( class_Lattices_Olattice(T_a) % 177.74/177.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf_Oleft__commute,axiom, % 177.74/177.79 ! [V_c,V_a,V_b,T_a] : % 177.74/177.79 ( class_Lattices_Osemilattice__inf(T_a) % 177.74/177.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf__left__idem,axiom, % 177.74/177.79 ! [V_y,V_x,T_a] : % 177.74/177.79 ( class_Lattices_Osemilattice__inf(T_a) % 177.74/177.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf__sup__aci_I4_J,axiom, % 177.74/177.79 ! [V_y,V_x,T_a] : % 177.74/177.79 ( class_Lattices_Olattice(T_a) % 177.74/177.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf_Oleft__idem,axiom, % 177.74/177.79 ! [V_b,V_a,T_a] : % 177.74/177.79 ( class_Lattices_Osemilattice__inf(T_a) % 177.74/177.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf__commute,axiom, % 177.74/177.79 ! [V_y,V_x,T_a] : % 177.74/177.79 ( class_Lattices_Osemilattice__inf(T_a) % 177.74/177.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf__sup__aci_I1_J,axiom, % 177.74/177.79 ! [V_y,V_x,T_a] : % 177.74/177.79 ( class_Lattices_Olattice(T_a) % 177.74/177.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf_Ocommute,axiom, % 177.74/177.79 ! [V_b,V_a,T_a] : % 177.74/177.79 ( class_Lattices_Osemilattice__inf(T_a) % 177.74/177.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_a) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_uminus__apply,axiom, % 177.74/177.79 ! [V_x_2,V_A_2,T_b,T_a] : % 177.74/177.79 ( class_Groups_Ouminus(T_a) % 177.74/177.79 => 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)) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf__idem,axiom, % 177.74/177.79 ! [V_x,T_a] : % 177.74/177.79 ( class_Lattices_Osemilattice__inf(T_a) % 177.74/177.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_inf_Oidem,axiom, % 177.74/177.79 ! [V_a,T_a] : % 177.74/177.79 ( class_Lattices_Osemilattice__inf(T_a) % 177.74/177.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_double__compl,axiom, % 177.74/177.79 ! [V_x,T_a] : % 177.74/177.79 ( class_Lattices_Oboolean__algebra(T_a) % 177.74/177.79 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_Compl__disjoint2,axiom, % 177.74/177.79 ! [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)) ). % 177.74/177.79 % 177.74/177.79 fof(fact_Compl__disjoint,axiom, % 177.74/177.79 ! [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)) ). % 177.74/177.79 % 177.74/177.79 fof(fact_compl__inf,axiom, % 177.74/177.79 ! [V_y,V_x,T_a] : % 177.74/177.79 ( class_Lattices_Oboolean__algebra(T_a) % 177.74/177.79 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_compl__sup,axiom, % 177.74/177.79 ! [V_y,V_x,T_a] : % 177.74/177.79 ( class_Lattices_Oboolean__algebra(T_a) % 177.74/177.79 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 177.74/177.79 % 177.74/177.79 fof(fact_diff__eq,axiom, % 177.74/177.79 ! [V_y,V_x,T_a] : % 177.74/177.79 ( class_Lattices_Oboolean__algebra(T_a) % 177.74/177.79 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inj__on__id2,axiom, % 177.74/177.80 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Compl__Un,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Compl__Int,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Diff__Compl,axiom, % 177.74/177.80 ! [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) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Diff__eq,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inf__Sup__absorb,axiom, % 177.74/177.80 ! [V_a_2,V_A_2,T_a] : % 177.74/177.80 ( class_Lattices_Olattice(T_a) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.80 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.74/177.80 => 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 ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inj__onD,axiom, % 177.74/177.80 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.80 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.74/177.80 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 177.74/177.80 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.80 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 177.74/177.80 => V_x_2 = V_y_2 ) ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inj__on__iff,axiom, % 177.74/177.80 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.80 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.74/177.80 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.80 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 177.74/177.80 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 177.74/177.80 <=> V_x_2 = V_y_2 ) ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inj__on__contraD,axiom, % 177.74/177.80 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.80 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.74/177.80 => ( V_x_2 != V_y_2 % 177.74/177.80 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.80 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 177.74/177.80 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inj__on__diff,axiom, % 177.74/177.80 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.80 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.74/177.80 => 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)) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inf__bot__left,axiom, % 177.74/177.80 ! [V_x,T_a] : % 177.74/177.80 ( class_Lattices_Obounded__lattice__bot(T_a) % 177.74/177.80 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inf__bot__right,axiom, % 177.74/177.80 ! [V_x,T_a] : % 177.74/177.80 ( class_Lattices_Obounded__lattice__bot(T_a) % 177.74/177.80 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_ComplE,axiom, % 177.74/177.80 ! [V_A_2,V_ca_2,T_a] : % 177.74/177.80 ( 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))) % 177.74/177.80 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_ComplD,axiom, % 177.74/177.80 ! [V_A_2,V_ca_2,T_a] : % 177.74/177.80 ( 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))) % 177.74/177.80 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Compl__iff,axiom, % 177.74/177.80 ! [V_A_2,V_ca_2,T_a] : % 177.74/177.80 ( 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))) % 177.74/177.80 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inf__sup__absorb,axiom, % 177.74/177.80 ! [V_y,V_x,T_a] : % 177.74/177.80 ( class_Lattices_Olattice(T_a) % 177.74/177.80 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = V_x ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_sup__inf__absorb,axiom, % 177.74/177.80 ! [V_y,V_x,T_a] : % 177.74/177.80 ( class_Lattices_Olattice(T_a) % 177.74/177.80 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = V_x ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inf__sup__distrib1,axiom, % 177.74/177.80 ! [V_z,V_y,V_x,T_a] : % 177.74/177.80 ( class_Lattices_Odistrib__lattice(T_a) % 177.74/177.80 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_sup__inf__distrib1,axiom, % 177.74/177.80 ! [V_z,V_y,V_x,T_a] : % 177.74/177.80 ( class_Lattices_Odistrib__lattice(T_a) % 177.74/177.80 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inf__sup__distrib2,axiom, % 177.74/177.80 ! [V_x,V_z,V_y,T_a] : % 177.74/177.80 ( class_Lattices_Odistrib__lattice(T_a) % 177.74/177.80 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_z),V_x)) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_sup__inf__distrib2,axiom, % 177.74/177.80 ! [V_x,V_z,V_y,T_a] : % 177.74/177.80 ( class_Lattices_Odistrib__lattice(T_a) % 177.74/177.80 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_z),V_x)) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inj__Some,axiom, % 177.74/177.80 ! [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) ). % 177.74/177.80 % 177.74/177.80 fof(fact_IntD2,axiom, % 177.74/177.80 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 177.74/177.80 ( 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))) % 177.74/177.80 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_IntD1,axiom, % 177.74/177.80 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 177.74/177.80 ( 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))) % 177.74/177.80 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Int__iff,axiom, % 177.74/177.80 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 177.74/177.80 ( 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))) % 177.74/177.80 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 177.74/177.80 & hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Int__empty__left,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Int__empty__right,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_disjoint__iff__not__equal,axiom, % 177.74/177.80 ! [V_B_2,V_A_2,T_a] : % 177.74/177.80 ( 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)) % 177.74/177.80 <=> ! [B_x] : % 177.74/177.80 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.74/177.80 => ! [B_xa] : % 177.74/177.80 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_B_2)) % 177.74/177.80 => B_x != B_xa ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_insert__inter__insert,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Un__Int__crazy,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Un__Int__distrib2,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Int__Un__distrib2,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Un__Int__distrib,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Int__Un__distrib,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Diff__Int2,axiom, % 177.74/177.80 ! [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) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Diff__Int__distrib2,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Int__Diff,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Diff__Int__distrib,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_restrict__restrict,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_fun__left__comm__idem__inf,axiom, % 177.74/177.80 ! [T_a] : % 177.74/177.80 ( class_Lattices_Osemilattice__inf(T_a) % 177.74/177.80 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_fold__graph_Oequations_I1_J,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_fold__graph_OemptyI,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_empty__fold__graphE,axiom, % 177.74/177.80 ! [V_x_2,V_z_2,V_f_2,T_b,T_a] : % 177.74/177.80 ( 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)) % 177.74/177.80 => V_x_2 = V_z_2 ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_fold__graph__imp__finite,axiom, % 177.74/177.80 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 177.74/177.80 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 177.74/177.80 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inf__Int__eq,axiom, % 177.74/177.80 ! [V_x_2,V_S_2,V_R_2,T_a] : % 177.74/177.80 ( 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)) % 177.74/177.80 <=> 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))) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Sup__fin_Osingleton,axiom, % 177.74/177.80 ! [V_x_2,T_a] : % 177.74/177.80 ( class_Lattices_Olattice(T_a) % 177.74/177.80 => 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 ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Sup__fin_Ounion__inter,axiom, % 177.74/177.80 ! [V_B_2,V_A_2,T_a] : % 177.74/177.80 ( class_Lattices_Olattice(T_a) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.74/177.80 => ( 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)) % 177.74/177.80 => 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)) ) ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Sup__fin_Ounion__disjoint,axiom, % 177.74/177.80 ! [V_B_2,V_A_2,T_a] : % 177.74/177.80 ( class_Lattices_Olattice(T_a) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.80 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.74/177.80 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.80 => ( 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)) % 177.74/177.80 => 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)) ) ) ) ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inj__on__Un,axiom, % 177.74/177.80 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.80 ( 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)) % 177.74/177.80 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.74/177.80 & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 177.74/177.80 & 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)) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_finite__imageD,axiom, % 177.74/177.80 ! [V_A_2,V_f_2,T_b,T_a] : % 177.74/177.80 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 177.74/177.80 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) % 177.74/177.80 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inj__on__Un__image__eq__iff,axiom, % 177.74/177.80 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.80 ( 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)) % 177.74/177.80 => ( 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) % 177.74/177.80 <=> V_A_2 = V_B_2 ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Int__insert__right,axiom, % 177.74/177.80 ! [V_B_2,V_A_2,V_a_2,T_a] : % 177.74/177.80 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.74/177.80 => 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)) ) % 177.74/177.80 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.74/177.80 => 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) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Int__insert__left,axiom, % 177.74/177.80 ! [V_B_2,V_C_2,V_a_2,T_a] : % 177.74/177.80 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 177.74/177.80 => 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)) ) % 177.74/177.80 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 177.74/177.80 => 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) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Int__insert__right__if0,axiom, % 177.74/177.80 ! [V_B_2,V_A_2,V_a_2,T_a] : % 177.74/177.80 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.74/177.80 => 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) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Int__insert__left__if0,axiom, % 177.74/177.80 ! [V_B_2,V_C_2,V_a_2,T_a] : % 177.74/177.80 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 177.74/177.80 => 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) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Int__insert__right__if1,axiom, % 177.74/177.80 ! [V_B_2,V_A_2,V_a_2,T_a] : % 177.74/177.80 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.74/177.80 => 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)) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Int__insert__left__if1,axiom, % 177.74/177.80 ! [V_B_2,V_C_2,V_a_2,T_a] : % 177.74/177.80 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 177.74/177.80 => 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)) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Compl__Diff__eq,axiom, % 177.74/177.80 ! [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) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Diff__disjoint,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Diff__triv,axiom, % 177.74/177.80 ! [V_B_2,V_A_2,T_a] : % 177.74/177.80 ( 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)) % 177.74/177.80 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Un__Diff__Int,axiom, % 177.74/177.80 ! [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 ). % 177.74/177.80 % 177.74/177.80 fof(fact_Diff__Un,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Diff__Int,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inj__on__map__add__dom,axiom, % 177.74/177.80 ! [V_m_H_2,V_m_2,T_b,T_a] : % 177.74/177.80 ( 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)) % 177.74/177.80 <=> 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)) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Sup__fin_Oin__idem,axiom, % 177.74/177.80 ! [V_x_2,V_A_2,T_a] : % 177.74/177.80 ( class_Lattices_Olattice(T_a) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.80 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.80 => 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) ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_dom__restrict,axiom, % 177.74/177.80 ! [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) ). % 177.74/177.80 % 177.74/177.80 fof(fact_fold__graph_OinsertI,axiom, % 177.74/177.80 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 177.74/177.80 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 177.74/177.80 => 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))) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inj__on__fun__updI,axiom, % 177.74/177.80 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.80 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.74/177.80 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 177.74/177.80 => 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) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Sup__fin_Oinsert__idem,axiom, % 177.74/177.80 ! [V_x_2,V_A_2,T_a] : % 177.74/177.80 ( class_Lattices_Olattice(T_a) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.80 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.80 => 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)) ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Sup__fin_Ounion__idem,axiom, % 177.74/177.80 ! [V_B_2,V_A_2,T_a] : % 177.74/177.80 ( class_Lattices_Olattice(T_a) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.80 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.74/177.80 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.80 => 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)) ) ) ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_map__add__comm,axiom, % 177.74/177.80 ! [V_m2_2,V_m1_2,T_b,T_a] : % 177.74/177.80 ( 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)) % 177.74/177.80 => 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) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Sup__fin_Oidem,axiom, % 177.74/177.80 ! [V_x,T_a] : % 177.74/177.80 ( class_Lattices_Olattice(T_a) % 177.74/177.80 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_folding__image__simple_Ounion__inter,axiom, % 177.74/177.80 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 177.74/177.80 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 177.74/177.80 => 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)) ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Sup__fin_Oinsert,axiom, % 177.74/177.80 ! [V_x_2,V_A_2,T_a] : % 177.74/177.80 ( class_Lattices_Olattice(T_a) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.80 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.80 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.80 => 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)) ) ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Sup__fin_Oinsert__remove,axiom, % 177.74/177.80 ! [V_x_2,V_A_2,T_a] : % 177.74/177.80 ( class_Lattices_Olattice(T_a) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.80 => ( ( 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)) % 177.74/177.80 => 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 ) % 177.74/177.80 & ( 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)) % 177.74/177.80 => 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)))))) ) ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_fold1Set_Ointros,axiom, % 177.74/177.80 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_a] : % 177.74/177.80 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2),V_x_2)) % 177.74/177.80 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.74/177.80 => 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)) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Sup__fin_Oclosed,axiom, % 177.74/177.80 ! [V_A_2,T_a] : % 177.74/177.80 ( class_Lattices_Olattice(T_a) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.80 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.80 => ( ! [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)))))) % 177.74/177.80 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_minus__diff__eq,axiom, % 177.74/177.80 ! [V_b,V_a,T_a] : % 177.74/177.80 ( class_Groups_Oab__group__add(T_a) % 177.74/177.80 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Inf__fin_Oremove,axiom, % 177.74/177.80 ! [V_x_2,V_A_2,T_a] : % 177.74/177.80 ( class_Lattices_Olattice(T_a) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.80 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.80 => ( ( 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)) % 177.74/177.80 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = V_x_2 ) % 177.74/177.80 & ( 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)) % 177.74/177.80 => 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)))))) ) ) ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Sup__fin_Ohom__commute,axiom, % 177.74/177.80 ! [V_N_2,V_h_2,T_a] : % 177.74/177.80 ( class_Lattices_Olattice(T_a) % 177.74/177.80 => ( ! [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)) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 177.74/177.80 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.80 => 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)) ) ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_image__eq__fold__image,axiom, % 177.74/177.80 ! [V_f_2,T_b,V_A_2,T_a] : % 177.74/177.80 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.80 => 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) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_compl__unique,axiom, % 177.74/177.80 ! [V_y,V_x,T_a] : % 177.74/177.80 ( class_Lattices_Oboolean__algebra(T_a) % 177.74/177.80 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) % 177.74/177.80 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) % 177.74/177.80 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Inf__fin_Ounion__inter,axiom, % 177.74/177.80 ! [V_B_2,V_A_2,T_a] : % 177.74/177.80 ( class_Lattices_Olattice(T_a) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.74/177.80 => ( 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)) % 177.74/177.80 => 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)) ) ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Inf__fin_Ounion__disjoint,axiom, % 177.74/177.80 ! [V_B_2,V_A_2,T_a] : % 177.74/177.80 ( class_Lattices_Olattice(T_a) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.80 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.74/177.80 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.80 => ( 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)) % 177.74/177.80 => 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)) ) ) ) ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Inf__fin_Oinsert__remove,axiom, % 177.74/177.80 ! [V_x_2,V_A_2,T_a] : % 177.74/177.80 ( class_Lattices_Olattice(T_a) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.80 => ( ( 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)) % 177.74/177.80 => 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 ) % 177.74/177.80 & ( 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)) % 177.74/177.80 => 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)))))) ) ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_UNIV__I,axiom, % 177.74/177.80 ! [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)))) ). % 177.74/177.80 % 177.74/177.80 fof(fact_top__apply,axiom, % 177.74/177.80 ! [V_x_2,T_b,T_a] : % 177.74/177.80 ( class_Orderings_Otop(T_a) % 177.74/177.80 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_finite__fun__UNIVD2,axiom, % 177.74/177.80 ! [T_b,T_a] : % 177.74/177.80 ( 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)))) % 177.74/177.80 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_finite__option__UNIV,axiom, % 177.74/177.80 ! [T_a] : % 177.74/177.80 ( 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)))) % 177.74/177.80 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_finite__Plus__UNIV__iff,axiom, % 177.74/177.80 ! [T_b,T_a] : % 177.74/177.80 ( 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)))) % 177.74/177.80 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 177.74/177.80 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_finite__Prod__UNIV,axiom, % 177.74/177.80 ! [T_b,T_a] : % 177.74/177.80 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 177.74/177.80 => 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)))) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_UNIV__not__empty,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_finite__UNIV,axiom, % 177.74/177.80 ! [T_a] : % 177.74/177.80 ( class_Finite__Set_Ofinite(T_a) % 177.74/177.80 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Un__UNIV__left,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Un__UNIV__right,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Int__UNIV__left,axiom, % 177.74/177.80 ! [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 ). % 177.74/177.80 % 177.74/177.80 fof(fact_Int__UNIV__right,axiom, % 177.74/177.80 ! [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 ). % 177.74/177.80 % 177.74/177.80 fof(fact_inj__eq,axiom, % 177.74/177.80 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 177.74/177.80 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.74/177.80 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 177.74/177.80 <=> V_x_2 = V_y_2 ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_injD,axiom, % 177.74/177.80 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 177.74/177.80 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.74/177.80 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 177.74/177.80 => V_x_2 = V_y_2 ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_fold__image__empty,axiom, % 177.74/177.80 ! [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 ). % 177.74/177.80 % 177.74/177.80 fof(fact_range__composition,axiom, % 177.74/177.80 ! [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)))) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inj__fun,axiom, % 177.74/177.80 ! [T_c,V_f_2,T_b,T_a] : % 177.74/177.80 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.74/177.80 => 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))) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_sup__top__right,axiom, % 177.74/177.80 ! [V_x,T_a] : % 177.74/177.80 ( class_Lattices_Obounded__lattice__top(T_a) % 177.74/177.80 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_sup__top__left,axiom, % 177.74/177.80 ! [V_x,T_a] : % 177.74/177.80 ( class_Lattices_Obounded__lattice__top(T_a) % 177.74/177.80 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inf__top__left,axiom, % 177.74/177.80 ! [V_x,T_a] : % 177.74/177.80 ( class_Lattices_Obounded__lattice__top(T_a) % 177.74/177.80 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inf__top__right,axiom, % 177.74/177.80 ! [V_x,T_a] : % 177.74/177.80 ( class_Lattices_Obounded__lattice__top(T_a) % 177.74/177.80 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inf__eq__top__iff,axiom, % 177.74/177.80 ! [V_y_2,V_x_2,T_a] : % 177.74/177.80 ( class_Lattices_Obounded__lattice__top(T_a) % 177.74/177.80 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_a) % 177.74/177.80 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_a) % 177.74/177.80 & V_y_2 = c_Orderings_Otop__class_Otop(T_a) ) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_UNIV__option__conv,axiom, % 177.74/177.80 ! [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)))) ). % 177.74/177.80 % 177.74/177.80 fof(fact_fold1Set__nonempty,axiom, % 177.74/177.80 ! [V_x_2,V_A_2,V_f_2,T_a] : % 177.74/177.80 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),V_x_2)) % 177.74/177.80 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_empty__fold1SetE,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_range__eqI,axiom, % 177.74/177.80 ! [T_b,T_a,V_x_2,V_f_2,V_b_2] : % 177.74/177.80 ( V_b_2 = hAPP(V_f_2,V_x_2) % 177.74/177.80 => 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))))) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_rangeI,axiom, % 177.74/177.80 ! [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))))) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Diff__UNIV,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inj__image__eq__iff,axiom, % 177.74/177.80 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.80 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.74/177.80 => ( 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) % 177.74/177.80 <=> V_A_2 = V_B_2 ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Compl__UNIV__eq,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Compl__empty__eq,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_finite__compl,axiom, % 177.74/177.80 ! [V_A_2,T_a] : % 177.74/177.80 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 177.74/177.80 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Compl__partition,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Compl__partition2,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Compl__eq__Diff__UNIV,axiom, % 177.74/177.80 ! [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) ). % 177.74/177.80 % 177.74/177.80 fof(fact_Inf__fin_Osingleton,axiom, % 177.74/177.80 ! [V_x_2,T_a] : % 177.74/177.80 ( class_Lattices_Olattice(T_a) % 177.74/177.80 => 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 ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_inj__singleton,axiom, % 177.74/177.80 ! [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))) ). % 177.74/177.80 % 177.74/177.80 fof(fact_finite__range__imageI,axiom, % 177.74/177.80 ! [V_f_2,T_c,V_g_2,T_b,T_a] : % 177.74/177.80 ( 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))))) % 177.74/177.80 => 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))))) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 177.74/177.80 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 177.74/177.80 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 177.74/177.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 177.74/177.80 => 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) ) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_dom__const,axiom, % 177.74/177.80 ! [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)) ). % 177.74/177.80 % 177.74/177.80 fof(fact_compl__top__eq,axiom, % 177.74/177.80 ! [T_a] : % 177.74/177.80 ( class_Lattices_Oboolean__algebra(T_a) % 177.74/177.80 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 177.74/177.80 % 177.74/177.80 fof(fact_compl__bot__eq,axiom, % 177.74/177.81 ! [T_a] : % 177.74/177.81 ( class_Lattices_Oboolean__algebra(T_a) % 177.74/177.81 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_sup__compl__top,axiom, % 177.74/177.81 ! [V_x,T_a] : % 177.74/177.81 ( class_Lattices_Oboolean__algebra(T_a) % 177.74/177.81 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_compl__sup__top,axiom, % 177.74/177.81 ! [V_x,T_a] : % 177.74/177.81 ( class_Lattices_Oboolean__algebra(T_a) % 177.74/177.81 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_inj__image__mem__iff,axiom, % 177.74/177.81 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.74/177.81 => ( 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))) % 177.74/177.81 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_range__ex1__eq,axiom, % 177.74/177.81 ! [V_b_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.74/177.81 => ( 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))))) % 177.74/177.81 <=> ? [B_x] : % 177.74/177.81 ( V_b_2 = hAPP(V_f_2,B_x) % 177.74/177.81 & ! [B_y] : % 177.74/177.81 ( V_b_2 = hAPP(V_f_2,B_y) % 177.74/177.81 => B_y = B_x ) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_finite__UNIV__surj__inj,axiom, % 177.74/177.81 ! [V_f_2,T_a] : % 177.74/177.81 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 177.74/177.81 => ( 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)) % 177.74/177.81 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_finite__UNIV__inj__surj,axiom, % 177.74/177.81 ! [V_f_2,T_a] : % 177.74/177.81 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 177.74/177.81 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.74/177.81 => 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)) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_image__Int,axiom, % 177.74/177.81 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.74/177.81 => 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)) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_image__set__diff,axiom, % 177.74/177.81 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.74/177.81 => 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)) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_diff__eq__diff__eq,axiom, % 177.74/177.81 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 177.74/177.81 ( class_Groups_Oab__group__add(T_a) % 177.74/177.81 => ( 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) % 177.74/177.81 => ( V_a_2 = V_b_2 % 177.74/177.81 <=> V_ca_2 = V_d_2 ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_neg__equal__iff__equal,axiom, % 177.74/177.81 ! [V_b_2,V_a_2,T_a] : % 177.74/177.81 ( class_Groups_Ogroup__add(T_a) % 177.74/177.81 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 177.74/177.81 <=> V_a_2 = V_b_2 ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_minus__equation__iff,axiom, % 177.74/177.81 ! [V_b_2,V_a_2,T_a] : % 177.74/177.81 ( class_Groups_Ogroup__add(T_a) % 177.74/177.81 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_b_2 % 177.74/177.81 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) = V_a_2 ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_equation__minus__iff,axiom, % 177.74/177.81 ! [V_b_2,V_a_2,T_a] : % 177.74/177.81 ( class_Groups_Ogroup__add(T_a) % 177.74/177.81 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 177.74/177.81 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_minus__minus,axiom, % 177.74/177.81 ! [V_a,T_a] : % 177.74/177.81 ( class_Groups_Ogroup__add(T_a) % 177.74/177.81 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_sup__Inf__absorb,axiom, % 177.74/177.81 ! [V_a_2,V_A_2,T_a] : % 177.74/177.81 ( class_Lattices_Olattice(T_a) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.74/177.81 => 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 ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_Inf__fin_Oin__idem,axiom, % 177.74/177.81 ! [V_x_2,V_A_2,T_a] : % 177.74/177.81 ( class_Lattices_Olattice(T_a) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.81 => 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) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fold1Set__sing,axiom, % 177.74/177.81 ! [V_b_2,V_a_2,V_f_2,T_a] : % 177.74/177.81 ( 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)) % 177.74/177.81 <=> V_a_2 = V_b_2 ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_finite__range__updI,axiom, % 177.74/177.81 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( 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))))) % 177.74/177.81 => 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))))) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_Inf__fin_Oinsert__idem,axiom, % 177.74/177.81 ! [V_x_2,V_A_2,T_a] : % 177.74/177.81 ( class_Lattices_Olattice(T_a) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => 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)) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_Inf__fin_Ounion__idem,axiom, % 177.74/177.81 ! [V_B_2,V_A_2,T_a] : % 177.74/177.81 ( class_Lattices_Olattice(T_a) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.74/177.81 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => 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)) ) ) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_Inf__fin_Oinsert,axiom, % 177.74/177.81 ! [V_x_2,V_A_2,T_a] : % 177.74/177.81 ( class_Lattices_Olattice(T_a) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.81 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => 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)) ) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_comm__monoid__big_OF__eq,axiom, % 177.74/177.81 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 177.74/177.81 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 177.74/177.81 => 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) ) % 177.74/177.81 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 177.74/177.81 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_Inf__fin_Oclosed,axiom, % 177.74/177.81 ! [V_A_2,T_a] : % 177.74/177.81 ( class_Lattices_Olattice(T_a) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => ( ! [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)))))) % 177.74/177.81 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_Inf__fin_Ohom__commute,axiom, % 177.74/177.81 ! [V_N_2,V_h_2,T_a] : % 177.74/177.81 ( class_Lattices_Olattice(T_a) % 177.74/177.81 => ( ! [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)) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 177.74/177.81 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => 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)) ) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_insert__fold1SetE,axiom, % 177.74/177.81 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_a] : % 177.74/177.81 ( 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)) % 177.74/177.81 => ~ ! [B_a,B_A] : % 177.74/177.81 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_x_2)) % 177.74/177.81 => hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fold1Set_Oequations,axiom, % 177.74/177.81 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a] : % 177.74/177.81 ( 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)) % 177.74/177.81 <=> ? [B_a,B_A] : % 177.74/177.81 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 177.74/177.81 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_a3_2)) % 177.74/177.81 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom, % 177.74/177.81 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 177.74/177.81 => ( ! [B_x] : % 177.74/177.81 ( 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))) % 177.74/177.81 => hAPP(V_g_2,B_x) = V_z_2 ) % 177.74/177.81 => 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)) ) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_setsum__diff1__ring,axiom, % 177.74/177.81 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 177.74/177.81 ( class_Rings_Oring(T_b) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.74/177.81 => 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)) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_setsum__diff1,axiom, % 177.74/177.81 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 177.74/177.81 ( class_Groups_Oab__group__add(T_b) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.74/177.81 => 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)) ) % 177.74/177.81 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.74/177.81 => 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) ) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fold__graph__permute__diff,axiom, % 177.74/177.81 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_a] : % 177.74/177.81 ( class_Groups_Oab__semigroup__mult(T_a) % 177.74/177.81 => ( 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)) % 177.74/177.81 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.74/177.81 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 177.74/177.81 => 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)) ) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_Inf__fin_Oeq__fold_H,axiom, % 177.74/177.81 ! [V_x_2,V_A_2,T_a] : % 177.74/177.81 ( class_Lattices_Olattice(T_a) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.81 => 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) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_top1I,axiom, % 177.74/177.81 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ). % 177.74/177.81 % 177.74/177.81 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 177.74/177.81 ! [V_c,V_b,V_a,T_a] : % 177.74/177.81 ( class_Groups_Oab__semigroup__mult(T_a) % 177.74/177.81 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_setsum__commute,axiom, % 177.74/177.81 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 177.74/177.81 ( class_Groups_Ocomm__monoid__add(T_a) % 177.74/177.81 => 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) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_mult__left__idem,axiom, % 177.74/177.81 ! [V_b,V_a,T_a] : % 177.74/177.81 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 177.74/177.81 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_mult__idem,axiom, % 177.74/177.81 ! [V_x,T_a] : % 177.74/177.81 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 177.74/177.81 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_times_Oidem,axiom, % 177.74/177.81 ! [V_a,T_a] : % 177.74/177.81 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 177.74/177.81 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_setsum__right__distrib,axiom, % 177.74/177.81 ! [V_A_2,V_f_2,T_b,V_r_2,T_a] : % 177.74/177.81 ( class_Rings_Osemiring__0(T_a) % 177.74/177.81 => 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) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_setsum__left__distrib,axiom, % 177.74/177.81 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( class_Rings_Osemiring__0(T_a) % 177.74/177.81 => 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) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_setsum__product,axiom, % 177.74/177.81 ! [V_B_2,V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( class_Rings_Osemiring__0(T_a) % 177.74/177.81 => 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) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fold__empty,axiom, % 177.74/177.81 ! [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 ). % 177.74/177.81 % 177.74/177.81 fof(fact_setsum__subtractf,axiom, % 177.74/177.81 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( class_Groups_Oab__group__add(T_a) % 177.74/177.81 => 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)) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_setsum__negf,axiom, % 177.74/177.81 ! [V_A_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( class_Groups_Oab__group__add(T_a) % 177.74/177.81 => 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)) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fun__left__comm__idem,axiom, % 177.74/177.81 ! [T_a] : % 177.74/177.81 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 177.74/177.81 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fold__image__def,axiom, % 177.74/177.81 ! [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)) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fold__def,axiom, % 177.74/177.81 ! [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)) ). % 177.74/177.81 % 177.74/177.81 fof(fact_union__fold__insert,axiom, % 177.74/177.81 ! [V_B_2,V_A_2,T_a] : % 177.74/177.81 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => 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) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fold__sup__insert,axiom, % 177.74/177.81 ! [V_a_2,V_b_2,V_A_2,T_a] : % 177.74/177.81 ( class_Lattices_Osemilattice__sup(T_a) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => 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)) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fold__inf__insert,axiom, % 177.74/177.81 ! [V_a_2,V_b_2,V_A_2,T_a] : % 177.74/177.81 ( class_Lattices_Osemilattice__inf(T_a) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => 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)) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fold__graph__insert__swap,axiom, % 177.74/177.81 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_a] : % 177.74/177.81 ( class_Groups_Oab__semigroup__mult(T_a) % 177.74/177.81 => ( 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)) % 177.74/177.81 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 177.74/177.81 => 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))) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom, % 177.74/177.81 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => 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)) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom, % 177.74/177.81 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => 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) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom, % 177.74/177.81 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_a] : % 177.74/177.81 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => 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) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_setsum__diff1__nat,axiom, % 177.74/177.81 ! [V_f_2,V_A_2,V_a_2,T_a] : % 177.74/177.81 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.74/177.81 => 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)) ) % 177.74/177.81 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.74/177.81 => 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) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom, % 177.74/177.81 ! [V_a_2,V_A_2,T_a] : % 177.74/177.81 ( class_Lattices_Olattice(T_a) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => 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) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom, % 177.74/177.81 ! [V_a_2,V_A_2,T_a] : % 177.74/177.81 ( class_Lattices_Olattice(T_a) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => 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) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fold__image__insert,axiom, % 177.74/177.81 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_a,T_b] : % 177.74/177.81 ( class_Groups_Oab__semigroup__mult(T_b) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.74/177.81 => 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)) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_minus__fold__remove,axiom, % 177.74/177.81 ! [V_B_2,V_A_2,T_a] : % 177.74/177.81 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => 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) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_folding__one_Oeq__fold_H,axiom, % 177.74/177.81 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 177.74/177.81 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.81 => 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) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_comm__monoid__big_Oinfinite,axiom, % 177.74/177.81 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 177.74/177.81 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 177.74/177.81 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_Sup__fin_Oeq__fold_H,axiom, % 177.74/177.81 ! [V_x_2,V_A_2,T_a] : % 177.74/177.81 ( class_Lattices_Olattice(T_a) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.81 => 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) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fun__left__comm_Ofold__rec,axiom, % 177.74/177.81 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.81 => 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)))))) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fun__left__comm_Ofold__insert__remove,axiom, % 177.74/177.81 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => 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)))))) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_minus__mult__right,axiom, % 177.74/177.81 ! [V_b,V_a,T_a] : % 177.74/177.81 ( class_Rings_Oring(T_a) % 177.74/177.81 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_minus__mult__left,axiom, % 177.74/177.81 ! [V_b,V_a,T_a] : % 177.74/177.81 ( class_Rings_Oring(T_a) % 177.74/177.81 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_minus__mult__commute,axiom, % 177.74/177.81 ! [V_b,V_a,T_a] : % 177.74/177.81 ( class_Rings_Oring(T_a) % 177.74/177.81 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_minus__mult__minus,axiom, % 177.74/177.81 ! [V_b,V_a,T_a] : % 177.74/177.81 ( class_Rings_Oring(T_a) % 177.74/177.81 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_square__eq__iff,axiom, % 177.74/177.81 ! [V_b_2,V_a_2,T_a] : % 177.74/177.81 ( class_Rings_Oidom(T_a) % 177.74/177.81 => ( 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) % 177.74/177.81 <=> ( V_a_2 = V_b_2 % 177.74/177.81 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_iso__tuple__UNIV__I,axiom, % 177.74/177.81 ! [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)))) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INFI__fold__inf,axiom, % 177.74/177.81 ! [V_f_2,V_A_2,T_a,T_b] : % 177.74/177.81 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => 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) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INF1__E,axiom, % 177.74/177.81 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 177.74/177.81 ( 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)) % 177.74/177.81 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 177.74/177.81 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INF1__D,axiom, % 177.74/177.81 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 177.74/177.81 ( 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)) % 177.74/177.81 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.74/177.81 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INF2__E,axiom, % 177.74/177.81 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 177.74/177.81 ( 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)) % 177.74/177.81 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) % 177.74/177.81 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INF2__D,axiom, % 177.74/177.81 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 177.74/177.81 ( 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)) % 177.74/177.81 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.74/177.81 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_finite__INT,axiom, % 177.74/177.81 ! [V_A_2,T_b,V_I_2,T_a] : % 177.74/177.81 ( ? [B_x] : % 177.74/177.81 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_I_2)) % 177.74/177.81 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_A_2,B_x))) ) % 177.74/177.81 => 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))) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fun__left__comm_Ofun__left__comm,axiom, % 177.74/177.81 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 177.74/177.81 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_y_2),V_z_2)) = hAPP(hAPP(V_f_2,V_y_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom, % 177.74/177.81 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 177.74/177.81 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 177.74/177.81 => 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)) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fun__left__comm,axiom, % 177.74/177.81 ! [T_a] : % 177.74/177.81 ( class_Groups_Oab__semigroup__mult(T_a) % 177.74/177.81 => c_Finite__Set_Ofun__left__comm(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fun__left__comm_Ofold__graph__determ,axiom, % 177.74/177.81 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 177.74/177.81 => V_y_2 = V_x_2 ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INF__INT__eq,axiom, % 177.74/177.81 ! [V_x_2,V_r_2,T_b,T_a] : % 177.74/177.81 ( 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)) % 177.74/177.81 <=> 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))) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fun__left__comm_Ofold__fun__comm,axiom, % 177.74/177.81 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => 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) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fun__left__comm_Ofold__equality,axiom, % 177.74/177.81 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 177.74/177.81 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_inf__INFI__fold__inf,axiom, % 177.74/177.81 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 177.74/177.81 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => 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) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fun__left__comm_Ofold__graph__fold,axiom, % 177.74/177.81 ! [V_z_2,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => 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))) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fun__left__comm_Ofold__insert2,axiom, % 177.74/177.81 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.81 => 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) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fun__left__comm_Ofold__insert,axiom, % 177.74/177.81 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.74/177.81 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.74/177.81 => 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)) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__extend__simps_I3_J,axiom, % 177.74/177.81 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 177.74/177.81 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => 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) ) % 177.74/177.81 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => 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)) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__simps_I3_J,axiom, % 177.74/177.81 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 177.74/177.81 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => 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)) ) % 177.74/177.81 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => 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) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__simps_I2_J,axiom, % 177.74/177.81 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 177.74/177.81 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => 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)) ) % 177.74/177.81 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => 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)) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__simps_I1_J,axiom, % 177.74/177.81 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 177.74/177.81 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => 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)) ) % 177.74/177.81 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => 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) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__E,axiom, % 177.74/177.81 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 177.74/177.81 ( 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))) % 177.74/177.81 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) % 177.74/177.81 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__D,axiom, % 177.74/177.81 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 177.74/177.81 ( 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))) % 177.74/177.81 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 177.74/177.81 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INF__const,axiom, % 177.74/177.81 ! [V_M_2,T_a,V_A_2,T_b] : % 177.74/177.81 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 177.74/177.81 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => 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 ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__Un,axiom, % 177.74/177.81 ! [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)) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__insert,axiom, % 177.74/177.81 ! [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)) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INF1__iff,axiom, % 177.74/177.81 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 177.74/177.81 ( 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)) % 177.74/177.81 <=> ! [B_x] : % 177.74/177.81 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.74/177.81 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INF2__iff,axiom, % 177.74/177.81 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 177.74/177.81 ( 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)) % 177.74/177.81 <=> ! [B_x] : % 177.74/177.81 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.74/177.81 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__iff,axiom, % 177.74/177.81 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 177.74/177.81 ( 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))) % 177.74/177.81 <=> ! [B_x] : % 177.74/177.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 177.74/177.81 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__simps_I5_J,axiom, % 177.74/177.81 ! [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)) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__extend__simps_I5_J,axiom, % 177.74/177.81 ! [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)) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INTER__UNIV__conv_I1_J,axiom, % 177.74/177.81 ! [V_B_2,V_A_2,T_b,T_a] : % 177.74/177.81 ( 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) % 177.74/177.81 <=> ! [B_x] : % 177.74/177.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 177.74/177.81 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INTER__UNIV__conv_I2_J,axiom, % 177.74/177.81 ! [V_B_2,V_A_2,T_a,T_b] : % 177.74/177.81 ( 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)) % 177.74/177.81 <=> ! [B_x] : % 177.74/177.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 177.74/177.81 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__simps_I10_J,axiom, % 177.74/177.81 ! [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)) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__extend__simps_I10_J,axiom, % 177.74/177.81 ! [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) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__simps_I7_J,axiom, % 177.74/177.81 ! [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)) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__simps_I6_J,axiom, % 177.74/177.81 ! [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) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__extend__simps_I7_J,axiom, % 177.74/177.81 ! [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)) ). % 177.74/177.81 % 177.74/177.81 fof(fact_Un__INT__distrib,axiom, % 177.74/177.81 ! [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)) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__extend__simps_I6_J,axiom, % 177.74/177.81 ! [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)) ). % 177.74/177.81 % 177.74/177.81 fof(fact_Un__INT__distrib2,axiom, % 177.74/177.81 ! [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))) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__Int__distrib,axiom, % 177.74/177.81 ! [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)) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INFI__apply,axiom, % 177.74/177.81 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 177.74/177.81 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.74/177.81 => 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)) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INF__commute,axiom, % 177.74/177.81 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 177.74/177.81 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.74/177.81 => 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))) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__insert__distrib,axiom, % 177.74/177.81 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 177.74/177.81 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 177.74/177.81 => 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)) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__absorb,axiom, % 177.74/177.81 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 177.74/177.81 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 177.74/177.81 => 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) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__empty,axiom, % 177.74/177.81 ! [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)) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__constant,axiom, % 177.74/177.81 ! [V_ca_2,T_b,T_a,V_A_2] : % 177.74/177.81 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => 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)) ) % 177.74/177.81 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => 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 ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__extend__simps_I1_J,axiom, % 177.74/177.81 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 177.74/177.81 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => 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 ) % 177.74/177.81 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => 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)) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_INT__extend__simps_I2_J,axiom, % 177.74/177.81 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 177.74/177.81 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => 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 ) % 177.74/177.81 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.74/177.81 => 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)) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom, % 177.74/177.81 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 177.74/177.81 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 177.74/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 177.74/177.81 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.74/177.81 => ? [B_y_H] : % 177.74/177.81 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) % 177.74/177.81 & 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)) ) ) ) ) ). % 177.74/177.81 % 177.74/177.81 fof(fact_SUPR__fold__sup,axiom, % 177.74/177.81 ! [V_f_2,V_A_2,T_a,T_b] : % 177.84/177.81 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 177.84/177.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.81 => 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) ) ) ). % 177.84/177.81 % 177.84/177.82 fof(fact_fold__Un__disjoint,axiom, % 177.84/177.82 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 177.84/177.82 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.84/177.82 => ( 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)) % 177.84/177.82 => 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)) ) ) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_setsum__diff1_H,axiom, % 177.84/177.82 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 177.84/177.82 ( class_Groups_Ocomm__monoid__add(T_b) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.84/177.82 => 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)))))) ) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_setsum_Oremove,axiom, % 177.84/177.82 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 177.84/177.82 ( class_Groups_Ocomm__monoid__add(T_b) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.84/177.82 => 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)))))) ) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Inf__fold__inf,axiom, % 177.84/177.82 ! [V_A_2,T_a] : % 177.84/177.82 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => 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) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Sup__fold__sup,axiom, % 177.84/177.82 ! [V_A_2,T_a] : % 177.84/177.82 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => 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) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_fold1__eq__fold,axiom, % 177.84/177.82 ! [V_a_2,V_A_2,T_a] : % 177.84/177.82 ( class_Groups_Oab__semigroup__mult(T_a) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.84/177.82 => 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) ) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_fold1__Un,axiom, % 177.84/177.82 ! [V_B_2,V_A_2,T_a] : % 177.84/177.82 ( class_Groups_Oab__semigroup__mult(T_a) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.84/177.82 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => ( 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)) % 177.84/177.82 => 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)) ) ) ) ) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UnionI,axiom, % 177.84/177.82 ! [V_A_2,V_C_2,V_X_2,T_a] : % 177.84/177.82 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 177.84/177.82 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) % 177.84/177.82 => 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))) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_InterE,axiom, % 177.84/177.82 ! [V_X_2,V_C_2,V_A_2,T_a] : % 177.84/177.82 ( 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))) % 177.84/177.82 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 177.84/177.82 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_InterD,axiom, % 177.84/177.82 ! [V_X_2,V_C_2,V_A_2,T_a] : % 177.84/177.82 ( 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))) % 177.84/177.82 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 177.84/177.82 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_finite__Inter,axiom, % 177.84/177.82 ! [V_M_2,T_a] : % 177.84/177.82 ( ? [B_x] : % 177.84/177.82 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_M_2)) % 177.84/177.82 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_x)) ) % 177.84/177.82 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_M_2))) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_SUP1__I,axiom, % 177.84/177.82 ! [T_b,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 177.84/177.82 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.84/177.82 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 177.84/177.82 => 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)) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__I,axiom, % 177.84/177.82 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 177.84/177.82 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.84/177.82 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 177.84/177.82 => 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))) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_SUP2__I,axiom, % 177.84/177.82 ! [T_c,T_b,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 177.84/177.82 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.84/177.82 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) % 177.84/177.82 => 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)) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_SUPR__apply,axiom, % 177.84/177.82 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 177.84/177.82 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.84/177.82 => 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)) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_one__reorient,axiom, % 177.84/177.82 ! [V_x_2,T_a] : % 177.84/177.82 ( class_Groups_Oone(T_a) % 177.84/177.82 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2 % 177.84/177.82 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 177.84/177.82 ! [V_c,V_b,V_a,T_a] : % 177.84/177.82 ( class_Groups_Oab__semigroup__add(T_a) % 177.84/177.82 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_add__left__cancel,axiom, % 177.84/177.82 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 177.84/177.82 ( class_Groups_Ocancel__semigroup__add(T_a) % 177.84/177.82 => ( 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) % 177.84/177.82 <=> V_b_2 = V_ca_2 ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_add__right__cancel,axiom, % 177.84/177.82 ! [V_ca_2,V_a_2,V_b_2,T_a] : % 177.84/177.82 ( class_Groups_Ocancel__semigroup__add(T_a) % 177.84/177.82 => ( 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) % 177.84/177.82 <=> V_b_2 = V_ca_2 ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_add__left__imp__eq,axiom, % 177.84/177.82 ! [V_c,V_b,V_a,T_a] : % 177.84/177.82 ( class_Groups_Ocancel__semigroup__add(T_a) % 177.84/177.82 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) % 177.84/177.82 => V_b = V_c ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_add__imp__eq,axiom, % 177.84/177.82 ! [V_c,V_b,V_a,T_a] : % 177.84/177.82 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 177.84/177.82 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) % 177.84/177.82 => V_b = V_c ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_add__right__imp__eq,axiom, % 177.84/177.82 ! [V_c,V_a,V_b,T_a] : % 177.84/177.82 ( class_Groups_Ocancel__semigroup__add(T_a) % 177.84/177.82 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) % 177.84/177.82 => V_b = V_c ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_image__Union,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Un__Union__image,axiom, % 177.84/177.82 ! [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))) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Int__Union,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Int__Union2,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_SUP__commute,axiom, % 177.84/177.82 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 177.84/177.82 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.84/177.82 => 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))) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_finite__UN,axiom, % 177.84/177.82 ! [V_B_2,T_b,V_A_2,T_a] : % 177.84/177.82 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => ( 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))) % 177.84/177.82 <=> ! [B_x] : % 177.84/177.82 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.84/177.82 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_combine__common__factor,axiom, % 177.84/177.82 ! [V_c,V_b,V_e,V_a,T_a] : % 177.84/177.82 ( class_Rings_Osemiring(T_a) % 177.84/177.82 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_comm__semiring__class_Odistrib,axiom, % 177.84/177.82 ! [V_c,V_b,V_a,T_a] : % 177.84/177.82 ( class_Rings_Ocomm__semiring(T_a) % 177.84/177.82 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Union__empty,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_finite__UnionD,axiom, % 177.84/177.82 ! [V_A_2,T_a] : % 177.84/177.82 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) % 177.84/177.82 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_add__diff__cancel,axiom, % 177.84/177.82 ! [V_b,V_a,T_a] : % 177.84/177.82 ( class_Groups_Ogroup__add(T_a) % 177.84/177.82 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_diff__add__cancel,axiom, % 177.84/177.82 ! [V_b,V_a,T_a] : % 177.84/177.82 ( class_Groups_Ogroup__add(T_a) % 177.84/177.82 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Union__UNIV,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_mult__1__left,axiom, % 177.84/177.82 ! [V_a,T_a] : % 177.84/177.82 ( class_Groups_Omonoid__mult(T_a) % 177.84/177.82 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_mult__1,axiom, % 177.84/177.82 ! [V_a,T_a] : % 177.84/177.82 ( class_Groups_Ocomm__monoid__mult(T_a) % 177.84/177.82 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_mult__1__right,axiom, % 177.84/177.82 ! [V_a,T_a] : % 177.84/177.82 ( class_Groups_Omonoid__mult(T_a) % 177.84/177.82 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_mult_Ocomm__neutral,axiom, % 177.84/177.82 ! [V_a,T_a] : % 177.84/177.82 ( class_Groups_Ocomm__monoid__mult(T_a) % 177.84/177.82 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_minus__add__cancel,axiom, % 177.84/177.82 ! [V_b,V_a,T_a] : % 177.84/177.82 ( class_Groups_Ogroup__add(T_a) % 177.84/177.82 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = V_b ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_add__minus__cancel,axiom, % 177.84/177.82 ! [V_b,V_a,T_a] : % 177.84/177.82 ( class_Groups_Ogroup__add(T_a) % 177.84/177.82 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) = V_b ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_minus__add,axiom, % 177.84/177.82 ! [V_b,V_a,T_a] : % 177.84/177.82 ( class_Groups_Ogroup__add(T_a) % 177.84/177.82 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_minus__add__distrib,axiom, % 177.84/177.82 ! [V_b,V_a,T_a] : % 177.84/177.82 ( class_Groups_Oab__group__add(T_a) % 177.84/177.82 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Union__Un__distrib,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Un__eq__Union,axiom, % 177.84/177.82 ! [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))))) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Union__insert,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Inter__UNIV,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Inter__empty,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Inter__Un__distrib,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Int__eq__Inter,axiom, % 177.84/177.82 ! [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))))) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Inter__insert,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__iff,axiom, % 177.84/177.82 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 177.84/177.82 ( 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))) % 177.84/177.82 <=> ? [B_x] : % 177.84/177.82 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 177.84/177.82 & hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UNION__empty__conv_I2_J,axiom, % 177.84/177.82 ! [V_B_2,V_A_2,T_a,T_b] : % 177.84/177.82 ( 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)) % 177.84/177.82 <=> ! [B_x] : % 177.84/177.82 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 177.84/177.82 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__constant,axiom, % 177.84/177.82 ! [V_ca_2,T_b,T_a,V_A_2] : % 177.84/177.82 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => 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)) ) % 177.84/177.82 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => 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 ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__empty2,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UNION__empty__conv_I1_J,axiom, % 177.84/177.82 ! [V_B_2,V_A_2,T_b,T_a] : % 177.84/177.82 ( 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) % 177.84/177.82 <=> ! [B_x] : % 177.84/177.82 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 177.84/177.82 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__extend__simps_I10_J,axiom, % 177.84/177.82 ! [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) ). % 177.84/177.82 % 177.84/177.82 fof(fact_image__UN,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__simps_I10_J,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__Un,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__Un__distrib,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__simps_I5_J,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__simps_I4_J,axiom, % 177.84/177.82 ! [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) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__extend__simps_I5_J,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Int__UN__distrib,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__extend__simps_I4_J,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Int__UN__distrib2,axiom, % 177.84/177.82 ! [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))) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__extend__simps_I6_J,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__simps_I6_J,axiom, % 177.84/177.82 ! [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) ). % 177.84/177.82 % 177.84/177.82 fof(fact_INT__simps_I9_J,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_INT__extend__simps_I9_J,axiom, % 177.84/177.82 ! [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) ). % 177.84/177.82 % 177.84/177.82 fof(fact_setsum__addf,axiom, % 177.84/177.82 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 177.84/177.82 ( class_Groups_Ocomm__monoid__add(T_a) % 177.84/177.82 => 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)) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_INT__simps_I8_J,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_INT__extend__simps_I8_J,axiom, % 177.84/177.82 ! [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) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Un__Inter,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Inter__image__eq,axiom, % 177.84/177.82 ! [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) ). % 177.84/177.82 % 177.84/177.82 fof(fact_INTER__eq__Inter__image,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_eq__add__iff1,axiom, % 177.84/177.82 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 177.84/177.82 ( class_Rings_Oring(T_a) % 177.84/177.82 => ( 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) % 177.84/177.82 <=> 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 ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_eq__add__iff2,axiom, % 177.84/177.82 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 177.84/177.82 ( class_Rings_Oring(T_a) % 177.84/177.82 => ( 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) % 177.84/177.82 <=> 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) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Union__disjoint,axiom, % 177.84/177.82 ! [V_A_2,V_C_2,T_a] : % 177.84/177.82 ( 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)) % 177.84/177.82 <=> ! [B_x] : % 177.84/177.82 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_C_2)) % 177.84/177.82 => 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)) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_diff__minus__eq__add,axiom, % 177.84/177.82 ! [V_b,V_a,T_a] : % 177.84/177.82 ( class_Groups_Ogroup__add(T_a) % 177.84/177.82 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_ab__diff__minus,axiom, % 177.84/177.82 ! [V_b,V_a,T_a] : % 177.84/177.82 ( class_Groups_Oab__group__add(T_a) % 177.84/177.82 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_diff__def,axiom, % 177.84/177.82 ! [V_b,V_a,T_a] : % 177.84/177.82 ( class_Groups_Ogroup__add(T_a) % 177.84/177.82 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_square__eq__1__iff,axiom, % 177.84/177.82 ! [V_x_2,T_a] : % 177.84/177.82 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 177.84/177.82 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 177.84/177.82 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a) % 177.84/177.82 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_SUP__const,axiom, % 177.84/177.82 ! [V_M_2,T_a,V_A_2,T_b] : % 177.84/177.82 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 177.84/177.82 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => 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 ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__insert__distrib,axiom, % 177.84/177.82 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 177.84/177.82 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 177.84/177.82 => 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)) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_SUP__UN__eq,axiom, % 177.84/177.82 ! [V_x_2,V_r_2,T_b,T_a] : % 177.84/177.82 ( 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)) % 177.84/177.82 <=> 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))) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__absorb,axiom, % 177.84/177.82 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 177.84/177.82 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 177.84/177.82 => 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) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__extend__simps_I1_J,axiom, % 177.84/177.82 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 177.84/177.82 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => 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))) ) % 177.84/177.82 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => 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)) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__singleton,axiom, % 177.84/177.82 ! [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 ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__simps_I1_J,axiom, % 177.84/177.82 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 177.84/177.82 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => 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)) ) % 177.84/177.82 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => 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)) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__extend__simps_I2_J,axiom, % 177.84/177.82 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 177.84/177.82 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => 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 ) % 177.84/177.82 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => 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)) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__extend__simps_I3_J,axiom, % 177.84/177.82 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 177.84/177.82 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => 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 ) % 177.84/177.82 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => 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)) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__simps_I2_J,axiom, % 177.84/177.82 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 177.84/177.82 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => 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)) ) % 177.84/177.82 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => 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) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__simps_I3_J,axiom, % 177.84/177.82 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 177.84/177.82 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => 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)) ) % 177.84/177.82 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => 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)) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__insert,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__simps_I7_J,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_UN__extend__simps_I7_J,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_fold1__singleton__def,axiom, % 177.84/177.82 ! [V_a_2,V_f_2,T_a,V_g_2] : % 177.84/177.82 ( V_g_2 = c_Finite__Set_Ofold1(T_a,V_f_2) % 177.84/177.82 => 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 ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_fold1__singleton,axiom, % 177.84/177.82 ! [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 ). % 177.84/177.82 % 177.84/177.82 fof(fact_Compl__INT,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Compl__UN,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_setsum_Odistrib,axiom, % 177.84/177.82 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 177.84/177.82 ( class_Groups_Ocomm__monoid__add(T_b) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => 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)) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Int__Inter__image,axiom, % 177.84/177.82 ! [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))) ). % 177.84/177.82 % 177.84/177.82 fof(fact_folding__one_Oeq__fold,axiom, % 177.84/177.82 ! [V_A_2,V_F_2,V_f_2,T_a] : % 177.84/177.82 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Sup__empty,axiom, % 177.84/177.82 ! [T_a] : % 177.84/177.82 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.84/177.82 => 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) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Sup__singleton,axiom, % 177.84/177.82 ! [V_a_2,T_a] : % 177.84/177.82 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.84/177.82 => 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 ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Sup__insert,axiom, % 177.84/177.82 ! [V_A_2,V_a_2,T_a] : % 177.84/177.82 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.84/177.82 => 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)) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Inf__singleton,axiom, % 177.84/177.82 ! [V_a_2,T_a] : % 177.84/177.82 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.84/177.82 => 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 ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Sup__UNIV,axiom, % 177.84/177.82 ! [T_a] : % 177.84/177.82 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.84/177.82 => 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) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Inf__empty,axiom, % 177.84/177.82 ! [T_a] : % 177.84/177.82 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.84/177.82 => 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) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Inf__UNIV,axiom, % 177.84/177.82 ! [T_a] : % 177.84/177.82 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.84/177.82 => 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) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Inf__insert,axiom, % 177.84/177.82 ! [V_A_2,V_a_2,T_a] : % 177.84/177.82 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.84/177.82 => 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)) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_image__eq__UN,axiom, % 177.84/177.82 ! [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)))) ). % 177.84/177.82 % 177.84/177.82 fof(fact_INT__extend__simps_I4_J,axiom, % 177.84/177.82 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 177.84/177.82 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => 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 ) % 177.84/177.82 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => 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)) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_fold1__def,axiom, % 177.84/177.82 ! [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)) ). % 177.84/177.82 % 177.84/177.82 fof(fact_fold__image__distrib,axiom, % 177.84/177.82 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 177.84/177.82 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => 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)) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Sup__fin_OF__eq,axiom, % 177.84/177.82 ! [V_A_2,T_a] : % 177.84/177.82 ( class_Lattices_Olattice(T_a) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => 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) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Inf__fin_OF__eq,axiom, % 177.84/177.82 ! [V_A_2,T_a] : % 177.84/177.82 ( class_Lattices_Olattice(T_a) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => 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) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_setsum_Oinsert,axiom, % 177.84/177.82 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 177.84/177.82 ( class_Groups_Ocomm__monoid__add(T_b) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.84/177.82 => 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)) ) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_setsum__insert,axiom, % 177.84/177.82 ! [V_f_2,V_a_2,V_F_2,T_a,T_b] : % 177.84/177.82 ( class_Groups_Ocomm__monoid__add(T_b) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 177.84/177.82 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_F_2)) % 177.84/177.82 => 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)) ) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_setsum__Un__Int,axiom, % 177.84/177.82 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 177.84/177.82 ( class_Groups_Ocomm__monoid__add(T_b) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.84/177.82 => 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)) ) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_INT__simps_I4_J,axiom, % 177.84/177.82 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 177.84/177.82 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => 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)) ) % 177.84/177.82 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => 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)) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Sup__binary,axiom, % 177.84/177.82 ! [V_b_2,V_a_2,T_a] : % 177.84/177.82 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.84/177.82 => 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) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Inf__binary,axiom, % 177.84/177.82 ! [V_b_2,V_a_2,T_a] : % 177.84/177.82 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.84/177.82 => 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) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_sup__Sup__fold__sup,axiom, % 177.84/177.82 ! [V_B_2,V_A_2,T_a] : % 177.84/177.82 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => 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) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Sup__fin__Sup,axiom, % 177.84/177.82 ! [V_A_2,T_a] : % 177.84/177.82 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) ) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_fold1__insert__idem,axiom, % 177.84/177.82 ! [V_x_2,V_A_2,T_a] : % 177.84/177.82 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 177.84/177.82 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => 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)) ) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_inf__Inf__fold__inf,axiom, % 177.84/177.82 ! [V_B_2,V_A_2,T_a] : % 177.84/177.82 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => 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) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_fold1__Un2,axiom, % 177.84/177.82 ! [V_B_2,V_A_2,T_a] : % 177.84/177.82 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.84/177.82 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => 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)) ) ) ) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_Inf__fin__Inf,axiom, % 177.84/177.82 ! [V_A_2,T_a] : % 177.84/177.82 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) ) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_fold1__eq__fold__idem,axiom, % 177.84/177.82 ! [V_a_2,V_A_2,T_a] : % 177.84/177.82 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => 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) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_setsum_Oinsert__remove,axiom, % 177.84/177.82 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 177.84/177.82 ( class_Groups_Ocomm__monoid__add(T_b) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => 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)))))) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_setsum__Un__disjoint,axiom, % 177.84/177.82 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 177.84/177.82 ( class_Groups_Ocomm__monoid__add(T_b) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.84/177.82 => ( 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)) % 177.84/177.82 => 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)) ) ) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_setsum__Un,axiom, % 177.84/177.82 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 177.84/177.82 ( class_Groups_Oab__group__add(T_b) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.84/177.82 => 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))) ) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_sup__SUPR__fold__sup,axiom, % 177.84/177.82 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 177.84/177.82 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => 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) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_fold__image__Un__Int,axiom, % 177.84/177.82 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 177.84/177.82 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.84/177.82 => 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))) ) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_setsum__Un__nat,axiom, % 177.84/177.82 ! [V_f_2,V_B_2,V_A_2,T_a] : % 177.84/177.82 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.84/177.82 => 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))) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_fold1__insert,axiom, % 177.84/177.82 ! [V_x_2,V_A_2,T_a] : % 177.84/177.82 ( class_Groups_Oab__semigroup__mult(T_a) % 177.84/177.82 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.84/177.82 => 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)) ) ) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_semilattice__big_OF__eq,axiom, % 177.84/177.82 ! [V_A_2,V_F_2,V_f_2,T_a] : % 177.84/177.82 ( c_Big__Operators_Osemilattice__big(T_a,V_f_2,V_F_2) % 177.84/177.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.82 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom, % 177.84/177.82 ! [V_x,T_a] : % 177.84/177.82 ( class_Rings_Ocomm__ring__1(T_a) % 177.84/177.82 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_x) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom, % 177.84/177.82 ! [V_y,V_x,T_a] : % 177.84/177.82 ( class_Rings_Ocomm__ring__1(T_a) % 177.84/177.82 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 177.84/177.82 ! [V_m,T_a] : % 177.84/177.82 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.82 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m) ) ). % 177.84/177.82 % 177.84/177.82 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 177.84/177.82 ! [V_a,V_m,T_a] : % 177.84/177.82 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.82 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 177.84/177.83 ! [V_m,V_a,T_a] : % 177.84/177.83 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.83 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_fold__image__Un__one,axiom, % 177.84/177.83 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 177.84/177.83 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.84/177.83 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 177.84/177.83 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 177.84/177.83 => ( ! [B_x] : % 177.84/177.83 ( 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))) % 177.84/177.83 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 177.84/177.83 => 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)) ) ) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_fold1__in,axiom, % 177.84/177.83 ! [V_A_2,T_a] : % 177.84/177.83 ( class_Groups_Oab__semigroup__mult(T_a) % 177.84/177.83 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.83 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.83 => ( ! [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)))))) % 177.84/177.83 => 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)) ) ) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 177.84/177.83 ! [V_a,T_a] : % 177.84/177.83 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.83 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_UN__UN__flatten,axiom, % 177.84/177.83 ! [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)) ). % 177.84/177.83 % 177.84/177.83 fof(fact_UN__simps_I9_J,axiom, % 177.84/177.83 ! [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)) ). % 177.84/177.83 % 177.84/177.83 fof(fact_UN__simps_I8_J,axiom, % 177.84/177.83 ! [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)) ). % 177.84/177.83 % 177.84/177.83 fof(fact_UN__extend__simps_I9_J,axiom, % 177.84/177.83 ! [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) ). % 177.84/177.83 % 177.84/177.83 fof(fact_UN__extend__simps_I8_J,axiom, % 177.84/177.83 ! [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) ). % 177.84/177.83 % 177.84/177.83 fof(fact_Union__def,axiom, % 177.84/177.83 ! [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))) ). % 177.84/177.83 % 177.84/177.83 fof(fact_Union__image__eq,axiom, % 177.84/177.83 ! [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) ). % 177.84/177.83 % 177.84/177.83 fof(fact_UNION__eq__Union__image,axiom, % 177.84/177.83 ! [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)) ). % 177.84/177.83 % 177.84/177.83 fof(fact_ball__UN,axiom, % 177.84/177.83 ! [V_P_2,V_B_2,V_A_2,T_b,T_a] : % 177.84/177.83 ( ! [B_x] : % 177.84/177.83 ( 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))) % 177.84/177.83 => hBOOL(hAPP(V_P_2,B_x)) ) % 177.84/177.83 <=> ! [B_x] : % 177.84/177.83 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 177.84/177.83 => ! [B_xa] : % 177.84/177.83 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(V_B_2,B_x))) % 177.84/177.83 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_SUP1__iff,axiom, % 177.84/177.83 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 177.84/177.83 ( 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)) % 177.84/177.83 <=> ? [B_x] : % 177.84/177.83 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.84/177.83 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_Inter__def,axiom, % 177.84/177.83 ! [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))) ). % 177.84/177.83 % 177.84/177.83 fof(fact_SUP2__iff,axiom, % 177.84/177.83 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 177.84/177.83 ( 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)) % 177.84/177.83 <=> ? [B_x] : % 177.84/177.83 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.84/177.83 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 177.84/177.83 ! [V_c,V_a,T_a] : % 177.84/177.83 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.83 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 177.84/177.83 ! [V_d,V_c,V_a,T_a] : % 177.84/177.83 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.83 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 177.84/177.83 ! [V_d,V_c,V_a,T_a] : % 177.84/177.83 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.83 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 177.84/177.83 ! [V_c,V_b,V_a,T_a] : % 177.84/177.83 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.83 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 177.84/177.83 ! [V_c,V_b,V_a,T_a] : % 177.84/177.83 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.83 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 177.84/177.83 ! [V_d,V_c,V_b,V_a,T_a] : % 177.84/177.83 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.83 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 177.84/177.83 ! [V_b,V_a,T_a] : % 177.84/177.83 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.83 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 177.84/177.83 ! [V_ry,V_rx,V_lx,T_a] : % 177.84/177.83 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.83 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 177.84/177.83 ! [V_ry,V_rx,V_lx,T_a] : % 177.84/177.83 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.83 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 177.84/177.83 ! [V_rx,V_ly,V_lx,T_a] : % 177.84/177.83 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.83 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 177.84/177.83 ! [V_rx,V_ly,V_lx,T_a] : % 177.84/177.83 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.83 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 177.84/177.83 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 177.84/177.83 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.83 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 177.84/177.83 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 177.84/177.83 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.83 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 177.84/177.83 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 177.84/177.83 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.83 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_crossproduct__eq,axiom, % 177.84/177.83 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] : % 177.84/177.83 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 177.84/177.83 => ( 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)) % 177.84/177.83 <=> ( V_w_2 = V_x_2 % 177.84/177.83 | V_y_2 = V_z_2 ) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 177.84/177.83 ! [V_b,V_m,V_a,T_a] : % 177.84/177.83 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.83 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 177.84/177.83 ! [V_c,V_b,V_a,T_a] : % 177.84/177.83 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.83 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_crossproduct__noteq,axiom, % 177.84/177.83 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 177.84/177.83 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 177.84/177.83 => ( ( V_a_2 != V_b_2 % 177.84/177.83 & V_ca_2 != V_d_2 ) % 177.84/177.83 <=> 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)) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 177.84/177.83 ! [V_z,V_y,V_x,T_a] : % 177.84/177.83 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.83 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 177.84/177.83 ! [V_a,T_a] : % 177.84/177.83 ( class_Rings_Ocomm__semiring__1(T_a) % 177.84/177.83 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_finite__Union,axiom, % 177.84/177.83 ! [V_A_2,T_a] : % 177.84/177.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) % 177.84/177.83 => ( ! [B_M] : % 177.84/177.83 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_M),V_A_2)) % 177.84/177.83 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_M)) ) % 177.84/177.83 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_diff__add__inverse2,axiom, % 177.84/177.83 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ). % 177.84/177.83 % 177.84/177.83 fof(fact_diff__add__inverse,axiom, % 177.84/177.83 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ). % 177.84/177.83 % 177.84/177.83 fof(fact_diff__diff__left,axiom, % 177.84/177.83 ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) ). % 177.84/177.83 % 177.84/177.83 fof(fact_diff__cancel,axiom, % 177.84/177.83 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ). % 177.84/177.83 % 177.84/177.83 fof(fact_diff__cancel2,axiom, % 177.84/177.83 ! [V_n,V_k,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ). % 177.84/177.83 % 177.84/177.83 fof(fact_insert__partition,axiom, % 177.84/177.83 ! [V_F_2,V_x_2,T_a] : % 177.84/177.83 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2)) % 177.84/177.83 => ( ! [B_x] : % 177.84/177.83 ( 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))) % 177.84/177.83 => ! [B_xa] : % 177.84/177.83 ( 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))) % 177.84/177.83 => ( B_x != B_xa % 177.84/177.83 => 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)) ) ) ) % 177.84/177.83 => 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)) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_hom__fold1__commute,axiom, % 177.84/177.83 ! [V_N_2,V_h_2,T_a] : % 177.84/177.83 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 177.84/177.83 => ( ! [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)) % 177.84/177.83 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 177.84/177.83 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.83 => 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)) ) ) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_nat__add__commute,axiom, % 177.84/177.83 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m) ). % 177.84/177.83 % 177.84/177.83 fof(fact_nat__add__left__commute,axiom, % 177.84/177.83 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)) ). % 177.84/177.83 % 177.84/177.83 fof(fact_nat__add__assoc,axiom, % 177.84/177.83 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) ). % 177.84/177.83 % 177.84/177.83 fof(fact_nat__add__left__cancel,axiom, % 177.84/177.83 ! [V_n_2,V_m_2,V_k_2] : % 177.84/177.83 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2) % 177.84/177.83 <=> V_m_2 = V_n_2 ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_nat__add__right__cancel,axiom, % 177.84/177.83 ! [V_n_2,V_k_2,V_m_2] : % 177.84/177.83 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2) % 177.84/177.83 <=> V_m_2 = V_n_2 ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_add__mult__distrib,axiom, % 177.84/177.83 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ). % 177.84/177.83 % 177.84/177.83 fof(fact_add__mult__distrib2,axiom, % 177.84/177.83 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ). % 177.84/177.83 % 177.84/177.83 fof(fact_diff__mult__distrib2,axiom, % 177.84/177.83 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ). % 177.84/177.83 % 177.84/177.83 fof(fact_diff__mult__distrib,axiom, % 177.84/177.83 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ). % 177.84/177.83 % 177.84/177.83 fof(fact_diff__commute,axiom, % 177.84/177.83 ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j) ). % 177.84/177.83 % 177.84/177.83 fof(fact_inj__on__add__nat,axiom, % 177.84/177.83 ! [V_N_2,V_k_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2),V_N_2) ). % 177.84/177.83 % 177.84/177.83 fof(fact_inj__on__Inter,axiom, % 177.84/177.83 ! [V_f_2,T_b,T_a,V_S_2] : % 177.84/177.83 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 177.84/177.83 => ( ! [B_A] : % 177.84/177.83 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_A),V_S_2)) % 177.84/177.83 => c_Fun_Oinj__on(T_a,T_b,V_f_2,B_A) ) % 177.84/177.83 => 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)) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_card__Diff__singleton__if,axiom, % 177.84/177.83 ! [V_x_2,V_A_2,T_a] : % 177.84/177.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.83 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.84/177.83 => 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)) ) % 177.84/177.83 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.84/177.83 => 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) ) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_card__Diff__singleton,axiom, % 177.84/177.83 ! [V_x_2,V_A_2,T_a] : % 177.84/177.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.83 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.84/177.83 => 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)) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_card_Oremove,axiom, % 177.84/177.83 ! [V_x_2,V_A_2,T_a] : % 177.84/177.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.83 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.84/177.83 => 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)))))) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_inj__on__INTER,axiom, % 177.84/177.83 ! [V_A_2,V_f_2,T_c,T_b,T_a,V_I_2] : % 177.84/177.83 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.84/177.83 => ( ! [B_i] : % 177.84/177.83 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_I_2)) % 177.84/177.83 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(V_A_2,B_i)) ) % 177.84/177.83 => 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)) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom, % 177.84/177.83 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_b,T_a] : % 177.84/177.83 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 177.84/177.83 => ( 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)) % 177.84/177.83 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.84/177.83 => ~ ! [B_y] : % 177.84/177.83 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) % 177.84/177.83 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_finite__range__map__of__map__add,axiom, % 177.84/177.83 ! [V_l_2,V_f_2,T_b,T_a] : % 177.84/177.83 ( 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))))) % 177.84/177.83 => 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))))) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_finite__UN__I,axiom, % 177.84/177.83 ! [V_B_2,T_b,V_A_2,T_a] : % 177.84/177.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.83 => ( ! [B_a] : % 177.84/177.83 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 177.84/177.83 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 177.84/177.83 => 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))) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_nat__mult__commute,axiom, % 177.84/177.83 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m) ). % 177.84/177.83 % 177.84/177.83 fof(fact_nat__mult__assoc,axiom, % 177.84/177.83 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ). % 177.84/177.83 % 177.84/177.83 fof(fact_nat__mult__eq__1__iff,axiom, % 177.84/177.83 ! [V_n_2,V_m_2] : % 177.84/177.83 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 177.84/177.83 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 177.84/177.83 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_nat__mult__1__right,axiom, % 177.84/177.83 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 177.84/177.83 % 177.84/177.83 fof(fact_nat__1__eq__mult__iff,axiom, % 177.84/177.83 ! [V_n_2,V_m_2] : % 177.84/177.83 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) % 177.84/177.83 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 177.84/177.83 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_nat__mult__1,axiom, % 177.84/177.83 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 177.84/177.83 % 177.84/177.83 fof(fact_card__UNIV__unit,axiom, % 177.84/177.83 hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 177.84/177.83 % 177.84/177.83 fof(fact_card__eq__setsum,axiom, % 177.84/177.83 ! [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) ). % 177.84/177.83 % 177.84/177.83 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 177.84/177.83 ! [V_A_2,T_a] : % 177.84/177.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 177.84/177.83 => ( 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))) % 177.84/177.83 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_card__image,axiom, % 177.84/177.83 ! [V_A_2,V_f_2,T_b,T_a] : % 177.84/177.83 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.84/177.83 => 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) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_finite__dom__map__of,axiom, % 177.84/177.83 ! [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)))) ). % 177.84/177.83 % 177.84/177.83 fof(fact_inj__on__iff__eq__card,axiom, % 177.84/177.83 ! [V_f_2,T_b,V_A_2,T_a] : % 177.84/177.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.83 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.84/177.83 <=> 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) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_eq__card__imp__inj__on,axiom, % 177.84/177.83 ! [V_f_2,T_b,V_A_2,T_a] : % 177.84/177.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.83 => ( 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) % 177.84/177.83 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_card_Oinsert,axiom, % 177.84/177.83 ! [V_x_2,V_A_2,T_a] : % 177.84/177.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.83 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.84/177.83 => 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)) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_card__Un__Int,axiom, % 177.84/177.83 ! [V_B_2,V_A_2,T_a] : % 177.84/177.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.83 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.84/177.83 => 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))) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_card_Ounion__inter,axiom, % 177.84/177.83 ! [V_B_2,V_A_2,T_a] : % 177.84/177.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.83 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.84/177.83 => 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)) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_card__Diff__subset__Int,axiom, % 177.84/177.83 ! [V_B_2,V_A_2,T_a] : % 177.84/177.83 ( 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))) % 177.84/177.83 => 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))) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_finite__range__map__of,axiom, % 177.84/177.83 ! [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))))) ). % 177.84/177.83 % 177.84/177.83 fof(fact_card__Diff__insert,axiom, % 177.84/177.83 ! [V_B_2,V_a_2,V_A_2,T_a] : % 177.84/177.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.83 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.84/177.83 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 177.84/177.83 => 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)) ) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_card_Oinsert__remove,axiom, % 177.84/177.83 ! [V_x_2,V_A_2,T_a] : % 177.84/177.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.83 => 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)))))) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_card__Un__disjoint,axiom, % 177.84/177.83 ! [V_B_2,V_A_2,T_a] : % 177.84/177.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.83 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.84/177.83 => ( 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)) % 177.84/177.83 => 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)) ) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_left__add__mult__distrib,axiom, % 177.84/177.83 ! [V_k,V_j,V_u,V_i] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k) ). % 177.84/177.83 % 177.84/177.83 fof(fact_card__Diff1__less,axiom, % 177.84/177.83 ! [V_x_2,V_A_2,T_a] : % 177.84/177.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.83 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.84/177.83 => 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))) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_card__Diff2__less,axiom, % 177.84/177.83 ! [V_y_2,V_x_2,V_A_2,T_a] : % 177.84/177.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.83 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.84/177.83 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 177.84/177.83 => 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))) ) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_body__def,axiom, % 177.84/177.83 c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies) ). % 177.84/177.83 % 177.84/177.83 fof(fact_card__Suc__Diff1,axiom, % 177.84/177.83 ! [V_x_2,V_A_2,T_a] : % 177.84/177.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.83 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.84/177.83 => 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) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_finite__map__freshness,axiom, % 177.84/177.83 ! [V_f_2,T_b,T_a] : % 177.84/177.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,V_f_2))) % 177.84/177.83 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 177.84/177.83 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_b) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_setprod_Oremove,axiom, % 177.84/177.83 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 177.84/177.83 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.84/177.83 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.83 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.84/177.83 => 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)))))) ) ) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_card__Diff1__le,axiom, % 177.84/177.83 ! [V_x_2,V_A_2,T_a] : % 177.84/177.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.84/177.83 => 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))) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_order__refl,axiom, % 177.84/177.83 ! [V_x,T_a] : % 177.84/177.83 ( class_Orderings_Opreorder(T_a) % 177.84/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ). % 177.84/177.83 % 177.84/177.83 fof(fact_lessI,axiom, % 177.84/177.83 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 177.84/177.83 % 177.84/177.83 fof(fact_Suc__mono,axiom, % 177.84/177.83 ! [V_n,V_m] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_Suc__mult__less__cancel1,axiom, % 177.89/177.83 ! [V_n_2,V_m_2,V_k_2] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))) % 177.89/177.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_Suc__mult__le__cancel1,axiom, % 177.89/177.83 ! [V_n_2,V_m_2,V_k_2] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))) % 177.89/177.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_INF__subset,axiom, % 177.89/177.83 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 177.89/177.83 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.83 => 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))) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_SUP__subset,axiom, % 177.89/177.83 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 177.89/177.83 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.83 => 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))) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_add__less__le__mono,axiom, % 177.89/177.83 ! [V_d,V_c,V_b,V_a,T_a] : % 177.89/177.83 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_add__le__less__mono,axiom, % 177.89/177.83 ! [V_d,V_c,V_b,V_a,T_a] : % 177.89/177.83 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__less__irrefl,axiom, % 177.89/177.83 ! [V_x,T_a] : % 177.89/177.83 ( class_Orderings_Opreorder(T_a) % 177.89/177.83 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_linorder__not__less,axiom, % 177.89/177.83 ! [V_y_2,V_x_2,T_a] : % 177.89/177.83 ( class_Orderings_Olinorder(T_a) % 177.89/177.83 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 177.89/177.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_linorder__not__le,axiom, % 177.89/177.83 ! [V_y_2,V_x_2,T_a] : % 177.89/177.83 ( class_Orderings_Olinorder(T_a) % 177.89/177.83 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 177.89/177.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_linorder__neq__iff,axiom, % 177.89/177.83 ! [V_y_2,V_x_2,T_a] : % 177.89/177.83 ( class_Orderings_Olinorder(T_a) % 177.89/177.83 => ( V_x_2 != V_y_2 % 177.89/177.83 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 177.89/177.83 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_not__less__iff__gr__or__eq,axiom, % 177.89/177.83 ! [V_y_2,V_x_2,T_a] : % 177.89/177.83 ( class_Orderings_Olinorder(T_a) % 177.89/177.83 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 177.89/177.83 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 177.89/177.83 | V_x_2 = V_y_2 ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_le__fun__def,axiom, % 177.89/177.83 ! [V_g_2,V_f_2,T_a,T_b] : % 177.89/177.83 ( class_Orderings_Oord(T_b) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 177.89/177.83 <=> ! [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))) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_linorder__le__less__linear,axiom, % 177.89/177.83 ! [V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Olinorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.89/177.83 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_linorder__linear,axiom, % 177.89/177.83 ! [V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Olinorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.89/177.83 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__less__le,axiom, % 177.89/177.83 ! [V_y_2,V_x_2,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 177.89/177.83 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 177.89/177.83 & V_x_2 != V_y_2 ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_less__le__not__le,axiom, % 177.89/177.83 ! [V_y_2,V_x_2,T_a] : % 177.89/177.83 ( class_Orderings_Opreorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 177.89/177.83 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 177.89/177.83 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__eq__iff,axiom, % 177.89/177.83 ! [V_y_2,V_x_2,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( V_x_2 = V_y_2 % 177.89/177.83 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 177.89/177.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__le__less,axiom, % 177.89/177.83 ! [V_y_2,V_x_2,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 177.89/177.83 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 177.89/177.83 | V_x_2 = V_y_2 ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_linorder__less__linear,axiom, % 177.89/177.83 ! [V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Olinorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.89/177.83 | V_x = V_y % 177.89/177.83 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_leI,axiom, % 177.89/177.83 ! [V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Olinorder(T_a) % 177.89/177.83 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_not__leE,axiom, % 177.89/177.83 ! [V_x,V_y,T_a] : % 177.89/177.83 ( class_Orderings_Olinorder(T_a) % 177.89/177.83 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_linorder__antisym__conv3,axiom, % 177.89/177.83 ! [V_x_2,V_y_2,T_a] : % 177.89/177.83 ( class_Orderings_Olinorder(T_a) % 177.89/177.83 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 177.89/177.83 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 177.89/177.83 <=> V_x_2 = V_y_2 ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_linorder__antisym__conv1,axiom, % 177.89/177.83 ! [V_y_2,V_x_2,T_a] : % 177.89/177.83 ( class_Orderings_Olinorder(T_a) % 177.89/177.83 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 177.89/177.83 <=> V_x_2 = V_y_2 ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__neq__le__trans,axiom, % 177.89/177.83 ! [V_b,V_a,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( V_a != V_b % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_xt1_I12_J,axiom, % 177.89/177.83 ! [V_b,V_a,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( V_a != V_b % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_linorder__neqE,axiom, % 177.89/177.83 ! [V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Olinorder(T_a) % 177.89/177.83 => ( V_x != V_y % 177.89/177.83 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_less__imp__neq,axiom, % 177.89/177.83 ! [V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.89/177.83 => V_x != V_y ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__less__not__sym,axiom, % 177.89/177.83 ! [V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Opreorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.89/177.83 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_leD,axiom, % 177.89/177.83 ! [V_x,V_y,T_a] : % 177.89/177.83 ( class_Orderings_Olinorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.89/177.83 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__eq__refl,axiom, % 177.89/177.83 ! [V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Opreorder(T_a) % 177.89/177.83 => ( V_x = V_y % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__less__imp__le,axiom, % 177.89/177.83 ! [V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Opreorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__less__imp__not__less,axiom, % 177.89/177.83 ! [V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Opreorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.89/177.83 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_linorder__antisym__conv2,axiom, % 177.89/177.83 ! [V_y_2,V_x_2,T_a] : % 177.89/177.83 ( class_Orderings_Olinorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 177.89/177.83 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 177.89/177.83 <=> V_x_2 = V_y_2 ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_le__funD,axiom, % 177.89/177.83 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 177.89/177.83 ( class_Orderings_Oord(T_b) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 177.89/177.83 => 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))) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__less__imp__not__eq,axiom, % 177.89/177.83 ! [V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.89/177.83 => V_x != V_y ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__less__imp__not__eq2,axiom, % 177.89/177.83 ! [V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.89/177.83 => V_y != V_x ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__le__imp__less__or__eq,axiom, % 177.89/177.83 ! [V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.89/177.83 | V_x = V_y ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__antisym__conv,axiom, % 177.89/177.83 ! [V_x_2,V_y_2,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 177.89/177.83 <=> V_x_2 = V_y_2 ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__le__neq__trans,axiom, % 177.89/177.83 ! [V_b,V_a,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.89/177.83 => ( V_a != V_b % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_xt1_I11_J,axiom, % 177.89/177.83 ! [V_a,V_b,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 177.89/177.83 => ( V_a != V_b % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__less__asym_H,axiom, % 177.89/177.83 ! [V_b,V_a,T_a] : % 177.89/177.83 ( class_Orderings_Opreorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.89/177.83 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_xt1_I9_J,axiom, % 177.89/177.83 ! [V_a,V_b,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 177.89/177.83 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_ord__eq__less__trans,axiom, % 177.89/177.83 ! [V_c,V_b,V_a,T_a] : % 177.89/177.83 ( class_Orderings_Oord(T_a) % 177.89/177.83 => ( V_a = V_b % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_xt1_I1_J,axiom, % 177.89/177.83 ! [V_c,V_b,V_a,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( V_a = V_b % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_ord__eq__le__trans,axiom, % 177.89/177.83 ! [V_c,V_b,V_a,T_a] : % 177.89/177.83 ( class_Orderings_Oord(T_a) % 177.89/177.83 => ( V_a = V_b % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_xt1_I3_J,axiom, % 177.89/177.83 ! [V_c,V_b,V_a,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( V_a = V_b % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_ord__less__eq__trans,axiom, % 177.89/177.83 ! [V_c,V_b,V_a,T_a] : % 177.89/177.83 ( class_Orderings_Oord(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.89/177.83 => ( V_b = V_c % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_xt1_I2_J,axiom, % 177.89/177.83 ! [V_c,V_a,V_b,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 177.89/177.83 => ( V_b = V_c % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__less__trans,axiom, % 177.89/177.83 ! [V_z,V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Opreorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__less__le__trans,axiom, % 177.89/177.83 ! [V_z,V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Opreorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_xt1_I10_J,axiom, % 177.89/177.83 ! [V_z,V_x,V_y,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_xt1_I7_J,axiom, % 177.89/177.83 ! [V_z,V_x,V_y,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_ord__le__eq__trans,axiom, % 177.89/177.83 ! [V_c,V_b,V_a,T_a] : % 177.89/177.83 ( class_Orderings_Oord(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.89/177.83 => ( V_b = V_c % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_xt1_I4_J,axiom, % 177.89/177.83 ! [V_c,V_a,V_b,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 177.89/177.83 => ( V_b = V_c % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__le__less__trans,axiom, % 177.89/177.83 ! [V_z,V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Opreorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__antisym,axiom, % 177.89/177.83 ! [V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.89/177.83 => V_x = V_y ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__trans,axiom, % 177.89/177.83 ! [V_z,V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Opreorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_xt1_I8_J,axiom, % 177.89/177.83 ! [V_z,V_x,V_y,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_xt1_I5_J,axiom, % 177.89/177.83 ! [V_x,V_y,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.89/177.83 => V_x = V_y ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_xt1_I6_J,axiom, % 177.89/177.83 ! [V_z,V_x,V_y,T_a] : % 177.89/177.83 ( class_Orderings_Oorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_order__less__asym,axiom, % 177.89/177.83 ! [V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Opreorder(T_a) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.89/177.83 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_le__funE,axiom, % 177.89/177.83 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 177.89/177.83 ( class_Orderings_Oord(T_b) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 177.89/177.83 => 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))) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_linorder__le__cases,axiom, % 177.89/177.83 ! [V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Olinorder(T_a) % 177.89/177.83 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_linorder__cases,axiom, % 177.89/177.83 ! [V_y,V_x,T_a] : % 177.89/177.83 ( class_Orderings_Olinorder(T_a) % 177.89/177.83 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.89/177.83 => ( V_x != V_y % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_linorder__neqE__linordered__idom,axiom, % 177.89/177.83 ! [V_y,V_x,T_a] : % 177.89/177.83 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.83 => ( V_x != V_y % 177.89/177.83 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_less__diff__iff,axiom, % 177.89/177.83 ! [V_n_2,V_m_2,V_k_2] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2))) % 177.89/177.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_diff__less__mono,axiom, % 177.89/177.83 ! [V_c,V_b,V_a] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c))) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_Suc__diff__le,axiom, % 177.89/177.83 ! [V_m,V_n] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.89/177.83 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_diff__less__Suc,axiom, % 177.89/177.83 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(c_Nat_OSuc,V_m))) ). % 177.89/177.83 % 177.89/177.83 fof(fact_less__eq__Suc__le__raw,axiom, % 177.89/177.83 ! [V_n_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) ). % 177.89/177.83 % 177.89/177.83 fof(fact_less__not__refl,axiom, % 177.89/177.83 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 177.89/177.83 % 177.89/177.83 fof(fact_n__not__Suc__n,axiom, % 177.89/177.83 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 177.89/177.83 % 177.89/177.83 fof(fact_Suc__n__not__n,axiom, % 177.89/177.83 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 177.89/177.83 % 177.89/177.83 fof(fact_Suc__n__not__le__n,axiom, % 177.89/177.83 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 177.89/177.83 % 177.89/177.83 fof(fact_le__refl,axiom, % 177.89/177.83 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ). % 177.89/177.83 % 177.89/177.83 fof(fact_not__less__eq,axiom, % 177.89/177.83 ! [V_n_2,V_m_2] : % 177.89/177.83 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_not__less__eq__eq,axiom, % 177.89/177.83 ! [V_n_2,V_m_2] : % 177.89/177.83 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_nat__neq__iff,axiom, % 177.89/177.83 ! [V_n_2,V_m_2] : % 177.89/177.83 ( V_m_2 != V_n_2 % 177.89/177.83 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.83 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_nat__le__linear,axiom, % 177.89/177.83 ! [V_n,V_m] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.89/177.83 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_less__eq__Suc__le,axiom, % 177.89/177.83 ! [V_m_2,V_n_2] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 177.89/177.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_nat__less__le,axiom, % 177.89/177.83 ! [V_n_2,V_m_2] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.83 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.83 & V_m_2 != V_n_2 ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_le__eq__less__or__eq,axiom, % 177.89/177.83 ! [V_n_2,V_m_2] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.83 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.83 | V_m_2 = V_n_2 ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_less__Suc__eq__le,axiom, % 177.89/177.83 ! [V_n_2,V_m_2] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 177.89/177.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_less__Suc__eq,axiom, % 177.89/177.83 ! [V_n_2,V_m_2] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 177.89/177.83 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.83 | V_m_2 = V_n_2 ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_le__Suc__eq,axiom, % 177.89/177.83 ! [V_n_2,V_m_2] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 177.89/177.83 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.83 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_Suc__le__eq,axiom, % 177.89/177.83 ! [V_n_2,V_m_2] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 177.89/177.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_nat_Oinject,axiom, % 177.89/177.83 ! [V_nat_H_2,V_nat_2] : % 177.89/177.83 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 177.89/177.83 <=> V_nat_2 = V_nat_H_2 ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_Suc__less__eq,axiom, % 177.89/177.83 ! [V_n_2,V_m_2] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) % 177.89/177.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_Suc__le__mono,axiom, % 177.89/177.83 ! [V_m_2,V_n_2] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2))) % 177.89/177.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_not__less__less__Suc__eq,axiom, % 177.89/177.83 ! [V_m_2,V_n_2] : % 177.89/177.83 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 177.89/177.83 <=> V_n_2 = V_m_2 ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_less__antisym,axiom, % 177.89/177.83 ! [V_m,V_n] : % 177.89/177.83 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 177.89/177.83 => V_m = V_n ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_linorder__neqE__nat,axiom, % 177.89/177.83 ! [V_y,V_x] : % 177.89/177.83 ( V_x != V_y % 177.89/177.83 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_less__irrefl__nat,axiom, % 177.89/177.83 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 177.89/177.83 % 177.89/177.83 fof(fact_less__not__refl2,axiom, % 177.89/177.83 ! [V_m,V_n] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 177.89/177.83 => V_m != V_n ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_less__not__refl3,axiom, % 177.89/177.83 ! [V_t,V_s] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 177.89/177.83 => V_s != V_t ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_eq__imp__le,axiom, % 177.89/177.83 ! [V_n,V_m] : % 177.89/177.83 ( V_m = V_n % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_less__imp__le__nat,axiom, % 177.89/177.83 ! [V_n,V_m] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_less__SucI,axiom, % 177.89/177.83 ! [V_n,V_m] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_le__imp__less__Suc,axiom, % 177.89/177.83 ! [V_n,V_m] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_le__SucI,axiom, % 177.89/177.83 ! [V_n,V_m] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_Suc__leI,axiom, % 177.89/177.83 ! [V_n,V_m] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_le__less__Suc__eq,axiom, % 177.89/177.83 ! [V_n_2,V_m_2] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 177.89/177.83 <=> V_n_2 = V_m_2 ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_le__neq__implies__less,axiom, % 177.89/177.83 ! [V_n,V_m] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.89/177.83 => ( V_m != V_n % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_Suc__lessI,axiom, % 177.89/177.83 ! [V_n,V_m] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.89/177.83 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_le__trans,axiom, % 177.89/177.83 ! [V_k,V_j,V_i] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_le__antisym,axiom, % 177.89/177.83 ! [V_n,V_m] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.89/177.83 => V_m = V_n ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_less__trans__Suc,axiom, % 177.89/177.83 ! [V_k,V_j,V_i] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.89/177.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_less__SucE,axiom, % 177.89/177.83 ! [V_n,V_m] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 177.89/177.83 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.89/177.83 => V_m = V_n ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_le__SucE,axiom, % 177.89/177.83 ! [V_n,V_m] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 177.89/177.83 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.89/177.83 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_Suc__lessD,axiom, % 177.89/177.83 ! [V_n,V_m] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_Suc__le__lessD,axiom, % 177.89/177.83 ! [V_n,V_m] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_Suc__leD,axiom, % 177.89/177.83 ! [V_n,V_m] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_Suc__inject,axiom, % 177.89/177.83 ! [V_y,V_x] : % 177.89/177.83 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 177.89/177.83 => V_x = V_y ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_Suc__less__SucD,axiom, % 177.89/177.83 ! [V_n,V_m] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_less__or__eq__imp__le,axiom, % 177.89/177.83 ! [V_n,V_m] : % 177.89/177.83 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.89/177.83 | V_m = V_n ) % 177.89/177.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_nat__less__cases,axiom, % 177.89/177.83 ! [V_P_2,V_n_2,V_m_2] : % 177.89/177.83 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.83 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 177.89/177.83 => ( ( V_m_2 = V_n_2 % 177.89/177.83 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 177.89/177.83 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 177.89/177.83 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 177.89/177.83 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_less__add__Suc1,axiom, % 177.89/177.83 ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))) ). % 177.89/177.83 % 177.89/177.83 fof(fact_less__add__Suc2,axiom, % 177.89/177.83 ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))) ). % 177.89/177.83 % 177.89/177.83 fof(fact_less__iff__Suc__add,axiom, % 177.89/177.83 ! [V_n_2,V_m_2] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.83 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_diff__Suc__diff__eq2,axiom, % 177.89/177.83 ! [V_m,V_j,V_k] : % 177.89/177.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 177.89/177.83 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))),V_m) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_j)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)) ) ). % 177.89/177.83 % 177.89/177.83 fof(fact_diff__Suc__diff__eq1,axiom, % 177.89/177.83 ! [V_m,V_j,V_k] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 177.89/177.84 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(c_Nat_OSuc,V_j)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__less__cancel__right,axiom, % 177.89/177.84 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 177.89/177.84 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__less__cancel__left,axiom, % 177.89/177.84 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 177.89/177.84 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__strict__right__mono,axiom, % 177.89/177.84 ! [V_c,V_b,V_a,T_a] : % 177.89/177.84 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__strict__left__mono,axiom, % 177.89/177.84 ! [V_c,V_b,V_a,T_a] : % 177.89/177.84 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__strict__mono,axiom, % 177.89/177.84 ! [V_d,V_c,V_b,V_a,T_a] : % 177.89/177.84 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__less__imp__less__right,axiom, % 177.89/177.84 ! [V_b,V_c,V_a,T_a] : % 177.89/177.84 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__less__imp__less__left,axiom, % 177.89/177.84 ! [V_b,V_a,V_c,T_a] : % 177.89/177.84 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__le__cancel__right,axiom, % 177.89/177.84 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 177.89/177.84 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__le__cancel__left,axiom, % 177.89/177.84 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 177.89/177.84 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__right__mono,axiom, % 177.89/177.84 ! [V_c,V_b,V_a,T_a] : % 177.89/177.84 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__left__mono,axiom, % 177.89/177.84 ! [V_c,V_b,V_a,T_a] : % 177.89/177.84 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__mono,axiom, % 177.89/177.84 ! [V_d,V_c,V_b,V_a,T_a] : % 177.89/177.84 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__le__imp__le__right,axiom, % 177.89/177.84 ! [V_b,V_c,V_a,T_a] : % 177.89/177.84 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__le__imp__le__left,axiom, % 177.89/177.84 ! [V_b,V_a,V_c,T_a] : % 177.89/177.84 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_diff__eq__diff__less,axiom, % 177.89/177.84 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 177.89/177.84 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.84 => ( 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) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_bot__least,axiom, % 177.89/177.84 ! [V_x,T_a] : % 177.89/177.84 ( class_Orderings_Obot(T_a) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__Suc__shift,axiom, % 177.89/177.84 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__Suc,axiom, % 177.89/177.84 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__Suc__right,axiom, % 177.89/177.84 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ). % 177.89/177.84 % 177.89/177.84 fof(fact_diff__eq__diff__less__eq,axiom, % 177.89/177.84 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 177.89/177.84 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.84 => ( 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) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_less__supI2,axiom, % 177.89/177.84 ! [V_a,V_b,V_x,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__sup(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_less__supI1,axiom, % 177.89/177.84 ! [V_b,V_a,V_x,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__sup(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_less__infI1,axiom, % 177.89/177.84 ! [V_b,V_x,V_a,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__inf(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_less__infI2,axiom, % 177.89/177.84 ! [V_a,V_x,V_b,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__inf(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_nat__less__add__iff2,axiom, % 177.89/177.84 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_nat__less__add__iff1,axiom, % 177.89/177.84 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__supE,axiom, % 177.89/177.84 ! [V_x,V_b,V_a,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__sup(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)) % 177.89/177.84 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 177.89/177.84 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_sup__mono,axiom, % 177.89/177.84 ! [V_d,V_b,V_c,V_a,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__sup(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_c),V_d))) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_sup__least,axiom, % 177.89/177.84 ! [V_z,V_x,V_y,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__sup(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__supI,axiom, % 177.89/177.84 ! [V_b,V_x,V_a,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__sup(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_sup__absorb1,axiom, % 177.89/177.84 ! [V_x,V_y,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__sup(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.89/177.84 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_sup__absorb2,axiom, % 177.89/177.84 ! [V_y,V_x,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__sup(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.89/177.84 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__supI2,axiom, % 177.89/177.84 ! [V_a,V_b,V_x,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__sup(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__supI1,axiom, % 177.89/177.84 ! [V_b,V_a,V_x,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__sup(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__sup__iff,axiom, % 177.89/177.84 ! [V_z_2,V_y_2,V_x_2,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__sup(T_a) % 177.89/177.84 => ( 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)) % 177.89/177.84 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 177.89/177.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__iff__sup,axiom, % 177.89/177.84 ! [V_y_2,V_x_2,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__sup(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 177.89/177.84 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_sup__ge2,axiom, % 177.89/177.84 ! [V_x,V_y,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__sup(T_a) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_inf__sup__ord_I4_J,axiom, % 177.89/177.84 ! [V_x,V_y,T_a] : % 177.89/177.84 ( class_Lattices_Olattice(T_a) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_sup__ge1,axiom, % 177.89/177.84 ! [V_y,V_x,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__sup(T_a) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_inf__sup__ord_I3_J,axiom, % 177.89/177.84 ! [V_y,V_x,T_a] : % 177.89/177.84 ( class_Lattices_Olattice(T_a) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_neg__less__iff__less,axiom, % 177.89/177.84 ! [V_a_2,V_b_2,T_a] : % 177.89/177.84 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_minus__less__iff,axiom, % 177.89/177.84 ! [V_b_2,V_a_2,T_a] : % 177.89/177.84 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_less__minus__iff,axiom, % 177.89/177.84 ! [V_b_2,V_a_2,T_a] : % 177.89/177.84 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_inf__sup__ord_I1_J,axiom, % 177.89/177.84 ! [V_y,V_x,T_a] : % 177.89/177.84 ( class_Lattices_Olattice(T_a) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_inf__le1,axiom, % 177.89/177.84 ! [V_y,V_x,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__inf(T_a) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_inf__sup__ord_I2_J,axiom, % 177.89/177.84 ! [V_y,V_x,T_a] : % 177.89/177.84 ( class_Lattices_Olattice(T_a) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_inf__le2,axiom, % 177.89/177.84 ! [V_y,V_x,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__inf(T_a) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__iff__inf,axiom, % 177.89/177.84 ! [V_y_2,V_x_2,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__inf(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 177.89/177.84 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__inf__iff,axiom, % 177.89/177.84 ! [V_z_2,V_y_2,V_x_2,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__inf(T_a) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 177.89/177.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__infI1,axiom, % 177.89/177.84 ! [V_b,V_x,V_a,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__inf(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__infI2,axiom, % 177.89/177.84 ! [V_a,V_x,V_b,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__inf(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_inf__absorb1,axiom, % 177.89/177.84 ! [V_y,V_x,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__inf(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.89/177.84 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_inf__absorb2,axiom, % 177.89/177.84 ! [V_x,V_y,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__inf(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.89/177.84 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__infI,axiom, % 177.89/177.84 ! [V_b,V_a,V_x,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__inf(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_inf__greatest,axiom, % 177.89/177.84 ! [V_z,V_y,V_x,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__inf(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_inf__mono,axiom, % 177.89/177.84 ! [V_d,V_b,V_c,V_a,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__inf(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_c),V_d))) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__infE,axiom, % 177.89/177.84 ! [V_b,V_a,V_x,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__inf(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) % 177.89/177.84 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 177.89/177.84 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_top__greatest,axiom, % 177.89/177.84 ! [V_x,T_a] : % 177.89/177.84 ( class_Orderings_Otop(T_a) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_diff__Suc__Suc,axiom, % 177.89/177.84 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Suc__diff__diff,axiom, % 177.89/177.84 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)),hAPP(c_Nat_OSuc,V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__imp__neg__le,axiom, % 177.89/177.84 ! [V_b,V_a,T_a] : % 177.89/177.84 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_neg__le__iff__le,axiom, % 177.89/177.84 ! [V_a_2,V_b_2,T_a] : % 177.89/177.84 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_minus__le__iff,axiom, % 177.89/177.84 ! [V_b_2,V_a_2,T_a] : % 177.89/177.84 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.84 => ( 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)) % 177.89/177.84 <=> 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)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__minus__iff,axiom, % 177.89/177.84 ! [V_b_2,V_a_2,T_a] : % 177.89/177.84 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> 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))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_compl__le__compl__iff,axiom, % 177.89/177.84 ! [V_y_2,V_x_2,T_a] : % 177.89/177.84 ( class_Lattices_Oboolean__algebra(T_a) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_compl__mono,axiom, % 177.89/177.84 ! [V_y,V_x,T_a] : % 177.89/177.84 ( class_Lattices_Oboolean__algebra(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Suc__mult__cancel1,axiom, % 177.89/177.84 ! [V_n_2,V_m_2,V_k_2] : % 177.89/177.84 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2) % 177.89/177.84 <=> V_m_2 = V_n_2 ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__lessD1,axiom, % 177.89/177.84 ! [V_k,V_j,V_i] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_less__add__eq__less,axiom, % 177.89/177.84 ! [V_n,V_m,V_l,V_k] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 177.89/177.84 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__less__mono,axiom, % 177.89/177.84 ! [V_l,V_k,V_j,V_i] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__less__mono1,axiom, % 177.89/177.84 ! [V_k,V_j,V_i] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_trans__less__add2,axiom, % 177.89/177.84 ! [V_m,V_j,V_i] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_trans__less__add1,axiom, % 177.89/177.84 ! [V_m,V_j,V_i] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_nat__add__left__cancel__less,axiom, % 177.89/177.84 ! [V_n_2,V_m_2,V_k_2] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_not__add__less2,axiom, % 177.89/177.84 ! [V_i,V_j] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)) ). % 177.89/177.84 % 177.89/177.84 fof(fact_not__add__less1,axiom, % 177.89/177.84 ! [V_j,V_i] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__leE,axiom, % 177.89/177.84 ! [V_n,V_k,V_m] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) % 177.89/177.84 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.89/177.84 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__leD1,axiom, % 177.89/177.84 ! [V_n,V_k,V_m] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__leD2,axiom, % 177.89/177.84 ! [V_n,V_k,V_m] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__le__mono,axiom, % 177.89/177.84 ! [V_l,V_k,V_j,V_i] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__le__mono1,axiom, % 177.89/177.84 ! [V_k,V_j,V_i] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_trans__le__add2,axiom, % 177.89/177.84 ! [V_m,V_j,V_i] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_trans__le__add1,axiom, % 177.89/177.84 ! [V_m,V_j,V_i] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_nat__add__left__cancel__le,axiom, % 177.89/177.84 ! [V_n_2,V_m_2,V_k_2] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__iff__add,axiom, % 177.89/177.84 ! [V_n_2,V_m_2] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.84 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__add1,axiom, % 177.89/177.84 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__add2,axiom, % 177.89/177.84 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) ). % 177.89/177.84 % 177.89/177.84 fof(fact_less__imp__diff__less,axiom, % 177.89/177.84 ! [V_n,V_k,V_j] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n)),V_k)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_diff__less__mono2,axiom, % 177.89/177.84 ! [V_l,V_n,V_m] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_diff__le__self,axiom, % 177.89/177.84 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)) ). % 177.89/177.84 % 177.89/177.84 fof(fact_diff__le__mono2,axiom, % 177.89/177.84 ! [V_l,V_n,V_m] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_diff__le__mono,axiom, % 177.89/177.84 ! [V_l,V_n,V_m] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_l)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_l))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_diff__diff__cancel,axiom, % 177.89/177.84 ! [V_n,V_i] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) % 177.89/177.84 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = V_i ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_eq__diff__iff,axiom, % 177.89/177.84 ! [V_n_2,V_m_2,V_k_2] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 177.89/177.84 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2) % 177.89/177.84 <=> V_m_2 = V_n_2 ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Nat_Odiff__diff__eq,axiom, % 177.89/177.84 ! [V_n,V_m,V_k] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 177.89/177.84 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__diff__iff,axiom, % 177.89/177.84 ! [V_n_2,V_m_2,V_k_2] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_mult__le__mono,axiom, % 177.89/177.84 ! [V_l,V_k,V_j,V_i] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_mult__le__mono2,axiom, % 177.89/177.84 ! [V_k,V_j,V_i] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_mult__le__mono1,axiom, % 177.89/177.84 ! [V_k,V_j,V_i] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__cube,axiom, % 177.89/177.84 ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__square,axiom, % 177.89/177.84 ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))) ). % 177.89/177.84 % 177.89/177.84 fof(fact_less__Sup__iff,axiom, % 177.89/177.84 ! [V_S_2,V_a_2,T_a] : % 177.89/177.84 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.89/177.84 & class_Orderings_Olinorder(T_a) ) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2))) % 177.89/177.84 <=> ? [B_x] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 177.89/177.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),B_x)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Sup__le__iff,axiom, % 177.89/177.84 ! [V_b_2,V_A_2,T_a] : % 177.89/177.84 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.89/177.84 => ( 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)) % 177.89/177.84 <=> ! [B_x] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Inf__less__iff,axiom, % 177.89/177.84 ! [V_a_2,V_S_2,T_a] : % 177.89/177.84 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.89/177.84 & class_Orderings_Olinorder(T_a) ) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2)),V_a_2)) % 177.89/177.84 <=> ? [B_x] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 177.89/177.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_a_2)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod__timesf,axiom, % 177.89/177.84 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_a) % 177.89/177.84 => 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)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__Inf__iff,axiom, % 177.89/177.84 ! [V_A_2,V_b_2,T_a] : % 177.89/177.84 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> ! [B_x] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod__1,axiom, % 177.89/177.84 ! [V_A_2,T_b,T_a] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_a) % 177.89/177.84 => 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) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_less__SUP__iff,axiom, % 177.89/177.84 ! [V_f_2,V_A_2,T_b,V_a_2,T_a] : % 177.89/177.84 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.89/177.84 & class_Orderings_Olinorder(T_a) ) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> ? [B_x] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 177.89/177.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_SUP__le__iff,axiom, % 177.89/177.84 ! [V_u_2,V_M_2,V_A_2,T_b,T_a] : % 177.89/177.84 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.89/177.84 => ( 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)) % 177.89/177.84 <=> ! [B_x] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_INF__less__iff,axiom, % 177.89/177.84 ! [V_a_2,V_f_2,V_A_2,T_b,T_a] : % 177.89/177.84 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.89/177.84 & class_Orderings_Olinorder(T_a) ) % 177.89/177.84 => ( 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)) % 177.89/177.84 <=> ? [B_x] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 177.89/177.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__INF__iff,axiom, % 177.89/177.84 ! [V_M_2,V_A_2,T_b,V_u_2,T_a] : % 177.89/177.84 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> ! [B_x] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod__empty,axiom, % 177.89/177.84 ! [V_f_2,T_b,T_a] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_a) % 177.89/177.84 => 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) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod_Oempty,axiom, % 177.89/177.84 ! [V_g_2,T_b,T_a] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_a) % 177.89/177.84 => 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) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod_Oinfinite,axiom, % 177.89/177.84 ! [V_g_2,V_A_2,T_a,T_b] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.84 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => 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) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod__infinite,axiom, % 177.89/177.84 ! [V_f_2,V_A_2,T_a,T_b] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.84 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => 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) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod__eq__1__iff,axiom, % 177.89/177.84 ! [V_f_2,V_F_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 177.89/177.84 => ( 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) % 177.89/177.84 <=> ! [B_x] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 177.89/177.84 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_inj__Suc,axiom, % 177.89/177.84 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 177.89/177.84 % 177.89/177.84 fof(fact_less__add__one,axiom, % 177.89/177.84 ! [V_a,T_a] : % 177.89/177.84 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_less__1__mult,axiom, % 177.89/177.84 ! [V_n,V_m,T_a] : % 177.89/177.84 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod_Odistrib,axiom, % 177.89/177.84 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => 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)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_distrib__sup__le,axiom, % 177.89/177.84 ! [V_z,V_y,V_x,T_a] : % 177.89/177.84 ( class_Lattices_Olattice(T_a) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_distrib__inf__le,axiom, % 177.89/177.84 ! [V_z,V_y,V_x,T_a] : % 177.89/177.84 ( class_Lattices_Olattice(T_a) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_mult__Suc__right,axiom, % 177.89/177.84 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ). % 177.89/177.84 % 177.89/177.84 fof(fact_mult__Suc,axiom, % 177.89/177.84 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Sup__upper,axiom, % 177.89/177.84 ! [V_A_2,V_x_2,T_a] : % 177.89/177.84 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.84 => 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))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_nat__le__add__iff1,axiom, % 177.89/177.84 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_nat__diff__add__eq1,axiom, % 177.89/177.84 ! [V_n,V_m,V_u,V_i,V_j] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 177.89/177.84 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_u)),V_m)),V_n) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_nat__eq__add__iff1,axiom, % 177.89/177.84 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 177.89/177.84 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2) % 177.89/177.84 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2) = V_n_2 ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_nat__le__add__iff2,axiom, % 177.89/177.84 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_nat__diff__add__eq2,axiom, % 177.89/177.84 ! [V_n,V_m,V_u,V_j,V_i] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.89/177.84 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i)),V_u)),V_n)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_nat__eq__add__iff2,axiom, % 177.89/177.84 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 177.89/177.84 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2) % 177.89/177.84 <=> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_diff__Suc__1,axiom, % 177.89/177.84 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 177.89/177.84 % 177.89/177.84 fof(fact_less__diff__conv,axiom, % 177.89/177.84 ! [V_k_2,V_j_2,V_i_2] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__diff__inverse,axiom, % 177.89/177.84 ! [V_n,V_m] : % 177.89/177.84 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.89/177.84 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_diff__diff__right,axiom, % 177.89/177.84 ! [V_i,V_j,V_k] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 177.89/177.84 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__diff__conv,axiom, % 177.89/177.84 ! [V_i_2,V_k_2,V_j_2] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2)) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__add__diff,axiom, % 177.89/177.84 ! [V_m,V_n,V_k] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_k))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__add__diff__inverse,axiom, % 177.89/177.84 ! [V_m,V_n] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.89/177.84 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__diff__assoc,axiom, % 177.89/177.84 ! [V_i,V_j,V_k] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 177.89/177.84 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__diff__conv2,axiom, % 177.89/177.84 ! [V_i_2,V_j_2,V_k_2] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__add__diff__inverse2,axiom, % 177.89/177.84 ! [V_m,V_n] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.89/177.84 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__imp__diff__is__add,axiom, % 177.89/177.84 ! [V_k_2,V_j_2,V_i_2] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 177.89/177.84 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 % 177.89/177.84 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_diff__add__assoc,axiom, % 177.89/177.84 ! [V_i,V_j,V_k] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 177.89/177.84 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_add__diff__assoc2,axiom, % 177.89/177.84 ! [V_i,V_j,V_k] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 177.89/177.84 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_diff__add__assoc2,axiom, % 177.89/177.84 ! [V_i,V_j,V_k] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 177.89/177.84 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Inf__lower,axiom, % 177.89/177.84 ! [V_A_2,V_x_2,T_a] : % 177.89/177.84 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.84 => 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)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__SUPI,axiom, % 177.89/177.84 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 177.89/177.84 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 177.89/177.84 => 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))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_INF__leI,axiom, % 177.89/177.84 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 177.89/177.84 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 177.89/177.84 => 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))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod__delta,axiom, % 177.89/177.84 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 177.89/177.84 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 177.89/177.84 => 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) ) % 177.89/177.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 177.89/177.84 => 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) ) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod__delta_H,axiom, % 177.89/177.84 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 177.89/177.84 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 177.89/177.84 => 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) ) % 177.89/177.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 177.89/177.84 => 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) ) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_less__add__iff1,axiom, % 177.89/177.84 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 177.89/177.84 ( class_Rings_Oordered__ring(T_a) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> 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)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_less__add__iff2,axiom, % 177.89/177.84 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 177.89/177.84 ( class_Rings_Oordered__ring(T_a) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> 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))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__add__iff1,axiom, % 177.89/177.84 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 177.89/177.84 ( class_Rings_Oordered__ring(T_a) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> 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)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_le__add__iff2,axiom, % 177.89/177.84 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 177.89/177.84 ( class_Rings_Oordered__ring(T_a) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> 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))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_card__insert__le,axiom, % 177.89/177.84 ! [V_x_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => 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)))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_card__image__le,axiom, % 177.89/177.84 ! [V_f_2,T_b,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => 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))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_pigeonhole,axiom, % 177.89/177.84 ! [V_A_2,V_f_2,T_b,T_a] : % 177.89/177.84 ( 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))) % 177.89/177.84 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod__insert,axiom, % 177.89/177.84 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.84 => 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)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod_Oinsert,axiom, % 177.89/177.84 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.84 => 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)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod_Ounion__inter,axiom, % 177.89/177.84 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.84 => 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)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod__Un__Int,axiom, % 177.89/177.84 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.84 => 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)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod_OF__eq,axiom, % 177.89/177.84 ! [V_g_2,V_A_2,T_a,T_b] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.84 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => 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) ) % 177.89/177.84 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => 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) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod_Oeq__fold,axiom, % 177.89/177.84 ! [V_g_2,V_A_2,T_a,T_b] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => 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) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_card__insert__disjoint,axiom, % 177.89/177.84 ! [V_x_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.84 => 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)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_card__insert__if,axiom, % 177.89/177.84 ! [V_x_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.84 => 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) ) % 177.89/177.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.84 => 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)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_sup__le__fold__sup,axiom, % 177.89/177.84 ! [V_b_2,V_a_2,V_A_2,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__sup(T_a) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.84 => 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))) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_fold__inf__le__inf,axiom, % 177.89/177.84 ! [V_b_2,V_a_2,V_A_2,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__inf(T_a) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.84 => 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))) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_fold1__belowI,axiom, % 177.89/177.84 ! [V_a_2,V_A_2,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__inf(T_a) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.84 => 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)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_below__fold1__iff,axiom, % 177.89/177.84 ! [V_x_2,V_A_2,T_a] : % 177.89/177.84 ( class_Lattices_Osemilattice__inf(T_a) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> ! [B_x] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_diff__card__le__card__Diff,axiom, % 177.89/177.84 ! [V_A_2,V_B_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.84 => 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)))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod_Oinsert__remove,axiom, % 177.89/177.84 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => 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)))))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod_Ounion__disjoint,axiom, % 177.89/177.84 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.84 => ( 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)) % 177.89/177.84 => 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)) ) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod__Un__disjoint,axiom, % 177.89/177.84 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.84 => ( 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)) % 177.89/177.84 => 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)) ) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Inf__le__Sup,axiom, % 177.89/177.84 ! [V_A_2,T_a] : % 177.89/177.84 ( class_Lattices_Olattice(T_a) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.84 => 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))) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_card__insert,axiom, % 177.89/177.84 ! [V_x_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => 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)))))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_diff__Suc__eq__diff__pred,axiom, % 177.89/177.84 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Suc__eq__plus1,axiom, % 177.89/177.84 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Suc__eq__plus1__left,axiom, % 177.89/177.84 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Body__triple__valid__Suc,axiom, % 177.89/177.84 ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_a] : % 177.89/177.84 ( 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)) % 177.89/177.84 <=> 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)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod__Un__one,axiom, % 177.89/177.84 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 177.89/177.84 => ( ! [B_x] : % 177.89/177.84 ( 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))) % 177.89/177.84 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 177.89/177.84 => 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)) ) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod_Ounion__inter__neutral,axiom, % 177.89/177.84 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.84 => ( ! [B_x] : % 177.89/177.84 ( 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))) % 177.89/177.84 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 177.89/177.84 => 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)) ) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod__gen__delta,axiom, % 177.89/177.84 ! [V_ca_2,V_b_2,V_a_2,V_S_2,T_a,T_b] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 177.89/177.84 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 177.89/177.84 => 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)))) ) % 177.89/177.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 177.89/177.84 => 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)) ) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_equalityI,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.89/177.84 => V_A_2 = V_B_2 ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_subsetD,axiom, % 177.89/177.84 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_empty__subsetI,axiom, % 177.89/177.84 ! [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)) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Union__mono,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,T_a] : % 177.89/177.84 ( 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)) % 177.89/177.84 => 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))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Inter__anti__mono,axiom, % 177.89/177.84 ! [V_A_2,V_B_2,T_a] : % 177.89/177.84 ( 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)) % 177.89/177.84 => 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))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_rev__predicate1D,axiom, % 177.89/177.84 ! [V_Q_2,T_a,V_x_2,V_P_2] : % 177.89/177.84 ( hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 177.89/177.84 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_predicate1D,axiom, % 177.89/177.84 ! [V_x_2,V_Q_2,V_P_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 177.89/177.84 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.84 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_subset__refl,axiom, % 177.89/177.84 ! [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)) ). % 177.89/177.84 % 177.89/177.84 fof(fact_psubset__eq,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 & V_A_2 != V_B_2 ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_set__eq__subset,axiom, % 177.89/177.84 ! [T_a,V_B_2,V_A_2] : % 177.89/177.84 ( V_A_2 = V_B_2 % 177.89/177.84 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_subset__iff__psubset__eq,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 | V_A_2 = V_B_2 ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_equalityD1,axiom, % 177.89/177.84 ! [T_a,V_B_2,V_A_2] : % 177.89/177.84 ( V_A_2 = V_B_2 % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_equalityD2,axiom, % 177.89/177.84 ! [T_a,V_B_2,V_A_2] : % 177.89/177.84 ( V_A_2 = V_B_2 % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_psubset__imp__subset,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_psubset__subset__trans,axiom, % 177.89/177.84 ! [V_C_2,V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_subset__psubset__trans,axiom, % 177.89/177.84 ! [V_C_2,V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_subset__trans,axiom, % 177.89/177.84 ! [V_C_2,V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_equalityE,axiom, % 177.89/177.84 ! [T_a,V_B_2,V_A_2] : % 177.89/177.84 ( V_A_2 = V_B_2 % 177.89/177.84 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_less__fun__def,axiom, % 177.89/177.84 ! [V_g_2,V_f_2,T_a,T_b] : % 177.89/177.84 ( class_Orderings_Oord(T_b) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 177.89/177.84 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 177.89/177.84 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_g_2),V_f_2)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 177.89/177.84 ! [V_q,V_y,V_x,T_a] : % 177.89/177.84 ( class_Rings_Ocomm__semiring__1(T_a) % 177.89/177.84 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_psubsetD,axiom, % 177.89/177.84 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 177.89/177.84 ! [V_q,V_p,V_x,T_a] : % 177.89/177.84 ( class_Rings_Ocomm__semiring__1(T_a) % 177.89/177.84 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_set__mp,axiom, % 177.89/177.84 ! [V_x_2,V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_set__rev__mp,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,V_x_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_in__mono,axiom, % 177.89/177.84 ! [V_x_2,V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_not__psubset__empty,axiom, % 177.89/177.84 ! [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)))) ). % 177.89/177.84 % 177.89/177.84 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 177.89/177.84 ! [V_x,T_a] : % 177.89/177.84 ( class_Rings_Ocomm__semiring__1(T_a) % 177.89/177.84 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_subset__empty,axiom, % 177.89/177.84 ! [V_A_2,T_a] : % 177.89/177.84 ( 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)))) % 177.89/177.84 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_rev__finite__subset,axiom, % 177.89/177.84 ! [V_A_2,V_B_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_finite__subset,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.84 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_subset__insertI,axiom, % 177.89/177.84 ! [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))) ). % 177.89/177.84 % 177.89/177.84 fof(fact_subset__insertI2,axiom, % 177.89/177.84 ! [V_b_2,V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => 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))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_insert__mono,axiom, % 177.89/177.84 ! [V_a_2,V_D_2,V_C_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)) % 177.89/177.84 => 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))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_subset__UNIV,axiom, % 177.89/177.84 ! [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)))) ). % 177.89/177.84 % 177.89/177.84 fof(fact_image__mono,axiom, % 177.89/177.84 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => 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))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_subset__image__iff,axiom, % 177.89/177.84 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] : % 177.89/177.84 ( 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))) % 177.89/177.84 <=> ? [B_AA] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_AA),V_A_2)) % 177.89/177.84 & V_B_2 = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),B_AA) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Un__mono,axiom, % 177.89/177.84 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 177.89/177.84 => 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))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Un__least,axiom, % 177.89/177.84 ! [V_B_2,V_C_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 177.89/177.84 => 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)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Un__absorb2,axiom, % 177.89/177.84 ! [V_A_2,V_B_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.89/177.84 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Un__absorb1,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_subset__Un__eq,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Un__upper2,axiom, % 177.89/177.84 ! [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))) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Un__upper1,axiom, % 177.89/177.84 ! [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))) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Int__mono,axiom, % 177.89/177.84 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 177.89/177.84 => 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))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Int__greatest,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,V_C_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) % 177.89/177.84 => 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))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Int__absorb1,axiom, % 177.89/177.84 ! [V_A_2,V_B_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.89/177.84 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Int__absorb2,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Int__lower2,axiom, % 177.89/177.84 ! [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)) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Int__lower1,axiom, % 177.89/177.84 ! [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)) ). % 177.89/177.84 % 177.89/177.84 fof(fact_double__diff,axiom, % 177.89/177.84 ! [V_C_2,V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 177.89/177.84 => 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 ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Diff__mono,axiom, % 177.89/177.84 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_D_2),V_B_2)) % 177.89/177.84 => 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))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Diff__subset,axiom, % 177.89/177.84 ! [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)) ). % 177.89/177.84 % 177.89/177.84 fof(fact_subset__inj__on,axiom, % 177.89/177.84 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 177.89/177.84 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Compl__anti__mono,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => 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))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Compl__subset__Compl__iff,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,T_a] : % 177.89/177.84 ( 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))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_asm,axiom, % 177.89/177.84 ! [V_G_2,V_ts_2,T_a] : % 177.89/177.84 ( 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)) % 177.89/177.84 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_weaken,axiom, % 177.89/177.84 ! [V_ts_2,V_ts_H_2,V_G_2,T_a] : % 177.89/177.84 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_H_2) % 177.89/177.84 => ( 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)) % 177.89/177.84 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_thin,axiom, % 177.89/177.84 ! [V_G_2,V_ts_2,V_G_H_2,T_a] : % 177.89/177.84 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 177.89/177.84 => ( 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)) % 177.89/177.84 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_card__psubset,axiom, % 177.89/177.84 ! [V_A_2,V_B_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => ( 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))) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_pred__subset__eq,axiom, % 177.89/177.84 ! [V_S_2,V_R_2,T_a] : % 177.89/177.84 ( 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))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_UN__subset__iff,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : % 177.89/177.84 ( 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)) % 177.89/177.84 <=> ! [B_x] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 177.89/177.84 => 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)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_INT__subset__iff,axiom, % 177.89/177.84 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : % 177.89/177.84 ( 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))) % 177.89/177.84 <=> ! [B_x] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 177.89/177.84 => 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))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_psubset__insert__iff,axiom, % 177.89/177.84 ! [V_B_2,V_x_2,V_A_2,T_a] : % 177.89/177.84 ( 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))) % 177.89/177.84 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 177.89/177.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 177.89/177.84 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.84 => 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)) ) % 177.89/177.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 177.89/177.84 ! [V_q,V_x,T_a] : % 177.89/177.84 ( class_Rings_Ocomm__semiring__1(T_a) % 177.89/177.84 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 177.89/177.84 ! [V_q,V_x,T_a] : % 177.89/177.84 ( class_Rings_Ocomm__semiring__1(T_a) % 177.89/177.84 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 177.89/177.84 ! [V_q,V_x,T_a] : % 177.89/177.84 ( class_Rings_Ocomm__semiring__1(T_a) % 177.89/177.84 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 177.89/177.84 ! [V_q,V_p,V_x,T_a] : % 177.89/177.84 ( class_Rings_Ocomm__semiring__1(T_a) % 177.89/177.84 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_triple__valid__Suc,axiom, % 177.89/177.84 ! [V_t,V_n,T_a] : % 177.89/177.84 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t) % 177.89/177.84 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_insert__subset,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,V_x_2,T_a] : % 177.89/177.84 ( 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)) % 177.89/177.84 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 177.89/177.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_subset__insert,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,V_x_2,T_a] : % 177.89/177.84 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_subset__singletonD,axiom, % 177.89/177.84 ! [V_x_2,V_A_2,T_a] : % 177.89/177.84 ( 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))))) % 177.89/177.84 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.84 | 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))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_finite__surj,axiom, % 177.89/177.84 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( 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))) % 177.89/177.84 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_inj__on__strict__subset,axiom, % 177.89/177.84 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 177.89/177.84 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => 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))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_image__Int__subset,axiom, % 177.89/177.84 ! [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)))) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Un__Int__assoc__eq,axiom, % 177.89/177.84 ! [V_C_2,V_B_2,V_A_2,T_a] : % 177.89/177.84 ( 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)) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_image__diff__subset,axiom, % 177.89/177.84 ! [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)))) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Diff__partition,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => 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 ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Diff__subset__conv,axiom, % 177.89/177.84 ! [V_C_2,V_B_2,V_A_2,T_a] : % 177.89/177.84 ( 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)) % 177.89/177.84 <=> 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))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_subset__Compl__self__eq,axiom, % 177.89/177.84 ! [V_A_2,T_a] : % 177.89/177.84 ( 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))) % 177.89/177.84 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Union__Int__subset,axiom, % 177.89/177.84 ! [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)))) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Union__upper,axiom, % 177.89/177.84 ! [V_A_2,V_B_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.89/177.84 => 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))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Inter__Un__subset,axiom, % 177.89/177.84 ! [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)))) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Inter__lower,axiom, % 177.89/177.84 ! [V_A_2,V_B_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.89/177.84 => 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)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_UN__upper,axiom, % 177.89/177.84 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.84 => 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))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_INT__lower,axiom, % 177.89/177.84 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.84 => 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))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 177.89/177.84 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.89/177.84 => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_psubset__card__mono,axiom, % 177.89/177.84 ! [V_A_2,V_B_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => 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))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_finite__surj__inj,axiom, % 177.89/177.84 ! [V_f_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( 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))) % 177.89/177.84 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_endo__inj__surj,axiom, % 177.89/177.84 ! [V_f_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( 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)) % 177.89/177.84 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) % 177.89/177.84 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2) = V_A_2 ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_card__mono,axiom, % 177.89/177.84 ! [V_A_2,V_B_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => 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))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_card__seteq,axiom, % 177.89/177.84 ! [V_A_2,V_B_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => ( 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))) % 177.89/177.84 => V_A_2 = V_B_2 ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_inj__image__subset__iff,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 177.89/177.84 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_inj__on__image__Int,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 177.89/177.84 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 177.89/177.84 => 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)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_inj__on__image__set__diff,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 177.89/177.84 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 177.89/177.84 => 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)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_disjoint__eq__subset__Compl,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,T_a] : % 177.89/177.84 ( 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)) % 177.89/177.84 <=> 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))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_surj__Compl__image__subset,axiom, % 177.89/177.84 ! [V_A_2,V_f_2,T_a,T_b] : % 177.89/177.84 ( 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)) % 177.89/177.84 => 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)))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setprod__constant,axiom, % 177.89/177.84 ! [V_y_2,V_A_2,T_a,T_b] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => 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)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_folding__one__idem_Osubset__idem,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 177.89/177.84 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.89/177.84 => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_subset__insert__iff,axiom, % 177.89/177.84 ! [V_B_2,V_x_2,V_A_2,T_a] : % 177.89/177.84 ( 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))) % 177.89/177.84 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.84 => 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)) ) % 177.89/177.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_diff__single__insert,axiom, % 177.89/177.84 ! [V_B_2,V_x_2,V_A_2,T_a] : % 177.89/177.84 ( 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)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.84 => 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))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setsum__diff,axiom, % 177.89/177.84 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 177.89/177.84 ( class_Groups_Oab__group__add(T_b) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.89/177.84 => 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)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_card__bij__eq,axiom, % 177.89/177.84 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 177.89/177.84 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.89/177.84 => ( 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)) % 177.89/177.84 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) % 177.89/177.84 => ( 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)) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 177.89/177.84 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),V_B_2) ) ) ) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_card__Diff__subset,axiom, % 177.89/177.84 ! [V_A_2,V_B_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.89/177.84 => 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)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Sup__fin_Osubset__idem,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,T_a] : % 177.89/177.84 ( class_Lattices_Olattice(T_a) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.89/177.84 => 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) ) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_Inf__fin_Osubset__idem,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,T_a] : % 177.89/177.84 ( class_Lattices_Olattice(T_a) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.89/177.84 => 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) ) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_inj__image__Compl__subset,axiom, % 177.89/177.84 ! [V_A_2,V_f_2,T_b,T_a] : % 177.89/177.84 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.89/177.84 => 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)))) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_setsum__diff__nat,axiom, % 177.89/177.84 ! [V_f_2,V_A_2,V_B_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.89/177.84 => 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)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_card__inj__on__le,axiom, % 177.89/177.84 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 177.89/177.84 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.89/177.84 => ( 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)) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 177.89/177.84 => 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))) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_inj__on__iff__card__le,axiom, % 177.89/177.84 ! [V_B_2,T_b,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 177.89/177.84 => ( ? [B_f] : % 177.89/177.84 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 177.89/177.84 & 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)) ) % 177.89/177.84 <=> 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))) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_power__increasing__iff,axiom, % 177.89/177.84 ! [V_y_2,V_x_2,V_b_2,T_a] : % 177.89/177.84 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_power__le__imp__le__exp,axiom, % 177.89/177.84 ! [V_n,V_m,V_a,T_a] : % 177.89/177.84 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_inj__on__iff__surj,axiom, % 177.89/177.84 ! [V_A_H_2,T_b,T_a,V_A_2] : % 177.89/177.84 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.84 => ( ? [B_f] : % 177.89/177.84 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 177.89/177.84 & 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)) ) % 177.89/177.84 <=> ? [B_g] : hAPP(c_Set_Oimage(T_b,T_a,B_g),V_A_H_2) = V_A_2 ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_power__minus,axiom, % 177.89/177.84 ! [V_n,V_a,T_a] : % 177.89/177.84 ( class_Rings_Oring__1(T_a) % 177.89/177.84 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_power__increasing,axiom, % 177.89/177.84 ! [V_a,V_N,V_n,T_a] : % 177.89/177.84 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_power__strict__increasing__iff,axiom, % 177.89/177.84 ! [V_y_2,V_x_2,V_b_2,T_a] : % 177.89/177.84 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 177.89/177.84 => ( 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))) % 177.89/177.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_psubset__trans,axiom, % 177.89/177.84 ! [V_C_2,V_B_2,V_A_2,T_a] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_finite__nat__set__iff__bounded,axiom, % 177.89/177.84 ! [V_N_2] : % 177.89/177.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 177.89/177.84 <=> ? [B_m] : % 177.89/177.84 ! [B_x] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 177.89/177.84 ! [V_N_2] : % 177.89/177.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 177.89/177.84 <=> ? [B_m] : % 177.89/177.84 ! [B_x] : % 177.89/177.84 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_power__mult__distrib,axiom, % 177.89/177.84 ! [V_n,V_b,V_a,T_a] : % 177.89/177.84 ( class_Groups_Ocomm__monoid__mult(T_a) % 177.89/177.84 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_power__commutes,axiom, % 177.89/177.84 ! [V_n,V_a,T_a] : % 177.89/177.84 ( class_Groups_Omonoid__mult(T_a) % 177.89/177.84 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_power__one,axiom, % 177.89/177.84 ! [V_n,T_a] : % 177.89/177.84 ( class_Groups_Omonoid__mult(T_a) % 177.89/177.84 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_power__mult,axiom, % 177.89/177.84 ! [V_n,V_m,V_a,T_a] : % 177.89/177.84 ( class_Groups_Omonoid__mult(T_a) % 177.89/177.84 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_power__one__right,axiom, % 177.89/177.84 ! [V_a,T_a] : % 177.89/177.84 ( class_Groups_Omonoid__mult(T_a) % 177.89/177.84 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_one__le__power,axiom, % 177.89/177.84 ! [V_n,V_a,T_a] : % 177.89/177.84 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_power__inject__exp,axiom, % 177.89/177.84 ! [V_n_2,V_m_2,V_a_2,T_a] : % 177.89/177.84 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)) % 177.89/177.84 => ( 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) % 177.89/177.84 <=> V_m_2 = V_n_2 ) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_power__Suc2,axiom, % 177.89/177.84 ! [V_n,V_a,T_a] : % 177.89/177.84 ( class_Groups_Omonoid__mult(T_a) % 177.89/177.84 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_power__Suc,axiom, % 177.89/177.84 ! [V_n,V_a,T_a] : % 177.89/177.84 ( class_Power_Opower(T_a) % 177.89/177.84 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_power__add,axiom, % 177.89/177.84 ! [V_n,V_m,V_a,T_a] : % 177.89/177.84 ( class_Groups_Omonoid__mult(T_a) % 177.89/177.84 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_power__gt1__lemma,axiom, % 177.89/177.84 ! [V_n,V_a,T_a] : % 177.89/177.84 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_power__less__power__Suc,axiom, % 177.89/177.84 ! [V_n,V_a,T_a] : % 177.89/177.84 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_power__gt1,axiom, % 177.89/177.84 ! [V_n,V_a,T_a] : % 177.89/177.84 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 177.89/177.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)))) ) ) ). % 177.89/177.84 % 177.89/177.84 fof(fact_power__strict__increasing,axiom, % 177.89/177.84 ! [V_a,V_N,V_n,T_a] : % 177.89/177.84 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_power__less__imp__less__exp,axiom, % 177.89/177.85 ! [V_n,V_m,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_flat__lub__def,axiom, % 177.89/177.85 ! [V_b_2,V_A_2,T_a] : % 177.89/177.85 ( ( 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))))) % 177.89/177.85 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = V_b_2 ) % 177.89/177.85 & ( ~ 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))))) % 177.89/177.85 => 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)))))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_power__power__power,axiom, % 177.89/177.85 ! [T_a] : % 177.89/177.85 ( class_Power_Opower(T_a) % 177.89/177.85 => 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)) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_finite__fun__UNIVD1,axiom, % 177.89/177.85 ! [T_b,T_a] : % 177.89/177.85 ( 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)))) % 177.89/177.85 => ( 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)) % 177.89/177.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 177.89/177.85 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 177.89/177.85 ( 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))) % 177.89/177.85 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 177.89/177.85 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_ord_OatLeastLessThan__iff,axiom, % 177.89/177.85 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 177.89/177.85 ( 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))) % 177.89/177.85 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 177.89/177.85 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 177.89/177.85 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] : % 177.89/177.85 ( 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))) % 177.89/177.85 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 177.89/177.85 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_ord_OatLeastAtMost__iff,axiom, % 177.89/177.85 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] : % 177.89/177.85 ( 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))) % 177.89/177.85 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 177.89/177.85 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_less__zeroE,axiom, % 177.89/177.85 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.89/177.85 % 177.89/177.85 fof(fact_le0,axiom, % 177.89/177.85 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zero__less__Suc,axiom, % 177.89/177.85 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n))) ). % 177.89/177.85 % 177.89/177.85 fof(fact_power__eq__0__iff,axiom, % 177.89/177.85 ! [V_n_2,V_a_2,T_a] : % 177.89/177.85 ( ( class_Power_Opower(T_a) % 177.89/177.85 & class_Rings_Omult__zero(T_a) % 177.89/177.85 & class_Rings_Ono__zero__divisors(T_a) % 177.89/177.85 & class_Rings_Ozero__neq__one(T_a) ) % 177.89/177.85 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.85 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.85 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_power_Opower_Opower__0,axiom, % 177.89/177.85 ! [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 ). % 177.89/177.85 % 177.89/177.85 fof(fact_infinite__UNIV__nat,axiom, % 177.89/177.85 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 177.89/177.85 % 177.89/177.85 fof(fact_bot__nat__def,axiom, % 177.89/177.85 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zero__reorient,axiom, % 177.89/177.85 ! [V_x_2,T_a] : % 177.89/177.85 ( class_Groups_Ozero(T_a) % 177.89/177.85 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2 % 177.89/177.85 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_power__0__left,axiom, % 177.89/177.85 ! [V_n,T_a] : % 177.89/177.85 ( ( class_Power_Opower(T_a) % 177.89/177.85 & class_Rings_Osemiring__0(T_a) ) % 177.89/177.85 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) % 177.89/177.85 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 177.89/177.85 ! [V_a,T_a] : % 177.89/177.85 ( class_Rings_Ocomm__semiring__1(T_a) % 177.89/177.85 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 177.89/177.85 ! [V_a,T_a] : % 177.89/177.85 ( class_Rings_Ocomm__semiring__1(T_a) % 177.89/177.85 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__0__iff,axiom, % 177.89/177.85 ! [V_a_2,V_b_2,T_a] : % 177.89/177.85 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 177.89/177.85 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) % 177.89/177.85 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add_Ocomm__neutral,axiom, % 177.89/177.85 ! [V_a,T_a] : % 177.89/177.85 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.85 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__0__right,axiom, % 177.89/177.85 ! [V_a,T_a] : % 177.89/177.85 ( class_Groups_Omonoid__add(T_a) % 177.89/177.85 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_double__zero__sym,axiom, % 177.89/177.85 ! [V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Olinordered__ab__group__add(T_a) % 177.89/177.85 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) % 177.89/177.85 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__0,axiom, % 177.89/177.85 ! [V_a,T_a] : % 177.89/177.85 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.85 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__0__left,axiom, % 177.89/177.85 ! [V_a,T_a] : % 177.89/177.85 ( class_Groups_Omonoid__add(T_a) % 177.89/177.85 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 177.89/177.85 ! [V_a,T_a] : % 177.89/177.85 ( class_Rings_Ocomm__semiring__1(T_a) % 177.89/177.85 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 177.89/177.85 ! [V_a,T_a] : % 177.89/177.85 ( class_Rings_Ocomm__semiring__1(T_a) % 177.89/177.85 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__zero__left,axiom, % 177.89/177.85 ! [V_a,T_a] : % 177.89/177.85 ( class_Rings_Omult__zero(T_a) % 177.89/177.85 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__zero__right,axiom, % 177.89/177.85 ! [V_a,T_a] : % 177.89/177.85 ( class_Rings_Omult__zero(T_a) % 177.89/177.85 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__eq__0__iff,axiom, % 177.89/177.85 ! [V_b_2,V_a_2,T_a] : % 177.89/177.85 ( class_Rings_Oring__no__zero__divisors(T_a) % 177.89/177.85 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.85 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.85 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_no__zero__divisors,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Ono__zero__divisors(T_a) % 177.89/177.85 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.85 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.85 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_divisors__zero,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Ono__zero__divisors(T_a) % 177.89/177.85 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.85 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.85 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_diff__0__right,axiom, % 177.89/177.85 ! [V_a,T_a] : % 177.89/177.85 ( class_Groups_Ogroup__add(T_a) % 177.89/177.85 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_diff__self,axiom, % 177.89/177.85 ! [V_a,T_a] : % 177.89/177.85 ( class_Groups_Ogroup__add(T_a) % 177.89/177.85 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_eq__iff__diff__eq__0,axiom, % 177.89/177.85 ! [V_b_2,V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Oab__group__add(T_a) % 177.89/177.85 => ( V_a_2 = V_b_2 % 177.89/177.85 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_right__minus__eq,axiom, % 177.89/177.85 ! [V_b_2,V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Ogroup__add(T_a) % 177.89/177.85 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.85 <=> V_a_2 = V_b_2 ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zero__neq__one,axiom, % 177.89/177.85 ! [T_a] : % 177.89/177.85 ( class_Rings_Ozero__neq__one(T_a) % 177.89/177.85 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_one__neq__zero,axiom, % 177.89/177.85 ! [T_a] : % 177.89/177.85 ( class_Rings_Ozero__neq__one(T_a) % 177.89/177.85 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_minus__zero,axiom, % 177.89/177.85 ! [T_a] : % 177.89/177.85 ( class_Groups_Ogroup__add(T_a) % 177.89/177.85 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_neg__0__equal__iff__equal,axiom, % 177.89/177.85 ! [V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Ogroup__add(T_a) % 177.89/177.85 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 177.89/177.85 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_equal__neg__zero,axiom, % 177.89/177.85 ! [V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Olinordered__ab__group__add(T_a) % 177.89/177.85 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 177.89/177.85 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_neg__equal__0__iff__equal,axiom, % 177.89/177.85 ! [V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Ogroup__add(T_a) % 177.89/177.85 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.85 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_neg__equal__zero,axiom, % 177.89/177.85 ! [V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Olinordered__ab__group__add(T_a) % 177.89/177.85 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_a_2 % 177.89/177.85 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_Suc__neq__Zero,axiom, % 177.89/177.85 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.85 % 177.89/177.85 fof(fact_Zero__neq__Suc,axiom, % 177.89/177.85 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 177.89/177.85 % 177.89/177.85 fof(fact_nat_Osimps_I3_J,axiom, % 177.89/177.85 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.85 % 177.89/177.85 fof(fact_Suc__not__Zero,axiom, % 177.89/177.85 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.85 % 177.89/177.85 fof(fact_nat_Osimps_I2_J,axiom, % 177.89/177.85 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 177.89/177.85 % 177.89/177.85 fof(fact_Zero__not__Suc,axiom, % 177.89/177.85 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 177.89/177.85 % 177.89/177.85 fof(fact_power__Suc__0,axiom, % 177.89/177.85 ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 177.89/177.85 ! [V_m_2,V_x_2] : % 177.89/177.85 ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 177.89/177.85 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_field__power__not__zero,axiom, % 177.89/177.85 ! [V_n,V_a,T_a] : % 177.89/177.85 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 177.89/177.85 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.85 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_gr0I,axiom, % 177.89/177.85 ! [V_n] : % 177.89/177.85 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_gr__implies__not0,axiom, % 177.89/177.85 ! [V_n,V_m] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.89/177.85 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_less__nat__zero__code,axiom, % 177.89/177.85 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.89/177.85 % 177.89/177.85 fof(fact_neq0__conv,axiom, % 177.89/177.85 ! [V_n_2] : % 177.89/177.85 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_not__less0,axiom, % 177.89/177.85 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.89/177.85 % 177.89/177.85 fof(fact_nat__zero__less__power__iff,axiom, % 177.89/177.85 ! [V_n_2,V_x_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))) % 177.89/177.85 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 177.89/177.85 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_nat__power__less__imp__less,axiom, % 177.89/177.85 ! [V_n,V_m,V_i] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_plus__nat_Oadd__0,axiom, % 177.89/177.85 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 177.89/177.85 % 177.89/177.85 fof(fact_Nat_Oadd__0__right,axiom, % 177.89/177.85 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__is__0,axiom, % 177.89/177.85 ! [V_n_2,V_m_2] : % 177.89/177.85 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__eq__self__zero,axiom, % 177.89/177.85 ! [V_n,V_m] : % 177.89/177.85 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 177.89/177.85 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_le__0__eq,axiom, % 177.89/177.85 ! [V_n_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 177.89/177.85 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 177.89/177.85 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_diff__0__eq__0,axiom, % 177.89/177.85 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.85 % 177.89/177.85 fof(fact_minus__nat_Odiff__0,axiom, % 177.89/177.85 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 177.89/177.85 % 177.89/177.85 fof(fact_diff__self__eq__0,axiom, % 177.89/177.85 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.85 % 177.89/177.85 fof(fact_diffs0__imp__equal,axiom, % 177.89/177.85 ! [V_n,V_m] : % 177.89/177.85 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 => V_m = V_n ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__0,axiom, % 177.89/177.85 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__0__right,axiom, % 177.89/177.85 ! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__is__0,axiom, % 177.89/177.85 ! [V_n_2,V_m_2] : % 177.89/177.85 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__cancel1,axiom, % 177.89/177.85 ! [V_n_2,V_m_2,V_k_2] : % 177.89/177.85 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 177.89/177.85 <=> ( V_m_2 = V_n_2 % 177.89/177.85 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__cancel2,axiom, % 177.89/177.85 ! [V_n_2,V_k_2,V_m_2] : % 177.89/177.85 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2) % 177.89/177.85 <=> ( V_m_2 = V_n_2 % 177.89/177.85 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_nat__mult__eq__cancel__disj,axiom, % 177.89/177.85 ! [V_n_2,V_m_2,V_k_2] : % 177.89/177.85 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 177.89/177.85 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 | V_m_2 = V_n_2 ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_power__eq__imp__eq__base,axiom, % 177.89/177.85 ! [V_b,V_n,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.89/177.85 => V_a = V_b ) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setsum__0,axiom, % 177.89/177.85 ! [V_A_2,T_b,T_a] : % 177.89/177.85 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.85 => 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) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_power__strict__mono,axiom, % 177.89/177.85 ! [V_n,V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__nonpos__nonpos,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__increasing2,axiom, % 177.89/177.85 ! [V_a,V_b,V_c,T_a] : % 177.89/177.85 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__increasing,axiom, % 177.89/177.85 ! [V_c,V_b,V_a,T_a] : % 177.89/177.85 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__nonneg__eq__0__iff,axiom, % 177.89/177.85 ! [V_y_2,V_x_2,T_a] : % 177.89/177.85 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y_2)) % 177.89/177.85 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.85 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.85 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__nonneg__nonneg,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 177.89/177.85 ! [V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Olinordered__ab__group__add(T_a) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 177.89/177.85 ! [V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Olinordered__ab__group__add(T_a) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_split__mult__neg__le,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Oordered__cancel__semiring(T_a) % 177.89/177.85 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 177.89/177.85 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_split__mult__pos__le,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Oordered__ring(T_a) % 177.89/177.85 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 177.89/177.85 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__mono,axiom, % 177.89/177.85 ! [V_d,V_c,V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Oordered__semiring(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__mono_H,axiom, % 177.89/177.85 ! [V_d,V_c,V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Oordered__semiring(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__left__mono__neg,axiom, % 177.89/177.85 ! [V_c,V_a,V_b,T_a] : % 177.89/177.85 ( class_Rings_Oordered__ring(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__right__mono__neg,axiom, % 177.89/177.85 ! [V_c,V_a,V_b,T_a] : % 177.89/177.85 ( class_Rings_Oordered__ring(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_comm__mult__left__mono,axiom, % 177.89/177.85 ! [V_c,V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Oordered__comm__semiring(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__left__mono,axiom, % 177.89/177.85 ! [V_c,V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Oordered__semiring(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__right__mono,axiom, % 177.89/177.85 ! [V_c,V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Oordered__semiring(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__nonpos__nonpos,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Oordered__ring(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__nonpos__nonneg,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Oordered__cancel__semiring(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__nonneg__nonpos2,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Oordered__cancel__semiring(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__nonneg__nonpos,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Oordered__cancel__semiring(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__nonneg__nonneg,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Oordered__cancel__semiring(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__le__0__iff,axiom, % 177.89/177.85 ! [V_b_2,V_a_2,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__ring__strict(T_a) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 177.89/177.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 177.89/177.85 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zero__le__mult__iff,axiom, % 177.89/177.85 ! [V_b_2,V_a_2,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__ring__strict(T_a) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 177.89/177.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 177.89/177.85 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zero__le__square,axiom, % 177.89/177.85 ! [V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__ring(T_a) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_pos__add__strict,axiom, % 177.89/177.85 ! [V_c,V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__neg__neg,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__pos__pos,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 177.89/177.85 ! [V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Olinordered__ab__group__add(T_a) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 177.89/177.85 ! [V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Olinordered__ab__group__add(T_a) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__strict__left__mono__neg,axiom, % 177.89/177.85 ! [V_c,V_a,V_b,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__ring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__strict__right__mono__neg,axiom, % 177.89/177.85 ! [V_c,V_a,V_b,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__ring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_comm__mult__strict__left__mono,axiom, % 177.89/177.85 ! [V_c,V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__strict__left__mono,axiom, % 177.89/177.85 ! [V_c,V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__strict__right__mono,axiom, % 177.89/177.85 ! [V_c,V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__neg__neg,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__ring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__neg__pos,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__less__cancel__left__neg,axiom, % 177.89/177.85 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__ring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zero__less__mult__pos2,axiom, % 177.89/177.85 ! [V_a,V_b,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zero__less__mult__pos,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__pos__neg2,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__pos__neg,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__pos__pos,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__less__cancel__left__pos,axiom, % 177.89/177.85 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__ring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__less__cancel__left__disj,axiom, % 177.89/177.85 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__ring__strict(T_a) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 177.89/177.85 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__less__cancel__right__disj,axiom, % 177.89/177.85 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__ring__strict(T_a) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 177.89/177.85 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_not__square__less__zero,axiom, % 177.89/177.85 ! [V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__ring(T_a) % 177.89/177.85 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_le__iff__diff__le__0,axiom, % 177.89/177.85 ! [V_b_2,V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 177.89/177.85 <=> 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))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_less__iff__diff__less__0,axiom, % 177.89/177.85 ! [V_b_2,V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 177.89/177.85 <=> 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))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_sum__squares__eq__zero__iff,axiom, % 177.89/177.85 ! [V_y_2,V_x_2,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__ring__strict(T_a) % 177.89/177.85 => ( 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) % 177.89/177.85 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.85 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__scale__eq__noteq,axiom, % 177.89/177.85 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 177.89/177.85 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 177.89/177.85 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.85 => ( ( V_a = V_b % 177.89/177.85 & V_c != V_d ) % 177.89/177.85 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zero__le__one,axiom, % 177.89/177.85 ! [T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_not__one__le__zero,axiom, % 177.89/177.85 ! [T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zero__less__one,axiom, % 177.89/177.85 ! [T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_not__one__less__zero,axiom, % 177.89/177.85 ! [T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_neg__0__le__iff__le,axiom, % 177.89/177.85 ! [V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_le__minus__self__iff,axiom, % 177.89/177.85 ! [V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Olinordered__ab__group__add(T_a) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_neg__le__0__iff__le,axiom, % 177.89/177.85 ! [V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_minus__le__self__iff,axiom, % 177.89/177.85 ! [V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Olinordered__ab__group__add(T_a) % 177.89/177.85 => ( 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)) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_less__minus__self__iff,axiom, % 177.89/177.85 ! [V_a_2,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_neg__0__less__iff__less,axiom, % 177.89/177.85 ! [V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_neg__less__0__iff__less,axiom, % 177.89/177.85 ! [V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_neg__less__nonneg,axiom, % 177.89/177.85 ! [V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Olinordered__ab__group__add(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2)) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_right__minus,axiom, % 177.89/177.85 ! [V_a,T_a] : % 177.89/177.85 ( class_Groups_Ogroup__add(T_a) % 177.89/177.85 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_eq__neg__iff__add__eq__0,axiom, % 177.89/177.85 ! [V_b_2,V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Ogroup__add(T_a) % 177.89/177.85 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 177.89/177.85 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_left__minus,axiom, % 177.89/177.85 ! [V_a,T_a] : % 177.89/177.85 ( class_Groups_Ogroup__add(T_a) % 177.89/177.85 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_ab__left__minus,axiom, % 177.89/177.85 ! [V_a,T_a] : % 177.89/177.85 ( class_Groups_Oab__group__add(T_a) % 177.89/177.85 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_minus__unique,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Groups_Ogroup__add(T_a) % 177.89/177.85 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.85 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_power__mono,axiom, % 177.89/177.85 ! [V_n,V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zero__le__power,axiom, % 177.89/177.85 ! [V_n,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zero__less__power,axiom, % 177.89/177.85 ! [V_n,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_diff__0,axiom, % 177.89/177.85 ! [V_a,T_a] : % 177.89/177.85 ( class_Groups_Ogroup__add(T_a) % 177.89/177.85 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setsum_Oempty,axiom, % 177.89/177.85 ! [V_g_2,T_b,T_a] : % 177.89/177.85 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.85 => 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) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setsum__empty,axiom, % 177.89/177.85 ! [V_f_2,T_b,T_a] : % 177.89/177.85 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.85 => 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) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setsum_Oinfinite,axiom, % 177.89/177.85 ! [V_g_2,V_A_2,T_a,T_b] : % 177.89/177.85 ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.85 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.85 => 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) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setsum__infinite,axiom, % 177.89/177.85 ! [V_f_2,V_A_2,T_a,T_b] : % 177.89/177.85 ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.85 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.85 => 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) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_power__0__Suc,axiom, % 177.89/177.85 ! [V_n,T_a] : % 177.89/177.85 ( ( class_Power_Opower(T_a) % 177.89/177.85 & class_Rings_Osemiring__0(T_a) ) % 177.89/177.85 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_OSuc,V_n)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setprod__zero,axiom, % 177.89/177.85 ! [V_f_2,V_A_2,T_a,T_b] : % 177.89/177.85 ( class_Rings_Ocomm__semiring__1(T_b) % 177.89/177.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.85 => ( ? [B_x] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.85 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 177.89/177.85 => 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) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setprod__zero__iff,axiom, % 177.89/177.85 ! [V_f_2,V_A_2,T_a,T_b] : % 177.89/177.85 ( ( class_Rings_Ocomm__semiring__1(T_b) % 177.89/177.85 & class_Rings_Ono__zero__divisors(T_b) ) % 177.89/177.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.85 => ( 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) % 177.89/177.85 <=> ? [B_x] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.85 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_less__Suc__eq__0__disj,axiom, % 177.89/177.85 ! [V_n_2,V_m_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 177.89/177.85 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 | ? [B_j] : % 177.89/177.85 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 177.89/177.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_less__Suc0,axiom, % 177.89/177.85 ! [V_n_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) % 177.89/177.85 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_gr0__conv__Suc,axiom, % 177.89/177.85 ! [V_n_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 177.89/177.85 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__is__1,axiom, % 177.89/177.85 ! [V_n_2,V_m_2] : % 177.89/177.85 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 177.89/177.85 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 177.89/177.85 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.89/177.85 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_one__is__add,axiom, % 177.89/177.85 ! [V_n_2,V_m_2] : % 177.89/177.85 ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) % 177.89/177.85 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 177.89/177.85 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.89/177.85 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__gr__0,axiom, % 177.89/177.85 ! [V_n_2,V_m_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2))) % 177.89/177.85 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 177.89/177.85 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_nat__one__le__power,axiom, % 177.89/177.85 ! [V_n,V_i] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 177.89/177.85 ! [V_x,T_a] : % 177.89/177.85 ( class_Rings_Ocomm__semiring__1(T_a) % 177.89/177.85 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_power__0,axiom, % 177.89/177.85 ! [V_a,T_a] : % 177.89/177.85 ( class_Power_Opower(T_a) % 177.89/177.85 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_card_Oempty,axiom, % 177.89/177.85 ! [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) ). % 177.89/177.85 % 177.89/177.85 fof(fact_card__infinite,axiom, % 177.89/177.85 ! [V_A_2,T_a] : % 177.89/177.85 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.85 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__eq__1__iff,axiom, % 177.89/177.85 ! [V_n_2,V_m_2] : % 177.89/177.85 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 177.89/177.85 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 177.89/177.85 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zero__less__diff,axiom, % 177.89/177.85 ! [V_m_2,V_n_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_diff__less,axiom, % 177.89/177.85 ! [V_m,V_n] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_nat__mult__eq__cancel1,axiom, % 177.89/177.85 ! [V_n_2,V_m_2,V_k_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 177.89/177.85 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 177.89/177.85 <=> V_m_2 = V_n_2 ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_nat__mult__less__cancel1,axiom, % 177.89/177.85 ! [V_n_2,V_m_2,V_k_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__less__mono2,axiom, % 177.89/177.85 ! [V_k,V_j,V_i] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__less__mono1,axiom, % 177.89/177.85 ! [V_k,V_j,V_i] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__less__cancel2,axiom, % 177.89/177.85 ! [V_n_2,V_k_2,V_m_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) % 177.89/177.85 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 177.89/177.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__less__cancel1,axiom, % 177.89/177.85 ! [V_n_2,V_m_2,V_k_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 177.89/177.85 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 177.89/177.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_nat__0__less__mult__iff,axiom, % 177.89/177.85 ! [V_n_2,V_m_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) % 177.89/177.85 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 177.89/177.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_diff__add__0,axiom, % 177.89/177.85 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.85 % 177.89/177.85 fof(fact_diff__is__0__eq,axiom, % 177.89/177.85 ! [V_n_2,V_m_2] : % 177.89/177.85 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_diff__is__0__eq_H,axiom, % 177.89/177.85 ! [V_n,V_m] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.89/177.85 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_One__nat__def,axiom, % 177.89/177.85 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__eq__self__implies__10,axiom, % 177.89/177.85 ! [V_n,V_m] : % 177.89/177.85 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 177.89/177.85 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 177.89/177.85 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setsum__eq__0__iff,axiom, % 177.89/177.85 ! [V_f_2,V_F_2,T_a] : % 177.89/177.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 177.89/177.85 => ( 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) % 177.89/177.85 <=> ! [B_x] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 177.89/177.85 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_power_Opower_Opower__Suc,axiom, % 177.89/177.85 ! [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)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__nonpos__neg,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__neg__nonpos,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__strict__increasing2,axiom, % 177.89/177.85 ! [V_c,V_b,V_a,T_a] : % 177.89/177.85 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__strict__increasing,axiom, % 177.89/177.85 ! [V_c,V_b,V_a,T_a] : % 177.89/177.85 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__nonneg__pos,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__pos__nonneg,axiom, % 177.89/177.85 ! [V_b,V_a,T_a] : % 177.89/177.85 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__left__le__imp__le,axiom, % 177.89/177.85 ! [V_b,V_a,V_c,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__right__le__imp__le,axiom, % 177.89/177.85 ! [V_b,V_c,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__less__imp__less__left,axiom, % 177.89/177.85 ! [V_b,V_a,V_c,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__left__less__imp__less,axiom, % 177.89/177.85 ! [V_b,V_a,V_c,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semiring(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__less__imp__less__right,axiom, % 177.89/177.85 ! [V_b,V_c,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__right__less__imp__less,axiom, % 177.89/177.85 ! [V_b,V_c,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semiring(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__le__less__imp__less,axiom, % 177.89/177.85 ! [V_d,V_c,V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__less__le__imp__less,axiom, % 177.89/177.85 ! [V_d,V_c,V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__strict__mono_H,axiom, % 177.89/177.85 ! [V_d,V_c,V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__strict__mono,axiom, % 177.89/177.85 ! [V_d,V_c,V_b,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__le__cancel__left__neg,axiom, % 177.89/177.85 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__ring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__le__cancel__left__pos,axiom, % 177.89/177.85 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__ring__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_sum__squares__le__zero__iff,axiom, % 177.89/177.85 ! [V_y_2,V_x_2,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__ring__strict(T_a) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.85 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_sum__squares__ge__zero,axiom, % 177.89/177.85 ! [V_y,V_x,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__ring(T_a) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_sum__squares__gt__zero__iff,axiom, % 177.89/177.85 ! [V_y_2,V_x_2,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__ring__strict(T_a) % 177.89/177.85 => ( 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)))) % 177.89/177.85 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.85 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_not__sum__squares__lt__zero,axiom, % 177.89/177.85 ! [V_y,V_x,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__ring(T_a) % 177.89/177.85 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__right__le__one__le,axiom, % 177.89/177.85 ! [V_y,V_x,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__left__le__one__le,axiom, % 177.89/177.85 ! [V_y,V_x,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zero__less__two,axiom, % 177.89/177.85 ! [T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_power__less__imp__less__base,axiom, % 177.89/177.85 ! [V_b,V_n,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_power__inject__base,axiom, % 177.89/177.85 ! [V_b,V_n,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.89/177.85 => V_a = V_b ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_power__le__imp__le__base,axiom, % 177.89/177.85 ! [V_b,V_n,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n)))) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_card__eq__0__iff,axiom, % 177.89/177.85 ! [V_A_2,T_a] : % 177.89/177.85 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.85 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_card__ge__0__finite,axiom, % 177.89/177.85 ! [V_A_2,T_a] : % 177.89/177.85 ( 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))) % 177.89/177.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_Suc__pred,axiom, % 177.89/177.85 ! [V_n] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.89/177.85 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_diff__Suc__less,axiom, % 177.89/177.85 ! [V_i,V_n] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_i))),V_n)) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_one__less__mult,axiom, % 177.89/177.85 ! [V_m,V_n] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_n__less__n__mult__m,axiom, % 177.89/177.85 ! [V_m,V_n] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_n__less__m__mult__n,axiom, % 177.89/177.85 ! [V_m,V_n] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_nat__diff__split__asm,axiom, % 177.89/177.85 ! [V_b_2,V_a_2,V_P_2] : % 177.89/177.85 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 177.89/177.85 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 177.89/177.85 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 177.89/177.85 | ? [B_d] : % 177.89/177.85 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 177.89/177.85 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_nat__diff__split,axiom, % 177.89/177.85 ! [V_b_2,V_a_2,V_P_2] : % 177.89/177.85 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 177.89/177.85 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 177.89/177.85 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 177.89/177.85 & ! [B_d] : % 177.89/177.85 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 177.89/177.85 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_one__le__mult__iff,axiom, % 177.89/177.85 ! [V_n_2,V_m_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) % 177.89/177.85 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)) % 177.89/177.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_nat__mult__le__cancel1,axiom, % 177.89/177.85 ! [V_n_2,V_m_2,V_k_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__le__cancel2,axiom, % 177.89/177.85 ! [V_n_2,V_k_2,V_m_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) % 177.89/177.85 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__le__cancel1,axiom, % 177.89/177.85 ! [V_n_2,V_m_2,V_k_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 177.89/177.85 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_power__eq__if,axiom, % 177.89/177.85 ! [V_p,V_m] : % 177.89/177.85 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 177.89/177.85 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setsum__eq__Suc0__iff,axiom, % 177.89/177.85 ! [V_f_2,V_A_2,T_a] : % 177.89/177.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.85 => ( 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)) % 177.89/177.85 <=> ? [B_x] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.85 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 177.89/177.85 & ! [B_xa] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 177.89/177.85 => ( B_x != B_xa % 177.89/177.85 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setsum__eq__1__iff,axiom, % 177.89/177.85 ! [V_f_2,V_A_2,T_a] : % 177.89/177.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.85 => ( 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) % 177.89/177.85 <=> ? [B_x] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.85 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 177.89/177.85 & ! [B_xa] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 177.89/177.85 => ( B_x != B_xa % 177.89/177.85 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setsum__delta_H,axiom, % 177.89/177.85 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 177.89/177.85 ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 177.89/177.85 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 177.89/177.85 => 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) ) % 177.89/177.85 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 177.89/177.85 => 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) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setsum__delta,axiom, % 177.89/177.85 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 177.89/177.85 ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 177.89/177.85 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 177.89/177.85 => 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) ) % 177.89/177.85 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 177.89/177.85 => 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) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setprod__pos__nat__iff,axiom, % 177.89/177.85 ! [V_f_2,V_S_2,T_a] : % 177.89/177.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> ! [B_x] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_Body__triple__valid__0,axiom, % 177.89/177.85 ! [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)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_convex__bound__le,axiom, % 177.89/177.85 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semiring__1(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 177.89/177.85 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_power__Suc__less,axiom, % 177.89/177.85 ! [V_n,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_power__Suc__less__one,axiom, % 177.89/177.85 ! [V_n,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),c_Groups_Oone__class_Oone(T_a))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_power__strict__decreasing,axiom, % 177.89/177.85 ! [V_a,V_N,V_n,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_power__decreasing,axiom, % 177.89/177.85 ! [V_a,V_N,V_n,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_one__less__power,axiom, % 177.89/177.85 ! [V_n,V_a,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_card__gt__0__iff,axiom, % 177.89/177.85 ! [V_A_2,T_a] : % 177.89/177.85 ( 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))) % 177.89/177.85 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.85 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_finite__UNIV__card__ge__0,axiom, % 177.89/177.85 ! [T_a] : % 177.89/177.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 177.89/177.85 => 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))))) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setsum_Oeq__fold,axiom, % 177.89/177.85 ! [V_g_2,V_A_2,T_a,T_b] : % 177.89/177.85 ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.85 => 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) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setsum_OF__eq,axiom, % 177.89/177.85 ! [V_g_2,V_A_2,T_a,T_b] : % 177.89/177.85 ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.85 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.85 => 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) ) % 177.89/177.85 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.85 => 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) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_Suc__pred_H,axiom, % 177.89/177.85 ! [V_n] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.89/177.85 => V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_Suc__diff__1,axiom, % 177.89/177.85 ! [V_n] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.89/177.85 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_add__eq__if,axiom, % 177.89/177.85 ! [V_n,V_m] : % 177.89/177.85 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 177.89/177.85 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_mult__eq__if,axiom, % 177.89/177.85 ! [V_n,V_m] : % 177.89/177.85 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.89/177.85 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setsum__restrict__set,axiom, % 177.89/177.85 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 177.89/177.85 ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.85 => 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) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_card_Oeq__fold__g,axiom, % 177.89/177.85 ! [V_A_2,T_a] : % 177.89/177.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.85 => 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) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_card__def,axiom, % 177.89/177.85 ! [V_A_2,T_a] : % 177.89/177.85 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.85 => 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) ) % 177.89/177.85 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.85 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_convex__bound__lt,axiom, % 177.89/177.85 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 177.89/177.85 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_triple_Osize_I1_J,axiom, % 177.89/177.85 ! [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) ). % 177.89/177.85 % 177.89/177.85 fof(fact_even__less__0__iff,axiom, % 177.89/177.85 ! [V_a_2,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_triple_Osize_I2_J,axiom, % 177.89/177.85 ! [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) ). % 177.89/177.85 % 177.89/177.85 fof(fact_card_Ounion__inter__neutral,axiom, % 177.89/177.85 ! [V_B_2,V_A_2,T_a] : % 177.89/177.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.85 => ( ( ? [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))) % 177.89/177.85 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.89/177.85 => 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)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setsum__mono2,axiom, % 177.89/177.85 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 177.89/177.85 ( class_Groups_Oordered__comm__monoid__add(T_b) % 177.89/177.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.85 => ( ! [B_b] : % 177.89/177.85 ( 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))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_b))) ) % 177.89/177.85 => 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))) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_arith__series__nat,axiom, % 177.89/177.85 ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_d_2)))) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setsum_Ounion__inter__neutral,axiom, % 177.89/177.85 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 177.89/177.85 ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.85 => ( ! [B_x] : % 177.89/177.85 ( 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))) % 177.89/177.85 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 177.89/177.85 => 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)) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_finite__lessThan,axiom, % 177.89/177.85 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ). % 177.89/177.85 % 177.89/177.85 fof(fact_card__lessThan,axiom, % 177.89/177.85 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_u_2)) = V_u_2 ). % 177.89/177.85 % 177.89/177.85 fof(fact_UN__lessThan__UNIV,axiom, % 177.89/177.85 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_lessThan__eq__iff,axiom, % 177.89/177.85 ! [V_y_2,V_x_2,T_a] : % 177.89/177.85 ( class_Orderings_Olinorder(T_a) % 177.89/177.85 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2) % 177.89/177.85 <=> V_x_2 = V_y_2 ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_lessThan__0,axiom, % 177.89/177.85 hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_lessThan__Suc,axiom, % 177.89/177.85 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_lessThan__Suc__eq__insert__0,axiom, % 177.89/177.85 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setsum__lessThan__Suc,axiom, % 177.89/177.85 ! [V_n_2,V_f_2,T_a] : % 177.89/177.85 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.85 => 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)) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_lessThan__iff,axiom, % 177.89/177.85 ! [V_k_2,V_i_2,T_a] : % 177.89/177.85 ( class_Orderings_Oord(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_i_2),V_k_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_lessThan__subset__iff,axiom, % 177.89/177.85 ! [V_y_2,V_x_2,T_a] : % 177.89/177.85 ( class_Orderings_Olinorder(T_a) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_lessThan__strict__subset__iff,axiom, % 177.89/177.85 ! [V_n_2,V_m_2,T_a] : % 177.89/177.85 ( class_Orderings_Olinorder(T_a) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_n_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zpower__zadd__distrib,axiom, % 177.89/177.85 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zpower__zpower,axiom, % 177.89/177.85 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_single__Diff__lessThan,axiom, % 177.89/177.85 ! [V_k_2,T_a] : % 177.89/177.85 ( class_Orderings_Oorder(T_a) % 177.89/177.85 => 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))) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_double__eq__0__iff,axiom, % 177.89/177.85 ! [V_a_2,T_a] : % 177.89/177.85 ( class_Groups_Olinordered__ab__group__add(T_a) % 177.89/177.85 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.85 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_arith__series__general,axiom, % 177.89/177.85 ! [V_n_2,V_d_2,V_a_2,T_a] : % 177.89/177.85 ( class_Rings_Ocomm__semiring__1(T_a) % 177.89/177.85 => 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)))) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setsum__Un__zero,axiom, % 177.89/177.85 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 177.89/177.85 ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 177.89/177.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 177.89/177.85 => ( ! [B_x] : % 177.89/177.85 ( 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))) % 177.89/177.85 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 177.89/177.85 => 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)) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_card__Suc__eq,axiom, % 177.89/177.85 ! [V_k_2,V_A_2,T_a] : % 177.89/177.85 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) % 177.89/177.85 <=> ? [B_b,B_B] : % 177.89/177.85 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_b),B_B) % 177.89/177.85 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_b),B_B)) % 177.89/177.85 & hAPP(c_Finite__Set_Ocard(T_a),B_B) = V_k_2 % 177.89/177.85 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setsum__mono3,axiom, % 177.89/177.85 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 177.89/177.85 ( ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.85 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 177.89/177.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.85 => ( ! [B_x] : % 177.89/177.85 ( 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))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 177.89/177.85 => 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))) ) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_ord_OgreaterThan__iff,axiom, % 177.89/177.85 ! [V_k_2,V_less_2,V_i_2,T_a] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_ord_OlessThan__iff,axiom, % 177.89/177.85 ! [V_k_2,V_less_2,V_i_2,T_a] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_negative__zless,axiom, % 177.89/177.85 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))) ). % 177.89/177.85 % 177.89/177.85 fof(fact_pos__zmult__eq__1__iff,axiom, % 177.89/177.85 ! [V_n_2,V_m_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 177.89/177.85 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 177.89/177.85 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 177.89/177.85 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zmult__zless__mono2,axiom, % 177.89/177.85 ! [V_k,V_j,V_i] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zmult__1,axiom, % 177.89/177.85 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 177.89/177.85 % 177.89/177.85 fof(fact_zmult__1__right,axiom, % 177.89/177.85 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 177.89/177.85 % 177.89/177.85 fof(fact_zdiff__zmult__distrib2,axiom, % 177.89/177.85 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zdiff__zmult__distrib,axiom, % 177.89/177.85 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zmult__assoc,axiom, % 177.89/177.85 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zmult__commute,axiom, % 177.89/177.85 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zmult__zminus,axiom, % 177.89/177.85 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_w) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zadd__zmult__distrib,axiom, % 177.89/177.85 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zadd__zmult__distrib2,axiom, % 177.89/177.85 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_of__nat__eq__iff,axiom, % 177.89/177.85 ! [V_n_2,V_m_2,T_a] : % 177.89/177.85 ( class_Nat_Osemiring__char__0(T_a) % 177.89/177.85 => ( 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) % 177.89/177.85 <=> V_m_2 = V_n_2 ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_int__eq__0__conv,axiom, % 177.89/177.85 ! [V_n_2] : % 177.89/177.85 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.85 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_int__0,axiom, % 177.89/177.85 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 177.89/177.85 % 177.89/177.85 fof(fact_negative__eq__positive,axiom, % 177.89/177.85 ! [V_m_2,V_n_2] : % 177.89/177.85 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) % 177.89/177.85 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_int__zle__neg,axiom, % 177.89/177.85 ! [V_m_2,V_n_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))) % 177.89/177.85 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.85 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_int__le__0__conv,axiom, % 177.89/177.85 ! [V_n_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.85 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zless__iff__Suc__zadd,axiom, % 177.89/177.85 ! [V_z_2,V_w_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 177.89/177.85 <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_int__Suc,axiom, % 177.89/177.85 ! [V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_not__zle__0__negative,axiom, % 177.89/177.85 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))) ). % 177.89/177.85 % 177.89/177.85 fof(fact_negative__zless__0,axiom, % 177.89/177.85 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zless__int,axiom, % 177.89/177.85 ! [V_n_2,V_m_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zadd__int,axiom, % 177.89/177.85 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zadd__int__left,axiom, % 177.89/177.85 ! [V_z,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),V_z) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zle__int,axiom, % 177.89/177.85 ! [V_n_2,V_m_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_int__mult,axiom, % 177.89/177.85 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zmult__int,axiom, % 177.89/177.85 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_int__1,axiom, % 177.89/177.85 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 177.89/177.85 % 177.89/177.85 fof(fact_inj__int,axiom, % 177.89/177.85 c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zpower__int,axiom, % 177.89/177.85 ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) ). % 177.89/177.85 % 177.89/177.85 fof(fact_int__power,axiom, % 177.89/177.85 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) ). % 177.89/177.85 % 177.89/177.85 fof(fact_int__setsum,axiom, % 177.89/177.85 ! [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) ). % 177.89/177.85 % 177.89/177.85 fof(fact_int__setprod,axiom, % 177.89/177.85 ! [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) ). % 177.89/177.85 % 177.89/177.85 fof(fact_int__Suc0__eq__1,axiom, % 177.89/177.85 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zmult__zless__mono2__lemma,axiom, % 177.89/177.85 ! [V_k,V_j,V_i] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_j))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zero__less__int__conv,axiom, % 177.89/177.85 ! [V_n_2] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zero__le__imp__of__nat,axiom, % 177.89/177.85 ! [V_m,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m))) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_of__nat__0__le__iff,axiom, % 177.89/177.85 ! [V_n,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_zdiff__int,axiom, % 177.89/177.85 ! [V_m,V_n] : % 177.89/177.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.89/177.85 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_of__nat__less__0__iff,axiom, % 177.89/177.85 ! [V_m,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_of__nat__0,axiom, % 177.89/177.85 ! [T_a] : % 177.89/177.85 ( class_Rings_Osemiring__1(T_a) % 177.89/177.85 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_of__nat__less__imp__less,axiom, % 177.89/177.85 ! [V_n,V_m,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_less__imp__of__nat__less,axiom, % 177.89/177.85 ! [V_n,V_m,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.89/177.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_of__nat__less__iff,axiom, % 177.89/177.85 ! [V_n_2,V_m_2,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_of__nat__le__iff,axiom, % 177.89/177.85 ! [V_n_2,V_m_2,T_a] : % 177.89/177.85 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.85 => ( 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))) % 177.89/177.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_of__nat__add,axiom, % 177.89/177.85 ! [V_n,V_m,T_a] : % 177.89/177.85 ( class_Rings_Osemiring__1(T_a) % 177.89/177.85 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_of__nat__mult,axiom, % 177.89/177.85 ! [V_n,V_m,T_a] : % 177.89/177.85 ( class_Rings_Osemiring__1(T_a) % 177.89/177.85 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_of__nat__1,axiom, % 177.89/177.85 ! [T_a] : % 177.89/177.85 ( class_Rings_Osemiring__1(T_a) % 177.89/177.85 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_of__nat__power,axiom, % 177.89/177.85 ! [V_n,V_m,T_a] : % 177.89/177.85 ( class_Rings_Osemiring__1(T_a) % 177.89/177.85 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),V_n) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_of__nat__setsum,axiom, % 177.89/177.85 ! [V_A_2,V_f_2,T_b,T_a] : % 177.89/177.85 ( class_Rings_Osemiring__1(T_a) % 177.89/177.85 => 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) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_inj__of__nat,axiom, % 177.89/177.85 ! [T_a] : % 177.89/177.85 ( class_Nat_Osemiring__char__0(T_a) % 177.89/177.85 => 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))) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_of__nat__setprod,axiom, % 177.89/177.85 ! [V_A_2,V_f_2,T_b,T_a] : % 177.89/177.85 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 177.89/177.85 & class_Rings_Osemiring__1(T_a) ) % 177.89/177.85 => 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) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_of__nat__Suc,axiom, % 177.89/177.85 ! [V_m,T_a] : % 177.89/177.85 ( class_Rings_Osemiring__1(T_a) % 177.89/177.85 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_of__nat__diff,axiom, % 177.89/177.85 ! [V_m,V_n,T_a] : % 177.89/177.85 ( class_Rings_Oring__1(T_a) % 177.89/177.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.89/177.85 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ) ). % 177.89/177.85 % 177.89/177.85 fof(fact_setsum__constant,axiom, % 177.89/177.85 ! [V_A_2,V_y_2,T_b,T_a] : % 177.89/177.85 ( class_Rings_Osemiring__1(T_a) % 177.89/177.85 => 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) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_of__nat__0__less__iff,axiom, % 177.89/177.86 ! [V_n_2,T_a] : % 177.89/177.86 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.86 => ( 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))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_semiring__1__class_Oof__nat__code,axiom, % 177.89/177.86 ! [V_n_2,T_a] : % 177.89/177.86 ( class_Rings_Osemiring__1(T_a) % 177.89/177.86 => 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)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zdiff__int__split,axiom, % 177.89/177.86 ! [V_y_2,V_x_2,V_P_2] : % 177.89/177.86 ( 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)))) % 177.89/177.86 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) % 177.89/177.86 => 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)))) ) % 177.89/177.86 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 177.89/177.86 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom, % 177.89/177.86 ! [V_n,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_setsum__bounded,axiom, % 177.89/177.86 ! [V_K_2,V_f_2,V_A_2,T_a,T_b] : % 177.89/177.86 ( ( class_Groups_Oordered__ab__semigroup__add(T_b) % 177.89/177.86 & class_Rings_Osemiring__1(T_b) ) % 177.89/177.86 => ( ! [B_i] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_A_2)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_i)),V_K_2)) ) % 177.89/177.86 => 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))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_ord_OatMost__iff,axiom, % 177.89/177.86 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_ord_OatLeast__iff,axiom, % 177.89/177.86 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_negative__zle,axiom, % 177.89/177.86 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom, % 177.89/177.86 ! [V_P_2] : % 177.89/177.86 ( ! [B_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 177.89/177.86 => hBOOL(hAPP(V_P_2,B_x)) ) % 177.89/177.86 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom, % 177.89/177.86 ! [V_P_2] : % 177.89/177.86 ( ? [B_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 177.89/177.86 & hBOOL(hAPP(V_P_2,B_x)) ) % 177.89/177.86 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom, % 177.89/177.86 ! [V_z] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zero__zle__int,axiom, % 177.89/177.86 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_int__less__0__conv,axiom, % 177.89/177.86 ! [V_k] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_negative__zle__0,axiom, % 177.89/177.86 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_int__int__eq,axiom, % 177.89/177.86 ! [V_n_2,V_m_2] : % 177.89/177.86 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) % 177.89/177.86 <=> V_m_2 = V_n_2 ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_not__int__zless__negative,axiom, % 177.89/177.86 ! [V_m,V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zle__iff__zadd,axiom, % 177.89/177.86 ! [V_z_2,V_w_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) % 177.89/177.86 <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__nat__int__set__relations_I5_J,axiom, % 177.89/177.86 ! [V_B_2,V_A_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__nat__int__set__relations_I4_J,axiom, % 177.89/177.86 ! [V_B_2,V_A_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__int__nat__relations_I1_J,axiom, % 177.89/177.86 ! [V_y_2,V_x_2] : % 177.89/177.86 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2) % 177.89/177.86 <=> V_x_2 = V_y_2 ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__nat__int__set__relations_I3_J,axiom, % 177.89/177.86 ! [V_B_2,V_A_2] : % 177.89/177.86 ( V_A_2 = V_B_2 % 177.89/177.86 <=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__nat__int__set__relations_I2_J,axiom, % 177.89/177.86 ! [V_A_2,V_x_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zle__diff1__eq,axiom, % 177.89/177.86 ! [V_z_2,V_w_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zle__add1__eq__le,axiom, % 177.89/177.86 ! [V_z_2,V_w_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zless__add1__eq,axiom, % 177.89/177.86 ! [V_z_2,V_w_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) % 177.89/177.86 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 177.89/177.86 | V_w_2 = V_z_2 ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_add1__zle__eq,axiom, % 177.89/177.86 ! [V_z_2,V_w_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2)) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zless__imp__add1__zle,axiom, % 177.89/177.86 ! [V_z,V_w] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zadd__zless__mono,axiom, % 177.89/177.86 ! [V_z,V_z_H,V_w,V_w_H] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zadd__left__mono,axiom, % 177.89/177.86 ! [V_k,V_j,V_i] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zadd__strict__right__mono,axiom, % 177.89/177.86 ! [V_k,V_j,V_i] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zle__antisym,axiom, % 177.89/177.86 ! [V_w,V_z] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) % 177.89/177.86 => V_z = V_w ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zle__trans,axiom, % 177.89/177.86 ! [V_k,V_j,V_i] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zless__linear,axiom, % 177.89/177.86 ! [V_y,V_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) % 177.89/177.86 | V_x = V_y % 177.89/177.86 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zless__le,axiom, % 177.89/177.86 ! [V_w_2,V_z_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) % 177.89/177.86 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) % 177.89/177.86 & V_z_2 != V_w_2 ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zle__linear,axiom, % 177.89/177.86 ! [V_w,V_z] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 177.89/177.86 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zle__refl,axiom, % 177.89/177.86 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zminus__zminus,axiom, % 177.89/177.86 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ). % 177.89/177.86 % 177.89/177.86 fof(fact_diff__int__def__symmetric,axiom, % 177.89/177.86 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) ). % 177.89/177.86 % 177.89/177.86 fof(fact_diff__int__def,axiom, % 177.89/177.86 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zminus__zadd__distrib,axiom, % 177.89/177.86 ! [V_w,V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zadd__commute,axiom, % 177.89/177.86 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zadd__left__commute,axiom, % 177.89/177.86 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zadd__assoc,axiom, % 177.89/177.86 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_int__0__neq__1,axiom, % 177.89/177.86 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 177.89/177.86 % 177.89/177.86 fof(fact_odd__nonzero,axiom, % 177.89/177.86 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zadd__0__right,axiom, % 177.89/177.86 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 177.89/177.86 % 177.89/177.86 fof(fact_zadd__0,axiom, % 177.89/177.86 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 177.89/177.86 % 177.89/177.86 fof(fact_zadd__zminus__inverse2,axiom, % 177.89/177.86 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zminus__0,axiom, % 177.89/177.86 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 177.89/177.86 % 177.89/177.86 fof(fact_less__bin__lemma,axiom, % 177.89/177.86 ! [V_l_2,V_k_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 177.89/177.86 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 177.89/177.86 ! [V_y,V_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_le__imp__0__less,axiom, % 177.89/177.86 ! [V_z] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_odd__less__0,axiom, % 177.89/177.86 ! [V_z_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_int__0__less__1,axiom, % 177.89/177.86 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 177.89/177.86 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_int__one__le__iff__zero__less,axiom, % 177.89/177.86 ! [V_z_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_of__nat__aux_Osimps_I1_J,axiom, % 177.89/177.86 ! [V_i_2,V_inc_2,T_a] : % 177.89/177.86 ( class_Rings_Osemiring__1(T_a) % 177.89/177.86 => 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 ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_of__nat__aux_Osimps_I2_J,axiom, % 177.89/177.86 ! [V_i_2,V_n_2,V_inc_2,T_a] : % 177.89/177.86 ( class_Rings_Osemiring__1(T_a) % 177.89/177.86 => 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)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__int__nat__numerals_I1_J,axiom, % 177.89/177.86 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__int__nat__relations_I2_J,axiom, % 177.89/177.86 ! [V_y_2,V_x_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom, % 177.89/177.86 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_y)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__int__nat__relations_I3_J,axiom, % 177.89/177.86 ! [V_y_2,V_x_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 177.89/177.86 ! [V_y,V_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__int__nat__numerals_I2_J,axiom, % 177.89/177.86 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom, % 177.89/177.86 c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 177.89/177.86 ! [V_n,V_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom, % 177.89/177.86 ! [V_A_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__nat__int__set__relations_I1_J,axiom, % 177.89/177.86 ! [V_A_2] : % 177.89/177.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) % 177.89/177.86 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom, % 177.89/177.86 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_self__quotient__aux2,axiom, % 177.89/177.86 ! [V_q,V_r,V_a] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.89/177.86 => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_self__quotient__aux1,axiom, % 177.89/177.86 ! [V_q,V_r,V_a] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.89/177.86 => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_q__pos__lemma,axiom, % 177.89/177.86 ! [V_r_H,V_q_H,V_b_H] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_q__neg__lemma,axiom, % 177.89/177.86 ! [V_r_H,V_q_H,V_b_H] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_unique__quotient__lemma,axiom, % 177.89/177.86 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zdiv__mono2__lemma,axiom, % 177.89/177.86 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 177.89/177.86 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_infinite__UNIV__int,axiom, % 177.89/177.86 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zdiv__mono2__neg__lemma,axiom, % 177.89/177.86 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 177.89/177.86 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_unique__quotient__lemma__neg,axiom, % 177.89/177.86 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_small_H_Osimps,axiom, % 177.89/177.86 ! [V_f_2,V_i_2,V_d_2] : % 177.89/177.86 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 177.89/177.86 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 177.89/177.86 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 177.89/177.86 => 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)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_tsub__def,axiom, % 177.89/177.86 ! [V_x,V_y] : % 177.89/177.86 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 177.89/177.86 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) % 177.89/177.86 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 177.89/177.86 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_option_Osize_I2_J,axiom, % 177.89/177.86 ! [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))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_termination__basic__simps_I3_J,axiom, % 177.89/177.86 ! [V_z,V_y,V_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_termination__basic__simps_I4_J,axiom, % 177.89/177.86 ! [V_y,V_z,V_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_option_Osize_I1_J,axiom, % 177.89/177.86 ! [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) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 177.89/177.86 ! [V_y,V_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(V_x,V_y))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_tsub__eq,axiom, % 177.89/177.86 ! [V_x,V_y] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 177.89/177.86 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom, % 177.89/177.86 ! [V_y,V_x] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x),V_y)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_termination__basic__simps_I2_J,axiom, % 177.89/177.86 ! [V_y,V_z,V_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_termination__basic__simps_I1_J,axiom, % 177.89/177.86 ! [V_z,V_y,V_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_termination__basic__simps_I5_J,axiom, % 177.89/177.86 ! [V_y,V_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat_Osize_I2_J,axiom, % 177.89/177.86 ! [V_nat] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat_Osize_I4_J,axiom, % 177.89/177.86 ! [V_nat] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_option_Osize_I4_J,axiom, % 177.89/177.86 ! [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) ). % 177.89/177.86 % 177.89/177.86 fof(fact_option_Osize_I3_J,axiom, % 177.89/177.86 ! [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) ). % 177.89/177.86 % 177.89/177.86 fof(fact_image__minus__const__atLeastLessThan__nat,axiom, % 177.89/177.86 ! [V_x_2,V_y_2,V_ca_2] : % 177.89/177.86 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 177.89/177.86 => 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)) ) % 177.89/177.86 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 177.89/177.86 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 177.89/177.86 => 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))) ) % 177.89/177.86 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 177.89/177.86 => 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)) ) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_finite__atLeastLessThan,axiom, % 177.89/177.86 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__size,axiom, % 177.89/177.86 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ). % 177.89/177.86 % 177.89/177.86 fof(fact_atLeastLessThan__eq__iff,axiom, % 177.89/177.86 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 177.89/177.86 ( class_Orderings_Olinorder(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 177.89/177.86 => ( 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) % 177.89/177.86 <=> ( V_a_2 = V_ca_2 % 177.89/177.86 & V_b_2 = V_d_2 ) ) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 177.89/177.86 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 177.89/177.86 ( class_Orderings_Olinorder(T_a) % 177.89/177.86 => ( 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) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 177.89/177.86 => V_a_2 = V_ca_2 ) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 177.89/177.86 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 177.89/177.86 ( class_Orderings_Olinorder(T_a) % 177.89/177.86 => ( 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) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 177.89/177.86 => V_b_2 = V_d_2 ) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_atLeastLessThan__add__Un,axiom, % 177.89/177.86 ! [V_k_2,V_j_2,V_i_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 177.89/177.86 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_atLeastLessThan0,axiom, % 177.89/177.86 ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_atLeast0LessThan,axiom, % 177.89/177.86 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) ). % 177.89/177.86 % 177.89/177.86 fof(fact_card__atLeastLessThan,axiom, % 177.89/177.86 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2) ). % 177.89/177.86 % 177.89/177.86 fof(fact_image__Suc__atLeastLessThan,axiom, % 177.89/177.86 ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2)),hAPP(c_Nat_OSuc,V_j_2)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_atLeastLessThan__empty,axiom, % 177.89/177.86 ! [V_a_2,V_b_2,T_a] : % 177.89/177.86 ( class_Orderings_Oorder(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 177.89/177.86 => 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)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_atLeastLessThan__empty__iff,axiom, % 177.89/177.86 ! [V_b_2,V_a_2,T_a] : % 177.89/177.86 ( class_Orderings_Oorder(T_a) % 177.89/177.86 => ( 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)) % 177.89/177.86 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_atLeastLessThan__empty__iff2,axiom, % 177.89/177.86 ! [V_b_2,V_a_2,T_a] : % 177.89/177.86 ( class_Orderings_Oorder(T_a) % 177.89/177.86 => ( 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) % 177.89/177.86 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_atLeastLessThan__subset__iff,axiom, % 177.89/177.86 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 177.89/177.86 ( class_Orderings_Olinorder(T_a) % 177.89/177.86 => ( 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))) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 177.89/177.86 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 177.89/177.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 177.89/177.86 ! [V_n_2,V_m_2,V_f_2,T_a] : % 177.89/177.86 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.86 => 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)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_ivl__disj__un_I17_J,axiom, % 177.89/177.86 ! [V_u_2,V_m_2,V_l_2,T_a] : % 177.89/177.86 ( class_Orderings_Olinorder(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 177.89/177.86 => 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) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 177.89/177.86 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 177.89/177.86 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.86 => 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)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_ivl__diff,axiom, % 177.89/177.86 ! [V_m_2,V_n_2,V_i_2,T_a] : % 177.89/177.86 ( class_Orderings_Olinorder(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_n_2)) % 177.89/177.86 => 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) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_ivl__disj__int_I11_J,axiom, % 177.89/177.86 ! [V_u_2,V_m_2,V_l_2,T_a] : % 177.89/177.86 ( class_Orderings_Oorder(T_a) % 177.89/177.86 => 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)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_image__add__atLeastLessThan,axiom, % 177.89/177.86 ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat_Osize_I3_J,axiom, % 177.89/177.86 hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.86 % 177.89/177.86 fof(fact_setsum__add__nat__ivl,axiom, % 177.89/177.86 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 177.89/177.86 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 177.89/177.86 => 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)) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_setsum__diff__nat__ivl,axiom, % 177.89/177.86 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 177.89/177.86 ( class_Groups_Oab__group__add(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 177.89/177.86 => 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)) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_atLeastLessThan__singleton,axiom, % 177.89/177.86 ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_m_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_m_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_UN__UN__finite__eq,axiom, % 177.89/177.86 ! [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) ). % 177.89/177.86 % 177.89/177.86 fof(fact_ivl__disj__un_I8_J,axiom, % 177.89/177.86 ! [V_u_2,V_l_2,T_a] : % 177.89/177.86 ( class_Orderings_Olinorder(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 177.89/177.86 => 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) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_subset__card__intvl__is__intvl,axiom, % 177.89/177.86 ! [V_k_2,V_A_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))))) % 177.89/177.86 => V_A_2 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_ivl__disj__int_I2_J,axiom, % 177.89/177.86 ! [V_u_2,V_l_2,T_a] : % 177.89/177.86 ( class_Orderings_Oorder(T_a) % 177.89/177.86 => 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)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat_Osize_I1_J,axiom, % 177.89/177.86 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.86 % 177.89/177.86 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 177.89/177.86 ! [V_k_2,V_f_2,T_a] : % 177.89/177.86 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.86 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => 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)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_setsum__head__upt__Suc,axiom, % 177.89/177.86 ! [V_f_2,V_n_2,V_m_2,T_a] : % 177.89/177.86 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.86 => 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))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_atLeastLessThanSuc,axiom, % 177.89/177.86 ! [V_n_2,V_m_2] : % 177.89/177.86 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.86 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_n_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) % 177.89/177.86 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.86 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_setsum__op__ivl__Suc,axiom, % 177.89/177.86 ! [V_f_2,V_m_2,V_n_2,T_a] : % 177.89/177.86 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.86 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 177.89/177.86 => 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) ) % 177.89/177.86 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 177.89/177.86 => 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)) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_all__nat__less__eq,axiom, % 177.89/177.86 ! [V_P_2,V_n_2] : % 177.89/177.86 ( ! [B_m] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 177.89/177.86 => hBOOL(hAPP(V_P_2,B_m)) ) % 177.89/177.86 <=> ! [B_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) % 177.89/177.86 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_ex__nat__less__eq,axiom, % 177.89/177.86 ! [V_P_2,V_n_2] : % 177.89/177.86 ( ? [B_m] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 177.89/177.86 & hBOOL(hAPP(V_P_2,B_m)) ) % 177.89/177.86 <=> ? [B_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) % 177.89/177.86 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_UN__finite2__subset,axiom, % 177.89/177.86 ! [V_B_2,V_k_2,V_A_2,T_a] : % 177.89/177.86 ( ! [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))) % 177.89/177.86 => 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))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_UN__finite2__eq,axiom, % 177.89/177.86 ! [V_B_2,V_k_2,V_A_2,T_a] : % 177.89/177.86 ( ! [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) % 177.89/177.86 => 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) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_UN__finite__subset,axiom, % 177.89/177.86 ! [V_C_2,V_A_2,T_a] : % 177.89/177.86 ( ! [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)) % 177.89/177.86 => 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)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_finite__atLeastLessThan__int,axiom, % 177.89/177.86 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_finite__atLeastZeroLessThan__int,axiom, % 177.89/177.86 ! [V_u_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_image__add__int__atLeastLessThan,axiom, % 177.89/177.86 ! [V_u_2,V_l_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2) ). % 177.89/177.86 % 177.89/177.86 fof(fact_ivl__disj__un_I3_J,axiom, % 177.89/177.86 ! [V_u_2,V_l_2,T_a] : % 177.89/177.86 ( class_Orderings_Olinorder(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 177.89/177.86 => 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) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Ints__odd__less__0,axiom, % 177.89/177.86 ! [V_a_2,T_a] : % 177.89/177.86 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 177.89/177.86 => ( 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))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_int__power__div__base,axiom, % 177.89/177.86 ! [V_k,V_m] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m)),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_image__INT,axiom, % 177.89/177.86 ! [V_j_2,V_B_2,V_A_2,T_c,V_C_2,V_f_2,T_b,T_a] : % 177.89/177.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 177.89/177.86 => ( ! [B_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.89/177.86 => 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)) ) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_j_2),V_A_2)) % 177.89/177.86 => 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)) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_com_Osize_I4_J,axiom, % 177.89/177.86 ! [V_com2,V_com1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1)),c_Com_Ocom_Ocom__size(V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_finite__greaterThanLessThan,axiom, % 177.89/177.86 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_finite__greaterThanLessThan__int,axiom, % 177.89/177.86 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zdiv__zero,axiom, % 177.89/177.86 ! [V_b] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zdiv__zminus__zminus,axiom, % 177.89/177.86 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zdiv__zminus2,axiom, % 177.89/177.86 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__by__0,axiom, % 177.89/177.86 ! [V_a,T_a] : % 177.89/177.86 ( class_Divides_Osemiring__div(T_a) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__0,axiom, % 177.89/177.86 ! [V_a,T_a] : % 177.89/177.86 ( class_Divides_Osemiring__div(T_a) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__by__1,axiom, % 177.89/177.86 ! [V_a,T_a] : % 177.89/177.86 ( class_Divides_Osemiring__div(T_a) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 177.89/177.86 ! [V_y,V_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__neg__pos__less0,axiom, % 177.89/177.86 ! [V_b,V_a] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 177.89/177.86 ! [V_a_2,V_b_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 177.89/177.86 ! [V_a_2,V_b_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zdiv__self,axiom, % 177.89/177.86 ! [V_a] : % 177.89/177.86 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__mult__mult1__if,axiom, % 177.89/177.86 ! [V_b,V_a,V_c,T_a] : % 177.89/177.86 ( class_Divides_Osemiring__div(T_a) % 177.89/177.86 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a) ) % 177.89/177.86 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__mult__self2__is__id,axiom, % 177.89/177.86 ! [V_a,V_b,T_a] : % 177.89/177.86 ( class_Divides_Osemiring__div(T_a) % 177.89/177.86 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_b) = V_a ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__mult__self1__is__id,axiom, % 177.89/177.86 ! [V_a,V_b,T_a] : % 177.89/177.86 ( class_Divides_Osemiring__div(T_a) % 177.89/177.86 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),V_b) = V_a ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__mult__mult2,axiom, % 177.89/177.86 ! [V_b,V_a,V_c,T_a] : % 177.89/177.86 ( class_Divides_Osemiring__div(T_a) % 177.89/177.86 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__mult__mult1,axiom, % 177.89/177.86 ! [V_b,V_a,V_c,T_a] : % 177.89/177.86 ( class_Divides_Osemiring__div(T_a) % 177.89/177.86 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__self,axiom, % 177.89/177.86 ! [V_a,T_a] : % 177.89/177.86 ( class_Divides_Osemiring__div(T_a) % 177.89/177.86 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_greaterThanLessThan__empty,axiom, % 177.89/177.86 ! [V_k_2,V_l_2,T_a] : % 177.89/177.86 ( class_Orderings_Oorder(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 177.89/177.86 => 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)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom, % 177.89/177.86 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Ints__0,axiom, % 177.89/177.86 ! [T_a] : % 177.89/177.86 ( class_Rings_Oring__1(T_a) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zdiv__mono1__neg,axiom, % 177.89/177.86 ! [V_b,V_a_H,V_a] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zdiv__mono1,axiom, % 177.89/177.86 ! [V_b,V_a_H,V_a] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__neg__neg__trivial,axiom, % 177.89/177.86 ! [V_b,V_a] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zdiv__mono2__neg,axiom, % 177.89/177.86 ! [V_b,V_b_H,V_a] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__nonpos__pos__le0,axiom, % 177.89/177.86 ! [V_b,V_a] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 177.89/177.86 ! [V_a_2,V_b_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__pos__pos__trivial,axiom, % 177.89/177.86 ! [V_b,V_a] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__nonneg__neg__le0,axiom, % 177.89/177.86 ! [V_b,V_a] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zdiv__mono2,axiom, % 177.89/177.86 ! [V_b,V_b_H,V_a] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H))) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 177.89/177.86 ! [V_b_2,V_a_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 177.89/177.86 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) % 177.89/177.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 177.89/177.86 ! [V_i_2,V_k_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 177.89/177.86 ! [V_a_2,V_b_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zdiv__eq__0__iff,axiom, % 177.89/177.86 ! [V_k_2,V_i_2] : % 177.89/177.86 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.86 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.86 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 177.89/177.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) ) % 177.89/177.86 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom, % 177.89/177.86 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Ints__add,axiom, % 177.89/177.86 ! [V_b_2,V_a_2,T_a] : % 177.89/177.86 ( class_Rings_Oring__1(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 177.89/177.86 => 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))) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Ints__mult,axiom, % 177.89/177.86 ! [V_b_2,V_a_2,T_a] : % 177.89/177.86 ( class_Rings_Oring__1(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 177.89/177.86 => 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))) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_image__uminus__greaterThanLessThan,axiom, % 177.89/177.86 ! [V_y_2,V_x_2,T_a] : % 177.89/177.86 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.86 => 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)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Ints__diff,axiom, % 177.89/177.86 ! [V_b_2,V_a_2,T_a] : % 177.89/177.86 ( class_Rings_Oring__1(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 177.89/177.86 => 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))) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_int__div__less__self,axiom, % 177.89/177.86 ! [V_k,V_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_k)),V_x)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zdiv__zmult2__eq,axiom, % 177.89/177.86 ! [V_b,V_a,V_c] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_c) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Ints__1,axiom, % 177.89/177.86 ! [T_a] : % 177.89/177.86 ( class_Rings_Oring__1(T_a) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Ints__minus,axiom, % 177.89/177.86 ! [V_a_2,T_a] : % 177.89/177.86 ( class_Rings_Oring__1(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 177.89/177.86 => 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))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Ints__of__nat,axiom, % 177.89/177.86 ! [V_n_2,T_a] : % 177.89/177.86 ( class_Rings_Oring__1(T_a) % 177.89/177.86 => 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))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Ints__power,axiom, % 177.89/177.86 ! [V_n_2,V_a_2,T_a] : % 177.89/177.86 ( class_Rings_Oring__1(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 177.89/177.86 => 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))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__mult__self2,axiom, % 177.89/177.86 ! [V_c,V_a,V_b,T_a] : % 177.89/177.86 ( class_Divides_Osemiring__div(T_a) % 177.89/177.86 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__mult__self1,axiom, % 177.89/177.86 ! [V_c,V_a,V_b,T_a] : % 177.89/177.86 ( class_Divides_Osemiring__div(T_a) % 177.89/177.86 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__add__self1,axiom, % 177.89/177.86 ! [V_a,V_b,T_a] : % 177.89/177.86 ( class_Divides_Osemiring__div(T_a) % 177.89/177.86 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__add__self2,axiom, % 177.89/177.86 ! [V_a,V_b,T_a] : % 177.89/177.86 ( class_Divides_Osemiring__div(T_a) % 177.89/177.86 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_com_Osize_I7_J,axiom, % 177.89/177.86 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.86 % 177.89/177.86 fof(fact_com_Osize_I8_J,axiom, % 177.89/177.86 ! [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) ). % 177.89/177.86 % 177.89/177.86 fof(fact_com_Osize_I1_J,axiom, % 177.89/177.86 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Ints__double__eq__0__iff,axiom, % 177.89/177.86 ! [V_a_2,T_a] : % 177.89/177.86 ( class_Int_Oring__char__0(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 177.89/177.86 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_ivl__disj__int_I9_J,axiom, % 177.89/177.86 ! [V_u_2,V_m_2,V_l_2,T_a] : % 177.89/177.86 ( class_Orderings_Oorder(T_a) % 177.89/177.86 => 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)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_card__greaterThanLessThan,axiom, % 177.89/177.86 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),hAPP(c_Nat_OSuc,V_l_2)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_split__zdiv,axiom, % 177.89/177.86 ! [V_k_2,V_n_2,V_P_2] : % 177.89/177.86 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) % 177.89/177.86 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.86 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.89/177.86 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 177.89/177.86 => ! [B_i] : % 177.89/177.86 ( ? [B_j] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 177.89/177.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 177.89/177.86 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 177.89/177.86 => hBOOL(hAPP(V_P_2,B_i)) ) ) % 177.89/177.86 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.86 => ! [B_i] : % 177.89/177.86 ( ? [B_j] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 177.89/177.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.86 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 177.89/177.86 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_divmod__int__rel__div__eq,axiom, % 177.89/177.86 ! [V_r_1,V_y,V_b_1,V_a_1] : % 177.89/177.86 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1) % 177.89/177.86 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 177.89/177.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) ) % 177.89/177.86 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) % 177.89/177.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 177.89/177.86 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_ivl__disj__un_I15_J,axiom, % 177.89/177.86 ! [V_u_2,V_m_2,V_l_2,T_a] : % 177.89/177.86 ( class_Orderings_Olinorder(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 177.89/177.86 => 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) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Ints__odd__nonzero,axiom, % 177.89/177.86 ! [V_a_2,T_a] : % 177.89/177.86 ( class_Int_Oring__char__0(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 177.89/177.86 => 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) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_com_Osize_I6_J,axiom, % 177.89/177.86 ! [V_com_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_z3div__def,axiom, % 177.89/177.86 ! [V_k,V_l] : % 177.89/177.86 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 177.89/177.86 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) % 177.89/177.86 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 177.89/177.86 => c_SMT_Oz3div(V_k,V_l) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_ivl__disj__un_I4_J,axiom, % 177.89/177.86 ! [V_u_2,V_l_2,T_a] : % 177.89/177.86 ( class_Orderings_Olinorder(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 177.89/177.86 => 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) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Powp__mono,axiom, % 177.89/177.86 ! [V_B_2,V_A_2,T_a] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.86 => 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))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_card__Plus__conv__if,axiom, % 177.89/177.86 ! [V_B_2,T_b,V_A_2,T_a] : % 177.89/177.86 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.86 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 177.89/177.86 => 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)) ) % 177.89/177.86 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.86 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 177.89/177.86 => 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) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_com_Osize_I12_J,axiom, % 177.89/177.86 ! [V_com2,V_com1] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_finite__greaterThanAtMost,axiom, % 177.89/177.86 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_finite__greaterThanAtMost__int,axiom, % 177.89/177.86 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__le__mono,axiom, % 177.89/177.86 ! [V_k,V_n,V_m] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),V_k))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__le__dividend,axiom, % 177.89/177.86 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__mult2__eq,axiom, % 177.89/177.86 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)),V_c) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__1,axiom, % 177.89/177.86 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__less,axiom, % 177.89/177.86 ! [V_n,V_m] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__mult__div__cancel__disj,axiom, % 177.89/177.86 ! [V_n,V_m,V_k] : % 177.89/177.86 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.89/177.86 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zdiv__int,axiom, % 177.89/177.86 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom, % 177.89/177.86 ! [V_y,V_x] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_x),V_y)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_greaterThanAtMost__empty,axiom, % 177.89/177.86 ! [V_k_2,V_l_2,T_a] : % 177.89/177.86 ( class_Orderings_Oorder(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 177.89/177.86 => 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)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_greaterThanAtMost__empty__iff2,axiom, % 177.89/177.86 ! [V_l_2,V_k_2,T_a] : % 177.89/177.86 ( class_Orderings_Oorder(T_a) % 177.89/177.86 => ( 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) % 177.89/177.86 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_greaterThanAtMost__empty__iff,axiom, % 177.89/177.86 ! [V_l_2,V_k_2,T_a] : % 177.89/177.86 ( class_Orderings_Oorder(T_a) % 177.89/177.86 => ( 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)) % 177.89/177.86 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_ivl__disj__un_I20_J,axiom, % 177.89/177.86 ! [V_u_2,V_m_2,V_l_2,T_a] : % 177.89/177.86 ( class_Orderings_Olinorder(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 177.89/177.86 => 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) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_ivl__disj__int_I14_J,axiom, % 177.89/177.86 ! [V_u_2,V_m_2,V_l_2,T_a] : % 177.89/177.86 ( class_Orderings_Oorder(T_a) % 177.89/177.86 => 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)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__le__mono2,axiom, % 177.89/177.86 ! [V_k,V_n,V_m] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_n)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_m))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__mult__div__cancel1,axiom, % 177.89/177.86 ! [V_n,V_m,V_k] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__mult__self1__is__m,axiom, % 177.89/177.86 ! [V_m,V_n] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__mult__self__is__m,axiom, % 177.89/177.86 ! [V_m,V_n] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__less__dividend,axiom, % 177.89/177.86 ! [V_m,V_n] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_card__greaterThanAtMost,axiom, % 177.89/177.86 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2) ). % 177.89/177.86 % 177.89/177.86 fof(fact_com_Osize_I15_J,axiom, % 177.89/177.86 ! [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) ). % 177.89/177.86 % 177.89/177.86 fof(fact_com_Osize_I16_J,axiom, % 177.89/177.86 ! [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) ). % 177.89/177.86 % 177.89/177.86 fof(fact_com_Osize_I9_J,axiom, % 177.89/177.86 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__if,axiom, % 177.89/177.86 ! [V_m,V_n] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.89/177.86 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.89/177.86 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_div__geq,axiom, % 177.89/177.86 ! [V_m,V_n] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.89/177.86 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_split__div,axiom, % 177.89/177.86 ! [V_k_2,V_n_2,V_P_2] : % 177.89/177.86 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) % 177.89/177.86 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.86 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 177.89/177.86 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.86 => ! [B_i,B_j] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 177.89/177.86 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j) % 177.89/177.86 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_image__uminus__atLeastLessThan,axiom, % 177.89/177.86 ! [V_y_2,V_x_2,T_a] : % 177.89/177.86 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.86 => 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)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_image__uminus__greaterThanAtMost,axiom, % 177.89/177.86 ! [V_y_2,V_x_2,T_a] : % 177.89/177.86 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.86 => 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)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_ivl__disj__int_I10_J,axiom, % 177.89/177.86 ! [V_u_2,V_m_2,V_l_2,T_a] : % 177.89/177.86 ( class_Orderings_Oorder(T_a) % 177.89/177.86 => 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)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_finite__PlusD_I2_J,axiom, % 177.89/177.86 ! [V_B_2,V_A_2,T_b,T_a] : % 177.89/177.86 ( 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))) % 177.89/177.86 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_finite__PlusD_I1_J,axiom, % 177.89/177.86 ! [V_B_2,V_A_2,T_b,T_a] : % 177.89/177.86 ( 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))) % 177.89/177.86 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_finite__Plus,axiom, % 177.89/177.86 ! [V_B_2,T_b,V_A_2,T_a] : % 177.89/177.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 177.89/177.86 => 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))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_finite__Plus__iff,axiom, % 177.89/177.86 ! [V_B_2,V_A_2,T_b,T_a] : % 177.89/177.86 ( 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))) % 177.89/177.86 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.86 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_le__div__geq,axiom, % 177.89/177.86 ! [V_m,V_n] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_split__div__lemma,axiom, % 177.89/177.86 ! [V_m_2,V_q_2,V_n_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 177.89/177.86 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2)) % 177.89/177.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_q_2)))) ) % 177.89/177.86 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_split__div_H,axiom, % 177.89/177.86 ! [V_n_2,V_m_2,V_P_2] : % 177.89/177.86 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) % 177.89/177.86 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.86 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 177.89/177.86 | ? [B_q] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) % 177.89/177.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q)))) % 177.89/177.86 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_card__Plus,axiom, % 177.89/177.86 ! [V_B_2,T_b,V_A_2,T_a] : % 177.89/177.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 177.89/177.86 => 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)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_ivl__disj__un_I16_J,axiom, % 177.89/177.86 ! [V_u_2,V_m_2,V_l_2,T_a] : % 177.89/177.86 ( class_Orderings_Olinorder(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 177.89/177.86 => 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) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_com_Osize_I14_J,axiom, % 177.89/177.86 ! [V_com_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_UNIV__Plus__UNIV,axiom, % 177.89/177.86 ! [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)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Plus__eq__empty__conv,axiom, % 177.89/177.86 ! [V_B_2,V_A_2,T_b,T_a] : % 177.89/177.86 ( 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)) % 177.89/177.86 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.86 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_setprod__diff1,axiom, % 177.89/177.86 ! [V_a_2,V_f_2,V_A_2,T_a,T_b] : % 177.89/177.86 ( class_Fields_Ofield(T_b) % 177.89/177.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.86 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b) % 177.89/177.86 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.86 => 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)) ) % 177.89/177.86 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.86 => 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) ) ) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_image__atLeastZeroLessThan__int,axiom, % 177.89/177.86 ! [V_u_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) % 177.89/177.86 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,V_u_2))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_the__inv__into__into,axiom, % 177.89/177.86 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 177.89/177.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.86 => 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)) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_minus__divide__left,axiom, % 177.89/177.86 ! [V_b,V_a,T_a] : % 177.89/177.86 ( class_Rings_Odivision__ring(T_a) % 177.89/177.86 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_power__divide,axiom, % 177.89/177.86 ! [V_n,V_b,V_a,T_a] : % 177.89/177.86 ( class_Fields_Ofield__inverse__zero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_diff__divide__distrib,axiom, % 177.89/177.86 ! [V_c,V_b,V_a,T_a] : % 177.89/177.86 ( class_Rings_Odivision__ring(T_a) % 177.89/177.86 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_divide__1,axiom, % 177.89/177.86 ! [V_a,T_a] : % 177.89/177.86 ( class_Rings_Odivision__ring(T_a) % 177.89/177.86 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_add__divide__distrib,axiom, % 177.89/177.86 ! [V_c,V_b,V_a,T_a] : % 177.89/177.86 ( class_Rings_Odivision__ring(T_a) % 177.89/177.86 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_times__divide__eq__right,axiom, % 177.89/177.86 ! [V_c,V_b,V_a,T_a] : % 177.89/177.86 ( class_Rings_Odivision__ring(T_a) % 177.89/177.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_divide__zero__left,axiom, % 177.89/177.86 ! [V_a,T_a] : % 177.89/177.86 ( class_Rings_Odivision__ring(T_a) % 177.89/177.86 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_divide__zero,axiom, % 177.89/177.86 ! [V_a,T_a] : % 177.89/177.86 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__int,axiom, % 177.89/177.86 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ). % 177.89/177.86 % 177.89/177.86 fof(fact_setsum__divide__distrib,axiom, % 177.89/177.86 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 177.89/177.86 ( class_Fields_Ofield(T_a) % 177.89/177.86 => 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) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_eq__divide__imp,axiom, % 177.89/177.86 ! [V_b,V_a,V_c,T_a] : % 177.89/177.86 ( class_Rings_Odivision__ring(T_a) % 177.89/177.86 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 177.89/177.86 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_divide__eq__imp,axiom, % 177.89/177.86 ! [V_a,V_b,V_c,T_a] : % 177.89/177.86 ( class_Rings_Odivision__ring(T_a) % 177.89/177.86 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 177.89/177.86 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nonzero__divide__eq__eq,axiom, % 177.89/177.86 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 177.89/177.86 ( class_Rings_Odivision__ring(T_a) % 177.89/177.86 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2 % 177.89/177.86 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nonzero__eq__divide__eq,axiom, % 177.89/177.86 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 177.89/177.86 ( class_Rings_Odivision__ring(T_a) % 177.89/177.86 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) % 177.89/177.86 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_right__inverse__eq,axiom, % 177.89/177.86 ! [V_a_2,V_b_2,T_a] : % 177.89/177.86 ( class_Rings_Odivision__ring(T_a) % 177.89/177.86 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a) % 177.89/177.86 <=> V_a_2 = V_b_2 ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_divide__self,axiom, % 177.89/177.86 ! [V_a,T_a] : % 177.89/177.86 ( class_Rings_Odivision__ring(T_a) % 177.89/177.86 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_divide__self__if,axiom, % 177.89/177.86 ! [V_a,T_a] : % 177.89/177.86 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 177.89/177.86 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 177.89/177.86 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nonzero__minus__divide__divide,axiom, % 177.89/177.86 ! [V_a,V_b,T_a] : % 177.89/177.86 ( class_Rings_Odivision__ring(T_a) % 177.89/177.86 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nonzero__minus__divide__right,axiom, % 177.89/177.86 ! [V_a,V_b,T_a] : % 177.89/177.86 ( class_Rings_Odivision__ring(T_a) % 177.89/177.86 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nonzero__power__divide,axiom, % 177.89/177.86 ! [V_n,V_a,V_b,T_a] : % 177.89/177.86 ( class_Fields_Ofield(T_a) % 177.89/177.86 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__0,axiom, % 177.89/177.86 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__nat__int__numerals_I1_J,axiom, % 177.89/177.86 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_eq__nat__nat__iff,axiom, % 177.89/177.86 ! [V_z_H_2,V_z_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) % 177.89/177.86 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) % 177.89/177.86 <=> V_z_2 = V_z_H_2 ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__nat__int__relations_I1_J,axiom, % 177.89/177.86 ! [V_y_2,V_x_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 177.89/177.86 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) % 177.89/177.86 <=> V_x_2 = V_y_2 ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_all__nat,axiom, % 177.89/177.86 ! [V_P_2] : % 177.89/177.86 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 177.89/177.86 <=> ! [B_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 177.89/177.86 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_ex__nat,axiom, % 177.89/177.86 ! [V_P_2] : % 177.89/177.86 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 177.89/177.86 <=> ? [B_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 177.89/177.86 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_power__one__over,axiom, % 177.89/177.86 ! [V_n,V_a,T_a] : % 177.89/177.86 ( class_Fields_Ofield__inverse__zero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)),V_n) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__nat__int__numerals_I2_J,axiom, % 177.89/177.86 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__int__nat__set__return__embed,axiom, % 177.89/177.86 ! [V_A_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) = V_A_2 ). % 177.89/177.86 % 177.89/177.86 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom, % 177.89/177.86 ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_setprod__dividef,axiom, % 177.89/177.86 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 177.89/177.86 ( class_Fields_Ofield__inverse__zero(T_b) % 177.89/177.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.86 => 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)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_card__greaterThanAtMost__int,axiom, % 177.89/177.86 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom, % 177.89/177.86 ! [V_A_2,V_f_2,T_a] : % 177.89/177.86 ( ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.86 & class_Groups_Ocomm__monoid__mult(T_a) ) % 177.89/177.86 => 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)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom, % 177.89/177.86 c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__0__iff,axiom, % 177.89/177.86 ! [V_i_2] : % 177.89/177.86 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__le__0,axiom, % 177.89/177.86 ! [V_z] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.86 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zless__nat__conj,axiom, % 177.89/177.86 ! [V_z_2,V_w_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) % 177.89/177.86 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 177.89/177.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__mono__iff,axiom, % 177.89/177.86 ! [V_w_2,V_z_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__nat__int__relations_I3_J,axiom, % 177.89/177.86 ! [V_y_2,V_x_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__1,axiom, % 177.89/177.86 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_int__nat__eq,axiom, % 177.89/177.86 ! [V_z] : % 177.89/177.86 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 177.89/177.86 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) % 177.89/177.86 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 177.89/177.86 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_int__eq__iff,axiom, % 177.89/177.86 ! [V_z_2,V_m_2] : % 177.89/177.86 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 % 177.89/177.86 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2) % 177.89/177.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__0__le,axiom, % 177.89/177.86 ! [V_z] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 177.89/177.86 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zless__nat__eq__int__zless,axiom, % 177.89/177.86 ! [V_z_2,V_m_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom, % 177.89/177.86 ! [V_y,V_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.89/177.86 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__div__distrib,axiom, % 177.89/177.86 ! [V_y,V_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.89/177.86 => hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__zminus__int,axiom, % 177.89/177.86 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.86 % 177.89/177.86 fof(fact_the__inv__into__f__eq,axiom, % 177.89/177.86 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 177.89/177.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.89/177.86 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.86 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_the__inv__into__f__f,axiom, % 177.89/177.86 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 177.89/177.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.86 => 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 ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_the__inv__f__f,axiom, % 177.89/177.86 ! [V_x_2,V_f_2,T_b,T_a] : % 177.89/177.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.89/177.86 => 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 ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_inj__on__the__inv__into,axiom, % 177.89/177.86 ! [V_A_2,V_f_2,T_b,T_a] : % 177.89/177.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.89/177.86 => 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)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_the__inv__into__onto,axiom, % 177.89/177.86 ! [V_A_2,V_f_2,T_b,T_a] : % 177.89/177.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.89/177.86 => 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 ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom, % 177.89/177.86 ! [V_A_2,V_f_2,T_a] : % 177.89/177.86 ( ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.86 & class_Groups_Ocomm__monoid__mult(T_a) ) % 177.89/177.86 => 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)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_card__atLeastZeroLessThan__int,axiom, % 177.89/177.86 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) = hAPP(c_Int_Onat,V_u_2) ). % 177.89/177.86 % 177.89/177.86 fof(fact_card__atLeastLessThan__int,axiom, % 177.89/177.86 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zero__less__nat__eq,axiom, % 177.89/177.86 ! [V_z_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_power__diff,axiom, % 177.89/177.86 ! [V_m,V_n,V_a,T_a] : % 177.89/177.86 ( class_Fields_Ofield(T_a) % 177.89/177.86 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.89/177.86 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__less__eq__zless,axiom, % 177.89/177.86 ! [V_z_2,V_w_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__nat__int__relations_I2_J,axiom, % 177.89/177.86 ! [V_y_2,V_x_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__eq__iff,axiom, % 177.89/177.86 ! [V_m_2,V_w_2] : % 177.89/177.86 ( hAPP(c_Int_Onat,V_w_2) = V_m_2 % 177.89/177.86 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 177.89/177.86 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 177.89/177.86 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 177.89/177.86 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__eq__iff2,axiom, % 177.89/177.86 ! [V_w_2,V_m_2] : % 177.89/177.86 ( V_m_2 = hAPP(c_Int_Onat,V_w_2) % 177.89/177.86 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 177.89/177.86 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 177.89/177.86 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 177.89/177.86 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__le__eq__zle,axiom, % 177.89/177.86 ! [V_z_2,V_w_2] : % 177.89/177.86 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 177.89/177.86 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_split__nat,axiom, % 177.89/177.86 ! [V_i_2,V_P_2] : % 177.89/177.86 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2))) % 177.89/177.86 <=> ( ! [B_n] : % 177.89/177.86 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) % 177.89/177.86 => hBOOL(hAPP(V_P_2,B_n)) ) % 177.89/177.86 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.86 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__add__distrib,axiom, % 177.89/177.86 ! [V_z_H,V_z] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 177.89/177.86 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom, % 177.89/177.86 ! [V_y,V_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.89/177.86 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__mult__distrib,axiom, % 177.89/177.86 ! [V_z_H,V_z] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 177.89/177.86 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom, % 177.89/177.86 ! [V_y,V_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.89/177.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom, % 177.89/177.86 ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__diff__distrib,axiom, % 177.89/177.86 ! [V_z,V_z_H] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 177.89/177.86 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom, % 177.89/177.86 ! [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)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_the__inv__into__def,axiom, % 177.89/177.86 ! [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))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom, % 177.89/177.86 ! [V_n,V_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.89/177.86 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__power__eq,axiom, % 177.89/177.86 ! [V_n,V_z] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 177.89/177.86 => hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),V_n) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom, % 177.89/177.86 ! [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)) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom, % 177.89/177.86 ! [V_y,V_x] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.89/177.86 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_one__less__nat__eq,axiom, % 177.89/177.86 ! [V_z_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,V_z_2))) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__less__iff,axiom, % 177.89/177.86 ! [V_m_2,V_w_2] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) % 177.89/177.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_Suc__nat__eq__nat__zadd1,axiom, % 177.89/177.86 ! [V_z] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 177.89/177.86 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_nat__mult__distrib__neg,axiom, % 177.89/177.86 ! [V_z_H,V_z] : % 177.89/177.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.86 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_H))) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_f__the__inv__into__f,axiom, % 177.89/177.86 ! [V_y_2,V_A_2,V_f_2,T_b,T_a] : % 177.89/177.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 177.89/177.86 => 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 ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_card__greaterThanLessThan__int,axiom, % 177.89/177.86 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ). % 177.89/177.86 % 177.89/177.86 fof(fact_geometric__sum,axiom, % 177.89/177.86 ! [V_n_2,V_x_2,T_a] : % 177.89/177.86 ( class_Fields_Ofield(T_a) % 177.89/177.86 => ( V_x_2 != c_Groups_Oone__class_Oone(T_a) % 177.89/177.86 => 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))) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_le__divide__eq,axiom, % 177.89/177.86 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 177.89/177.86 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.86 => ( 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))) % 177.89/177.86 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.86 => 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)) ) % 177.89/177.86 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.86 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.86 => 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))) ) % 177.89/177.86 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_divide__le__eq,axiom, % 177.89/177.86 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 177.89/177.86 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.86 => ( 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)) % 177.89/177.86 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.86 => 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))) ) % 177.89/177.86 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.86 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.86 => 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)) ) % 177.89/177.86 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_pos__le__divide__eq,axiom, % 177.89/177.86 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 177.89/177.86 ( class_Fields_Olinordered__field(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.86 => ( 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))) % 177.89/177.86 <=> 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)) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_pos__divide__le__eq,axiom, % 177.89/177.86 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 177.89/177.86 ( class_Fields_Olinordered__field(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.86 => ( 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)) % 177.89/177.86 <=> 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))) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_mult__imp__div__pos__le,axiom, % 177.89/177.86 ! [V_z,V_x,V_y,T_a] : % 177.89/177.86 ( class_Fields_Olinordered__field(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_times__divide__times__eq,axiom, % 177.89/177.86 ! [V_w,V_z,V_y,V_x,T_a] : % 177.89/177.86 ( class_Fields_Ofield__inverse__zero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_z),V_w)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_minus__divide__divide,axiom, % 177.89/177.86 ! [V_b,V_a,T_a] : % 177.89/177.86 ( class_Fields_Ofield__inverse__zero(T_a) % 177.89/177.86 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_minus__divide__right,axiom, % 177.89/177.86 ! [V_b,V_a,T_a] : % 177.89/177.86 ( class_Fields_Ofield__inverse__zero(T_a) % 177.89/177.86 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zero__le__divide__iff,axiom, % 177.89/177.86 ! [V_b_2,V_a_2,T_a] : % 177.89/177.86 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.86 => ( 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))) % 177.89/177.86 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 177.89/177.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 177.89/177.86 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_divide__le__0__iff,axiom, % 177.89/177.86 ! [V_b_2,V_a_2,T_a] : % 177.89/177.86 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.86 => ( 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))) % 177.89/177.86 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 177.89/177.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 177.89/177.86 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_divide__right__mono,axiom, % 177.89/177.86 ! [V_c,V_b,V_a,T_a] : % 177.89/177.86 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_divide__right__mono__neg,axiom, % 177.89/177.86 ! [V_c,V_b,V_a,T_a] : % 177.89/177.86 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c))) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_zero__less__divide__iff,axiom, % 177.89/177.86 ! [V_b_2,V_a_2,T_a] : % 177.89/177.86 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.86 => ( 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))) % 177.89/177.86 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 177.89/177.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 177.89/177.86 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_divide__less__0__iff,axiom, % 177.89/177.86 ! [V_b_2,V_a_2,T_a] : % 177.89/177.86 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.86 => ( 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))) % 177.89/177.86 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 177.89/177.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 177.89/177.86 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_divide__pos__pos,axiom, % 177.89/177.86 ! [V_y,V_x,T_a] : % 177.89/177.86 ( class_Fields_Olinordered__field(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_divide__pos__neg,axiom, % 177.89/177.86 ! [V_y,V_x,T_a] : % 177.89/177.86 ( class_Fields_Olinordered__field(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_divide__neg__pos,axiom, % 177.89/177.86 ! [V_y,V_x,T_a] : % 177.89/177.86 ( class_Fields_Olinordered__field(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_divide__neg__neg,axiom, % 177.89/177.86 ! [V_y,V_x,T_a] : % 177.89/177.86 ( class_Fields_Olinordered__field(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_divide__strict__right__mono,axiom, % 177.89/177.86 ! [V_c,V_b,V_a,T_a] : % 177.89/177.86 ( class_Fields_Olinordered__field(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_divide__strict__right__mono__neg,axiom, % 177.89/177.86 ! [V_c,V_a,V_b,T_a] : % 177.89/177.86 ( class_Fields_Olinordered__field(T_a) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 177.89/177.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ). % 177.89/177.86 % 177.89/177.86 fof(fact_frac__eq__eq,axiom, % 177.89/177.86 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] : % 177.89/177.86 ( class_Fields_Ofield(T_a) % 177.89/177.86 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.86 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.87 => ( 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) % 177.89/177.87 <=> 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) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mult__divide__mult__cancel__left,axiom, % 177.89/177.87 ! [V_b,V_a,V_c,T_a] : % 177.89/177.87 ( class_Fields_Ofield__inverse__zero(T_a) % 177.89/177.87 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.87 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mult__divide__mult__cancel__right,axiom, % 177.89/177.87 ! [V_b,V_a,V_c,T_a] : % 177.89/177.87 ( class_Fields_Ofield__inverse__zero(T_a) % 177.89/177.87 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.87 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_divide__eq__eq,axiom, % 177.89/177.87 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 177.89/177.87 ( class_Fields_Ofield__inverse__zero(T_a) % 177.89/177.87 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2 % 177.89/177.87 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.87 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) ) % 177.89/177.87 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.87 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_eq__divide__eq,axiom, % 177.89/177.87 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 177.89/177.87 ( class_Fields_Ofield__inverse__zero(T_a) % 177.89/177.87 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) % 177.89/177.87 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.87 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 ) % 177.89/177.87 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.87 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_divide__nonneg__pos,axiom, % 177.89/177.87 ! [V_y,V_x,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_divide__nonneg__neg,axiom, % 177.89/177.87 ! [V_y,V_x,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_frac__less2,axiom, % 177.89/177.87 ! [V_z,V_w,V_y,V_x,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_frac__less,axiom, % 177.89/177.87 ! [V_z,V_w,V_y,V_x,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_frac__le,axiom, % 177.89/177.87 ! [V_z,V_w,V_y,V_x,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_divide__nonpos__pos,axiom, % 177.89/177.87 ! [V_y,V_x,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_divide__nonpos__neg,axiom, % 177.89/177.87 ! [V_y,V_x,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_less__divide__eq,axiom, % 177.89/177.87 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.87 => ( 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))) % 177.89/177.87 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.87 => 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)) ) % 177.89/177.87 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.87 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.87 => 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))) ) % 177.89/177.87 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_divide__less__eq,axiom, % 177.89/177.87 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.87 => ( 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)) % 177.89/177.87 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.87 => 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))) ) % 177.89/177.87 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.87 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.87 => 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)) ) % 177.89/177.87 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_pos__less__divide__eq,axiom, % 177.89/177.87 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.87 => ( 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))) % 177.89/177.87 <=> 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)) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_pos__divide__less__eq,axiom, % 177.89/177.87 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.87 => ( 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)) % 177.89/177.87 <=> 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))) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mult__imp__div__pos__less,axiom, % 177.89/177.87 ! [V_z,V_x,V_y,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mult__imp__less__div__pos,axiom, % 177.89/177.87 ! [V_x,V_z,V_y,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_neg__less__divide__eq,axiom, % 177.89/177.87 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.87 => ( 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))) % 177.89/177.87 <=> 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))) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_neg__divide__less__eq,axiom, % 177.89/177.87 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.87 => ( 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)) % 177.89/177.87 <=> 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)) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_divide__strict__left__mono,axiom, % 177.89/177.87 ! [V_c,V_a,V_b,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_divide__strict__left__mono__neg,axiom, % 177.89/177.87 ! [V_c,V_b,V_a,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_add__num__frac,axiom, % 177.89/177.87 ! [V_x,V_z,V_y,T_a] : % 177.89/177.87 ( class_Fields_Ofield__inverse__zero(T_a) % 177.89/177.87 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.87 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_add__divide__eq__iff,axiom, % 177.89/177.87 ! [V_y,V_x,V_z,T_a] : % 177.89/177.87 ( class_Fields_Ofield(T_a) % 177.89/177.87 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.87 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_add__frac__num,axiom, % 177.89/177.87 ! [V_z,V_x,V_y,T_a] : % 177.89/177.87 ( class_Fields_Ofield__inverse__zero(T_a) % 177.89/177.87 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.87 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_divide__add__eq__iff,axiom, % 177.89/177.87 ! [V_y,V_x,V_z,T_a] : % 177.89/177.87 ( class_Fields_Ofield(T_a) % 177.89/177.87 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.87 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_add__frac__eq,axiom, % 177.89/177.87 ! [V_w,V_x,V_z,V_y,T_a] : % 177.89/177.87 ( class_Fields_Ofield(T_a) % 177.89/177.87 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.87 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.87 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_diff__frac__eq,axiom, % 177.89/177.87 ! [V_w,V_x,V_z,V_y,T_a] : % 177.89/177.87 ( class_Fields_Ofield(T_a) % 177.89/177.87 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.87 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.87 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_divide__diff__eq__iff,axiom, % 177.89/177.87 ! [V_y,V_x,V_z,T_a] : % 177.89/177.87 ( class_Fields_Ofield(T_a) % 177.89/177.87 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.87 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_diff__divide__eq__iff,axiom, % 177.89/177.87 ! [V_y,V_x,V_z,T_a] : % 177.89/177.87 ( class_Fields_Ofield(T_a) % 177.89/177.87 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.87 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_gt__half__sum,axiom, % 177.89/177.87 ! [V_b,V_a,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))),V_b)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_less__half__sum,axiom, % 177.89/177.87 ! [V_b,V_a,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))))) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_divide__left__mono__neg,axiom, % 177.89/177.87 ! [V_c,V_b,V_a,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_divide__left__mono,axiom, % 177.89/177.87 ! [V_c,V_a,V_b,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_neg__divide__le__eq,axiom, % 177.89/177.87 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.87 => ( 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)) % 177.89/177.87 <=> 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)) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_neg__le__divide__eq,axiom, % 177.89/177.87 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.87 => ( 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))) % 177.89/177.87 <=> 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))) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mult__imp__le__div__pos,axiom, % 177.89/177.87 ! [V_x,V_z,V_y,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_nat__aux__def,axiom, % 177.89/177.87 ! [V_n,V_i] : c_Int_Onat__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_i)),V_n) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom, % 177.89/177.87 ! [V_B_2,V_A_2] : % 177.89/177.87 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.89/177.87 => ( c_Nat__Transfer_Onat__set(V_B_2) % 177.89/177.87 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom, % 177.89/177.87 ! [V_B_2,V_A_2] : % 177.89/177.87 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.89/177.87 => ( c_Nat__Transfer_Onat__set(V_B_2) % 177.89/177.87 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_transfer__morphism__nat__int,axiom, % 177.89/177.87 c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom, % 177.89/177.87 ! [V_f_2,V_A_2,T_a] : % 177.89/177.87 ( ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.87 & class_Groups_Ocomm__monoid__mult(T_a) ) % 177.89/177.87 => ( c_Nat__Transfer_Onat__set(V_A_2) % 177.89/177.87 => 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)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom, % 177.89/177.87 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom, % 177.89/177.87 ! [V_B_2,V_A_2] : % 177.89/177.87 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.89/177.87 => ( c_Nat__Transfer_Onat__set(V_B_2) % 177.89/177.87 => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom, % 177.89/177.87 ! [V_B_2,V_A_2] : % 177.89/177.87 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.89/177.87 => ( c_Nat__Transfer_Onat__set(V_B_2) % 177.89/177.87 => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_nat__set__def,axiom, % 177.89/177.87 ! [V_S_2] : % 177.89/177.87 ( c_Nat__Transfer_Onat__set(V_S_2) % 177.89/177.87 <=> ! [B_x] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom, % 177.89/177.87 ! [V_C_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_C_2)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_transfer__int__nat__set__relations_I3_J,axiom, % 177.89/177.87 ! [V_B_2,V_A_2] : % 177.89/177.87 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.89/177.87 => ( c_Nat__Transfer_Onat__set(V_B_2) % 177.89/177.87 => ( V_A_2 = V_B_2 % 177.89/177.87 <=> hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom, % 177.89/177.87 ! [V_x_2,V_A_2] : % 177.89/177.87 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_transfer__nat__int__set__return__embed,axiom, % 177.89/177.87 ! [V_A_2] : % 177.89/177.87 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.89/177.87 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) = V_A_2 ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_transfer__int__nat__set__relations_I1_J,axiom, % 177.89/177.87 ! [V_A_2] : % 177.89/177.87 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.89/177.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) % 177.89/177.87 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom, % 177.89/177.87 ! [V_A_2] : % 177.89/177.87 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.89/177.87 => hAPP(c_Finite__Set_Ocard(tc_Int_Oint),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_transfer__int__nat__set__relations_I5_J,axiom, % 177.89/177.87 ! [V_B_2,V_A_2] : % 177.89/177.87 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.89/177.87 => ( c_Nat__Transfer_Onat__set(V_B_2) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_transfer__int__nat__set__relations_I4_J,axiom, % 177.89/177.87 ! [V_B_2,V_A_2] : % 177.89/177.87 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.89/177.87 => ( c_Nat__Transfer_Onat__set(V_B_2) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom, % 177.89/177.87 ! [V_f_2,V_A_2,T_a] : % 177.89/177.87 ( ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.87 & class_Groups_Ocomm__monoid__mult(T_a) ) % 177.89/177.87 => ( c_Nat__Transfer_Onat__set(V_A_2) % 177.89/177.87 => 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)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_setprod__Un,axiom, % 177.89/177.87 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 177.89/177.87 ( class_Fields_Ofield(T_b) % 177.89/177.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.87 => ( ! [B_x] : % 177.89/177.87 ( 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))) % 177.89/177.87 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b) ) % 177.89/177.87 => 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))) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_transfer__int__nat__set__relations_I2_J,axiom, % 177.89/177.87 ! [V_A_2,V_x_2] : % 177.89/177.87 ( c_Nat__Transfer_Ois__nat(V_x_2) % 177.89/177.87 => ( c_Nat__Transfer_Onat__set(V_A_2) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 177.89/177.87 <=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__of__nat,axiom, % 177.89/177.87 ! [V_k,T_a] : % 177.89/177.87 ( class_Rings_Oring__1(T_a) % 177.89/177.87 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.87 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)))) ) % 177.89/177.87 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.87 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_k)) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_setsum__nonneg__0,axiom, % 177.89/177.87 ! [V_i_2,V_f_2,V_s_2,T_a,T_b] : % 177.89/177.87 ( class_Groups_Oordered__ab__group__add(T_b) % 177.89/177.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 177.89/177.87 => ( ! [B_i] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 177.89/177.87 => ( 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) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 177.89/177.87 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_setsum__nonneg__leq__bound,axiom, % 177.89/177.87 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_a,T_b] : % 177.89/177.87 ( class_Groups_Oordered__ab__group__add(T_b) % 177.89/177.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 177.89/177.87 => ( ! [B_i] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 177.89/177.87 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = V_B_2 % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__eq__iff,axiom, % 177.89/177.87 ! [V_z_2,V_w_2,T_a] : % 177.89/177.87 ( class_Int_Oring__char__0(T_a) % 177.89/177.87 => ( 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) % 177.89/177.87 <=> V_w_2 = V_z_2 ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__int__eq,axiom, % 177.89/177.87 ! [V_n] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom, % 177.89/177.87 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom, % 177.89/177.87 ! [V_y,V_x] : % 177.89/177.87 ( c_Nat__Transfer_Ois__nat(V_x) % 177.89/177.87 => ( c_Nat__Transfer_Ois__nat(V_y) % 177.89/177.87 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom, % 177.89/177.87 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom, % 177.89/177.87 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom, % 177.89/177.87 ! [V_y,V_x] : % 177.89/177.87 ( c_Nat__Transfer_Ois__nat(V_x) % 177.89/177.87 => ( c_Nat__Transfer_Ois__nat(V_y) % 177.89/177.87 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom, % 177.89/177.87 ! [V_y,V_x] : % 177.89/177.87 ( c_Nat__Transfer_Ois__nat(V_x) % 177.89/177.87 => ( c_Nat__Transfer_Ois__nat(V_y) % 177.89/177.87 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom, % 177.89/177.87 ! [V_n,V_x] : % 177.89/177.87 ( c_Nat__Transfer_Ois__nat(V_x) % 177.89/177.87 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom, % 177.89/177.87 ! [V_y,V_x] : % 177.89/177.87 ( c_Nat__Transfer_Ois__nat(V_x) % 177.89/177.87 => ( c_Nat__Transfer_Ois__nat(V_y) % 177.89/177.87 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__0,axiom, % 177.89/177.87 ! [T_a] : % 177.89/177.87 ( class_Rings_Oring__1(T_a) % 177.89/177.87 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__0__eq__iff,axiom, % 177.89/177.87 ! [V_z_2,T_a] : % 177.89/177.87 ( class_Int_Oring__char__0(T_a) % 177.89/177.87 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) % 177.89/177.87 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__eq__0__iff,axiom, % 177.89/177.87 ! [V_z_2,T_a] : % 177.89/177.87 ( class_Int_Oring__char__0(T_a) % 177.89/177.87 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.87 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__le__iff,axiom, % 177.89/177.87 ! [V_z_2,V_w_2,T_a] : % 177.89/177.87 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.87 => ( 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))) % 177.89/177.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__less__iff,axiom, % 177.89/177.87 ! [V_z_2,V_w_2,T_a] : % 177.89/177.87 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.87 => ( 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))) % 177.89/177.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__add,axiom, % 177.89/177.87 ! [V_z,V_w,T_a] : % 177.89/177.87 ( class_Rings_Oring__1(T_a) % 177.89/177.87 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__mult,axiom, % 177.89/177.87 ! [V_z,V_w,T_a] : % 177.89/177.87 ( class_Rings_Oring__1(T_a) % 177.89/177.87 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__1,axiom, % 177.89/177.87 ! [T_a] : % 177.89/177.87 ( class_Rings_Oring__1(T_a) % 177.89/177.87 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(T_a) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__diff,axiom, % 177.89/177.87 ! [V_z,V_w,T_a] : % 177.89/177.87 ( class_Rings_Oring__1(T_a) % 177.89/177.87 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__of__nat__eq,axiom, % 177.89/177.87 ! [V_n,T_a] : % 177.89/177.87 ( class_Rings_Oring__1(T_a) % 177.89/177.87 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__minus,axiom, % 177.89/177.87 ! [V_z,T_a] : % 177.89/177.87 ( class_Rings_Oring__1(T_a) % 177.89/177.87 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Ints__of__int,axiom, % 177.89/177.87 ! [V_z_2,T_a] : % 177.89/177.87 ( class_Rings_Oring__1(T_a) % 177.89/177.87 => 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))) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__power,axiom, % 177.89/177.87 ! [V_n,V_z,T_a] : % 177.89/177.87 ( class_Rings_Oring__1(T_a) % 177.89/177.87 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)),V_n) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_is__nat__def,axiom, % 177.89/177.87 ! [V_x_2] : % 177.89/177.87 ( c_Nat__Transfer_Ois__nat(V_x_2) % 177.89/177.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__setsum,axiom, % 177.89/177.87 ! [V_A_2,V_f_2,T_b,T_a] : % 177.89/177.87 ( class_Rings_Oring__1(T_a) % 177.89/177.87 => 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) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom, % 177.89/177.87 ! [V_x_2,V_A_2] : % 177.89/177.87 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 177.89/177.87 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__setprod,axiom, % 177.89/177.87 ! [V_A_2,V_f_2,T_b,T_a] : % 177.89/177.87 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 177.89/177.87 & class_Rings_Oring__1(T_a) ) % 177.89/177.87 => 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) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__0__le__iff,axiom, % 177.89/177.87 ! [V_z_2,T_a] : % 177.89/177.87 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.87 => ( 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))) % 177.89/177.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__le__0__iff,axiom, % 177.89/177.87 ! [V_z_2,T_a] : % 177.89/177.87 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.87 => ( 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))) % 177.89/177.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__0__less__iff,axiom, % 177.89/177.87 ! [V_z_2,T_a] : % 177.89/177.87 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.87 => ( 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))) % 177.89/177.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__int__less__0__iff,axiom, % 177.89/177.87 ! [V_z_2,T_a] : % 177.89/177.87 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.87 => ( 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))) % 177.89/177.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_of__nat__nat,axiom, % 177.89/177.87 ! [V_z,T_a] : % 177.89/177.87 ( class_Rings_Oring__1(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 177.89/177.87 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom, % 177.89/177.87 ! [V_f_2,V_A_2,T_a] : % 177.89/177.87 ( ! [B_x] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.87 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom, % 177.89/177.87 ! [V_f_2,V_A_2,T_a] : % 177.89/177.87 ( ! [B_x] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.87 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_greaterThan__0,axiom, % 177.89/177.87 hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_inj__vimage__singleton,axiom, % 177.89/177.87 ! [V_a_2,V_f_2,T_b,T_a] : % 177.89/177.87 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.89/177.87 => 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))))) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_sum__diff__distrib,axiom, % 177.89/177.87 ! [V_n_2,V_P_2,V_Q_2] : % 177.89/177.87 ( ! [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))) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimageI,axiom, % 177.89/177.87 ! [T_b,V_B_2,T_a,V_b_2,V_a_2,V_f_2] : % 177.89/177.87 ( hAPP(V_f_2,V_a_2) = V_b_2 % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_B_2)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimage__Un,axiom, % 177.89/177.87 ! [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)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimage__Int,axiom, % 177.89/177.87 ! [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)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimage__Diff,axiom, % 177.89/177.87 ! [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)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_greaterThan__eq__iff,axiom, % 177.89/177.87 ! [V_y_2,V_x_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2) % 177.89/177.87 <=> V_x_2 = V_y_2 ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimage__code,axiom, % 177.89/177.87 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2),V_x_2)) % 177.89/177.87 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimage__ident,axiom, % 177.89/177.87 ! [V_Y_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimage__eq,axiom, % 177.89/177.87 ! [V_B_2,V_f_2,T_b,V_a_2,T_a] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2))) % 177.89/177.87 <=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimageD,axiom, % 177.89/177.87 ! [V_A_2,V_f_2,T_b,V_a_2,T_a] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2))) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimageI2,axiom, % 177.89/177.87 ! [T_b,V_A_2,V_a_2,V_f_2,T_a] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_a_2)),V_A_2)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimage__UNIV,axiom, % 177.89/177.87 ! [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)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimage__mono,axiom, % 177.89/177.87 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.87 => 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))) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimage__empty,axiom, % 177.89/177.87 ! [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)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimage__Compl,axiom, % 177.89/177.87 ! [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)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimage__UN,axiom, % 177.89/177.87 ! [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)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimage__INT,axiom, % 177.89/177.87 ! [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)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_image__vimage__subset,axiom, % 177.89/177.87 ! [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)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_surj__image__vimage__eq,axiom, % 177.89/177.87 ! [V_A_2,V_f_2,T_a,T_b] : % 177.89/177.87 ( 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)) % 177.89/177.87 => 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 ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimage__Union,axiom, % 177.89/177.87 ! [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)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimage__singleton__eq,axiom, % 177.89/177.87 ! [V_b_2,V_f_2,T_b,V_a_2,T_a] : % 177.89/177.87 ( 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)))))) % 177.89/177.87 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimage__insert,axiom, % 177.89/177.87 ! [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)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_finite__vimageD,axiom, % 177.89/177.87 ! [V_F_2,V_h_2,T_b,T_a] : % 177.89/177.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Ovimage(T_a,T_b,V_h_2),V_F_2))) % 177.89/177.87 => ( 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)) % 177.89/177.87 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimage__subsetD,axiom, % 177.89/177.87 ! [V_A_2,V_B_2,V_f_2,T_a,T_b] : % 177.89/177.87 ( 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)) % 177.89/177.87 => ( 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)) % 177.89/177.87 => 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))) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_image__vimage__eq,axiom, % 177.89/177.87 ! [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)))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_finite__vimageI,axiom, % 177.89/177.87 ! [V_h_2,T_b,V_F_2,T_a] : % 177.89/177.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 177.89/177.87 => ( c_Fun_Oinj__on(T_b,T_a,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 177.89/177.87 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_a,V_h_2),V_F_2))) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_inj__vimage__image__eq,axiom, % 177.89/177.87 ! [V_A_2,V_f_2,T_b,T_a] : % 177.89/177.87 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.89/177.87 => 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 ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_greaterThan__iff,axiom, % 177.89/177.87 ! [V_k_2,V_i_2,T_a] : % 177.89/177.87 ( class_Orderings_Oord(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2))) % 177.89/177.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_i_2)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_greaterThan__subset__iff,axiom, % 177.89/177.87 ! [V_y_2,V_x_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => ( 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))) % 177.89/177.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimage__const,axiom, % 177.89/177.87 ! [T_b,V_A_2,V_ca_2,T_a] : % 177.89/177.87 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 177.89/177.87 => 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)) ) % 177.89/177.87 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 177.89/177.87 => 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)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimage__eq__UN,axiom, % 177.89/177.87 ! [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))))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_INT__greaterThan__UNIV,axiom, % 177.89/177.87 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimage__subsetI,axiom, % 177.89/177.87 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 177.89/177.87 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.89/177.87 => ( 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))) % 177.89/177.87 => 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)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_vimage__if,axiom, % 177.89/177.87 ! [V_B_2,T_b,V_d_2,V_A_2,V_ca_2,T_a] : % 177.89/177.87 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 177.89/177.87 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 177.89/177.87 => 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)) ) % 177.89/177.87 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 177.89/177.87 => 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 ) ) ) % 177.89/177.87 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 177.89/177.87 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 177.89/177.87 => 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) ) % 177.89/177.87 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 177.89/177.87 => 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)) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__un_I11_J,axiom, % 177.89/177.87 ! [V_u_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 177.89/177.87 => 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) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_image__uminus__greaterThan,axiom, % 177.89/177.87 ! [V_x_2,T_a] : % 177.89/177.87 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_image__uminus__lessThan,axiom, % 177.89/177.87 ! [V_x_2,T_a] : % 177.89/177.87 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__int_I5_J,axiom, % 177.89/177.87 ! [V_u_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_greaterThan__Suc,axiom, % 177.89/177.87 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_setsum__natinterval__difff,axiom, % 177.89/177.87 ! [V_f_2,V_n_2,V_m_2,T_a] : % 177.89/177.87 ( class_Groups_Oab__group__add(T_a) % 177.89/177.87 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.87 => 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)))) ) % 177.89/177.87 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.87 => 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) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_gauss__sum,axiom, % 177.89/177.87 ! [V_n_2,T_a] : % 177.89/177.87 ( class_Rings_Ocomm__semiring__1(T_a) % 177.89/177.87 => 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))) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__un_I12_J,axiom, % 177.89/177.87 ! [V_u_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 177.89/177.87 => 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) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_decr__mult__lemma,axiom, % 177.89/177.87 ! [V_k_2,V_P_2,V_d_2] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 177.89/177.87 => ( ! [B_x] : % 177.89/177.87 ( hBOOL(hAPP(V_P_2,B_x)) % 177.89/177.87 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) ) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 177.89/177.87 => ! [B_x] : % 177.89/177.87 ( hBOOL(hAPP(V_P_2,B_x)) % 177.89/177.87 => 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)))) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_negD,axiom, % 177.89/177.87 ! [V_x] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.87 => ? [B_n] : V_x = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_finite__atLeastAtMost,axiom, % 177.89/177.87 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atLeast__eq__iff,axiom, % 177.89/177.87 ! [V_y_2,V_x_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2) % 177.89/177.87 <=> V_x_2 = V_y_2 ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__un_I13_J,axiom, % 177.89/177.87 ! [V_u_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 177.89/177.87 => 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) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ex__nat__less,axiom, % 177.89/177.87 ! [V_P_2,V_n_2] : % 177.89/177.87 ( ? [B_m] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 177.89/177.87 & hBOOL(hAPP(V_P_2,B_m)) ) % 177.89/177.87 <=> ? [B_x] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) % 177.89/177.87 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_all__nat__less,axiom, % 177.89/177.87 ! [V_P_2,V_n_2] : % 177.89/177.87 ( ! [B_m] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 177.89/177.87 => hBOOL(hAPP(V_P_2,B_m)) ) % 177.89/177.87 <=> ! [B_x] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) % 177.89/177.87 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom, % 177.89/177.87 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),hAPP(c_Nat_OSuc,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atLeastatMost__empty__iff2,axiom, % 177.89/177.87 ! [V_b_2,V_a_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => ( 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) % 177.89/177.87 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atLeastatMost__empty__iff,axiom, % 177.89/177.87 ! [V_b_2,V_a_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => ( 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)) % 177.89/177.87 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atLeastatMost__empty,axiom, % 177.89/177.87 ! [V_a_2,V_b_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) % 177.89/177.87 => 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)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atLeastatMost__subset__iff,axiom, % 177.89/177.87 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => ( 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))) % 177.89/177.87 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 177.89/177.87 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 177.89/177.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atLeastAtMost__singleton_H,axiom, % 177.89/177.87 ! [V_b_2,V_a_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => ( V_a_2 = V_b_2 % 177.89/177.87 => 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))) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atLeastAtMost__singleton__iff,axiom, % 177.89/177.87 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => ( 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))) % 177.89/177.87 <=> ( V_a_2 = V_b_2 % 177.89/177.87 & V_b_2 = V_ca_2 ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atLeastAtMost__singleton,axiom, % 177.89/177.87 ! [V_a_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => 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))) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_image__uminus__atLeastAtMost,axiom, % 177.89/177.87 ! [V_y_2,V_x_2,T_a] : % 177.89/177.87 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_image__Suc__atLeastAtMost,axiom, % 177.89/177.87 ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom, % 177.89/177.87 ! [V_n_2,V_m_2,V_f_2,T_a] : % 177.89/177.87 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom, % 177.89/177.87 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 177.89/177.87 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom, % 177.89/177.87 ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2) ). % 177.89/177.87 % 177.89/177.87 fof(fact_image__add__atLeastAtMost,axiom, % 177.89/177.87 ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atLeast__iff,axiom, % 177.89/177.87 ! [V_k_2,V_i_2,T_a] : % 177.89/177.87 ( class_Orderings_Oord(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2))) % 177.89/177.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_k_2),V_i_2)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atLeast__subset__iff,axiom, % 177.89/177.87 ! [V_y_2,V_x_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => ( 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))) % 177.89/177.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atLeast__0,axiom, % 177.89/177.87 hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_card__atLeastAtMost,axiom, % 177.89/177.87 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_u_2)),V_l_2) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atLeastAtMostSuc__conv,axiom, % 177.89/177.87 ! [V_n_2,V_m_2] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 177.89/177.87 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Compl__atLeast,axiom, % 177.89/177.87 ! [V_k_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => 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) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Compl__lessThan,axiom, % 177.89/177.87 ! [V_k_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => 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) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_setsum__shift__lb__Suc0__0,axiom, % 177.89/177.87 ! [V_k_2,V_f_2] : % 177.89/177.87 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.87 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atLeast__Suc__greaterThan,axiom, % 177.89/177.87 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__un_I21_J,axiom, % 177.89/177.87 ! [V_u_2,V_m_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 177.89/177.87 => 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) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__int_I15_J,axiom, % 177.89/177.87 ! [V_u_2,V_m_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atLeastatMost__psubset__iff,axiom, % 177.89/177.87 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => ( 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))) % 177.89/177.87 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 177.89/177.87 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 177.89/177.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) % 177.89/177.87 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_a_2)) % 177.89/177.87 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_d_2)) ) ) ) % 177.89/177.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__un_I22_J,axiom, % 177.89/177.87 ! [V_u_2,V_m_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 177.89/177.87 => 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) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__int_I4_J,axiom, % 177.89/177.87 ! [V_u_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__int_I16_J,axiom, % 177.89/177.87 ! [V_u_2,V_m_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__int_I13_J,axiom, % 177.89/177.87 ! [V_u_2,V_m_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__int_I12_J,axiom, % 177.89/177.87 ! [V_u_2,V_m_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__int_I7_J,axiom, % 177.89/177.87 ! [V_u_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_setsum__head__Suc,axiom, % 177.89/177.87 ! [V_f_2,V_n_2,V_m_2,T_a] : % 177.89/177.87 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.87 => 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))) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__un_I14_J,axiom, % 177.89/177.87 ! [V_u_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 177.89/177.87 => 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) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__int_I8_J,axiom, % 177.89/177.87 ! [V_u_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_UN__atLeast__UNIV,axiom, % 177.89/177.87 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__int_I6_J,axiom, % 177.89/177.87 ! [V_u_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atLeast__Suc,axiom, % 177.89/177.87 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_setsum__cl__ivl__Suc,axiom, % 177.89/177.87 ! [V_f_2,V_m_2,V_n_2,T_a] : % 177.89/177.87 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.87 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 177.89/177.87 => 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) ) % 177.89/177.87 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 177.89/177.87 => 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))) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_setsum__head,axiom, % 177.89/177.87 ! [V_P_2,V_n_2,V_m_2,T_a] : % 177.89/177.87 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.87 => 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))) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_setsum__ub__add__nat,axiom, % 177.89/177.87 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_a] : % 177.89/177.87 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) % 177.89/177.87 => 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)))) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__un_I6_J,axiom, % 177.89/177.87 ! [V_u_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 177.89/177.87 => 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) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__un_I5_J,axiom, % 177.89/177.87 ! [V_u_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 177.89/177.87 => 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) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__un_I18_J,axiom, % 177.89/177.87 ! [V_u_2,V_m_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 177.89/177.87 => 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) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__un_I1_J,axiom, % 177.89/177.87 ! [V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => 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) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__un_I19_J,axiom, % 177.89/177.87 ! [V_u_2,V_m_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 177.89/177.87 => 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) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_UN__le__eq__Un0,axiom, % 177.89/177.87 ! [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))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_incr__mult__lemma,axiom, % 177.89/177.87 ! [V_k_2,V_P_2,V_d_2] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 177.89/177.87 => ( ! [B_x] : % 177.89/177.87 ( hBOOL(hAPP(V_P_2,B_x)) % 177.89/177.87 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) ) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 177.89/177.87 => ! [B_x] : % 177.89/177.87 ( hBOOL(hAPP(V_P_2,B_x)) % 177.89/177.87 => 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)))) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ex__least__nat__less,axiom, % 177.89/177.87 ! [V_n_2,V_P_2] : % 177.89/177.87 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 177.89/177.87 => ( hBOOL(hAPP(V_P_2,V_n_2)) % 177.89/177.87 => ? [B_k] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) % 177.89/177.87 & ! [B_i] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) % 177.89/177.87 => ~ hBOOL(hAPP(V_P_2,B_i)) ) % 177.89/177.87 & 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)))) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_setprod__mono__one__left,axiom, % 177.89/177.87 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 177.89/177.87 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 177.89/177.87 => ( ! [B_x] : % 177.89/177.87 ( 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))) % 177.89/177.87 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 177.89/177.87 => 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) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_setprod__mono__one__right,axiom, % 177.89/177.87 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 177.89/177.87 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 177.89/177.87 => ( ! [B_x] : % 177.89/177.87 ( 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))) % 177.89/177.87 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 177.89/177.87 => 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) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_finite__atLeastAtMost__int,axiom, % 177.89/177.87 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_finite__atMost,axiom, % 177.89/177.87 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atMost__eq__iff,axiom, % 177.89/177.87 ! [V_y_2,V_x_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2) % 177.89/177.87 <=> V_x_2 = V_y_2 ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom, % 177.89/177.87 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom, % 177.89/177.87 ! [V_y_2,V_x_2] : % 177.89/177.87 ( c_Nat__Transfer_Ois__nat(V_x_2) % 177.89/177.87 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atLeast0AtMost,axiom, % 177.89/177.87 ! [V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) ). % 177.89/177.87 % 177.89/177.87 fof(fact_lessThan__Suc__atMost,axiom, % 177.89/177.87 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2) ). % 177.89/177.87 % 177.89/177.87 fof(fact_card__atMost,axiom, % 177.89/177.87 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_u_2)) = hAPP(c_Nat_OSuc,V_u_2) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atMost__Suc,axiom, % 177.89/177.87 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atMost__iff,axiom, % 177.89/177.87 ! [V_k_2,V_i_2,T_a] : % 177.89/177.87 ( class_Orderings_Oord(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2))) % 177.89/177.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_k_2)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atMost__subset__iff,axiom, % 177.89/177.87 ! [V_y_2,V_x_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => ( 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))) % 177.89/177.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom, % 177.89/177.87 ! [V_y_2,V_x_2] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 177.89/177.87 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom, % 177.89/177.87 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_u_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Compl__atMost,axiom, % 177.89/177.87 ! [V_k_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => 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) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Compl__greaterThan,axiom, % 177.89/177.87 ! [V_k_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => 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) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom, % 177.89/177.87 ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2) ). % 177.89/177.87 % 177.89/177.87 fof(fact_UN__atMost__UNIV,axiom, % 177.89/177.87 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom, % 177.89/177.87 ! [V_n_2,V_m_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_setsum__atMost__Suc,axiom, % 177.89/177.87 ! [V_n_2,V_f_2,T_a] : % 177.89/177.87 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.87 => 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))) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atMost__0,axiom, % 177.89/177.87 hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_simp__from__to,axiom, % 177.89/177.87 ! [V_i_2,V_j_2] : % 177.89/177.87 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 177.89/177.87 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) ) % 177.89/177.87 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 177.89/177.87 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),V_i_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__un_I9_J,axiom, % 177.89/177.87 ! [V_u_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 177.89/177.87 => 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) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_UN__le__add__shift,axiom, % 177.89/177.87 ! [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) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__int_I3_J,axiom, % 177.89/177.87 ! [V_u_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__int_I1_J,axiom, % 177.89/177.87 ! [V_u_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_image__uminus__atLeast,axiom, % 177.89/177.87 ! [V_x_2,T_a] : % 177.89/177.87 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_image__uminus__atMost,axiom, % 177.89/177.87 ! [V_x_2,T_a] : % 177.89/177.87 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_card__atLeastAtMost__int,axiom, % 177.89/177.87 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom, % 177.89/177.87 ! [V_n_2,V_m_2] : % 177.89/177.87 ( c_Nat__Transfer_Ois__nat(V_m_2) % 177.89/177.87 => ( c_Nat__Transfer_Ois__nat(V_n_2) % 177.89/177.87 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,V_m_2),hAPP(c_Int_Onat,V_n_2))) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__un_I2_J,axiom, % 177.89/177.87 ! [V_u_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => 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) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__un_I10_J,axiom, % 177.89/177.87 ! [V_u_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 177.89/177.87 => 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) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_atMost__Int__atLeast,axiom, % 177.89/177.87 ! [V_n_2,T_a] : % 177.89/177.87 ( class_Orderings_Oorder(T_a) % 177.89/177.87 => 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))) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_ivl__disj__un_I7_J,axiom, % 177.89/177.87 ! [V_u_2,V_l_2,T_a] : % 177.89/177.87 ( class_Orderings_Olinorder(T_a) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 177.89/177.87 => 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) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_bset_I8_J,axiom, % 177.89/177.87 ! [V_B_2,V_t_2,V_D_2] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2)) % 177.89/177.87 => ! [B_x] : % 177.89/177.87 ( ! [B_xa] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 177.89/177.87 => ! [B_xb] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 177.89/177.87 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_aset_I6_J,axiom, % 177.89/177.87 ! [V_A_2,V_t_2,V_D_2] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2)) % 177.89/177.87 => ! [B_x] : % 177.89/177.87 ( ! [B_xa] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 177.89/177.87 => ! [B_xb] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 177.89/177.87 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_aset_I4_J,axiom, % 177.89/177.87 ! [V_A_2,V_t_2,V_D_2] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 177.89/177.87 => ! [B_x] : % 177.89/177.87 ( ! [B_xa] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 177.89/177.87 => ! [B_xb] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 177.89/177.87 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 177.89/177.87 => ( B_x != V_t_2 % 177.89/177.87 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_bset_I4_J,axiom, % 177.89/177.87 ! [V_B_2,V_t_2,V_D_2] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 177.89/177.87 => ! [B_x] : % 177.89/177.87 ( ! [B_xa] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 177.89/177.87 => ! [B_xb] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 177.89/177.87 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 177.89/177.87 => ( B_x != V_t_2 % 177.89/177.87 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_bset_I3_J,axiom, % 177.89/177.87 ! [V_B_2,V_t_2,V_D_2] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2)) % 177.89/177.87 => ( ! [B_x] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 177.89/177.87 => ! [B_xa] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) % 177.89/177.87 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) ) % 177.89/177.87 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_aset_I3_J,axiom, % 177.89/177.87 ! [V_A_2,V_t_2,V_D_2] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2)) % 177.89/177.87 => ( ! [B_x] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 177.89/177.87 => ! [B_xa] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) % 177.89/177.87 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) ) % 177.89/177.87 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_aset_I5_J,axiom, % 177.89/177.87 ! [V_A_2,V_t_2,V_D_2] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 177.89/177.87 => ! [B_x] : % 177.89/177.87 ( ! [B_xa] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 177.89/177.87 => ! [B_xb] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 177.89/177.87 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_bset_I7_J,axiom, % 177.89/177.87 ! [V_B_2,V_t_2,V_D_2] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 177.89/177.87 => ! [B_x] : % 177.89/177.87 ( ! [B_xa] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 177.89/177.87 => ! [B_xb] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 177.89/177.87 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_bset_I6_J,axiom, % 177.89/177.87 ! [V_t_2,V_B_2,V_D_2] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.89/177.87 => ! [B_x] : % 177.89/177.87 ( ! [B_xa] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 177.89/177.87 => ! [B_xb] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 177.89/177.87 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_aset_I8_J,axiom, % 177.89/177.87 ! [V_t_2,V_A_2,V_D_2] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.89/177.87 => ! [B_x] : % 177.89/177.87 ( ! [B_xa] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 177.89/177.87 => ! [B_xb] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 177.89/177.87 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_periodic__finite__ex,axiom, % 177.89/177.87 ! [V_P_2,V_d_2] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 177.89/177.87 => ( ! [B_x,B_k] : % 177.89/177.87 ( hBOOL(hAPP(V_P_2,B_x)) % 177.89/177.87 <=> 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)))) ) % 177.89/177.87 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 177.89/177.87 <=> ? [B_x] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2))) % 177.89/177.87 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_bset_I5_J,axiom, % 177.89/177.87 ! [V_t_2,V_B_2,V_D_2] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.89/177.87 => ! [B_x] : % 177.89/177.87 ( ! [B_xa] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 177.89/177.87 => ! [B_xb] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 177.89/177.87 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_aset_I7_J,axiom, % 177.89/177.87 ! [V_t_2,V_A_2,V_D_2] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.89/177.87 => ! [B_x] : % 177.89/177.87 ( ! [B_xa] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 177.89/177.87 => ! [B_xb] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 177.89/177.87 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_zero__less__imp__eq__int,axiom, % 177.89/177.87 ! [V_k] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 177.89/177.87 => ? [B_n] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 177.89/177.87 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_setsum__mono__zero__left,axiom, % 177.89/177.87 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 177.89/177.87 ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 177.89/177.87 => ( ! [B_x] : % 177.89/177.87 ( 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))) % 177.89/177.87 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 177.89/177.87 => 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) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_setsum__mono__zero__right,axiom, % 177.89/177.87 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 177.89/177.87 ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 177.89/177.87 => ( ! [B_x] : % 177.89/177.87 ( 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))) % 177.89/177.87 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 177.89/177.87 => 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) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_card__Pow,axiom, % 177.89/177.87 ! [V_A_2,T_a] : % 177.89/177.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.87 => 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)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_finite__subset__induct,axiom, % 177.89/177.87 ! [V_P_2,V_A_2,V_F_2,T_a] : % 177.89/177.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_A_2)) % 177.89/177.87 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 177.89/177.87 => ( ! [B_a,B_F] : % 177.89/177.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 177.89/177.87 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_F)) % 177.89/177.87 => ( hBOOL(hAPP(V_P_2,B_F)) % 177.89/177.87 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_F))) ) ) ) ) % 177.89/177.87 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_setsum__strict__mono,axiom, % 177.89/177.87 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 177.89/177.87 ( ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.87 & class_Groups_Oordered__cancel__ab__semigroup__add(T_b) ) % 177.89/177.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.87 => ( ! [B_x] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 177.89/177.87 => 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))) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_field__le__mult__one__interval,axiom, % 177.89/177.87 ! [V_y,V_x,T_a] : % 177.89/177.87 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.87 => ( ! [B_z] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) % 177.89/177.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_z),V_x)),V_y)) ) ) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_PowI,axiom, % 177.89/177.87 ! [V_B_2,V_A_2,T_a] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_image__Pow__surj,axiom, % 177.89/177.87 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : % 177.89/177.87 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_B_2 % 177.89/177.87 => 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) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Pow__top,axiom, % 177.89/177.87 ! [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))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Union__Pow__eq,axiom, % 177.89/177.87 ! [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 ). % 177.89/177.87 % 177.89/177.87 fof(fact_Cantors__paradox,axiom, % 177.89/177.87 ! [V_A_2,T_a] : % 177.89/177.87 ~ ? [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) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Pow__not__empty,axiom, % 177.89/177.87 ! [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)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Pow__INT__eq,axiom, % 177.89/177.87 ! [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)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Pow__bottom,axiom, % 177.89/177.87 ! [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))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Pow__iff,axiom, % 177.89/177.87 ! [V_B_2,V_A_2,T_a] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 177.89/177.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_PowD,axiom, % 177.89/177.87 ! [V_B_2,V_A_2,T_a] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 177.89/177.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Pow__mono,axiom, % 177.89/177.87 ! [V_B_2,V_A_2,T_a] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.87 => 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))) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_finite__Pow__iff,axiom, % 177.89/177.87 ! [V_A_2,T_a] : % 177.89/177.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2))) % 177.89/177.87 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_subset__Pow__Union,axiom, % 177.89/177.87 ! [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)))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Pow__insert,axiom, % 177.89/177.87 ! [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))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Pow__UNIV,axiom, % 177.89/177.87 ! [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)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_UN__Pow__subset,axiom, % 177.89/177.87 ! [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)))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Pow__Int__eq,axiom, % 177.89/177.87 ! [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)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_image__Pow__mono,axiom, % 177.89/177.87 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 177.89/177.87 ( 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)) % 177.89/177.87 => 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))) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Pow__empty,axiom, % 177.89/177.87 ! [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))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Un__Pow__subset,axiom, % 177.89/177.87 ! [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)))) ). % 177.89/177.87 % 177.89/177.87 fof(fact_Powp__Pow__eq,axiom, % 177.89/177.87 ! [V_x_2,V_A_2,T_a] : % 177.89/177.87 ( 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)) % 177.89/177.87 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_a),V_A_2))) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_card__partition,axiom, % 177.89/177.87 ! [V_k_2,V_C_2,T_a] : % 177.89/177.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) % 177.89/177.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 177.89/177.87 => ( ! [B_c] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c),V_C_2)) % 177.89/177.87 => hAPP(c_Finite__Set_Ocard(T_a),B_c) = V_k_2 ) % 177.89/177.87 => ( ! [B_c1] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c1),V_C_2)) % 177.89/177.87 => ! [B_c2] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c2),V_C_2)) % 177.89/177.87 => ( B_c1 != B_c2 % 177.89/177.87 => 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)) ) ) ) % 177.89/177.87 => 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)) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom, % 177.89/177.87 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 177.89/177.87 ( ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.87 & class_Groups_Ocomm__monoid__mult(T_a) ) % 177.89/177.87 => ( V_A_2 = V_B_2 % 177.89/177.87 => ( c_Nat__Transfer_Onat__set(V_B_2) % 177.89/177.87 => ( ! [B_x] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 177.89/177.87 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 177.89/177.87 => 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) ) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_split__neg__lemma,axiom, % 177.89/177.87 ! [V_n_2,V_P_2,V_k_2] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.87 => ( 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))) % 177.89/177.87 <=> ! [B_i,B_j] : % 177.89/177.87 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 177.89/177.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.87 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 177.89/177.87 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_split__pos__lemma,axiom, % 177.89/177.87 ! [V_n_2,V_P_2,V_k_2] : % 177.89/177.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 177.89/177.87 => ( 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))) % 177.89/177.87 <=> ! [B_i,B_j] : % 177.89/177.87 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 177.89/177.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 177.89/177.87 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 177.89/177.87 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__diff__cong,axiom, % 177.89/177.87 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 177.89/177.87 ( class_Divides_Oring__div(T_a) % 177.89/177.87 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 177.89/177.87 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_H),V_b_H),V_c) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__diff__eq,axiom, % 177.89/177.87 ! [V_c,V_b,V_a,T_a] : % 177.89/177.87 ( class_Divides_Oring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__diff__left__eq,axiom, % 177.89/177.87 ! [V_c,V_b,V_a,T_a] : % 177.89/177.87 ( class_Divides_Oring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__diff__right__eq,axiom, % 177.89/177.87 ! [V_c,V_b,V_a,T_a] : % 177.89/177.87 ( class_Divides_Oring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_zdiff__zmod__right,axiom, % 177.89/177.87 ! [V_m,V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m) ). % 177.89/177.87 % 177.89/177.87 fof(fact_zdiff__zmod__left,axiom, % 177.89/177.87 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m) ). % 177.89/177.87 % 177.89/177.87 fof(fact_zmod__zmult1__eq,axiom, % 177.89/177.87 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) ). % 177.89/177.87 % 177.89/177.87 fof(fact_zmod__simps_I3_J,axiom, % 177.89/177.87 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) ). % 177.89/177.87 % 177.89/177.87 fof(fact_zmod__zminus2,axiom, % 177.89/177.87 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_zmod__zminus__zminus,axiom, % 177.89/177.87 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ). % 177.89/177.87 % 177.89/177.87 fof(fact_zminus__zmod,axiom, % 177.89/177.87 ! [V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_x),V_m) ). % 177.89/177.87 % 177.89/177.87 fof(fact_zmod__zero,axiom, % 177.89/177.87 ! [V_b] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 177.89/177.87 % 177.89/177.87 fof(fact_zmod__self,axiom, % 177.89/177.87 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__minus__cong,axiom, % 177.89/177.87 ! [V_a_H,V_b,V_a,T_a] : % 177.89/177.87 ( class_Divides_Oring__div(T_a) % 177.89/177.87 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_H),V_b) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__minus__eq,axiom, % 177.89/177.87 ! [V_b,V_a,T_a] : % 177.89/177.87 ( class_Divides_Oring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__mult__right__eq,axiom, % 177.89/177.87 ! [V_c,V_b,V_a,T_a] : % 177.89/177.87 ( class_Divides_Osemiring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__mult__left__eq,axiom, % 177.89/177.87 ! [V_c,V_b,V_a,T_a] : % 177.89/177.87 ( class_Divides_Osemiring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__mult__eq,axiom, % 177.89/177.87 ! [V_c,V_b,V_a,T_a] : % 177.89/177.87 ( class_Divides_Osemiring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__mult__mult1,axiom, % 177.89/177.87 ! [V_b,V_a,V_c,T_a] : % 177.89/177.87 ( class_Divides_Osemiring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__mult__mult2,axiom, % 177.89/177.87 ! [V_b,V_c,V_a,T_a] : % 177.89/177.87 ( class_Divides_Osemiring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_zmod__simps_I4_J,axiom, % 177.89/177.87 ! [V_b,V_c,V_a,T_a] : % 177.89/177.87 ( class_Divides_Osemiring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__mult__cong,axiom, % 177.89/177.87 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 177.89/177.87 ( class_Divides_Osemiring__div(T_a) % 177.89/177.87 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 177.89/177.87 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c) ) ) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__mod__trivial,axiom, % 177.89/177.87 ! [V_b,V_a,T_a] : % 177.89/177.87 ( class_Divides_Osemiring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__0,axiom, % 177.89/177.87 ! [V_a,T_a] : % 177.89/177.87 ( class_Divides_Osemiring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__by__0,axiom, % 177.89/177.87 ! [V_a,T_a] : % 177.89/177.87 ( class_Divides_Osemiring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__self,axiom, % 177.89/177.87 ! [V_a,T_a] : % 177.89/177.87 ( class_Divides_Osemiring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__add__self2,axiom, % 177.89/177.87 ! [V_b,V_a,T_a] : % 177.89/177.87 ( class_Divides_Osemiring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__add__self1,axiom, % 177.89/177.87 ! [V_a,V_b,T_a] : % 177.89/177.87 ( class_Divides_Osemiring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__add__right__eq,axiom, % 177.89/177.87 ! [V_c,V_b,V_a,T_a] : % 177.89/177.87 ( class_Divides_Osemiring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__add__left__eq,axiom, % 177.89/177.87 ! [V_c,V_b,V_a,T_a] : % 177.89/177.87 ( class_Divides_Osemiring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__add__eq,axiom, % 177.89/177.87 ! [V_c,V_b,V_a,T_a] : % 177.89/177.87 ( class_Divides_Osemiring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_zmod__simps_I2_J,axiom, % 177.89/177.87 ! [V_c,V_b,V_a,T_a] : % 177.89/177.87 ( class_Divides_Osemiring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_zmod__simps_I1_J,axiom, % 177.89/177.87 ! [V_b,V_c,V_a,T_a] : % 177.89/177.87 ( class_Divides_Osemiring__div(T_a) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ) ). % 177.89/177.87 % 177.89/177.87 fof(fact_mod__add__cong,axiom, % 177.89/177.87 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 177.89/177.87 ( class_Divides_Osemiring__div(T_a) % 177.89/177.87 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 177.89/177.87 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 177.89/177.87 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zpower__zmod,axiom, % 177.89/177.88 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom, % 177.89/177.88 ! [V_y,V_x] : % 177.89/177.88 ( c_Nat__Transfer_Ois__nat(V_x) % 177.89/177.88 => ( c_Nat__Transfer_Ois__nat(V_y) % 177.89/177.88 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__mult__self2__is__0,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Divides_Osemiring__div(T_a) % 177.89/177.88 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__mult__self1__is__0,axiom, % 177.89/177.88 ! [V_a,V_b,T_a] : % 177.89/177.88 ( class_Divides_Osemiring__div(T_a) % 177.89/177.88 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__mult__self1,axiom, % 177.89/177.88 ! [V_b,V_c,V_a,T_a] : % 177.89/177.88 ( class_Divides_Osemiring__div(T_a) % 177.89/177.88 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__mult__self2,axiom, % 177.89/177.88 ! [V_c,V_b,V_a,T_a] : % 177.89/177.88 ( class_Divides_Osemiring__div(T_a) % 177.89/177.88 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__by__1,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Divides_Osemiring__div(T_a) % 177.89/177.88 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__div__trivial,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Divides_Osemiring__div(T_a) % 177.89/177.88 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom, % 177.89/177.88 ! [V_y,V_x] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zmod__le__nonneg__dividend,axiom, % 177.89/177.88 ! [V_k,V_m] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k)),V_m)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_neg__mod__bound,axiom, % 177.89/177.88 ! [V_a,V_b] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_pos__mod__bound,axiom, % 177.89/177.88 ! [V_a,V_b] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zmod__eq__0__iff,axiom, % 177.89/177.88 ! [V_d_2,V_m_2] : % 177.89/177.88 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.88 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zmod__zminus2__not__zero,axiom, % 177.89/177.88 ! [V_l,V_k] : % 177.89/177.88 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zmod__zminus1__not__zero,axiom, % 177.89/177.88 ! [V_l,V_k] : % 177.89/177.88 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_DIVISION__BY__ZERO,axiom, % 177.89/177.88 ! [V_a] : % 177.89/177.88 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.88 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zmod__zdiv__trivial,axiom, % 177.89/177.88 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zdiv__zadd1__eq,axiom, % 177.89/177.88 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_semiring__div__class_Omod__div__equality_H,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Divides_Osemiring__div(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)) = V_a ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__div__equality2,axiom, % 177.89/177.88 ! [V_a,V_b,T_a] : % 177.89/177.88 ( class_Divides_Osemiring__div(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__div__equality,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Divides_Osemiring__div(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_div__mod__equality2,axiom, % 177.89/177.88 ! [V_c,V_a,V_b,T_a] : % 177.89/177.88 ( class_Divides_Osemiring__div(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_div__mod__equality,axiom, % 177.89/177.88 ! [V_c,V_b,V_a,T_a] : % 177.89/177.88 ( class_Divides_Osemiring__div(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__neg__neg__trivial,axiom, % 177.89/177.88 ! [V_b,V_a] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_neg__mod__conj,axiom, % 177.89/177.88 ! [V_a,V_b] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.88 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_neg__mod__sign,axiom, % 177.89/177.88 ! [V_a,V_b] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__pos__pos__trivial,axiom, % 177.89/177.88 ! [V_b,V_a] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_pos__mod__conj,axiom, % 177.89/177.88 ! [V_a,V_b] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) % 177.89/177.88 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_pos__mod__sign,axiom, % 177.89/177.88 ! [V_a,V_b] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zmod__zminus1__eq__if,axiom, % 177.89/177.88 ! [V_b,V_a] : % 177.89/177.88 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 177.89/177.88 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zmod__zminus2__eq__if,axiom, % 177.89/177.88 ! [V_b,V_a] : % 177.89/177.88 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 177.89/177.88 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zdiv__zmod__equality2,axiom, % 177.89/177.88 ! [V_k,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zdiv__zmod__equality,axiom, % 177.89/177.88 ! [V_k,V_a,V_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zdiv__zmult1__eq,axiom, % 177.89/177.88 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zmod__zdiv__equality,axiom, % 177.89/177.88 ! [V_b,V_a] : V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zmod__zdiv__equality_H,axiom, % 177.89/177.88 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)),V_n)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zmult__div__cancel,axiom, % 177.89/177.88 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__pos__neg__trivial,axiom, % 177.89/177.88 ! [V_b,V_a] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_split__zmod,axiom, % 177.89/177.88 ! [V_k_2,V_n_2,V_P_2] : % 177.89/177.88 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 177.89/177.88 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.88 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 177.89/177.88 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 177.89/177.88 => ! [B_i,B_j] : % 177.89/177.88 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 177.89/177.88 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 177.89/177.88 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 177.89/177.88 => hBOOL(hAPP(V_P_2,B_j)) ) ) % 177.89/177.88 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.88 => ! [B_i,B_j] : % 177.89/177.88 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 177.89/177.88 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.88 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 177.89/177.88 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zmult2__lemma__aux3,axiom, % 177.89/177.88 ! [V_q,V_b,V_r,V_c] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zmult2__lemma__aux4,axiom, % 177.89/177.88 ! [V_q,V_b,V_r,V_c] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zmult2__lemma__aux1,axiom, % 177.89/177.88 ! [V_q,V_r,V_b,V_c] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zmult2__lemma__aux2,axiom, % 177.89/177.88 ! [V_q,V_r,V_b,V_c] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_divmod__int__rel__mod__eq,axiom, % 177.89/177.88 ! [V_y,V_q_1,V_b_1,V_a_1] : % 177.89/177.88 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_q_1)),V_y) % 177.89/177.88 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.89/177.88 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) % 177.89/177.88 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 177.89/177.88 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zmod__zmult2__eq,axiom, % 177.89/177.88 ! [V_b,V_a,V_c] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zdiv__zminus1__eq__if,axiom, % 177.89/177.88 ! [V_a,V_b] : % 177.89/177.88 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.88 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.88 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) % 177.89/177.88 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.88 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zdiv__zminus2__eq__if,axiom, % 177.89/177.88 ! [V_a,V_b] : % 177.89/177.88 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.88 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.88 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) % 177.89/177.88 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.88 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_z3mod__def,axiom, % 177.89/177.88 ! [V_k,V_l] : % 177.89/177.88 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 177.89/177.88 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 177.89/177.88 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_sgn__neg,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.88 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_sgn__1__neg,axiom, % 177.89/177.88 ! [V_a_2,T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => ( 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)) % 177.89/177.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_sgn__if,axiom, % 177.89/177.88 ! [V_x,T_a] : % 177.89/177.88 ( class_Groups_Osgn__if(T_a) % 177.89/177.88 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.88 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) % 177.89/177.88 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.88 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.89/177.88 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.89/177.88 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__Suc__eq__Suc__mod,axiom, % 177.89/177.88 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__less,axiom, % 177.89/177.88 ! [V_n,V_m] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__less__eq__dividend,axiom, % 177.89/177.88 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_m)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__mult__distrib2,axiom, % 177.89/177.88 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__mult__distrib,axiom, % 177.89/177.88 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_k) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_sgn__sgn,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_sgn0,axiom, % 177.89/177.88 ! [T_a] : % 177.89/177.88 ( class_Groups_Osgn__if(T_a) % 177.89/177.88 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_sgn__0__0,axiom, % 177.89/177.88 ! [V_a_2,T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.88 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_sgn__times,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__1,axiom, % 177.89/177.88 ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__Suc,axiom, % 177.89/177.88 ! [V_n,V_m] : % 177.89/177.88 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.89/177.88 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__less__divisor,axiom, % 177.89/177.88 ! [V_m,V_n] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__eq__0__iff,axiom, % 177.89/177.88 ! [V_d_2,V_m_2] : % 177.89/177.88 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.88 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__if,axiom, % 177.89/177.88 ! [V_n,V_m] : % 177.89/177.88 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__geq,axiom, % 177.89/177.88 ! [V_n,V_m] : % 177.89/177.88 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__mult__self3,axiom, % 177.89/177.88 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) ). % 177.89/177.88 % 177.89/177.88 fof(fact_le__mod__geq,axiom, % 177.89/177.88 ! [V_m,V_n] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zmod__int,axiom, % 177.89/177.88 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom, % 177.89/177.88 ! [V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_div__add1__eq,axiom, % 177.89/177.88 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__le__divisor,axiom, % 177.89/177.88 ! [V_m,V_n] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__mult__self4,axiom, % 177.89/177.88 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m)),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) ). % 177.89/177.88 % 177.89/177.88 fof(fact_sgn__less,axiom, % 177.89/177.88 ! [V_a_2,T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_sgn__greater,axiom, % 177.89/177.88 ! [V_a_2,T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_div__mult1__eq,axiom, % 177.89/177.88 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__mult2__eq,axiom, % 177.89/177.88 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Divides_Omod__div__equality_H,axiom, % 177.89/177.88 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mult__div__cancel,axiom, % 177.89/177.88 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_div__mod__equality_H,axiom, % 177.89/177.88 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__lemma,axiom, % 177.89/177.88 ! [V_q,V_b,V_r,V_c] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_split__mod,axiom, % 177.89/177.88 ! [V_k_2,V_n_2,V_P_2] : % 177.89/177.88 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) % 177.89/177.88 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.88 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 177.89/177.88 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.88 => ! [B_i,B_j] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 177.89/177.88 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j) % 177.89/177.88 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Suc__times__mod__eq,axiom, % 177.89/177.88 ! [V_m,V_k] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_nat__mod__distrib,axiom, % 177.89/177.88 ! [V_y,V_x] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.89/177.88 => hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom, % 177.89/177.88 ! [V_y,V_x] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_sgn__1__pos,axiom, % 177.89/177.88 ! [V_a_2,T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a) % 177.89/177.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_sgn__pos,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.88 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zsgn__def,axiom, % 177.89/177.88 ! [V_i] : % 177.89/177.88 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.88 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 177.89/177.88 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.88 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 177.89/177.88 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 177.89/177.88 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_incr__lemma,axiom, % 177.89/177.88 ! [V_x,V_z,V_d] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_decr__lemma,axiom, % 177.89/177.88 ! [V_z,V_x,V_d] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))),V_z)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom, % 177.89/177.88 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 177.89/177.88 ( ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.88 & class_Groups_Ocomm__monoid__mult(T_a) ) % 177.89/177.88 => ( V_A_2 = V_B_2 % 177.89/177.88 => ( c_Nat__Transfer_Onat__set(V_B_2) % 177.89/177.88 => ( ! [B_x] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 177.89/177.88 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 177.89/177.88 => 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) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_diff__Suc,axiom, % 177.89/177.88 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_setsum__abs,axiom, % 177.89/177.88 ! [V_A_2,V_f_2,T_b,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => 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))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_setsum__abs__ge__zero,axiom, % 177.89/177.88 ! [V_A_2,V_f_2,T_b,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => 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))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__minus__commute,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__divide,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__int__eq,axiom, % 177.89/177.88 ! [V_m] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m) ). % 177.89/177.88 % 177.89/177.88 fof(fact_power__abs,axiom, % 177.89/177.88 ! [V_n,V_a,T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__of__nat,axiom, % 177.89/177.88 ! [V_n,T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__minus__cancel,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__zero,axiom, % 177.89/177.88 ! [T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__eq__0,axiom, % 177.89/177.88 ! [V_a_2,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.88 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__idempotent,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__one,axiom, % 177.89/177.88 ! [T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__mult,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__mult__self,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__add__abs,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__le__D1,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__ge__self,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__setsum__abs,axiom, % 177.89/177.88 ! [V_A_2,V_f_2,T_b,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => 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) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__setprod,axiom, % 177.89/177.88 ! [V_A_2,V_f_2,T_b,T_a] : % 177.89/177.88 ( class_Fields_Olinordered__field(T_a) % 177.89/177.88 => 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) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__ge__zero,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__le__zero__iff,axiom, % 177.89/177.88 ! [V_a_2,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__of__nonneg,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__not__less__zero,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zero__less__abs__iff,axiom, % 177.89/177.88 ! [V_a_2,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__of__pos,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__triangle__ineq,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__mult__less,axiom, % 177.89/177.88 ! [V_d,V_b,V_c,V_a,T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__triangle__ineq3,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__triangle__ineq2,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__triangle__ineq2__sym,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__ge__minus__self,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__le__iff,axiom, % 177.89/177.88 ! [V_b_2,V_a_2,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => ( 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)) % 177.89/177.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 177.89/177.88 & 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)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__leI,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__le__D2,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__less__iff,axiom, % 177.89/177.88 ! [V_b_2,V_a_2,T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2)) % 177.89/177.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 177.89/177.88 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_nonzero__abs__divide,axiom, % 177.89/177.88 ! [V_a,V_b,T_a] : % 177.89/177.88 ( class_Fields_Olinordered__field(T_a) % 177.89/177.88 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__power__minus,axiom, % 177.89/177.88 ! [V_n,V_a,T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__zmult__eq__1,axiom, % 177.89/177.88 ! [V_n,V_m] : % 177.89/177.88 ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__sgn,axiom, % 177.89/177.88 ! [V_k,T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mult__sgn__abs,axiom, % 177.89/177.88 ! [V_x,T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)) = V_x ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_nat__case__0,axiom, % 177.89/177.88 ! [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 ). % 177.89/177.88 % 177.89/177.88 fof(fact_nat__case__Suc,axiom, % 177.89/177.88 ! [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) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__eq__mult,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Rings_Oordered__ring__abs(T_a) % 177.89/177.88 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.89/177.88 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 177.89/177.88 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.89/177.88 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__mult__pos,axiom, % 177.89/177.88 ! [V_y,V_x,T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.89/177.88 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_y)),V_x) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__triangle__ineq4,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__diff__triangle__ineq,axiom, % 177.89/177.88 ! [V_d,V_c,V_b,V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_c))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_d))))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__minus__le__zero,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__of__nonpos,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__if,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Groups_Oabs__if(T_a) % 177.89/177.88 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__of__neg,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zero__le__power__abs,axiom, % 177.89/177.88 ! [V_n,V_a,T_a] : % 177.89/177.88 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__div__pos,axiom, % 177.89/177.88 ! [V_x,V_y,T_a] : % 177.89/177.88 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.89/177.88 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)),V_y) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zabs__less__one__iff,axiom, % 177.89/177.88 ! [V_z_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))) % 177.89/177.88 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zabs__def,axiom, % 177.89/177.88 ! [V_i] : % 177.89/177.88 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_nat__abs__mult__distrib,axiom, % 177.89/177.88 ! [V_z,V_w] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_w))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zero__le__zpower__abs,axiom, % 177.89/177.88 ! [V_n,V_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),V_n))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zero__less__zpower__abs__iff,axiom, % 177.89/177.88 ! [V_n_2,V_x_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2)),V_n_2))) % 177.89/177.88 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.88 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Nitpick_Oint__lcm__def,axiom, % 177.89/177.88 ! [V_y,V_x] : c_Nitpick_Oint__lcm(V_x,V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Inter__subset,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( ! [B_X] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_A_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_X),V_B_2)) ) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 177.89/177.88 => 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)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_int__val__lemma,axiom, % 177.89/177.88 ! [V_k_2,V_f_2,V_n_2] : % 177.89/177.88 ( ! [B_i] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 177.89/177.88 => ? [B_i] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 177.89/177.88 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_nat0__intermed__int__val,axiom, % 177.89/177.88 ! [V_k_2,V_f_2,V_n_2] : % 177.89/177.88 ( ! [B_i] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 177.89/177.88 => ? [B_i] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 177.89/177.88 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 177.89/177.88 ! [V_n_2,V_m_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 177.89/177.88 <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Nitpick_Onat__lcm__def,axiom, % 177.89/177.88 ! [V_y,V_x] : c_Nitpick_Onat__lcm(V_x,V_y) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),c_Nitpick_Onat__gcd(V_x,V_y)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_setprod__pos__nat,axiom, % 177.89/177.88 ! [V_f_2,V_S_2,T_a] : % 177.89/177.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 177.89/177.88 => ( ! [B_x] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) % 177.89/177.88 => 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))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evaln_OBody,axiom, % 177.89/177.88 ! [V_s1,V_n,V_s0,V_pn] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_n),V_s1)) % 177.89/177.88 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),hAPP(c_Nat_OSuc,V_n)),V_s1)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_card__less__Suc2,axiom, % 177.89/177.88 ! [V_i_2,V_M_2] : % 177.89/177.88 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 177.89/177.88 => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evaln_OWhileFalse,axiom, % 177.89/177.88 ! [V_n_2,V_ca_2,V_s_2,V_b_2] : % 177.89/177.88 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_n_2),V_s_2)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evaln_OWhileTrue,axiom, % 177.89/177.88 ! [V_s2_2,V_s1_2,V_n_2,V_ca_2,V_s0_2,V_b_2] : % 177.89/177.88 ( hBOOL(hAPP(V_b_2,V_s0_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s0_2),V_n_2),V_s1_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s1_2),V_n_2),V_s2_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s0_2),V_n_2),V_s2_2)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evaln_OSemi,axiom, % 177.89/177.88 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0),V_s0),V_n),V_s1)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s1),V_n),V_s2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_n),V_s2)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evaln_OSkip,axiom, % 177.89/177.88 ! [V_n,V_s] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_s)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evaln__elim__cases_I1_J,axiom, % 177.89/177.88 ! [V_t,V_n,V_s] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_t)) % 177.89/177.88 => V_t = V_s ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_CollectI,axiom, % 177.89/177.88 ! [T_a,V_a_2,V_P_2] : % 177.89/177.88 ( hBOOL(hAPP(V_P_2,V_a_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_finite__Collect__conjI,axiom, % 177.89/177.88 ! [V_Q_2,V_P_2,T_a] : % 177.89/177.88 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 177.89/177.88 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) % 177.89/177.88 => 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)))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_finite__Collect__less__nat,axiom, % 177.89/177.88 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_k_2)))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_finite__Collect__le__nat,axiom, % 177.89/177.88 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_k_2)))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Collect__mem__eq,axiom, % 177.89/177.88 ! [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 ). % 177.89/177.88 % 177.89/177.88 fof(fact_mem__Collect__eq,axiom, % 177.89/177.88 ! [V_P_2,V_a_2,T_a] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 177.89/177.88 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_CollectD,axiom, % 177.89/177.88 ! [V_P_2,V_a_2,T_a] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 177.89/177.88 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_CollectE,axiom, % 177.89/177.88 ! [V_P_2,V_a_2,T_a] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 177.89/177.88 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_empty__def,axiom, % 177.89/177.88 ! [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)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_finite__Collect__disjI,axiom, % 177.89/177.88 ! [V_Q_2,V_P_2,T_a] : % 177.89/177.88 ( 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)))) % 177.89/177.88 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 177.89/177.88 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evaln_Oequations_I4_J,axiom, % 177.89/177.88 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_a1_2,V_a5_2)),V_a2_2),V_a3_2),V_a6_2)) % 177.89/177.88 <=> ? [B_s1] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a1_2),V_a2_2),V_a3_2),B_s1)) % 177.89/177.88 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a5_2),B_s1),V_a3_2),V_a6_2)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evaln_Oequations_I1_J,axiom, % 177.89/177.88 ! [V_a2,V_a1] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_a1),V_a2),V_a1)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evaln__nonstrict,axiom, % 177.89/177.88 ! [V_m,V_t,V_n,V_s,V_c] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.89/177.88 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_m),V_t)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Collect__def,axiom, % 177.89/177.88 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),V_P_2) = V_P_2 ). % 177.89/177.88 % 177.89/177.88 fof(fact_evaln__Suc,axiom, % 177.89/177.88 ! [V_s_H,V_n,V_s,V_c] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_s_H)) % 177.89/177.88 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),hAPP(c_Nat_OSuc,V_n)),V_s_H)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_empty__Collect__eq,axiom, % 177.89/177.88 ! [V_P_2,T_a] : % 177.89/177.88 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),V_P_2) % 177.89/177.88 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Collect__empty__eq,axiom, % 177.89/177.88 ! [V_P_2,T_a] : % 177.89/177.88 ( hAPP(c_Set_OCollect(T_a),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evaln__evalc,axiom, % 177.89/177.88 ! [V_t,V_n,V_s,V_c] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_eval__eq,axiom, % 177.89/177.88 ! [V_t_2,V_s_2,V_ca_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s_2),V_t_2)) % 177.89/177.88 <=> ? [B_n] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s_2),B_n),V_t_2)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evaln_Oequations_I8_J,axiom, % 177.89/177.88 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a4_2),V_a6_2)) % 177.89/177.88 <=> ( ( V_a6_2 = V_a2_2 % 177.89/177.88 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 177.89/177.88 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 177.89/177.88 & ? [B_s1] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1)) % 177.89/177.88 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a4_2),V_a6_2)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evaln_Oequations_I7_J,axiom, % 177.89/177.88 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a4_2),V_a2_2)) % 177.89/177.88 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 177.89/177.88 => ? [B_s1] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1)) % 177.89/177.88 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a4_2),V_a2_2)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Collect__conj__eq,axiom, % 177.89/177.88 ! [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)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Collect__disj__eq,axiom, % 177.89/177.88 ! [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)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_UNIV__def,axiom, % 177.89/177.88 ! [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)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_insert__Collect,axiom, % 177.89/177.88 ! [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)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Collect__neg__eq,axiom, % 177.89/177.88 ! [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)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_vimage__Collect__eq,axiom, % 177.89/177.88 ! [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)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_insert__compr,axiom, % 177.89/177.88 ! [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))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_insert__compr__raw,axiom, % 177.89/177.88 ! [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))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Un__def,axiom, % 177.89/177.88 ! [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))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Int__Collect,axiom, % 177.89/177.88 ! [V_P_2,V_A_2,V_x_2,T_a] : % 177.89/177.88 ( 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)))) % 177.89/177.88 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Int__def,axiom, % 177.89/177.88 ! [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))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_singleton__conv2,axiom, % 177.89/177.88 ! [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))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_singleton__conv,axiom, % 177.89/177.88 ! [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))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Collect__conv__if2,axiom, % 177.89/177.88 ! [T_a,V_a_2,V_P_2] : % 177.89/177.88 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 177.89/177.88 => 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))) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 177.89/177.88 => 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)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Collect__conv__if,axiom, % 177.89/177.88 ! [T_a,V_a_2,V_P_2] : % 177.89/177.88 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 177.89/177.88 => 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))) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 177.89/177.88 => 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)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_set__diff__eq,axiom, % 177.89/177.88 ! [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)))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_finite__Collect__not,axiom, % 177.89/177.88 ! [V_P_2,T_a] : % 177.89/177.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 177.89/177.88 => ( 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)))) % 177.89/177.88 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_insert__def,axiom, % 177.89/177.88 ! [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) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Compl__eq,axiom, % 177.89/177.88 ! [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))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_vimage__def,axiom, % 177.89/177.88 ! [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)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Collect__imp__eq,axiom, % 177.89/177.88 ! [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)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_dom__def,axiom, % 177.89/177.88 ! [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)))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_triple__valid__def2,axiom, % 177.89/177.88 ! [V_Q_2,V_ca_2,V_P_2,V_n_2,T_a] : % 177.89/177.88 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)) % 177.89/177.88 <=> ! [B_Z,B_s] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 177.89/177.88 => ! [B_s_H] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),B_s),V_n_2),B_s_H)) % 177.89/177.88 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_finite__M__bounded__by__nat,axiom, % 177.89/177.88 ! [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))))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_setsum__setsum__restrict,axiom, % 177.89/177.88 ! [V_R_2,V_f_2,V_T_2,T_b,V_S_2,T_a,T_c] : % 177.89/177.88 ( class_Groups_Ocomm__monoid__add(T_c) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 177.89/177.88 => 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) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_if__image__distrib,axiom, % 177.89/177.88 ! [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))))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Collect__all__eq,axiom, % 177.89/177.88 ! [V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),V_P_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_P_2))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_dom__if,axiom, % 177.89/177.88 ! [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)))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_nat__seg__image__imp__finite,axiom, % 177.89/177.88 ! [V_n_2,V_f_2,T_a,V_A_2] : % 177.89/177.88 ( 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))) % 177.89/177.88 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_setsum__restrict__set_H,axiom, % 177.89/177.88 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 177.89/177.88 ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => 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) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_setsum__image__gen,axiom, % 177.89/177.88 ! [V_f_2,T_c,V_g_2,V_S_2,T_a,T_b] : % 177.89/177.88 ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 177.89/177.88 => 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)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_triple__valid__def,axiom, % 177.89/177.88 ! [V_t_2,V_n_2,T_a] : % 177.89/177.88 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,V_t_2) % 177.89/177.88 <=> hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(T_a,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),V_n_2))))))))),V_t_2)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evaln_Oequations_I9_J,axiom, % 177.89/177.88 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),hAPP(c_Nat_OSuc,V_a3_2)),V_a4_2)) % 177.89/177.88 <=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2))),V_a2_2),V_a3_2),V_a4_2)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_nat__gcd_Osimps,axiom, % 177.89/177.88 ! [V_x,V_y] : % 177.89/177.88 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.88 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) % 177.89/177.88 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.88 => c_Nitpick_Onat__gcd(V_x,V_y) = c_Nitpick_Onat__gcd(V_y,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_setsum__cases,axiom, % 177.89/177.88 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_a,T_b] : % 177.89/177.88 ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => 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))))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_card__less__Suc,axiom, % 177.89/177.88 ! [V_i_2,V_M_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 177.89/177.88 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_card__less,axiom, % 177.89/177.88 ! [V_i_2,V_M_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 177.89/177.88 => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_dom__override__on,axiom, % 177.89/177.88 ! [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))))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Nitpick_Oint__gcd__def,axiom, % 177.89/177.88 ! [V_y,V_x] : hAPP(hAPP(c_Nitpick_Oint__gcd,V_x),V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evaln__elim__cases_I6_J,axiom, % 177.89/177.88 ! [V_s1,V_n,V_s,V_P] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_n),V_s1)) % 177.89/177.88 => ~ ! [B_n] : % 177.89/177.88 ( V_n = hAPP(c_Nat_OSuc,B_n) % 177.89/177.88 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),B_n),V_s1)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_setsum__multicount,axiom, % 177.89/177.88 ! [V_k_2,V_R_2,V_T_2,T_b,V_S_2,T_a] : % 177.89/177.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 177.89/177.88 => ( ! [B_x] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_T_2)) % 177.89/177.88 => 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 ) % 177.89/177.88 => 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)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_finite__Collect__subsets,axiom, % 177.89/177.88 ! [V_A_2,T_a] : % 177.89/177.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => 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)))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Pow__def,axiom, % 177.89/177.88 ! [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)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_override__on__apply__notin,axiom, % 177.89/177.88 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 177.89/177.88 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.88 => 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) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_override__on__apply__in,axiom, % 177.89/177.88 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.88 => 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) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_override__on__emptyset,axiom, % 177.89/177.88 ! [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 ). % 177.89/177.88 % 177.89/177.88 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom, % 177.89/177.88 ! [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))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_override__on__def,axiom, % 177.89/177.88 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 177.89/177.88 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.88 => 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) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.88 => 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) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom, % 177.89/177.88 ! [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)))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom, % 177.89/177.88 ! [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)))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_setsum__multicount__gen,axiom, % 177.89/177.88 ! [V_k_2,V_R_2,V_t_2,T_b,V_s_2,T_a] : % 177.89/177.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_t_2)) % 177.89/177.88 => ( ! [B_x] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_t_2)) % 177.89/177.88 => 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) ) % 177.89/177.88 => 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) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_inf__Sup2__distrib,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Lattices_Odistrib__lattice(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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))))))) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_inf__Sup1__distrib,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Lattices_Odistrib__lattice(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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))))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_sup__Inf2__distrib,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Lattices_Odistrib__lattice(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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))))))) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_finite__Collect__bounded__ex,axiom, % 177.89/177.88 ! [V_Q_2,T_b,V_P_2,T_a] : % 177.89/177.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 177.89/177.88 => ( 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))))) % 177.89/177.88 <=> ! [B_y] : % 177.89/177.88 ( hBOOL(hAPP(V_P_2,B_y)) % 177.89/177.88 => 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)))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_finite__image__set,axiom, % 177.89/177.88 ! [V_f_2,T_b,V_P_2,T_a] : % 177.89/177.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 177.89/177.88 => 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))))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Pow__Compl,axiom, % 177.89/177.88 ! [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))))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_ran__def,axiom, % 177.89/177.88 ! [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)))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_sup__Inf1__distrib,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Lattices_Odistrib__lattice(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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))))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_add__Min__commute,axiom, % 177.89/177.88 ! [V_k_2,V_N_2,T_a] : % 177.89/177.88 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 177.89/177.88 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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))))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_add__Max__commute,axiom, % 177.89/177.88 ! [V_k_2,V_N_2,T_a] : % 177.89/177.88 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 177.89/177.88 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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))))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_finite__conv__nat__seg__image,axiom, % 177.89/177.88 ! [V_A_2,T_a] : % 177.89/177.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 <=> ? [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))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_pigeonhole__infinite,axiom, % 177.89/177.88 ! [V_f_2,T_b,V_A_2,T_a] : % 177.89/177.88 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 177.89/177.88 => ? [B_x] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.88 & ~ 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)))))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_minus__Min__eq__Max,axiom, % 177.89/177.88 ! [V_S_2,T_a] : % 177.89/177.88 ( class_Groups_Olinordered__ab__group__add(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 177.89/177.88 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_minus__Max__eq__Min,axiom, % 177.89/177.88 ! [V_S_2,T_a] : % 177.89/177.88 ( class_Groups_Olinordered__ab__group__add(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 177.89/177.88 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Min_Osingleton,axiom, % 177.89/177.88 ! [V_x_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => 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 ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Max_Osingleton,axiom, % 177.89/177.88 ! [V_x_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => 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 ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Min__le,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => 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)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Max__ge,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => 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))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Min__in,axiom, % 177.89/177.88 ! [V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Max__in,axiom, % 177.89/177.88 ! [V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Min__antimono,axiom, % 177.89/177.88 ! [V_N_2,V_M_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 177.89/177.88 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 177.89/177.88 => 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))) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Max__mono,axiom, % 177.89/177.88 ! [V_N_2,V_M_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 177.89/177.88 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 177.89/177.88 => 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))) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Min_Oremove,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => ( ( 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)) % 177.89/177.88 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) % 177.89/177.88 & ( 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)) % 177.89/177.88 => 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)))))) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Max_Oremove,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => ( ( 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)) % 177.89/177.88 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) % 177.89/177.88 & ( 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)) % 177.89/177.88 => 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)))))) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_card__quotient__disjoint,axiom, % 177.89/177.88 ! [V_r_2,V_A_2,T_a] : % 177.89/177.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( 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) % 177.89/177.88 => 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) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_inj__on__diff__nat,axiom, % 177.89/177.88 ! [V_k_2,V_N_2] : % 177.89/177.88 ( ! [B_x] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) ) % 177.89/177.88 => c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_k_2),V_N_2) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom, % 177.89/177.88 ! [T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom, % 177.89/177.88 ! [T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Int__atLeastAtMost,axiom, % 177.89/177.88 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => 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)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__diff,axiom, % 177.89/177.88 ! [V_n,V_i,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_i)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)),V_i) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__diff__distrib__left,axiom, % 177.89/177.88 ! [V_z,V_y,V_x,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_max__diff__distrib__left,axiom, % 177.89/177.88 ! [V_z,V_y,V_x,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__group__add(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Int__greaterThanAtMost,axiom, % 177.89/177.88 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => 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)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Int__atLeastLessThan,axiom, % 177.89/177.88 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => 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)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_inf__min,axiom, % 177.89/177.88 ! [T_a] : % 177.89/177.88 ( ( class_Lattices_Osemilattice__inf(T_a) % 177.89/177.88 & class_Orderings_Olinorder(T_a) ) % 177.89/177.88 => c_Lattices_Osemilattice__inf__class_Oinf(T_a) = c_Orderings_Oord__class_Omin(T_a) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_sup__max,axiom, % 177.89/177.88 ! [T_a] : % 177.89/177.88 ( ( class_Lattices_Osemilattice__sup(T_a) % 177.89/177.88 & class_Orderings_Olinorder(T_a) ) % 177.89/177.88 => c_Lattices_Osemilattice__sup__class_Osup(T_a) = c_Orderings_Oord__class_Omax(T_a) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Int__greaterThanLessThan,axiom, % 177.89/177.88 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => 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)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_max__0L,axiom, % 177.89/177.88 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 177.89/177.88 % 177.89/177.88 fof(fact_max__0R,axiom, % 177.89/177.88 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__0L,axiom, % 177.89/177.88 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__0R,axiom, % 177.89/177.88 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.88 % 177.89/177.88 fof(fact_max__Suc__Suc,axiom, % 177.89/177.88 ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m),V_n)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__Suc__Suc,axiom, % 177.89/177.88 ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_max__add__distrib__left,axiom, % 177.89/177.88 ! [V_z,V_y,V_x,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__add__distrib__left,axiom, % 177.89/177.88 ! [V_z,V_y,V_x,T_a] : % 177.89/177.88 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oless__supI1,axiom, % 177.89/177.88 ! [V_b,V_a,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oless__supI2,axiom, % 177.89/177.88 ! [V_a,V_b,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_less__max__iff__disj,axiom, % 177.89/177.88 ! [V_y_2,V_x_2,V_z_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 177.89/177.88 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_max__less__iff__conj,axiom, % 177.89/177.88 ! [V_z_2,V_y_2,V_x_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( 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)) % 177.89/177.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 177.89/177.88 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oless__infI1,axiom, % 177.89/177.88 ! [V_b,V_x,V_a,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oless__infI2,axiom, % 177.89/177.88 ! [V_a,V_x,V_b,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__less__iff__conj,axiom, % 177.89/177.88 ! [V_y_2,V_x_2,V_z_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 177.89/177.88 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__less__iff__disj,axiom, % 177.89/177.88 ! [V_z_2,V_y_2,V_x_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( 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)) % 177.89/177.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 177.89/177.88 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_minus__min__eq__max,axiom, % 177.89/177.88 ! [V_y,V_x,T_a] : % 177.89/177.88 ( class_Groups_Olinordered__ab__group__add(T_a) % 177.89/177.88 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_minus__max__eq__min,axiom, % 177.89/177.88 ! [V_y,V_x,T_a] : % 177.89/177.88 ( class_Groups_Olinordered__ab__group__add(T_a) % 177.89/177.88 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf__sup__distrib2,axiom, % 177.89/177.88 ! [V_x,V_z,V_y,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_z),V_x)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Osup__inf__distrib2,axiom, % 177.89/177.88 ! [V_x,V_z,V_y,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_z),V_x)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf__assoc,axiom, % 177.89/177.88 ! [V_z,V_y,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf_Oassoc,axiom, % 177.89/177.88 ! [V_c,V_b,V_a,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Osup__assoc,axiom, % 177.89/177.88 ! [V_z,V_y,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Osup_Oassoc,axiom, % 177.89/177.88 ! [V_c,V_b,V_a,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf__sup__distrib1,axiom, % 177.89/177.88 ! [V_z,V_y,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Osup__inf__distrib1,axiom, % 177.89/177.88 ! [V_z,V_y,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf__left__commute,axiom, % 177.89/177.88 ! [V_z,V_y,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf_Oleft__commute,axiom, % 177.89/177.88 ! [V_c,V_a,V_b,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Osup__left__commute,axiom, % 177.89/177.88 ! [V_z,V_y,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Osup_Oleft__commute,axiom, % 177.89/177.88 ! [V_c,V_a,V_b,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf__left__idem,axiom, % 177.89/177.88 ! [V_y,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf_Oleft__idem,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Osup__left__idem,axiom, % 177.89/177.88 ! [V_y,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Osup_Oleft__idem,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf__sup__absorb,axiom, % 177.89/177.88 ! [V_y,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = V_x ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Osup__inf__absorb,axiom, % 177.89/177.88 ! [V_y,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = V_x ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf__commute,axiom, % 177.89/177.88 ! [V_y,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf_Ocommute,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_a) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Osup__commute,axiom, % 177.89/177.88 ! [V_y,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Osup_Ocommute,axiom, % 177.89/177.88 ! [V_b,V_a,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_a) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf_Oidem,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Osup_Oidem,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Min_Oidem,axiom, % 177.89/177.88 ! [V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Max_Oidem,axiom, % 177.89/177.88 ! [V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf__le1,axiom, % 177.89/177.88 ! [V_y,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_x)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf__le2,axiom, % 177.89/177.88 ! [V_y,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_y)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Ole__iff__inf,axiom, % 177.89/177.88 ! [V_y_2,V_x_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 177.89/177.88 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Ole__inf__iff,axiom, % 177.89/177.88 ! [V_z_2,V_y_2,V_x_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 177.89/177.88 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Ole__infI1,axiom, % 177.89/177.88 ! [V_b,V_x,V_a,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Ole__infI2,axiom, % 177.89/177.88 ! [V_a,V_x,V_b,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf__absorb1,axiom, % 177.89/177.88 ! [V_y,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf__absorb2,axiom, % 177.89/177.88 ! [V_x,V_y,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Ole__infI,axiom, % 177.89/177.88 ! [V_b,V_a,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf__greatest,axiom, % 177.89/177.88 ! [V_z,V_y,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf__mono,axiom, % 177.89/177.88 ! [V_d,V_b,V_c,V_a,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_c),V_d))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Ole__infE,axiom, % 177.89/177.88 ! [V_b,V_a,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))) % 177.89/177.88 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 177.89/177.88 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__le__iff__disj,axiom, % 177.89/177.88 ! [V_z_2,V_y_2,V_x_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( 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)) % 177.89/177.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 177.89/177.88 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_le__maxI1,axiom, % 177.89/177.88 ! [V_y,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_le__maxI2,axiom, % 177.89/177.88 ! [V_x,V_y,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Ole__iff__sup,axiom, % 177.89/177.88 ! [V_y_2,V_x_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 177.89/177.88 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Ole__sup__iff,axiom, % 177.89/177.88 ! [V_z_2,V_y_2,V_x_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( 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)) % 177.89/177.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 177.89/177.88 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Ole__supI1,axiom, % 177.89/177.88 ! [V_b,V_a,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Ole__supI2,axiom, % 177.89/177.88 ! [V_a,V_b,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Osup__absorb2,axiom, % 177.89/177.88 ! [V_y,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Osup__absorb1,axiom, % 177.89/177.88 ! [V_x,V_y,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Ole__supI,axiom, % 177.89/177.88 ! [V_b,V_x,V_a,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Osup__least,axiom, % 177.89/177.88 ! [V_z,V_x,V_y,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Osup__mono,axiom, % 177.89/177.88 ! [V_d,V_b,V_c,V_a,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_c),V_d))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Ole__supE,axiom, % 177.89/177.88 ! [V_x,V_b,V_a,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) % 177.89/177.88 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 177.89/177.88 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_le__max__iff__disj,axiom, % 177.89/177.88 ! [V_y_2,V_x_2,V_z_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_x_2)) % 177.89/177.88 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_y_2)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Odistrib__sup__le,axiom, % 177.89/177.88 ! [V_z,V_y,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Odistrib__inf__le,axiom, % 177.89/177.88 ! [V_z,V_y,V_x,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_quotient__empty,axiom, % 177.89/177.88 ! [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)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_quotient__is__empty2,axiom, % 177.89/177.88 ! [V_r_2,V_A_2,T_a] : % 177.89/177.88 ( 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) % 177.89/177.88 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_quotient__is__empty,axiom, % 177.89/177.88 ! [V_r_2,V_A_2,T_a] : % 177.89/177.88 ( 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)) % 177.89/177.88 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_nat__minus__add__max,axiom, % 177.89/177.88 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),V_m) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),V_m) ). % 177.89/177.88 % 177.89/177.88 fof(fact_max__Suc1,axiom, % 177.89/177.88 ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),V_m_2) ). % 177.89/177.88 % 177.89/177.88 fof(fact_max__Suc2,axiom, % 177.89/177.88 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),V_n_2)),V_m_2) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Ofold__sup__insert,axiom, % 177.89/177.88 ! [V_a_2,V_b_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => 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)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Ofold__inf__insert,axiom, % 177.89/177.88 ! [V_a_2,V_b_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => 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)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Max_Oin__idem,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => 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) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Min_Oin__idem,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => 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) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Int__atLeastAtMostL1,axiom, % 177.89/177.88 ! [V_d_2,V_b_2,V_a_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => 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)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Int__atLeastAtMostR1,axiom, % 177.89/177.88 ! [V_d_2,V_ca_2,V_b_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => 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)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Int__atLeastAtMostR2,axiom, % 177.89/177.88 ! [V_d_2,V_ca_2,V_a_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => 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) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Int__atLeastAtMostL2,axiom, % 177.89/177.88 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => 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) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Max_OF__eq,axiom, % 177.89/177.88 ! [V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => 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) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Min_OF__eq,axiom, % 177.89/177.88 ! [V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => 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) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_quotient__diff1,axiom, % 177.89/177.88 ! [V_a_2,V_A_2,V_r_2,T_a] : % 177.89/177.88 ( 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) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.88 => 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)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__Suc1,axiom, % 177.89/177.88 ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),V_m_2) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__Suc2,axiom, % 177.89/177.88 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),V_n_2)),V_m_2) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Osup__le__fold__sup,axiom, % 177.89/177.88 ! [V_b_2,V_a_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.88 => 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))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Ofold__inf__le__inf,axiom, % 177.89/177.88 ! [V_b_2,V_a_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.88 => 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))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Ofold1__belowI,axiom, % 177.89/177.88 ! [V_a_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.88 => 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)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_fold1__below__iff,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( 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)) % 177.89/177.88 <=> ? [B_x] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.88 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Obelow__fold1__iff,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> ! [B_x] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_fold1__strict__below__iff,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( 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)) % 177.89/177.88 <=> ? [B_x] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.88 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_strict__below__fold1__iff,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> ! [B_x] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Max__insert,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Min__insert,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Max_Osubset__idem,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.89/177.88 => 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) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Min_Osubset__idem,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.89/177.88 => 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) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Max__Un,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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)) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Min__Un,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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)) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Max_Oeq__fold__idem_H,axiom, % 177.89/177.88 ! [V_a_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => 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) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Min_Oeq__fold__idem_H,axiom, % 177.89/177.88 ! [V_a_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => 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) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Max_Oinsert,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Min_Oinsert,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_fold1__antimono,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.88 => 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))) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Max_Oinsert__remove,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( ( 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)) % 177.89/177.88 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 177.89/177.88 & ( 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)) % 177.89/177.88 => 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)))))) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Max_Ounion__inter,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.88 => ( 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)) % 177.89/177.88 => 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)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Max_Ounion__disjoint,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( 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)) % 177.89/177.88 => 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)) ) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Min_Oinsert__remove,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( ( 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)) % 177.89/177.88 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 177.89/177.88 & ( 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)) % 177.89/177.88 => 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)))))) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Min_Ounion__inter,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.88 => ( 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)) % 177.89/177.88 => 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)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Min_Ounion__disjoint,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( 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)) % 177.89/177.88 => 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)) ) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Max_Oeq__fold_H,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => 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) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Min_Oeq__fold_H,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => 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) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_dual__min,axiom, % 177.89/177.88 ! [T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => 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) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_dual__max,axiom, % 177.89/177.88 ! [T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => 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) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_max__ord__max,axiom, % 177.89/177.88 ! [T_a] : % 177.89/177.88 ( class_Orderings_Oord(T_a) % 177.89/177.88 => c_Orderings_Oord__class_Omax(T_a) = c_Orderings_Oord_Omax(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__ord__min,axiom, % 177.89/177.88 ! [T_a] : % 177.89/177.88 ( class_Orderings_Oord(T_a) % 177.89/177.88 => c_Orderings_Oord__class_Omin(T_a) = c_Orderings_Oord_Omin(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_inf__nat__def,axiom, % 177.89/177.88 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ). % 177.89/177.88 % 177.89/177.88 fof(fact_sup__nat__def,axiom, % 177.89/177.88 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf__Sup2__distrib,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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))))))) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Osup__Inf2__distrib,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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))))))) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf__Sup1__distrib,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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))))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Osup__Inf1__distrib,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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))))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OInf__le__Sup,axiom, % 177.89/177.88 ! [V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OInf__fin_Oin__idem,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => 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) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OSup__fin_Oin__idem,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => 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) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OInf__fin_Osingleton,axiom, % 177.89/177.88 ! [V_x_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => 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 ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OSup__fin_Osingleton,axiom, % 177.89/177.88 ! [V_x_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => 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 ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OInf__fin_OF__eq,axiom, % 177.89/177.88 ! [V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => 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) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OSup__fin_OF__eq,axiom, % 177.89/177.88 ! [V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => 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) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OInf__fin_Osubset__idem,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.89/177.88 => 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) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OSup__fin_Osubset__idem,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.89/177.88 => 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) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Osup__Inf__absorb,axiom, % 177.89/177.88 ! [V_a_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.88 => 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 ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf__Sup__absorb,axiom, % 177.89/177.88 ! [V_a_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.88 => 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 ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OInf__fin_Ounion__idem,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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)) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OSup__fin_Ounion__idem,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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)) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom, % 177.89/177.88 ! [V_a_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => 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) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom, % 177.89/177.88 ! [V_a_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => 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) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OInf__fin_Oinsert,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OSup__fin_Oinsert,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( ( 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)) % 177.89/177.88 => 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 ) % 177.89/177.88 & ( 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)) % 177.89/177.88 => 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)))))) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( ( 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)) % 177.89/177.88 => 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 ) % 177.89/177.88 & ( 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)) % 177.89/177.88 => 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)))))) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OInf__fin_Ounion__inter,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.88 => ( 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)) % 177.89/177.88 => 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)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( 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)) % 177.89/177.88 => 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)) ) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OSup__fin_Ounion__inter,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.88 => ( 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)) % 177.89/177.88 => 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)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom, % 177.89/177.88 ! [V_B_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( 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)) % 177.89/177.88 => 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)) ) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => 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) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => 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) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OInf__fin_Oremove,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => ( ( 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)) % 177.89/177.88 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = V_x_2 ) % 177.89/177.88 & ( 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)) % 177.89/177.88 => 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)))))) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OSup__fin_Oremove,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => ( ( 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)) % 177.89/177.88 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = V_x_2 ) % 177.89/177.88 & ( 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)) % 177.89/177.88 => 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)))))) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_quotient__def,axiom, % 177.89/177.88 ! [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)))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OSup__fin_Oclosed,axiom, % 177.89/177.88 ! [V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( ! [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)))))) % 177.89/177.88 => 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)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OInf__fin_Oclosed,axiom, % 177.89/177.88 ! [V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( ! [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)))))) % 177.89/177.88 => 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)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Max_Oclosed,axiom, % 177.89/177.88 ! [V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( ! [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)))))) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_quotientI,axiom, % 177.89/177.88 ! [V_r_2,V_A_2,V_x_2,T_a] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => 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))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_singleton__quotient,axiom, % 177.89/177.88 ! [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))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Image__eq__UN,axiom, % 177.89/177.88 ! [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))))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Image__INT__subset,axiom, % 177.89/177.88 ! [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)))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Image__Int__subset,axiom, % 177.89/177.88 ! [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)))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Image__UN,axiom, % 177.89/177.88 ! [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)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Image__empty,axiom, % 177.89/177.88 ! [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)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Image__mono,axiom, % 177.89/177.88 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_b,T_a] : % 177.89/177.88 ( 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)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_H_2),V_A_2)) % 177.89/177.88 => 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))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Image__Un,axiom, % 177.89/177.88 ! [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)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Un__Image,axiom, % 177.89/177.88 ! [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)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_quotientE,axiom, % 177.89/177.88 ! [V_r_2,V_A_2,V_X_2,T_a] : % 177.89/177.88 ( 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))) % 177.89/177.88 => ~ ! [B_x] : % 177.89/177.88 ( 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)))) % 177.89/177.88 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Min_Oclosed,axiom, % 177.89/177.88 ! [V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => ( ! [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)))))) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OSup__fin_Ohom__commute,axiom, % 177.89/177.88 ! [V_N_2,V_h_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( ! [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)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 177.89/177.88 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_OInf__fin_Ohom__commute,axiom, % 177.89/177.88 ! [V_N_2,V_h_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( ! [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)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 177.89/177.88 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_less__by__empty,axiom, % 177.89/177.88 ! [V_B_2,T_a,V_A_2] : % 177.89/177.88 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 177.89/177.88 => 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)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Max_Ohom__commute,axiom, % 177.89/177.88 ! [V_N_2,V_h_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( ! [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)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 177.89/177.88 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Min_Ohom__commute,axiom, % 177.89/177.88 ! [V_N_2,V_h_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( ! [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)) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 177.89/177.88 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.88 => 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)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_diff__nat__eq__if,axiom, % 177.89/177.88 ! [V_z_2,V_z_H_2] : % 177.89/177.88 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 177.89/177.88 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(c_Int_Onat,V_z_2) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 177.89/177.88 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),V_z_H_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_setsum__SucD,axiom, % 177.89/177.88 ! [V_n_2,V_A_2,V_f_2,T_a] : % 177.89/177.88 ( 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) % 177.89/177.88 => ? [B_x] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.88 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_not__neg__int,axiom, % 177.89/177.88 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_not__neg__1,axiom, % 177.89/177.88 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_not__neg__0,axiom, % 177.89/177.88 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_not__neg__eq__ge__0,axiom, % 177.89/177.88 ! [V_x_2] : % 177.89/177.88 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) % 177.89/177.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_neg__def,axiom, % 177.89/177.88 ! [V_Z_2] : % 177.89/177.88 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) % 177.89/177.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_neg__nat,axiom, % 177.89/177.88 ! [V_z] : % 177.89/177.88 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 177.89/177.88 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_not__neg__nat,axiom, % 177.89/177.88 ! [V_z] : % 177.89/177.88 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 177.89/177.88 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_neg__zminus__int,axiom, % 177.89/177.88 ! [V_n] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_nat__mod__eq__lemma,axiom, % 177.89/177.88 ! [V_y,V_n,V_x] : % 177.89/177.88 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) % 177.89/177.88 => ? [B_q] : V_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),B_q)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_com_Osize_I5_J,axiom, % 177.89/177.88 ! [V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1_2)),c_Com_Ocom_Ocom__size(V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_com_Osize_I13_J,axiom, % 177.89/177.88 ! [V_com2_2,V_com1_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1_2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_fold__image__1,axiom, % 177.89/177.88 ! [V_f_2,V_S_2,T_a,T_b] : % 177.89/177.88 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 177.89/177.88 => ( ! [B_x] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 177.89/177.88 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 177.89/177.88 => 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) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evaln_OIfFalse,axiom, % 177.89/177.88 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] : % 177.89/177.88 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_s1_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_n_2),V_s1_2)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evaln_OIfTrue,axiom, % 177.89/177.88 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] : % 177.89/177.88 ( hBOOL(hAPP(V_b_2,V_s_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0_2),V_s_2),V_n_2),V_s1_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_n_2),V_s1_2)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evaln__elim__cases_I5_J,axiom, % 177.89/177.88 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_n_2),V_t_2)) % 177.89/177.88 => ( ( hBOOL(hAPP(V_b_2,V_s_2)) % 177.89/177.88 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_t_2)) ) % 177.89/177.88 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 177.89/177.88 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2_2),V_s_2),V_n_2),V_t_2)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evalc__elim__cases_I5_J,axiom, % 177.89/177.88 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_t_2)) % 177.89/177.88 => ( ( hBOOL(hAPP(V_b_2,V_s_2)) % 177.89/177.88 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) ) % 177.89/177.88 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 177.89/177.88 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evalc_OIfTrue,axiom, % 177.89/177.88 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] : % 177.89/177.88 ( hBOOL(hAPP(V_b_2,V_s_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evalc_OIfFalse,axiom, % 177.89/177.88 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] : % 177.89/177.88 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_WTs__elim__cases_I5_J,axiom, % 177.89/177.88 ! [V_c2_2,V_c1_2,V_b_2] : % 177.89/177.88 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2))) % 177.89/177.88 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 177.89/177.88 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evaln_Oequations_I6_J,axiom, % 177.89/177.88 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_a1_2,V_a6_2,V_a3_2)),V_a2_2),V_a4_2),V_a5_2)) % 177.89/177.88 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 177.89/177.88 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) % 177.89/177.88 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 177.89/177.88 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evaln_Oequations_I5_J,axiom, % 177.89/177.88 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a6_2)),V_a2_2),V_a4_2),V_a5_2)) % 177.89/177.88 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 177.89/177.88 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) % 177.89/177.88 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 177.89/177.88 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_com_Osimps_I4_J,axiom, % 177.89/177.88 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : % 177.89/177.88 ( c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) = c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) % 177.89/177.88 <=> ( V_fun_2 = V_fun_H_2 % 177.89/177.88 & V_com1_2 = V_com1_H_2 % 177.89/177.88 & V_com2_2 = V_com2_H_2 ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evalc_Oequations_I5_J,axiom, % 177.89/177.88 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a5_2)),V_a2_2),V_a4_2)) % 177.89/177.88 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 177.89/177.88 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) % 177.89/177.88 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 177.89/177.88 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_evalc_Oequations_I6_J,axiom, % 177.89/177.88 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a5_2,V_a3_2)),V_a2_2),V_a4_2)) % 177.89/177.88 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 177.89/177.88 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) % 177.89/177.88 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 177.89/177.88 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_com_Osimps_I15_J,axiom, % 177.89/177.88 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSKIP ). % 177.89/177.88 % 177.89/177.88 fof(fact_com_Osimps_I14_J,axiom, % 177.89/177.88 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 177.89/177.88 % 177.89/177.88 fof(fact_com_Osimps_I57_J,axiom, % 177.89/177.88 ! [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) ). % 177.89/177.88 % 177.89/177.88 fof(fact_com_Osimps_I56_J,axiom, % 177.89/177.88 ! [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) ). % 177.89/177.88 % 177.89/177.88 fof(fact_com_Osimps_I45_J,axiom, % 177.89/177.88 ! [V_com2_2,V_com1_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ). % 177.89/177.88 % 177.89/177.88 fof(fact_com_Osimps_I44_J,axiom, % 177.89/177.88 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 177.89/177.88 % 177.89/177.88 fof(fact_com_Osimps_I52_J,axiom, % 177.89/177.88 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 177.89/177.88 % 177.89/177.88 fof(fact_com_Osimps_I53_J,axiom, % 177.89/177.88 ! [V_com2_2,V_com1_2,V_fun_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ). % 177.89/177.88 % 177.89/177.88 fof(fact_WT_OIf,axiom, % 177.89/177.88 ! [V_b_2,V_c1_2,V_c0_2] : % 177.89/177.88 ( hBOOL(hAPP(c_Com_OWT,V_c0_2)) % 177.89/177.88 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 177.89/177.88 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_WT_Oequations_I5_J,axiom, % 177.89/177.88 ! [V_a2_2,V_a1_2,V_a3_2] : % 177.89/177.88 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2))) % 177.89/177.88 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 177.89/177.88 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_com_Osimps_I54_J,axiom, % 177.89/177.88 ! [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) ). % 177.89/177.88 % 177.89/177.88 fof(fact_com_Osimps_I55_J,axiom, % 177.89/177.88 ! [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) ). % 177.89/177.88 % 177.89/177.88 fof(fact_card_Oneutral,axiom, % 177.89/177.88 ! [V_A_2,T_a] : % 177.89/177.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.88 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.89/177.88 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Ofold__sup__le__sup,axiom, % 177.89/177.88 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( ! [B_x] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) % 177.89/177.88 => 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))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__max_Oinf__le__fold__inf,axiom, % 177.89/177.88 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( ! [B_x] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) % 177.89/177.88 => 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))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__induct__0,axiom, % 177.89/177.88 ! [V_i_2,V_P_2,V_p_2] : % 177.89/177.88 ( ! [B_i] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) % 177.89/177.88 => ( hBOOL(hAPP(V_P_2,B_i)) % 177.89/177.88 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) ) % 177.89/177.88 => ( hBOOL(hAPP(V_P_2,V_i_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) % 177.89/177.88 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_InterI,axiom, % 177.89/177.88 ! [V_A_2,V_C_2,T_a] : % 177.89/177.88 ( ! [B_X] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) ) % 177.89/177.88 => 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))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_fold__image__cong,axiom, % 177.89/177.88 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_a,T_b] : % 177.89/177.88 ( class_Groups_Oab__semigroup__mult(T_b) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( ! [B_x] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.88 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 177.89/177.88 => 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) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Max__eqI,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( ! [B_y] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_y),V_x_2)) ) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Min__eqI,axiom, % 177.89/177.88 ! [V_x_2,V_A_2,T_a] : % 177.89/177.88 ( class_Orderings_Olinorder(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( ! [B_y] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_y)) ) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.88 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_inf__le__fold__inf,axiom, % 177.89/177.88 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 177.89/177.88 ( class_Lattices_Osemilattice__inf(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( ! [B_x] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) % 177.89/177.88 => 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))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_fold__sup__le__sup,axiom, % 177.89/177.88 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 177.89/177.88 ( class_Lattices_Osemilattice__sup(T_a) % 177.89/177.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.88 => ( ! [B_x] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) % 177.89/177.88 => 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))) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_expand__Suc,axiom, % 177.89/177.88 ! [V_v] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v))) % 177.89/177.88 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_quotient__disj,axiom, % 177.89/177.88 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 177.89/177.88 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 177.89/177.88 => ( 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))) % 177.89/177.88 => ( 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))) % 177.89/177.88 => ( V_X_2 = V_Y_2 % 177.89/177.88 | 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)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_of__nat__number__of__eq,axiom, % 177.89/177.88 ! [V_v,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.88 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.88 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_of__int__number__of__eq,axiom, % 177.89/177.88 ! [V_v,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_number__of__eq,axiom, % 177.89/177.88 ! [V_k,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_number__of__reorient,axiom, % 177.89/177.88 ! [V_x_2,V_w_2,T_a] : % 177.89/177.88 ( class_Int_Onumber(T_a) % 177.89/177.88 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = V_x_2 % 177.89/177.88 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_eq__number__of,axiom, % 177.89/177.88 ! [V_y_2,V_x_2,T_a] : % 177.89/177.88 ( ( class_Int_Onumber__ring(T_a) % 177.89/177.88 & class_Int_Oring__char__0(T_a) ) % 177.89/177.88 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 177.89/177.88 <=> V_x_2 = V_y_2 ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_of__nat__number__of__lemma,axiom, % 177.89/177.88 ! [V_v,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.88 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.88 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_le__number__of__eq__not__less,axiom, % 177.89/177.88 ! [V_w_2,V_v_2,T_a] : % 177.89/177.88 ( ( class_Int_Onumber(T_a) % 177.89/177.88 & class_Orderings_Olinorder(T_a) ) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> ~ 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))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_right__distrib__number__of,axiom, % 177.89/177.88 ! [V_c,V_b,V_v,T_b] : % 177.89/177.88 ( ( class_Int_Onumber(T_b) % 177.89/177.88 & class_Rings_Osemiring(T_b) ) % 177.89/177.88 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_left__distrib__number__of,axiom, % 177.89/177.88 ! [V_v,V_b,V_a,T_b] : % 177.89/177.88 ( ( class_Int_Onumber(T_b) % 177.89/177.88 & class_Rings_Osemiring(T_b) ) % 177.89/177.88 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_left__diff__distrib__number__of,axiom, % 177.89/177.88 ! [V_v,V_b,V_a,T_b] : % 177.89/177.88 ( ( class_Int_Onumber(T_b) % 177.89/177.88 & class_Rings_Oring(T_b) ) % 177.89/177.88 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_right__diff__distrib__number__of,axiom, % 177.89/177.88 ! [V_c,V_b,V_v,T_b] : % 177.89/177.88 ( ( class_Int_Onumber(T_b) % 177.89/177.88 & class_Rings_Oring(T_b) ) % 177.89/177.88 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_le__number__of,axiom, % 177.89/177.88 ! [V_y_2,V_x_2,T_a] : % 177.89/177.88 ( ( class_Int_Onumber__ring(T_a) % 177.89/177.88 & class_Rings_Olinordered__idom(T_a) ) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_less__number__of,axiom, % 177.89/177.88 ! [V_y_2,V_x_2,T_a] : % 177.89/177.88 ( ( class_Int_Onumber__ring(T_a) % 177.89/177.88 & class_Rings_Olinordered__idom(T_a) ) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__number__of,axiom, % 177.89/177.88 ! [V_v,V_u,T_b] : % 177.89/177.88 ( ( class_Int_Onumber(T_b) % 177.89/177.88 & class_Orderings_Oord(T_b) ) % 177.89/177.88 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_max__number__of,axiom, % 177.89/177.88 ! [V_v,V_u,T_b] : % 177.89/177.88 ( ( class_Int_Onumber(T_b) % 177.89/177.88 & class_Orderings_Oord(T_b) ) % 177.89/177.88 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) % 177.89/177.88 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_add__number__of__left,axiom, % 177.89/177.88 ! [V_z,V_w,V_v,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_z) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_add__number__of__eq,axiom, % 177.89/177.88 ! [V_w,V_v,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_number__of__add,axiom, % 177.89/177.88 ! [V_w,V_v,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mult__number__of__left,axiom, % 177.89/177.88 ! [V_z,V_w,V_v,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_arith__simps_I32_J,axiom, % 177.89/177.88 ! [V_w,V_v,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_number__of__mult,axiom, % 177.89/177.88 ! [V_w,V_v,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_number__of__diff,axiom, % 177.89/177.88 ! [V_w,V_v,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_arith__simps_I30_J,axiom, % 177.89/177.88 ! [V_w,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_number__of__minus,axiom, % 177.89/177.88 ! [V_w,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Ints__number__of,axiom, % 177.89/177.88 ! [V_w_2,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => 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))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Union__quotient,axiom, % 177.89/177.88 ! [V_r_2,V_A_2,T_a] : % 177.89/177.88 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 177.89/177.88 => 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 ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_divide__eq__eq__number__of1,axiom, % 177.89/177.88 ! [V_a_2,V_w_2,V_b_2,T_a] : % 177.89/177.88 ( ( class_Fields_Ofield__inverse__zero(T_a) % 177.89/177.88 & class_Int_Onumber(T_a) ) % 177.89/177.88 => ( 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 % 177.89/177.88 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.88 => 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)) ) % 177.89/177.88 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.88 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_divide__eq__eq__number__of,axiom, % 177.89/177.88 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 177.89/177.88 ( ( class_Fields_Ofield__inverse__zero(T_a) % 177.89/177.88 & class_Int_Onumber(T_a) ) % 177.89/177.88 => ( 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) % 177.89/177.88 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.88 => 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) ) % 177.89/177.88 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.88 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_eq__divide__eq__number__of,axiom, % 177.89/177.88 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 177.89/177.88 ( ( class_Fields_Ofield__inverse__zero(T_a) % 177.89/177.88 & class_Int_Onumber(T_a) ) % 177.89/177.88 => ( 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) % 177.89/177.88 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.88 => 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 ) % 177.89/177.88 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.88 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_eq__divide__eq__number__of1,axiom, % 177.89/177.88 ! [V_w_2,V_b_2,V_a_2,T_a] : % 177.89/177.88 ( ( class_Fields_Ofield__inverse__zero(T_a) % 177.89/177.88 & class_Int_Onumber(T_a) ) % 177.89/177.88 => ( 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)) % 177.89/177.88 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.88 => 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 ) % 177.89/177.88 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.88 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_add__number__of__diff1,axiom, % 177.89/177.88 ! [V_c,V_w,V_v,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_c) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_minus__number__of__mult,axiom, % 177.89/177.88 ! [V_z,V_w,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),V_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))),V_z) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_diff__number__of__eq,axiom, % 177.89/177.88 ! [V_w,V_v,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_less__divide__eq__number__of1,axiom, % 177.89/177.88 ! [V_w_2,V_b_2,V_a_2,T_a] : % 177.89/177.88 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.88 & class_Int_Onumber(T_a) ) % 177.89/177.88 => ( 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)))) % 177.89/177.88 <=> ( ( 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))) % 177.89/177.88 => 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)) ) % 177.89/177.88 & ( ~ 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))) % 177.89/177.88 => ( ( 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))) % 177.89/177.88 => 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)))) ) % 177.89/177.88 & ( ~ 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))) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_less__divide__eq__number__of,axiom, % 177.89/177.88 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 177.89/177.88 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.88 & class_Int_Onumber(T_a) ) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.88 => 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)) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.88 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.88 => 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))) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.88 => 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))) ) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_divide__less__eq__number__of,axiom, % 177.89/177.88 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 177.89/177.88 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.88 & class_Int_Onumber(T_a) ) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.88 => 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))) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.88 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.88 => 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)) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.88 => 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))) ) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_divide__less__eq__number__of1,axiom, % 177.89/177.88 ! [V_a_2,V_w_2,V_b_2,T_a] : % 177.89/177.88 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.88 & class_Int_Onumber(T_a) ) % 177.89/177.88 => ( 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)) % 177.89/177.88 <=> ( ( 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))) % 177.89/177.88 => 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)))) ) % 177.89/177.88 & ( ~ 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))) % 177.89/177.88 => ( ( 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))) % 177.89/177.88 => 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)) ) % 177.89/177.88 & ( ~ 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))) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_abs__number__of,axiom, % 177.89/177.88 ! [V_x,T_a] : % 177.89/177.88 ( ( class_Int_Onumber__ring(T_a) % 177.89/177.88 & class_Rings_Olinordered__idom(T_a) ) % 177.89/177.88 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.88 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_add__number__of__diff2,axiom, % 177.89/177.88 ! [V_w,V_c,V_v,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)))),V_c) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_le__divide__eq__number__of1,axiom, % 177.89/177.88 ! [V_w_2,V_b_2,V_a_2,T_a] : % 177.89/177.88 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.88 & class_Int_Onumber(T_a) ) % 177.89/177.88 => ( 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)))) % 177.89/177.88 <=> ( ( 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))) % 177.89/177.88 => 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)) ) % 177.89/177.88 & ( ~ 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))) % 177.89/177.88 => ( ( 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))) % 177.89/177.88 => 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)))) ) % 177.89/177.88 & ( ~ 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))) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_le__divide__eq__number__of,axiom, % 177.89/177.88 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 177.89/177.88 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.88 & class_Int_Onumber(T_a) ) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.88 => 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)) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.88 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.88 => 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))) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.88 => 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))) ) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_divide__le__eq__number__of,axiom, % 177.89/177.88 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 177.89/177.88 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.88 & class_Int_Onumber(T_a) ) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.88 => 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))) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 177.89/177.88 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.88 => 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)) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.88 => 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))) ) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_divide__le__eq__number__of1,axiom, % 177.89/177.88 ! [V_a_2,V_w_2,V_b_2,T_a] : % 177.89/177.88 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.88 & class_Int_Onumber(T_a) ) % 177.89/177.88 => ( 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)) % 177.89/177.88 <=> ( ( 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))) % 177.89/177.88 => 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)))) ) % 177.89/177.88 & ( ~ 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))) % 177.89/177.88 => ( ( 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))) % 177.89/177.88 => 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)) ) % 177.89/177.88 & ( ~ 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))) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_equiv__class__self,axiom, % 177.89/177.88 ! [V_a_2,V_r_2,V_A_2,T_a] : % 177.89/177.88 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.88 => 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)))))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_UN__equiv__class,axiom, % 177.89/177.88 ! [V_a_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 177.89/177.88 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 177.89/177.88 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.88 => 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) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_UN__equiv__class2,axiom, % 177.89/177.88 ! [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] : % 177.89/177.88 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 177.89/177.88 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 177.89/177.88 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a1_2),V_A1_2)) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a2_2),V_A2_2)) % 177.89/177.88 => 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) ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_one__mod__nat__number__of,axiom, % 177.89/177.88 ! [V_v_H] : % 177.89/177.88 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_times__numeral__code_I5_J,axiom, % 177.89/177.88 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_minus__numeral__code_I5_J,axiom, % 177.89/177.88 ! [V_w] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_number__of__is__id,axiom, % 177.89/177.88 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ). % 177.89/177.88 % 177.89/177.88 fof(fact_plus__numeral__code_I9_J,axiom, % 177.89/177.88 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_less__number__of__int__code,axiom, % 177.89/177.88 ! [V_l_2,V_k_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) % 177.89/177.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_less__eq__number__of__int__code,axiom, % 177.89/177.88 ! [V_l_2,V_k_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) % 177.89/177.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_int__number__of__def,axiom, % 177.89/177.88 ! [V_w] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),V_w) ). % 177.89/177.88 % 177.89/177.88 fof(fact_nat__number__of__def,axiom, % 177.89/177.88 ! [V_v] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_nat__number__of,axiom, % 177.89/177.88 ! [V_w] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w) ). % 177.89/177.88 % 177.89/177.88 fof(fact_congruent2__implies__congruent,axiom, % 177.89/177.88 ! [V_a_2,V_f_2,V_r2_2,T_c,T_b,V_r1_2,V_A_2,T_a] : % 177.89/177.88 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r1_2) % 177.89/177.88 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.88 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_minus__numeral__code_I6_J,axiom, % 177.89/177.88 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_neg__imp__number__of__eq__0,axiom, % 177.89/177.88 ! [V_v] : % 177.89/177.88 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.88 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_int__eq__iff__number__of,axiom, % 177.89/177.88 ! [V_v_2,V_m_2] : % 177.89/177.88 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) % 177.89/177.88 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) % 177.89/177.88 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_eq__nat__number__of,axiom, % 177.89/177.88 ! [V_v_H_2,V_v_2] : % 177.89/177.88 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2) % 177.89/177.88 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 177.89/177.88 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 177.89/177.88 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 177.89/177.88 => V_v_2 = V_v_H_2 ) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_nat__number__of__add__left,axiom, % 177.89/177.88 ! [V_k,V_v_H,V_v] : % 177.89/177.88 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.88 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_k) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H))),V_k) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_int__nat__number__of,axiom, % 177.89/177.88 ! [V_v] : % 177.89/177.88 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.88 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.88 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mod__nat__number__of,axiom, % 177.89/177.88 ! [V_v_H,V_v] : % 177.89/177.88 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.88 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 177.89/177.88 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_congruent2__implies__congruent__UN,axiom, % 177.89/177.88 ! [V_a_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] : % 177.89/177.88 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 177.89/177.88 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 177.89/177.88 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 177.89/177.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A2_2)) % 177.89/177.88 => 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)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_div__nat__number__of,axiom, % 177.89/177.88 ! [V_v_H,V_v] : % 177.89/177.88 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.88 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.88 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_power__nat__number__of,axiom, % 177.89/177.88 ! [V_n,V_v] : % 177.89/177.88 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.88 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.88 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),V_n)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_power__nat__number__of__number__of,axiom, % 177.89/177.88 ! [V_w,V_v] : % 177.89/177.88 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.88 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.88 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w))) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_one__div__nat__number__of,axiom, % 177.89/177.88 ! [V_v_H] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Suc__nat__number__of__add,axiom, % 177.89/177.88 ! [V_n,V_v] : % 177.89/177.88 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.88 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.88 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))),V_n) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_diff__nat__number__of,axiom, % 177.89/177.88 ! [V_v_2,V_v_H_2] : % 177.89/177.88 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 177.89/177.88 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 177.89/177.88 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_v_H_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_min__Suc__number__of,axiom, % 177.89/177.88 ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_minus__Pls,axiom, % 177.89/177.88 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ). % 177.89/177.88 % 177.89/177.88 fof(fact_rel__simps_I2_J,axiom, % 177.89/177.88 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_add__Pls__right,axiom, % 177.89/177.88 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 177.89/177.88 % 177.89/177.88 fof(fact_add__Pls,axiom, % 177.89/177.88 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ). % 177.89/177.88 % 177.89/177.88 fof(fact_succ__pred,axiom, % 177.89/177.88 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ). % 177.89/177.88 % 177.89/177.88 fof(fact_Pls__def,axiom, % 177.89/177.88 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mult__Pls,axiom, % 177.89/177.88 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ). % 177.89/177.88 % 177.89/177.88 fof(fact_diff__bin__simps_I1_J,axiom, % 177.89/177.88 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 177.89/177.88 % 177.89/177.88 fof(fact_rel__simps_I19_J,axiom, % 177.89/177.88 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_number__of__Pls,axiom, % 177.89/177.88 ! [T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_semiring__norm_I112_J,axiom, % 177.89/177.88 ! [T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_add__numeral__0,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)),V_a) = V_a ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_add__numeral__0__right,axiom, % 177.89/177.88 ! [V_a,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = V_a ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_bin__less__0__simps_I1_J,axiom, % 177.89/177.88 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_nat__number__of__Pls,axiom, % 177.89/177.88 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.88 % 177.89/177.88 fof(fact_semiring__norm_I113_J,axiom, % 177.89/177.88 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ). % 177.89/177.88 % 177.89/177.88 fof(fact_zero__is__num__zero,axiom, % 177.89/177.88 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ). % 177.89/177.88 % 177.89/177.88 fof(fact_Suc__diff__number__of,axiom, % 177.89/177.88 ! [V_m,V_v] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) % 177.89/177.88 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v))) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_not__neg__number__of__Pls,axiom, % 177.89/177.88 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_nat__1__add__number__of,axiom, % 177.89/177.88 ! [V_v] : % 177.89/177.88 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_nat__number__of__add__1,axiom, % 177.89/177.88 ! [V_v] : % 177.89/177.88 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_le__iff__pred__less,axiom, % 177.89/177.88 ! [V_l_2,V_k_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) % 177.89/177.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_pred__def,axiom, % 177.89/177.88 ! [V_k] : c_Int_Opred(V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_nat__number__of__diff__1,axiom, % 177.89/177.88 ! [V_v] : % 177.89/177.88 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 177.89/177.88 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 177.89/177.88 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_divide__Numeral0,axiom, % 177.89/177.88 ! [V_x,T_a] : % 177.89/177.88 ( ( class_Fields_Ofield__inverse__zero(T_a) % 177.89/177.88 & class_Int_Onumber__ring(T_a) ) % 177.89/177.88 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_eq__number__of__0,axiom, % 177.89/177.88 ! [V_v_2] : % 177.89/177.88 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_eq__0__number__of,axiom, % 177.89/177.88 ! [V_v_2] : % 177.89/177.88 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 177.89/177.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_number__of2,axiom, % 177.89/177.88 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 177.89/177.88 % 177.89/177.88 fof(fact_less__nat__number__of,axiom, % 177.89/177.88 ! [V_v_H_2,V_v_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2))) % 177.89/177.88 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) % 177.89/177.88 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_le__nat__number__of,axiom, % 177.89/177.88 ! [V_v_H_2,V_v_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2))) % 177.89/177.88 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) % 177.89/177.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_succ__def,axiom, % 177.89/177.88 ! [V_k] : c_Int_Osucc(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 177.89/177.88 % 177.89/177.88 fof(fact_le__special_I1_J,axiom, % 177.89/177.88 ! [V_y_2,T_a] : % 177.89/177.88 ( ( class_Int_Onumber__ring(T_a) % 177.89/177.88 & class_Rings_Olinordered__idom(T_a) ) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_le__special_I3_J,axiom, % 177.89/177.88 ! [V_x_2,T_a] : % 177.89/177.88 ( ( class_Int_Onumber__ring(T_a) % 177.89/177.88 & class_Rings_Olinordered__idom(T_a) ) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_less__special_I3_J,axiom, % 177.89/177.88 ! [V_x_2,T_a] : % 177.89/177.88 ( ( class_Int_Onumber__ring(T_a) % 177.89/177.88 & class_Rings_Olinordered__idom(T_a) ) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_less__special_I1_J,axiom, % 177.89/177.88 ! [V_y_2,T_a] : % 177.89/177.88 ( ( class_Int_Onumber__ring(T_a) % 177.89/177.88 & class_Rings_Olinordered__idom(T_a) ) % 177.89/177.88 => ( 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))) % 177.89/177.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_less__0__number__of,axiom, % 177.89/177.88 ! [V_v_2] : % 177.89/177.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) % 177.89/177.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_add__nat__number__of,axiom, % 177.89/177.88 ! [V_v_H,V_v] : % 177.89/177.88 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 177.89/177.88 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 177.89/177.88 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H)) ) ) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_number__of__succ,axiom, % 177.89/177.88 ! [V_k,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Osucc(V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_number__of__pred,axiom, % 177.89/177.88 ! [V_w,T_a] : % 177.89/177.88 ( class_Int_Onumber__ring(T_a) % 177.89/177.88 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Opred(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_mult__nat__number__of,axiom, % 177.89/177.88 ! [V_v_H,V_v] : % 177.89/177.88 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 177.89/177.88 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 177.89/177.88 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H)) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_nat__number__of__mult__left,axiom, % 177.89/177.88 ! [V_k,V_v_H,V_v] : % 177.89/177.88 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 177.89/177.88 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.89/177.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 177.89/177.88 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))),V_k) ) ) ). % 177.89/177.88 % 177.89/177.88 fof(fact_neg__number__of__pred__iff__0,axiom, % 177.89/177.88 ! [V_v_2] : % 177.89/177.88 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) % 177.89/177.88 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Suc__eq__number__of,axiom, % 177.89/177.89 ! [V_v_2,V_n_2] : % 177.89/177.89 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_eq__number__of__Suc,axiom, % 177.89/177.89 ! [V_n_2,V_v_2] : % 177.89/177.89 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nat__case__number__of,axiom, % 177.89/177.89 ! [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))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_less__number__of__Suc,axiom, % 177.89/177.89 ! [V_n_2,V_v_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_less__Suc__number__of,axiom, % 177.89/177.89 ! [V_v_2,V_n_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_le__Suc__number__of,axiom, % 177.89/177.89 ! [V_v_2,V_n_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_le__number__of__Suc,axiom, % 177.89/177.89 ! [V_n_2,V_v_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Suc__nat__number__of,axiom, % 177.89/177.89 ! [V_v] : % 177.89/177.89 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.89 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.89 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_max__number__of__Suc,axiom, % 177.89/177.89 ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),c_Int_Onat)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_max__Suc__number__of,axiom, % 177.89/177.89 ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nat__case__add__eq__if,axiom, % 177.89/177.89 ! [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)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_min__number__of__Suc,axiom, % 177.89/177.89 ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),c_Int_Onat)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nat__rec__add__eq__if,axiom, % 177.89/177.89 ! [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))))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nat__rec__number__of,axiom, % 177.89/177.89 ! [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)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_UN__equiv__class__type2,axiom, % 177.89/177.89 ! [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] : % 177.89/177.89 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 177.89/177.89 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 177.89/177.89 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 177.89/177.89 => ( 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))) % 177.89/177.89 => ( 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))) % 177.89/177.89 => ( ! [B_x1] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x1),V_A1_2)) % 177.89/177.89 => ! [B_x2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x2),V_A2_2)) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) ) % 177.89/177.89 => 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)) ) ) ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nat__rec__0,axiom, % 177.89/177.89 ! [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 ). % 177.89/177.89 % 177.89/177.89 fof(fact_nat__rec__Suc,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_UN__equiv__class__type,axiom, % 177.89/177.89 ! [V_B_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 177.89/177.89 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 177.89/177.89 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 177.89/177.89 => ( 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))) % 177.89/177.89 => ( ! [B_x] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) ) % 177.89/177.89 => 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)) ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_eq__special_I3_J,axiom, % 177.89/177.89 ! [V_x_2,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.89 <=> 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)))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_eq__special_I1_J,axiom, % 177.89/177.89 ! [V_y_2,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 177.89/177.89 <=> 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)))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_iszero__def,axiom, % 177.89/177.89 ! [V_z_2,T_a] : % 177.89/177.89 ( class_Rings_Osemiring__1(T_a) % 177.89/177.89 => ( c_Int_Oiszero(T_a,V_z_2) % 177.89/177.89 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_iszero__0,axiom, % 177.89/177.89 ! [T_a] : % 177.89/177.89 ( class_Rings_Osemiring__1(T_a) % 177.89/177.89 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_not__iszero__1,axiom, % 177.89/177.89 ! [T_a] : % 177.89/177.89 ( class_Rings_Osemiring__1(T_a) % 177.89/177.89 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_iszero__Numeral0,axiom, % 177.89/177.89 ! [T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_eq__number__of__eq,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 177.89/177.89 <=> 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)))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power__number__of__odd__number__of,axiom, % 177.89/177.89 ! [V_v_2,V_w_2,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 177.89/177.89 => 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))) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 177.89/177.89 => 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) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zpower__number__of__odd,axiom, % 177.89/177.89 ! [V_z_2,V_w_2] : % 177.89/177.89 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 177.89/177.89 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z_2))),c_COMBI(tc_Int_Oint))) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 177.89/177.89 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power__number__of__odd,axiom, % 177.89/177.89 ! [V_z_2,V_w_2,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 177.89/177.89 => 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))) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 177.89/177.89 => 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) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I39_J,axiom, % 177.89/177.89 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I46_J,axiom, % 177.89/177.89 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I34_J,axiom, % 177.89/177.89 ! [V_l_2,V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_less__eq__int__code_I16_J,axiom, % 177.89/177.89 ! [V_k2_2,V_k1_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I51_J,axiom, % 177.89/177.89 ! [V_l_2,V_k_2] : % 177.89/177.89 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) % 177.89/177.89 <=> V_k_2 = V_l_2 ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_less__int__code_I16_J,axiom, % 177.89/177.89 ! [V_k2_2,V_k1_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I17_J,axiom, % 177.89/177.89 ! [V_l_2,V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_bin__less__0__simps_I4_J,axiom, % 177.89/177.89 ! [V_w_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I22_J,axiom, % 177.89/177.89 ! [V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I12_J,axiom, % 177.89/177.89 ! [V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Bit1__def,axiom, % 177.89/177.89 ! [V_k] : c_Int_OBit1(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)),V_k) ). % 177.89/177.89 % 177.89/177.89 fof(fact_neg__number__of__Bit1,axiom, % 177.89/177.89 ! [V_w_2] : % 177.89/177.89 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) % 177.89/177.89 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_minus__Bit1,axiom, % 177.89/177.89 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_iszero__number__of__Bit1,axiom, % 177.89/177.89 ! [V_w,T_a] : % 177.89/177.89 ( ( class_Int_Onumber__ring(T_a) % 177.89/177.89 & class_Int_Oring__char__0(T_a) ) % 177.89/177.89 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_succ__Pls,axiom, % 177.89/177.89 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ). % 177.89/177.89 % 177.89/177.89 fof(fact_number__of__Bit1,axiom, % 177.89/177.89 ! [V_w,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mult__numeral__1__right,axiom, % 177.89/177.89 ! [V_a,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mult__numeral__1,axiom, % 177.89/177.89 ! [V_a,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))),V_a) = V_a ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_semiring__norm_I110_J,axiom, % 177.89/177.89 ! [T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_numeral__1__eq__1,axiom, % 177.89/177.89 ! [T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I29_J,axiom, % 177.89/177.89 ! [V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I5_J,axiom, % 177.89/177.89 ! [V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divide__numeral__1,axiom, % 177.89/177.89 ! [V_a,T_a] : % 177.89/177.89 ( ( class_Fields_Ofield(T_a) % 177.89/177.89 & class_Int_Onumber__ring(T_a) ) % 177.89/177.89 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divide__Numeral1,axiom, % 177.89/177.89 ! [V_x,T_a] : % 177.89/177.89 ( ( class_Fields_Ofield(T_a) % 177.89/177.89 & class_Int_Onumber__ring(T_a) ) % 177.89/177.89 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_x ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_one__is__num__one,axiom, % 177.89/177.89 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Numeral1__eq1__nat,axiom, % 177.89/177.89 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nat__numeral__1__eq__1,axiom, % 177.89/177.89 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom, % 177.89/177.89 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_not__iszero__Numeral1,axiom, % 177.89/177.89 ! [T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_numeral__3__eq__3,axiom, % 177.89/177.89 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_numeral__1__eq__Suc__0,axiom, % 177.89/177.89 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power3__eq__cube,axiom, % 177.89/177.89 ! [V_a,T_a] : % 177.89/177.89 ( class_Groups_Omonoid__mult(T_a) % 177.89/177.89 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),V_a) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom, % 177.89/177.89 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Suc3__eq__add__3,axiom, % 177.89/177.89 ! [V_n] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n) ). % 177.89/177.89 % 177.89/177.89 fof(fact_transfer__int__nat__numerals_I4_J,axiom, % 177.89/177.89 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_transfer__nat__int__numerals_I4_J,axiom, % 177.89/177.89 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_le__special_I4_J,axiom, % 177.89/177.89 ! [V_x_2,T_a] : % 177.89/177.89 ( ( class_Int_Onumber__ring(T_a) % 177.89/177.89 & class_Rings_Olinordered__idom(T_a) ) % 177.89/177.89 => ( 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))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_le__special_I2_J,axiom, % 177.89/177.89 ! [V_y_2,T_a] : % 177.89/177.89 ( ( class_Int_Onumber__ring(T_a) % 177.89/177.89 & class_Rings_Olinordered__idom(T_a) ) % 177.89/177.89 => ( 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))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_less__special_I2_J,axiom, % 177.89/177.89 ! [V_y_2,T_a] : % 177.89/177.89 ( ( class_Int_Onumber__ring(T_a) % 177.89/177.89 & class_Rings_Olinordered__idom(T_a) ) % 177.89/177.89 => ( 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))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_less__special_I4_J,axiom, % 177.89/177.89 ! [V_x_2,T_a] : % 177.89/177.89 ( ( class_Int_Onumber__ring(T_a) % 177.89/177.89 & class_Rings_Olinordered__idom(T_a) ) % 177.89/177.89 => ( 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))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_add__special_I3_J,axiom, % 177.89/177.89 ! [V_v,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),c_Int_OBit1(c_Int_OPls))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_add__special_I2_J,axiom, % 177.89/177.89 ! [V_w,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Suc__diff__eq__diff__pred,axiom, % 177.89/177.89 ! [V_m,V_n] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),V_n)) % 177.89/177.89 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mod__Suc__eq__mod__add3,axiom, % 177.89/177.89 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Suc__mod__eq__add3__mod,axiom, % 177.89/177.89 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),V_n) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom, % 177.89/177.89 ! [V_v,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_div__Suc__eq__div__add3,axiom, % 177.89/177.89 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Suc__div__eq__add3__div,axiom, % 177.89/177.89 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),V_n) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Suc__div__eq__add3__div__number__of,axiom, % 177.89/177.89 ! [V_v,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_diff__special_I1_J,axiom, % 177.89/177.89 ! [V_w,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_diff__special_I2_J,axiom, % 177.89/177.89 ! [V_v,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_eq__special_I4_J,axiom, % 177.89/177.89 ! [V_x_2,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 177.89/177.89 <=> 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))))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_eq__special_I2_J,axiom, % 177.89/177.89 ! [V_y_2,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 177.89/177.89 <=> 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)))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nat__number__of__Bit1,axiom, % 177.89/177.89 ! [V_w_2] : % 177.89/177.89 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 177.89/177.89 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 177.89/177.89 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zmod__number__of__Bit1,axiom, % 177.89/177.89 ! [V_v,V_w] : % 177.89/177.89 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 177.89/177.89 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 177.89/177.89 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_neg__zmod__mult__2,axiom, % 177.89/177.89 ! [V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_arith__series__int,axiom, % 177.89/177.89 ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I50_J,axiom, % 177.89/177.89 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I49_J,axiom, % 177.89/177.89 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 177.89/177.89 % 177.89/177.89 fof(fact_add__Bit0__Bit0,axiom, % 177.89/177.89 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Bit0__def,axiom, % 177.89/177.89 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mult__Bit0,axiom, % 177.89/177.89 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I48_J,axiom, % 177.89/177.89 ! [V_l_2,V_k_2] : % 177.89/177.89 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) % 177.89/177.89 <=> V_k_2 = V_l_2 ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I14_J,axiom, % 177.89/177.89 ! [V_l_2,V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_less__int__code_I13_J,axiom, % 177.89/177.89 ! [V_k2_2,V_k1_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_minus__Bit0,axiom, % 177.89/177.89 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(V_k)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_diff__bin__simps_I7_J,axiom, % 177.89/177.89 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_less__eq__int__code_I13_J,axiom, % 177.89/177.89 ! [V_k2_2,V_k1_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I31_J,axiom, % 177.89/177.89 ! [V_l_2,V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I44_J,axiom, % 177.89/177.89 ! [V_k_2] : % 177.89/177.89 ( c_Int_OBit0(V_k_2) = c_Int_OPls % 177.89/177.89 <=> V_k_2 = c_Int_OPls ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I38_J,axiom, % 177.89/177.89 ! [V_l_2] : % 177.89/177.89 ( c_Int_OPls = c_Int_OBit0(V_l_2) % 177.89/177.89 <=> c_Int_OPls = V_l_2 ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Bit0__Pls,axiom, % 177.89/177.89 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 177.89/177.89 % 177.89/177.89 fof(fact_bin__less__0__simps_I3_J,axiom, % 177.89/177.89 ! [V_w_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I21_J,axiom, % 177.89/177.89 ! [V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I27_J,axiom, % 177.89/177.89 ! [V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I32_J,axiom, % 177.89/177.89 ! [V_l_2,V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_less__eq__int__code_I14_J,axiom, % 177.89/177.89 ! [V_k2_2,V_k1_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I10_J,axiom, % 177.89/177.89 ! [V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I4_J,axiom, % 177.89/177.89 ! [V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_less__int__code_I15_J,axiom, % 177.89/177.89 ! [V_k2_2,V_k1_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I16_J,axiom, % 177.89/177.89 ! [V_l_2,V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_add__Bit1__Bit0,axiom, % 177.89/177.89 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_add__Bit0__Bit1,axiom, % 177.89/177.89 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_diff__bin__simps_I3_J,axiom, % 177.89/177.89 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),V_l)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_diff__bin__simps_I9_J,axiom, % 177.89/177.89 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_diff__bin__simps_I10_J,axiom, % 177.89/177.89 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zdiv__number__of__Bit0,axiom, % 177.89/177.89 ! [V_w,V_v] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_neg__number__of__Bit0,axiom, % 177.89/177.89 ! [V_w_2] : % 177.89/177.89 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) % 177.89/177.89 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_pred__Bit0,axiom, % 177.89/177.89 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_pred__Bit1,axiom, % 177.89/177.89 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ). % 177.89/177.89 % 177.89/177.89 fof(fact_iszero__number__of__Bit0,axiom, % 177.89/177.89 ! [V_w_2,T_a] : % 177.89/177.89 ( ( class_Int_Onumber__ring(T_a) % 177.89/177.89 & class_Int_Oring__char__0(T_a) ) % 177.89/177.89 => ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w_2))) % 177.89/177.89 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_succ__Bit1,axiom, % 177.89/177.89 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_succ__Bit0,axiom, % 177.89/177.89 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nat__number__of__Bit0,axiom, % 177.89/177.89 ! [V_w_2] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_number__of__Bit0,axiom, % 177.89/177.89 ! [V_w,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I15_J,axiom, % 177.89/177.89 ! [V_l_2,V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_less__int__code_I14_J,axiom, % 177.89/177.89 ! [V_k2_2,V_k1_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I33_J,axiom, % 177.89/177.89 ! [V_l_2,V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_less__eq__int__code_I15_J,axiom, % 177.89/177.89 ! [V_k2_2,V_k1_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_card__UNIV__bool,axiom, % 177.89/177.89 hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mult__Bit1,axiom, % 177.89/177.89 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(V_k)),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l))),V_l) ). % 177.89/177.89 % 177.89/177.89 fof(fact_diff__bin__simps_I8_J,axiom, % 177.89/177.89 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(V_k)),V_l)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_add__Bit1__Bit1,axiom, % 177.89/177.89 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_Osucc(V_l))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power__number__of__even,axiom, % 177.89/177.89 ! [V_w_2,V_z_2,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => 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))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zpower__number__of__even,axiom, % 177.89/177.89 ! [V_w_2,V_z_2] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_double__number__of__Bit0,axiom, % 177.89/177.89 ! [V_w,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_number__of1,axiom, % 177.89/177.89 ! [V_n] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_n)))) % 177.89/177.89 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_n)))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom, % 177.89/177.89 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power__number__of__even__number__of,axiom, % 177.89/177.89 ! [V_w_2,V_v_2,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => 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))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mult__2__right,axiom, % 177.89/177.89 ! [V_z,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mult__2,axiom, % 177.89/177.89 ! [V_z,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_one__add__one__is__two,axiom, % 177.89/177.89 ! [T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zero__power2,axiom, % 177.89/177.89 ! [T_a] : % 177.89/177.89 ( class_Rings_Osemiring__1(T_a) % 177.89/177.89 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zero__eq__power2,axiom, % 177.89/177.89 ! [V_a_2,T_a] : % 177.89/177.89 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 177.89/177.89 => ( 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) % 177.89/177.89 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_semiring__norm_I115_J,axiom, % 177.89/177.89 hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_numeral__2__eq__2,axiom, % 177.89/177.89 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 177.89/177.89 ! [V_x,T_a] : % 177.89/177.89 ( class_Rings_Ocomm__semiring__1(T_a) % 177.89/177.89 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power2__eq__square,axiom, % 177.89/177.89 ! [V_a,T_a] : % 177.89/177.89 ( class_Groups_Omonoid__mult(T_a) % 177.89/177.89 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom, % 177.89/177.89 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_add__2__eq__Suc_H,axiom, % 177.89/177.89 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_add__2__eq__Suc,axiom, % 177.89/177.89 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_one__power2,axiom, % 177.89/177.89 ! [T_a] : % 177.89/177.89 ( class_Rings_Osemiring__1(T_a) % 177.89/177.89 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power2__minus,axiom, % 177.89/177.89 ! [V_a,T_a] : % 177.89/177.89 ( class_Rings_Oring__1(T_a) % 177.89/177.89 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nat__mult__2__right,axiom, % 177.89/177.89 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_z),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nat__mult__2,axiom, % 177.89/177.89 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power__even__eq,axiom, % 177.89/177.89 ! [V_n,V_a,T_a] : % 177.89/177.89 ( class_Groups_Omonoid__mult(T_a) % 177.89/177.89 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_transfer__int__nat__numerals_I3_J,axiom, % 177.89/177.89 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_transfer__nat__int__numerals_I3_J,axiom, % 177.89/177.89 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_abs__power2,axiom, % 177.89/177.89 ! [V_a,T_a] : % 177.89/177.89 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.89 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power2__abs,axiom, % 177.89/177.89 ! [V_a,T_a] : % 177.89/177.89 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.89 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nat__1__add__1,axiom, % 177.89/177.89 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mod2__Suc__Suc,axiom, % 177.89/177.89 ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_div2__Suc__Suc,axiom, % 177.89/177.89 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zmod__number__of__Bit0,axiom, % 177.89/177.89 ! [V_w,V_v] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_add__self__div__2,axiom, % 177.89/177.89 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_m ). % 177.89/177.89 % 177.89/177.89 fof(fact_half__gt__zero,axiom, % 177.89/177.89 ! [V_r,T_a] : % 177.89/177.89 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.89 & class_Int_Onumber__ring(T_a) ) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_r),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_half__gt__zero__iff,axiom, % 177.89/177.89 ! [V_r_2,T_a] : % 177.89/177.89 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.89/177.89 & class_Int_Onumber__ring(T_a) ) % 177.89/177.89 => ( 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)))))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zero__le__power2,axiom, % 177.89/177.89 ! [V_a,T_a] : % 177.89/177.89 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power2__le__imp__le,axiom, % 177.89/177.89 ! [V_y,V_x,T_a] : % 177.89/177.89 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power2__eq__imp__eq,axiom, % 177.89/177.89 ! [V_y,V_x,T_a] : % 177.89/177.89 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.89 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.89/177.89 => V_x = V_y ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zero__less__power2,axiom, % 177.89/177.89 ! [V_a_2,T_a] : % 177.89/177.89 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.89 => ( 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)))))) % 177.89/177.89 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power2__less__0,axiom, % 177.89/177.89 ! [V_a,T_a] : % 177.89/177.89 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.89 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_sum__power2__eq__zero__iff,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,T_a] : % 177.89/177.89 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.89 => ( 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) % 177.89/177.89 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.89 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power2__eq__square__number__of,axiom, % 177.89/177.89 ! [V_w,T_b] : % 177.89/177.89 ( ( class_Groups_Omonoid__mult(T_b) % 177.89/177.89 & class_Int_Onumber(T_b) ) % 177.89/177.89 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_less__2__cases,axiom, % 177.89/177.89 ! [V_n] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) % 177.89/177.89 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.89 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nat__2,axiom, % 177.89/177.89 hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power2__eq__1__iff,axiom, % 177.89/177.89 ! [V_a_2,T_a] : % 177.89/177.89 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 177.89/177.89 => ( 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) % 177.89/177.89 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_a) % 177.89/177.89 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 177.89/177.89 ! [V_n,V_x,T_a] : % 177.89/177.89 ( class_Rings_Ocomm__semiring__1(T_a) % 177.89/177.89 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power__minus__even,axiom, % 177.89/177.89 ! [V_n,V_a,T_a] : % 177.89/177.89 ( class_Rings_Oring__1(T_a) % 177.89/177.89 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power2__less__imp__less,axiom, % 177.89/177.89 ! [V_y,V_x,T_a] : % 177.89/177.89 ( class_Rings_Olinordered__semidom(T_a) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_sum__power2__ge__zero,axiom, % 177.89/177.89 ! [V_y,V_x,T_a] : % 177.89/177.89 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_sum__power2__le__zero__iff,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,T_a] : % 177.89/177.89 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.89 => ( 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))) % 177.89/177.89 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.89 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_sum__power2__gt__zero__iff,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,T_a] : % 177.89/177.89 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.89 => ( 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))))))) % 177.89/177.89 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 177.89/177.89 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_not__sum__power2__lt__zero,axiom, % 177.89/177.89 ! [V_y,V_x,T_a] : % 177.89/177.89 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.89 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power2__sum,axiom, % 177.89/177.89 ! [V_y,V_x,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zero__le__even__power_H,axiom, % 177.89/177.89 ! [V_n,V_a,T_a] : % 177.89/177.89 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom, % 177.89/177.89 ! [V_n,V_x,T_a] : % 177.89/177.89 ( class_Rings_Ocomm__semiring__1(T_a) % 177.89/177.89 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power__odd__eq,axiom, % 177.89/177.89 ! [V_n,V_a,T_a] : % 177.89/177.89 ( class_Groups_Omonoid__mult(T_a) % 177.89/177.89 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power__minus1__even,axiom, % 177.89/177.89 ! [V_n,T_a] : % 177.89/177.89 ( class_Rings_Oring__1(T_a) % 177.89/177.89 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zdiv__number__of__Bit1,axiom, % 177.89/177.89 ! [V_v,V_w] : % 177.89/177.89 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 177.89/177.89 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 177.89/177.89 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mod2__gr__0,axiom, % 177.89/177.89 ! [V_m_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 177.89/177.89 <=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_div__2__gt__zero,axiom, % 177.89/177.89 ! [V_n] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power2__diff,axiom, % 177.89/177.89 ! [V_y,V_x,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_odd__0__le__power__imp__0__le,axiom, % 177.89/177.89 ! [V_n,V_a,T_a] : % 177.89/177.89 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))))) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_odd__power__less__zero,axiom, % 177.89/177.89 ! [V_n,V_a,T_a] : % 177.89/177.89 ( class_Rings_Olinordered__idom(T_a) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power__minus1__odd,axiom, % 177.89/177.89 ! [V_n,T_a] : % 177.89/177.89 ( class_Rings_Oring__1(T_a) % 177.89/177.89 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Suc__n__div__2__gt__zero,axiom, % 177.89/177.89 ! [V_n] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_of__nat__double,axiom, % 177.89/177.89 ! [V_x,T_a] : % 177.89/177.89 ( class_Rings_Osemiring__1(T_a) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.89/177.89 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_pos__zmod__mult__2,axiom, % 177.89/177.89 ! [V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.89/177.89 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_a))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_pos__zdiv__mult__2,axiom, % 177.89/177.89 ! [V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.89/177.89 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_a) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_neg__zdiv__mult__2,axiom, % 177.89/177.89 ! [V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_a) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_int__of__code,axiom, % 177.89/177.89 ! [V_k] : % 177.89/177.89 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.89/177.89 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 177.89/177.89 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.89/177.89 => ( ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.89/177.89 => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) % 177.89/177.89 & ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.89/177.89 => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_of__int__num,axiom, % 177.89/177.89 ! [V_k_2,T_a] : % 177.89/177.89 ( class_Rings_Oring__1(T_a) % 177.89/177.89 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = c_Groups_Ozero__class_Ozero(T_a) ) % 177.89/177.89 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => 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))) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => 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))))) ) ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power__m1__odd,axiom, % 177.89/177.89 ! [V_n,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I42_J,axiom, % 177.89/177.89 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I45_J,axiom, % 177.89/177.89 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I40_J,axiom, % 177.89/177.89 c_Int_OMin != c_Int_OPls ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I37_J,axiom, % 177.89/177.89 c_Int_OPls != c_Int_OMin ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I24_J,axiom, % 177.89/177.89 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_code__numeral__zero__minus__one,axiom, % 177.89/177.89 hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I7_J,axiom, % 177.89/177.89 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Bit1__Min,axiom, % 177.89/177.89 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I43_J,axiom, % 177.89/177.89 ! [V_l_2] : % 177.89/177.89 ( c_Int_OMin = c_Int_OBit1(V_l_2) % 177.89/177.89 <=> c_Int_OMin = V_l_2 ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I47_J,axiom, % 177.89/177.89 ! [V_k_2] : % 177.89/177.89 ( c_Int_OBit1(V_k_2) = c_Int_OMin % 177.89/177.89 <=> V_k_2 = c_Int_OMin ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_bin__less__0__simps_I2_J,axiom, % 177.89/177.89 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I20_J,axiom, % 177.89/177.89 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I23_J,axiom, % 177.89/177.89 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I30_J,axiom, % 177.89/177.89 ! [V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I26_J,axiom, % 177.89/177.89 ! [V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I6_J,axiom, % 177.89/177.89 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I3_J,axiom, % 177.89/177.89 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I9_J,axiom, % 177.89/177.89 ! [V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I13_J,axiom, % 177.89/177.89 ! [V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I28_J,axiom, % 177.89/177.89 ! [V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I8_J,axiom, % 177.89/177.89 ! [V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_eq__number__of__Pls__Min,axiom, % 177.89/177.89 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Int_OMin__def,axiom, % 177.89/177.89 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mult__Min,axiom, % 177.89/177.89 ! [V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k) ). % 177.89/177.89 % 177.89/177.89 fof(fact_neg__number__of__Min,axiom, % 177.89/177.89 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_pred__Pls,axiom, % 177.89/177.89 c_Int_Opred(c_Int_OPls) = c_Int_OMin ). % 177.89/177.89 % 177.89/177.89 fof(fact_add__Min,axiom, % 177.89/177.89 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ). % 177.89/177.89 % 177.89/177.89 fof(fact_add__Min__right,axiom, % 177.89/177.89 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ). % 177.89/177.89 % 177.89/177.89 fof(fact_pred__Min,axiom, % 177.89/177.89 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nonzero__number__of__Min,axiom, % 177.89/177.89 ! [T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_succ__Min,axiom, % 177.89/177.89 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ). % 177.89/177.89 % 177.89/177.89 fof(fact_diff__bin__simps_I2_J,axiom, % 177.89/177.89 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mult__minus1,axiom, % 177.89/177.89 ! [V_z,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_z) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mult__minus1__right,axiom, % 177.89/177.89 ! [V_z,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_arith__simps_I31_J,axiom, % 177.89/177.89 ! [T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_number__of__Min,axiom, % 177.89/177.89 ! [T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_abs__minus__one,axiom, % 177.89/177.89 ! [T_a] : % 177.89/177.89 ( ( class_Int_Onumber__ring(T_a) % 177.89/177.89 & class_Rings_Olinordered__idom(T_a) ) % 177.89/177.89 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = c_Groups_Oone__class_Oone(T_a) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divide__minus1,axiom, % 177.89/177.89 ! [V_x,T_a] : % 177.89/177.89 ( ( class_Fields_Ofield__inverse__zero(T_a) % 177.89/177.89 & class_Int_Onumber__ring(T_a) ) % 177.89/177.89 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I11_J,axiom, % 177.89/177.89 ! [V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rel__simps_I25_J,axiom, % 177.89/177.89 ! [V_k_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zmod__minus1__right,axiom, % 177.89/177.89 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 177.89/177.89 % 177.89/177.89 fof(fact_diff__bin__simps_I4_J,axiom, % 177.89/177.89 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_minus__Min,axiom, % 177.89/177.89 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ). % 177.89/177.89 % 177.89/177.89 fof(fact_pos__zmult__eq__1__iff__lemma,axiom, % 177.89/177.89 ! [V_n,V_m] : % 177.89/177.89 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 177.89/177.89 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) % 177.89/177.89 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zmult__eq__1__iff,axiom, % 177.89/177.89 ! [V_n_2,V_m_2] : % 177.89/177.89 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 177.89/177.89 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 177.89/177.89 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 177.89/177.89 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) % 177.89/177.89 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_diff__bin__simps_I5_J,axiom, % 177.89/177.89 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_diff__bin__simps_I6_J,axiom, % 177.89/177.89 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_of__int__m1,axiom, % 177.89/177.89 ! [T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zdiv__minus1__right,axiom, % 177.89/177.89 ! [V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zero__code__numeral__code,axiom, % 177.89/177.89 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls) ). % 177.89/177.89 % 177.89/177.89 fof(fact_minus1__divide,axiom, % 177.89/177.89 ! [V_x,T_a] : % 177.89/177.89 ( ( class_Fields_Ofield__inverse__zero(T_a) % 177.89/177.89 & class_Int_Onumber__ring(T_a) ) % 177.89/177.89 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_x)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_abs__power__minus__one,axiom, % 177.89/177.89 ! [V_n,T_a] : % 177.89/177.89 ( ( class_Int_Onumber__ring(T_a) % 177.89/177.89 & class_Rings_Olinordered__idom(T_a) ) % 177.89/177.89 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_div__eq__minus1,axiom, % 177.89/177.89 ! [V_b] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.89 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_div__pos__neg__trivial,axiom, % 177.89/177.89 ! [V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zmod__minus1,axiom, % 177.89/177.89 ! [V_b] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.89 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_one__code__numeral__code,axiom, % 177.89/177.89 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_power__m1__even,axiom, % 177.89/177.89 ! [V_n,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Nitpick_OFrac__def,axiom, % 177.89/177.89 c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_small__int__def,axiom, % 177.89/177.89 ! [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))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_int__ge__less__than__def,axiom, % 177.89/177.89 ! [V_d_2] : c_Int_Oint__ge__less__than(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_inj__graph,axiom, % 177.89/177.89 ! [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))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_int__ge__less__than2__def,axiom, % 177.89/177.89 ! [V_d_2] : c_Int_Oint__ge__less__than2(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Nitpick_Oprod__def,axiom, % 177.89/177.89 ! [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)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nat__of__aux__code,axiom, % 177.89/177.89 ! [V_n,V_i] : % 177.89/177.89 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.89/177.89 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) % 177.89/177.89 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.89/177.89 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,V_n)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__int__rel__def,axiom, % 177.89/177.89 ! [V_b_2,V_a_2] : c_Divides_Odivmod__int__rel(V_a_2,V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,V_a_2))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_2)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_finite__psubset__def,axiom, % 177.89/177.89 ! [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)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_full__small__int__def,axiom, % 177.89/177.89 ! [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))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__int__correct,axiom, % 177.89/177.89 ! [V_a,V_b] : % 177.89/177.89 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zmult2__lemma,axiom, % 177.89/177.89 ! [V_c,V_r,V_q,V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 177.89/177.89 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 177.89/177.89 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)))) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_code__numeral_Osize_I1_J,axiom, % 177.89/177.89 c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Nats__number__of,axiom, % 177.89/177.89 ! [V_w_2,T_a] : % 177.89/177.89 ( class_Int_Onumber__ring(T_a) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) % 177.89/177.89 => 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))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_congruent2D,axiom, % 177.89/177.89 ! [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] : % 177.89/177.89 ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 177.89/177.89 => ( 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)) % 177.89/177.89 => ( 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)) % 177.89/177.89 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_congruentD,axiom, % 177.89/177.89 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_b,T_a] : % 177.89/177.89 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 177.89/177.89 => ( 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)) % 177.89/177.89 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_pred__subset__eq2,axiom, % 177.89/177.89 ! [V_S_2,V_R_2,T_b,T_a] : % 177.89/177.89 ( 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))) % 177.89/177.89 <=> 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_pred__equals__eq2,axiom, % 177.89/177.89 ! [V_S_2,V_R_2,T_b,T_a] : % 177.89/177.89 ( 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) % 177.89/177.89 <=> V_R_2 = V_S_2 ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_inf__Int__eq2,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 177.89/177.89 ( 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)) % 177.89/177.89 <=> 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))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_bot__empty__eq2,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,T_b,T_a] : % 177.89/177.89 ( 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)) % 177.89/177.89 <=> 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)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_sup__Un__eq2,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 177.89/177.89 ( 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)) % 177.89/177.89 <=> 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))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_small__prod__def,axiom, % 177.89/177.89 ! [V_d_2,V_f_2,T_a,T_b] : % 177.89/177.89 ( ( class_Smallcheck_Osmall(T_b) % 177.89/177.89 & class_Smallcheck_Osmall(T_a) ) % 177.89/177.89 => 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) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rev__ImageI,axiom, % 177.89/177.89 ! [V_r_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.89 => ( 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)) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Image__iff,axiom, % 177.89/177.89 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 177.89/177.89 <=> ? [B_x] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 177.89/177.89 & 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)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_unique__remainder,axiom, % 177.89/177.89 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 177.89/177.89 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H))) % 177.89/177.89 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => V_r = V_r_H ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_unique__quotient,axiom, % 177.89/177.89 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 177.89/177.89 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H))) % 177.89/177.89 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => V_q = V_q_H ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_self__remainder,axiom, % 177.89/177.89 ! [V_r,V_q,V_a] : % 177.89/177.89 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 177.89/177.89 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__int__rel__0,axiom, % 177.89/177.89 ! [V_b] : % 177.89/177.89 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_SUP__UN__eq2,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 177.89/177.89 ( 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)) % 177.89/177.89 <=> 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))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_INF__INT__eq2,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 177.89/177.89 ( 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)) % 177.89/177.89 <=> 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))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_self__quotient,axiom, % 177.89/177.89 ! [V_r,V_q,V_a] : % 177.89/177.89 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 177.89/177.89 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__int__rel__mod,axiom, % 177.89/177.89 ! [V_r,V_q,V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 177.89/177.89 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__int__rel__div,axiom, % 177.89/177.89 ! [V_r,V_q,V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 177.89/177.89 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Nats__0,axiom, % 177.89/177.89 ! [T_a] : % 177.89/177.89 ( class_Rings_Osemiring__1(T_a) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__int__mod__div,axiom, % 177.89/177.89 ! [V_q,V_p] : c_Divides_Odivmod__int(V_p,V_q) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_p),V_q)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_p,V_q)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Nats__add,axiom, % 177.89/177.89 ! [V_b_2,V_a_2,T_a] : % 177.89/177.89 ( class_Rings_Osemiring__1(T_a) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 177.89/177.89 => 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))) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Nats__mult,axiom, % 177.89/177.89 ! [V_b_2,V_a_2,T_a] : % 177.89/177.89 ( class_Rings_Osemiring__1(T_a) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 177.89/177.89 => 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))) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Nats__1,axiom, % 177.89/177.89 ! [T_a] : % 177.89/177.89 ( class_Rings_Osemiring__1(T_a) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_of__nat__in__Nats,axiom, % 177.89/177.89 ! [V_n_2,T_a] : % 177.89/177.89 ( class_Rings_Osemiring__1(T_a) % 177.89/177.89 => 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))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Image__singleton__iff,axiom, % 177.89/177.89 ! [V_a_2,V_r_2,T_b,V_b_2,T_a] : % 177.89/177.89 ( 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)))))) % 177.89/177.89 <=> 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_equiv__class__eq,axiom, % 177.89/177.89 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 177.89/177.89 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 177.89/177.89 => ( 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)) % 177.89/177.89 => 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)))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_quotient__eq__iff,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 177.89/177.89 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 177.89/177.89 => ( 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))) % 177.89/177.89 => ( 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))) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 177.89/177.89 => ( V_X_2 = V_Y_2 % 177.89/177.89 <=> 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)) ) ) ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_quotient__eqI,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 177.89/177.89 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 177.89/177.89 => ( 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))) % 177.89/177.89 => ( 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))) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 177.89/177.89 => ( 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)) % 177.89/177.89 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__int__rel__div__mod,axiom, % 177.89/177.89 ! [V_a,V_b] : % 177.89/177.89 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Image__singleton,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_eq__equiv__class,axiom, % 177.89/177.89 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_a] : % 177.89/177.89 ( 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)))) % 177.89/177.89 => ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 177.89/177.89 => 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)) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_eq__equiv__class__iff,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 177.89/177.89 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 177.89/177.89 => ( 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)))) % 177.89/177.89 <=> 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)) ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_equiv__class__eq__iff,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 177.89/177.89 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 177.89/177.89 => ( 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)) % 177.89/177.89 <=> ( 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)))) % 177.89/177.89 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.89 & hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_equiv__class__subset,axiom, % 177.89/177.89 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 177.89/177.89 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 177.89/177.89 => ( 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)) % 177.89/177.89 => 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)))))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_eq__equiv__class__iff2,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 177.89/177.89 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 177.89/177.89 => ( 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) % 177.89/177.89 <=> 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)) ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zadd1__lemma,axiom, % 177.89/177.89 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 177.89/177.89 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_aq),V_ar))) % 177.89/177.89 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_bq),V_br))) % 177.89/177.89 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br),V_c)))) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zminus1__lemma,axiom, % 177.89/177.89 ! [V_r_2,V_q_2,V_b_2,V_a_2] : % 177.89/177.89 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a_2,V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2))) % 177.89/177.89 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b_2),V_r_2))))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_subset__equiv__class,axiom, % 177.89/177.89 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_a] : % 177.89/177.89 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 177.89/177.89 => ( 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)))))) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 177.89/177.89 => 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)) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_equiv__class__nondisjoint,axiom, % 177.89/177.89 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_a] : % 177.89/177.89 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 177.89/177.89 => ( 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))))))) % 177.89/177.89 => 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)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__int__relI,axiom, % 177.89/177.89 ! [V_r,V_q,V_b,V_a] : % 177.89/177.89 ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) % 177.89/177.89 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 177.89/177.89 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 177.89/177.89 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 177.89/177.89 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zmult1__lemma,axiom, % 177.89/177.89 ! [V_a,V_r,V_q,V_c,V_b] : % 177.89/177.89 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 177.89/177.89 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r),V_c)))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_pair__imageI,axiom, % 177.89/177.89 ! [V_f_2,T_c,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 177.89/177.89 ( 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)) % 177.89/177.89 => 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))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_norm__frac_Osimps,axiom, % 177.89/177.89 ! [V_a_2,V_b_2] : % 177.89/177.89 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 177.89/177.89 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) % 177.89/177.89 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 177.89/177.89 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_adjust__def,axiom, % 177.89/177.89 ! [V_b_2] : c_Divides_Oadjust(V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_sup2E,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 177.89/177.89 ( 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)) % 177.89/177.89 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 177.89/177.89 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_sup2CI,axiom, % 177.89/177.89 ! [T_b,T_a,V_A_2,V_y_2,V_x_2,V_B_2] : % 177.89/177.89 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 177.89/177.89 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) % 177.89/177.89 => 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_inf2E,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 177.89/177.89 ( 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)) % 177.89/177.89 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 177.89/177.89 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_inf2I,axiom, % 177.89/177.89 ! [T_b,T_a,V_B_2,V_y_2,V_x_2,V_A_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 177.89/177.89 => 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)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mem__splitI,axiom, % 177.89/177.89 ! [T_c,T_b,V_b_2,V_a_2,V_ca_2,V_z_2,T_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2))) % 177.89/177.89 => 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)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_prod__caseI,axiom, % 177.89/177.89 ! [T_b,T_a,V_b_2,V_a_2,V_f1_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) % 177.89/177.89 => 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))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_splitI,axiom, % 177.89/177.89 ! [T_b,T_a,V_b_2,V_a_2,V_f_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) % 177.89/177.89 => 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))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_bot2E,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_splitD_H,axiom, % 177.89/177.89 ! [V_ca_2,V_b_2,V_a_2,V_R_2,T_c,T_b,T_a] : % 177.89/177.89 ( 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)) % 177.89/177.89 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_swap__inj__on,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_inf2D2,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 177.89/177.89 ( 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)) % 177.89/177.89 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_inf2D1,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 177.89/177.89 ( 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)) % 177.89/177.89 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_predicate2D,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_b,T_a] : % 177.89/177.89 ( 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)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 177.89/177.89 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rev__predicate2D,axiom, % 177.89/177.89 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_P_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 177.89/177.89 => ( 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)) % 177.89/177.89 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_sup2I1,axiom, % 177.89/177.89 ! [V_B_2,T_b,T_a,V_y_2,V_x_2,V_A_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 177.89/177.89 => 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_sup2I2,axiom, % 177.89/177.89 ! [V_A_2,T_b,T_a,V_y_2,V_x_2,V_B_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 177.89/177.89 => 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Pair__inject,axiom, % 177.89/177.89 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] : % 177.89/177.89 ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H),V_b_H) % 177.89/177.89 => ~ ( V_a = V_a_H % 177.89/177.89 => V_b != V_b_H ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Pair__eq,axiom, % 177.89/177.89 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 177.89/177.89 ( 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) % 177.89/177.89 <=> ( V_a_2 = V_a_H_2 % 177.89/177.89 & V_b_2 = V_b_H_2 ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_split__paired__All,axiom, % 177.89/177.89 ! [T_b,T_a,V_P_2] : % 177.89/177.89 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 177.89/177.89 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_split__weak__cong,axiom, % 177.89/177.89 ! [V_ca_2,T_c,T_b,T_a,V_q_2,V_p_2] : % 177.89/177.89 ( V_p_2 = V_q_2 % 177.89/177.89 => 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) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_in__finite__psubset,axiom, % 177.89/177.89 ! [V_B_2,V_A_2,T_a] : % 177.89/177.89 ( 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))) % 177.89/177.89 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.89 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_split__twice,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_prod_Osimps_I2_J,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_split__conv,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_splitD,axiom, % 177.89/177.89 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( 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))) % 177.89/177.89 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_split__eta,axiom, % 177.89/177.89 ! [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 ). % 177.89/177.89 % 177.89/177.89 fof(fact_The__split__eq,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_split__paired__The,axiom, % 177.89/177.89 ! [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)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_adjust__eq,axiom, % 177.89/177.89 ! [V_r_2,V_q_2,V_b_2] : hAPP(c_Divides_Oadjust(V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_r_2),V_b_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),V_r_2))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_in__rel__def,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2)) % 177.89/177.89 <=> 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_div__mod__code__numeral__def,axiom, % 177.89/177.89 ! [V_m,V_n] : c_Code__Numeral_Odiv__mod__code__numeral(V_n,V_m) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_negDivAlg__eqn__1__number__of,axiom, % 177.89/177.89 ! [V_w] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 177.89/177.89 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) % 177.89/177.89 => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) % 177.89/177.89 => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_negDivAlg__correct,axiom, % 177.89/177.89 ! [V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.89 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_negDivAlg__div__mod,axiom, % 177.89/177.89 ! [V_l,V_k] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 177.89/177.89 => c_Divides_OnegDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_negDivAlg__minus1,axiom, % 177.89/177.89 ! [V_b] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_negDivAlg_Osimps,axiom, % 177.89/177.89 ! [V_b,V_a] : % 177.89/177.89 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) % 177.89/177.89 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.89/177.89 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) ) % 177.89/177.89 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) % 177.89/177.89 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.89/177.89 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_negDivAlg__eqn__number__of,axiom, % 177.89/177.89 ! [V_w,V_v] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.89 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) % 177.89/177.89 => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) % 177.89/177.89 => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_negDivAlg__eqn,axiom, % 177.89/177.89 ! [V_a,V_b] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.89 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) % 177.89/177.89 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) % 177.89/177.89 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Nitpick_Orefl_H__def,axiom, % 177.89/177.89 ! [V_r_2,T_a] : % 177.89/177.89 ( c_Nitpick_Orefl_H(T_a,V_r_2) % 177.89/177.89 <=> ! [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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_posDivAlg__eqn__1__number__of,axiom, % 177.89/177.89 ! [V_w] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 177.89/177.89 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 177.89/177.89 => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 177.89/177.89 => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_posDivAlg_Osimps,axiom, % 177.89/177.89 ! [V_b,V_a] : % 177.89/177.89 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 177.89/177.89 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.89/177.89 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) ) % 177.89/177.89 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 177.89/177.89 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.89/177.89 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_posDivAlg__0,axiom, % 177.89/177.89 ! [V_b] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_posDivAlg__correct,axiom, % 177.89/177.89 ! [V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.89 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_posDivAlg__div__mod,axiom, % 177.89/177.89 ! [V_l,V_k] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 177.89/177.89 => c_Divides_OposDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_posDivAlg__eqn__number__of,axiom, % 177.89/177.89 ! [V_w,V_v] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.89 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.89 => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.89/177.89 => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_posDivAlg__eqn,axiom, % 177.89/177.89 ! [V_a,V_b] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.89 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 177.89/177.89 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 177.89/177.89 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__int__def,axiom, % 177.89/177.89 ! [V_b,V_a] : % 177.89/177.89 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.89/177.89 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.89 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.89 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) % 177.89/177.89 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))) ) ) ) ) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.89/177.89 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.89 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.89 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))) ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__nat__step,axiom, % 177.89/177.89 ! [V_m,V_n] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.89/177.89 => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__int__pdivmod,axiom, % 177.89/177.89 ! [V_l_2,V_k_2] : % 177.89/177.89 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) % 177.89/177.89 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) ) % 177.89/177.89 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l_2)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_negateSnd__def,axiom, % 177.89/177.89 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_apsnd__conv,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__nat__zero,axiom, % 177.89/177.89 ! [V_m] : c_Divides_Odivmod__nat(V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__nat__base,axiom, % 177.89/177.89 ! [V_n,V_m] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.89/177.89 => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_negateSnd__eq,axiom, % 177.89/177.89 ! [V_r,V_q] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_r)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__nat__div__mod,axiom, % 177.89/177.89 ! [V_n,V_m] : c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__int__rel__neg,axiom, % 177.89/177.89 ! [V_qr,V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)),V_qr)) % 177.89/177.89 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__nat__if,axiom, % 177.89/177.89 ! [V_m_2,V_n_2] : % 177.89/177.89 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.89 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 177.89/177.89 => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) ) % 177.89/177.89 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.89 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 177.89/177.89 => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2),V_n_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_pdivmod__def,axiom, % 177.89/177.89 ! [V_l,V_k] : c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_pdivmod__posDivAlg,axiom, % 177.89/177.89 ! [V_k,V_l] : % 177.89/177.89 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)) ) % 177.89/177.89 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => c_Divides_Opdivmod(V_k,V_l) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__int__code,axiom, % 177.89/177.89 ! [V_l_2,V_k_2] : % 177.89/177.89 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) % 177.89/177.89 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) ) % 177.89/177.89 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_k_2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_UN__equiv__class__inject,axiom, % 177.89/177.89 ! [V_Y_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 177.89/177.89 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 177.89/177.89 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 177.89/177.89 => ( 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) % 177.89/177.89 => ( 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))) % 177.89/177.89 => ( 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))) % 177.89/177.89 => ( ! [B_x] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.89 => ! [B_y] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 177.89/177.89 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 177.89/177.89 => 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)) ) ) ) % 177.89/177.89 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__nat__rel__mult2__eq,axiom, % 177.89/177.89 ! [V_c,V_r,V_q,V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 177.89/177.89 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)))) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__nat__rel__mult1__eq,axiom, % 177.89/177.89 ! [V_a,V_r,V_q,V_c,V_b] : % 177.89/177.89 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 177.89/177.89 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r),V_c)))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__nat__rel__unique,axiom, % 177.89/177.89 ! [V_qr_H,V_qr,V_n,V_m] : % 177.89/177.89 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 177.89/177.89 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) % 177.89/177.89 => V_qr = V_qr_H ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__nat__rel__divmod__nat,axiom, % 177.89/177.89 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__nat__eq,axiom, % 177.89/177.89 ! [V_qr,V_n,V_m] : % 177.89/177.89 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 177.89/177.89 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__nat__def,axiom, % 177.89/177.89 ! [V_n_2,V_m_2] : c_Divides_Odivmod__nat(V_m_2,V_n_2) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(V_m_2,V_n_2)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mod__eq,axiom, % 177.89/177.89 ! [V_r,V_q,V_n,V_m] : % 177.89/177.89 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) % 177.89/177.89 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_div__eq,axiom, % 177.89/177.89 ! [V_r,V_q,V_n,V_m] : % 177.89/177.89 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) % 177.89/177.89 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__nat__rel,axiom, % 177.89/177.89 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__nat__rel__add1__eq,axiom, % 177.89/177.89 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 177.89/177.89 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_aq),V_ar))) % 177.89/177.89 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_bq),V_br))) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 177.89/177.89 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br),V_c)))) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_negDivAlg_Opsimps,axiom, % 177.89/177.89 ! [V_b_2,V_a_2] : % 177.89/177.89 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) % 177.89/177.89 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) % 177.89/177.89 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.89/177.89 => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)) ) % 177.89/177.89 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) % 177.89/177.89 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.89/177.89 => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OnegDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_small_H_Opsimps,axiom, % 177.89/177.89 ! [V_i_2,V_d_2,V_f_2] : % 177.89/177.89 ( 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)))) % 177.89/177.89 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 177.89/177.89 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 177.89/177.89 => 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)) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_posDivAlg_Opsimps,axiom, % 177.89/177.89 ! [V_b_2,V_a_2] : % 177.89/177.89 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) % 177.89/177.89 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 177.89/177.89 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.89/177.89 => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2) ) % 177.89/177.89 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 177.89/177.89 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.89/177.89 => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OposDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_accp__downward,axiom, % 177.89/177.89 ! [V_a_2,V_b_2,V_r_2,T_a] : % 177.89/177.89 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_b_2)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 177.89/177.89 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_accp_Oequations,axiom, % 177.89/177.89 ! [V_a_2,V_r_2,T_a] : % 177.89/177.89 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 177.89/177.89 <=> ! [B_x] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 177.89/177.89 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_accp_Osimps,axiom, % 177.89/177.89 ! [V_a_2,V_r_2,T_a] : % 177.89/177.89 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 177.89/177.89 <=> ! [B_x] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 177.89/177.89 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_accp__subset,axiom, % 177.89/177.89 ! [V_R2_2,V_R1_2,T_a] : % 177.89/177.89 ( 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)) % 177.89/177.89 => 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))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_norm__frac_Opsimps,axiom, % 177.89/177.89 ! [V_b_2,V_a_2] : % 177.89/177.89 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) % 177.89/177.89 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 177.89/177.89 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) % 177.89/177.89 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.89/177.89 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 177.89/177.89 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_negDivAlg_Opinduct,axiom, % 177.89/177.89 ! [V_P_2,V_a1_2,V_a0_2] : % 177.89/177.89 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) % 177.89/177.89 => ( ! [B_a,B_b] : % 177.89/177.89 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) % 177.89/177.89 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_a),B_b))) % 177.89/177.89 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.89/177.89 => 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))) ) % 177.89/177.89 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 177.89/177.89 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_posDivAlg_Opinduct,axiom, % 177.89/177.89 ! [V_P_2,V_a1_2,V_a0_2] : % 177.89/177.89 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) % 177.89/177.89 => ( ! [B_a,B_b] : % 177.89/177.89 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) % 177.89/177.89 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) % 177.89/177.89 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.89/177.89 => 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))) ) % 177.89/177.89 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 177.89/177.89 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nat__gcd_Opsimps,axiom, % 177.89/177.89 ! [V_y_2,V_x_2] : % 177.89/177.89 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2))) % 177.89/177.89 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.89 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) % 177.89/177.89 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.89 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = c_Nitpick_Onat__gcd(V_y_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,V_y_2)) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_small_H_Opinduct,axiom, % 177.89/177.89 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] : % 177.89/177.89 ( 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)))) % 177.89/177.89 => ( ! [B_f,B_d,B_i] : % 177.89/177.89 ( 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)))) % 177.89/177.89 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 177.89/177.89 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) % 177.89/177.89 => 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)))) ) ) % 177.89/177.89 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) ) % 177.89/177.89 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mod__pos__neg__1__number__of,axiom, % 177.89/177.89 ! [V_w] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_apsnd__eq__conv,axiom, % 177.89/177.89 ! [V_g_2,V_x_2,V_f_2,T_a,T_b,T_c] : % 177.89/177.89 ( 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) % 177.89/177.89 <=> 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_snd__apsnd,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_snd__def,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_snd__eqD,axiom, % 177.89/177.89 ! [V_a,V_y,V_x,T_a,T_b] : % 177.89/177.89 ( hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x),V_y)) = V_a % 177.89/177.89 => V_y = V_a ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_snd__conv,axiom, % 177.89/177.89 ! [V_b,V_a,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a),V_b)) = V_b ). % 177.89/177.89 % 177.89/177.89 fof(fact_mod__int__def,axiom, % 177.89/177.89 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mod__neg__pos,axiom, % 177.89/177.89 ! [V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.89 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mod__pos__pos,axiom, % 177.89/177.89 ! [V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.89 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mod__pos__pos__1__number__of,axiom, % 177.89/177.89 ! [V_w] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 177.89/177.89 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mod__pos__neg,axiom, % 177.89/177.89 ! [V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mod__neg__neg,axiom, % 177.89/177.89 ! [V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_in__measure,axiom, % 177.89/177.89 ! [V_f_2,V_y_2,V_x_2,T_a] : % 177.89/177.89 ( 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))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_irrefl__def,axiom, % 177.89/177.89 ! [V_r_2,T_a] : % 177.89/177.89 ( c_Relation_Oirrefl(T_a,V_r_2) % 177.89/177.89 <=> ! [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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_norm__frac_Opinduct,axiom, % 177.89/177.89 ! [V_P_2,V_a1_2,V_a0_2] : % 177.89/177.89 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) % 177.89/177.89 => ( ! [B_a,B_b] : % 177.89/177.89 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) % 177.89/177.89 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => 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))) ) % 177.89/177.89 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 177.89/177.89 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mod__nat__def,axiom, % 177.89/177.89 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_div__pos__neg__1__number__of,axiom, % 177.89/177.89 ! [V_w] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nat__def,axiom, % 177.89/177.89 ! [V_z_2] : hAPP(c_Int_Onat,V_z_2) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nat__gcd_Opinduct,axiom, % 177.89/177.89 ! [V_P_2,V_a1_2,V_a0_2] : % 177.89/177.89 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a0_2),V_a1_2))) % 177.89/177.89 => ( ! [B_x,B_y] : % 177.89/177.89 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y))) % 177.89/177.89 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.89 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) ) % 177.89/177.89 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) ) % 177.89/177.89 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_prod__eqI,axiom, % 177.89/177.89 ! [V_q,V_p,T_b,T_a] : % 177.89/177.89 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) % 177.89/177.89 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) % 177.89/177.89 => V_p = V_q ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Pair__fst__snd__eq,axiom, % 177.89/177.89 ! [T_b,T_a,V_t_2,V_s_2] : % 177.89/177.89 ( V_s_2 = V_t_2 % 177.89/177.89 <=> ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_t_2) % 177.89/177.89 & hAPP(c_Product__Type_Osnd(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_t_2) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_fst__apsnd,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_fst__def,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Rep__Integ__inject,axiom, % 177.89/177.89 ! [V_y_2,V_x_2] : % 177.89/177.89 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) % 177.89/177.89 <=> V_x_2 = V_y_2 ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_fst__eqD,axiom, % 177.89/177.89 ! [V_a,V_y,V_x,T_b,T_a] : % 177.89/177.89 ( hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) = V_a % 177.89/177.89 => V_x = V_a ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_fst__conv,axiom, % 177.89/177.89 ! [V_b,V_a,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b)) = V_a ). % 177.89/177.89 % 177.89/177.89 fof(fact_pair__collapse,axiom, % 177.89/177.89 ! [V_p,T_b,T_a] : hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p)) = V_p ). % 177.89/177.89 % 177.89/177.89 fof(fact_surjective__pairing,axiom, % 177.89/177.89 ! [T_b,T_a,V_t] : V_t = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_t)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_t)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_prod__case__beta,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_div__int__def,axiom, % 177.89/177.89 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_split__comp__eq,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_split__beta,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_split__def,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_The__split,axiom, % 177.89/177.89 ! [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))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_div__neg__pos,axiom, % 177.89/177.89 ! [V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.89 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_div__pos__pos,axiom, % 177.89/177.89 ! [V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.89/177.89 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_div__pos__pos__1__number__of,axiom, % 177.89/177.89 ! [V_w] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 177.89/177.89 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_div__pos__neg,axiom, % 177.89/177.89 ! [V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_div__neg__neg,axiom, % 177.89/177.89 ! [V_b,V_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.89/177.89 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_prod__size__simp,axiom, % 177.89/177.89 ! [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))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_exI__realizer,axiom, % 177.89/177.89 ! [T_a,T_b,V_x_2,V_y_2,V_P_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2)) % 177.89/177.89 => 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)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_conjI__realizer,axiom, % 177.89/177.89 ! [T_b,T_a,V_q_2,V_Q_2,V_p_2,V_P_2] : % 177.89/177.89 ( hBOOL(hAPP(V_P_2,V_p_2)) % 177.89/177.89 => ( hBOOL(hAPP(V_Q_2,V_q_2)) % 177.89/177.89 => ( 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)))) % 177.89/177.89 & 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)))) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_div__nat__def,axiom, % 177.89/177.89 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_divmod__nat__rel__def,axiom, % 177.89/177.89 ! [V_qr_2,V_n_2,V_m_2] : % 177.89/177.89 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) % 177.89/177.89 <=> ( V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)) % 177.89/177.89 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.89 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.89/177.89 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.89 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) % 177.89/177.89 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)) ) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) % 177.89/177.89 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_inv__image__def,axiom, % 177.89/177.89 ! [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))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mlex__leq,axiom, % 177.89/177.89 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 177.89/177.89 => ( 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)) % 177.89/177.89 => 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))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_code__numeral_Osize_I2_J,axiom, % 177.89/177.89 ! [V_code__numeral] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_code__numeral_Oinject,axiom, % 177.89/177.89 ! [V_code__numeral_H_2,V_code__numeral_2] : % 177.89/177.89 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) % 177.89/177.89 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_code__numeral_Osimps_I3_J,axiom, % 177.89/177.89 ! [V_code__numeral_H_1] : c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_1) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 177.89/177.89 % 177.89/177.89 fof(fact_code__numeral_Osimps_I2_J,axiom, % 177.89/177.89 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ). % 177.89/177.89 % 177.89/177.89 fof(fact_in__inv__image,axiom, % 177.89/177.89 ! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] : % 177.89/177.89 ( 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))) % 177.89/177.89 <=> 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Suc__code__numeral__minus__one,axiom, % 177.89/177.89 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_n)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = V_n ). % 177.89/177.89 % 177.89/177.89 fof(fact_mlex__less,axiom, % 177.89/177.89 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 177.89/177.89 => 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))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_code__numeral_Osize_I4_J,axiom, % 177.89/177.89 ! [V_code__numeral] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rp__inv__image__def,axiom, % 177.89/177.89 ! [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))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_prod_Orecs,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_code__numeral_Osize_I3_J,axiom, % 177.89/177.89 hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__add__map__of__foldr,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_in__lex__prod,axiom, % 177.89/177.89 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 177.89/177.89 ( 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))) % 177.89/177.89 <=> ( 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)) % 177.89/177.89 | ( V_a_2 = V_a_H_2 % 177.89/177.89 & 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)) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_equivp__equiv,axiom, % 177.89/177.89 ! [V_A_2,T_a] : % 177.89/177.89 ( c_Equiv__Relations_Oequiv(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_A_2) % 177.89/177.89 <=> 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_equivp__transp,axiom, % 177.89/177.89 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_a] : % 177.89/177.89 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 177.89/177.89 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_equivp__symp,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_R_2,T_a] : % 177.89/177.89 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 177.89/177.89 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_equivp__reflp,axiom, % 177.89/177.89 ! [V_x_2,V_R_2,T_a] : % 177.89/177.89 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 177.89/177.89 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_equivp__def,axiom, % 177.89/177.89 ! [V_R_2,T_a] : % 177.89/177.89 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 177.89/177.89 <=> ! [B_x,B_y] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 177.89/177.89 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_identity__equivp,axiom, % 177.89/177.89 ! [T_a] : c_Equiv__Relations_Oequivp(T_a,c_fequal) ). % 177.89/177.89 % 177.89/177.89 fof(fact_same__fstI,axiom, % 177.89/177.89 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_P_2] : % 177.89/177.89 ( hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.89 => ( 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))) % 177.89/177.89 => 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))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_apfst__apsnd,axiom, % 177.89/177.89 ! [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))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_apsnd__apfst,axiom, % 177.89/177.89 ! [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))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_apfst__conv,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_apfst__eq__conv,axiom, % 177.89/177.89 ! [V_g_2,V_x_2,V_f_2,T_b,T_a,T_c] : % 177.89/177.89 ( 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) % 177.89/177.89 <=> 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_fst__apfst,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_snd__apfst,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_apsnd__apfst__commute,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_pair__lessI2,axiom, % 177.89/177.89 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_ImageE,axiom, % 177.89/177.89 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 177.89/177.89 => ~ ! [B_x] : % 177.89/177.89 ( 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)) % 177.89/177.89 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mlex__prod__def,axiom, % 177.89/177.89 ! [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))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_pair__less__def,axiom, % 177.89/177.89 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ). % 177.89/177.89 % 177.89/177.89 fof(fact_measure__def,axiom, % 177.89/177.89 ! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than) ). % 177.89/177.89 % 177.89/177.89 fof(fact_less__than__iff,axiom, % 177.89/177.89 ! [V_y_2,V_x_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than)) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_pair__lessI1,axiom, % 177.89/177.89 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_pair__leqI2,axiom, % 177.89/177.89 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_smax__insertI,axiom, % 177.89/177.89 ! [V_X_2,V_x_2,V_Y_2,V_y_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),V_Y_2)),c_FunDef_Omax__strict)) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_X_2)),V_Y_2)),c_FunDef_Omax__strict)) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_smin__insertI,axiom, % 177.89/177.89 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__strict)) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__strict)) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_smax__emptyI,axiom, % 177.89/177.89 ! [V_Y_2] : % 177.89/177.89 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) % 177.89/177.89 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_Y_2)),c_FunDef_Omax__strict)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_smin__emptyI,axiom, % 177.89/177.89 ! [V_X_2] : % 177.89/177.89 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_pair__leqI1,axiom, % 177.89/177.89 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_wmin__insertI,axiom, % 177.89/177.89 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__weak)) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__weak)) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_wmax__insertI,axiom, % 177.89/177.89 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omax__weak)) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)),V_YS_2)),c_FunDef_Omax__weak)) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Field__insert,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Field__Union,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Field__empty,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mono__Field,axiom, % 177.89/177.89 ! [V_s_2,V_r_2,T_a] : % 177.89/177.89 ( 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)) % 177.89/177.89 => 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))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Field__Un,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_finite__Field,axiom, % 177.89/177.89 ! [V_r_2,T_a] : % 177.89/177.89 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 177.89/177.89 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_OField(T_a),V_r_2))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_wmin__emptyI,axiom, % 177.89/177.89 ! [V_X_2] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_wmax__emptyI,axiom, % 177.89/177.89 ! [V_X_2] : % 177.89/177.89 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_X_2)),c_FunDef_Omax__weak)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_min__weak__def,axiom, % 177.89/177.89 c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_max__weak__def,axiom, % 177.89/177.89 c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Id__on__def,axiom, % 177.89/177.89 ! [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)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Id__on__def_H,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Id__on__empty,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Image__Id__on,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Id__on__iff,axiom, % 177.89/177.89 ! [V_A_2,V_y_2,V_x_2,T_a] : % 177.89/177.89 ( 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))) % 177.89/177.89 <=> ( V_x_2 = V_y_2 % 177.89/177.89 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Id__on__eqI,axiom, % 177.89/177.89 ! [V_A_2,T_a,V_b_2,V_a_2] : % 177.89/177.89 ( V_a_2 = V_b_2 % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.89 => 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))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_max__strict__def,axiom, % 177.89/177.89 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 177.89/177.89 % 177.89/177.89 fof(fact_max__ext__additive,axiom, % 177.89/177.89 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_a] : % 177.89/177.89 ( 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))) % 177.89/177.89 => ( 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))) % 177.89/177.89 => 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))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_min__strict__def,axiom, % 177.89/177.89 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 177.89/177.89 % 177.89/177.89 fof(fact_max__extp__max__ext__eq,axiom, % 177.89/177.89 ! [V_xa_2,V_x_2,V_R_2,T_a] : % 177.89/177.89 ( 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) % 177.89/177.89 <=> 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))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_min__rpair__set,axiom, % 177.89/177.89 c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_max__rpair__set,axiom, % 177.89/177.89 c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_rp__inv__image__rp,axiom, % 177.89/177.89 ! [V_f_2,T_b,V_P_2,T_a] : % 177.89/177.89 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 177.89/177.89 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_P_2),V_f_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_equiv__intrel__iff,axiom, % 177.89/177.89 ! [V_y_2,V_x_2] : % 177.89/177.89 ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_Int_Ointrel)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_intrel__iff,axiom, % 177.89/177.89 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2))),c_Int_Ointrel)) % 177.89/177.89 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Id__onE,axiom, % 177.89/177.89 ! [V_A_2,V_ca_2,T_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_ca_2),c_Relation_OId__on(T_a,V_A_2))) % 177.89/177.89 => ~ ! [B_x] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.89 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_equiv__intrel,axiom, % 177.89/177.89 c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel) ). % 177.89/177.89 % 177.89/177.89 fof(fact_of__int,axiom, % 177.89/177.89 ! [V_j_2,V_i_2,T_a] : % 177.89/177.89 ( class_Rings_Oring__1(T_a) % 177.89/177.89 => 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_One__int__def,axiom, % 177.89/177.89 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_mult,axiom, % 177.89/177.89 ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_v_2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_u_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Rep__Integ__inverse,axiom, % 177.89/177.89 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ). % 177.89/177.89 % 177.89/177.89 fof(fact_minus,axiom, % 177.89/177.89 ! [V_y_2,V_x_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_y_2),V_x_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Zero__int__def,axiom, % 177.89/177.89 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_int__def,axiom, % 177.89/177.89 ! [V_m_2] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_add,axiom, % 177.89/177.89 ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),V_v_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nat,axiom, % 177.89/177.89 ! [V_y_2,V_x_2] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2) ). % 177.89/177.89 % 177.89/177.89 fof(fact_minus__int__def,axiom, % 177.89/177.89 ! [V_z_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_2) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_less,axiom, % 177.89/177.89 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_le,axiom, % 177.89/177.89 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_eq__Abs__Integ,axiom, % 177.89/177.89 ! [V_z_2] : % 177.89/177.89 ~ ! [B_x,B_y] : V_z_2 != hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Integ__def,axiom, % 177.89/177.89 c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__of__mapk__SomeI,axiom, % 177.89/177.89 ! [V_x_2,V_k_2,V_t_2,T_c,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.89/177.89 => ( 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) % 177.89/177.89 => 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) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_inj__mapI,axiom, % 177.89/177.89 ! [V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.89/177.89 => 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))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_inj__map,axiom, % 177.89/177.89 ! [V_f_2,T_b,T_a] : % 177.89/177.89 ( 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))) % 177.89/177.89 <=> c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_inj__map__eq__map,axiom, % 177.89/177.89 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.89/177.89 => ( 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) % 177.89/177.89 <=> V_xs_2 = V_ys_2 ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_inj__mapD,axiom, % 177.89/177.89 ! [V_f_2,T_b,T_a] : % 177.89/177.89 ( 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))) % 177.89/177.89 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__injective,axiom, % 177.89/177.89 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 177.89/177.89 ( 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) % 177.89/177.89 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 177.89/177.89 => V_xs_2 = V_ys_2 ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__ident,axiom, % 177.89/177.89 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)),V_xs_2) = V_xs_2 ). % 177.89/177.89 % 177.89/177.89 fof(fact_Rep__Integ,axiom, % 177.89/177.89 ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_x_2)),c_Int_OInteg)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_type__definition__Integ,axiom, % 177.89/177.89 c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__of__map__keys,axiom, % 177.89/177.89 ! [V_m_2,T_b,V_xs_2,T_a] : % 177.89/177.89 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Map_Odom(T_a,T_b,V_m_2) % 177.89/177.89 => 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 ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__of__map,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_finite__set,axiom, % 177.89/177.89 ! [V_xs_2,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__map,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_List_Omap_Ocompositionality,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__comp__map,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_List_Omap_Ocomp,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__eq__conv,axiom, % 177.89/177.89 ! [V_g_2,V_xs_2,V_f_2,T_a,T_b] : % 177.89/177.89 ( 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) % 177.89/177.89 <=> ! [B_x] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 177.89/177.89 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_set__map,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_comp__inj__on__iff,axiom, % 177.89/177.89 ! [V_f_H_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.89/177.89 => ( 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)) % 177.89/177.89 <=> 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) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_comp__inj__on,axiom, % 177.89/177.89 ! [V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.89/177.89 => ( 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)) % 177.89/177.89 => 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) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_inj__on__imageI,axiom, % 177.89/177.89 ! [V_A_2,V_f_2,V_g_2,T_c,T_b,T_a] : % 177.89/177.89 ( 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) % 177.89/177.89 => 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_image__compose,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_apfst__compose,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_apsnd__compose,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom, % 177.89/177.89 ! [V_x_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 177.89/177.89 => 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) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_option__map__comp,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Option_Omap_Ocompositionality,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_comp__cong,axiom, % 177.89/177.89 ! [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] : % 177.89/177.89 ( hAPP(V_f_2,hAPP(V_g_2,V_x_2)) = hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2)) % 177.89/177.89 => 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) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_o__eq__dest__lhs,axiom, % 177.89/177.89 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 177.89/177.89 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = V_ca_2 % 177.89/177.89 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_K__record__comp,axiom, % 177.89/177.89 ! [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 ). % 177.89/177.89 % 177.89/177.89 fof(fact_o__def,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Option_Omap_Ocomp,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_o__eq__elim,axiom, % 177.89/177.89 ! [V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 177.89/177.89 ( 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) % 177.89/177.89 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_o__eq__dest,axiom, % 177.89/177.89 ! [V_v_2,V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 177.89/177.89 ( 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) % 177.89/177.89 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_o__apply,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_o__assoc,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_fun__upd__comp,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_vimage__compose,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_fun__left__comm_Ofun__comp__comm,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 177.89/177.89 => 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_inj__on__imageI2,axiom, % 177.89/177.89 ! [V_A_2,V_f_2,V_f_H_2,T_c,T_b,T_a] : % 177.89/177.89 ( 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) % 177.89/177.89 => c_Fun_Oinj__on(T_a,T_c,V_f_2,V_A_2) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_infinite__UNIV__listI,axiom, % 177.89/177.89 ! [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)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_inj__comp,axiom, % 177.89/177.89 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.89/177.89 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.89/177.89 => 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))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_comp__surj,axiom, % 177.89/177.89 ! [V_g_2,T_c,V_f_2,T_a,T_b] : % 177.89/177.89 ( 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)) % 177.89/177.89 => ( 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)) % 177.89/177.89 => 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)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_option__map__o__empty,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__of__map__restrict,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_setsum__reindex,axiom, % 177.89/177.89 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 177.89/177.89 ( class_Groups_Ocomm__monoid__add(T_c) % 177.89/177.89 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 177.89/177.89 => 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) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_setprod__reindex__cong,axiom, % 177.89/177.89 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 177.89/177.89 ( class_Groups_Ocomm__monoid__mult(T_c) % 177.89/177.89 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.89/177.89 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 177.89/177.89 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2) % 177.89/177.89 => 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) ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_setprod__reindex,axiom, % 177.89/177.89 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 177.89/177.89 ( class_Groups_Ocomm__monoid__mult(T_c) % 177.89/177.89 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 177.89/177.89 => 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) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_inj__on__map__eq__map,axiom, % 177.89/177.89 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( 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))) % 177.89/177.89 => ( 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) % 177.89/177.89 <=> V_xs_2 = V_ys_2 ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__inj__on,axiom, % 177.89/177.89 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 177.89/177.89 ( 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) % 177.89/177.89 => ( 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))) % 177.89/177.89 => V_xs_2 = V_ys_2 ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__fun__upd,axiom, % 177.89/177.89 ! [V_v_2,V_f_2,T_b,V_xs_2,V_y_2,T_a] : % 177.89/177.89 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.89 => 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) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_inj__on__mapI,axiom, % 177.89/177.89 ! [V_A_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( 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))) % 177.89/177.89 => 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) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_option__map__o__map__upd,axiom, % 177.89/177.89 ! [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))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__of__eq__dom,axiom, % 177.89/177.89 ! [V_ys_2,V_xs_2,T_b,T_a] : % 177.89/177.89 ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) % 177.89/177.89 => 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_setsum_Oreindex,axiom, % 177.89/177.89 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 177.89/177.89 ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.89 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 177.89/177.89 => 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) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_setprod_Oreindex,axiom, % 177.89/177.89 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 177.89/177.89 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.89 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 177.89/177.89 => 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) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_the__inv__into__comp,axiom, % 177.89/177.89 ! [V_x_2,V_A_2,V_g_2,T_c,V_f_2,T_b,T_a] : % 177.89/177.89 ( 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)) % 177.89/177.89 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,V_A_2) % 177.89/177.89 => ( 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)))) % 177.89/177.89 => 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) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__of__SomeD,axiom, % 177.89/177.89 ! [V_y_2,V_k_2,V_xs_2,T_a,T_b] : % 177.89/177.89 ( 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) % 177.89/177.89 => 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))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__of__is__SomeD,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_xys_2,T_a,T_b] : % 177.89/177.89 ( 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) % 177.89/177.89 => 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))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_dom__map__of__conv__image__fst,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_fold__image__reindex,axiom, % 177.89/177.89 ! [V_z_2,V_g_2,V_h_2,T_b,V_A_2,T_a,T_c] : % 177.89/177.89 ( class_Groups_Oab__semigroup__mult(T_c) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.89 => ( c_Fun_Oinj__on(T_a,T_b,V_h_2,V_A_2) % 177.89/177.89 => 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) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__of__eq__None__iff,axiom, % 177.89/177.89 ! [V_x_2,V_xys_2,T_a,T_b] : % 177.89/177.89 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_a) % 177.89/177.89 <=> ~ 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)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_type__definition_ORep__range,axiom, % 177.89/177.89 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 177.89/177.89 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 177.89/177.89 => 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 ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_type__definition_OAbs__image,axiom, % 177.89/177.89 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 177.89/177.89 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 177.89/177.89 => 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding_Oremove,axiom, % 177.89/177.89 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.89 => 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)) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_UN__o,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding_Ocommute__left__comp,axiom, % 177.89/177.89 ! [V_g_2,V_x_2,V_y_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 177.89/177.89 => 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding_Ocommute__comp,axiom, % 177.89/177.89 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 177.89/177.89 => 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding_Ocommute__comps_I1_J,axiom, % 177.89/177.89 ! [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] : % 177.89/177.89 ( c_Finite__Set_Ofolding(T_a,T_b,V_fa_2,V_F_2) % 177.89/177.89 => hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_f_2),hAPP(c_Fun_Ocomp(T_f,T_e,T_c,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_f,T_d,T_c,hAPP(c_Fun_Ocomp(T_e,T_d,T_f,V_f_2),V_g_2)),V_h_2) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_foldr__map,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_split__comp,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding_Ocommute__left__comp_H_H,axiom, % 177.89/177.89 ! [V_g_2,T_c,V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.89 => 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)) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding_Ocommute__comp_H_H,axiom, % 177.89/177.89 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.89 => 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)) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding_Ocommute__left__comp_H,axiom, % 177.89/177.89 ! [V_g_2,V_x_2,T_c,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.89 => 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)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding_Ocommute__comp_H,axiom, % 177.89/177.89 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.89 => 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)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding_Oeq__fold,axiom, % 177.89/177.89 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.89 => 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) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_type__definition_ORep__inject,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 177.89/177.89 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 177.89/177.89 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) % 177.89/177.89 <=> V_x_2 = V_y_2 ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_type__definition_ORep__inverse,axiom, % 177.89/177.89 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 177.89/177.89 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 177.89/177.89 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding_Oinsert,axiom, % 177.89/177.89 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.89 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.89 => 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)) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding_Ounion__inter,axiom, % 177.89/177.89 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.89 => 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)) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_type__definition_ORep,axiom, % 177.89/177.89 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 177.89/177.89 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_type__definition_OAbs__inverse,axiom, % 177.89/177.89 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 177.89/177.89 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 177.89/177.89 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_type__definition_OAbs__inject,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 177.89/177.89 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 177.89/177.89 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) % 177.89/177.89 <=> V_x_2 = V_y_2 ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding_Oinsert__remove,axiom, % 177.89/177.89 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.89 => 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)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding_Ounion,axiom, % 177.89/177.89 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.89 => ( 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)) % 177.89/177.89 => 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)) ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Loop__sound__lemma,axiom, % 177.89/177.89 ! [V_ca_2,V_b_2,V_P_2,V_G_2,T_a] : % 177.89/177.89 ( 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)))) % 177.89/177.89 => 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)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_hoare__derivs_OIf,axiom, % 177.89/177.89 ! [V_d_2,V_Q_2,V_ca_2,V_b_2,V_P_2,V_G_2,T_a] : % 177.89/177.89 ( 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)))) % 177.89/177.89 => ( 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)))) % 177.89/177.89 => 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)))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Loop,axiom, % 177.89/177.89 ! [V_ca_2,V_b_2,V_P_2,V_G_2,T_a] : % 177.89/177.89 ( 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)))) % 177.89/177.89 => 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)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_peek__and__def,axiom, % 177.89/177.89 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_p_2),V_Z_2),V_s_2)) % 177.89/177.89 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2)) % 177.89/177.89 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_ran__distinct,axiom, % 177.89/177.89 ! [V_al_2,T_b,T_a] : % 177.89/177.89 ( 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))) % 177.89/177.89 => 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_set__map__of__compr,axiom, % 177.89/177.89 ! [V_xs_2,T_b,T_a] : % 177.89/177.89 ( 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))) % 177.89/177.89 => 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)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding__image_Oreindex,axiom, % 177.89/177.89 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 177.89/177.89 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 177.89/177.89 => 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) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding__image_Odistrib,axiom, % 177.89/177.89 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 177.89/177.89 => 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)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_distinct__map,axiom, % 177.89/177.89 ! [V_xs_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) % 177.89/177.89 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 177.89/177.89 & c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding__image_Oeq__fold,axiom, % 177.89/177.89 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 177.89/177.89 => 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) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__of__inject__set,axiom, % 177.89/177.89 ! [V_ys_2,V_xs_2,T_b,T_a] : % 177.89/177.89 ( 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))) % 177.89/177.89 => ( 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))) % 177.89/177.89 => ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) % 177.89/177.89 <=> 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) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__of__is__SomeI,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] : % 177.89/177.89 ( 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))) % 177.89/177.89 => ( 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))) % 177.89/177.89 => 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) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__of__eq__Some__iff,axiom, % 177.89/177.89 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] : % 177.89/177.89 ( 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))) % 177.89/177.89 => ( 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) % 177.89/177.89 <=> 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))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_Some__eq__map__of__iff,axiom, % 177.89/177.89 ! [V_x_2,V_y_2,V_xys_2,T_b,T_a] : % 177.89/177.89 ( 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))) % 177.89/177.89 => ( 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) % 177.89/177.89 <=> 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))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_setsum__reindex__nonzero,axiom, % 177.89/177.89 ! [T_b,V_h_2,V_f_2,V_S_2,T_a,T_c] : % 177.89/177.89 ( class_Groups_Ocomm__monoid__add(T_c) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 177.89/177.89 => ( ! [B_x] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 177.89/177.89 => ! [B_y] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_S_2)) % 177.89/177.89 => ( B_x != B_y % 177.89/177.89 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 177.89/177.89 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) % 177.89/177.89 => 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) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_greaterThanLessThan__upto,axiom, % 177.89/177.89 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_weak__map__of__SomeI,axiom, % 177.89/177.89 ! [V_l_2,V_x_2,V_k_2,T_b,T_a] : % 177.89/177.89 ( 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))) % 177.89/177.89 => ? [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) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_distinct__upto,axiom, % 177.89/177.89 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_set__upto,axiom, % 177.89/177.89 ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) ). % 177.89/177.89 % 177.89/177.89 fof(fact_atLeastAtMost__upto,axiom, % 177.89/177.89 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_atLeastLessThan__upto,axiom, % 177.89/177.89 ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_greaterThanAtMost__upto,axiom, % 177.89/177.89 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nat__list__def,axiom, % 177.89/177.89 ! [V_l_2] : % 177.89/177.89 ( c_List_Onat__list(V_l_2) % 177.89/177.89 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding__idem_Ounion__idem,axiom, % 177.89/177.89 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 177.89/177.89 => 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)) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding__idem_Osubset__comp__idem,axiom, % 177.89/177.89 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.89/177.89 => 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) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding__idem_Oidem__comp,axiom, % 177.89/177.89 ! [V_x_2,V_F_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 177.89/177.89 => 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) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding__idem_Oidem__left__comp,axiom, % 177.89/177.89 ! [V_g_2,V_x_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 177.89/177.89 => 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) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding__idem_Oin__comp__idem,axiom, % 177.89/177.89 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.89 => 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) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_folding__idem_Oinsert__idem,axiom, % 177.89/177.89 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.89 => 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)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_set__remove1__eq,axiom, % 177.89/177.89 ! [V_x_2,V_xs_2,T_a] : % 177.89/177.89 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 177.89/177.89 => 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)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__of__zip__map,axiom, % 177.89/177.89 ! [V_f_2,T_b,V_xs_2,V_x_2,T_a] : % 177.89/177.89 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.89 => 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)) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.89 => 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) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_strong__setprod__reindex__cong,axiom, % 177.89/177.89 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 177.89/177.89 ( class_Groups_Ocomm__monoid__mult(T_c) % 177.89/177.89 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.89/177.89 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 177.89/177.89 => ( ! [B_x] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.89 => 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) ) % 177.89/177.89 => 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) ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_distinct__zipI2,axiom, % 177.89/177.89 ! [V_xs,T_b,V_ys,T_a] : % 177.89/177.89 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) % 177.89/177.89 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_distinct__remove1,axiom, % 177.89/177.89 ! [V_x,V_xs,T_a] : % 177.89/177.89 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.89/177.89 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_distinct__zipI1,axiom, % 177.89/177.89 ! [V_ys,T_b,V_xs,T_a] : % 177.89/177.89 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.89/177.89 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_remove1__commute,axiom, % 177.89/177.89 ! [V_zs,V_y,V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Oremove1(T_a,V_y,V_zs)) = c_List_Oremove1(T_a,V_y,c_List_Oremove1(T_a,V_x,V_zs)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_in__set__remove1,axiom, % 177.89/177.89 ! [V_xs_2,T_a,V_b_2,V_a_2] : % 177.89/177.89 ( V_a_2 != V_b_2 % 177.89/177.89 => ( 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)))) % 177.89/177.89 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_notin__set__remove1,axiom, % 177.89/177.89 ! [V_y_2,V_xs_2,V_x_2,T_a] : % 177.89/177.89 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.89 => ~ 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)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_remove1__idem,axiom, % 177.89/177.89 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.89 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.89 => c_List_Oremove1(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zip__same__conv__map,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_set__remove1__subset,axiom, % 177.89/177.89 ! [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))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zip__map__fst__snd,axiom, % 177.89/177.89 ! [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 ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__zip__map2,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__zip__map,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_in__set__zipE,axiom, % 177.89/177.89 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 177.89/177.89 ( 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)))) % 177.89/177.89 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.89 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_set__zip__rightD,axiom, % 177.89/177.89 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 177.89/177.89 ( 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)))) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_set__zip__leftD,axiom, % 177.89/177.89 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 177.89/177.89 ( 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)))) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zip__same,axiom, % 177.89/177.89 ! [V_xs_2,V_b_2,V_a_2,T_a] : % 177.89/177.89 ( 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)))) % 177.89/177.89 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.89 & V_a_2 = V_b_2 ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zip__map2,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zip__map1,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zip__map__map,axiom, % 177.89/177.89 ! [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)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_sorted__list__of__set__remove,axiom, % 177.89/177.89 ! [V_x_2,V_A_2,T_a] : % 177.89/177.89 ( class_Orderings_Olinorder(T_a) % 177.89/177.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.89 => 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)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__of__zip__upd,axiom, % 177.89/177.89 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_b,V_ys_2,T_a] : % 177.89/177.89 ( 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) % 177.89/177.89 => ( 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) % 177.89/177.89 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 177.89/177.89 => ( 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)) % 177.89/177.89 => 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)) ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__removeAll__inj__on,axiom, % 177.89/177.89 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( 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))) % 177.89/177.89 => 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_length__zip,axiom, % 177.89/177.89 ! [V_ys,V_xs,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(T_a,T_b))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)) ). % 177.89/177.89 % 177.89/177.89 fof(fact_neq__if__length__neq,axiom, % 177.89/177.89 ! [V_ys,V_xs,T_a] : % 177.89/177.89 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) % 177.89/177.89 => V_xs != V_ys ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__eq__imp__length__eq,axiom, % 177.89/177.89 ! [V_ys_2,V_g_2,T_c,V_xs_2,V_f_2,T_a,T_b] : % 177.89/177.89 ( 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) % 177.89/177.89 => 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) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_length__map,axiom, % 177.89/177.89 ! [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) ). % 177.89/177.89 % 177.89/177.89 fof(fact_distinct__removeAll,axiom, % 177.89/177.89 ! [V_x,V_xs,T_a] : % 177.89/177.89 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.89/177.89 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_card__length,axiom, % 177.89/177.89 ! [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))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_removeAll__id,axiom, % 177.89/177.89 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.89 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.89 => hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2) = V_xs_2 ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_distinct__card,axiom, % 177.89/177.89 ! [V_xs_2,T_a] : % 177.89/177.89 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 177.89/177.89 => 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) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_card__distinct,axiom, % 177.89/177.89 ! [V_xs_2,T_a] : % 177.89/177.89 ( 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) % 177.89/177.89 => hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__of__zip__inject,axiom, % 177.89/177.89 ! [V_zs_2,V_xs_2,T_b,V_ys_2,T_a] : % 177.89/177.89 ( 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) % 177.89/177.89 => ( 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) % 177.89/177.89 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 177.89/177.89 => ( 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)) % 177.89/177.89 => V_ys_2 = V_zs_2 ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__fst__zip,axiom, % 177.89/177.89 ! [V_ys_2,T_b,V_xs_2,T_a] : % 177.89/177.89 ( 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) % 177.89/177.89 => 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 ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__snd__zip,axiom, % 177.89/177.89 ! [V_ys_2,T_b,V_xs_2,T_a] : % 177.89/177.89 ( 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) % 177.89/177.89 => 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 ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_distinct__remove1__removeAll,axiom, % 177.89/177.89 ! [V_x,V_xs,T_a] : % 177.89/177.89 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.89/177.89 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_length__pos__if__in__set,axiom, % 177.89/177.89 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.89 => 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))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_zip__eq__conv,axiom, % 177.89/177.89 ! [V_zs_2,V_ys_2,T_b,V_xs_2,T_a] : % 177.89/177.89 ( 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) % 177.89/177.89 => ( hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2) = V_zs_2 % 177.89/177.89 <=> ( 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 % 177.89/177.89 & 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 ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__removeAll__inj,axiom, % 177.89/177.89 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 177.89/177.89 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.89/177.89 => 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_finite__lists__length__eq,axiom, % 177.89/177.89 ! [V_n_2,V_A_2,T_a] : % 177.89/177.89 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.89 => 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))))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__of__zip__is__None,axiom, % 177.89/177.89 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] : % 177.89/177.89 ( 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) % 177.89/177.89 => ( 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) % 177.89/177.89 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_map__of__zip__is__Some,axiom, % 177.89/177.89 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] : % 177.89/177.89 ( 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) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.89 <=> ? [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) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_length__remove1,axiom, % 177.89/177.89 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.89 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.89 => 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)) ) % 177.89/177.89 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.89 => 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) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_dom__map__of__zip,axiom, % 177.89/177.89 ! [V_ys_2,T_b,V_xs_2,T_a] : % 177.89/177.89 ( 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) % 177.89/177.89 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 177.89/177.89 => 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) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_finite__lists__length__le,axiom, % 177.89/177.89 ! [V_n_2,V_A_2,T_a] : % 177.89/177.89 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.89 => 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))))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_set__removeAll,axiom, % 177.89/177.89 ! [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)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_length__sublist,axiom, % 177.89/177.89 ! [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)))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_set__zip,axiom, % 177.89/177.89 ! [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)))))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nth__zip,axiom, % 177.89/177.89 ! [V_ys,T_b,V_xs,T_a,V_i] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys))) % 177.89/177.89 => hAPP(hAPP(c_List_Onth(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys),V_i)) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_list__eq__iff__nth__eq,axiom, % 177.89/177.89 ! [T_a,V_ys_2,V_xs_2] : % 177.89/177.89 ( V_xs_2 = V_ys_2 % 177.89/177.89 <=> ( 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) % 177.89/177.89 & ! [B_i] : % 177.89/177.89 ( 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))) % 177.89/177.89 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_i) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_distinct__sublistI,axiom, % 177.89/177.89 ! [V_I_2,V_xs_2,T_a] : % 177.89/177.89 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 177.89/177.89 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_all__set__conv__all__nth,axiom, % 177.89/177.89 ! [V_P_2,V_xs_2,T_a] : % 177.89/177.89 ( ! [B_x] : % 177.89/177.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.89 => hBOOL(hAPP(V_P_2,B_x)) ) % 177.89/177.89 <=> ! [B_i] : % 177.89/177.89 ( 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))) % 177.89/177.89 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nth__map,axiom, % 177.89/177.89 ! [V_f_2,T_b,V_xs_2,T_a,V_n_2] : % 177.89/177.89 ( 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))) % 177.89/177.89 => 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)) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_distinct__conv__nth,axiom, % 177.89/177.89 ! [V_xs_2,T_a] : % 177.89/177.89 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 177.89/177.89 <=> ! [B_i] : % 177.89/177.89 ( 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))) % 177.89/177.89 => ! [B_j] : % 177.89/177.89 ( 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))) % 177.89/177.89 => ( B_i != B_j % 177.89/177.89 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j) ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nth__eq__iff__index__eq,axiom, % 177.89/177.89 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 177.89/177.89 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 177.89/177.89 => ( 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))) % 177.89/177.89 => ( 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))) % 177.89/177.89 => ( 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) % 177.89/177.89 <=> V_i_2 = V_j_2 ) ) ) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_set__sublist,axiom, % 177.89/177.89 ! [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))))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_notin__set__sublistI,axiom, % 177.89/177.89 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 177.89/177.89 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.89 => ~ 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)))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_in__set__sublistD,axiom, % 177.89/177.89 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 177.89/177.89 ( 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)))) % 177.89/177.89 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 177.89/177.89 % 177.89/177.89 fof(fact_set__sublist__subset,axiom, % 177.89/177.89 ! [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))) ). % 177.89/177.89 % 177.89/177.89 fof(fact_nth__mem,axiom, % 177.89/177.89 ! [V_xs_2,T_a,V_n_2] : % 177.89/177.89 ( 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))) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_in__set__conv__nth,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 <=> ? [B_i] : % 177.89/177.90 ( 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))) % 177.89/177.90 & hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = V_x_2 ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__conv__nth,axiom, % 177.89/177.90 ! [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))))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_distinct__list__update,axiom, % 177.89/177.90 ! [V_i_2,V_a_2,V_xs_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 177.89/177.90 => ( ~ 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)))))) % 177.89/177.90 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_a_2))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__list__of__set__insert,axiom, % 177.89/177.90 ! [V_x_2,V_A_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.90 => 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)))))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__list__update,axiom, % 177.89/177.90 ! [V_x,V_i,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth__list__update__neq,axiom, % 177.89/177.90 ! [V_x,V_xs,T_a,V_j,V_i] : % 177.89/177.90 ( V_i != V_j % 177.89/177.90 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list__update__id,axiom, % 177.89/177.90 ! [V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)) = V_xs ). % 177.89/177.90 % 177.89/177.90 fof(fact_remove1__insort,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => 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 ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_update__zip,axiom, % 177.89/177.90 ! [V_xy,V_i,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),V_xy) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(c_Product__Type_Ofst(T_a,T_b),V_xy))),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),hAPP(c_Product__Type_Osnd(T_a,T_b),V_xy))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_zip__update,axiom, % 177.89/177.90 ! [V_y,V_ys,V_x,V_i,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),V_y)) = hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_fun__left__comm__insort,axiom, % 177.89/177.90 ! [T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_insort__left__comm,axiom, % 177.89/177.90 ! [V_xs_2,V_y_2,V_x_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => 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)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list__update__overwrite,axiom, % 177.89/177.90 ! [V_y,V_x,V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i),V_y) = hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list__update__swap,axiom, % 177.89/177.90 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] : % 177.89/177.90 ( V_i != V_i_H % 177.89/177.90 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i_H),V_x_H) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i_H),V_x_H)),V_i),V_x) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_insort__key__left__comm,axiom, % 177.89/177.90 ! [V_xs_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__update,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list__update__beyond,axiom, % 177.89/177.90 ! [V_x,V_i,V_xs,T_a] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)) % 177.89/177.90 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__insort,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 177.89/177.90 ( class_Orderings_Olinorder(T_b) % 177.89/177.90 => 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)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__insort,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 177.89/177.90 ( class_Orderings_Olinorder(T_b) % 177.89/177.90 => 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)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__update__subsetI,axiom, % 177.89/177.90 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_a] : % 177.89/177.90 ( 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)) % 177.89/177.90 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__update__subset__insert,axiom, % 177.89/177.90 ! [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)))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth__list__update__eq,axiom, % 177.89/177.90 ! [V_x,V_xs,T_a,V_i] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i) = V_x ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list__update__same__conv,axiom, % 177.89/177.90 ! [V_x_2,V_xs_2,T_a,V_i_2] : % 177.89/177.90 ( 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))) % 177.89/177.90 => ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2) = V_xs_2 % 177.89/177.90 <=> hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = V_x_2 ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth__list__update,axiom, % 177.89/177.90 ! [V_x,V_j,V_xs,T_a,V_i] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => ( ( V_i = V_j % 177.89/177.90 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = V_x ) % 177.89/177.90 & ( V_i != V_j % 177.89/177.90 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_distinct__insort,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 177.89/177.90 ( class_Orderings_Olinorder(T_b) % 177.89/177.90 => ( 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))) % 177.89/177.90 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__update__memI,axiom, % 177.89/177.90 ! [V_x_2,V_xs_2,T_a,V_n_2] : % 177.89/177.90 ( 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))) % 177.89/177.90 => 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)))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_insort__insert__insort__key,axiom, % 177.89/177.90 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( ~ 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)))) % 177.89/177.90 => 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) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_insort__insert__insort,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => 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) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_distinct__insort__insert,axiom, % 177.89/177.90 ! [V_x_2,V_f_2,V_xs_2,T_a,T_b] : % 177.89/177.90 ( class_Orderings_Olinorder(T_b) % 177.89/177.90 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 177.89/177.90 => 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))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_insort__insert__triv,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = V_xs_2 ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__insort__insert,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => 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)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_insort__insert__key__triv,axiom, % 177.89/177.90 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( 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)))) % 177.89/177.90 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listsum__setsum__nth,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_restrict__map__upds,axiom, % 177.89/177.90 ! [V_m_2,V_D_2,V_ys_2,T_b,V_xs_2,T_a] : % 177.89/177.90 ( 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) % 177.89/177.90 => ( 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)) % 177.89/177.90 => 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) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listsum__eq__0__nat__iff__nat,axiom, % 177.89/177.90 ! [V_ns_2] : % 177.89/177.90 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.90 <=> ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 177.89/177.90 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__add__upds,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_elem__le__listsum__nat,axiom, % 177.89/177.90 ! [V_ns,V_k] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns))) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__upds__apply__nontin,axiom, % 177.89/177.90 ! [V_ys_2,V_f_2,T_b,V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listsum__0,axiom, % 177.89/177.90 ! [V_xs_2,T_b,T_a] : % 177.89/177.90 ( class_Groups_Omonoid__add(T_a) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listsum__addf,axiom, % 177.89/177.90 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 177.89/177.90 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listsum__const__mult,axiom, % 177.89/177.90 ! [V_xs_2,V_f_2,V_ca_2,T_b,T_a] : % 177.89/177.90 ( class_Rings_Osemiring__0(T_a) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listsum__mult__const,axiom, % 177.89/177.90 ! [V_xs_2,V_ca_2,V_f_2,T_b,T_a] : % 177.89/177.90 ( class_Rings_Osemiring__0(T_a) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listsum__subtractf,axiom, % 177.89/177.90 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 177.89/177.90 ( class_Groups_Oab__group__add(T_a) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listsum__update__nat,axiom, % 177.89/177.90 ! [V_n,V_ns,V_k] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns))) % 177.89/177.90 => hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,V_ns),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns)),V_n)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listsum__abs,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.89/177.90 => 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)))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_uminus__listsum__map,axiom, % 177.89/177.90 ! [V_xs_2,V_f_2,T_b,T_a] : % 177.89/177.90 ( class_Groups_Oab__group__add(T_a) % 177.89/177.90 => 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)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_distinct__listsum__conv__Setsum,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.90 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listsum__distinct__conv__setsum__set,axiom, % 177.89/177.90 ! [V_f_2,V_xs_2,T_a,T_b] : % 177.89/177.90 ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.90 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_setsum__set__upto__conv__listsum__int,axiom, % 177.89/177.90 ! [V_j_2,V_i_2,V_f_2,T_a] : % 177.89/177.90 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_interv__listsum__conv__setsum__set__int,axiom, % 177.89/177.90 ! [V_l_2,V_k_2,V_f_2,T_a] : % 177.89/177.90 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__upds__list__update2__drop,axiom, % 177.89/177.90 ! [V_y_2,V_m_2,V_ys_2,T_b,V_i_2,V_xs_2,T_a] : % 177.89/177.90 ( 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)) % 177.89/177.90 => ( 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))) % 177.89/177.90 => 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) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listsum__triv,axiom, % 177.89/177.90 ! [V_xs_2,V_r_2,T_b,T_a] : % 177.89/177.90 ( class_Rings_Osemiring__1(T_a) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__upds__twist,axiom, % 177.89/177.90 ! [V_bs_2,V_b_2,V_m_2,T_b,V_as_2,V_a_2,T_a] : % 177.89/177.90 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_as_2))) % 177.89/177.90 => 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)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listsum__map__remove1,axiom, % 177.89/177.90 ! [V_f_2,V_xs_2,V_x_2,T_a,T_b] : % 177.89/177.90 ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.90 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => 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)))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Nitpick_Osetsum_H__def,axiom, % 177.89/177.90 ! [V_f_2,V_A_2,T_a,T_b] : % 177.89/177.90 ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.90 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.90 => 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))))) ) % 177.89/177.90 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.90 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listsum__mono,axiom, % 177.89/177.90 ! [V_g_2,V_f_2,V_xs_2,T_a,T_b] : % 177.89/177.90 ( ( class_Groups_Omonoid__add(T_b) % 177.89/177.90 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 177.89/177.90 => ( ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 177.89/177.90 => 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)))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_some__sym__eq__trivial,axiom, % 177.89/177.90 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 177.89/177.90 % 177.89/177.90 fof(fact_some__eq__trivial,axiom, % 177.89/177.90 ! [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 ). % 177.89/177.90 % 177.89/177.90 fof(fact_some__eq__ex,axiom, % 177.89/177.90 ! [T_a,V_P_2] : % 177.89/177.90 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) % 177.89/177.90 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_someI__ex,axiom, % 177.89/177.90 ! [T_a,V_P_2] : % 177.89/177.90 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 177.89/177.90 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_someI,axiom, % 177.89/177.90 ! [T_a,V_x_2,V_P_2] : % 177.89/177.90 ( hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.90 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_tfl__some,axiom, % 177.89/177.90 ! [T_a,B_P] : % 177.89/177.90 ( ? [B_x] : hBOOL(hAPP(B_P,B_x)) % 177.89/177.90 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_a,B_P))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_exE__some,axiom, % 177.89/177.90 ! [T_a,V_ca_2,V_P_2] : % 177.89/177.90 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 177.89/177.90 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_a,V_P_2) % 177.89/177.90 => hBOOL(hAPP(V_P_2,V_ca_2)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Nitpick_Ocard_H__def,axiom, % 177.89/177.90 ! [V_A_2,T_a] : % 177.89/177.90 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.90 => 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)))) ) % 177.89/177.90 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.90 => c_Nitpick_Ocard_H(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_LeastM__def,axiom, % 177.89/177.90 ! [V_P_2,V_m_2,T_a,T_b] : % 177.89/177.90 ( class_Orderings_Oord(T_b) % 177.89/177.90 => c_Hilbert__Choice_OLeastM(T_a,T_b,V_m_2,V_P_2) = c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_m_2))),V_m_2))))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_LeastM__nat__le,axiom, % 177.89/177.90 ! [T_a,V_m_2,V_x_2,V_P_2] : % 177.89/177.90 ( hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_m_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))),hAPP(V_m_2,V_x_2))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_LeastM__nat__lemma,axiom, % 177.89/177.90 ! [V_m_2,T_a,V_k_2,V_P_2] : % 177.89/177.90 ( hBOOL(hAPP(V_P_2,V_k_2)) % 177.89/177.90 => ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) % 177.89/177.90 & ! [B_y] : % 177.89/177.90 ( hBOOL(hAPP(V_P_2,B_y)) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_m_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))),hAPP(V_m_2,B_y))) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Eps__split__eq,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_split__paired__Eps,axiom, % 177.89/177.90 ! [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)))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Eps__split,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_GreatestM__def,axiom, % 177.89/177.90 ! [V_P_2,V_m_2,T_a,T_b] : % 177.89/177.90 ( class_Orderings_Oord(T_b) % 177.89/177.90 => hAPP(c_Hilbert__Choice_OGreatestM(T_a,T_b,V_m_2),V_P_2) = c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2))),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_m_2))),V_m_2))))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_all__nth__imp__all__set,axiom, % 177.89/177.90 ! [V_x_2,V_P_2,V_xs_2,T_a] : % 177.89/177.90 ( ! [B_i] : % 177.89/177.90 ( 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))) % 177.89/177.90 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 177.89/177.90 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_LeastM__natI,axiom, % 177.89/177.90 ! [V_m_2,T_a,V_k_2,V_P_2] : % 177.89/177.90 ( hBOOL(hAPP(V_P_2,V_k_2)) % 177.89/177.90 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Greatest__def,axiom, % 177.89/177.90 ! [T_a] : % 177.89/177.90 ( class_Orderings_Oord(T_a) % 177.89/177.90 => c_Hilbert__Choice_OGreatest(T_a) = c_Hilbert__Choice_OGreatestM(T_a,T_a,c_COMBI(T_a)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list__size__conv__listsum,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list__size__map,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list__size__estimation,axiom, % 177.89/177.90 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 177.89/177.90 => 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))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list__size__estimation_H,axiom, % 177.89/177.90 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 177.89/177.90 => 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))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list__size__pointwise,axiom, % 177.89/177.90 ! [V_g_2,V_f_2,V_xs_2,T_a] : % 177.89/177.90 ( ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__upd__upds__conv__if,axiom, % 177.89/177.90 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_b,V_x_2,T_a] : % 177.89/177.90 ( ( 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)))) % 177.89/177.90 => 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) ) % 177.89/177.90 & ( ~ 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)))) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__map,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_distinct__take,axiom, % 177.89/177.90 ! [V_i,V_xs,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.89/177.90 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__take,axiom, % 177.89/177.90 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),V_m)),V_xs) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__zip,axiom, % 177.89/177.90 ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Otake(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_b),V_n),V_ys)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__all,axiom, % 177.89/177.90 ! [V_n,V_xs,T_a] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) % 177.89/177.90 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__take,axiom, % 177.89/177.90 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ). % 177.89/177.90 % 177.89/177.90 fof(fact_in__set__takeD,axiom, % 177.89/177.90 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 177.89/177.90 ( 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)))) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__take__subset,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth__take,axiom, % 177.89/177.90 ! [V_xs,T_a,V_n,V_i] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 177.89/177.90 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sublist__upt__eq__take,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__take__subset__set__take,axiom, % 177.89/177.90 ! [V_xs_2,T_a,V_n_2,V_m_2] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.90 => 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)))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_dom__map__upds,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lexord__take__index__conv,axiom, % 177.89/177.90 ! [V_r_2,V_y_2,V_x_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 <=> ( ( 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))) % 177.89/177.90 & 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 ) % 177.89/177.90 | ? [B_i] : % 177.89/177.90 ( 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)))) % 177.89/177.90 & hAPP(hAPP(c_List_Otake(T_a),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_a),B_i),V_y_2) % 177.89/177.90 & 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)) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_butlast__take,axiom, % 177.89/177.90 ! [V_xs,T_a,V_n] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__butlast,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_in__set__butlastD,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__butlast,axiom, % 177.89/177.90 ! [V_xs,T_a,V_n] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__butlast,axiom, % 177.89/177.90 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_butlast__conv__take,axiom, % 177.89/177.90 ! [V_xs,T_a] : c_List_Obutlast(T_a,V_xs) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ). % 177.89/177.90 % 177.89/177.90 fof(fact_butlast__list__update,axiom, % 177.89/177.90 ! [V_x,V_xs,T_a,V_k] : % 177.89/177.90 ( ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) % 177.89/177.90 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Obutlast(T_a,V_xs) ) % 177.89/177.90 & ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) % 177.89/177.90 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = hAPP(hAPP(c_List_Olist__update(T_a,c_List_Obutlast(T_a,V_xs)),V_k),V_x) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel__iff__nth,axiom, % 177.89/177.90 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 <=> ( 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) % 177.89/177.90 & ! [B_n] : % 177.89/177.90 ( 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))) % 177.89/177.90 => 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)) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lexord__lex,axiom, % 177.89/177.90 ! [V_r_2,V_y_2,V_x_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 <=> ( 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))) % 177.89/177.90 & 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) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel__mono,axiom, % 177.89/177.90 ! [V_s_2,V_r_2,T_a] : % 177.89/177.90 ( 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)) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel__eq__len,axiom, % 177.89/177.90 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lenlex__conv,axiom, % 177.89/177.90 ! [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)))))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lenlex__def,axiom, % 177.89/177.90 ! [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)))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrelp__listrel__eq,axiom, % 177.89/177.90 ! [V_xa_2,V_x_2,V_r_2,T_a] : % 177.89/177.90 ( 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) % 177.89/177.90 <=> 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel__iff__zip,axiom, % 177.89/177.90 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 <=> ( 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) % 177.89/177.90 & ! [B_x] : % 177.89/177.90 ( 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)))) % 177.89/177.90 => 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)) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_ball__empty,axiom, % 177.89/177.90 ! [V_P_2,T_a,B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 177.89/177.90 => hBOOL(hAPP(V_P_2,B_x)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Powp__def,axiom, % 177.89/177.90 ! [V_B_2,V_A_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,V_A_2),V_B_2)) % 177.89/177.90 <=> ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 177.89/177.90 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_INFI__bool__eq,axiom, % 177.89/177.90 ! [T_a] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_HOL_Obool) = c_Set_OBall(T_a) ). % 177.89/177.90 % 177.89/177.90 fof(fact_ball__UNIV,axiom, % 177.89/177.90 ! [V_P_2,T_a] : % 177.89/177.90 ( ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 177.89/177.90 => hBOOL(hAPP(V_P_2,B_x)) ) % 177.89/177.90 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Collect__ball__eq,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_congruent__def,axiom, % 177.89/177.90 ! [V_f_2,V_r_2,T_b,T_a] : % 177.89/177.90 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 177.89/177.90 <=> ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_INTER__def,axiom, % 177.89/177.90 ! [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)))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Inf__Sup,axiom, % 177.89/177.90 ! [V_A_2,T_a] : % 177.89/177.90 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.89/177.90 => 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))))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Sup__Inf,axiom, % 177.89/177.90 ! [V_A_2,T_a] : % 177.89/177.90 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.89/177.90 => 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)))))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list__eq__iff__zip__eq,axiom, % 177.89/177.90 ! [T_a,V_ys_2,V_xs_2] : % 177.89/177.90 ( V_xs_2 = V_ys_2 % 177.89/177.90 <=> ( 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) % 177.89/177.90 & ! [B_x] : % 177.89/177.90 ( 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)))) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_WT__bodies__def,axiom, % 177.89/177.90 ( c_Com_OWT__bodies % 177.89/177.90 <=> ! [B_x] : % 177.89/177.90 ( 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))) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lexn__length,axiom, % 177.89/177.90 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = V_n_2 % 177.89/177.90 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_refl__on__def_H,axiom, % 177.89/177.90 ! [V_r_2,V_A_2,T_a] : % 177.89/177.90 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 177.89/177.90 <=> ( ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 177.89/177.90 => 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)) ) % 177.89/177.90 & ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.90 => 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)) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_refl__on__Id__on,axiom, % 177.89/177.90 ! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_triples__valid__Suc,axiom, % 177.89/177.90 ! [V_n_2,V_ts_2,T_a] : % 177.89/177.90 ( ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 177.89/177.90 => c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),B_x) ) % 177.89/177.90 => ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 177.89/177.90 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,B_x) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lexn_Osimps_I1_J,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_refl__on__empty,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_hoare__valids__def,axiom, % 177.89/177.90 ! [V_ts_2,V_G_2,T_a] : % 177.89/177.90 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,V_ts_2) % 177.89/177.90 <=> ! [B_n] : % 177.89/177.90 ( ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_G_2)) % 177.89/177.90 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) % 177.89/177.90 => ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 177.89/177.90 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_refl__on__Un,axiom, % 177.89/177.90 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 177.89/177.90 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 177.89/177.90 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_refl__on__Int,axiom, % 177.89/177.90 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 177.89/177.90 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 177.89/177.90 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Inter__eq,axiom, % 177.89/177.90 ! [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)))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_refl__onD,axiom, % 177.89/177.90 ! [V_a_2,V_r_2,V_A_2,T_a] : % 177.89/177.90 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 177.89/177.90 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_refl__onD1,axiom, % 177.89/177.90 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 177.89/177.90 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 177.89/177.90 => ( 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)) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_refl__onD2,axiom, % 177.89/177.90 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 177.89/177.90 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 177.89/177.90 => ( 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)) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lex__def,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_reflp__def,axiom, % 177.89/177.90 ! [V_r_2,T_a] : % 177.89/177.90 ( c_Predicate_Oreflp(T_a,V_r_2) % 177.89/177.90 <=> 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel1__subset__listrel,axiom, % 177.89/177.90 ! [V_r_H_2,V_r_2,T_a] : % 177.89/177.90 ( 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)) % 177.89/177.90 => ( c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_r_H_2) % 177.89/177.90 => 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))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_reflpE,axiom, % 177.89/177.90 ! [V_x_2,V_r_2,T_a] : % 177.89/177.90 ( c_Predicate_Oreflp(T_a,V_r_2) % 177.89/177.90 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel1__mono,axiom, % 177.89/177.90 ! [V_s_2,V_r_2,T_a] : % 177.89/177.90 ( 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)) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel1__eq__len,axiom, % 177.89/177.90 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel1__iff__update,axiom, % 177.89/177.90 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 <=> ? [B_y,B_n] : % 177.89/177.90 ( 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)) % 177.89/177.90 & 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))) % 177.89/177.90 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),B_n),B_y) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lexord__linear,axiom, % 177.89/177.90 ! [V_y_2,V_x_2,V_r_2,T_a] : % 177.89/177.90 ( ! [B_a,B_b] : % 177.89/177.90 ( 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)) % 177.89/177.90 | B_a = B_b % 177.89/177.90 | 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)) ) % 177.89/177.90 => ( 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))) % 177.89/177.90 | V_x_2 = V_y_2 % 177.89/177.90 | 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))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lexord__irreflexive,axiom, % 177.89/177.90 ! [V_y_2,V_r_2,T_a] : % 177.89/177.90 ( ! [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)) % 177.89/177.90 => ~ 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth__take__lemma,axiom, % 177.89/177.90 ! [V_ys,V_xs,T_a,V_k] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys))) % 177.89/177.90 => ( ! [B_i] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) % 177.89/177.90 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) ) % 177.89/177.90 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Cons__in__lex,axiom, % 177.89/177.90 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 <=> ( ( 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)) % 177.89/177.90 & 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) ) % 177.89/177.90 | ( V_x_2 = V_y_2 % 177.89/177.90 & 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))) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_partition__set,axiom, % 177.89/177.90 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 177.89/177.90 ( 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) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrelp_OCons,axiom, % 177.89/177.90 ! [V_ys_2,V_xs_2,T_a,V_y_2,V_x_2,V_r_2] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 177.89/177.90 => ( c_List_Olistrelp(T_a,V_r_2,V_xs_2,V_ys_2) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrelp_Oequations_I2_J,axiom, % 177.89/177.90 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_a] : % 177.89/177.90 ( 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)) % 177.89/177.90 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) % 177.89/177.90 & c_List_Olistrelp(T_a,V_r_2,V_a3_2,V_a4_2) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listsum__simps_I2_J,axiom, % 177.89/177.90 ! [V_xs,V_x,T_a] : % 177.89/177.90 ( class_Groups_Omonoid__add(T_a) % 177.89/177.90 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth__Cons__Suc,axiom, % 177.89/177.90 ! [V_n,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth__Cons__0,axiom, % 177.89/177.90 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_x ). % 177.89/177.90 % 177.89/177.90 fof(fact_list__update__code_I3_J,axiom, % 177.89/177.90 ! [V_y,V_i,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_i)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list__update_Osimps_I2_J,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list__update__code_I2_J,axiom, % 177.89/177.90 ! [V_y,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs) ). % 177.89/177.90 % 177.89/177.90 fof(fact_remove1_Osimps_I2_J,axiom, % 177.89/177.90 ! [V_xs,T_a,V_y,V_x] : % 177.89/177.90 ( ( V_x = V_y % 177.89/177.90 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) % 177.89/177.90 & ( V_x != V_y % 177.89/177.90 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Oremove1(T_a,V_x,V_xs)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_foldr_Osimps_I2_J,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_not__Cons__self,axiom, % 177.89/177.90 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ). % 177.89/177.90 % 177.89/177.90 fof(fact_not__Cons__self2,axiom, % 177.89/177.90 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ). % 177.89/177.90 % 177.89/177.90 fof(fact_list_Oinject,axiom, % 177.89/177.90 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_a] : % 177.89/177.90 ( 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) % 177.89/177.90 <=> ( V_a_2 = V_a_H_2 % 177.89/177.90 & V_list_2 = V_list_H_2 ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_removeAll_Osimps_I2_J,axiom, % 177.89/177.90 ! [V_xs,T_a,V_y,V_x] : % 177.89/177.90 ( ( V_x = V_y % 177.89/177.90 => hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) % 177.89/177.90 & ( V_x != V_y % 177.89/177.90 => hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map_Osimps_I2_J,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__Suc__Cons,axiom, % 177.89/177.90 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_zip__Cons__Cons,axiom, % 177.89/177.90 ! [V_ys,V_y,V_xs,V_x,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_insort__key_Osimps_I2_J,axiom, % 177.89/177.90 ! [V_ys_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( ( 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))) % 177.89/177.90 => 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)) ) % 177.89/177.90 & ( ~ 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))) % 177.89/177.90 => 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)) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_impossible__Cons,axiom, % 177.89/177.90 ! [V_x,V_ys,V_xs,T_a] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys))) % 177.89/177.90 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__subset__Cons,axiom, % 177.89/177.90 ! [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)))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_partition_Osimps_I2_J,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__ConsD,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,V_y_2,T_a] : % 177.89/177.90 ( 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)))) % 177.89/177.90 => ( V_y_2 = V_x_2 % 177.89/177.90 | hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_List_Oset_Osimps_I2_J,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth_Osimps,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_distinct_Osimps_I2_J,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) % 177.89/177.90 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__of__Cons__code_I2_J,axiom, % 177.89/177.90 ! [V_ps,V_v,T_c,T_b,V_k,V_l] : % 177.89/177.90 ( ( V_l = V_k % 177.89/177.90 => 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) ) % 177.89/177.90 & ( V_l != V_k % 177.89/177.90 => 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) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel1I2,axiom, % 177.89/177.90 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__upds__Cons,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list_Osize_I4_J,axiom, % 177.89/177.90 ! [V_list,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),V_list)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_list)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth__Cons_H,axiom, % 177.89/177.90 ! [V_xs,V_x,T_a,V_n] : % 177.89/177.90 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.90 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) % 177.89/177.90 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.90 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list_Osize_I2_J,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_partition__P,axiom, % 177.89/177.90 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 177.89/177.90 ( 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) % 177.89/177.90 => ( ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_yes_2))) % 177.89/177.90 => hBOOL(hAPP(V_P_2,B_x)) ) % 177.89/177.90 & ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_no_2))) % 177.89/177.90 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth__Cons__number__of,axiom, % 177.89/177.90 ! [V_xs,V_x,T_a,V_v] : % 177.89/177.90 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.90 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = V_x ) % 177.89/177.90 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.90 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel1I1,axiom, % 177.89/177.90 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 177.89/177.90 ( 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)) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Cons__listrel1__Cons,axiom, % 177.89/177.90 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 <=> ( ( 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)) % 177.89/177.90 & V_xs_2 = V_ys_2 ) % 177.89/177.90 | ( V_x_2 = V_y_2 % 177.89/177.90 & 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))) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel_OCons,axiom, % 177.89/177.90 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 177.89/177.90 ( 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)) % 177.89/177.90 => ( 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))) % 177.89/177.90 => 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))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lexord__cons__cons,axiom, % 177.89/177.90 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 <=> ( 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)) % 177.89/177.90 | ( V_a_2 = V_b_2 % 177.89/177.90 & 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))) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__of_Osimps_I2_J,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel__Cons,axiom, % 177.89/177.90 ! [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))))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__Cons__def,axiom, % 177.89/177.90 ! [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)))))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lexn_Osimps_I2_J,axiom, % 177.89/177.90 ! [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)))))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel__Cons1,axiom, % 177.89/177.90 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => ~ ! [B_y,B_ys] : % 177.89/177.90 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys) % 177.89/177.90 => ( 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)) % 177.89/177.90 => ~ 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))) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__pair__imageI,axiom, % 177.89/177.90 ! [V_g_2,V_f_2,T_d,T_c,V_R_2,V_b_2,V_a_2,T_b,T_a] : % 177.89/177.90 ( 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)) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_fst__comp__map__pair,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_snd__comp__map__pair,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__pair_Ocomp,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__pair__compose,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__pair_Ocompositionality,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_fst__map__pair,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_snd__prod__fun,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__pair__ident,axiom, % 177.89/177.90 ! [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 ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__pair__simp,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__pair__def,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__pair__surj,axiom, % 177.89/177.90 ! [V_g_2,T_c,T_d,V_f_2,T_a,T_b] : % 177.89/177.90 ( 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)) % 177.89/177.90 => ( 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)) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel__Cons2,axiom, % 177.89/177.90 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => ~ ! [B_x,B_xs] : % 177.89/177.90 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 177.89/177.90 => ( 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)) % 177.89/177.90 => ~ 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))) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_prod__fun__imageE,axiom, % 177.89/177.90 ! [V_R_2,V_g_2,V_f_2,T_d,T_c,V_ca_2,T_b,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => ~ ! [B_x,B_y] : % 177.89/177.90 ( 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)) % 177.89/177.90 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)),V_R_2)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_image__split__eq__Sigma,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__Cons__number__of,axiom, % 177.89/177.90 ! [V_xs,V_x,T_a,V_v] : % 177.89/177.90 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.90 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 177.89/177.90 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.90 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_SigmaI,axiom, % 177.89/177.90 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.90 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 177.89/177.90 => 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))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel__Nil1,axiom, % 177.89/177.90 ! [V_r_2,V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel__Nil2,axiom, % 177.89/177.90 ! [V_r_2,V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_upto__empty,axiom, % 177.89/177.90 ! [V_i,V_j] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) % 177.89/177.90 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list_Osimps_I2_J,axiom, % 177.89/177.90 ! [V_list_H,V_a_H,T_a] : c_List_Olist_ONil(T_a) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list_Osimps_I3_J,axiom, % 177.89/177.90 ! [V_list_H,V_a_H,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) != c_List_Olist_ONil(T_a) ). % 177.89/177.90 % 177.89/177.90 fof(fact_insort__key_Osimps_I1_J,axiom, % 177.89/177.90 ! [V_x_2,V_f_2,T_a,T_b] : % 177.89/177.90 ( class_Orderings_Olinorder(T_b) % 177.89/177.90 => 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)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_butlast_Osimps_I2_J,axiom, % 177.89/177.90 ! [V_x,T_a,V_xs] : % 177.89/177.90 ( ( V_xs = c_List_Olist_ONil(T_a) % 177.89/177.90 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 177.89/177.90 & ( V_xs != c_List_Olist_ONil(T_a) % 177.89/177.90 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Obutlast(T_a,V_xs)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Times__eq__cancel2,axiom, % 177.89/177.90 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 177.89/177.90 => ( 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)) % 177.89/177.90 <=> V_A_2 = V_B_2 ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Sigma__empty1,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Sigma__empty2,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Times__empty,axiom, % 177.89/177.90 ! [V_B_2,V_A_2,T_b,T_a] : % 177.89/177.90 ( 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)) % 177.89/177.90 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.90 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__empty,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.90 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__empty2,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),V_xs_2) % 177.89/177.90 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_List_Oset_Osimps_I1_J,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Sigma__Union,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_equiv__type,axiom, % 177.89/177.90 ! [V_r_2,V_A_2,T_a] : % 177.89/177.90 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 177.89/177.90 => 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)))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrelp_ONil,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrelp_Oequations_I1_J,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listsum__simps_I1_J,axiom, % 177.89/177.90 ! [T_a] : % 177.89/177.90 ( class_Groups_Omonoid__add(T_a) % 177.89/177.90 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list_Osize_I3_J,axiom, % 177.89/177.90 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__0__conv,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.90 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list__update__code_I1_J,axiom, % 177.89/177.90 ! [V_y,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_y) = c_List_Olist_ONil(T_a) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list__update_Osimps_I1_J,axiom, % 177.89/177.90 ! [V_v,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_v) = c_List_Olist_ONil(T_a) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list__update__nonempty,axiom, % 177.89/177.90 ! [V_x_2,V_k_2,V_xs_2,T_a] : % 177.89/177.90 ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_a) % 177.89/177.90 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Sigma__Un__distrib1,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Times__Un__distrib1,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Sigma__Un__distrib2,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sublist__nil,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Compl__Times__UNIV1,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Compl__Times__UNIV2,axiom, % 177.89/177.90 ! [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)))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_remove1_Osimps_I1_J,axiom, % 177.89/177.90 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 177.89/177.90 % 177.89/177.90 fof(fact_zip_Osimps_I1_J,axiom, % 177.89/177.90 ! [V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_zip__Nil,axiom, % 177.89/177.90 ! [V_ys,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Olist_ONil(T_a)),V_ys) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_card__cartesian__product,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_foldr_Osimps_I1_J,axiom, % 177.89/177.90 ! [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 ). % 177.89/177.90 % 177.89/177.90 fof(fact_Sigma__Diff__distrib1,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Times__Diff__distrib1,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Sigma__Diff__distrib2,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_distinct_Osimps_I1_J,axiom, % 177.89/177.90 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_removeAll_Osimps_I1_J,axiom, % 177.89/177.90 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 177.89/177.90 % 177.89/177.90 fof(fact_insort__not__Nil,axiom, % 177.89/177.90 ! [V_xs_2,V_a_2,V_f_2,T_a,T_b] : % 177.89/177.90 ( class_Orderings_Olinorder(T_b) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__upds__Nil2,axiom, % 177.89/177.90 ! [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 ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__upds__Nil1,axiom, % 177.89/177.90 ! [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 ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__is__Nil__conv,axiom, % 177.89/177.90 ! [V_xs_2,V_f_2,T_a,T_b] : % 177.89/177.90 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = c_List_Olist_ONil(T_a) % 177.89/177.90 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map_Osimps_I1_J,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Nil__is__map__conv,axiom, % 177.89/177.90 ! [V_xs_2,V_f_2,T_b,T_a] : % 177.89/177.90 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) % 177.89/177.90 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_butlast_Osimps_I1_J,axiom, % 177.89/177.90 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__0,axiom, % 177.89/177.90 ! [V_xs,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = c_List_Olist_ONil(T_a) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__eq__Nil,axiom, % 177.89/177.90 ! [V_xs_2,V_n_2,T_a] : % 177.89/177.90 ( hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 177.89/177.90 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.90 | V_xs_2 = c_List_Olist_ONil(T_a) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__Nil,axiom, % 177.89/177.90 ! [V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 177.89/177.90 % 177.89/177.90 fof(fact_finite__cartesian__product,axiom, % 177.89/177.90 ! [V_B_2,T_b,V_A_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 177.89/177.90 => 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)))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__of__Cons__code_I1_J,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Sigma__Int__distrib2,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Times__Int__distrib1,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Sigma__Int__distrib1,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_setprod__cartesian__product,axiom, % 177.89/177.90 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 177.89/177.90 ( class_Groups_Ocomm__monoid__mult(T_a) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_setsum__cartesian__product,axiom, % 177.89/177.90 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 177.89/177.90 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_distinct__butlast,axiom, % 177.89/177.90 ! [T_a,V_xs] : % 177.89/177.90 ( V_xs != c_List_Olist_ONil(T_a) % 177.89/177.90 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.89/177.90 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Id__on__subset__Times,axiom, % 177.89/177.90 ! [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)))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list_Osize_I1_J,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__list__of__set__empty,axiom, % 177.89/177.90 ! [T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_UNIV__Times__UNIV,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_mem__Sigma__iff,axiom, % 177.89/177.90 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.90 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_SigmaD1,axiom, % 177.89/177.90 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_SigmaD2,axiom, % 177.89/177.90 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_SigmaE2,axiom, % 177.89/177.90 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 177.89/177.90 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sublist__empty,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_partition_Osimps_I1_J,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__of_Osimps_I1_J,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_card__cartesian__product__singleton,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Times__subset__cancel2,axiom, % 177.89/177.90 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 177.89/177.90 => ( 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)))) % 177.89/177.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__greater__0__conv,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 <=> V_xs_2 != c_List_Olist_ONil(T_a) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Image__subset,axiom, % 177.89/177.90 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 177.89/177.90 ( 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)))) % 177.89/177.90 => 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)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_finite__cartesian__productD1,axiom, % 177.89/177.90 ! [V_B_2,V_A_2,T_b,T_a] : % 177.89/177.90 ( 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)))) % 177.89/177.90 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 177.89/177.90 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_finite__cartesian__productD2,axiom, % 177.89/177.90 ! [V_B_2,V_A_2,T_b,T_a] : % 177.89/177.90 ( 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)))) % 177.89/177.90 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.90 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Collect__split,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_SetCompr__Sigma__eq,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_fst__image__times,axiom, % 177.89/177.90 ! [V_A_2,T_b,T_a,V_B_2] : % 177.89/177.90 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.90 => 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)) ) % 177.89/177.90 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.90 => 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 ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_snd__image__times,axiom, % 177.89/177.90 ! [V_B_2,T_b,T_a,V_A_2] : % 177.89/177.90 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.90 => 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)) ) % 177.89/177.90 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.90 => 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 ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__1__Cons,axiom, % 177.89/177.90 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_not__listrel1__Nil,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_not__Nil__listrel1,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel_ONil,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__pair__surj__on,axiom, % 177.89/177.90 ! [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] : % 177.89/177.90 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_A_H_2 % 177.89/177.90 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2) = V_B_H_2 % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_swap__product,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lexord__Nil__right,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Nil__notin__lex,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Nil2__notin__lex,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_refl__on__def,axiom, % 177.89/177.90 ! [V_r_2,V_A_2,T_a] : % 177.89/177.90 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 177.89/177.90 <=> ( 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)))) % 177.89/177.90 & ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.90 => 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)) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_insert__times__insert,axiom, % 177.89/177.90 ! [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)))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_finite__equiv__class,axiom, % 177.89/177.90 ! [V_X_2,V_r_2,V_A_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.90 => ( 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)))) % 177.89/177.90 => ( 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))) % 177.89/177.90 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__pair__inj__on,axiom, % 177.89/177.90 ! [V_B_2,V_g_2,T_d,T_c,V_A_2,V_f_2,T_b,T_a] : % 177.89/177.90 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.89/177.90 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,V_B_2) % 177.89/177.90 => 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))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_UN__Times__distrib,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Sigma__def,axiom, % 177.89/177.90 ! [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))))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_finite__quotient,axiom, % 177.89/177.90 ! [V_r_2,V_A_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.90 => ( 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)))) % 177.89/177.90 => 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))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__Cons,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_upto_Osimps,axiom, % 177.89/177.90 ! [V_j,V_i] : % 177.89/177.90 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 177.89/177.90 => c_List_Oupto(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j)) ) % 177.89/177.90 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 177.89/177.90 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sublist__singleton,axiom, % 177.89/177.90 ! [V_x_2,T_a,V_A_2] : % 177.89/177.90 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 177.89/177.90 => 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)) ) % 177.89/177.90 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 177.89/177.90 => 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) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_vimage__Times,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__Cons_H,axiom, % 177.89/177.90 ! [V_xs,V_x,T_a,V_n] : % 177.89/177.90 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.90 => hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 177.89/177.90 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.90 => hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_upto__rec__number__of,axiom, % 177.89/177.90 ! [V_n,V_m] : % 177.89/177.90 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) % 177.89/177.90 => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) ) % 177.89/177.90 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) % 177.89/177.90 => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel__Nil,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__Cons__sing__Nil,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_upto_Opsimps,axiom, % 177.89/177.90 ! [V_j_2,V_i_2] : % 177.89/177.90 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_i_2),V_j_2))) % 177.89/177.90 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 177.89/177.90 => c_List_Oupto(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i_2),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ) % 177.89/177.90 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 177.89/177.90 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_anamorph_Osimps,axiom, % 177.89/177.90 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 177.89/177.90 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.89/177.90 => 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) ) % 177.89/177.90 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listset_Osimps_I1_J,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_zip__Cons,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list_Osimps_I5_J,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list_Osimps_I4_J,axiom, % 177.89/177.90 ! [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 ). % 177.89/177.90 % 177.89/177.90 fof(fact_listset_Osimps_I2_J,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_zip__Cons1,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_setsum__mult__setsum__if__inj,axiom, % 177.89/177.90 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] : % 177.89/177.90 ( class_Rings_Osemiring__0(T_c) % 177.89/177.90 => ( 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))) % 177.89/177.90 => 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))))))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_upto_Opinduct,axiom, % 177.89/177.90 ! [V_P_2,V_a1_2,V_a0_2] : % 177.89/177.90 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) % 177.89/177.90 => ( ! [B_i,B_j] : % 177.89/177.90 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_i),B_j))) % 177.89/177.90 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) % 177.89/177.90 => 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)) ) % 177.89/177.90 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) % 177.89/177.90 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_List_Omap_Oidentity,axiom, % 177.89/177.90 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_List_Omap_Oid,axiom, % 177.89/177.90 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_apfst__id,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_apsnd__id,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_id__apply,axiom, % 177.89/177.90 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 177.89/177.90 % 177.89/177.90 fof(fact_Option_Omap_Oid,axiom, % 177.89/177.90 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_id__def,axiom, % 177.89/177.90 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ). % 177.89/177.90 % 177.89/177.90 fof(fact_Option_Omap_Oidentity,axiom, % 177.89/177.90 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_of__int__eq__id,axiom, % 177.89/177.90 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ). % 177.89/177.90 % 177.89/177.90 fof(fact_inj__on__id,axiom, % 177.89/177.90 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_Fun_Oid(T_a),V_A_2) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__pair_Oid,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__pair_Oidentity,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_o__eq__id__dest,axiom, % 177.89/177.90 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 177.89/177.90 ( 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) % 177.89/177.90 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_o__id,axiom, % 177.89/177.90 ! [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 ). % 177.89/177.90 % 177.89/177.90 fof(fact_id__o,axiom, % 177.89/177.90 ! [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 ). % 177.89/177.90 % 177.89/177.90 fof(fact_vimage__id,axiom, % 177.89/177.90 ! [V_A_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_Fun_Oid(T_a)),V_A_2) = V_A_2 ). % 177.89/177.90 % 177.89/177.90 fof(fact_surj__id,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_image__id,axiom, % 177.89/177.90 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),V_Y_2) = V_Y_2 ). % 177.89/177.90 % 177.89/177.90 fof(fact_folding_Oempty,axiom, % 177.89/177.90 ! [V_F_2,V_f_2,T_b,T_a] : % 177.89/177.90 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 177.89/177.90 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Fun_Oid(T_b) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_apfst__def,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_apsnd__def,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_split__Pair,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_setsum__reindex__id,axiom, % 177.89/177.90 ! [V_B_2,V_f_2,T_a,T_b] : % 177.89/177.90 ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.90 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_setprod__reindex__id,axiom, % 177.89/177.90 ! [V_B_2,V_f_2,T_a,T_b] : % 177.89/177.90 ( class_Groups_Ocomm__monoid__mult(T_b) % 177.89/177.90 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Ex__inj__on__UNION__Sigma,axiom, % 177.89/177.90 ! [V_A_2,V_I_2,T_b,T_a] : % 177.89/177.90 ? [B_f] : % 177.89/177.90 ( 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)) % 177.89/177.90 & 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_setprod__Sigma,axiom, % 177.89/177.90 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 177.89/177.90 ( class_Groups_Ocomm__monoid__mult(T_c) % 177.89/177.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.90 => ( ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.90 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 177.89/177.90 => 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)) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_refl__onI,axiom, % 177.89/177.90 ! [V_A_2,V_r_2,T_a] : % 177.89/177.90 ( 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)))) % 177.89/177.90 => ( ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.90 => 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)) ) % 177.89/177.90 => c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_setsum__Sigma,axiom, % 177.89/177.90 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 177.89/177.90 ( class_Groups_Ocomm__monoid__add(T_c) % 177.89/177.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.90 => ( ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.90 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 177.89/177.90 => 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)) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_fold__image__Sigma,axiom, % 177.89/177.90 ! [V_g_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 177.89/177.90 ( class_Groups_Ocomm__monoid__mult(T_c) % 177.89/177.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.90 => ( ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.90 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 177.89/177.90 => 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)) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__upds__append1,axiom, % 177.89/177.90 ! [V_x_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => 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)))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_append__eq__Cons__conv,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a] : % 177.89/177.90 ( 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) % 177.89/177.90 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 177.89/177.90 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) % 177.89/177.90 | ? [B_ys_H] : % 177.89/177.90 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) % 177.89/177.90 & hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Cons__eq__append__conv,axiom, % 177.89/177.90 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( 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) % 177.89/177.90 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 177.89/177.90 & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2 ) % 177.89/177.90 | ? [B_ys_H] : % 177.89/177.90 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2 % 177.89/177.90 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_append1__eq__conv,axiom, % 177.89/177.90 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 <=> ( V_xs_2 = V_ys_2 % 177.89/177.90 & V_x_2 = V_y_2 ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_append__Cons,axiom, % 177.89/177.90 ! [V_ys,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_ys) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Cons__eq__appendI,axiom, % 177.89/177.90 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] : % 177.89/177.90 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys % 177.89/177.90 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) % 177.89/177.90 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_fun__upds__append2__drop,axiom, % 177.89/177.90 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 177.89/177.90 ( 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) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_fun__upds__append__drop,axiom, % 177.89/177.90 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 177.89/177.90 ( 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) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listsum__append,axiom, % 177.89/177.90 ! [V_ys,V_xs,T_a] : % 177.89/177.90 ( class_Groups_Omonoid__add(T_a) % 177.89/177.90 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_ys)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__append,axiom, % 177.89/177.90 ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_zip__append,axiom, % 177.89/177.90 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] : % 177.89/177.90 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_us) % 177.89/177.90 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_vs) % 177.89/177.90 => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_List_Oappend(T_b),V_us),V_vs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_us)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),V_vs)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__of__append,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_foldr__append,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_append__assoc,axiom, % 177.89/177.90 ! [V_zs,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_append__eq__append__conv2,axiom, % 177.89/177.90 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( 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) % 177.89/177.90 <=> ? [B_us] : % 177.89/177.90 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us) % 177.89/177.90 & hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) = V_ts_2 ) % 177.89/177.90 | ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us) = V_zs_2 % 177.89/177.90 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_same__append__eq,axiom, % 177.89/177.90 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( 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) % 177.89/177.90 <=> V_ys_2 = V_zs_2 ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_append__same__eq,axiom, % 177.89/177.90 ! [V_zs_2,V_xs_2,V_ys_2,T_a] : % 177.89/177.90 ( 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) % 177.89/177.90 <=> V_ys_2 = V_zs_2 ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_append__eq__appendI,axiom, % 177.89/177.90 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] : % 177.89/177.90 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs % 177.89/177.90 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) % 177.89/177.90 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_removeAll__append,axiom, % 177.89/177.90 ! [V_ys,V_xs,V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)),hAPP(c_List_OremoveAll(T_a,V_x),V_ys)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__append,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__append,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_butlast__append,axiom, % 177.89/177.90 ! [V_xs,T_a,V_ys] : % 177.89/177.90 ( ( V_ys = c_List_Olist_ONil(T_a) % 177.89/177.90 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) % 177.89/177.90 & ( V_ys != c_List_Olist_ONil(T_a) % 177.89/177.90 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Obutlast(T_a,V_ys)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_eq__Nil__appendI,axiom, % 177.89/177.90 ! [T_a,V_ys,V_xs] : % 177.89/177.90 ( V_xs = V_ys % 177.89/177.90 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_append__self__conv2,axiom, % 177.89/177.90 ! [V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_ys_2 % 177.89/177.90 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_append__self__conv,axiom, % 177.89/177.90 ! [V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_xs_2 % 177.89/177.90 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_append__is__Nil__conv,axiom, % 177.89/177.90 ! [V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_a) % 177.89/177.90 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 177.89/177.90 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_self__append__conv2,axiom, % 177.89/177.90 ! [V_xs_2,T_a,V_ys_2] : % 177.89/177.90 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 177.89/177.90 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_self__append__conv,axiom, % 177.89/177.90 ! [V_ys_2,T_a,V_xs_2] : % 177.89/177.90 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 177.89/177.90 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_append__Nil2,axiom, % 177.89/177.90 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ). % 177.89/177.90 % 177.89/177.90 fof(fact_Nil__is__append__conv,axiom, % 177.89/177.90 ! [V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 177.89/177.90 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 177.89/177.90 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_append__Nil,axiom, % 177.89/177.90 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth__append__length,axiom, % 177.89/177.90 ! [V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = V_x ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth__append__length__plus,axiom, % 177.89/177.90 ! [V_n,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_ys),V_n) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__append,axiom, % 177.89/177.90 ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list__update__append1,axiom, % 177.89/177.90 ! [V_x,V_ys,V_xs,T_a,V_i] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_i),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_ys) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list__update__length,axiom, % 177.89/177.90 ! [V_y,V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_y) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_remove1__append,axiom, % 177.89/177.90 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => 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) ) % 177.89/177.90 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_in__set__butlast__appendI,axiom, % 177.89/177.90 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 177.89/177.90 | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_ys_2)))) ) % 177.89/177.90 => 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))))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_butlast__snoc,axiom, % 177.89/177.90 ! [V_x,V_xs,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_xs ). % 177.89/177.90 % 177.89/177.90 fof(fact_append__listrel1I,axiom, % 177.89/177.90 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( ( ( 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))) % 177.89/177.90 & V_us_2 = V_vs_2 ) % 177.89/177.90 | ( V_xs_2 = V_ys_2 % 177.89/177.90 & 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))) ) ) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lexord__append__leftI,axiom, % 177.89/177.90 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_distinct__append,axiom, % 177.89/177.90 ! [V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 177.89/177.90 <=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 177.89/177.90 & hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 177.89/177.90 & 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth__append,axiom, % 177.89/177.90 ! [V_ys,V_xs,T_a,V_n] : % 177.89/177.90 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ) % 177.89/177.90 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_list__update__append,axiom, % 177.89/177.90 ! [V_x,V_ys,V_xs,T_a,V_n] : % 177.89/177.90 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_n),V_x)),V_ys) ) % 177.89/177.90 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist__update(T_a,V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_x)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sublist__append,axiom, % 177.89/177.90 ! [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)))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel1I,axiom, % 177.89/177.90 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 177.89/177.90 ( 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)) % 177.89/177.90 => ( 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)) % 177.89/177.90 => ( 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)) % 177.89/177.90 => 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))) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lexord__append__left__rightI,axiom, % 177.89/177.90 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_a] : % 177.89/177.90 ( 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)) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__Suc__conv__app__nth,axiom, % 177.89/177.90 ! [V_xs,T_a,V_i] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),c_List_Olist_ONil(T_a))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_snoc__listrel1__snoc__iff,axiom, % 177.89/177.90 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 <=> ( ( 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))) % 177.89/177.90 & V_x_2 = V_y_2 ) % 177.89/177.90 | ( V_xs_2 = V_ys_2 % 177.89/177.90 & 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)) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sublist__Cons,axiom, % 177.89/177.90 ! [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)))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel1E,axiom, % 177.89/177.90 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => ~ ! [B_x,B_y] : % 177.89/177.90 ( 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)) % 177.89/177.90 => ! [B_us,B_vs] : % 177.89/177.90 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_vs)) % 177.89/177.90 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_vs)) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_card__SigmaI,axiom, % 177.89/177.90 ! [V_B_2,T_b,V_A_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.90 => ( ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.90 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 177.89/177.90 => 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) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lexord__append__leftD,axiom, % 177.89/177.90 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => ( ! [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)) % 177.89/177.90 => 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))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rotate1__def,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__rotate1,axiom, % 177.89/177.90 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate1(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ). % 177.89/177.90 % 177.89/177.90 fof(fact_distinct1__rotate,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2))) % 177.89/177.90 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__rotate1,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rotate1__is__Nil__conv,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( hAPP(c_List_Orotate1(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 177.89/177.90 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rotate__simps,axiom, % 177.89/177.90 ! [V_xs,V_x,T_b,T_a] : % 177.89/177.90 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) % 177.89/177.90 & hAPP(c_List_Orotate1(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),c_List_Olist_ONil(T_b))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rotate1__length01,axiom, % 177.89/177.90 ! [V_xs,T_a] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) % 177.89/177.90 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_finite__SigmaI,axiom, % 177.89/177.90 ! [V_B_2,T_b,V_A_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.90 => ( ! [B_a] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 177.89/177.90 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 177.89/177.90 => 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))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_upd__conv__take__nth__drop,axiom, % 177.89/177.90 ! [V_a,V_xs,T_a,V_i] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_a) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_drop__Nil,axiom, % 177.89/177.90 ! [V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__drop__subset,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__drop,axiom, % 177.89/177.90 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_m),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_butlast__drop,axiom, % 177.89/177.90 ! [V_xs,V_n,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_drop__butlast,axiom, % 177.89/177.90 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_drop__map,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_distinct__drop,axiom, % 177.89/177.90 ! [V_i,V_xs,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.89/177.90 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_drop__drop,axiom, % 177.89/177.90 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs) ). % 177.89/177.90 % 177.89/177.90 fof(fact_drop__0,axiom, % 177.89/177.90 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ). % 177.89/177.90 % 177.89/177.90 fof(fact_drop__zip,axiom, % 177.89/177.90 ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Odrop(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_b),V_n),V_ys)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_in__set__dropD,axiom, % 177.89/177.90 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 177.89/177.90 ( 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)))) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__drop,axiom, % 177.89/177.90 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ). % 177.89/177.90 % 177.89/177.90 fof(fact_drop__take,axiom, % 177.89/177.90 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_drop__1__Cons,axiom, % 177.89/177.90 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs ). % 177.89/177.90 % 177.89/177.90 fof(fact_drop__Suc__Cons,axiom, % 177.89/177.90 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth__via__drop,axiom, % 177.89/177.90 ! [V_ys,V_y,V_xs,V_n,T_a] : % 177.89/177.90 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) % 177.89/177.90 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_append__take__drop__id,axiom, % 177.89/177.90 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = V_xs ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__drop__subset__set__drop,axiom, % 177.89/177.90 ! [V_xs_2,T_a,V_m_2,V_n_2] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) % 177.89/177.90 => 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)))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_drop__eq__Nil,axiom, % 177.89/177.90 ! [V_xs_2,V_n_2,T_a] : % 177.89/177.90 ( hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 177.89/177.90 <=> 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)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_drop__all,axiom, % 177.89/177.90 ! [V_n,V_xs,T_a] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) % 177.89/177.90 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_drop__append,axiom, % 177.89/177.90 ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_append__eq__conv__conj,axiom, % 177.89/177.90 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_zs_2 % 177.89/177.90 <=> ( 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) % 177.89/177.90 & 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) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_drop__Cons,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_drop__Cons_H,axiom, % 177.89/177.90 ! [V_xs,V_x,T_a,V_n] : % 177.89/177.90 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.90 => hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ) % 177.89/177.90 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.90 => hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth__drop,axiom, % 177.89/177.90 ! [V_xs,T_a,V_i,V_n] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_append__eq__append__conv__if,axiom, % 177.89/177.90 ! [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] : % 177.89/177.90 ( 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) % 177.89/177.90 <=> ( ( 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))) % 177.89/177.90 => ( 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) % 177.89/177.90 & 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) ) ) % 177.89/177.90 & ( ~ 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))) % 177.89/177.90 => ( 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 % 177.89/177.90 & 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 ) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth__drop_H,axiom, % 177.89/177.90 ! [V_xs,T_a,V_i] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_drop__Cons__number__of,axiom, % 177.89/177.90 ! [V_xs,V_x,T_a,V_v] : % 177.89/177.90 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.90 => hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ) % 177.89/177.90 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.90 => hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__add,axiom, % 177.89/177.90 ! [V_xs,T_a,V_j,V_i] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_j),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_zip__append1,axiom, % 177.89/177.90 ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_zip__append2,axiom, % 177.89/177.90 ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Oappend(T_b),V_ys),V_zs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_ys)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_zs)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_id__take__nth__drop,axiom, % 177.89/177.90 ! [V_xs,T_a,V_i] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__hd__drop,axiom, % 177.89/177.90 ! [V_xs,T_a,V_n] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_hd__drop__conv__nth,axiom, % 177.89/177.90 ! [V_n,T_a,V_xs] : % 177.89/177.90 ( V_xs != c_List_Olist_ONil(T_a) % 177.89/177.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_hd_Osimps,axiom, % 177.89/177.90 ! [V_xs,V_x,T_a] : hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ). % 177.89/177.90 % 177.89/177.90 fof(fact_hd__map,axiom, % 177.89/177.90 ! [V_f_2,T_b,T_a,V_xs_2] : % 177.89/177.90 ( V_xs_2 != c_List_Olist_ONil(T_a) % 177.89/177.90 => 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)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_hd__append2,axiom, % 177.89/177.90 ! [V_ys,T_a,V_xs] : % 177.89/177.90 ( V_xs != c_List_Olist_ONil(T_a) % 177.89/177.90 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_hd__append,axiom, % 177.89/177.90 ! [V_ys,T_a,V_xs] : % 177.89/177.90 ( ( V_xs = c_List_Olist_ONil(T_a) % 177.89/177.90 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_ys) ) % 177.89/177.90 & ( V_xs != c_List_Olist_ONil(T_a) % 177.89/177.90 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_hd__in__set,axiom, % 177.89/177.90 ! [T_a,V_xs_2] : % 177.89/177.90 ( V_xs_2 != c_List_Olist_ONil(T_a) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_hd__conv__nth,axiom, % 177.89/177.90 ! [T_a,V_xs] : % 177.89/177.90 ( V_xs != c_List_Olist_ONil(T_a) % 177.89/177.90 => hAPP(c_List_Ohd(T_a),V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rotate1__hd__tl,axiom, % 177.89/177.90 ! [T_a,V_xs] : % 177.89/177.90 ( V_xs != c_List_Olist_ONil(T_a) % 177.89/177.90 => hAPP(c_List_Orotate1(T_a),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),c_List_Olist_ONil(T_a))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_hd__rotate__conv__nth,axiom, % 177.89/177.90 ! [V_n,T_a,V_xs] : % 177.89/177.90 ( V_xs != c_List_Olist_ONil(T_a) % 177.89/177.90 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_drop__tl,axiom, % 177.89/177.90 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_tl__drop,axiom, % 177.89/177.90 ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rotate1__rotate__swap,axiom, % 177.89/177.90 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orotate1(T_a),V_xs)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_tl_Osimps_I1_J,axiom, % 177.89/177.90 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rotate__is__Nil__conv,axiom, % 177.89/177.90 ! [V_xs_2,V_n_2,T_a] : % 177.89/177.90 ( hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 177.89/177.90 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__rotate,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__tl,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rotate__map,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_distinct__rotate,axiom, % 177.89/177.90 ! [V_xs_2,V_n_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2))) % 177.89/177.90 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_distinct__tl,axiom, % 177.89/177.90 ! [V_xs,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.89/177.90 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rotate__rotate,axiom, % 177.89/177.90 ! [V_xs,V_n,V_m,T_a] : hAPP(c_List_Orotate(T_a,V_m),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_xs) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__rotate,axiom, % 177.89/177.90 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ). % 177.89/177.90 % 177.89/177.90 fof(fact_tl_Osimps_I2_J,axiom, % 177.89/177.90 ! [V_xs,V_x,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs ). % 177.89/177.90 % 177.89/177.90 fof(fact_tl__append2,axiom, % 177.89/177.90 ! [V_ys,T_a,V_xs] : % 177.89/177.90 ( V_xs != c_List_Olist_ONil(T_a) % 177.89/177.90 => hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),V_ys) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__tl,axiom, % 177.89/177.90 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rotate__conv__mod,axiom, % 177.89/177.90 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(c_List_Orotate(T_a,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs) ). % 177.89/177.90 % 177.89/177.90 fof(fact_drop__Suc,axiom, % 177.89/177.90 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rotate__Suc,axiom, % 177.89/177.90 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_tl__append,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rotate0,axiom, % 177.89/177.90 ! [T_a] : c_List_Orotate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rotate__add,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rotate__id,axiom, % 177.89/177.90 ! [V_xs,T_a,V_n] : % 177.89/177.90 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.90 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rotate__length01,axiom, % 177.89/177.90 ! [V_n,V_xs,T_a] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) % 177.89/177.90 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__tl,axiom, % 177.89/177.90 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_tl__take,axiom, % 177.89/177.90 ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(T_a),V_xs)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__Suc,axiom, % 177.89/177.90 ! [V_n,T_a,V_xs] : % 177.89/177.90 ( V_xs != c_List_Olist_ONil(T_a) % 177.89/177.90 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rotate__drop__take,axiom, % 177.89/177.90 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)),hAPP(hAPP(c_List_Otake(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_fold1__set,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 177.89/177.90 => ( V_xs_2 != c_List_Olist_ONil(T_a) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel__subset,axiom, % 177.89/177.90 ! [V_A_2,V_r_2,T_a] : % 177.89/177.90 ( 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)))) % 177.89/177.90 => 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))))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lists_ONil,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_foldl__append,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_foldl__Cons,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_foldr__conv__foldl,axiom, % 177.89/177.90 ! [V_a_2,V_xs_2,T_a] : % 177.89/177.90 ( class_Groups_Oab__semigroup__add(T_a) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_foldl__assoc,axiom, % 177.89/177.90 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 177.89/177.90 ( class_Groups_Osemigroup__add(T_a) % 177.89/177.90 => 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)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_foldl__absorb0,axiom, % 177.89/177.90 ! [V_zs_2,V_x_2,T_a] : % 177.89/177.90 ( class_Groups_Omonoid__add(T_a) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_foldl__map,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lists__mono,axiom, % 177.89/177.90 ! [V_B_2,V_A_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_start__le__sum,axiom, % 177.89/177.90 ! [V_ns_2,V_n_2,V_m_2] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_ns_2))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_foldl__Nil,axiom, % 177.89/177.90 ! [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 ). % 177.89/177.90 % 177.89/177.90 fof(fact_append__in__lists__conv,axiom, % 177.89/177.90 ! [V_A_2,V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 177.89/177.90 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lists__UNIV,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_equiv__listrel,axiom, % 177.89/177.90 ! [V_r_2,V_A_2,T_a] : % 177.89/177.90 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 177.89/177.90 => 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)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listrel__refl__on,axiom, % 177.89/177.90 ! [V_r_2,V_A_2,T_a] : % 177.89/177.90 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 177.89/177.90 => 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)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_listsum__foldl,axiom, % 177.89/177.90 ! [T_a] : % 177.89/177.90 ( class_Groups_Omonoid__add(T_a) % 177.89/177.90 => 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)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_foldl__foldr1,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( class_Groups_Omonoid__add(T_a) % 177.89/177.90 => 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)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_foldl__foldr1__lemma,axiom, % 177.89/177.90 ! [V_xs_2,V_a_2,T_a] : % 177.89/177.90 ( class_Groups_Omonoid__add(T_a) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sum__eq__0__conv,axiom, % 177.89/177.90 ! [V_ns_2,V_m_2] : % 177.89/177.90 ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.90 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.90 & ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 177.89/177.90 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_fun__left__comm__idem_Ofold__set,axiom, % 177.89/177.90 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 177.89/177.90 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Cons__in__lists__iff,axiom, % 177.89/177.90 ! [V_A_2,V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 177.89/177.90 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_in__lists__conv__set,axiom, % 177.89/177.90 ! [V_A_2,V_xs_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 177.89/177.90 <=> ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Sup__set__fold,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Inf__set__fold,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Sup__fin__set__fold,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( class_Lattices_Olattice(T_a) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Inf__fin__set__fold,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( class_Lattices_Olattice(T_a) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Min__fin__set__fold,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Max__fin__set__fold,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_min__max_OInf__fin__set__fold,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_min__max_OSup__fin__set__fold,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_SUPR__set__fold,axiom, % 177.89/177.90 ! [V_f_2,V_xs_2,T_b,T_a] : % 177.89/177.90 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_INFI__set__fold,axiom, % 177.89/177.90 ! [V_f_2,V_xs_2,T_b,T_a] : % 177.89/177.90 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lists__eq__set,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__upds__fold__map__upd,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_elem__le__sum,axiom, % 177.89/177.90 ! [V_ns_2,V_n_2] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_ns_2))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lists__empty,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lexord__append__rightI,axiom, % 177.89/177.90 ! [V_r_2,V_x_2,T_a,V_y_2] : % 177.89/177.90 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_b),B_z) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lexord__Nil__left,axiom, % 177.89/177.90 ! [V_r_2,V_y_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_last__list__update,axiom, % 177.89/177.90 ! [V_x,V_k,T_a,V_xs] : % 177.89/177.90 ( V_xs != c_List_Olist_ONil(T_a) % 177.89/177.90 => ( ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) % 177.89/177.90 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) % 177.89/177.90 & ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) % 177.89/177.90 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Olast(T_a,V_xs) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_last__conv__nth,axiom, % 177.89/177.90 ! [T_a,V_xs] : % 177.89/177.90 ( V_xs != c_List_Olist_ONil(T_a) % 177.89/177.90 => c_List_Olast(T_a,V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_last_Osimps,axiom, % 177.89/177.90 ! [V_x,T_a,V_xs] : % 177.89/177.90 ( ( V_xs = c_List_Olist_ONil(T_a) % 177.89/177.90 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) % 177.89/177.90 & ( V_xs != c_List_Olist_ONil(T_a) % 177.89/177.90 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_last__ConsR,axiom, % 177.89/177.90 ! [V_x,T_a,V_xs] : % 177.89/177.90 ( V_xs != c_List_Olist_ONil(T_a) % 177.89/177.90 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_last__ConsL,axiom, % 177.89/177.90 ! [V_x,T_a,V_xs] : % 177.89/177.90 ( V_xs = c_List_Olist_ONil(T_a) % 177.89/177.90 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_last__map,axiom, % 177.89/177.90 ! [V_f_2,T_b,T_a,V_xs_2] : % 177.89/177.90 ( V_xs_2 != c_List_Olist_ONil(T_a) % 177.89/177.90 => 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)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_last__appendL,axiom, % 177.89/177.90 ! [V_xs,T_a,V_ys] : % 177.89/177.90 ( V_ys = c_List_Olist_ONil(T_a) % 177.89/177.90 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_last__appendR,axiom, % 177.89/177.90 ! [V_xs,T_a,V_ys] : % 177.89/177.90 ( V_ys != c_List_Olist_ONil(T_a) % 177.89/177.90 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_last__append,axiom, % 177.89/177.90 ! [V_xs,T_a,V_ys] : % 177.89/177.90 ( ( V_ys = c_List_Olist_ONil(T_a) % 177.89/177.90 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) % 177.89/177.90 & ( V_ys != c_List_Olist_ONil(T_a) % 177.89/177.90 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_last__in__set,axiom, % 177.89/177.90 ! [T_a,V_as_2] : % 177.89/177.90 ( V_as_2 != c_List_Olist_ONil(T_a) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_member(T_a),c_List_Olast(T_a,V_as_2)),hAPP(c_List_Oset(T_a),V_as_2))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_last__snoc,axiom, % 177.89/177.90 ! [V_x,V_xs,T_a] : c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_x ). % 177.89/177.90 % 177.89/177.90 fof(fact_last__drop,axiom, % 177.89/177.90 ! [V_xs,T_a,V_n] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_append__butlast__last__id,axiom, % 177.89/177.90 ! [T_a,V_xs] : % 177.89/177.90 ( V_xs != c_List_Olist_ONil(T_a) % 177.89/177.90 => hAPP(hAPP(c_List_Oappend(T_a),c_List_Obutlast(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Olast(T_a,V_xs)),c_List_Olist_ONil(T_a))) = V_xs ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_snoc__eq__iff__butlast,axiom, % 177.89/177.90 ! [V_ys_2,V_x_2,V_xs_2,T_a] : % 177.89/177.90 ( 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 % 177.89/177.90 <=> ( V_ys_2 != c_List_Olist_ONil(T_a) % 177.89/177.90 & c_List_Obutlast(T_a,V_ys_2) = V_xs_2 % 177.89/177.90 & c_List_Olast(T_a,V_ys_2) = V_x_2 ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_lists_Osimps,axiom, % 177.89/177.90 ! [V_A_2,V_a_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_a_2),c_List_Olists(T_a,V_A_2))) % 177.89/177.90 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 177.89/177.90 | ? [B_a,B_l] : % 177.89/177.90 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l) % 177.89/177.90 & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 177.89/177.90 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2))) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_transpose__aux__max,axiom, % 177.89/177.90 ! [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)))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_filter_Osimps_I1_J,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_filter__empty__conv,axiom, % 177.89/177.90 ! [V_xs_2,V_P_2,T_a] : % 177.89/177.90 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = c_List_Olist_ONil(T_a) % 177.89/177.90 <=> ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_partition__filter1,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_filter__id__conv,axiom, % 177.89/177.90 ! [V_xs_2,V_P_2,T_a] : % 177.89/177.90 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = V_xs_2 % 177.89/177.90 <=> ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_filter__insort__triv,axiom, % 177.89/177.90 ! [V_xs_2,V_f_2,T_a,V_x_2,V_P_2,T_b] : % 177.89/177.90 ( class_Orderings_Olinorder(T_b) % 177.89/177.90 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.90 => 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) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_removeAll__filter__not__eq,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_removeAll__filter__not,axiom, % 177.89/177.90 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 177.89/177.90 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_distinct__filter,axiom, % 177.89/177.90 ! [V_P_2,V_xs_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 177.89/177.90 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_filter__filter,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_filter__remove1,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_remove1__filter__not,axiom, % 177.89/177.90 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 177.89/177.90 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sum__length__filter__compl,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_filter__map,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_filter_Osimps_I2_J,axiom, % 177.89/177.90 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 177.89/177.90 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.90 => 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)) ) % 177.89/177.90 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.90 => 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) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_filter__append,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__filter__le,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_filter__is__subset,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_partition__filter2,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__filter,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__filter__map,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__filter__less,axiom, % 177.89/177.90 ! [V_P_2,V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.90 => 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))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_partition__filter__conv,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__minus__filter__out,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_filter__in__sublist,axiom, % 177.89/177.90 ! [V_s_2,V_xs_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__filter__conv__card,axiom, % 177.89/177.90 ! [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))))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__filter__def,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_transpose__max__length,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__filter__simps_I2_J,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_transpose_Osimps_I2_J,axiom, % 177.89/177.90 ! [V_xss,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss)) = c_List_Otranspose(T_a,V_xss) ). % 177.89/177.90 % 177.89/177.90 fof(fact_transpose__map__map,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_transpose__empty,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( c_List_Otranspose(T_a,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_a)) % 177.89/177.90 <=> ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 177.89/177.90 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_transpose_Osimps_I1_J,axiom, % 177.89/177.90 ! [T_a] : c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__of__filter__in,axiom, % 177.89/177.90 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_a,T_b] : % 177.89/177.90 ( 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) % 177.89/177.90 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2)) % 177.89/177.90 => 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) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__filter__simps_I1_J,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sublist__shift__lemma__Suc,axiom, % 177.89/177.90 ! [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)))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth__transpose,axiom, % 177.89/177.90 ! [V_xs_2,T_a,V_i_2] : % 177.89/177.90 ( 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)))) % 177.89/177.90 => 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)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__transpose,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__filter__map__filter,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_insort__key__remove1,axiom, % 177.89/177.90 ! [V_f_2,V_xs_2,V_a_2,T_a,T_b] : % 177.89/177.90 ( class_Orderings_Olinorder(T_b) % 177.89/177.90 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 177.89/177.90 => ( 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 % 177.89/177.90 => 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 ) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sublist__def,axiom, % 177.89/177.90 ! [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))))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted_ONil,axiom, % 177.89/177.90 ! [T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__single,axiom, % 177.89/177.90 ! [V_x,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__filter,axiom, % 177.89/177.90 ! [V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 177.89/177.90 => 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))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__same,axiom, % 177.89/177.90 ! [V_xs_2,V_g_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => 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)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__insort__insert__key,axiom, % 177.89/177.90 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 177.89/177.90 => 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))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__drop,axiom, % 177.89/177.90 ! [V_n,V_xs,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 177.89/177.90 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_drop__upt,axiom, % 177.89/177.90 ! [V_j,V_i,V_m] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_j)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m),V_j) ). % 177.89/177.90 % 177.89/177.90 fof(fact_hd__upt,axiom, % 177.89/177.90 ! [V_j,V_i] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.89/177.90 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_upt__0,axiom, % 177.89/177.90 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted_Oequations_I1_J,axiom, % 177.89/177.90 ! [T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__butlast,axiom, % 177.89/177.90 ! [V_xs,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( V_xs != c_List_Olist_ONil(T_a) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 177.89/177.90 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__distinct__set__unique,axiom, % 177.89/177.90 ! [V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 177.89/177.90 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 177.89/177.90 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 177.89/177.90 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 177.89/177.90 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__take,axiom, % 177.89/177.90 ! [V_n,V_xs,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 177.89/177.90 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__Suc__upt,axiom, % 177.89/177.90 ! [V_n_2,V_m_2] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(V_m_2,V_n_2)) = c_List_Oupt(hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__insort,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( 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)) % 177.89/177.90 <=> c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__list__of__set__range,axiom, % 177.89/177.90 ! [V_n_2,V_m_2] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = c_List_Oupt(V_m_2,V_n_2) ). % 177.89/177.90 % 177.89/177.90 fof(fact_distinct__upt,axiom, % 177.89/177.90 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__upt,axiom, % 177.89/177.90 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__upto,axiom, % 177.89/177.90 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__remove1,axiom, % 177.89/177.90 ! [V_a,V_xs,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 177.89/177.90 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__insort__insert,axiom, % 177.89/177.90 ! [V_x_2,V_xs_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__insort__key,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( 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))) % 177.89/177.90 <=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__map__remove1,axiom, % 177.89/177.90 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 177.89/177.90 => 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))) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_upt__conv__Cons,axiom, % 177.89/177.90 ! [V_j,V_i] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.89/177.90 => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_upt__rec,axiom, % 177.89/177.90 ! [V_j,V_i] : % 177.89/177.90 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.89/177.90 => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) ) % 177.89/177.90 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.89/177.90 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__tl,axiom, % 177.89/177.90 ! [V_xs,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 177.89/177.90 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_upt__Suc,axiom, % 177.89/177.90 ! [V_j,V_i] : % 177.89/177.90 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.89/177.90 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ) % 177.89/177.90 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.89/177.90 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_upt__Suc__append,axiom, % 177.89/177.90 ! [V_j,V_i] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.89/177.90 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_upt__add__eq__append,axiom, % 177.89/177.90 ! [V_k,V_j,V_i] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.89/177.90 => c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),c_List_Oupt(V_j,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__many__eq,axiom, % 177.89/177.90 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( 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))) % 177.89/177.90 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 177.89/177.90 & c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__many,axiom, % 177.89/177.90 ! [V_zs,V_y,V_x,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) % 177.89/177.90 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_take__upt,axiom, % 177.89/177.90 ! [V_n,V_m,V_i] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)),V_n)) % 177.89/177.90 => hAPP(hAPP(c_List_Otake(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_n)) = c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_upt__conv__Nil,axiom, % 177.89/177.90 ! [V_i,V_j] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 177.89/177.90 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_upt__eq__Nil__conv,axiom, % 177.89/177.90 ! [V_j_2,V_i_2] : % 177.89/177.90 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) % 177.89/177.90 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.90 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__upt,axiom, % 177.89/177.90 ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) ). % 177.89/177.90 % 177.89/177.90 fof(fact_atLeastLessThan__upt,axiom, % 177.89/177.90 ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__map__same,axiom, % 177.89/177.90 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__upt,axiom, % 177.89/177.90 ! [V_j,V_i] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__Cons,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 177.89/177.90 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 177.89/177.90 & ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__append,axiom, % 177.89/177.90 ! [V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 177.89/177.90 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 177.89/177.90 & c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 177.89/177.90 & ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => ! [B_xa] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),V_ys_2))) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) ) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_upt__rec__number__of,axiom, % 177.89/177.90 ! [V_n,V_m] : % 177.89/177.90 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) % 177.89/177.90 => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) ) % 177.89/177.90 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) % 177.89/177.90 => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_upt__eq__Cons__conv,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,V_j_2,V_i_2] : % 177.89/177.90 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) % 177.89/177.90 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) % 177.89/177.90 & V_i_2 = V_x_2 % 177.89/177.90 & c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_j_2) = V_xs_2 ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_last__upt,axiom, % 177.89/177.90 ! [V_j,V_i] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.89/177.90 => c_List_Olast(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_filter__insort,axiom, % 177.89/177.90 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 177.89/177.90 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.90 => 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)) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__nth,axiom, % 177.89/177.90 ! [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 ). % 177.89/177.90 % 177.89/177.90 fof(fact_atLeastAtMost__upt,axiom, % 177.89/177.90 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_n_2,hAPP(c_Nat_OSuc,V_m_2))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_atLeast__upt,axiom, % 177.89/177.90 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_setsum__set__upt__conv__listsum__nat,axiom, % 177.89/177.90 ! [V_n_2,V_m_2,V_f_2,T_a] : % 177.89/177.90 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_interv__listsum__conv__setsum__set__nat,axiom, % 177.89/177.90 ! [V_n_2,V_m_2,V_f_2,T_a] : % 177.89/177.90 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.90 => 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth__upt,axiom, % 177.89/177.90 ! [V_j,V_k,V_i] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j)) % 177.89/177.90 => hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_greaterThanAtMost__upt,axiom, % 177.89/177.90 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted_Oequations_I2_J,axiom, % 177.89/177.90 ! [V_a1_2,V_a2_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a1_2)) % 177.89/177.90 <=> ( ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_a1_2))) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a2_2),B_x)) ) % 177.89/177.90 & c_List_Olinorder__class_Osorted(T_a,V_a1_2) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_greaterThanLessThan__upt,axiom, % 177.89/177.90 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),V_m_2)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth__map__upt,axiom, % 177.89/177.90 ! [V_f_2,T_a,V_m_2,V_n_2,V_i_2] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2))) % 177.89/177.90 => 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)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__list__of__set,axiom, % 177.89/177.90 ! [V_A_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.90 => ( hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) = V_A_2 % 177.89/177.90 & c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) % 177.89/177.90 & hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_atMost__upto,axiom, % 177.89/177.90 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_insort__remove1,axiom, % 177.89/177.90 ! [V_xs_2,V_a_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 177.89/177.90 => 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 ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__equals__nth__mono,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 177.89/177.90 <=> ! [B_j] : % 177.89/177.90 ( 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))) % 177.89/177.90 => ! [B_i] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 177.89/177.90 => 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))) ) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__nth__mono,axiom, % 177.89/177.90 ! [V_j,V_i,V_xs,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 177.89/177.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.89/177.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j))) ) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__sorted__distinct__set__unique,axiom, % 177.89/177.90 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 177.89/177.90 ( class_Orderings_Olinorder(T_b) % 177.89/177.90 => ( 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))) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 177.89/177.90 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)) % 177.89/177.90 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2))) % 177.89/177.90 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 177.89/177.90 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sublist__shift__lemma,axiom, % 177.89/177.90 ! [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))))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_transpose__rectangle,axiom, % 177.89/177.90 ! [V_n_2,T_a,V_xs_2] : % 177.89/177.90 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 177.89/177.90 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.89/177.90 => ( ! [B_i] : % 177.89/177.90 ( 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))) % 177.89/177.90 => 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 ) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_transpose_Opsimps_I2_J,axiom, % 177.89/177.90 ! [V_xss_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_transpose_Opsimps_I1_J,axiom, % 177.89/177.90 ! [T_a] : % 177.89/177.90 ( 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)))) % 177.89/177.90 => c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_transpose__column,axiom, % 177.89/177.90 ! [V_i_2,V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => ( 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))) % 177.89/177.90 => 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) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_transpose__aux__filter__head,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_inj__on__rev,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rev_Osimps_I1_J,axiom, % 177.89/177.90 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Nil__is__rev__conv,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( c_List_Olist_ONil(T_a) = hAPP(c_List_Orev(T_a),V_xs_2) % 177.89/177.90 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rev__is__Nil__conv,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( hAPP(c_List_Orev(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 177.89/177.90 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rev__concat,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rev__map,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_singleton__rev__conv,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( 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) % 177.89/177.90 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rev__singleton__conv,axiom, % 177.89/177.90 ! [V_x_2,V_xs_2,T_a] : % 177.89/177.90 ( 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)) % 177.89/177.90 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_concat__conv__foldl,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rev__foldl__cons,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_foldl__conv__concat,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rev__append,axiom, % 177.89/177.90 ! [V_ys,V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys)),hAPP(c_List_Orev(T_a),V_xs)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_concat__append,axiom, % 177.89/177.90 ! [V_ys,V_xs,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Oappend(tc_List_Olist(T_a)),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oconcat(T_a,V_xs)),c_List_Oconcat(T_a,V_ys)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_distinct__rev,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orev(T_a),V_xs_2))) % 177.89/177.90 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__rev,axiom, % 177.89/177.90 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rev__is__rev__conv,axiom, % 177.89/177.90 ! [V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Orev(T_a),V_ys_2) % 177.89/177.90 <=> V_xs_2 = V_ys_2 ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rev__swap,axiom, % 177.89/177.90 ! [V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( hAPP(c_List_Orev(T_a),V_xs_2) = V_ys_2 % 177.89/177.90 <=> V_xs_2 = hAPP(c_List_Orev(T_a),V_ys_2) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rev__rev__ident,axiom, % 177.89/177.90 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ). % 177.89/177.90 % 177.89/177.90 fof(fact_listsum__rev,axiom, % 177.89/177.90 ! [V_xs,T_a] : % 177.89/177.90 ( class_Groups_Ocomm__monoid__add(T_a) % 177.89/177.90 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__rev,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_zip__rev,axiom, % 177.89/177.90 ! [V_ys,T_b,V_xs,T_a] : % 177.89/177.90 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys) % 177.89/177.90 => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(c_List_Orev(T_a),V_xs)),hAPP(c_List_Orev(T_b),V_ys)) = hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rev__filter,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_foldr__foldl,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_foldl__foldr,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_concat_Osimps_I1_J,axiom, % 177.89/177.90 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ). % 177.89/177.90 % 177.89/177.90 fof(fact_concat_Osimps_I2_J,axiom, % 177.89/177.90 ! [V_xs,V_x,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),V_x),c_List_Oconcat(T_a,V_xs)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_concat__eq__Nil__conv,axiom, % 177.89/177.90 ! [V_xss_2,T_a] : % 177.89/177.90 ( c_List_Oconcat(T_a,V_xss_2) = c_List_Olist_ONil(T_a) % 177.89/177.90 <=> ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 177.89/177.90 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_Nil__eq__concat__conv,axiom, % 177.89/177.90 ! [V_xss_2,T_a] : % 177.89/177.90 ( c_List_Olist_ONil(T_a) = c_List_Oconcat(T_a,V_xss_2) % 177.89/177.90 <=> ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 177.89/177.90 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__concat,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_filter__concat,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rev__eq__Cons__iff,axiom, % 177.89/177.90 ! [V_ys_2,V_y_2,V_xs_2,T_a] : % 177.89/177.90 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2) % 177.89/177.90 <=> 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))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rev_Osimps_I2_J,axiom, % 177.89/177.90 ! [V_xs,V_x,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__concat,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__concat,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_last__rev,axiom, % 177.89/177.90 ! [T_a,V_xs] : % 177.89/177.90 ( V_xs != c_List_Olist_ONil(T_a) % 177.89/177.90 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_hd__rev,axiom, % 177.89/177.90 ! [T_a,V_xs] : % 177.89/177.90 ( V_xs != c_List_Olist_ONil(T_a) % 177.89/177.90 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__transpose,axiom, % 177.89/177.90 ! [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)))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rev__drop,axiom, % 177.89/177.90 ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rev__take,axiom, % 177.89/177.90 ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rotate__rev,axiom, % 177.89/177.90 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))),V_xs)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_transpose_Osimps_I3_J,axiom, % 177.89/177.90 ! [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))))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rev__nth,axiom, % 177.89/177.90 ! [V_xs,T_a,V_n] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => hAPP(hAPP(c_List_Onth(T_a),hAPP(c_List_Orev(T_a),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_OSuc,V_n))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_concat__injective,axiom, % 177.89/177.90 ! [V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 177.89/177.90 => ( 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) % 177.89/177.90 => ( ! [B_x] : % 177.89/177.90 ( 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)))) % 177.89/177.90 => 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)) ) % 177.89/177.90 => V_xs_2 = V_ys_2 ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_concat__eq__concat__iff,axiom, % 177.89/177.90 ! [V_ys_2,V_xs_2,T_a] : % 177.89/177.90 ( ! [B_x] : % 177.89/177.90 ( 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)))) % 177.89/177.90 => 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)) ) % 177.89/177.90 => ( 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) % 177.89/177.90 => ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 177.89/177.90 <=> V_xs_2 = V_ys_2 ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_rev__update,axiom, % 177.89/177.90 ! [V_y,V_xs,T_a,V_k] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_y)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_k)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_y) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_concat__map__singleton,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__rev__nth__mono,axiom, % 177.89/177.90 ! [V_j,V_i,V_xs,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) % 177.89/177.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.89/177.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i))) ) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_foldr__max__sorted,axiom, % 177.89/177.90 ! [V_y_2,V_xs_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs_2)) % 177.89/177.90 => ( ( V_xs_2 = c_List_Olist_ONil(T_a) % 177.89/177.90 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = V_y_2 ) % 177.89/177.90 & ( V_xs_2 != c_List_Olist_ONil(T_a) % 177.89/177.90 => 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) ) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_transpose_Opsimps_I3_J,axiom, % 177.89/177.90 ! [V_xss_2,V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => 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))))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__transpose__sorted,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 177.89/177.90 => 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) ) % 177.89/177.90 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_a)) % 177.89/177.90 => 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))) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_transpose__column__length,axiom, % 177.89/177.90 ! [V_i_2,V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => ( 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))) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_transpose__aux__filter__tail,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth__nth__transpose__sorted,axiom, % 177.89/177.90 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => ( 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)))) % 177.89/177.90 => ( 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)))) % 177.89/177.90 => 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) ) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_transpose__transpose,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_transfer__nat__int__list__functions_I2_J,axiom, % 177.89/177.90 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_zip__takeWhile__snd,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_zip__takeWhile__fst,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_takeWhile__eq__all__conv,axiom, % 177.89/177.90 ! [V_xs_2,V_P_2,T_a] : % 177.89/177.90 ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = V_xs_2 % 177.89/177.90 <=> ! [B_x] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__takeWhileD,axiom, % 177.89/177.90 ! [V_xs_2,V_P_2,V_x_2,T_a] : % 177.89/177.90 ( 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)))) % 177.89/177.90 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__takeWhile__le,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_takeWhile__eq__take,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_distinct__takeWhile,axiom, % 177.89/177.90 ! [V_P_2,V_xs_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 177.89/177.90 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_takeWhile__tail,axiom, % 177.89/177.90 ! [V_l_2,V_xs_2,T_a,V_x_2,V_P_2] : % 177.89/177.90 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_takeWhile_Osimps_I2_J,axiom, % 177.89/177.90 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 177.89/177.90 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.90 => 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)) ) % 177.89/177.90 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.90 => 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) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__takeWhile,axiom, % 177.89/177.90 ! [V_P_2,V_xs_2,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 177.89/177.90 => c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_takeWhile_Osimps_I1_J,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_takeWhile__map,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_return__list__def,axiom, % 177.89/177.90 ! [V_l_2] : c_List_Oreturn__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),V_l_2) ). % 177.89/177.90 % 177.89/177.90 fof(fact_takeWhile__append1,axiom, % 177.89/177.90 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.90 => 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) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_takeWhile__nth,axiom, % 177.89/177.90 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 177.89/177.90 ( 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)))) % 177.89/177.90 => 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) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_nth__length__takeWhile,axiom, % 177.89/177.90 ! [V_xs_2,V_P_2,T_a] : % 177.89/177.90 ( 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))) % 177.89/177.90 => ~ 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))))) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_map__upds__def,axiom, % 177.89/177.90 ! [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)))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_takeWhile__not__last,axiom, % 177.89/177.90 ! [T_a,V_xs_2] : % 177.89/177.90 ( V_xs_2 != c_List_Olist_ONil(T_a) % 177.89/177.90 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 177.89/177.90 => 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) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_filter__equals__takeWhile__sorted__rev,axiom, % 177.89/177.90 ! [V_t_2,V_xs_2,V_f_2,T_b,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( 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))) % 177.89/177.90 => 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) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_transfer__nat__int__list__return__embed,axiom, % 177.89/177.90 ! [V_l] : % 177.89/177.90 ( c_List_Onat__list(V_l) % 177.89/177.90 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__remdups__concat,axiom, % 177.89/177.90 ! [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))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_distinct__remdups,axiom, % 177.89/177.90 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__remdups__leq,axiom, % 177.89/177.90 ! [V_xs,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_remdups__map__remdups,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_set__remdups,axiom, % 177.89/177.90 ! [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) ). % 177.89/177.90 % 177.89/177.90 fof(fact_remdups_Osimps_I1_J,axiom, % 177.89/177.90 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 177.89/177.90 % 177.89/177.90 fof(fact_remdups__eq__nil__right__iff,axiom, % 177.89/177.90 ! [V_x_2,T_a] : % 177.89/177.90 ( c_List_Olist_ONil(T_a) = c_List_Oremdups(T_a,V_x_2) % 177.89/177.90 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_remdups__eq__nil__iff,axiom, % 177.89/177.90 ! [V_x_2,T_a] : % 177.89/177.90 ( c_List_Oremdups(T_a,V_x_2) = c_List_Olist_ONil(T_a) % 177.89/177.90 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_sorted__remdups,axiom, % 177.89/177.90 ! [V_l,T_a] : % 177.89/177.90 ( class_Orderings_Olinorder(T_a) % 177.89/177.90 => ( c_List_Olinorder__class_Osorted(T_a,V_l) % 177.89/177.90 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_distinct__remdups__id,axiom, % 177.89/177.90 ! [V_xs,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.89/177.90 => c_List_Oremdups(T_a,V_xs) = V_xs ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_remdups__id__iff__distinct,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( c_List_Oremdups(T_a,V_xs_2) = V_xs_2 % 177.89/177.90 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__remdups__eq,axiom, % 177.89/177.90 ! [V_xs_2,T_a] : % 177.89/177.90 ( 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) % 177.89/177.90 <=> c_List_Oremdups(T_a,V_xs_2) = V_xs_2 ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_remdups__remdups,axiom, % 177.89/177.90 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ). % 177.89/177.90 % 177.89/177.90 fof(fact_remdups__filter,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_remove1__remdups,axiom, % 177.89/177.90 ! [V_x,V_xs,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.89/177.90 => c_List_Oremove1(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oremove1(T_a,V_x,V_xs)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_embed__list__def,axiom, % 177.89/177.90 ! [V_l_2] : c_List_Oembed__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_l_2) ). % 177.89/177.90 % 177.89/177.90 fof(fact_remdups_Osimps_I2_J,axiom, % 177.89/177.90 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.90 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => 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) ) % 177.89/177.90 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => 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)) ) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_length__remdups__card__conv,axiom, % 177.89/177.90 ! [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)) ). % 177.89/177.90 % 177.89/177.90 fof(fact_fun__left__comm_Ofold__set__remdups,axiom, % 177.89/177.90 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 177.89/177.90 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 177.89/177.90 => 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)) ) ). % 177.89/177.90 % 177.89/177.90 fof(fact_transfer__nat__int__list__functions_I1_J,axiom, % 177.89/177.90 ! [V_m,V_l] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),V_l),V_m) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(V_l)),c_List_Oembed__list(V_m))) ). % 177.89/177.90 % 177.89/177.90 fof(fact_takeWhile__neq__rev,axiom, % 177.89/177.90 ! [V_x_2,V_xs_2,T_a] : % 177.89/177.90 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 177.89/177.90 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.90 => 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_dropWhile__neq__rev,axiom, % 177.89/177.91 ! [V_x_2,V_xs_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 177.89/177.91 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.91 => 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_distinct__dropWhile,axiom, % 177.89/177.91 ! [V_P_2,V_xs_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 177.89/177.91 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_dropWhile_Osimps_I2_J,axiom, % 177.89/177.91 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 177.89/177.91 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.91 => 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) ) % 177.89/177.91 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.91 => 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) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_sorted__dropWhile,axiom, % 177.89/177.91 ! [V_P_2,V_xs_2,T_a] : % 177.89/177.91 ( class_Orderings_Olinorder(T_a) % 177.89/177.91 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 177.89/177.91 => c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_dropWhile_Osimps_I1_J,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_length__dropWhile__le,axiom, % 177.89/177.91 ! [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))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_dropWhile__eq__Nil__conv,axiom, % 177.89/177.91 ! [V_xs_2,V_P_2,T_a] : % 177.89/177.91 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = c_List_Olist_ONil(T_a) % 177.89/177.91 <=> ! [B_x] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.91 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_takeWhile__dropWhile__id,axiom, % 177.89/177.91 ! [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 ). % 177.89/177.91 % 177.89/177.91 fof(fact_hd__dropWhile,axiom, % 177.89/177.91 ! [V_xs_2,V_P_2,T_a] : % 177.89/177.91 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) != c_List_Olist_ONil(T_a) % 177.89/177.91 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_dropWhile__map,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_dropWhile__append1,axiom, % 177.89/177.91 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.91 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.91 => 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) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_dropWhile__eq__Cons__conv,axiom, % 177.89/177.91 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_a] : % 177.89/177.91 ( 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) % 177.89/177.91 <=> ( 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)) % 177.89/177.91 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_dropWhile__eq__drop,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_dropWhile__nth,axiom, % 177.89/177.91 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 177.89/177.91 ( 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)))) % 177.89/177.91 => 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)))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_listsum__map__filter,axiom, % 177.89/177.91 ! [V_f_2,V_P_2,V_xs_2,T_a,T_b] : % 177.89/177.91 ( class_Groups_Omonoid__add(T_b) % 177.89/177.91 => ( ! [B_x] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.91 => ( ~ hBOOL(hAPP(V_P_2,B_x)) % 177.89/177.91 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) % 177.89/177.91 => 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)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_sorted__nth__monoI,axiom, % 177.89/177.91 ! [V_xs,T_a] : % 177.89/177.91 ( class_Orderings_Olinorder(T_a) % 177.89/177.91 => ( ! [B_i,B_j] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 177.89/177.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_j))) ) ) % 177.89/177.91 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_n__lists_Osimps_I2_J,axiom, % 177.89/177.91 ! [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))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_sublists__powset,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_distinct__n__lists,axiom, % 177.89/177.91 ! [V_n,V_xs,T_a] : % 177.89/177.91 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.89/177.91 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_distinct__set__sublists,axiom, % 177.89/177.91 ! [V_xs_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 177.89/177.91 => 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)))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_length__n__lists,axiom, % 177.89/177.91 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_On__lists(T_a,V_n,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ). % 177.89/177.91 % 177.89/177.91 fof(fact_length__n__lists__elem,axiom, % 177.89/177.91 ! [V_xs_2,V_n_2,V_ys_2,T_a] : % 177.89/177.91 ( 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)))) % 177.89/177.91 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_sublists_Osimps_I1_J,axiom, % 177.89/177.91 ! [T_a] : c_Enum_Osublists(T_a,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_n__lists__Nil,axiom, % 177.89/177.91 ! [T_a,V_n] : % 177.89/177.91 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.91 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ) % 177.89/177.91 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.89/177.91 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_n__lists_Osimps_I1_J,axiom, % 177.89/177.91 ! [V_xs,T_a] : c_Enum_On__lists(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xs) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_sublists_Osimps_I2_J,axiom, % 177.89/177.91 ! [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))))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_set__n__lists,axiom, % 177.89/177.91 ! [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)))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_length__sublists,axiom, % 177.89/177.91 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_product_Osimps_I2_J,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_enum__the__def,axiom, % 177.89/177.91 ! [V_P_2,T_a] : c_Enum_Oenum__the(T_a,V_P_2) = c_HOL_OThe(T_a,V_P_2) ). % 177.89/177.91 % 177.89/177.91 fof(fact_product_Osimps_I1_J,axiom, % 177.89/177.91 ! [V_uu,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,c_List_Olist_ONil(T_a),V_uu) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_distinct__product,axiom, % 177.89/177.91 ! [V_ys,T_b,V_xs,T_a] : % 177.89/177.91 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.89/177.91 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys)) % 177.89/177.91 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_product__list__set,axiom, % 177.89/177.91 ! [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))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_map__of__zip__enum__inject,axiom, % 177.89/177.91 ! [V_ys_2,V_xs_2,T_a,T_b] : % 177.89/177.91 ( ( class_Enum_Oenum(T_b) % 177.89/177.91 & class_Enum_Oenum(T_a) ) % 177.89/177.91 => ( 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)) % 177.89/177.91 => ( 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)) % 177.89/177.91 => ( 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))) % 177.89/177.91 => V_xs_2 = V_ys_2 ) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_sort__foldl__insort,axiom, % 177.89/177.91 ! [V_xs_2,T_a] : % 177.89/177.91 ( class_Orderings_Olinorder(T_a) % 177.89/177.91 => 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) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_enum__prod__def,axiom, % 177.89/177.91 ! [T_b,T_a] : % 177.89/177.91 ( ( class_Enum_Oenum(T_a) % 177.89/177.91 & class_Enum_Oenum(T_b) ) % 177.89/177.91 => 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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_enum__distinct,axiom, % 177.89/177.91 ! [T_a] : % 177.89/177.91 ( class_Enum_Oenum(T_a) % 177.89/177.91 => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_enum__option__def,axiom, % 177.89/177.91 ! [T_a] : % 177.89/177.91 ( class_Enum_Oenum(T_a) % 177.89/177.91 => 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_distinct__sort,axiom, % 177.89/177.91 ! [V_xs_2,V_f_2,T_a,T_b] : % 177.89/177.91 ( class_Orderings_Olinorder(T_b) % 177.89/177.91 => ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))) % 177.89/177.91 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_filter__sort,axiom, % 177.89/177.91 ! [V_xs_2,V_f_2,V_P_2,T_a,T_b] : % 177.89/177.91 ( class_Orderings_Olinorder(T_b) % 177.89/177.91 => 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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_length__sort,axiom, % 177.89/177.91 ! [V_xs_2,V_f_2,T_a,T_b] : % 177.89/177.91 ( class_Orderings_Olinorder(T_b) % 177.89/177.91 => 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) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_sorted__sort,axiom, % 177.89/177.91 ! [V_xs_2,T_a] : % 177.89/177.91 ( class_Orderings_Olinorder(T_a) % 177.89/177.91 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_sort__key__simps_I1_J,axiom, % 177.89/177.91 ! [V_f_2,T_a,T_b] : % 177.89/177.91 ( class_Orderings_Olinorder(T_b) % 177.89/177.91 => 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) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_set__sort,axiom, % 177.89/177.91 ! [V_xs_2,V_f_2,T_a,T_b] : % 177.89/177.91 ( class_Orderings_Olinorder(T_b) % 177.89/177.91 => 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) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_enum__UNIV,axiom, % 177.89/177.91 ! [T_a] : % 177.89/177.91 ( class_Enum_Oenum(T_a) % 177.89/177.91 => 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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_UNIV__enum,axiom, % 177.89/177.91 ! [T_a] : % 177.89/177.91 ( class_Enum_Oenum(T_a) % 177.89/177.91 => 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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_in__enum,axiom, % 177.89/177.91 ! [V_x_2,T_a] : % 177.89/177.91 ( class_Enum_Oenum(T_a) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_sorted__sort__key,axiom, % 177.89/177.91 ! [V_xs_2,V_f_2,T_b,T_a] : % 177.89/177.91 ( class_Orderings_Olinorder(T_a) % 177.89/177.91 => 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_sort__key__simps_I2_J,axiom, % 177.89/177.91 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 177.89/177.91 ( class_Orderings_Olinorder(T_b) % 177.89/177.91 => 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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_enum__fun__code,axiom, % 177.89/177.91 ! [T_b,T_a] : % 177.89/177.91 ( ( class_Enum_Oenum(T_a) % 177.89/177.91 & class_HOL_Oequal(T_a) % 177.89/177.91 & class_Enum_Oenum(T_b) ) % 177.89/177.91 => 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_enum__fun__def,axiom, % 177.89/177.91 ! [T_b,T_a] : % 177.89/177.91 ( ( class_Enum_Oenum(T_a) % 177.89/177.91 & class_Enum_Oenum(T_b) ) % 177.89/177.91 => 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_sorted__list__of__set__sort__remdups,axiom, % 177.89/177.91 ! [V_xs_2,T_a] : % 177.89/177.91 ( class_Orderings_Olinorder(T_a) % 177.89/177.91 => 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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_all__n__lists__def,axiom, % 177.89/177.91 ! [V_n_2,V_P_2,T_a] : % 177.89/177.91 ( class_Enum_Oenum(T_a) % 177.89/177.91 => ( c_Enum_Oall__n__lists(T_a,V_P_2,V_n_2) % 177.89/177.91 <=> ! [B_x] : % 177.89/177.91 ( 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))))) % 177.89/177.91 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_ex__n__lists__def,axiom, % 177.89/177.91 ! [V_n_2,V_P_2,T_a] : % 177.89/177.91 ( class_Enum_Oenum(T_a) % 177.89/177.91 => ( c_Enum_Oex__n__lists(T_a,V_P_2,V_n_2) % 177.89/177.91 <=> ? [B_x] : % 177.89/177.91 ( 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))))) % 177.89/177.91 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_enum__all__fun__def,axiom, % 177.89/177.91 ! [V_P_2,T_a,T_b] : % 177.89/177.91 ( ( class_Enum_Oenum(T_b) % 177.89/177.91 & class_Enum_Oenum(T_a) ) % 177.89/177.91 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) % 177.89/177.91 <=> 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_enum__ex__fun__def,axiom, % 177.89/177.91 ! [V_P_2,T_a,T_b] : % 177.89/177.91 ( ( class_Enum_Oenum(T_b) % 177.89/177.91 & class_Enum_Oenum(T_a) ) % 177.89/177.91 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) % 177.89/177.91 <=> 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_enum__ex,axiom, % 177.89/177.91 ! [V_P_2,T_a] : % 177.89/177.91 ( class_Enum_Oenum(T_a) % 177.89/177.91 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) % 177.89/177.91 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_enum__all,axiom, % 177.89/177.91 ! [V_P_2,T_a] : % 177.89/177.91 ( class_Enum_Oenum(T_a) % 177.89/177.91 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) % 177.89/177.91 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_exists__code,axiom, % 177.89/177.91 ! [V_P_2,T_a] : % 177.89/177.91 ( class_Enum_Oenum(T_a) % 177.89/177.91 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 177.89/177.91 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_all__code,axiom, % 177.89/177.91 ! [V_P_2,T_a] : % 177.89/177.91 ( class_Enum_Oenum(T_a) % 177.89/177.91 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 177.89/177.91 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_enum__all__option__def,axiom, % 177.89/177.91 ! [V_P_2,T_a] : % 177.89/177.91 ( class_Enum_Oenum(T_a) % 177.89/177.91 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_a)),V_P_2)) % 177.89/177.91 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) % 177.89/177.91 & 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)))) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_enum__ex__option__def,axiom, % 177.89/177.91 ! [V_P_2,T_a] : % 177.89/177.91 ( class_Enum_Oenum(T_a) % 177.89/177.91 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_a)),V_P_2)) % 177.89/177.91 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) % 177.89/177.91 | 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)))) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_enum__ex__prod__def,axiom, % 177.89/177.91 ! [V_P_2,T_a,T_b] : % 177.89/177.91 ( ( class_Enum_Oenum(T_b) % 177.89/177.91 & class_Enum_Oenum(T_a) ) % 177.89/177.91 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_a,T_b)),V_P_2)) % 177.89/177.91 <=> 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))))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_enum__all__prod__def,axiom, % 177.89/177.91 ! [V_P_2,T_a,T_b] : % 177.89/177.91 ( ( class_Enum_Oenum(T_b) % 177.89/177.91 & class_Enum_Oenum(T_a) ) % 177.89/177.91 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_a,T_b)),V_P_2)) % 177.89/177.91 <=> 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))))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_order__fun_I1_J,axiom, % 177.89/177.91 ! [V_g_2,V_f_2,T_a,T_b] : % 177.89/177.91 ( ( class_Orderings_Oorder(T_b) % 177.89/177.91 & class_Enum_Oenum(T_a) ) % 177.89/177.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 177.89/177.91 <=> 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_order__fun_I2_J,axiom, % 177.89/177.91 ! [V_g_2,V_f_2,T_a,T_b] : % 177.89/177.91 ( ( class_Orderings_Oorder(T_b) % 177.89/177.91 & class_Enum_Oenum(T_a) ) % 177.89/177.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 177.89/177.91 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 177.89/177.91 & 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)))) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_enum__ex__fun__code,axiom, % 177.89/177.91 ! [V_P_2,T_a,T_b] : % 177.89/177.91 ( ( class_Enum_Oenum(T_b) % 177.89/177.91 & class_Enum_Oenum(T_a) % 177.89/177.91 & class_HOL_Oequal(T_a) ) % 177.89/177.91 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) % 177.89/177.91 <=> 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_enum__all__fun__code,axiom, % 177.89/177.91 ! [V_P_2,T_a,T_b] : % 177.89/177.91 ( ( class_Enum_Oenum(T_b) % 177.89/177.91 & class_Enum_Oenum(T_a) % 177.89/177.91 & class_HOL_Oequal(T_a) ) % 177.89/177.91 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) % 177.89/177.91 <=> 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_map__of__zip__enum__is__Some,axiom, % 177.89/177.91 ! [V_x,V_ys,T_b,T_a] : % 177.89/177.91 ( class_Enum_Oenum(T_a) % 177.89/177.91 => ( 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)) % 177.89/177.91 => ? [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) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_takeWhile__eq__filter,axiom, % 177.89/177.91 ! [V_xs_2,V_P_2,T_a] : % 177.89/177.91 ( ! [B_x] : % 177.89/177.91 ( 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)))) % 177.89/177.91 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 177.89/177.91 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_takeWhile__eq__take__P__nth,axiom, % 177.89/177.91 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 177.89/177.91 ( ! [B_i] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 177.89/177.91 => ( 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))) % 177.89/177.91 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) % 177.89/177.91 => ( ( 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))) % 177.89/177.91 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) % 177.89/177.91 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_length__takeWhile__less__P__nth,axiom, % 177.89/177.91 ! [V_xs_2,T_a,V_P_2,V_j_2] : % 177.89/177.91 ( ! [B_i] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2)) % 177.89/177.91 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 177.89/177.91 => ( 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))) % 177.89/177.91 => 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)))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_lists__IntI,axiom, % 177.89/177.91 ! [V_B_2,V_A_2,V_l_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_A_2))) % 177.89/177.91 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_B_2))) % 177.89/177.91 => 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)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_lists__Int__eq,axiom, % 177.89/177.91 ! [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))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_listsp_ONil,axiom, % 177.89/177.91 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_append__in__listsp__conv,axiom, % 177.89/177.91 ! [V_ys_2,V_xs_2,V_A_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 177.89/177.91 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 177.89/177.91 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_in__listsp__conv__set,axiom, % 177.89/177.91 ! [V_xs_2,V_A_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 177.89/177.91 <=> ! [B_x] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.91 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_listsp_Oequations_I1_J,axiom, % 177.89/177.91 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_listsp__inf__eq,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_listsp__infI,axiom, % 177.89/177.91 ! [V_B_2,V_l_2,V_A_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_l_2)) % 177.89/177.91 => ( hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_l_2)) % 177.89/177.91 => 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)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_listsp__conj__eq,axiom, % 177.89/177.91 ! [V_x_2,V_B_2,V_A_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2)) % 177.89/177.91 & hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_listsp_Oequations_I2_J,axiom, % 177.89/177.91 ! [V_a2_2,V_a1_2,V_A_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2))) % 177.89/177.91 <=> ( hBOOL(hAPP(V_A_2,V_a1_2)) % 177.89/177.91 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_listsp__mono,axiom, % 177.89/177.91 ! [V_B_2,V_A_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.89/177.91 => 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_listsp__lists__eq,axiom, % 177.89/177.91 ! [V_x_2,V_A_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2__def,axiom, % 177.89/177.91 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 177.89/177.91 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 177.89/177.91 <=> ( 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) % 177.89/177.91 & ! [B_x] : % 177.89/177.91 ( 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)))) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_sorted_Osimps,axiom, % 177.89/177.91 ! [V_a_2,T_a] : % 177.89/177.91 ( class_Orderings_Olinorder(T_a) % 177.89/177.91 => ( c_List_Olinorder__class_Osorted(T_a,V_a_2) % 177.89/177.91 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 177.89/177.91 | ? [B_xs,B_x] : % 177.89/177.91 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 177.89/177.91 & ! [B_xa] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),B_xs))) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) % 177.89/177.91 & c_List_Olinorder__class_Osorted(T_a,B_xs) ) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2__Cons,axiom, % 177.89/177.91 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_b,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 177.89/177.91 & c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2__map2,axiom, % 177.89/177.91 ! [V_bs_2,V_f_2,T_c,V_as_2,V_P_2,T_b,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 <=> 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) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2__map1,axiom, % 177.89/177.91 ! [V_bs_2,V_as_2,V_f_2,T_c,V_P_2,T_b,T_a] : % 177.89/177.91 ( 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) % 177.89/177.91 <=> 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) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2__eq,axiom, % 177.89/177.91 ! [T_a,V_ys_2,V_xs_2] : % 177.89/177.91 ( V_xs_2 = V_ys_2 % 177.89/177.91 <=> c_List_Olist__all2(T_a,T_a,c_fequal,V_xs_2,V_ys_2) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2__lengthD,axiom, % 177.89/177.91 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 177.89/177.91 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 177.89/177.91 => 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) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2__dropI,axiom, % 177.89/177.91 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_b,T_a] : % 177.89/177.91 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,V_bs_2) % 177.89/177.91 => 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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2__takeI,axiom, % 177.89/177.91 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 177.89/177.91 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 177.89/177.91 => 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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2__Nil2,axiom, % 177.89/177.91 ! [V_xs_2,V_P_2,T_b,T_a] : % 177.89/177.91 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,c_List_Olist_ONil(T_b)) % 177.89/177.91 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2__Nil,axiom, % 177.89/177.91 ! [V_ys_2,V_P_2,T_b,T_a] : % 177.89/177.91 ( c_List_Olist__all2(T_a,T_b,V_P_2,c_List_Olist_ONil(T_a),V_ys_2) % 177.89/177.91 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2__rev1,axiom, % 177.89/177.91 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 177.89/177.91 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),V_ys_2) % 177.89/177.91 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,hAPP(c_List_Orev(T_b),V_ys_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2__rev,axiom, % 177.89/177.91 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2__append,axiom, % 177.89/177.91 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 177.89/177.91 ( 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) % 177.89/177.91 => ( 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)) % 177.89/177.91 <=> ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 177.89/177.91 & c_List_Olist__all2(T_a,T_b,V_P_2,V_us_2,V_vs_2) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2__appendI,axiom, % 177.89/177.91 ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_P_2,T_b,T_a] : % 177.89/177.91 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) % 177.89/177.91 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_ca_2,V_d_2) % 177.89/177.91 => 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)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2__conv__all__nth,axiom, % 177.89/177.91 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 177.89/177.91 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 177.89/177.91 <=> ( 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) % 177.89/177.91 & ! [B_i] : % 177.89/177.91 ( 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))) % 177.89/177.91 => 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))) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2__nthD,axiom, % 177.89/177.91 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 177.89/177.91 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 177.89/177.91 => ( 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))) % 177.89/177.91 => 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2__nthD2,axiom, % 177.89/177.91 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 177.89/177.91 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 177.89/177.91 => ( 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))) % 177.89/177.91 => 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2__update__cong2,axiom, % 177.89/177.91 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 177.89/177.91 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 177.89/177.91 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 177.89/177.91 => ( 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))) % 177.89/177.91 => 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)) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2__update__cong,axiom, % 177.89/177.91 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_b,V_xs_2,T_a,V_i_2] : % 177.89/177.91 ( 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))) % 177.89/177.91 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 177.89/177.91 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 177.89/177.91 => 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)) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2I,axiom, % 177.89/177.91 ! [V_P_2,V_b_2,V_a_2,T_b,T_a] : % 177.89/177.91 ( ! [B_x] : % 177.89/177.91 ( 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)))) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) % 177.89/177.91 => ( 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) % 177.89/177.91 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_SigmaE,axiom, % 177.89/177.91 ! [V_B_2,V_A_2,V_ca_2,T_b,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 => ~ ! [B_x] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.91 => ! [B_y] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(V_B_2,B_x))) % 177.89/177.91 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_List_Oinsert__def,axiom, % 177.89/177.91 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.91 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.91 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) % 177.89/177.91 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.91 => 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) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_not__in__set__insert,axiom, % 177.89/177.91 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.91 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.91 => 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) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_distinct__insert,axiom, % 177.89/177.91 ! [V_x,V_xs,T_a] : % 177.89/177.91 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.89/177.91 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_insert__remdups,axiom, % 177.89/177.91 ! [V_xs,V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oinsert(T_a,V_x,V_xs)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_in__set__insert,axiom, % 177.89/177.91 ! [V_xs_2,V_x_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.91 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_List_Oset__insert,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_insert__Nil,axiom, % 177.89/177.91 ! [V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_maps__def,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_concat__map__maps,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_maps__simps_I2_J,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_maps__simps_I1_J,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_distinct__concat,axiom, % 177.89/177.91 ! [V_xs_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),V_xs_2)) % 177.89/177.91 => ( ! [B_ys] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 177.89/177.91 => hBOOL(hAPP(c_List_Odistinct(T_a),B_ys)) ) % 177.89/177.91 => ( ! [B_ys] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 177.89/177.91 => ! [B_zs] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 177.89/177.91 => ( B_ys != B_zs % 177.89/177.91 => 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)) ) ) ) % 177.89/177.91 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oconcat(T_a,V_xs_2))) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_code__numeral_Osimps_I5_J,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_code__numeral_Osimps_I4_J,axiom, % 177.89/177.91 ! [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 ). % 177.89/177.91 % 177.89/177.91 fof(fact_accp__acc__eq,axiom, % 177.89/177.91 ! [V_x_2,V_r_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_measures__lesseq,axiom, % 177.89/177.91 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 177.89/177.91 => ( 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))) % 177.89/177.91 => 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)))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Cons__acc__listrel1I,axiom, % 177.89/177.91 ! [V_xs_2,V_r_2,V_x_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 177.89/177.91 => ( 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)))) % 177.89/177.91 => 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)))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_lists__accI,axiom, % 177.89/177.91 ! [V_r_2,V_xs_2,T_a] : % 177.89/177.91 ( 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)))) % 177.89/177.91 => 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)))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_lists__accD,axiom, % 177.89/177.91 ! [V_r_2,V_xs_2,T_a] : % 177.89/177.91 ( 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)))) % 177.89/177.91 => 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)))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_acc__subset,axiom, % 177.89/177.91 ! [V_R2_2,V_R1_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_acc__downward,axiom, % 177.89/177.91 ! [V_a_2,V_r_2,V_b_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 177.89/177.91 => ( 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)) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_acc_Osimps,axiom, % 177.89/177.91 ! [V_r_2,V_a_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 177.89/177.91 <=> ! [B_x] : % 177.89/177.91 ( 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)) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_in__measures_I1_J,axiom, % 177.89/177.91 ! [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))))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_measures__def,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_in__measures_I2_J,axiom, % 177.89/177.91 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_a] : % 177.89/177.91 ( 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)))) % 177.89/177.91 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 177.89/177.91 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 177.89/177.91 & 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))) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_measures__less,axiom, % 177.89/177.91 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 177.89/177.91 => 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)))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rel__comp__def,axiom, % 177.89/177.91 ! [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))))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_max__extp_Oequations,axiom, % 177.89/177.91 ! [V_a2_2,V_a1_2,V_R_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2) % 177.89/177.91 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 177.89/177.91 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 177.89/177.91 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.91 & ! [B_x] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 177.89/177.91 => ? [B_xa] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 177.89/177.91 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rel__compI,axiom, % 177.89/177.91 ! [V_s_2,V_ca_2,T_c,V_r_2,V_b_2,V_a_2,T_b,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => ( 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)) % 177.89/177.91 => 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rel__comp__mono,axiom, % 177.89/177.91 ! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => ( 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)) % 177.89/177.91 => 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rel__comp__subset__Sigma,axiom, % 177.89/177.91 ! [V_C_2,V_s_2,T_c,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 177.89/177.91 ( 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)))) % 177.89/177.91 => ( 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)))) % 177.89/177.91 => 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)))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rel__comp__empty2,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rel__comp__empty1,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_union__comp__emptyR,axiom, % 177.89/177.91 ! [V_C_2,V_B_2,V_A_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => ( 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)) % 177.89/177.91 => 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)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_union__comp__emptyL,axiom, % 177.89/177.91 ! [V_B_2,V_C_2,V_A_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => ( 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)) % 177.89/177.91 => 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)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_O__assoc,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rel__comp__distrib2,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rel__comp__distrib,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rel__comp__UNION__distrib,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rel__comp__UNION__distrib2,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_max__ext__compat,axiom, % 177.89/177.91 ! [V_S_2,V_R_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_min__ext__compat,axiom, % 177.89/177.91 ! [V_S_2,V_R_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_pred__comp__rel__comp__eq,axiom, % 177.89/177.91 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 <=> 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_reduction__pairI,axiom, % 177.89/177.91 ! [V_S_2,V_R_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_R_2) % 177.89/177.91 => ( 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)) % 177.89/177.91 => 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)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__less__than,axiom, % 177.89/177.91 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 177.89/177.91 % 177.89/177.91 fof(fact_pred__comp_Ointros,axiom, % 177.89/177.91 ! [T_c,T_b,T_a,V_ca_2,V_s_2,V_b_2,V_a_2,V_r_2] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 177.89/177.91 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2)) % 177.89/177.91 => 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)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__empty,axiom, % 177.89/177.91 ! [T_a] : c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__inv__image,axiom, % 177.89/177.91 ! [V_f_2,T_b,V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__lex,axiom, % 177.89/177.91 ! [V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olex(T_a,V_r_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__lex__prod,axiom, % 177.89/177.91 ! [V_rb_2,T_b,V_ra_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_ra_2) % 177.89/177.91 => ( c_Wellfounded_Owf(T_b,V_rb_2) % 177.89/177.91 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__measure,axiom, % 177.89/177.91 ! [V_f_2,T_a] : c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__lenlex,axiom, % 177.89/177.91 ! [V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olenlex(T_a,V_r_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_acc__wfD,axiom, % 177.89/177.91 ! [V_x_2,V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__acc__iff,axiom, % 177.89/177.91 ! [V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__no__loop,axiom, % 177.89/177.91 ! [V_R_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__comp__self,axiom, % 177.89/177.91 ! [V_R_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_R_2) % 177.89/177.91 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__union__merge,axiom, % 177.89/177.91 ! [V_S_2,V_R_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 <=> 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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__lexn,axiom, % 177.89/177.91 ! [V_n_2,V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 => c_Wellfounded_Owf(tc_List_Olist(T_a),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__int__ge__less__than,axiom, % 177.89/177.91 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__int__ge__less__than2,axiom, % 177.89/177.91 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_min__ext__wf,axiom, % 177.89/177.91 ! [V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__finite__psubset,axiom, % 177.89/177.91 ! [T_a] : c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_pred__comp_Oequations,axiom, % 177.89/177.91 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 <=> ? [B_b] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) % 177.89/177.91 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__mlex,axiom, % 177.89/177.91 ! [V_f_2,V_R_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_R_2) % 177.89/177.91 => c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__pair__less,axiom, % 177.89/177.91 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 177.89/177.91 % 177.89/177.91 fof(fact_max__ext__wf,axiom, % 177.89/177.91 ! [V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__not__refl,axiom, % 177.89/177.91 ! [V_a_2,V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 => ~ 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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__not__sym,axiom, % 177.89/177.91 ! [V_x_2,V_a_2,V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 => ( 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)) % 177.89/177.91 => ~ 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)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__asym,axiom, % 177.89/177.91 ! [V_x_2,V_a_2,V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 => ( 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)) % 177.89/177.91 => ~ 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)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__irrefl,axiom, % 177.89/177.91 ! [V_a_2,V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 => ~ 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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__less,axiom, % 177.89/177.91 c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__subset,axiom, % 177.89/177.91 ! [V_p_2,V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 => ( 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)) % 177.89/177.91 => c_Wellfounded_Owf(T_a,V_p_2) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__Int2,axiom, % 177.89/177.91 ! [V_r_H_2,V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 => 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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__Int1,axiom, % 177.89/177.91 ! [V_r_H_2,V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 => 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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__iff__no__infinite__down__chain,axiom, % 177.89/177.91 ! [V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 <=> ~ ? [B_f] : % 177.89/177.91 ! [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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__measures,axiom, % 177.89/177.91 ! [V_fs_2,T_a] : c_Wellfounded_Owf(T_a,c_List_Omeasures(T_a,V_fs_2)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wfE__pf,axiom, % 177.89/177.91 ! [V_A_2,V_R_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_R_2) % 177.89/177.91 => ( 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))) % 177.89/177.91 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__union__compatible,axiom, % 177.89/177.91 ! [V_S_2,V_R_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_R_2) % 177.89/177.91 => ( c_Wellfounded_Owf(T_a,V_S_2) % 177.89/177.91 => ( 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)) % 177.89/177.91 => 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)) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf,axiom, % 177.89/177.91 ! [T_a] : % 177.89/177.91 ( class_Orderings_Owellorder(T_a) % 177.89/177.91 => 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)))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_reduction__pair__def,axiom, % 177.89/177.91 ! [V_P_2,T_a] : % 177.89/177.91 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 177.89/177.91 <=> ( 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)) % 177.89/177.91 & 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_reduction__pair__lemma,axiom, % 177.89/177.91 ! [V_S_2,V_R_2,V_P_2,T_a] : % 177.89/177.91 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 177.89/177.91 => ( 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))) % 177.89/177.91 => ( 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))) % 177.89/177.91 => ( c_Wellfounded_Owf(T_a,V_S_2) % 177.89/177.91 => 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)) ) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__map__pair__image,axiom, % 177.89/177.91 ! [V_f_2,T_b,V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 177.89/177.91 => 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)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__if__measure,axiom, % 177.89/177.91 ! [T_a,V_g_2,V_f_2,V_P_2] : % 177.89/177.91 ( ! [B_x] : % 177.89/177.91 ( hBOOL(hAPP(V_P_2,B_x)) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,hAPP(V_g_2,B_x))),hAPP(V_f_2,B_x))) ) % 177.89/177.91 => 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))))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_max__ext_Ointros,axiom, % 177.89/177.91 ! [V_R_2,V_Y_2,V_X_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) % 177.89/177.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Y_2)) % 177.89/177.91 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.91 => ( ! [B_x] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2)) % 177.89/177.91 => ? [B_xa] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2)) % 177.89/177.91 & 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)) ) ) % 177.89/177.91 => 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))) ) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_pred__nat__def,axiom, % 177.89/177.91 c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__same__fst,axiom, % 177.89/177.91 ! [T_a,V_R_2,T_b,V_P_2] : % 177.89/177.91 ( ! [B_x] : % 177.89/177.91 ( hBOOL(hAPP(V_P_2,B_x)) % 177.89/177.91 => c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)) ) % 177.89/177.91 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__pred__nat,axiom, % 177.89/177.91 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Nitpick_Ozero__frac__def,axiom, % 177.89/177.91 ! [T_a] : c_Nitpick_Ozero__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Range__Collect__split,axiom, % 177.89/177.91 ! [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))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_RangeI,axiom, % 177.89/177.91 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Range__empty__iff,axiom, % 177.89/177.91 ! [V_r_2,T_a,T_b] : % 177.89/177.91 ( hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.91 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Range__empty,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Range__Un__eq,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Range__Id__on,axiom, % 177.89/177.91 ! [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 ). % 177.89/177.91 % 177.89/177.91 fof(fact_finite__Range,axiom, % 177.89/177.91 ! [V_r_2,T_b,T_a] : % 177.89/177.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 177.89/177.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Range__Union,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_snd__eq__Range,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Range__iff,axiom, % 177.89/177.91 ! [V_r_2,T_b,V_a_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 177.89/177.91 <=> ? [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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Range__insert,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Range__Int__subset,axiom, % 177.89/177.91 ! [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)))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Range__Diff__subset,axiom, % 177.89/177.91 ! [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)))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Nitpick_Oone__frac__def,axiom, % 177.89/177.91 ! [T_a] : c_Nitpick_Oone__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Nitpick_Onumber__of__frac__def,axiom, % 177.89/177.91 ! [V_n,T_a] : c_Nitpick_Onumber__of__frac(T_a,V_n) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_n),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_RangeP__Range__eq,axiom, % 177.89/177.91 ! [V_x_2,V_r_2,T_b,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Nitpick_Ofrac__def,axiom, % 177.89/177.91 ! [V_b,V_a,T_a] : hAPP(hAPP(c_Nitpick_Ofrac(T_a),V_a),V_b) = c_Nitpick_OAbs__Frac(T_a,c_Nitpick_Onorm__frac(V_a,V_b)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_RangeP_Ointros,axiom, % 177.89/177.91 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 177.89/177.91 => hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_b_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_RangeP_Oequations,axiom, % 177.89/177.91 ! [V_a2_2,V_r_2,T_b,T_a] : % 177.89/177.91 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_a2_2)) % 177.89/177.91 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_RangeE,axiom, % 177.89/177.91 ! [V_r_2,T_b,V_b_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 177.89/177.91 => ~ ! [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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__Un,axiom, % 177.89/177.91 ! [V_s_2,V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 => ( c_Wellfounded_Owf(T_a,V_s_2) % 177.89/177.91 => ( 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)) % 177.89/177.91 => 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)) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_DomainI,axiom, % 177.89/177.91 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_fst__eq__Domain,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_finite__Domain,axiom, % 177.89/177.91 ! [V_r_2,T_b,T_a] : % 177.89/177.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 177.89/177.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Domain__Id__on,axiom, % 177.89/177.91 ! [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 ). % 177.89/177.91 % 177.89/177.91 fof(fact_Domain__mono,axiom, % 177.89/177.91 ! [V_s_2,V_r_2,T_b,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Domain__empty,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Domain__empty__iff,axiom, % 177.89/177.91 ! [V_r_2,T_b,T_a] : % 177.89/177.91 ( hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.91 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Domain__Un__eq,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Domain__iff,axiom, % 177.89/177.91 ! [V_r_2,T_b,V_a_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 177.89/177.91 <=> ? [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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Domain__insert,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Domain__Int__subset,axiom, % 177.89/177.91 ! [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)))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Domain__Diff__subset,axiom, % 177.89/177.91 ! [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)))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Field__def,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Domain__Union,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Domain__Collect__split,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_DomainP__Domain__eq,axiom, % 177.89/177.91 ! [V_x_2,V_r_2,T_b,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_DomainE,axiom, % 177.89/177.91 ! [V_r_2,T_b,V_a_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 177.89/177.91 => ~ ! [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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_DomainP_Ointros,axiom, % 177.89/177.91 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 177.89/177.91 => hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_DomainP_Oequations,axiom, % 177.89/177.91 ! [V_a1_2,V_r_2,T_b,T_a] : % 177.89/177.91 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a1_2)) % 177.89/177.91 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_foldl__apply,axiom, % 177.89/177.91 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_b,T_c,V_xs_2,T_a] : % 177.89/177.91 ( ! [B_x] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.91 => 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)) ) % 177.89/177.91 => 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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wfP__def,axiom, % 177.89/177.91 ! [V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_OwfP(T_a,V_r_2) % 177.89/177.91 <=> 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wfP__empty,axiom, % 177.89/177.91 ! [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))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_accp__wfPD,axiom, % 177.89/177.91 ! [V_x_2,V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_OwfP(T_a,V_r_2) % 177.89/177.91 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wfP__accp__iff,axiom, % 177.89/177.91 ! [V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_OwfP(T_a,V_r_2) % 177.89/177.91 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wfP__subset,axiom, % 177.89/177.91 ! [V_p_2,V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_OwfP(T_a,V_r_2) % 177.89/177.91 => ( 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)) % 177.89/177.91 => c_Wellfounded_OwfP(T_a,V_p_2) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__in__rel,axiom, % 177.89/177.91 ! [V_R_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_R_2) % 177.89/177.91 => c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wfP__wf__eq,axiom, % 177.89/177.91 ! [V_r_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 <=> c_Wellfounded_Owf(T_a,V_r_2) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wfP__acyclicP,axiom, % 177.89/177.91 ! [V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_OwfP(T_a,V_r_2) % 177.89/177.91 => 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Rep__Integ__cases,axiom, % 177.89/177.91 ! [V_y_2] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 177.89/177.91 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_acyclic__subset,axiom, % 177.89/177.91 ! [V_r_2,V_s_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Oacyclic(T_a,V_s_2) % 177.89/177.91 => ( 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)) % 177.89/177.91 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__acyclic,axiom, % 177.89/177.91 ! [V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__iff__acyclic__if__finite,axiom, % 177.89/177.91 ! [V_r_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 177.89/177.91 => ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_finite__acyclic__wf,axiom, % 177.89/177.91 ! [V_r_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 177.89/177.91 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 177.89/177.91 => c_Wellfounded_Owf(T_a,V_r_2) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Nitpick_Owf_H__def,axiom, % 177.89/177.91 ! [V_r_2,T_a] : % 177.89/177.91 ( c_Nitpick_Owf_H(T_a,V_r_2) % 177.89/177.91 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 177.89/177.91 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 177.89/177.91 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Rep__Integ__induct,axiom, % 177.89/177.91 ! [V_P_2,V_y_2] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 177.89/177.91 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x))) % 177.89/177.91 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_zip__obtain__same__length,axiom, % 177.89/177.91 ! [V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 177.89/177.91 ( ( 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)) % 177.89/177.91 => 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)))) ) % 177.89/177.91 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_map__of__eqI,axiom, % 177.89/177.91 ! [V_ys_2,V_xs_2,T_b,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => ( ! [B_x] : % 177.89/177.91 ( 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)))) % 177.89/177.91 => 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) ) % 177.89/177.91 => hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Abs__Integ__cases,axiom, % 177.89/177.91 ! [V_x_2] : % 177.89/177.91 ~ ! [B_y] : % 177.89/177.91 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) % 177.89/177.91 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Abs__Integ__induct,axiom, % 177.89/177.91 ! [V_x_2,V_P_2] : % 177.89/177.91 ( ! [B_y] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) % 177.89/177.91 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) ) % 177.89/177.91 => hBOOL(hAPP(V_P_2,V_x_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wfP__SUP,axiom, % 177.89/177.91 ! [T_a,V_r_2,T_b] : % 177.89/177.91 ( ! [B_i] : c_Wellfounded_OwfP(T_b,hAPP(V_r_2,B_i)) % 177.89/177.91 => ( ! [B_i,B_j] : % 177.89/177.91 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) % 177.89/177.91 => 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)) ) % 177.89/177.91 => 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)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_dropWhile__append2,axiom, % 177.89/177.91 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 177.89/177.91 ( ! [B_x] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.91 => hBOOL(hAPP(V_P_2,B_x)) ) % 177.89/177.91 => 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) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__all2__all__nthI,axiom, % 177.89/177.91 ! [V_P_2,V_b_2,T_b,V_a_2,T_a] : % 177.89/177.91 ( 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) % 177.89/177.91 => ( ! [B_n] : % 177.89/177.91 ( 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))) % 177.89/177.91 => 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))) ) % 177.89/177.91 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_mem__splitI2,axiom, % 177.89/177.91 ! [V_ca_2,V_z_2,T_c,T_b,T_a,V_p_2] : % 177.89/177.91 ( ! [B_a,B_b] : % 177.89/177.91 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) ) % 177.89/177.91 => 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_mem__splitE,axiom, % 177.89/177.91 ! [V_p_2,V_ca_2,T_c,T_b,V_z_2,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 => ~ ! [B_x,B_y] : % 177.89/177.91 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) % 177.89/177.91 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_finite__sorted__distinct__unique,axiom, % 177.89/177.91 ! [V_A_2,T_a] : % 177.89/177.91 ( class_Orderings_Olinorder(T_a) % 177.89/177.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 177.89/177.91 => ? [B_x] : % 177.89/177.91 ( hAPP(c_List_Oset(T_a),B_x) = V_A_2 % 177.89/177.91 & c_List_Olinorder__class_Osorted(T_a,B_x) % 177.89/177.91 & hBOOL(hAPP(c_List_Odistinct(T_a),B_x)) % 177.89/177.91 & ! [B_y] : % 177.89/177.91 ( ( hAPP(c_List_Oset(T_a),B_y) = V_A_2 % 177.89/177.91 & c_List_Olinorder__class_Osorted(T_a,B_y) % 177.89/177.91 & hBOOL(hAPP(c_List_Odistinct(T_a),B_y)) ) % 177.89/177.91 => B_y = B_x ) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_takeWhile__append2,axiom, % 177.89/177.91 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 177.89/177.91 ( ! [B_x] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.91 => hBOOL(hAPP(V_P_2,B_x)) ) % 177.89/177.91 => 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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_insort__is__Cons,axiom, % 177.89/177.91 ! [V_a_2,V_f_2,V_xs_2,T_a,T_b] : % 177.89/177.91 ( class_Orderings_Olinorder(T_b) % 177.89/177.91 => ( ! [B_x] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) ) % 177.89/177.91 => 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) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wfI__pf,axiom, % 177.89/177.91 ! [V_R_2,T_a] : % 177.89/177.91 ( ! [B_A] : % 177.89/177.91 ( 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))) % 177.89/177.91 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) % 177.89/177.91 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_filter__eq__Cons__iff,axiom, % 177.89/177.91 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_a] : % 177.89/177.91 ( 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) % 177.89/177.91 <=> ? [B_us,B_vs] : % 177.89/177.91 ( 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)) % 177.89/177.91 & ! [B_x] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 177.89/177.91 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 177.89/177.91 & hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.91 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Cons__eq__filter__iff,axiom, % 177.89/177.91 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 177.89/177.91 ( 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) % 177.89/177.91 <=> ? [B_us,B_vs] : % 177.89/177.91 ( 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)) % 177.89/177.91 & ! [B_x] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 177.89/177.91 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 177.89/177.91 & hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.91 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Sigma__mono,axiom, % 177.89/177.91 ! [V_D_2,V_B_2,T_b,V_C_2,V_A_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 177.89/177.91 => ( ! [B_x] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 177.89/177.91 => 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))) ) % 177.89/177.91 => 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_acc_OaccI,axiom, % 177.89/177.91 ! [V_r_2,V_x_2,T_a] : % 177.89/177.91 ( ! [B_y] : % 177.89/177.91 ( 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)) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))) ) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_not__acc__down,axiom, % 177.89/177.91 ! [V_R_2,V_x_2,T_a] : % 177.89/177.91 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2))) % 177.89/177.91 => ~ ! [B_z] : % 177.89/177.91 ( 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)) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__ball__nth,axiom, % 177.89/177.91 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 177.89/177.91 ( 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))) % 177.89/177.91 => ( ! [B_x] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.91 => hBOOL(hAPP(V_P_2,B_x)) ) % 177.89/177.91 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_max__ext_Osimps,axiom, % 177.89/177.91 ! [V_R_2,V_a2_2,V_a1_2,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 177.89/177.91 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 177.89/177.91 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 177.89/177.91 & ! [B_x] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 177.89/177.91 => ? [B_xa] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 177.89/177.91 & 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)) ) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_sorted_OCons,axiom, % 177.89/177.91 ! [V_x_2,V_xs_2,T_a] : % 177.89/177.91 ( class_Orderings_Olinorder(T_a) % 177.89/177.91 => ( ! [B_x] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) % 177.89/177.91 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 177.89/177.91 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__no__infinite__down__chainE,axiom, % 177.89/177.91 ! [V_f_2,V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 => ~ ! [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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_com_Osize_I11_J,axiom, % 177.89/177.91 ! [V_com_2,V_fun_2,V_loc_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_com_Osize_I3_J,axiom, % 177.89/177.91 ! [V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_WTs__elim__cases_I3_J,axiom, % 177.89/177.91 ! [V_ca_2,V_a_2,V_Y_2] : % 177.89/177.91 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2))) % 177.89/177.91 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_com_Osimps_I37_J,axiom, % 177.89/177.91 ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 177.89/177.91 % 177.89/177.91 fof(fact_com_Osimps_I36_J,axiom, % 177.89/177.91 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 177.89/177.91 % 177.89/177.91 fof(fact_com_Osimps_I35_J,axiom, % 177.89/177.91 ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 177.89/177.91 % 177.89/177.91 fof(fact_com_Osimps_I34_J,axiom, % 177.89/177.91 ! [V_com2_H_2,V_com1_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) ). % 177.89/177.91 % 177.89/177.91 fof(fact_com_Osimps_I42_J,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_com_Osimps_I43_J,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_com_Osimps_I10_J,axiom, % 177.89/177.91 ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) ). % 177.89/177.91 % 177.89/177.91 fof(fact_com_Osimps_I11_J,axiom, % 177.89/177.91 ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 177.89/177.91 % 177.89/177.91 fof(fact_com_Osimps_I41_J,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_com_Osimps_I40_J,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_WT_Oequations_I3_J,axiom, % 177.89/177.91 ! [V_a1_2,V_a3_2,V_a2_2] : % 177.89/177.91 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2))) % 177.89/177.91 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_WT_OLocal,axiom, % 177.89/177.91 ! [V_a_2,V_Y_2,V_ca_2] : % 177.89/177.91 ( hBOOL(hAPP(c_Com_OWT,V_ca_2)) % 177.89/177.91 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_com_Osimps_I2_J,axiom, % 177.89/177.91 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] : % 177.89/177.91 ( c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) = c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) % 177.89/177.91 <=> ( V_loc_2 = V_loc_H_2 % 177.89/177.91 & V_fun_2 = V_fun_H_2 % 177.89/177.91 & V_com_2 = V_com_H_2 ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_com_Osimps_I39_J,axiom, % 177.89/177.91 ! [V_com_2,V_fun_2,V_loc_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 177.89/177.91 % 177.89/177.91 fof(fact_com_Osimps_I38_J,axiom, % 177.89/177.91 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__ex__length,axiom, % 177.89/177.91 ! [V_xs_2,V_P_2,T_a] : % 177.89/177.91 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 177.89/177.91 <=> ? [B_n] : % 177.89/177.91 ( 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))) % 177.89/177.91 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_setsum__reindex__cong,axiom, % 177.89/177.91 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 177.89/177.91 ( class_Groups_Ocomm__monoid__add(T_c) % 177.89/177.91 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 177.89/177.91 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 177.89/177.91 => ( ! [B_a] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 177.89/177.91 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) ) % 177.89/177.91 => 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) ) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__ex__simps_I1_J,axiom, % 177.89/177.91 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 177.89/177.91 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 177.89/177.91 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 177.89/177.91 | c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__ex__iff,axiom, % 177.89/177.91 ! [V_xs_2,V_P_2,T_a] : % 177.89/177.91 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 177.89/177.91 <=> ? [B_x] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 177.89/177.91 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__ex__rev,axiom, % 177.89/177.91 ! [V_xs_2,V_P_2,T_a] : % 177.89/177.91 ( c_List_Olist__ex(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 177.89/177.91 <=> c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__ex__append,axiom, % 177.89/177.91 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 177.89/177.91 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 177.89/177.91 <=> ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 177.89/177.91 | c_List_Olist__ex(T_a,V_P_2,V_ys_2) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_list__ex__simps_I2_J,axiom, % 177.89/177.91 ! [V_P_2,T_a] : ~ c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_scomp__unfold,axiom, % 177.89/177.91 ! [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))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_setsum__ivl__cong,axiom, % 177.89/177.91 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_a,T_b] : % 177.89/177.91 ( ( class_Groups_Ocomm__monoid__add(T_b) % 177.89/177.91 & class_Orderings_Oord(T_a) ) % 177.89/177.91 => ( V_a_2 = V_ca_2 % 177.89/177.91 => ( V_b_2 = V_d_2 % 177.89/177.91 => ( ! [B_x] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),B_x)) % 177.89/177.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_d_2)) % 177.89/177.91 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) % 177.89/177.91 => 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)) ) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_scomp__def,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_scomp__apply,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_scomp__scomp,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Pair__scomp,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_scomp__Pair,axiom, % 177.89/177.91 ! [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 ). % 177.89/177.91 % 177.89/177.91 fof(fact_iterate_Osimps,axiom, % 177.89/177.91 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 177.89/177.91 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.89/177.91 => 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) ) % 177.89/177.91 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.89/177.91 => 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)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_less__eq,axiom, % 177.89/177.91 ! [V_n_2,V_m_2] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) % 177.89/177.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_less__than__def,axiom, % 177.89/177.91 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__trancl,axiom, % 177.89/177.91 ! [V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 => c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_acyclic__def,axiom, % 177.89/177.91 ! [V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 177.89/177.91 <=> ! [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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl_Or__into__trancl,axiom, % 177.89/177.91 ! [V_r_2,V_b_2,V_a_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl__subset__Field2,axiom, % 177.89/177.91 ! [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))))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_r__into__trancl_H,axiom, % 177.89/177.91 ! [V_r_2,V_p_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl__empty,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl__domain,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl__range,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_finite__trancl,axiom, % 177.89/177.91 ! [V_r_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 177.89/177.91 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl__trans,axiom, % 177.89/177.91 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 => ( 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))) % 177.89/177.91 => 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom, % 177.89/177.91 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 => ( 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)) % 177.89/177.91 => 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl__into__trancl2,axiom, % 177.89/177.91 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => ( 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))) % 177.89/177.91 => 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_r__r__into__trancl,axiom, % 177.89/177.91 ! [V_ca_2,V_R_2,V_b_2,V_a_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => ( 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)) % 177.89/177.91 => 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl__mono,axiom, % 177.89/177.91 ! [V_s_2,V_r_2,V_p_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 177.89/177.91 => ( 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)) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl__unfold,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl__subset__Sigma,axiom, % 177.89/177.91 ! [V_A_2,V_r_2,T_a] : % 177.89/177.91 ( 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)))) % 177.89/177.91 => 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)))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl__Int__subset,axiom, % 177.89/177.91 ! [V_s_2,V_r_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => ( 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)) % 177.89/177.91 => 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)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_log_Osimps,axiom, % 177.89/177.91 ! [V_i,V_b] : % 177.89/177.91 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) % 177.89/177.91 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 177.89/177.91 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 177.89/177.91 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) % 177.89/177.91 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 177.89/177.91 => c_Random_Olog(V_b,V_i) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(V_b,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_i),V_b))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_minus__shift__def,axiom, % 177.89/177.91 ! [V_r,V_l,V_k] : % 177.89/177.91 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 177.89/177.91 => c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_r),V_k)),V_l) ) % 177.89/177.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 177.89/177.91 => c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k),V_l) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_inc__shift__def,axiom, % 177.89/177.91 ! [V_k,V_v] : % 177.89/177.91 ( ( V_v = V_k % 177.89/177.91 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 177.89/177.91 & ( V_v != V_k % 177.89/177.91 => c_Random_Oinc__shift(V_v,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_k),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_select,axiom, % 177.89/177.91 ! [V_s_2,T_a,V_xs_2] : % 177.89/177.91 ( V_xs_2 != c_List_Olist_ONil(T_a) % 177.89/177.91 => 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_select__weight__member,axiom, % 177.89/177.91 ! [V_s_2,V_xs_2,T_a] : % 177.89/177.91 ( 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)))) % 177.89/177.91 => 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)))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_select__weigth__select,axiom, % 177.89/177.91 ! [T_a,V_xs_2] : % 177.89/177.91 ( V_xs_2 != c_List_Olist_ONil(T_a) % 177.89/177.91 => 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) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_select__weight__cons__zero,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_select__weigth__drop__zero,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_pick__member,axiom, % 177.89/177.91 ! [V_xs_2,T_a,V_i_2] : % 177.89/177.91 ( 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)))) % 177.89/177.91 => 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)))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_pick_Osimps,axiom, % 177.89/177.91 ! [V_xs,V_x,T_a,V_i] : % 177.89/177.91 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) % 177.89/177.91 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a),V_x) ) % 177.89/177.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) % 177.89/177.91 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Random_Opick(T_a,V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_pick__drop__zero,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_select__weight__def,axiom, % 177.89/177.91 ! [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))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_pick__same,axiom, % 177.89/177.91 ! [V_xs_2,T_a,V_l_2] : % 177.89/177.91 ( 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))) % 177.89/177.91 => 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) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_number__of__code__numeral__def,axiom, % 177.89/177.91 c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Code__Numeral_Oof__nat__code,axiom, % 177.89/177.91 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Code__Numeral_Oof__nat__inject,axiom, % 177.89/177.91 ! [V_m_2,V_n_2] : % 177.89/177.91 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) % 177.89/177.91 <=> V_n_2 = V_m_2 ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_times__code__numeral__code,axiom, % 177.89/177.91 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_zero__code__numeral__def,axiom, % 177.89/177.91 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_code__numeral_Oof__nat__inject,axiom, % 177.89/177.91 ! [V_y_2,V_x_2] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 177.89/177.91 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 177.89/177.91 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) % 177.89/177.91 <=> V_x_2 = V_y_2 ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_one__code__numeral__def,axiom, % 177.89/177.91 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_less__code__numeral__code,axiom, % 177.89/177.91 ! [V_m_2,V_n_2] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2))) % 177.89/177.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_plus__code__numeral__code,axiom, % 177.89/177.91 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_less__eq__code__numeral__code,axiom, % 177.89/177.91 ! [V_m_2,V_n_2] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2))) % 177.89/177.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_code__numeral__not__eq__zero,axiom, % 177.89/177.91 ! [V_i_2] : % 177.89/177.91 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 177.89/177.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_i_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_range,axiom, % 177.89/177.91 ! [V_s,V_k] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_k)) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(V_k),V_s))),V_k)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_select__def,axiom, % 177.89/177.91 ! [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))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl__insert,axiom, % 177.89/177.91 ! [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)))))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_r__into__rtrancl,axiom, % 177.89/177.91 ! [V_r_2,V_p_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl_Ortrancl__refl,axiom, % 177.89/177.91 ! [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))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl__into__rtrancl,axiom, % 177.89/177.91 ! [V_r_2,V_b_2,V_a_2,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 => 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_listrel__rtrancl__refl,axiom, % 177.89/177.91 ! [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)))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl__listrel1__ConsI2,axiom, % 177.89/177.91 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 => ( 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)))) % 177.89/177.91 => 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)))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_nat__of__of__nat,axiom, % 177.89/177.91 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ). % 177.89/177.91 % 177.89/177.91 fof(fact_of__nat__nat__of,axiom, % 177.89/177.91 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ). % 177.89/177.91 % 177.89/177.91 fof(fact_nat__of__inverse,axiom, % 177.89/177.91 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ). % 177.89/177.91 % 177.89/177.91 fof(fact_times__code__numeral__def,axiom, % 177.89/177.91 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_type__definition__code__numeral,axiom, % 177.89/177.91 c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_listrel__rtrancl__trans,axiom, % 177.89/177.91 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 177.89/177.91 ( 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)))) % 177.89/177.91 => ( 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)))) % 177.89/177.91 => 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)))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_converse__rtrancl__into__rtrancl,axiom, % 177.89/177.91 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => ( 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))) % 177.89/177.91 => 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom, % 177.89/177.91 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 => ( 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)) % 177.89/177.91 => 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl__trans,axiom, % 177.89/177.91 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 => ( 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))) % 177.89/177.91 => 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl__trancl__trancl,axiom, % 177.89/177.91 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 => ( 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))) % 177.89/177.91 => 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl__rtrancl__trancl,axiom, % 177.89/177.91 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 => ( 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))) % 177.89/177.91 => 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl__into__trancl1,axiom, % 177.89/177.91 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 => ( 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)) % 177.89/177.91 => 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtranclD,axiom, % 177.89/177.91 ! [V_R_2,V_b_2,V_a_2,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 => ( V_a_2 = V_b_2 % 177.89/177.91 | ( V_a_2 != V_b_2 % 177.89/177.91 & 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))) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl__into__trancl2,axiom, % 177.89/177.91 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => ( 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))) % 177.89/177.91 => 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl__eq__or__trancl,axiom, % 177.89/177.91 ! [V_R_2,V_y_2,V_x_2,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 <=> ( V_x_2 = V_y_2 % 177.89/177.91 | ( V_x_2 != V_y_2 % 177.89/177.91 & 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))) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl__mono,axiom, % 177.89/177.91 ! [V_s_2,V_r_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl__subset,axiom, % 177.89/177.91 ! [V_S_2,V_R_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => ( 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))) % 177.89/177.91 => c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl__subset__rtrancl,axiom, % 177.89/177.91 ! [V_s_2,V_r_2,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 => 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl__Un__subset,axiom, % 177.89/177.91 ! [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)))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Image__closed__trancl,axiom, % 177.89/177.91 ! [V_X_2,V_r_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => hAPP(c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_X_2) = V_X_2 ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom, % 177.89/177.91 ! [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)))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_less__code__numeral__def,axiom, % 177.89/177.91 ! [V_m_2,V_n_2] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 177.89/177.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_nat__of__number,axiom, % 177.89/177.91 ! [V_k] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),V_k)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_k) ). % 177.89/177.91 % 177.89/177.91 fof(fact_int__of__def,axiom, % 177.89/177.91 c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of) ). % 177.89/177.91 % 177.89/177.91 fof(fact_code__numeral_Onat__of__inject,axiom, % 177.89/177.91 ! [V_y_2,V_x_2] : % 177.89/177.91 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) % 177.89/177.91 <=> V_x_2 = V_y_2 ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Code__Numeral_Onat__of__inject,axiom, % 177.89/177.91 ! [V_l_2,V_k_2] : % 177.89/177.91 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) % 177.89/177.91 <=> V_k_2 = V_l_2 ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_nat__of,axiom, % 177.89/177.91 ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_x_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Domain__rtrancl,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl__idemp__self__comp,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_r__comp__rtrancl__eq,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl__Un__rtrancl,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_in__rtrancl__UnI,axiom, % 177.89/177.91 ! [V_S_2,V_R_2,V_x_2,T_a] : % 177.89/177.91 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 177.89/177.91 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) ) % 177.89/177.91 => 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)))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_refl__rtrancl,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl__idemp,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Range__rtrancl,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl__trancl__absorb,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl__rtrancl__absorb,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl__unfold__left,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl__unfold__right,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_less__eq__code__numeral__def,axiom, % 177.89/177.91 ! [V_m_2,V_n_2] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 177.89/177.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_nat__of__code,axiom, % 177.89/177.91 ! [V_i] : hAPP(c_Code__Numeral_Onat__of,V_i) = c_Code__Numeral_Onat__of__aux(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_nat__of__aux__def,axiom, % 177.89/177.91 ! [V_n,V_i] : c_Code__Numeral_Onat__of__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_i)),V_n) ). % 177.89/177.91 % 177.89/177.91 fof(fact_listrel__subset__rtrancl__listrel1,axiom, % 177.89/177.91 ! [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)))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Not__Domain__rtrancl,axiom, % 177.89/177.91 ! [V_y_2,V_R_2,V_x_2,T_a] : % 177.89/177.91 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_a),V_R_2))) % 177.89/177.91 => ( 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))) % 177.89/177.91 <=> V_x_2 = V_y_2 ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_acc__downwards,axiom, % 177.89/177.91 ! [V_b_2,V_r_2,V_a_2,T_a] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 177.89/177.91 => ( 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))) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_acc__downwards__aux,axiom, % 177.89/177.91 ! [V_r_2,V_a_2,V_b_2,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__insert,axiom, % 177.89/177.91 ! [V_r_2,V_x_2,V_y_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 <=> ( c_Wellfounded_Owf(T_a,V_r_2) % 177.89/177.91 & ~ 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl__listrel1__ConsI1,axiom, % 177.89/177.91 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 177.89/177.91 ( 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)))) % 177.89/177.91 => 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)))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl__listrel1__eq__len,axiom, % 177.89/177.91 ! [V_r_2,V_y_2,V_x_2,T_a] : % 177.89/177.91 ( 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)))) % 177.89/177.91 => 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) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_acyclic__insert,axiom, % 177.89/177.91 ! [V_r_2,V_x_2,V_y_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 177.89/177.91 & ~ 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))) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_listrel__reflcl__if__listrel1,axiom, % 177.89/177.91 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 => 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)))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl__listrel1__if__listrel,axiom, % 177.89/177.91 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 => 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)))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Suc__code__numeral__def,axiom, % 177.89/177.91 ! [V_k] : c_Code__Numeral_OSuc__code__numeral(V_k) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,V_k))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_minus__code__numeral__def,axiom, % 177.89/177.91 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_of__nat__inverse,axiom, % 177.89/177.91 ! [V_y_2] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 177.89/177.91 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_plus__code__numeral__def,axiom, % 177.89/177.91 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_div__code__numeral__def,axiom, % 177.89/177.91 ! [V_m,V_n] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_pred__nat__trancl__eq__le,axiom, % 177.89/177.91 ! [V_n_2,V_m_2] : % 177.89/177.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) % 177.89/177.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_mod__code__numeral__def,axiom, % 177.89/177.91 ! [V_m,V_n] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,V_n),hAPP(c_Code__Numeral_Onat__of,V_m))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl__subset__Sigma__aux,axiom, % 177.89/177.91 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 => ( 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)))) % 177.89/177.91 => ( V_a_2 = V_b_2 % 177.89/177.91 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_code__numeral__decr,axiom, % 177.89/177.91 ! [V_k] : % 177.89/177.91 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 177.89/177.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_k)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,V_k))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_subtract__code__numeral__code,axiom, % 177.89/177.91 ! [V_m,V_n] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_New__DSequence_Opos__not__seq__def,axiom, % 177.89/177.91 ! [V_i_2,V_xq_2] : hAPP(c_New__DSequence_Opos__not__seq(V_xq_2),V_i_2) = c_Lazy__Sequence_Ohb__not__seq(hAPP(V_xq_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_i_2))) ). % 177.89/177.91 % 177.89/177.91 fof(fact_subtract__code__numeral__def,axiom, % 177.89/177.91 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 177.89/177.91 % 177.89/177.91 fof(fact_minus__code__numeral__code,axiom, % 177.89/177.91 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,V_n),V_m) ). % 177.89/177.91 % 177.89/177.91 fof(fact_irrefl__tranclI,axiom, % 177.89/177.91 ! [V_x_2,V_r_2,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => ~ 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_sequence__trans,axiom, % 177.89/177.91 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_a] : % 177.89/177.91 ( ! [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))) % 177.89/177.91 => 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl__converseI,axiom, % 177.89/177.91 ! [V_r_2,V_x_2,V_y_2,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 => 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)))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl__converseD,axiom, % 177.89/177.91 ! [V_r_2,V_y_2,V_x_2,T_a] : % 177.89/177.91 ( 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)))) % 177.89/177.91 => 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_rtrancl__converse,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_converse__iff,axiom, % 177.89/177.91 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 <=> 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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_converseI,axiom, % 177.89/177.91 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 177.89/177.91 ( 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)) % 177.89/177.91 => 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))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_converseD,axiom, % 177.89/177.91 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 177.89/177.91 ( 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))) % 177.89/177.91 => 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)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_in__listrel1__converse,axiom, % 177.89/177.91 ! [V_r_2,V_y_2,V_x_2,T_a] : % 177.89/177.91 ( 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)))) % 177.89/177.91 <=> 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)))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl__converseD,axiom, % 177.89/177.91 ! [V_r_2,V_y_2,V_x_2,T_a] : % 177.89/177.91 ( 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)))) % 177.89/177.91 => 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)))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl__converseI,axiom, % 177.89/177.91 ! [V_r_2,V_y_2,V_x_2,T_a] : % 177.89/177.91 ( 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)))) % 177.89/177.91 => 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)))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_acyclic__converse,axiom, % 177.89/177.91 ! [V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 177.89/177.91 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_converse__inv__image,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_converse__INTER,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_finite__converse,axiom, % 177.89/177.91 ! [V_r_2,T_b,T_a] : % 177.89/177.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 177.89/177.91 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_a)),V_r_2)) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_converse__Id__on,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_converse__converse,axiom, % 177.89/177.91 ! [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 ). % 177.89/177.91 % 177.89/177.91 fof(fact_Field__converse,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_listrel1__converse,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_refl__on__converse,axiom, % 177.89/177.91 ! [V_r_2,V_A_2,T_a] : % 177.89/177.91 ( c_Relation_Orefl__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 177.89/177.91 <=> c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_converse__Int,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_converse__Un,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_converse__rel__comp,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_equiv__comp__eq,axiom, % 177.89/177.91 ! [V_r_2,V_A_2,T_a] : % 177.89/177.91 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 177.89/177.91 => 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 ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_converse__UNION,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Range__def,axiom, % 177.89/177.91 ! [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)) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Domain__converse,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_Range__converse,axiom, % 177.89/177.91 ! [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) ). % 177.89/177.91 % 177.89/177.91 fof(fact_wf__converse__trancl,axiom, % 177.89/177.91 ! [V_r_2,T_a] : % 177.89/177.91 ( c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 177.89/177.91 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 177.89/177.91 % 177.89/177.91 fof(fact_trancl__converse,axiom, % 177.89/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_Image__subset__eq,axiom, % 178.07/177.91 ! [V_B_2,V_A_2,V_r_2,T_b,T_a] : % 178.07/177.91 ( 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)) % 178.07/177.91 <=> 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))))) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_refl__on__comp__subset,axiom, % 178.07/177.91 ! [V_r_2,V_A_2,T_a] : % 178.07/177.91 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 178.07/177.91 => 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))) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_comp__equivI,axiom, % 178.07/177.91 ! [V_A_2,V_r_2,T_a] : % 178.07/177.91 ( 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 % 178.07/177.91 => ( hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) = V_A_2 % 178.07/177.91 => c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_finite__acyclic__wf__converse,axiom, % 178.07/177.91 ! [V_r_2,T_a] : % 178.07/177.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 178.07/177.91 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 178.07/177.91 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_converse__def,axiom, % 178.07/177.91 ! [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))) ). % 178.07/177.91 % 178.07/177.91 fof(fact_Image__INT__eq,axiom, % 178.07/177.91 ! [V_B_2,T_c,V_A_2,V_r_2,T_b,T_a] : % 178.07/177.91 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) % 178.07/177.91 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 178.07/177.91 => 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)) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_reflcl__set__eq,axiom, % 178.07/177.91 ! [V_y_2,V_x_2,V_r_2,T_a] : % 178.07/177.91 ( 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)) % 178.07/177.91 <=> 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)))) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_IdI,axiom, % 178.07/177.91 ! [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))) ). % 178.07/177.91 % 178.07/177.91 fof(fact_converse__Id,axiom, % 178.07/177.91 ! [T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId(T_a)) = c_Relation_OId(T_a) ). % 178.07/177.91 % 178.07/177.91 fof(fact_Domain__Id,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_Id__O__R,axiom, % 178.07/177.91 ! [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 ). % 178.07/177.91 % 178.07/177.91 fof(fact_R__O__Id,axiom, % 178.07/177.91 ! [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 ). % 178.07/177.91 % 178.07/177.91 fof(fact_single__valued__rel__comp,axiom, % 178.07/177.91 ! [V_s_2,T_c,V_r_2,T_b,T_a] : % 178.07/177.91 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 178.07/177.91 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2) % 178.07/177.91 => 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)) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_refl__Id,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_Image__Id,axiom, % 178.07/177.91 ! [V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a)),V_A_2) = V_A_2 ). % 178.07/177.91 % 178.07/177.91 fof(fact_single__valued__Id__on,axiom, % 178.07/177.91 ! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_single__valued__Id,axiom, % 178.07/177.91 ! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_Range__Id,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_single__valued__subset,axiom, % 178.07/177.91 ! [V_s_2,V_r_2,T_b,T_a] : % 178.07/177.91 ( 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)) % 178.07/177.91 => ( c_Relation_Osingle__valued(T_a,T_b,V_s_2) % 178.07/177.91 => c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_pair__in__Id__conv,axiom, % 178.07/177.91 ! [V_b_2,V_a_2,T_a] : % 178.07/177.91 ( 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))) % 178.07/177.91 <=> V_a_2 = V_b_2 ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rtrancl__r__diff__Id,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rtrancl__empty,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rtrancl__reflcl,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rtrancl__reflcl__absorb,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact_single__valuedD,axiom, % 178.07/177.91 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] : % 178.07/177.91 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 178.07/177.91 => ( 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)) % 178.07/177.91 => ( 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)) % 178.07/177.91 => V_y_2 = V_z_2 ) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_single__valued__def,axiom, % 178.07/177.91 ! [V_r_2,T_b,T_a] : % 178.07/177.91 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 178.07/177.91 <=> ! [B_x,B_y] : % 178.07/177.91 ( 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)) % 178.07/177.91 => ! [B_z] : % 178.07/177.91 ( 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)) % 178.07/177.91 => B_y = B_z ) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_pair__leq__def,axiom, % 178.07/177.91 c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))) ). % 178.07/177.91 % 178.07/177.91 fof(fact_reflcl__trancl,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact_trancl__reflcl,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rtrancl__unfold,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_refl__reflcl,axiom, % 178.07/177.91 ! [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))) ). % 178.07/177.91 % 178.07/177.91 fof(fact_Id__def,axiom, % 178.07/177.91 ! [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))))) ). % 178.07/177.91 % 178.07/177.91 fof(fact_irrefl__diff__Id,axiom, % 178.07/177.91 ! [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))) ). % 178.07/177.91 % 178.07/177.91 fof(fact_single__valued__confluent,axiom, % 178.07/177.91 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] : % 178.07/177.91 ( c_Relation_Osingle__valued(T_a,T_a,V_r_2) % 178.07/177.91 => ( 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))) % 178.07/177.91 => ( 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))) % 178.07/177.91 => ( 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))) % 178.07/177.91 | 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))) ) ) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_Image__Int__eq,axiom, % 178.07/177.91 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] : % 178.07/177.91 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_R_2)) % 178.07/177.91 => 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)) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rtrancl__Int__subset,axiom, % 178.07/177.91 ! [V_r_2,V_s_2,T_a] : % 178.07/177.91 ( 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)) % 178.07/177.91 => ( 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)) % 178.07/177.91 => 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)) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_total__on__diff__Id,axiom, % 178.07/177.91 ! [V_r_2,V_A_2,T_a] : % 178.07/177.91 ( 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))) % 178.07/177.91 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rtrancl__imp__UN__rel__pow,axiom, % 178.07/177.91 ! [V_R_2,V_p_2,T_a] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 178.07/177.91 => 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)))) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_total__on__converse,axiom, % 178.07/177.91 ! [V_r_2,V_A_2,T_a] : % 178.07/177.91 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 178.07/177.91 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_single__valued__rel__pow,axiom, % 178.07/177.91 ! [V_n_2,V_R_2,T_a] : % 178.07/177.91 ( c_Relation_Osingle__valued(T_a,T_a,V_R_2) % 178.07/177.91 => 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)) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_relpow_Osimps_I1_J,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact_funpow__add,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_comp__funpow,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rel__pow__imp__rtrancl,axiom, % 178.07/177.91 ! [V_R_2,V_n_2,V_p_2,T_a] : % 178.07/177.91 ( 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))) % 178.07/177.91 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rtrancl__power,axiom, % 178.07/177.91 ! [V_R_2,V_p_2,T_a] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 178.07/177.91 <=> ? [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))) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rel__pow__0__E,axiom, % 178.07/177.91 ! [V_R_2,V_y_2,V_x_2,T_a] : % 178.07/177.91 ( 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))) % 178.07/177.91 => V_x_2 = V_y_2 ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rel__pow__0__I,axiom, % 178.07/177.91 ! [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))) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rel__pow__Suc__I2,axiom, % 178.07/177.91 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_a] : % 178.07/177.91 ( 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)) % 178.07/177.91 => ( 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))) % 178.07/177.91 => 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))) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rel__pow__Suc__I,axiom, % 178.07/177.91 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_a] : % 178.07/177.91 ( 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))) % 178.07/177.91 => ( 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)) % 178.07/177.91 => 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))) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_funpow_Osimps_I2_J,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rel__pow__add,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_wf__exp,axiom, % 178.07/177.91 ! [V_R_2,V_n_2,T_a] : % 178.07/177.91 ( 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)) % 178.07/177.91 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_funpow__swap1,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_total__on__empty,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rel__pow__commute,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact_relpow_Osimps_I2_J,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rel__pow__1,axiom, % 178.07/177.91 ! [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 ). % 178.07/177.91 % 178.07/177.91 fof(fact_funpow__mult,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact_funpow_Osimps_I1_J,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact_trancl__power,axiom, % 178.07/177.91 ! [V_R_2,V_p_2,T_a] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))) % 178.07/177.91 <=> ? [B_n] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 178.07/177.91 & 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))) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_total__on__def,axiom, % 178.07/177.91 ! [V_r_2,V_A_2,T_a] : % 178.07/177.91 ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2) % 178.07/177.91 <=> ! [B_x] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 178.07/177.91 => ! [B_xa] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 178.07/177.91 => ( B_x != B_xa % 178.07/177.91 => ( 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)) % 178.07/177.91 | 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)) ) ) ) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rtrancl__is__UN__rel__pow,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_funpow__code__def,axiom, % 178.07/177.91 ! [T_a] : c_Nat_Ofunpow(T_a) = c_Nat_Ocompow(T_a,T_a) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rel__pow__E,axiom, % 178.07/177.91 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 178.07/177.91 ( 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))) % 178.07/177.91 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 178.07/177.91 => V_x_2 != V_z_2 ) % 178.07/177.91 => ~ ! [B_y,B_m] : % 178.07/177.91 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 178.07/177.91 => ( 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))) % 178.07/177.91 => ~ 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)) ) ) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rotate__def,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rel__pow__E2,axiom, % 178.07/177.91 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 178.07/177.91 ( 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))) % 178.07/177.91 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 178.07/177.91 => V_x_2 != V_z_2 ) % 178.07/177.91 => ~ ! [B_y,B_m] : % 178.07/177.91 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 178.07/177.91 => ( 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)) % 178.07/177.91 => ~ 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))) ) ) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_acyclicI,axiom, % 178.07/177.91 ! [V_r_2,T_a] : % 178.07/177.91 ( ! [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))) % 178.07/177.91 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_pos__not__random__dseq__def,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rtrancl__Un__separator__converseE,axiom, % 178.07/177.91 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 178.07/177.91 ( 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)))) % 178.07/177.91 => ( ! [B_x] : % 178.07/177.91 ( 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))) % 178.07/177.91 => ! [B_y] : % 178.07/177.91 ( 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)) % 178.07/177.91 => B_y = B_x ) ) % 178.07/177.91 => 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))) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rtrancl__Un__separatorE,axiom, % 178.07/177.91 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 178.07/177.91 ( 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)))) % 178.07/177.91 => ( ! [B_x] : % 178.07/177.91 ( 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))) % 178.07/177.91 => ! [B_y] : % 178.07/177.91 ( 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)) % 178.07/177.91 => B_x = B_y ) ) % 178.07/177.91 => 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))) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rel__pow__Suc__D2,axiom, % 178.07/177.91 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 178.07/177.91 ( 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))) % 178.07/177.91 => ? [B_y] : % 178.07/177.91 ( 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)) % 178.07/177.91 & 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))) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rel__pow__Suc__E,axiom, % 178.07/177.91 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 178.07/177.91 ( 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))) % 178.07/177.91 => ~ ! [B_y] : % 178.07/177.91 ( 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))) % 178.07/177.91 => ~ 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)) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rel__pow__Suc__E2,axiom, % 178.07/177.91 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 178.07/177.91 ( 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))) % 178.07/177.91 => ~ ! [B_y] : % 178.07/177.91 ( 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)) % 178.07/177.91 => ~ 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))) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_tranclD,axiom, % 178.07/177.91 ! [V_R_2,V_y_2,V_x_2,T_a] : % 178.07/177.91 ( 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))) % 178.07/177.91 => ? [B_z] : % 178.07/177.91 ( 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)) % 178.07/177.91 & 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))) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_tranclD2,axiom, % 178.07/177.91 ! [V_R_2,V_y_2,V_x_2,T_a] : % 178.07/177.91 ( 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))) % 178.07/177.91 => ? [B_z] : % 178.07/177.91 ( 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))) % 178.07/177.91 & 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)) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_IdE,axiom, % 178.07/177.91 ! [V_p_2,T_a] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a))) % 178.07/177.91 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_nat__intermed__int__val,axiom, % 178.07/177.91 ! [V_k_2,V_f_2,V_n_2,V_m_2] : % 178.07/177.91 ( ! [B_i] : % 178.07/177.91 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 178.07/177.91 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) % 178.07/177.91 => 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))) ) % 178.07/177.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 178.07/177.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) % 178.07/177.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 178.07/177.91 => ? [B_i] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 178.07/177.91 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 178.07/177.91 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_in__set__conv__decomp__first,axiom, % 178.07/177.91 ! [V_xs_2,V_x_2,T_a] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 178.07/177.91 <=> ? [B_ys] : % 178.07/177.91 ( ? [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)) % 178.07/177.91 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_ys))) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_in__set__conv__decomp__last,axiom, % 178.07/177.91 ! [V_xs_2,V_x_2,T_a] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 178.07/177.91 <=> ? [B_ys,B_zs] : % 178.07/177.91 ( 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)) % 178.07/177.91 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_zs))) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_in__set__conv__decomp,axiom, % 178.07/177.91 ! [V_xs_2,V_x_2,T_a] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 178.07/177.91 <=> ? [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)) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_mod__div__decomp,axiom, % 178.07/177.91 ! [V_b,V_a,T_a] : % 178.07/177.91 ( class_Divides_Osemiring__div(T_a) % 178.07/177.91 => 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)) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_wf__eq__minimal,axiom, % 178.07/177.91 ! [V_r_2,T_a] : % 178.07/177.91 ( c_Wellfounded_Owf(T_a,V_r_2) % 178.07/177.91 <=> ! [B_Q] : % 178.07/177.91 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) % 178.07/177.91 => ? [B_x] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) % 178.07/177.91 & ! [B_y] : % 178.07/177.91 ( 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)) % 178.07/177.91 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),B_Q)) ) ) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_transfer__nat__int__set__cong,axiom, % 178.07/177.91 ! [V_P_H_2,V_P_2] : % 178.07/177.91 ( ! [B_x] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 178.07/177.91 => ( hBOOL(hAPP(V_P_2,B_x)) % 178.07/177.91 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) ) % 178.07/177.91 => 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)) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_Int__Collect__mono,axiom, % 178.07/177.91 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_a] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 178.07/177.91 => ( ! [B_x] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 178.07/177.91 => ( hBOOL(hAPP(V_P_2,B_x)) % 178.07/177.91 => hBOOL(hAPP(V_Q_2,B_x)) ) ) % 178.07/177.91 => 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)))) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_UnionE,axiom, % 178.07/177.91 ! [V_C_2,V_A_2,T_a] : % 178.07/177.91 ( 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))) % 178.07/177.91 => ~ ! [B_X] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) % 178.07/177.91 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_rel__compE,axiom, % 178.07/177.91 ! [V_s_2,V_r_2,T_c,V_xz_2,T_b,T_a] : % 178.07/177.91 ( 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))) % 178.07/177.91 => ~ ! [B_x,B_y,B_z] : % 178.07/177.91 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z) % 178.07/177.91 => ( 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)) % 178.07/177.91 => ~ 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)) ) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_converseE,axiom, % 178.07/177.91 ! [V_r_2,V_yx_2,T_b,T_a] : % 178.07/177.91 ( 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))) % 178.07/177.91 => ~ ! [B_x,B_y] : % 178.07/177.91 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_y),B_x) % 178.07/177.91 => ~ 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)) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_Nitpick_Oplus__frac__def,axiom, % 178.07/177.91 ! [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))) ). % 178.07/177.91 % 178.07/177.91 fof(fact_setprod__pos,axiom, % 178.07/177.91 ! [V_f_2,V_A_2,T_a,T_b] : % 178.07/177.91 ( class_Rings_Olinordered__semidom(T_b) % 178.07/177.91 => ( ! [B_x] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 178.07/177.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 178.07/177.91 => 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))) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_Nitpick_Otimes__frac__def,axiom, % 178.07/177.91 ! [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))) ). % 178.07/177.91 % 178.07/177.91 fof(fact_Nitpick_Oof__frac__def,axiom, % 178.07/177.91 ! [V_q,T_a,T_b] : % 178.07/177.91 ( ( class_Rings_Oinverse(T_b) % 178.07/177.91 & class_Rings_Oring__1(T_b) ) % 178.07/177.91 => 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))) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_Nitpick_Oinverse__frac__def,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_Nitpick_Ouminus__frac__def,axiom, % 178.07/177.91 ! [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))) ). % 178.07/177.91 % 178.07/177.91 fof(fact_Nitpick_Oless__frac__def,axiom, % 178.07/177.91 ! [V_r_2,V_q_2,T_a] : % 178.07/177.91 ( c_Nitpick_Oless__frac(T_a,V_q_2,V_r_2) % 178.07/177.91 <=> 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))) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_Nitpick_Oless__eq__frac__def,axiom, % 178.07/177.91 ! [V_r_2,V_q_2,T_a] : % 178.07/177.91 ( c_Nitpick_Oless__eq__frac(T_a,V_q_2,V_r_2) % 178.07/177.91 <=> 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))) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_Nitpick_Onum__def,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_Nitpick_Odenom__def,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_list__all__length,axiom, % 178.07/177.91 ! [V_xs_2,V_P_2,T_a] : % 178.07/177.91 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 178.07/177.91 <=> ! [B_n] : % 178.07/177.91 ( 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))) % 178.07/177.91 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_internal__split__def,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact_list__all__simps_I2_J,axiom, % 178.07/177.91 ! [V_P_2,T_a] : c_List_Olist__all(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_list__all__append,axiom, % 178.07/177.91 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 178.07/177.91 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 178.07/177.91 <=> ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 178.07/177.91 & c_List_Olist__all(T_a,V_P_2,V_ys_2) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_list__all__rev,axiom, % 178.07/177.91 ! [V_xs_2,V_P_2,T_a] : % 178.07/177.91 ( c_List_Olist__all(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 178.07/177.91 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_list__all__iff,axiom, % 178.07/177.91 ! [V_xs_2,V_P_2,T_a] : % 178.07/177.91 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 178.07/177.91 <=> ! [B_x] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 178.07/177.91 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_list__all__simps_I1_J,axiom, % 178.07/177.91 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 178.07/177.91 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 178.07/177.91 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 178.07/177.91 & c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_Ball__set__list__all,axiom, % 178.07/177.91 ! [V_P_2,V_xs_2,T_a] : % 178.07/177.91 ( ! [B_x] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 178.07/177.91 => hBOOL(hAPP(V_P_2,B_x)) ) % 178.07/177.91 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_list__all__iff__raw,axiom, % 178.07/177.91 ! [V_xs_2,V_P_2,T_a] : % 178.07/177.91 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 178.07/177.91 <=> ! [B_x] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 178.07/177.91 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_internal__split__conv,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact_list__ex1__simps_I2_J,axiom, % 178.07/177.91 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 178.07/177.91 ( c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 178.07/177.91 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 178.07/177.91 => 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) ) % 178.07/177.91 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 178.07/177.91 => c_List_Olist__ex1(T_a,V_P_2,V_xs_2) ) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_setprod__nonneg,axiom, % 178.07/177.91 ! [V_f_2,V_A_2,T_a,T_b] : % 178.07/177.91 ( class_Rings_Olinordered__semidom(T_b) % 178.07/177.91 => ( ! [B_x] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 178.07/177.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 178.07/177.91 => 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))) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_exists1__code,axiom, % 178.07/177.91 ! [V_P_2,T_a] : % 178.07/177.91 ( class_Enum_Oenum(T_a) % 178.07/177.91 => ( ? [B_x] : % 178.07/177.91 ( hBOOL(hAPP(V_P_2,B_x)) % 178.07/177.91 & ! [B_y] : % 178.07/177.91 ( hBOOL(hAPP(V_P_2,B_y)) % 178.07/177.91 => B_y = B_x ) ) % 178.07/177.91 <=> c_List_Olist__ex1(T_a,V_P_2,c_Enum_Oenum__class_Oenum(T_a)) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_list__ex1__simps_I1_J,axiom, % 178.07/177.91 ! [V_P_2,T_a] : ~ c_List_Olist__ex1(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_list__ex1__iff,axiom, % 178.07/177.91 ! [V_xs_2,V_P_2,T_a] : % 178.07/177.91 ( c_List_Olist__ex1(T_a,V_P_2,V_xs_2) % 178.07/177.91 <=> ? [B_x] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 178.07/177.91 & hBOOL(hAPP(V_P_2,B_x)) % 178.07/177.91 & ! [B_y] : % 178.07/177.91 ( ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),hAPP(c_List_Oset(T_a),V_xs_2))) % 178.07/177.91 & hBOOL(hAPP(V_P_2,B_y)) ) % 178.07/177.91 => B_y = B_x ) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_bool_Osize_I2_J,axiom, % 178.07/177.91 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(fact_bool_Osize_I1_J,axiom, % 178.07/177.91 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(fact_finite__less__ub,axiom, % 178.07/177.91 ! [V_u_2,V_f_2] : % 178.07/177.91 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n))) % 178.07/177.91 => 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)))) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_measure__function__int,axiom, % 178.07/177.91 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))) ). % 178.07/177.91 % 178.07/177.91 fof(fact_measure__fst,axiom, % 178.07/177.91 ! [T_b,V_f_2,T_a] : % 178.07/177.91 ( c_FunDef_Ois__measure(T_a,V_f_2) % 178.07/177.91 => 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))) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_is__measure_Ointros,axiom, % 178.07/177.91 ! [V_f_2,T_a] : c_FunDef_Ois__measure(T_a,V_f_2) ). % 178.07/177.91 % 178.07/177.91 fof(fact_is__measure_Oequations,axiom, % 178.07/177.91 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ). % 178.07/177.91 % 178.07/177.91 fof(fact_is__measure_Osimps,axiom, % 178.07/177.91 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ). % 178.07/177.91 % 178.07/177.91 fof(fact_measure__size,axiom, % 178.07/177.91 ! [T_a] : % 178.07/177.91 ( class_Nat_Osize(T_a) % 178.07/177.91 => c_FunDef_Ois__measure(T_a,c_Nat_Osize__class_Osize(T_a)) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_measure__snd,axiom, % 178.07/177.91 ! [T_b,V_f_2,T_a] : % 178.07/177.91 ( c_FunDef_Ois__measure(T_a,V_f_2) % 178.07/177.91 => 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))) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_equal__fun__def,axiom, % 178.07/177.91 ! [V_g_2,V_f_2,T_a,T_b] : % 178.07/177.91 ( ( class_HOL_Oequal(T_b) % 178.07/177.91 & class_Enum_Oenum(T_a) ) % 178.07/177.91 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 178.07/177.91 <=> ! [B_x] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) % 178.07/177.91 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_transfer__morphism__int__nat,axiom, % 178.07/177.91 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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_eq__equal,axiom, % 178.07/177.91 ! [T_a] : % 178.07/177.91 ( class_HOL_Oequal(T_a) % 178.07/177.91 => c_fequal = c_HOL_Oequal__class_Oequal(T_a) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_equal__eq,axiom, % 178.07/177.91 ! [V_y_2,V_x_2,T_a] : % 178.07/177.91 ( class_HOL_Oequal(T_a) % 178.07/177.91 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x_2),V_y_2)) % 178.07/177.91 <=> V_x_2 = V_y_2 ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_equal__refl,axiom, % 178.07/177.91 ! [V_x,T_a] : % 178.07/177.91 ( class_HOL_Oequal(T_a) % 178.07/177.91 => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_equal,axiom, % 178.07/177.91 ! [T_a] : % 178.07/177.91 ( class_HOL_Oequal(T_a) % 178.07/177.91 => c_HOL_Oequal__class_Oequal(T_a) = c_fequal ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_bool_Osize_I3_J,axiom, % 178.07/177.91 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(fact_bool_Osize_I4_J,axiom, % 178.07/177.91 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(fact_size__code,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom, % 178.07/177.91 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] : % 178.07/177.91 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 178.07/177.91 => 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) ) % 178.07/177.91 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 178.07/177.91 => 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)) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_eq__int__code_I2_J,axiom, % 178.07/177.91 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_eq__int__code_I5_J,axiom, % 178.07/177.91 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_eq__int__code_I12_J,axiom, % 178.07/177.91 ! [V_k1_2] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin)) % 178.07/177.91 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_eq__int__code_I8_J,axiom, % 178.07/177.91 ! [V_k2_2] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2))) % 178.07/177.91 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_eq__int__code_I13_J,axiom, % 178.07/177.91 ! [V_k2_2,V_k1_2] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 178.07/177.91 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_eq__int__code_I1_J,axiom, % 178.07/177.91 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_eq__int__code_I16_J,axiom, % 178.07/177.91 ! [V_k2_2,V_k1_2] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 178.07/177.91 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_eq__number__of__int__code,axiom, % 178.07/177.91 ! [V_l_2,V_k_2] : % 178.07/177.91 ( 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))) % 178.07/177.91 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_eq__int__code_I6_J,axiom, % 178.07/177.91 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_equal__int__def,axiom, % 178.07/177.91 ! [V_l_2,V_k_2] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) % 178.07/177.91 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_eq__int__code_I15_J,axiom, % 178.07/177.91 ! [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))) ). % 178.07/177.91 % 178.07/177.91 fof(fact_eq__int__code_I14_J,axiom, % 178.07/177.91 ! [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))) ). % 178.07/177.91 % 178.07/177.91 fof(fact_eq__int__code_I9_J,axiom, % 178.07/177.91 ! [V_k1_2] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls)) % 178.07/177.91 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_eq__int__code_I3_J,axiom, % 178.07/177.91 ! [V_k2_2] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2))) % 178.07/177.91 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_eq__int__code_I10_J,axiom, % 178.07/177.91 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_eq__int__code_I4_J,axiom, % 178.07/177.91 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))) ). % 178.07/177.91 % 178.07/177.91 fof(fact_eq__int__code_I11_J,axiom, % 178.07/177.91 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_eq__int__code_I7_J,axiom, % 178.07/177.91 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))) ). % 178.07/177.91 % 178.07/177.91 fof(fact_lazy__sequence__size__code,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_eq__int__refl,axiom, % 178.07/177.91 ! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_seq__case,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_yieldn__def,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_New__DSequence_Oneg__bind__def,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_lazy__sequence_Osize_I4_J,axiom, % 178.07/177.91 ! [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))) ). % 178.07/177.91 % 178.07/177.91 fof(fact_lazy__sequence_Osimps_I5_J,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact__01,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_lazy__sequence_Oinject,axiom, % 178.07/177.91 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_a] : % 178.07/177.91 ( 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) % 178.07/177.91 <=> ( V_a_2 = V_a_H_2 % 178.07/177.91 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_lazy__sequence_Osize_I2_J,axiom, % 178.07/177.91 ! [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))) ). % 178.07/177.91 % 178.07/177.91 fof(fact_neg__bind__def,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_New__DSequence_Opos__decr__bind__def,axiom, % 178.07/177.91 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] : % 178.07/177.91 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 178.07/177.91 => 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) ) % 178.07/177.91 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 178.07/177.91 => 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)) ) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_New__DSequence_Opos__empty__def,axiom, % 178.07/177.91 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ). % 178.07/177.91 % 178.07/177.91 fof(fact_pos__empty__def,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact_New__DSequence_Opos__bind__def,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_pos__bind__def,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_neg__map__def,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_neg__single__def,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact_pos__map__def,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_New__DSequence_Oneg__single__def,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact_pos__single__def,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact_New__DSequence_Opos__single__def,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact_length__splice,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_splice_Osimps_I3_J,axiom, % 178.07/177.91 ! [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))) ). % 178.07/177.91 % 178.07/177.91 fof(fact_splice_Osimps_I1_J,axiom, % 178.07/177.91 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ). % 178.07/177.91 % 178.07/177.91 fof(fact_splice__Nil2,axiom, % 178.07/177.91 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ). % 178.07/177.91 % 178.07/177.91 fof(fact_splice_Osimps_I2_J,axiom, % 178.07/177.91 ! [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) ). % 178.07/177.91 % 178.07/177.91 fof(fact__02,axiom, % 178.07/177.91 ! [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)))) ). % 178.07/177.91 % 178.07/177.91 fof(fact_acyclicP__converse,axiom, % 178.07/177.91 ! [V_r_2,T_a] : % 178.07/177.91 ( 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)))) % 178.07/177.91 <=> 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))) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_conversepD,axiom, % 178.07/177.91 ! [V_b_2,V_a_2,V_r_2,T_b,T_a] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2)) % 178.07/177.91 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_conversep_Ointros,axiom, % 178.07/177.91 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 178.07/177.91 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_b_2),V_a_2)) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_conversep_Oequations,axiom, % 178.07/177.91 ! [V_a1_2,V_a2_2,V_r_2,T_b,T_a] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a2_2),V_a1_2)) % 178.07/177.91 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_conversep__iff,axiom, % 178.07/177.91 ! [V_b_2,V_a_2,V_r_2,T_b,T_a] : % 178.07/177.91 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2)) % 178.07/177.91 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_conversep__conversep,axiom, % 178.07/177.91 ! [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 ). % 178.07/177.91 % 178.07/177.91 fof(fact_conversep__eq,axiom, % 178.07/177.91 ! [T_a] : c_Predicate_Oconversep(T_a,T_a,c_fequal) = c_fequal ). % 178.07/177.91 % 178.07/177.91 fof(fact_conversep__noteq,axiom, % 178.07/177.91 ! [V_y_2,V_x_2,T_a] : % 178.07/177.91 ( 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)) % 178.07/177.91 <=> V_x_2 != V_y_2 ) ). % 178.07/177.91 % 178.07/177.91 fof(fact_converse__meet,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_converse__pred__comp,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_converse__join,axiom, % 178.07/177.91 ! [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)) ). % 178.07/177.91 % 178.07/177.91 fof(fact_conversep__converse__eq,axiom, % 178.07/177.91 ! [V_y_2,V_x_2,V_r_2,T_b,T_a] : % 178.07/177.91 ( 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)) % 178.07/177.91 <=> 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))) ) ). % 178.07/177.91 % 178.07/177.91 %----Arity declarations (233) % 178.07/177.91 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom, % 178.07/177.91 class_Lattices_Obounded__lattice(tc_HOL_Obool) ). % 178.07/177.91 % 178.07/177.91 fof(arity_fun__Lattices_Obounded__lattice,axiom, % 178.07/177.91 ! [T_2,T_1] : % 178.07/177.91 ( class_Lattices_Obounded__lattice(T_1) % 178.07/177.91 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ). % 178.07/177.91 % 178.07/177.91 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom, % 178.07/177.91 ! [T_2,T_1] : % 178.07/177.91 ( class_Complete__Lattice_Ocomplete__lattice(T_1) % 178.07/177.91 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ). % 178.07/177.91 % 178.07/177.91 fof(arity_fun__Lattices_Obounded__lattice__top,axiom, % 178.07/177.91 ! [T_2,T_1] : % 178.07/177.91 ( class_Lattices_Obounded__lattice(T_1) % 178.07/177.91 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ). % 178.07/177.91 % 178.07/177.91 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom, % 178.07/177.91 ! [T_2,T_1] : % 178.07/177.91 ( class_Lattices_Obounded__lattice(T_1) % 178.07/177.91 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ). % 178.07/177.91 % 178.07/177.91 fof(arity_fun__Lattices_Osemilattice__sup,axiom, % 178.07/177.91 ! [T_2,T_1] : % 178.07/177.91 ( class_Lattices_Olattice(T_1) % 178.07/177.91 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ). % 178.07/177.91 % 178.07/177.91 fof(arity_fun__Lattices_Osemilattice__inf,axiom, % 178.07/177.91 ! [T_2,T_1] : % 178.07/177.91 ( class_Lattices_Olattice(T_1) % 178.07/177.91 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ). % 178.07/177.91 % 178.07/177.91 fof(arity_fun__Lattices_Odistrib__lattice,axiom, % 178.07/177.91 ! [T_2,T_1] : % 178.07/177.91 ( class_Lattices_Odistrib__lattice(T_1) % 178.07/177.91 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ). % 178.07/177.91 % 178.07/177.91 fof(arity_fun__Lattices_Oboolean__algebra,axiom, % 178.07/177.91 ! [T_2,T_1] : % 178.07/177.91 ( class_Lattices_Oboolean__algebra(T_1) % 178.07/177.91 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ). % 178.07/177.91 % 178.07/177.91 fof(arity_fun__Orderings_Opreorder,axiom, % 178.07/177.91 ! [T_2,T_1] : % 178.07/177.91 ( class_Orderings_Opreorder(T_1) % 178.07/177.91 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 178.07/177.91 % 178.07/177.91 fof(arity_fun__Finite__Set_Ofinite,axiom, % 178.07/177.91 ! [T_1,T_2] : % 178.07/177.91 ( ( class_Finite__Set_Ofinite(T_2) % 178.07/177.91 & class_Finite__Set_Ofinite(T_1) ) % 178.07/177.91 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 178.07/177.91 % 178.07/177.91 fof(arity_fun__Lattices_Olattice,axiom, % 178.07/177.91 ! [T_2,T_1] : % 178.07/177.91 ( class_Lattices_Olattice(T_1) % 178.07/177.91 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ). % 178.07/177.91 % 178.07/177.91 fof(arity_fun__Orderings_Oorder,axiom, % 178.07/177.91 ! [T_2,T_1] : % 178.07/177.91 ( class_Orderings_Oorder(T_1) % 178.07/177.91 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 178.07/177.91 % 178.07/177.91 fof(arity_fun__Orderings_Otop,axiom, % 178.07/177.91 ! [T_2,T_1] : % 178.07/177.91 ( class_Orderings_Otop(T_1) % 178.07/177.91 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 178.07/177.91 % 178.07/177.91 fof(arity_fun__Orderings_Oord,axiom, % 178.07/177.91 ! [T_2,T_1] : % 178.07/177.91 ( class_Orderings_Oord(T_1) % 178.07/177.91 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 178.07/177.91 % 178.07/177.91 fof(arity_fun__Orderings_Obot,axiom, % 178.07/177.91 ! [T_2,T_1] : % 178.07/177.91 ( class_Orderings_Obot(T_1) % 178.07/177.91 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 178.07/177.91 % 178.07/177.91 fof(arity_fun__Groups_Ouminus,axiom, % 178.07/177.91 ! [T_2,T_1] : % 178.07/177.91 ( class_Groups_Ouminus(T_1) % 178.07/177.91 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ). % 178.07/177.91 % 178.07/177.91 fof(arity_fun__Groups_Ominus,axiom, % 178.07/177.91 ! [T_2,T_1] : % 178.07/177.91 ( class_Groups_Ominus(T_1) % 178.07/177.91 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ). % 178.07/177.91 % 178.07/177.91 fof(arity_fun__HOL_Oequal,axiom, % 178.07/177.91 ! [T_1,T_2] : % 178.07/177.91 ( ( class_Enum_Oenum(T_2) % 178.07/177.91 & class_HOL_Oequal(T_1) ) % 178.07/177.91 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ). % 178.07/177.91 % 178.07/177.91 fof(arity_fun__Enum_Oenum,axiom, % 178.07/177.91 ! [T_1,T_2] : % 178.07/177.91 ( ( class_Enum_Oenum(T_2) % 178.07/177.91 & class_Enum_Oenum(T_1) ) % 178.07/177.91 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Com__Ocom__HOL_Oequal,axiom, % 178.07/177.91 class_HOL_Oequal(tc_Com_Ocom) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Com__Ocom__Nat_Osize,axiom, % 178.07/177.91 class_Nat_Osize(tc_Com_Ocom) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 178.07/177.91 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 178.07/177.91 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 178.07/177.91 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 178.07/177.91 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 178.07/177.91 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom, % 178.07/177.91 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 178.07/177.91 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 178.07/177.91 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 178.07/177.91 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 178.07/177.91 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 178.07/177.91 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 178.07/177.91 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 178.07/177.91 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 178.07/177.91 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 178.07/177.91 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 178.07/177.91 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 178.07/177.91 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 178.07/177.91 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 178.07/177.91 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 178.07/177.91 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 178.07/177.91 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 178.07/177.91 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom, % 178.07/177.91 class_Lattices_Osemilattice__sup(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom, % 178.07/177.91 class_Lattices_Osemilattice__inf(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom, % 178.07/177.91 class_Lattices_Odistrib__lattice(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 178.07/177.91 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 178.07/177.91 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 178.07/177.91 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 178.07/177.91 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 178.07/177.91 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 178.07/177.91 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 178.07/177.91 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 178.07/177.91 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 178.07/177.91 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 178.07/177.91 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom, % 178.07/177.91 class_Groups_Osemigroup__add(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 178.07/177.91 class_Divides_Osemiring__div(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 178.07/177.91 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom, % 178.07/177.91 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 178.07/177.91 class_Groups_Oab__group__add(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 178.07/177.91 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 178.07/177.91 class_Rings_Oordered__ring(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 178.07/177.91 class_Orderings_Opreorder(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 178.07/177.91 class_Orderings_Olinorder(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 178.07/177.91 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 178.07/177.91 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 178.07/177.91 class_Groups_Omonoid__add(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Smallcheck_Osmall,axiom, % 178.07/177.91 class_Smallcheck_Osmall(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Osemiring__1,axiom, % 178.07/177.91 class_Rings_Osemiring__1(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 178.07/177.91 class_Rings_Osemiring__0(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Lattices_Olattice,axiom, % 178.07/177.91 class_Lattices_Olattice(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 178.07/177.91 class_Groups_Ogroup__add(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Divides_Oring__div,axiom, % 178.07/177.91 class_Divides_Oring__div(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 178.07/177.91 class_Rings_Omult__zero(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 178.07/177.91 class_Orderings_Oorder(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Int_Oring__char__0,axiom, % 178.07/177.91 class_Int_Oring__char__0(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Int_Onumber__ring,axiom, % 178.07/177.91 class_Int_Onumber__ring(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 178.07/177.91 class_Rings_Osemiring(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Orderings_Oord,axiom, % 178.07/177.91 class_Orderings_Oord(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Ouminus,axiom, % 178.07/177.91 class_Groups_Ouminus(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 178.07/177.91 class_Groups_Osgn__if(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Oabs__if,axiom, % 178.07/177.91 class_Groups_Oabs__if(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 178.07/177.91 class_Rings_Oring__1(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Ominus,axiom, % 178.07/177.91 class_Groups_Ominus(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Power_Opower,axiom, % 178.07/177.91 class_Power_Opower(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Ozero,axiom, % 178.07/177.91 class_Groups_Ozero(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Oring,axiom, % 178.07/177.91 class_Rings_Oring(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Rings_Oidom,axiom, % 178.07/177.91 class_Rings_Oidom(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Int_Onumber,axiom, % 178.07/177.91 class_Int_Onumber(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__Groups_Oone,axiom, % 178.07/177.91 class_Groups_Oone(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Int__Oint__HOL_Oequal,axiom, % 178.07/177.91 class_HOL_Oequal(tc_Int_Oint) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 178.07/177.91 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 178.07/177.91 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 178.07/177.91 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 178.07/177.91 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom, % 178.07/177.91 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 178.07/177.91 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 178.07/177.91 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 178.07/177.91 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 178.07/177.91 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 178.07/177.91 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 178.07/177.91 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 178.07/177.91 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 178.07/177.91 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 178.07/177.91 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom, % 178.07/177.91 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom, % 178.07/177.91 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom, % 178.07/177.91 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 178.07/177.91 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 178.07/177.91 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 178.07/177.91 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 178.07/177.91 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 178.07/177.91 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 178.07/177.91 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 178.07/177.91 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom, % 178.07/177.91 class_Groups_Osemigroup__add(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 178.07/177.91 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 178.07/177.91 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Orderings_Owellorder,axiom, % 178.07/177.91 class_Orderings_Owellorder(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom, % 178.07/177.91 class_Nat_Osemiring__char__0(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 178.07/177.91 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 178.07/177.91 class_Orderings_Opreorder(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 178.07/177.91 class_Orderings_Olinorder(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 178.07/177.91 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 178.07/177.91 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom, % 178.07/177.91 class_Rings_Osemiring__1(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 178.07/177.91 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Lattices_Olattice,axiom, % 178.07/177.91 class_Lattices_Olattice(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 178.07/177.91 class_Rings_Omult__zero(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 178.07/177.91 class_Orderings_Oorder(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 178.07/177.91 class_Rings_Osemiring(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 178.07/177.91 class_Orderings_Oord(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 178.07/177.91 class_Orderings_Obot(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Groups_Ominus,axiom, % 178.07/177.91 class_Groups_Ominus(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Power_Opower,axiom, % 178.07/177.91 class_Power_Opower(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 178.07/177.91 class_Groups_Ozero(tc_Nat_Onat) ). % 178.07/177.91 % 178.07/177.91 fof(arity_Nat__Onat__Int_Onumber,axiom, % 178.07/177.92 class_Int_Onumber(tc_Nat_Onat) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Nat__Onat__Groups_Oone,axiom, % 178.07/177.92 class_Groups_Oone(tc_Nat_Onat) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Nat__Onat__HOL_Oequal,axiom, % 178.07/177.92 class_HOL_Oequal(tc_Nat_Onat) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Nat__Onat__Nat_Osize,axiom, % 178.07/177.92 class_Nat_Osize(tc_Nat_Onat) ). % 178.07/177.92 % 178.07/177.92 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom, % 178.07/177.92 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ). % 178.07/177.92 % 178.07/177.92 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom, % 178.07/177.92 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ). % 178.07/177.92 % 178.07/177.92 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom, % 178.07/177.92 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ). % 178.07/177.92 % 178.07/177.92 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom, % 178.07/177.92 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ). % 178.07/177.92 % 178.07/177.92 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom, % 178.07/177.92 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ). % 178.07/177.92 % 178.07/177.92 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom, % 178.07/177.92 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ). % 178.07/177.92 % 178.07/177.92 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom, % 178.07/177.92 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ). % 178.07/177.92 % 178.07/177.92 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 178.07/177.92 class_Orderings_Opreorder(tc_HOL_Obool) ). % 178.07/177.92 % 178.07/177.92 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 178.07/177.92 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 178.07/177.92 % 178.07/177.92 fof(arity_HOL__Obool__Lattices_Olattice,axiom, % 178.07/177.92 class_Lattices_Olattice(tc_HOL_Obool) ). % 178.07/177.92 % 178.07/177.92 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 178.07/177.92 class_Orderings_Oorder(tc_HOL_Obool) ). % 178.07/177.92 % 178.07/177.92 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 178.07/177.92 class_Orderings_Otop(tc_HOL_Obool) ). % 178.07/177.92 % 178.07/177.92 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 178.07/177.92 class_Orderings_Oord(tc_HOL_Obool) ). % 178.07/177.92 % 178.07/177.92 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 178.07/177.92 class_Orderings_Obot(tc_HOL_Obool) ). % 178.07/177.92 % 178.07/177.92 fof(arity_HOL__Obool__Groups_Ouminus,axiom, % 178.07/177.92 class_Groups_Ouminus(tc_HOL_Obool) ). % 178.07/177.92 % 178.07/177.92 fof(arity_HOL__Obool__Groups_Ominus,axiom, % 178.07/177.92 class_Groups_Ominus(tc_HOL_Obool) ). % 178.07/177.92 % 178.07/177.92 fof(arity_HOL__Obool__HOL_Oequal,axiom, % 178.07/177.92 class_HOL_Oequal(tc_HOL_Obool) ). % 178.07/177.92 % 178.07/177.92 fof(arity_HOL__Obool__Enum_Oenum,axiom, % 178.07/177.92 class_Enum_Oenum(tc_HOL_Obool) ). % 178.07/177.92 % 178.07/177.92 fof(arity_HOL__Obool__Nat_Osize,axiom, % 178.07/177.92 class_Nat_Osize(tc_HOL_Obool) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Com__Ostate__HOL_Oequal,axiom, % 178.07/177.92 class_HOL_Oequal(tc_Com_Ostate) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Com__Ostate__Nat_Osize,axiom, % 178.07/177.92 class_Nat_Osize(tc_Com_Ostate) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Com__Ovname__HOL_Oequal,axiom, % 178.07/177.92 class_HOL_Oequal(tc_Com_Ovname) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Com__Ovname__Nat_Osize,axiom, % 178.07/177.92 class_Nat_Osize(tc_Com_Ovname) ). % 178.07/177.92 % 178.07/177.92 fof(arity_List__Olist__HOL_Oequal,axiom, % 178.07/177.92 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ). % 178.07/177.92 % 178.07/177.92 fof(arity_List__Olist__Nat_Osize,axiom, % 178.07/177.92 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ). % 178.07/177.92 % 178.07/177.92 fof(arity_sum__Finite__Set_Ofinite,axiom, % 178.07/177.92 ! [T_1,T_2] : % 178.07/177.92 ( ( class_Finite__Set_Ofinite(T_2) % 178.07/177.92 & class_Finite__Set_Ofinite(T_1) ) % 178.07/177.92 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 178.07/177.92 % 178.07/177.92 fof(arity_sum__HOL_Oequal,axiom, % 178.07/177.92 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ). % 178.07/177.92 % 178.07/177.92 fof(arity_sum__Enum_Oenum,axiom, % 178.07/177.92 ! [T_1,T_2] : % 178.07/177.92 ( ( class_Enum_Oenum(T_2) % 178.07/177.92 & class_Enum_Oenum(T_1) ) % 178.07/177.92 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ). % 178.07/177.92 % 178.07/177.92 fof(arity_sum__Nat_Osize,axiom, % 178.07/177.92 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 178.07/177.92 ! [T_1] : % 178.07/177.92 ( class_Finite__Set_Ofinite(T_1) % 178.07/177.92 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Option__Ooption__HOL_Oequal,axiom, % 178.07/177.92 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Option__Ooption__Enum_Oenum,axiom, % 178.07/177.92 ! [T_1] : % 178.07/177.92 ( class_Enum_Oenum(T_1) % 178.07/177.92 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Option__Ooption__Nat_Osize,axiom, % 178.07/177.92 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ). % 178.07/177.92 % 178.07/177.92 fof(arity_prod__Finite__Set_Ofinite,axiom, % 178.07/177.92 ! [T_1,T_2] : % 178.07/177.92 ( ( class_Finite__Set_Ofinite(T_2) % 178.07/177.92 & class_Finite__Set_Ofinite(T_1) ) % 178.07/177.92 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 178.07/177.92 % 178.07/177.92 fof(arity_prod__Smallcheck_Osmall,axiom, % 178.07/177.92 ! [T_1,T_2] : % 178.07/177.92 ( ( class_Smallcheck_Osmall(T_2) % 178.07/177.92 & class_Smallcheck_Osmall(T_1) ) % 178.07/177.92 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ). % 178.07/177.92 % 178.07/177.92 fof(arity_prod__HOL_Oequal,axiom, % 178.07/177.92 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ). % 178.07/177.92 % 178.07/177.92 fof(arity_prod__Enum_Oenum,axiom, % 178.07/177.92 ! [T_1,T_2] : % 178.07/177.92 ( ( class_Enum_Oenum(T_2) % 178.07/177.92 & class_Enum_Oenum(T_1) ) % 178.07/177.92 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ). % 178.07/177.92 % 178.07/177.92 fof(arity_prod__Nat_Osize,axiom, % 178.07/177.92 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 178.07/177.92 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom, % 178.07/177.92 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom, % 178.07/177.92 class_HOL_Oequal(tc_Product__Type_Ounit) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom, % 178.07/177.92 class_Enum_Oenum(tc_Product__Type_Ounit) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Product____Type__Ounit__Nat_Osize,axiom, % 178.07/177.92 class_Nat_Osize(tc_Product__Type_Ounit) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom, % 178.07/177.92 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom, % 178.07/177.92 class_Nat_Osize(tc_Code__Evaluation_Oterm) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom, % 178.07/177.92 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom, % 178.07/177.92 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 178.07/177.92 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 178.07/177.92 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom, % 178.07/177.92 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom, % 178.07/177.92 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom, % 178.07/177.92 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom, % 178.07/177.92 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom, % 178.07/177.92 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom, % 178.07/177.92 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom, % 178.07/177.92 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom, % 178.07/177.92 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom, % 178.07/177.92 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom, % 178.07/177.92 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom, % 178.07/177.92 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom, % 178.07/177.92 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom, % 178.07/177.92 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom, % 178.07/177.92 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom, % 178.07/177.92 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom, % 178.07/177.92 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom, % 178.07/177.92 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom, % 178.07/177.92 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom, % 178.07/177.92 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom, % 178.07/177.92 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom, % 178.07/177.92 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom, % 178.07/177.92 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom, % 178.07/177.92 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom, % 178.07/177.92 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom, % 178.07/177.92 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom, % 178.07/177.92 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom, % 178.07/177.92 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom, % 178.07/177.92 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom, % 178.07/177.92 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom, % 178.07/177.92 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom, % 178.07/177.92 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom, % 178.07/177.92 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom, % 178.07/177.92 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom, % 178.07/177.92 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom, % 178.07/177.92 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom, % 178.07/177.92 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom, % 178.07/177.92 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom, % 178.07/177.92 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom, % 178.07/177.92 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom, % 178.07/177.92 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom, % 178.07/177.92 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 178.07/177.92 % 178.07/177.92 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom, % 178.07/177.92 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 178.07/177.92 % 178.07/177.92 %----Helper facts (20) % 178.07/177.92 fof(help_c__COMBI__1,axiom, % 178.07/177.92 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 178.07/177.92 % 178.07/177.92 fof(help_c__COMBK__1,axiom, % 178.07/177.92 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 178.07/177.92 % 178.07/177.92 fof(help_c__COMBB__1,axiom, % 178.07/177.92 ! [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)) ). % 178.07/177.92 % 178.07/177.92 fof(help_c__COMBC__1,axiom, % 178.07/177.92 ! [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) ). % 178.07/177.92 % 178.07/177.92 fof(help_c__COMBS__1,axiom, % 178.07/177.92 ! [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)) ). % 178.07/177.92 % 178.07/177.92 fof(help_c__fequal__1,axiom, % 178.07/177.92 ! [V_y_2,V_x_2] : % 178.07/177.92 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 178.07/177.92 | V_x_2 = V_y_2 ) ). % 178.07/177.92 % 178.07/177.92 fof(help_c__fequal__2,axiom, % 178.07/177.92 ! [V_y_2,V_x_2] : % 178.07/177.92 ( V_x_2 != V_y_2 % 178.07/177.92 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 178.07/177.92 % 178.07/177.92 fof(help_c__fFalse__1,axiom, % 178.07/177.92 ~ hBOOL(c_fFalse) ). % 178.07/177.92 % 178.07/177.92 fof(help_c__fTrue__1,axiom, % 178.07/177.92 hBOOL(c_fTrue) ). % 178.07/177.92 % 178.07/177.92 fof(help_c__fNot__1,axiom, % 178.07/177.92 ! [V_P_2] : % 178.07/177.92 ( ~ hBOOL(hAPP(c_fNot,V_P_2)) % 178.07/177.92 | ~ hBOOL(V_P_2) ) ). % 178.07/177.92 % 178.07/177.92 fof(help_c__fNot__2,axiom, % 178.07/177.92 ! [V_P_2] : % 178.07/177.92 ( ~ ~ hBOOL(V_P_2) % 178.07/177.92 | hBOOL(hAPP(c_fNot,V_P_2)) ) ). % 178.07/177.92 % 178.07/177.92 fof(help_c__fconj__1,axiom, % 178.07/177.92 ! [V_Q_2,V_P_2] : % 178.07/177.92 ( ~ hBOOL(V_P_2) % 178.07/177.92 | ~ hBOOL(V_Q_2) % 178.07/177.92 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ). % 178.07/177.92 % 178.07/177.92 fof(help_c__fconj__2,axiom, % 178.07/177.92 ! [V_Q_2,V_P_2] : % 178.07/177.92 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 178.07/177.92 | hBOOL(V_P_2) ) ). % 178.07/177.92 % 178.07/177.92 fof(help_c__fconj__3,axiom, % 178.07/177.92 ! [V_Q_2,V_P_2] : % 178.07/177.92 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 178.07/177.92 | hBOOL(V_Q_2) ) ). % 178.07/177.92 % 178.07/177.92 fof(help_c__fdisj__1,axiom, % 178.07/177.92 ! [V_Q_2,V_P_2] : % 178.07/177.92 ( ~ hBOOL(V_P_2) % 178.07/177.92 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 178.07/177.92 % 178.07/177.92 fof(help_c__fdisj__2,axiom, % 178.07/177.92 ! [V_P_2,V_Q_2] : % 178.07/177.92 ( ~ hBOOL(V_Q_2) % 178.07/177.92 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 178.07/177.92 % 178.07/177.92 fof(help_c__fdisj__3,axiom, % 178.07/177.92 ! [V_Q_2,V_P_2] : % 178.07/177.92 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) % 178.07/177.92 | hBOOL(V_P_2) % 178.07/177.92 | hBOOL(V_Q_2) ) ). % 178.07/177.92 % 178.07/177.92 fof(help_c__fimplies__1,axiom, % 178.07/177.92 ! [V_Q_2,V_P_2] : % 178.07/177.92 ( hBOOL(V_P_2) % 178.07/177.92 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 178.07/177.92 % 178.07/177.92 fof(help_c__fimplies__2,axiom, % 178.07/177.92 ! [V_P_2,V_Q_2] : % 178.07/177.92 ( ~ hBOOL(V_Q_2) % 178.07/177.92 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 178.07/177.92 % 178.07/177.92 fof(help_c__fimplies__3,axiom, % 178.07/177.92 ! [V_Q_2,V_P_2] : % 178.07/177.92 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) % 178.07/177.92 | ~ hBOOL(V_P_2) % 178.07/177.92 | hBOOL(V_Q_2) ) ). % 178.07/177.92 % 178.07/177.92 %----Conjectures (4) % 178.07/177.92 fof(conj_0,hypothesis, % 178.07/177.92 c_Hoare__Mirabelle_Ostate__not__singleton ). % 178.07/177.92 % 178.07/177.92 fof(conj_1,hypothesis, % 178.07/177.92 c_Com_OWT__bodies ). % 178.07/177.92 % 178.07/177.92 fof(conj_2,hypothesis, % 178.07/177.92 hBOOL(hAPP(c_Com_OWT,v_c)) ). % 178.07/177.92 % 178.07/177.92 fof(conj_3,conjecture, % 178.07/177.92 v_Sledgehammer_058uG__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)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)) ). % 178.07/177.92 % 178.07/177.92 %------------------------------------------------------------------------------ % 178.07/177.92 %------------------------------------------- % 178.07/177.92 % Proof found % 178.07/177.92 % SZS status Theorem for theBenchmark % 178.07/177.92 % SZS output start Proof % 178.07/177.92 %ClaNum:10184(EqnAxiom:2853) % 178.07/177.92 %VarNum:70012(SingletonVarNum:20426) % 178.07/177.92 %MaxLitNum:8 % 178.07/177.92 %MaxfuncDepth:15 % 178.07/177.92 %SharedTerms:1085 % 178.07/177.92 %goalClause: 4546 % 178.07/177.92 %singleGoalClaCount:1 % 178.07/177.92 [2854]P1(a5000) % 178.07/177.92 [2855]P4(a5000) % 178.07/177.92 [2859]P24(a192) % 178.07/177.92 [2860]P25(a869) % 178.07/177.92 [2861]P25(a875) % 178.07/177.92 [2862]P26(a869) % 178.07/177.92 [2863]P26(a878) % 178.07/177.92 [2864]P63(a869) % 178.07/177.92 [2865]P63(a875) % 178.07/177.92 [2866]P63(a1) % 178.07/177.92 [2867]P64(a869) % 178.07/177.92 [2868]P99(a869) % 178.07/177.92 [2869]P99(a875) % 178.07/177.92 [2870]P99(a1) % 178.07/177.92 [2871]P65(a869) % 178.07/177.92 [2872]P65(a875) % 178.07/177.92 [2873]P65(a1) % 178.07/177.92 [2874]P65(a105) % 178.07/177.92 [2875]P77(a1) % 178.07/177.92 [2876]P81(a869) % 178.07/177.92 [2877]P81(a1) % 178.07/177.92 [2878]P89(a869) % 178.07/177.92 [2879]P100(a869) % 178.07/177.92 [2880]P100(a875) % 178.07/177.92 [2881]P100(a1) % 178.07/177.92 [2882]P97(a869) % 178.07/177.92 [2883]P97(a875) % 178.07/177.92 [2884]P97(a1) % 178.07/177.92 [2885]P66(a1) % 178.07/177.92 [2886]P103(a869) % 178.07/177.92 [2887]P98(a869) % 178.07/177.92 [2888]P67(a1) % 178.07/177.92 [2889]P108(a1) % 178.07/177.92 [2890]P68(a875) % 178.07/177.92 [2891]P68(a1) % 178.07/177.92 [2892]P68(a105) % 178.07/177.92 [2893]P70(a875) % 178.07/177.92 [2894]P70(a1) % 178.07/177.92 [2895]P70(a105) % 178.07/177.92 [2896]P134(a875) % 178.07/177.92 [2897]P134(a1) % 178.07/177.92 [2898]P134(a105) % 178.07/177.92 [2899]P109(a1) % 178.07/177.92 [2900]P27(a869) % 178.07/177.92 [2901]P74(a875) % 178.07/177.92 [2902]P74(a1) % 178.07/177.92 [2903]P74(a105) % 178.07/177.92 [2904]P78(a875) % 178.07/177.92 [2905]P78(a1) % 178.07/177.92 [2906]P78(a105) % 178.07/177.92 [2907]P69(a875) % 178.07/177.92 [2908]P69(a1) % 178.07/177.92 [2909]P69(a105) % 178.07/177.92 [2910]P71(a875) % 178.07/177.92 [2911]P71(a1) % 178.07/177.92 [2912]P71(a105) % 178.07/177.92 [2913]P72(a875) % 178.07/177.92 [2914]P72(a1) % 178.07/177.92 [2915]P72(a105) % 178.07/177.92 [2916]P135(a875) % 178.07/177.92 [2917]P135(a1) % 178.07/177.92 [2918]P135(a105) % 178.07/177.92 [2919]P110(a875) % 178.07/177.92 [2920]P110(a1) % 178.07/177.92 [2921]P110(a105) % 178.07/177.92 [2922]P79(a875) % 178.07/177.92 [2923]P79(a1) % 178.07/177.92 [2924]P79(a105) % 178.07/177.92 [2925]P136(a1) % 178.07/177.92 [2926]P111(a1) % 178.07/177.92 [2927]P114(a875) % 178.07/177.92 [2928]P114(a1) % 178.07/177.92 [2929]P114(a105) % 178.07/177.92 [2930]P139(a875) % 178.07/177.92 [2931]P139(a1) % 178.07/177.92 [2932]P104(a869) % 178.07/177.92 [2933]P104(a875) % 178.07/177.92 [2934]P104(a1) % 178.07/177.92 [2935]P104(a105) % 178.07/177.92 [2936]P82(a875) % 178.07/177.92 [2937]P82(a1) % 178.07/177.92 [2938]P82(a105) % 178.07/177.92 [2939]P105(a875) % 178.07/177.92 [2940]P105(a1) % 178.07/177.92 [2941]P105(a105) % 178.07/177.92 [2942]P106(a869) % 178.07/177.92 [2943]P106(a875) % 178.07/177.92 [2944]P106(a1) % 178.07/177.92 [2945]P106(a105) % 178.07/177.92 [2946]P107(a869) % 178.07/177.92 [2947]P107(a875) % 178.07/177.92 [2948]P107(a1) % 178.07/177.92 [2949]P107(a105) % 178.07/177.92 [2950]P117(a1) % 178.07/177.92 [2951]P83(a875) % 178.07/177.92 [2952]P83(a1) % 178.07/177.92 [2953]P83(a105) % 178.07/177.92 [2954]P84(a875) % 178.07/177.92 [2955]P84(a1) % 178.07/177.92 [2956]P84(a105) % 178.07/177.92 [2957]P120(a875) % 178.07/177.92 [2958]P120(a1) % 178.07/177.92 [2959]P120(a105) % 178.07/177.92 [2960]P123(a1) % 178.07/177.92 [2961]P137(a1) % 178.07/177.92 [2962]P112(a875) % 178.07/177.92 [2963]P112(a1) % 178.07/177.92 [2964]P112(a105) % 178.07/177.92 [2965]P124(a875) % 178.07/177.92 [2966]P124(a1) % 178.07/177.92 [2967]P124(a105) % 178.07/177.92 [2968]P129(a875) % 178.07/177.92 [2969]P129(a1) % 178.07/177.92 [2970]P129(a105) % 178.07/177.92 [2971]P140(a875) % 178.07/177.92 [2972]P140(a1) % 178.07/177.92 [2973]P140(a105) % 178.07/177.92 [2974]P90(a875) % 178.07/177.92 [2975]P90(a1) % 178.07/177.92 [2976]P90(a105) % 178.07/177.92 [2977]P80(a875) % 178.07/177.92 [2978]P80(a1) % 178.07/177.92 [2979]P80(a105) % 178.07/177.92 [2980]P75(a1) % 178.07/177.92 [2981]P138(a1) % 178.07/177.92 [2982]P86(a875) % 178.07/177.92 [2983]P86(a1) % 178.07/177.92 [2984]P86(a105) % 178.07/177.92 [2985]P130(a875) % 178.07/177.92 [2986]P130(a1) % 178.07/177.92 [2987]P130(a105) % 178.07/177.92 [2988]P132(a875) % 178.07/177.92 [2989]P132(a1) % 178.07/177.92 [2990]P132(a105) % 178.07/177.92 [2991]P131(a875) % 178.07/177.92 [2992]P131(a1) % 178.07/177.92 [2993]P131(a105) % 178.07/177.92 [2994]P121(a1) % 178.07/177.92 [2995]P122(a1) % 178.07/177.92 [2996]P118(a875) % 178.07/177.92 [2997]P118(a1) % 178.07/177.92 [2998]P118(a105) % 178.07/177.92 [2999]P125(a875) % 178.07/177.92 [3000]P125(a1) % 178.07/177.92 [3001]P125(a105) % 178.07/177.92 [3002]P126(a875) % 178.07/177.92 [3003]P126(a1) % 178.07/177.92 [3004]P126(a105) % 178.07/177.92 [3005]P127(a1) % 178.07/177.92 [3006]P128(a1) % 178.07/177.92 [3007]P101(a875) % 178.07/177.92 [3008]P101(a1) % 178.07/177.92 [3009]P101(a105) % 178.07/177.92 [3010]P141(a875) % 178.07/177.92 [3011]P141(a1) % 178.07/177.92 [3012]P141(a105) % 178.07/177.92 [3013]P56(a875) % 178.07/177.92 [3014]P56(a1) % 178.07/177.92 [3015]P56(a105) % 178.07/177.92 [3016]P91(a1) % 178.07/177.92 [3017]P57(a1) % 178.07/177.92 [3018]P87(a1) % 178.07/177.92 [3019]P85(a1) % 178.07/177.92 [3020]P133(a1) % 178.07/177.92 [3021]P73(a1) % 178.07/177.92 [3022]P76(a875) % 178.07/177.92 [3023]P76(a1) % 178.07/177.92 [3024]P76(a105) % 178.07/177.92 [3025]P92(a1) % 178.07/177.92 [3026]P93(a875) % 178.07/177.92 [3027]P93(a1) % 178.07/177.92 [3028]P93(a105) % 178.07/177.92 [3029]P142(a878) % 178.07/177.92 [3030]P142(a1) % 178.07/177.92 [3031]P88(a875) % 178.07/177.92 [3032]P88(a1) % 178.07/177.92 [3033]P88(a105) % 178.07/177.92 [3034]P58(a869) % 178.07/177.92 [3035]P58(a878) % 178.07/177.92 [3036]P94(a870) % 178.07/177.92 [3037]P94(a871) % 178.07/177.92 [3038]P94(a869) % 178.07/177.92 [3039]P94(a875) % 178.07/177.92 [3040]P94(a878) % 178.07/177.92 [3041]P94(a1) % 178.07/177.92 [3042]P94(a325) % 178.07/177.92 [3043]P94(a105) % 178.07/177.92 [3044]P94(a873) % 178.07/177.92 [3045]P113(a875) % 178.07/177.92 [3046]P102(a870) % 178.07/177.92 [3047]P102(a871) % 178.07/177.92 [3048]P102(a869) % 178.07/177.92 [3049]P102(a875) % 178.07/177.92 [3050]P102(a878) % 178.07/177.92 [3051]P102(a325) % 178.07/177.92 [3052]P102(a105) % 178.07/177.92 [3053]P102(a873) % 178.07/177.92 [3054]P96(a869) % 178.07/177.92 [3074]P38(a875,a248) % 178.07/177.92 [3075]P38(a875,a319) % 178.07/177.92 [4436]~E(a103,a84) % 178.07/177.92 [4437]~P24(a247) % 178.07/177.92 [2856]E(f2(a1),a84) % 178.07/177.92 [2857]E(f106(a105),a3) % 178.07/177.92 [2858]E(f22(a105),a23) % 178.07/177.92 [3055]E(f193(a875),f2(a875)) % 178.07/177.92 [3056]E(f32(a24),f2(a875)) % 178.07/177.92 [3057]E(f107(a875),f241(a875)) % 178.07/177.92 [3058]E(f116(a875),f242(a875)) % 178.07/177.92 [3059]E(f108(a1),f35(a1)) % 178.07/177.92 [3060]E(f85(a247),f2(a875)) % 178.07/177.92 [3061]E(f85(a192),f2(a875)) % 178.07/177.92 [3062]P28(f79(a1)) % 178.07/177.92 [3063]P28(f2(a1)) % 178.07/177.92 [3112]P24(f329(a25,a24)) % 178.07/177.92 [3113]P24(f329(a25,a880)) % 178.07/177.92 [3126]P38(f882(a875,a875),a36) % 178.07/177.92 [3479]E(f321(a875,a875,a248,a248),a36) % 178.07/177.92 [4438]~E(f79(a1),f2(a1)) % 178.07/177.92 [3064]E(f117(f2(a875)),f2(a875)) % 178.07/177.92 [3065]E(f4(f2(a105)),f2(a875)) % 178.07/177.92 [3077]E(f329(f80(a1),a84),a84) % 178.07/177.92 [3080]E(f329(a118,f2(a875)),f79(a875)) % 178.07/177.92 [3081]E(f329(a110,f79(a1)),f79(a875)) % 178.07/177.92 [3082]E(f329(a3,f79(a875)),f79(a105)) % 178.07/177.92 [3084]E(f329(a3,f2(a875)),f2(a105)) % 178.07/177.92 [3086]E(f329(f109(a1),a84),f2(a1)) % 178.07/177.92 [3087]E(f329(f109(a105),a84),f2(a105)) % 178.07/177.92 [3088]E(f329(a110,f2(a1)),f2(a875)) % 178.07/177.92 [3089]E(f329(f194(a870),a24),f2(a875)) % 178.07/177.92 [3090]E(f329(f194(a869),a247),f2(a875)) % 178.07/177.92 [3091]E(f329(f194(a869),a192),f2(a875)) % 178.07/177.92 [3092]E(f329(f109(a875),a84),f2(a875)) % 178.07/177.92 [3096]E(f329(f80(a1),f79(a1)),a103) % 178.07/177.92 [3103]E(f329(f80(a1),f2(a1)),f2(a1)) % 178.07/177.92 [3105]E(f329(f194(a105),f2(a105)),f2(a875)) % 178.07/177.92 [3106]E(f329(f106(a1),f79(a875)),f79(a1)) % 178.07/177.92 [3107]E(f329(f106(a1),f2(a875)),f2(a1)) % 178.07/177.92 [3122]E(f329(a110,f79(a1)),f329(a118,f2(a875))) % 178.07/177.92 [3123]E(f329(f177(a872,a870),a27),a28) % 178.07/177.92 [3124]E(f320(f882(a875,a875),a36),a37) % 178.07/177.92 [3125]E(f322(f882(a875,a875),a36),a69) % 178.07/177.92 [3147]E(f329(f250(a875),f2(a875)),f193(f883(a875,a869))) % 178.07/177.92 [3148]E(f329(f251(a875),f2(a875)),f252(f883(a875,a869))) % 178.07/177.92 [3156]P39(f193(f883(a1,a869))) % 178.07/177.92 [3192]E(f329(f329(f22(a105),f2(a105)),f79(a105)),f2(a105)) % 178.07/177.92 [3271]P24(f329(f329(f244(a1),a103),f2(a1))) % 178.07/177.92 [3296]P24(f329(f329(f244(a1),f2(a1)),f79(a1))) % 178.07/177.92 [3297]P24(f329(f329(f243(a1),f2(a1)),f79(a1))) % 178.07/177.92 [3472]P24(f329(f62(a872),f183(a872,a870,a28))) % 178.07/177.92 [3509]E(f329(f329(f286(a875,a875,a875),a319),f305(a875,a319)),a248) % 178.07/177.92 [3547]P41(a1,a875,a110,f329(f243(a1),f2(a1))) % 178.07/177.92 [3551]E(f329(f329(f42(a875,f883(a875,a869)),f252(f883(a875,a869))),f301(a875)),f193(f883(a875,a869))) % 178.07/177.92 [3552]E(f329(f329(f43(a875,f883(a875,a869)),f252(f883(a875,a869))),f250(a875)),f252(f883(a875,a869))) % 178.07/177.92 [3553]E(f329(f329(f43(a875,f883(a875,a869)),f252(f883(a875,a869))),f251(a875)),f252(f883(a875,a869))) % 178.07/177.92 [3554]E(f329(f329(f43(a875,f883(a875,a869)),f252(f883(a875,a869))),f298(a875)),f252(f883(a875,a869))) % 178.07/177.92 [3570]P21(a875,a1,f106(a1),f252(f883(a875,a869))) % 178.07/177.92 [3581]P41(a875,a1,f106(a1),f329(f16(a869,a875),a192)) % 178.07/177.92 [3716]E(f329(f74(a875,a105,a1,a3),a110),f109(a105)) % 178.07/177.92 [3937]P52(a105,a875,a19,a3,f252(f883(a875,a869))) % 178.07/177.92 [3946]P52(a1,f883(f882(a875,a875),a869),a112,a90,a104) % 178.07/177.92 [4211]E(f269(a1,a1,a1,a1,f35(a1),f80(a1)),a51) % 178.07/177.92 [4461]~E(f329(f109(a1),a103),f329(f109(a1),a84)) % 178.07/177.92 [4462]~P24(f329(a198,f79(a1))) % 178.07/177.92 [4463]~P24(f329(a198,f2(a1))) % 178.07/177.92 [4512]~P24(f329(f329(f244(a1),a84),f2(a1))) % 178.07/177.92 [4546]~E(f329(f308(a872,f874(a871),f329(f329(f8(a870,f874(a871),a872),a94),a26)),f183(a872,a870,a28)),a884) % 178.07/177.92 [3139]E(f329(f329(f22(a1),a103),a103),a84) % 178.07/177.92 [3154]E(f329(f106(a1),f329(a118,f2(a875))),f79(a1)) % 178.07/177.92 [3220]E(f329(f38(a878),f252(f883(a878,a869))),f79(a875)) % 178.07/177.92 [3241]P24(f329(a198,f329(f109(a1),a103))) % 178.07/177.92 [3242]P24(f329(f329(f244(a1),a103),a84)) % 178.07/177.92 [3244]P24(f329(f329(f243(a1),a103),a84)) % 178.07/177.92 [3309]E(f329(f329(f307(a875),f2(a875)),f193(f883(a875,a869))),f329(f298(a875),f2(a875))) % 178.07/177.92 [3365]P24(f329(f329(f243(a1),f2(a1)),f329(f109(a1),a84))) % 178.07/177.92 [3377]E(f329(f308(a875,a875,a118),f252(f883(a875,a869))),f329(f301(a875),f2(a875))) % 178.07/177.92 [3416]P6(f882(a875,a875),f252(f883(f882(a875,a875),a869)),a114) % 178.07/177.92 [3724]E(f329(f74(a875,a1,a105,f106(a1)),a19),a20) % 178.07/177.92 [3783]P38(a875,f329(f249(f882(a875,a875)),f329(f268(a875,a875,a869),f244(a875)))) % 178.07/177.92 [4501]~P24(f329(a198,f329(f109(a1),a84))) % 178.07/177.92 [4502]~P24(f329(f329(f244(a1),a84),a84)) % 178.07/177.92 [4503]~P24(f329(f329(f244(a1),a84),a103)) % 178.07/177.92 [4504]~P24(f329(f329(f244(a1),a103),a103)) % 178.07/177.92 [4505]~P24(f329(f329(f243(a1),a84),a103)) % 178.07/177.92 [4506]~P24(f329(f329(f92(a1),a84),a103)) % 178.07/177.92 [4507]~P24(f329(f329(f92(a1),a103),a84)) % 178.07/177.92 [4522]~P24(f329(f62(a875),f252(f883(a875,a869)))) % 178.07/177.92 [4523]~P24(f329(f62(a1),f252(f883(a1,a869)))) % 178.07/177.92 [4382]E(f329(f268(a1,a1,a869),f329(f329(f8(f883(a1,a869),f883(a1,a869),a1),f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f244(a1),f2(a1))))),f329(f329(f7(a1,a1,f883(a1,a869)),f329(f329(f8(f883(a1,f883(a1,a869)),f883(a1,f883(a1,a869)),a1),f7(a1,a1,a869)),f329(f329(f8(f883(a1,a1),f883(a1,f883(a1,a869)),a1),f329(f8(a1,f883(a1,a869),a1),a326)),a225))),f79(a1)))),a221) % 178.07/177.92 [3454]E(f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103),f329(f80(a1),a103)) % 178.07/177.92 [3492]E(f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103),f329(f329(f22(a1),a84),a103)) % 178.07/177.92 [3650]E(f329(f329(f61(f882(a875,a875)),f252(f883(f882(a875,a875),a869))),a114),a104) % 178.07/177.92 [3679]E(f329(f109(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f79(a1)) % 178.07/177.92 [3680]E(f329(f109(a105),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f79(a105)) % 178.07/177.92 [3681]E(f329(f109(a875),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f79(a875)) % 178.07/177.92 [3685]E(f329(f109(a875),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(a118,f2(a875))) % 178.07/177.92 [4071]E(f329(f329(f116(f883(f882(f882(a875,a875),f882(a875,a875)),a869)),a36),f305(f882(a875,a875),f193(f883(f882(f882(a875,a875),f882(a875,a875)),a869)))),a71) % 178.07/177.92 [4142]E(f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),f79(a875)),f2(a875))),f193(f883(f882(a875,a875),a869))))),f79(a1)) % 178.07/177.92 [4143]E(f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),f2(a875)),f2(a875))),f193(f883(f882(a875,a875),a869))))),f2(a1)) % 178.07/177.92 [4158]E(f329(f249(f882(a875,a875)),f329(f268(a875,a875,a869),f329(f329(f8(a875,f883(a875,a869),a875),f329(f7(a875,a875,a869),a326)),a118))),a319) % 178.07/177.92 [4128]E(f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))),f329(a118,f329(a118,f2(a875)))) % 178.07/177.92 [4131]E(f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))),f329(f329(f81(a875),f79(a875)),f79(a875))) % 178.07/177.92 [4132]E(f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))),f329(f38(a869),f252(f883(a869,a869)))) % 178.07/177.92 [4197]P28(f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))) % 178.07/177.92 [4269]P22(f883(f882(a875,a875),a869),f329(f329(f264(f883(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),a869),f883(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),a869)),a37),a70)) % 178.07/177.92 [4270]P22(f883(f882(a875,a875),a869),f329(f329(f264(f883(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),a869),f883(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),a869)),a69),a72)) % 178.07/177.92 [4310]E(f329(f329(f116(f883(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),a869)),f322(f882(a875,a875),a71)),f329(f329(f307(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869))),f329(f329(f264(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),f193(f883(f882(a875,a875),a869))),f193(f883(f882(a875,a875),a869)))),f193(f883(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),a869)))),a72) % 178.07/177.92 [4311]E(f329(f329(f116(f883(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),a869)),f320(f882(a875,a875),a71)),f329(f329(f307(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869))),f329(f329(f264(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),f193(f883(f882(a875,a875),a869))),f193(f883(f882(a875,a875),a869)))),f193(f883(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),a869)))),a70) % 178.07/177.92 [4199]E(f329(a110,f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f329(a118,f329(a118,f2(a875)))) % 178.07/177.92 [4246]E(f329(f106(a1),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))) % 178.07/177.92 [4281]P24(f329(f329(f243(a1),f2(a1)),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))) % 178.07/177.92 [4282]E(f329(f109(a875),f329(f329(f22(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))),a103)),f329(a118,f329(a118,f329(a118,f2(a875))))) % 178.07/177.92 [4324]P28(f329(f109(a1),f329(f329(f22(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))),a103))) % 178.07/177.92 [4352]E(f329(f106(a1),f329(f109(a875),f329(f329(f22(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))),a103))),f329(f109(a1),f329(f329(f22(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))),a103))) % 178.07/177.92 [4367]P24(f329(f329(f243(a1),f2(a1)),f329(f109(a1),f329(f329(f22(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))),a103)))) % 178.07/177.92 [3076]P5(x30761,a326) % 178.07/177.92 [3480]P21(a875,a875,a118,x34801) % 178.07/177.92 [3066]P94(f874(x30661)) % 178.07/177.92 [3067]P94(f879(x30671)) % 178.07/177.92 [3068]P94(f876(x30681)) % 178.07/177.92 [3069]P94(f877(x30691)) % 178.07/177.92 [3070]P102(f874(x30701)) % 178.07/177.92 [3071]P102(f879(x30711)) % 178.07/177.92 [3072]P102(f876(x30721)) % 178.07/177.92 [3073]P102(f877(x30731)) % 178.07/177.92 [3093]P38(a1,f111(x30931)) % 178.07/177.92 [3094]P38(a1,f113(x30941)) % 178.07/177.92 [3144]P38(f883(x31441,a869),f304(x31441)) % 178.07/177.92 [3168]E(f253(x31681,x31681,a326),a326) % 178.07/177.92 [3183]E(f45(a1,x31831,x31831),f2(a1)) % 178.07/177.92 [3238]P11(x32381,f883(x32381,a869),f307(x32381)) % 178.07/177.92 [4440]~E(f329(a26,x44401),a24) % 178.07/177.92 [4442]~E(f329(a118,x44421),x44421) % 178.07/177.92 [4452]~E(f329(a118,x44521),f2(a875)) % 178.07/177.92 [3078]E(f329(f194(a875),x30781),x30781) % 178.07/177.92 [3079]E(f329(f109(a1),x30791),x30791) % 178.07/177.92 [3095]E(f329(a90,f330(x30951)),x30951) % 178.07/177.92 [3108]E(f120(x31081,f119(x31081)),f119(x31081)) % 178.07/177.92 [3109]E(f151(x31091,f119(x31091)),f119(x31091)) % 178.07/177.92 [3114]E(f32(f329(a26,x31141)),f2(a875)) % 178.07/177.92 [3119]E(f329(f167(x31191),f119(x31191)),f119(x31191)) % 178.07/177.92 [3120]E(f329(f170(x31201),f119(x31201)),f119(x31201)) % 178.07/177.92 [3121]E(f329(f168(x31211),f119(x31211)),f119(x31211)) % 178.07/177.92 [3127]E(f329(f109(a1),x31271),f329(f108(a1),x31271)) % 178.07/177.92 [3128]E(f329(a90,f329(a112,x31281)),x31281) % 178.07/177.92 [3130]E(f329(a3,f329(a19,x31301)),x31301) % 178.07/177.92 [3131]E(f329(a19,f329(a3,x31311)),x31311) % 178.07/177.92 [3132]P28(f329(f106(a1),x31321)) % 178.07/177.92 [3137]E(f329(f194(f879(x31371)),f206(x31371)),f2(a875)) % 178.07/177.92 [3138]E(f329(f194(f876(x31381)),f119(x31381)),f2(a875)) % 178.07/177.92 [3143]E(f329(f194(a870),f329(a26,x31431)),f2(a875)) % 178.07/177.92 [3152]E(f235(x31521,f206(x31521)),f193(f883(x31521,a869))) % 178.07/177.92 [3159]E(f329(f329(f22(a875),x31591),f2(a875)),x31591) % 178.07/177.92 [3160]E(f329(f329(f82(a875),x31601),f79(a875)),x31601) % 178.07/177.92 [3161]E(f329(f329(f82(a1),x31611),f79(a1)),x31611) % 178.07/177.92 [3162]E(f329(f329(f81(a875),x31621),f2(a875)),x31621) % 178.07/177.92 [3163]E(f329(f329(f81(a1),x31631),f2(a1)),x31631) % 178.07/177.92 [3164]E(f329(f329(f242(a875),x31641),f2(a875)),x31641) % 178.07/177.92 [3165]E(f329(f329(f82(a875),x31651),f2(a875)),f2(a875)) % 178.07/177.92 [3166]E(f329(f329(f39(a1),x31661),f2(a1)),f2(a1)) % 178.07/177.92 [3167]E(f329(f329(f241(a875),x31671),f2(a875)),f2(a875)) % 178.07/177.92 [3174]E(f329(f171(x31741),f119(x31741)),f193(f883(x31741,a869))) % 178.07/177.92 [3178]P24(f329(f136(x31781),f119(x31781))) % 178.07/177.92 [3184]E(f329(f207(x31841,x31841),f5(x31841)),f35(f879(x31841))) % 178.07/177.92 [3185]E(f329(f207(x31851,x31851),f35(x31851)),f35(f879(x31851))) % 178.07/177.92 [3186]E(f329(f153(x31861,x31861),f5(x31861)),f35(f876(x31861))) % 178.07/177.92 [3187]E(f329(f153(x31871,x31871),f35(x31871)),f35(f876(x31871))) % 178.07/177.92 [3188]E(f45(a1,x31881,f2(a1)),x31881) % 178.07/177.92 [3189]E(f329(f243(a875),f329(a118,x31891)),f329(f244(a875),x31891)) % 178.07/177.92 [3190]E(f329(f250(a875),f329(a118,x31901)),f329(f298(a875),x31901)) % 178.07/177.92 [3191]E(f329(f251(a875),f329(a118,x31911)),f329(f301(a875),x31911)) % 178.07/177.92 [3193]E(f45(a1,f2(a1),x31931),f2(a1)) % 178.07/177.92 [3204]E(f329(f329(f81(a875),x32041),f79(a875)),f329(a118,x32041)) % 178.07/177.92 [3214]E(f329(f299(a875,x32141),f2(a875)),f193(f883(a875,a869))) % 178.07/177.92 [3226]E(f300(a875,f2(a875),x32261),f329(f298(a875),x32261)) % 178.07/177.92 [3274]E(f329(f329(f22(a875),f329(a118,x32741)),f79(a875)),x32741) % 178.07/177.92 [3287]E(f47(f2(a1),x32871),f329(f329(f264(a1,a1),f2(a1)),f2(a1))) % 178.07/177.92 [3304]E(f329(f329(f329(f93(a871),a326),x33041),f199(x33041)),f329(a94,x33041)) % 178.07/177.92 [3339]P24(f329(f329(f244(a875),x33391),f329(a118,x33391))) % 178.07/177.92 [3351]P24(f329(f329(f244(a875),f2(a875)),f329(a118,x33511))) % 178.07/177.92 [3636]E(f329(f329(f22(a105),f329(a3,f329(a118,f329(a19,x36361)))),f79(a105)),x36361) % 178.07/177.92 [3708]P24(f329(f329(f243(a1),f329(f80(a1),f329(f106(a1),x37081))),f2(a1))) % 178.07/177.92 [3854]P24(f329(f329(f244(a1),f329(f80(a1),f329(f106(a1),f329(a118,x38541)))),f2(a1))) % 178.07/177.92 [4468]~E(f252(f883(x44681,a869)),f193(f883(x44681,a869))) % 178.07/177.92 [4515]~P24(f329(f329(f244(a875),x45151),f2(a875))) % 178.07/177.92 [4531]~P24(f329(f329(f244(a1),f329(f106(a1),x45311)),f2(a1))) % 178.07/177.92 [3142]E(f179(x31421,f119(f876(x31421))),f119(f876(x31421))) % 178.07/177.92 [3145]E(f329(f329(f82(a1),a84),x31451),a84) % 178.07/177.92 [3146]E(f329(f329(f81(a1),a84),x31461),x31461) % 178.07/177.92 [3149]E(f329(a110,f329(f106(a1),x31491)),x31491) % 178.07/177.92 [3150]E(f329(f329(f22(a1),x31501),a84),x31501) % 178.07/177.92 [3151]E(f329(f329(f81(a1),x31511),a84),x31511) % 178.07/177.92 [3153]E(f329(f329(f22(a875),x31531),x31531),f2(a875)) % 178.07/177.92 [3157]E(f329(f80(a1),f329(f80(a1),x31571)),x31571) % 178.07/177.92 [3158]E(f329(f38(a875),f329(f250(a875),x31581)),x31581) % 178.07/177.92 [3169]E(f329(f329(f82(a875),f79(a875)),x31691),x31691) % 178.07/177.92 [3170]E(f329(f329(f82(a1),f79(a1)),x31701),x31701) % 178.07/177.92 [3171]E(f329(f329(f81(a875),f2(a875)),x31711),x31711) % 178.07/177.92 [3172]E(f329(f329(f81(a1),f2(a1)),x31721),x31721) % 178.07/177.92 [3173]E(f329(f329(f242(a875),f2(a875)),x31731),x31731) % 178.07/177.92 [3179]E(f329(f329(f22(a875),f2(a875)),x31791),f2(a875)) % 178.07/177.92 [3180]E(f329(f329(f82(a875),f2(a875)),x31801),f2(a875)) % 178.07/177.92 [3181]E(f329(f329(f39(a1),f2(a1)),x31811),f2(a1)) % 178.07/177.92 [3182]E(f329(f329(f241(a875),f2(a875)),x31821),f2(a875)) % 178.07/177.92 [3199]E(f329(f299(a875,f2(a875)),x31991),f329(f250(a875),x31991)) % 178.07/177.92 [3200]E(f329(f329(f82(a1),a103),x32001),f329(f80(a1),x32001)) % 178.07/177.92 [3206]E(f329(a110,f329(f109(a1),x32061)),f329(f109(a875),x32061)) % 178.07/177.92 [3207]E(f329(a19,f329(f109(a105),x32071)),f329(f109(a875),x32071)) % 178.07/177.92 [3208]E(f329(f38(a875),f329(f298(a875),x32081)),f329(a118,x32081)) % 178.07/177.92 [3218]E(f329(f329(f81(a875),f79(a875)),x32181),f329(a118,x32181)) % 178.07/177.92 [3222]E(f329(f108(a1),f329(f106(a1),x32221)),f329(f106(a1),x32221)) % 178.07/177.92 [3223]E(f329(f76(a1),f329(f106(a1),x32231)),f329(f106(a1),x32231)) % 178.07/177.92 [3228]E(f329(f38(x32281),f193(f883(x32281,a869))),f2(a875)) % 178.07/177.92 [3230]E(f329(f329(f39(a875),x32301),f329(a118,f2(a875))),x32301) % 178.07/177.92 [3239]E(f45(a875,x32391,f329(a118,f2(a875))),f2(a875)) % 178.07/177.92 [3240]E(f45(a1,x32401,f329(f109(a1),a103)),f2(a1)) % 178.07/177.92 [3256]E(f329(f329(f39(a1),x32561),f329(f109(a1),a103)),f329(f80(a1),x32561)) % 178.07/177.92 [3260]E(f138(a875,f329(f299(a875,x32601),f2(a875))),f119(a875)) % 178.07/177.92 [3261]E(f329(f329(f81(a1),x32611),f79(a1)),f329(f329(f22(a1),x32611),a103)) % 178.07/177.92 [3262]E(f329(f329(f22(a1),x32621),f79(a1)),f329(f329(f81(a1),x32621),a103)) % 178.07/177.92 [3267]P24(f329(f329(f199(a24),x32671),x32671)) % 178.07/177.92 [3268]P24(f329(f329(f243(a875),x32681),x32681)) % 178.07/177.92 [3269]P24(f329(f329(f243(a1),x32691),x32691)) % 178.07/177.92 [3270]P24(f329(f329(f92(a1),x32701),x32701)) % 178.07/177.92 [3275]E(f329(f80(a1),f329(f109(a1),x32751)),f329(f109(a1),f329(f80(a1),x32751))) % 178.07/177.92 [3276]P24(f329(f62(a875),f329(f250(a875),x32761))) % 178.07/177.92 [3277]P24(f329(f62(a875),f329(f298(a875),x32771))) % 178.07/177.92 [3285]E(f160(x32851,f252(f883(x32851,a869))),f252(f883(f876(x32851),a869))) % 178.07/177.92 [3290]P24(f329(f329(f243(a875),f2(a875)),x32901)) % 178.07/177.92 [3301]E(f329(f329(f81(a875),f117(x33011)),f329(a118,f2(a875))),f117(f329(a118,x33011))) % 178.07/177.92 [3302]E(f329(f249(x33021),f329(f16(a869,x33021),a247)),f193(f883(x33021,a869))) % 178.07/177.92 [3303]E(f329(f249(x33031),f329(f16(a869,x33031),a192)),f252(f883(x33031,a869))) % 178.07/177.92 [3308]E(f329(f329(f307(a875),x33081),f329(f250(a875),x33081)),f329(f250(a875),f329(a118,x33081))) % 178.07/177.92 [3320]E(f329(f329(f81(a1),f79(a1)),f329(f106(a1),x33201)),f329(f106(a1),f329(a118,x33201))) % 178.07/177.92 [3323]E(f329(f329(f150(f876(x33231)),f119(x33231)),f119(f876(x33231))),f54(x33231,f119(x33231))) % 178.07/177.92 [3342]E(f193(f883(f882(x33421,x33421),a869)),f261(x33421,f193(f883(x33421,a869)))) % 178.07/177.92 [3343]E(f329(f306(x33431),f252(f883(x33431,a869))),f252(f883(f883(x33431,a869),a869))) % 178.07/177.92 [3344]E(f329(f80(f883(x33441,a869)),f193(f883(x33441,a869))),f252(f883(x33441,a869))) % 178.07/177.92 [3345]E(f329(f80(f883(x33451,a869)),f252(f883(x33451,a869))),f193(f883(x33451,a869))) % 178.07/177.92 [3347]P24(f329(f62(x33471),f193(f883(x33471,a869)))) % 178.07/177.92 [3349]E(f329(f299(a875,x33491),f329(a118,x33491)),f329(f329(f307(a875),x33491),f193(f883(a875,a869)))) % 178.07/177.92 [3350]E(f86(f882(a875,a875),f48(x33501,f2(a875))),f329(f329(f264(a875,a875),f2(a875)),x33501)) % 178.07/177.92 [3364]E(f329(f329(f307(a875),f329(a118,x33641)),f329(f298(a875),x33641)),f329(f298(a875),f329(a118,x33641))) % 178.07/177.92 [3368]P38(x33681,f193(f883(f882(x33681,x33681),a869))) % 178.07/177.92 [3371]P24(f329(f329(f243(a1),f2(a1)),f329(f106(a1),x33711))) % 178.07/177.92 [3379]E(f329(f329(f81(a875),f329(f194(a875),x33791)),f329(a118,f2(a875))),f329(f194(a875),f329(a118,x33791))) % 178.07/177.92 [3487]P39(f329(f308(a875,a1,f106(a1)),x34871)) % 178.07/177.92 [3525]P40(x35251,f193(f883(x35251,a869)),f193(f883(f882(x35251,x35251),a869))) % 178.07/177.92 [3544]E(f329(f329(f264(a1,a1),f329(f109(a1),a103)),f329(f329(f22(a1),x35441),f79(a1))),f50(f329(f109(a1),a103),x35441)) % 178.07/177.92 [3593]P55(x35931,f329(f16(f883(x35931,a869),x35931),f329(f16(a869,x35931),a247))) % 178.07/177.92 [3795]P24(f329(f329(f331(f883(f882(a875,a875),a869)),f330(x37951)),a104)) % 178.07/177.92 [3820]P24(f329(f329(f331(f883(f882(a875,a875),a869)),f329(a112,x38201)),a104)) % 178.07/177.92 [3955]P21(x39551,f883(x39551,a869),f329(f329(f7(x39551,f883(x39551,a869),f883(x39551,a869)),f307(x39551)),f193(f883(x39551,a869))),f252(f883(x39551,a869))) % 178.07/177.92 [4465]~E(f329(f329(f81(a1),x44651),x44651),a103) % 178.07/177.92 [4500]~E(f329(a3,f329(a118,f329(a19,x45001))),f2(a105)) % 178.07/177.92 [4508]~P24(f329(a198,f329(f106(a1),x45081))) % 178.07/177.92 [4511]~P24(f329(f329(f244(a875),x45111),x45111)) % 178.07/177.92 [4524]~P24(f329(f329(f243(a875),f329(a118,x45241)),x45241)) % 178.07/177.92 [3292]E(f329(a110,f329(f80(a1),f329(f106(a1),x32921))),f2(a875)) % 178.07/177.92 [3295]E(f329(f329(f81(a1),f329(f80(a1),x32951)),x32951),f2(a1)) % 178.07/177.92 [3300]E(f329(f38(a1),f329(f299(a1,f2(a1)),x33001)),f329(a110,x33001)) % 178.07/177.92 [3313]E(f329(f329(f254(a875),f329(a118,f2(a875))),x33131),f329(a118,f2(a875))) % 178.07/177.92 [3413]E(f329(f282(x34131),f193(f883(f882(x34131,x34131),a869))),f193(f883(x34131,a869))) % 178.07/177.92 [3421]E(f41(f883(x34211,a869),f193(f883(f883(x34211,a869),a869))),f252(f883(x34211,a869))) % 178.07/177.92 [3422]E(f41(f883(x34221,a869),f252(f883(f883(x34221,a869),a869))),f193(f883(x34221,a869))) % 178.07/177.92 [3423]E(f40(f883(x34231,a869),f193(f883(f883(x34231,a869),a869))),f193(f883(x34231,a869))) % 178.07/177.92 [3424]E(f40(f883(x34241,a869),f252(f883(f883(x34241,a869),a869))),f252(f883(x34241,a869))) % 178.07/177.92 [3470]E(f329(f329(f307(f876(x34701)),f119(x34701)),f193(f883(f876(x34701),a869))),f161(x34701,f119(f883(x34701,a869)))) % 178.07/177.92 [3471]E(f329(f329(f307(f876(x34711)),f119(x34711)),f193(f883(f876(x34711),a869))),f160(x34711,f193(f883(x34711,a869)))) % 178.07/177.92 [3508]E(f329(f329(f81(a875),f4(x35081)),f329(a118,f2(a875))),f4(f329(a3,f329(a118,f329(a19,x35081))))) % 178.07/177.92 [3536]E(f329(f38(a1),f329(f308(a875,a1,f106(a1)),x35361)),f329(f38(a875),x35361)) % 178.07/177.92 [3537]P24(f329(f329(f243(a875),x35371),f329(f329(f82(a875),x35371),x35371))) % 178.07/177.92 [3574]E(f329(f308(a1,a875,a110),f300(a1,f2(a1),f329(f106(a1),x35741))),f329(f298(a875),x35741)) % 178.07/177.92 [3588]E(f329(f329(f39(a875),f329(a118,f2(a875))),f329(f109(a875),x35881)),f329(a110,f329(f329(f39(a1),f79(a1)),f329(f109(a1),x35881)))) % 178.07/177.92 [3590]E(f329(f171(a875),f138(a875,f329(f299(a875,f2(a875)),f329(a118,x35901)))),f329(f298(a875),x35901)) % 178.07/177.92 [3591]E(f329(f329(f81(a875),f329(f194(a105),x35911)),f329(a118,f2(a875))),f329(f194(a105),f329(a3,f329(a118,f329(a19,x35911))))) % 178.07/177.92 [3610]E(f329(f308(a1,a875,a110),f329(f308(a875,a1,f106(a1)),x36101)),x36101) % 178.07/177.92 [3642]E(f329(f329(f307(a875),f2(a875)),f329(f308(a875,a875,a118),f329(f250(a875),x36421))),f329(f250(a875),f329(a118,x36421))) % 178.07/177.92 [3649]P50(x36491,x36491,f305(x36491,f193(f883(f882(x36491,x36491),a869)))) % 178.07/177.92 [3655]P24(f329(a198,f329(f80(a1),f329(f106(a1),f329(a118,x36551))))) % 178.07/177.92 [3666]E(f329(f329(f22(f883(a875,a869)),f329(f251(a875),x36661)),f329(f329(f307(a875),x36661),f193(f883(a875,a869)))),f329(f251(a875),f329(a118,x36661))) % 178.07/177.92 [3682]E(f329(f329(f81(a1),f329(f329(f22(a1),a84),x36821)),f329(f329(f22(a1),a84),x36821)),f329(f329(f22(a1),a84),f329(f329(f81(a1),x36821),x36821))) % 178.07/177.92 [3698]E(f329(f329(f307(f883(x36981,a869)),f193(f883(x36981,a869))),f193(f883(f883(x36981,a869),a869))),f329(f306(x36981),f193(f883(x36981,a869)))) % 178.07/177.92 [3725]E(f329(f329(f22(f883(a875,a869)),f329(f301(a875),x37251)),f329(f329(f307(a875),f329(a118,x37251)),f193(f883(a875,a869)))),f329(f301(a875),f329(a118,x37251))) % 178.07/177.92 [3733]E(f329(f329(f307(f879(x37331)),f206(x37331)),f329(f308(x37331,f879(x37331),f236(x37331)),f252(f883(x37331,a869)))),f252(f883(f879(x37331),a869))) % 178.07/177.92 [3832]E(f329(f109(a875),f329(f329(f81(a1),x38321),x38321)),f329(f329(f87(a875,a875),f329(f109(a875),x38321)),f329(f329(f18(a875,a875,a875),f81(a875)),f5(a875)))) % 178.07/177.92 [4220]P11(x42201,f883(x42201,a869),f329(f329(f8(f883(x42201,a869),f883(f883(x42201,a869),f883(x42201,a869)),x42201),f329(f7(f883(x42201,a869),f883(x42201,a869),f883(x42201,a869)),f22(f883(x42201,a869)))),f329(f329(f7(x42201,f883(x42201,a869),f883(x42201,a869)),f307(x42201)),f193(f883(x42201,a869))))) % 178.07/177.92 [4309]E(f329(f249(f882(a1,a1)),f329(f268(a1,a1,a869),f329(f329(f8(f883(a1,a869),f883(a1,a869),a1),f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f243(a1),x43091)))),f244(a1)))),f113(x43091)) % 178.07/177.92 [4342]E(f329(f249(f882(a1,a1)),f329(f268(a1,a1,a869),f329(f329(f18(a1,f883(a1,a869),f883(a1,a869)),f329(f329(f8(f883(a869,a869),f883(f883(a1,a869),f883(a1,a869)),a1),f8(a869,a869,a1)),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f243(a1),x43421)))),f244(a1)))),f111(x43421)) % 178.07/177.92 [4397]E(f329(f249(f882(f883(x43971,a869),f883(x43971,a869))),f329(f268(f883(x43971,a869),f883(x43971,a869),a869),f329(f329(f7(f883(x43971,a869),f883(f883(x43971,a869),a869),f883(f883(x43971,a869),a869)),f329(f329(f8(f883(f883(x43971,a869),f883(a869,a869)),f883(f883(f883(x43971,a869),a869),f883(f883(x43971,a869),a869)),f883(x43971,a869)),f18(f883(x43971,a869),a869,a869)),f329(f329(f8(f883(f883(x43971,a869),a869),f883(f883(x43971,a869),f883(a869,a869)),f883(x43971,a869)),f329(f8(a869,f883(a869,a869),f883(x43971,a869)),a327)),f244(f883(x43971,a869))))),f62(x43971)))),f304(x43971)) % 178.07/177.92 [4528]~P24(f329(f62(f876(x45281)),f252(f883(f876(x45281),a869)))) % 178.07/177.92 [4533]~P24(f329(f329(f92(a1),a103),f329(f329(f81(a1),x45331),x45331))) % 178.07/177.92 [4543]~P24(f329(f329(f243(a1),f2(a1)),f329(f80(a1),f329(f106(a1),f329(a118,x45431))))) % 178.07/177.92 [3448]E(f329(f329(f22(a1),f329(f329(f81(a1),x34481),a103)),a103),x34481) % 178.07/177.92 [3464]E(f329(f171(a875),f138(a875,f329(f299(a875,f2(a875)),x34641))),f329(f250(a875),x34641)) % 178.07/177.92 [3704]E(f329(f329(f81(a1),f329(f329(f81(a1),f79(a1)),x37041)),x37041),f329(f329(f22(a1),f329(f329(f81(a1),x37041),x37041)),a103)) % 178.07/177.92 [3750]E(f329(f284(x37501,x37501),f305(x37501,f193(f883(f882(x37501,x37501),a869)))),f305(x37501,f193(f883(f882(x37501,x37501),a869)))) % 178.07/177.92 [3798]P24(f329(f329(f243(a875),x37981),f329(f329(f82(a875),x37981),f329(f329(f82(a875),x37981),x37981)))) % 178.07/177.92 [4075]P24(f329(f62(a875),f329(f249(a875),f329(f329(f7(a875,a875,a869),f244(a875)),x40751)))) % 178.07/177.92 [4076]P24(f329(f62(a875),f329(f249(a875),f329(f329(f7(a875,a875,a869),f243(a875)),x40761)))) % 178.07/177.92 [4362]E(f329(f249(f882(x43621,x43621)),f329(f329(f8(f883(x43621,a869),a869,f882(x43621,x43621)),f88(x43621)),f329(f329(f7(f882(x43621,x43621),f883(x43621,f882(x43621,x43621)),f883(x43621,a869)),f329(f329(f8(f883(f882(x43621,x43621),a869),f883(f883(x43621,f882(x43621,x43621)),f883(x43621,a869)),f882(x43621,x43621)),f8(f882(x43621,x43621),a869,x43621)),a326)),f329(f329(f18(x43621,x43621,f882(x43621,x43621)),f264(x43621,x43621)),f5(x43621))))),f305(x43621,f193(f883(f882(x43621,x43621),a869)))) % 178.07/177.92 [4530]~E(f329(f329(f22(a1),f329(f329(f81(a1),x45301),x45301)),a103),a84) % 178.07/177.92 [4532]~E(f329(f329(f81(a1),f329(f329(f81(a1),f79(a1)),x45321)),x45321),f2(a1)) % 178.07/177.92 [4540]~P24(f329(f329(f92(a1),f329(f329(f81(a1),x45401),x45401)),a103)) % 178.07/177.92 [3843]E(f329(f329(f81(a1),f329(f329(f22(a1),a103),x38431)),f329(f329(f22(a1),a103),x38431)),f329(f329(f22(a1),a103),f329(f329(f22(a1),f329(f329(f81(a1),x38431),x38431)),a103))) % 178.07/177.92 [3964]E(f329(f329(f22(a1),f329(f329(f81(a1),f329(f329(f22(a1),a103),x39641)),f329(f329(f22(a1),a103),x39641))),a103),f329(f329(f22(a1),a103),f329(f329(f81(a1),x39641),x39641))) % 178.07/177.92 [3999]E(f329(f329(f22(a1),f329(f329(f81(a1),f329(f329(f81(a1),x39991),a103)),f329(f329(f81(a1),x39991),a103))),a103),f329(f329(f81(a1),f329(f329(f81(a1),x39991),x39991)),a103)) % 178.07/177.92 [4037]E(f329(f329(f22(a1),f329(f329(f81(a1),f329(f329(f22(a1),a103),x40371)),f329(f329(f22(a1),a103),x40371))),a103),f329(f329(f22(a1),a84),f329(f329(f22(a1),f329(f329(f81(a1),x40371),x40371)),a103))) % 178.07/177.92 [4138]E(f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),x41381),f2(a875))),f193(f883(f882(a875,a875),a869))))),f329(f106(a1),x41381)) % 178.07/177.92 [4148]E(f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),f334(x41481)),f565(x41481))),f193(f883(f882(a875,a875),a869))))),x41481) % 178.07/177.92 [4182]E(f329(f249(a1),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f243(a1),f2(a1)))),x41821)),f329(f308(a875,a1,f106(a1)),f329(f249(a875),f329(f329(f8(a1,a869,a875),x41821),f106(a1))))) % 178.07/177.92 [4228]P39(f329(f249(a1),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f243(a1),f2(a1)))),x42281))) % 178.07/177.92 [4249]P24(f329(f329(f331(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869))),f329(f329(f264(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),x42491),f193(f883(f882(a875,a875),a869)))),a72)) % 178.07/177.92 [4255]E(f329(f308(a1,a875,a110),f329(f249(a1),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f243(a1),f2(a1)))),f329(f329(f8(a875,a869,a1),x42551),a110)))),f329(f249(a875),x42551)) % 178.07/177.92 [4411]E(f310(a875,f329(f329(f43(f882(a875,a875),f883(a875,a869)),f329(a112,x44111)),f329(f268(a875,a875,f883(a875,a869)),f329(f329(f7(a875,f883(a875,a869),f883(a875,f883(a875,a869))),f329(f329(f8(f883(a875,f883(f883(a875,a869),f883(a875,a869))),f883(f883(a875,a869),f883(a875,f883(a875,a869))),a875),f7(a875,f883(a875,a869),f883(a875,a869))),f329(f329(f8(f883(a875,a875),f883(a875,f883(f883(a875,a869),f883(a875,a869))),a875),f329(f8(a875,f883(f883(a875,a869),f883(a875,a869)),a875),f307(a875))),f22(a875)))),f193(f883(a875,a869)))))),f329(a110,x44111)) % 178.07/177.92 [4545]~P24(f329(f329(f92(a1),a84),f329(f329(f22(a1),f329(f329(f81(a1),x45451),x45451)),a103))) % 178.07/177.92 [3887]E(f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),x38871),x38871)),a103)),a103),f329(f329(f81(a1),x38871),x38871)) % 178.07/177.92 [3938]E(f329(f329(f22(a1),f329(f329(f22(a1),f329(f329(f81(a1),x39381),x39381)),a103)),a103),f329(f329(f81(a1),f329(f329(f22(a1),x39381),a103)),f329(f329(f22(a1),x39381),a103))) % 178.07/177.92 [4156]E(f329(f329(f22(a1),f329(f329(f81(a1),f329(f329(f81(a1),f329(f80(a1),x41561)),a103)),f329(f329(f81(a1),f329(f80(a1),x41561)),a103))),a103),f329(f80(a1),f329(f329(f22(a1),f329(f329(f81(a1),x41561),x41561)),a103))) % 178.07/177.92 [4554]~P24(f329(f329(f92(a1),f329(f329(f22(a1),f329(f329(f81(a1),x45541),x45541)),a103)),a84)) % 178.07/177.92 [4200]E(f329(f329(f81(a875),x42001),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f329(a118,f329(a118,x42001))) % 178.07/177.92 [4201]E(f329(f329(f82(a875),x42011),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f329(f329(f81(a875),x42011),x42011)) % 178.07/177.92 [4202]E(f329(f329(f39(a875),f329(f329(f81(a875),x42021),x42021)),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x42021) % 178.07/177.92 [4284]E(f45(a875,f329(a118,f329(a118,x42841)),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f45(a875,x42841,f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))) % 178.07/177.92 [4426]E(f329(a90,f329(f329(f43(f882(a875,a875),f883(f882(a875,a875),a869)),f329(a112,x44261)),f329(f268(a875,a875,f883(f882(a875,a875),a869)),f329(f329(f8(f883(a875,f883(f882(a875,a875),a869)),f883(a875,f883(f882(a875,a875),a869)),a875),f329(f8(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869),a875),f283(f882(a875,a875),f882(a875,a875),a114))),f329(f329(f7(a875,f883(f882(a875,a875),a869),f883(a875,f883(f882(a875,a875),a869))),f329(f329(f8(f883(a875,f883(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869))),f883(f883(f882(a875,a875),a869),f883(a875,f883(f882(a875,a875),a869))),a875),f7(a875,f883(f882(a875,a875),a869),f883(f882(a875,a875),a869))),f329(f329(f8(f883(a875,f882(a875,a875)),f883(a875,f883(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869))),a875),f329(f8(f882(a875,a875),f883(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),a875),f307(f882(a875,a875)))),f329(f7(a875,a875,f882(a875,a875)),f264(a875,a875))))),f193(f883(f882(a875,a875),a869))))))),f329(f80(a1),x44261)) % 178.07/177.92 [4279]E(f329(f329(f81(a875),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x42791),f329(a118,f329(a118,x42791))) % 178.07/177.92 [4280]E(f329(f329(f82(a875),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x42801),f329(f329(f81(a875),x42801),x42801)) % 178.07/177.92 [4314]E(f329(f329(f39(a875),f329(a118,f329(a118,x43141))),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f329(a118,f329(f329(f39(a875),x43141),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))))) % 178.07/177.92 [4368]E(f329(f329(f81(a875),f329(f109(a875),f329(f329(f22(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))),a103))),x43681),f329(a118,f329(a118,f329(a118,x43681)))) % 178.07/177.92 [4434]E(f329(f268(a1,a1,f882(a1,a1)),f329(f329(f18(a1,f883(a1,f882(a1,a1)),f883(a1,f882(a1,a1))),f329(f329(f8(f883(a1,f883(f882(a1,a1),f882(a1,a1))),f883(f883(a1,f882(a1,a1)),f883(a1,f882(a1,a1))),a1),f18(a1,f882(a1,a1),f882(a1,a1))),f329(f329(f8(f883(a1,f882(a1,a1)),f883(a1,f883(f882(a1,a1),f882(a1,a1))),a1),f329(f18(a1,f882(a1,a1),f883(f882(a1,a1),f882(a1,a1))),f329(f329(f8(a869,f883(f882(a1,a1),f883(f882(a1,a1),f882(a1,a1))),a1),f102(f882(a1,a1))),f329(f329(f8(a1,a869,a1),f329(f243(a1),f2(a1))),f329(f329(f7(a1,a1,a1),f22(a1)),x44341))))),f329(f329(f7(a1,f883(a1,a1),f883(a1,f882(a1,a1))),f329(f329(f8(f883(a1,f882(a1,a1)),f883(f883(a1,a1),f883(a1,f882(a1,a1))),a1),f8(a1,f882(a1,a1),a1)),f329(f329(f8(a1,f883(a1,f882(a1,a1)),a1),f264(a1,a1)),f329(f329(f7(a1,a1,a1),f329(f329(f8(a1,f883(a1,a1),a1),f81(a1)),f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))))),f79(a1))))),f329(f329(f7(a1,a1,a1),f22(a1)),x44341))))),f329(f329(f8(a1,f883(a1,f882(a1,a1)),a1),f264(a1,a1)),f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))))),f44(x44341)) % 178.07/177.92 [3115]P94(f881(x31151,x31152)) % 178.07/177.92 [3116]P94(f882(x31161,x31162)) % 178.07/177.92 [3117]P102(f881(x31171,x31172)) % 178.07/177.92 [3118]P102(f882(x31181,x31182)) % 178.07/177.92 [3135]P29(a1,f178(x31351,x31352)) % 178.07/177.92 [3136]P38(x31361,f152(x31361,x31362)) % 178.07/177.92 [3201]P32(x32011,x32012,f119(x32011)) % 178.07/177.92 [3234]P40(x32341,x32342,f261(x32341,x32342)) % 178.07/177.92 [3235]P50(x32351,x32351,f261(x32351,x32352)) % 178.07/177.92 [3511]P21(x35111,x35111,f5(x35111),x35112) % 178.07/177.92 [3512]P21(x35121,x35121,f35(x35121),x35122) % 178.07/177.92 [3520]P33(x35201,x35202,f119(x35201),f119(x35201)) % 178.07/177.92 [3521]P21(x35211,f879(x35211),f236(x35211),x35212) % 178.07/177.92 [3530]P21(f876(x35301),f876(x35301),f168(x35301),x35302) % 178.07/177.92 [4445]~E(f34(x44451,x44452),a24) % 178.07/177.92 [4446]~E(f33(x44461,x44462),a24) % 178.07/177.92 [4477]~P34(x44771,x44772,f119(x44771)) % 178.07/177.92 [4478]~P36(x44781,x44782,f119(x44781)) % 178.07/177.92 [3097]E(f329(f5(x30971),x30972),x30972) % 178.07/177.92 [3098]E(f329(f249(x30981),x30982),x30982) % 178.07/177.92 [3100]E(f329(f35(x31001),x31002),x31002) % 178.07/177.92 [3110]E(f329(f196(x31101),x31102),f121(x31101)) % 178.07/177.92 [3133]E(f86(x31331,f329(a326,x31332)),x31332) % 178.07/177.92 [3134]E(f91(x31341,f329(a326,x31342)),x31342) % 178.07/177.92 [3155]E(f329(f135(x31551,x31552),f119(x31551)),f119(x31551)) % 178.07/177.92 [3175]E(f151(x31751,f151(x31751,x31752)),f151(x31751,x31752)) % 178.07/177.92 [3176]E(f305(x31761,f305(x31761,x31762)),f305(x31761,x31762)) % 178.07/177.92 [3196]E(f329(f329(f127(x31961),x31962),f119(x31961)),x31962) % 178.07/177.92 [3202]E(f172(x32021,x32022,f119(x32021)),x32022) % 178.07/177.92 [3203]E(f172(x32031,f119(x32031),x32032),x32032) % 178.07/177.92 [3209]E(f329(f329(f174(x32091),x32092),f119(x32091)),f119(x32091)) % 178.07/177.92 [3210]E(f329(f329(f137(x32101),x32102),f119(x32101)),f119(x32101)) % 178.07/177.92 [3212]E(f237(x32121,x32122,f206(x32121)),f2(a875)) % 178.07/177.92 [3213]E(f154(x32131,x32132,f119(x32131)),f2(a875)) % 178.07/177.92 [3215]E(f169(x32151,x32152,f119(x32151)),f119(x32151)) % 178.07/177.92 [3216]E(f176(x32161,x32162,f119(x32161)),f119(x32161)) % 178.07/177.92 [3217]E(f175(x32171,f119(x32171),x32172),f119(x32171)) % 178.07/177.92 [3221]E(f329(f171(x32211),f151(x32211,x32212)),f329(f171(x32211),x32212)) % 178.07/177.92 [3224]E(f329(f260(x32241,x32241),f261(x32241,x32242)),x32242) % 178.07/177.92 [3225]E(f329(f262(x32251,x32251),f261(x32251,x32252)),x32252) % 178.07/177.92 [3233]E(f329(f284(x32331,x32331),f261(x32331,x32332)),f261(x32331,x32332)) % 178.07/177.92 [3248]E(f305(f876(x32481),f156(x32481,x32482)),f157(x32481,f305(x32481,x32482))) % 178.07/177.92 [3250]P24(f329(f136(a1),f178(x32501,x32502))) % 178.07/177.92 [3258]E(f329(f260(x32581,x32581),f305(x32581,x32582)),f252(f883(x32581,a869))) % 178.07/177.92 [3259]E(f329(f262(x32591,x32591),f305(x32591,x32592)),f252(f883(x32591,a869))) % 178.07/177.92 [3263]P24(f329(f136(x32631),f151(x32631,x32632))) % 178.07/177.92 [3265]P24(f329(f159(x32651,x32652),f119(x32651))) % 178.07/177.92 [3273]E(f329(f171(a1),f178(x32731,x32732)),f300(a1,x32731,x32732)) % 178.07/177.92 [3288]P51(x32881,f193(f883(x32881,a869)),x32882) % 178.07/177.92 [3293]E(f329(f267(a1,a1),f46(x32931,x32932)),f45(a1,x32931,x32932)) % 178.07/177.92 [3294]E(f329(f299(a875,x32941),f329(a118,x32942)),f300(a875,x32941,x32942)) % 178.07/177.92 [3312]E(f329(f329(f150(x33121),x33122),f119(x33121)),f139(x33121,x33122,f119(x33121))) % 178.07/177.92 [3325]E(f300(a875,f329(a118,x33251),x33252),f302(a875,x33251,x33252)) % 178.07/177.92 [3328]P40(x33281,f252(f883(x33281,a869)),f305(x33281,x33282)) % 178.07/177.92 [3390]E(f329(f329(f22(a875),x33901),f329(a118,x33902)),f329(f38(a875),f303(a875,x33902,x33901))) % 178.07/177.92 [3449]E(f166(x34491,x34492,f119(x34491)),f329(f329(f264(f876(x34491),f876(x34491)),f119(x34491)),f119(x34491))) % 178.07/177.92 [3468]E(f329(f268(x34681,x34682,f882(x34681,x34682)),f264(x34681,x34682)),f35(f882(x34681,x34682))) % 178.07/177.92 [3473]P24(f329(f329(f331(f876(x34731)),f119(x34731)),f160(x34731,x34732))) % 178.07/177.92 [3474]E(f329(f194(f876(x34741)),f120(x34741,x34742)),f329(f329(f22(a875),f329(f194(f876(x34741)),x34742)),f79(a875))) % 178.07/177.92 [3481]P24(f329(f62(a875),f303(a875,x34811,x34812))) % 178.07/177.92 [3482]P24(f329(f62(a875),f302(a875,x34821,x34822))) % 178.07/177.92 [3483]P24(f329(f62(a875),f300(a875,x34831,x34832))) % 178.07/177.92 [3484]P24(f329(f62(a1),f303(a1,x34841,x34842))) % 178.07/177.92 [3485]P24(f329(f62(a1),f302(a1,x34851,x34852))) % 178.07/177.92 [3486]P24(f329(f62(a1),f300(a1,x34861,x34862))) % 178.07/177.92 [3587]E(f329(f308(a875,a875,a118),f300(a875,x35871,x35872)),f300(a875,f329(a118,x35871),f329(a118,x35872))) % 178.07/177.92 [3607]E(f329(f329(f286(x36071,x36071,x36071),f305(x36071,x36072)),f305(x36071,x36072)),f305(x36071,x36072)) % 178.07/177.92 [3640]E(f329(f329(f264(a1,a1),f329(f329(f39(a1),x36401),x36402)),f45(a1,x36401,x36402)),f46(x36401,x36402)) % 178.07/177.92 [3641]E(f329(f329(f264(a105,a105),f329(f329(f39(a105),x36411),x36412)),f45(a105,x36411,x36412)),f21(x36411,x36412)) % 178.07/177.92 [3670]E(f329(f329(f264(a875,a875),f329(f329(f39(a875),x36701),x36702)),f45(a875,x36701,x36702)),f86(f882(a875,a875),f48(x36701,x36702))) % 178.07/177.92 [3721]P24(f329(f329(f244(a875),f329(f329(f22(a875),x37211),x37212)),f329(a118,x37211))) % 178.07/177.92 [3819]E(f329(f329(f81(a1),f329(f329(f82(a1),x38191),f329(f329(f39(a1),x38192),x38191))),f45(a1,x38192,x38191)),x38192) % 178.07/177.92 [3823]E(f329(f329(f43(a875,f883(f882(f876(x38231),f876(x38231)),a869)),f252(f883(a875,a869))),f142(x38231,x38232)),f144(x38231,x38232)) % 178.07/177.92 [4050]P24(f329(f329(f331(f882(f876(x40501),f876(x40501))),f329(f329(f264(f876(x40501),f876(x40501)),f119(x40501)),f119(x40501))),f157(x40501,x40502))) % 178.07/177.92 [4213]E(f269(x42131,x42131,x42132,x42132,f5(x42131),f5(x42132)),f35(f882(x42131,x42132))) % 178.07/177.92 [4215]E(f269(x42151,x42151,x42152,x42152,f35(x42151),f35(x42152)),f35(f882(x42151,x42152))) % 178.07/177.92 [4454]~E(f329(f236(x44541),x44542),f206(x44541)) % 178.07/177.92 [3194]E(f329(f240(x31941),f329(f236(x31941),x31942)),x31942) % 178.07/177.92 [3195]E(f329(f168(x31951),f329(f168(x31951),x31952)),x31952) % 178.07/177.92 [3197]E(f329(f329(f137(x31971),f2(a875)),x31972),x31972) % 178.07/177.92 [3211]E(f329(f329(f174(x32111),f2(a875)),x32112),f119(x32111)) % 178.07/177.92 [3219]E(f329(f329(f127(x32191),f119(x32191)),x32192),x32192) % 178.07/177.92 [3227]E(f329(f194(f879(x32271)),f329(f236(x32271),x32272)),f2(a875)) % 178.07/177.92 [3229]E(f40(f883(x32291,a869),f329(f306(x32291),x32292)),x32292) % 178.07/177.92 [3231]E(f329(f171(x32311),f329(f167(x32311),x32312)),f329(f171(x32311),x32312)) % 178.07/177.92 [3232]E(f329(f171(x32321),f329(f168(x32321),x32322)),f329(f171(x32321),x32322)) % 178.07/177.92 [3237]E(f329(f329(f22(a105),x32371),x32372),f329(f329(a23,x32371),x32372)) % 178.07/177.92 [3252]E(f329(f329(f82(a875),x32521),x32522),f329(f329(f82(a875),x32522),x32521)) % 178.07/177.92 [3253]E(f329(f329(f82(a1),x32531),x32532),f329(f329(f82(a1),x32532),x32531)) % 178.07/177.92 [3254]E(f329(f329(f81(a875),x32541),x32542),f329(f329(f81(a875),x32542),x32541)) % 178.07/177.92 [3255]E(f329(f329(f81(a1),x32551),x32552),f329(f329(f81(a1),x32552),x32551)) % 178.07/177.92 [3280]E(f329(f329(f188(x32801,x32801),f2(a875)),x32802),f35(x32801)) % 178.07/177.92 [3281]E(f329(f194(f876(x32811)),f329(f167(x32811),x32812)),f329(f194(f876(x32811)),x32812)) % 178.07/177.92 [3282]E(f329(f194(f876(x32821)),f329(f168(x32821),x32822)),f329(f194(f876(x32821)),x32822)) % 178.07/177.92 [3283]E(f175(x32831,x32832,f193(f883(a875,a869))),f119(x32831)) % 178.07/177.92 [3284]E(f329(f329(f153(x32841,x32841),f5(x32841)),x32842),x32842) % 178.07/177.92 [3286]E(f329(f263(a1,a1),f46(x32861,x32862)),f329(f329(f39(a1),x32861),x32862)) % 178.07/177.92 [3305]E(f329(f194(f876(x33051)),f151(x33051,x33052)),f329(f38(x33051),f329(f171(x33051),x33052))) % 178.07/177.92 [3306]E(f32(f33(x33061,x33062)),f329(f329(f81(a875),f32(x33062)),f329(a118,f2(a875)))) % 178.07/177.92 [3307]E(f329(f282(x33071),f329(f284(x33071,x33071),x33072)),f329(f282(x33071),x33072)) % 178.07/177.92 [3311]P24(f329(f62(x33111),f329(f171(x33111),x33112))) % 178.07/177.92 [3319]E(f329(f329(f81(a1),x33191),f329(f80(a1),x33192)),f329(f329(f22(a1),x33191),x33192)) % 178.07/177.92 [3327]P20(x33271,x33272,f193(f883(f874(x33271),a869))) % 178.07/177.92 [3329]E(f329(f308(x33291,x33291,f5(x33291)),x33292),x33292) % 178.07/177.92 [3330]E(f329(f308(x33301,x33301,f35(x33301)),x33302),x33302) % 178.07/177.92 [3331]E(f329(f309(x33311,x33311,f5(x33311)),x33312),x33312) % 178.07/177.92 [3332]E(f329(f309(x33321,x33321,f35(x33321)),x33322),x33322) % 178.07/177.92 [3333]P24(f329(f252(f883(x33331,a869)),x33332)) % 178.07/177.92 [3335]E(f329(f38(a875),f329(f299(a875,x33351),x33352)),f329(f329(f22(a875),x33352),x33351)) % 178.07/177.92 [3336]E(f329(f299(a875,f329(a118,x33361)),x33362),f303(a875,x33361,x33362)) % 178.07/177.92 [3348]E(f329(f329(f307(x33481),x33482),f193(f883(x33481,a869))),f329(f249(x33481),f329(a326,x33482))) % 178.07/177.92 [3352]E(f329(f329(f307(x33521),x33522),f193(f883(x33521,a869))),f235(x33521,f329(f236(x33521),x33522))) % 178.07/177.92 [3355]E(f305(x33551,f329(f284(x33551,x33551),x33552)),f329(f284(x33551,x33551),f305(x33551,x33552))) % 178.07/177.92 [3359]E(f329(f329(f81(a875),f329(a118,x33591)),x33592),f329(f329(f81(a875),x33591),f329(a118,x33592))) % 178.07/177.92 [3360]E(f329(f329(f22(a875),f329(a118,x33601)),f329(a118,x33602)),f329(f329(f22(a875),x33601),x33602)) % 178.07/177.92 [3366]E(f55(x33661,f2(a875),x33662),f329(f329(f150(f876(x33661)),f119(x33661)),f119(f876(x33661)))) % 178.07/177.92 [3367]E(f329(f38(a875),f302(a875,x33671,x33672)),f329(f329(f22(a875),x33672),x33671)) % 178.07/177.92 [3376]P38(x33761,f329(f329(f285(a875,x33761),a248),x33762)) % 178.07/177.92 [3378]P29(a875,f138(a875,f329(f299(a875,x33781),x33782))) % 178.07/177.92 [3380]P24(f329(f62(a875),f329(f299(a875,x33801),x33802))) % 178.07/177.92 [3381]P24(f329(f62(a1),f329(f299(a1,x33811),x33812))) % 178.07/177.92 [3383]E(f329(f284(f876(x33831),f876(x33831)),f156(x33831,x33832)),f156(x33831,f329(f284(x33831,x33831),x33832))) % 178.07/177.92 [3384]E(f329(f194(a870),f33(x33841,x33842)),f329(f329(f81(a875),f329(f194(a870),x33842)),f329(a118,f2(a875)))) % 178.07/177.92 [3386]E(f329(f299(a1,x33861),f329(f329(f81(a1),x33862),f79(a1))),f300(a1,x33861,x33862)) % 178.07/177.92 [3389]E(f329(f329(f39(a1),f329(f80(a1),x33891)),f329(f80(a1),x33892)),f329(f329(f39(a1),x33891),x33892)) % 178.07/177.92 [3397]E(f183(x33971,x33972,f329(f16(f879(x33972),x33971),f206(x33972))),f193(f883(x33971,a869))) % 178.07/177.92 [3398]E(f185(x33981,x33982,f329(f16(f879(x33982),x33981),f206(x33982))),f193(f883(x33982,a869))) % 178.07/177.92 [3399]E(f329(f329(f188(f882(x33991,x33991),a869),f79(a875)),x33992),x33992) % 178.07/177.92 [3401]E(f329(f329(f116(f883(x34011,a869)),x34012),f193(f883(x34011,a869))),x34012) % 178.07/177.92 [3402]E(f329(f329(f22(f883(x34021,a869)),x34022),f193(f883(x34021,a869))),x34022) % 178.07/177.92 [3403]E(f329(f329(f107(f883(x34031,a869)),x34032),f252(f883(x34031,a869))),x34032) % 178.07/177.92 [3404]E(f329(f263(a875,a875),f86(f882(a875,a875),f48(x34041,x34042))),f329(f329(f39(a875),x34041),x34042)) % 178.07/177.92 [3411]E(f311(x34111,f329(a20,x34112),f329(f80(a1),f329(a20,x34112))),f329(f329(f314(a1),x34111),x34112)) % 178.07/177.92 [3412]E(f300(a1,f329(f329(f81(a1),x34121),f79(a1)),x34122),f302(a1,x34121,x34122)) % 178.07/177.92 [3417]E(f329(f267(a875,a875),f86(f882(a875,a875),f48(x34171,x34172))),f45(a875,x34171,x34172)) % 178.07/177.92 [3425]E(f312(x34251,f329(a20,x34252),f329(f80(a1),f329(a20,x34252))),f313(a1,x34251,x34252)) % 178.07/177.92 [3428]P24(f329(f329(f331(x34281),x34282),f252(f883(x34281,a869)))) % 178.07/177.92 [3433]E(f329(f329(f22(a875),f329(a118,x34331)),x34332),f329(f38(a875),f300(a875,x34332,x34331))) % 178.07/177.92 [3460]E(f329(f329(f116(f883(x34601,a869)),x34602),f252(f883(x34601,a869))),f252(f883(x34601,a869))) % 178.07/177.92 [3461]E(f329(f329(f22(f883(x34611,a869)),x34612),f252(f883(x34611,a869))),f193(f883(x34611,a869))) % 178.07/177.92 [3462]E(f329(f329(f107(f883(x34621,a869)),x34622),f193(f883(x34621,a869))),f193(f883(x34621,a869))) % 178.07/177.92 [3476]E(f45(a1,f329(f80(a1),x34761),f329(f80(a1),x34762)),f329(f80(a1),f45(a1,x34761,x34762))) % 178.07/177.92 [3477]E(f45(a1,f329(f106(a1),x34771),f329(f106(a1),x34772)),f329(f106(a1),f45(a875,x34771,x34772))) % 178.07/177.92 [3488]E(f329(f194(f876(x34881)),f329(f170(x34881),x34882)),f329(f329(f22(a875),f329(f194(f876(x34881)),x34882)),f79(a875))) % 178.07/177.92 [3513]E(f329(f329(f39(a1),f45(a1,x35131,x35132)),x35132),f2(a1)) % 178.07/177.92 [3523]E(f329(a3,f45(a875,f329(a19,x35231),f329(a19,x35232))),f45(a105,x35231,x35232)) % 178.07/177.92 [3556]E(f329(a3,f329(f329(f22(a875),f329(a19,x35561)),f329(a19,x35562))),f329(f329(f22(a105),x35561),x35562)) % 178.07/177.92 [3557]E(f329(a3,f329(f329(f82(a875),f329(a19,x35571)),f329(a19,x35572))),f329(f329(f82(a105),x35571),x35572)) % 178.07/177.92 [3558]E(f329(a3,f329(f329(f81(a875),f329(a19,x35581)),f329(a19,x35582))),f329(f329(f81(a105),x35581),x35582)) % 178.07/177.92 [3559]E(f329(a3,f329(f329(f39(a875),f329(a19,x35591)),f329(a19,x35592))),f329(f329(f39(a105),x35591),x35592)) % 178.07/177.92 [3568]E(f329(f308(a875,a875,a118),f329(f299(a875,x35681),x35682)),f329(f299(a875,f329(a118,x35681)),f329(a118,x35682))) % 178.07/177.92 [3592]P24(f329(f48(x35921,x35922),f86(f882(a875,a875),f48(x35921,x35922)))) % 178.07/177.92 [3613]E(f329(f329(f81(a875),f329(f329(f81(a875),f32(x36131)),f32(x36132))),f329(a118,f2(a875))),f32(f34(x36131,x36132))) % 178.07/177.92 [3614]E(f45(a875,f329(a118,f45(a875,x36141,x36142)),x36142),f45(a875,f329(a118,x36141),x36142)) % 178.07/177.92 [3628]E(f329(f329(f42(f883(x36281,a869),f883(x36281,a869)),x36282),f5(f883(x36281,a869))),f41(f883(x36281,a869),x36282)) % 178.07/177.92 [3629]E(f329(f329(f43(f883(x36291,a869),f883(x36291,a869)),x36292),f5(f883(x36291,a869))),f40(f883(x36291,a869),x36292)) % 178.07/177.92 [3630]E(f329(f308(f876(x36301),f883(x36301,a869),f171(x36301)),f329(f171(f876(x36301)),f54(x36301,x36302))),f329(f306(x36301),f329(f171(x36301),x36302))) % 178.07/177.92 [3633]P24(f329(f329(f331(f883(x36331,a869)),x36332),f329(f306(x36331),x36332))) % 178.07/177.92 [3639]E(f45(a1,f329(f80(a1),f45(a1,x36391,x36392)),x36392),f45(a1,f329(f80(a1),x36391),x36392)) % 178.07/177.92 [3651]P24(f329(f329(f243(f883(x36511,a869)),x36512),f252(f883(x36511,a869)))) % 178.07/177.92 [3653]E(f329(f329(f286(x36531,x36531,x36531),f305(x36531,x36532)),f305(x36531,f305(x36531,x36532))),f305(x36531,x36532)) % 178.07/177.92 [3654]E(f329(f329(f116(f883(x36541,a869)),f329(f262(x36541,x36541),x36542)),f329(f260(x36541,x36541),x36542)),f329(f282(x36541),x36542)) % 178.07/177.92 [3675]E(f316(x36751,x36752,f252(f883(x36751,a869)),f252(f883(x36752,a869))),f252(f883(f881(x36751,x36752),a869))) % 178.07/177.92 [3726]P24(f329(f329(f243(a875),f45(a875,x37261,x37262)),x37261)) % 178.07/177.92 [3748]P24(f329(f329(f243(a1),f329(f80(a1),f329(f106(a1),x37481))),f329(f106(a1),x37482))) % 178.07/177.92 [3774]P24(f329(f329(f331(f883(x37741,a869)),f193(f883(x37741,a869))),f329(f306(x37741),x37742))) % 178.07/177.92 [3779]E(f305(x37791,f329(f329(f286(x37791,x37791,x37791),x37792),f305(x37791,x37792))),f305(x37791,x37792)) % 178.07/177.92 [3782]E(f329(f329(f286(x37821,x37821,x37821),f305(x37821,x37822)),x37822),f329(f329(f286(x37821,x37821,x37821),x37822),f305(x37821,x37822))) % 178.07/177.92 [3784]E(f329(a110,f329(f329(f81(a1),f329(f329(f22(a1),x37841),x37842)),f79(a1))),f329(f38(a1),f300(a1,x37842,x37841))) % 178.07/177.92 [3799]E(f329(f260(x37991,x37991),f329(f329(f286(x37991,x37991,x37991),x37992),f305(x37991,x37992))),f329(f260(x37991,x37991),x37992)) % 178.07/177.92 [3800]E(f329(f262(x38001,x38001),f329(f329(f286(x38001,x38001,x38001),x38002),f305(x38001,x38002))),f329(f262(x38001,x38001),x38002)) % 178.07/177.92 [3816]E(f329(f329(f81(a875),f329(f329(f81(a875),f329(f194(a870),x38161)),f329(f194(a870),x38162))),f329(a118,f2(a875))),f329(f194(a870),f34(x38161,x38162))) % 178.07/177.92 [3827]P21(a875,a875,f329(f329(f7(a875,a875,a875),f81(a875)),x38271),x38272) % 178.07/177.92 [3829]P29(a875,f329(f168(a875),f329(f329(f153(f876(x38291),a875),f194(f876(x38291))),f179(x38291,x38292)))) % 178.07/177.92 [3874]P24(f329(f329(f244(a1),f329(f80(a1),f329(f106(a1),f329(a118,x38741)))),f329(f106(a1),x38742))) % 178.07/177.92 [3919]E(f329(f141(f876(x39191),x39191,f329(f7(x39191,f876(x39191),f876(x39191)),f150(x39191)),f119(x39191)),x39192),f329(f168(x39191),x39192)) % 178.07/177.92 [3971]P24(f329(f329(f243(f883(f882(f876(x39711),f876(x39711)),a869)),f157(x39711,x39712)),f305(f876(x39711),f156(x39711,x39712)))) % 178.07/177.92 [4003]P24(f329(f48(x40031,x40032),f329(f329(f264(a875,a875),f329(f329(f39(a875),x40031),x40032)),f45(a875,x40031,x40032)))) % 178.07/177.92 [4014]P24(f329(f329(f243(f883(f882(f876(x40141),f876(x40141)),a869)),f156(x40141,f305(x40141,x40142))),f305(f876(x40141),f156(x40141,x40142)))) % 178.07/177.92 [4239]E(f329(f329(f270(f882(a105,a105),a105,f882(a105,a105),f882(x42391,f882(a105,a105))),f274(f329(f165(a105),f329(f329(f153(f882(a105,x42391),a105),f263(a105,x42391)),x42392)))),f329(f329(f8(x42391,f883(f882(a105,a105),f882(x42391,f882(a105,a105))),a105),f264(x42391,f882(a105,a105))),f275(x42391,x42392))),f273(x42391,x42392)) % 178.07/177.92 [4350]E(f329(f238(a875,f882(x43501,f877(x43501)),f2(a875),f329(f268(x43501,f877(x43501),a875),f329(f16(f883(f877(x43501),a875),x43501),f329(f329(f7(f877(x43501),a875,a875),f329(f329(f8(a875,f883(a875,a875),f877(x43501)),f81(a875)),f194(f877(x43501)))),f79(a875))))),f329(f134(x43501),x43502)),f329(f194(f877(x43501)),x43502)) % 178.07/177.92 [4425]E(f329(f268(f883(f882(x44251,x44251),a869),f883(f882(x44251,x44251),a869),f883(f883(x44252,x44251),f882(f883(f882(x44252,x44252),a869),f883(f882(x44252,x44252),a869)))),f329(f329(f7(f883(f882(x44251,x44251),a869),f883(f883(f882(x44251,x44251),a869),f883(f883(x44252,x44251),f883(f882(x44252,x44252),a869))),f883(f883(f882(x44251,x44251),a869),f883(f883(x44252,x44251),f882(f883(f882(x44252,x44252),a869),f883(f882(x44252,x44252),a869))))),f329(f329(f8(f883(f883(f883(x44252,x44251),f883(f882(x44252,x44252),a869)),f883(f883(x44252,x44251),f882(f883(f882(x44252,x44252),a869),f883(f882(x44252,x44252),a869)))),f883(f883(f883(f882(x44251,x44251),a869),f883(f883(x44252,x44251),f883(f882(x44252,x44252),a869))),f883(f883(f882(x44251,x44251),a869),f883(f883(x44252,x44251),f882(f883(f882(x44252,x44252),a869),f883(f882(x44252,x44252),a869))))),f883(f882(x44251,x44251),a869)),f8(f883(f883(x44252,x44251),f883(f882(x44252,x44252),a869)),f883(f883(x44252,x44251),f882(f883(f882(x44252,x44252),a869),f883(f882(x44252,x44252),a869))),f883(f882(x44251,x44251),a869))),f329(f329(f8(f883(f883(x44252,x44251),f883(f883(f882(x44252,x44252),a869),f882(f883(f882(x44252,x44252),a869),f883(f882(x44252,x44252),a869)))),f883(f883(f883(x44252,x44251),f883(f882(x44252,x44252),a869)),f883(f883(x44252,x44251),f882(f883(f882(x44252,x44252),a869),f883(f882(x44252,x44252),a869)))),f883(f882(x44251,x44251),a869)),f18(f883(x44252,x44251),f883(f882(x44252,x44252),a869),f882(f883(f882(x44252,x44252),a869),f883(f882(x44252,x44252),a869)))),f329(f329(f8(f883(f883(x44252,x44251),f883(f882(x44252,x44252),a869)),f883(f883(x44252,x44251),f883(f883(f882(x44252,x44252),a869),f882(f883(f882(x44252,x44252),a869),f883(f882(x44252,x44252),a869)))),f883(f882(x44251,x44251),a869)),f329(f8(f883(f882(x44252,x44252),a869),f883(f883(f882(x44252,x44252),a869),f882(f883(f882(x44252,x44252),a869),f883(f882(x44252,x44252),a869))),f883(x44252,x44251)),f264(f883(f882(x44252,x44252),a869),f883(f882(x44252,x44252),a869)))),f285(x44251,x44252))))),f285(x44251,x44252))),f75(x44251,x44252)) % 178.07/177.92 [4509]~E(f329(f306(x45091),x45092),f193(f883(f883(x45091,a869),a869))) % 178.07/177.92 [4527]~P24(f329(f329(f331(x45271),x45272),f193(f883(x45271,a869)))) % 178.07/177.92 [4537]~P24(f329(f329(f244(f883(x45371,a869)),x45372),f193(f883(x45371,a869)))) % 178.07/177.92 [3338]E(f329(f329(f22(a875),x33381),f329(f329(f81(a875),x33381),x33382)),f2(a875)) % 178.07/177.92 [3340]E(f329(f329(f116(f883(x33401,a869)),x33402),x33402),x33402) % 178.07/177.92 [3341]E(f329(f329(f107(f883(x33411,a869)),x33412),x33412),x33412) % 178.07/177.92 [3369]E(f329(f329(f22(f883(x33691,a869)),x33692),x33692),f193(f883(x33691,a869))) % 178.07/177.92 [3372]E(f329(f142(x33721,x33722),f2(a875)),f193(f883(f882(f876(x33721),f876(x33721)),a869))) % 178.07/177.92 [3373]E(f329(f329(f81(a875),x33731),f329(a118,x33732)),f329(a118,f329(f329(f81(a875),x33731),x33732))) % 178.07/177.92 [3385]E(f200(f329(f106(a1),x33851),f329(f106(a1),x33852)),f329(f106(a1),f329(f329(f22(a875),x33851),x33852))) % 178.07/177.92 [3388]E(f329(f329(f39(a1),f329(f80(a1),x33881)),x33882),f329(f329(f39(a1),x33881),f329(f80(a1),x33882))) % 178.07/177.92 [3392]E(f329(f38(a1),f329(f299(a1,x33921),x33922)),f329(a110,f329(f329(f22(a1),x33922),x33921))) % 178.07/177.92 [3395]E(f329(f329(f81(a875),f329(a118,x33951)),x33952),f329(a118,f329(f329(f81(a875),x33951),x33952))) % 178.07/177.92 [3400]E(f329(f80(f883(x34001,a869)),f329(f80(f883(x34001,a869)),x34002)),x34002) % 178.07/177.92 [3414]E(f179(x34141,f329(f329(f150(f876(x34141)),f119(x34141)),x34142)),f179(x34141,x34142)) % 178.07/177.92 [3418]E(f329(f329(f81(a875),x34181),f329(f329(f82(a875),x34181),x34182)),f329(f329(f82(a875),x34181),f329(a118,x34182))) % 178.07/177.92 [3426]E(f329(f329(a23,f329(a3,x34261)),f329(a3,x34262)),f329(a3,f329(f329(f22(a875),x34261),x34262))) % 178.07/177.92 [3440]E(f329(f329(f82(a1),f329(f80(a1),x34401)),x34402),f329(f80(a1),f329(f329(f82(a1),x34401),x34402))) % 178.07/177.92 [3442]E(f329(f329(f254(a1),f329(f106(a1),x34421)),x34422),f329(f106(a1),f329(f329(f254(a875),x34421),x34422))) % 178.07/177.92 [3443]E(f329(f329(f82(a105),f329(a3,x34431)),f329(a3,x34432)),f329(a3,f329(f329(f82(a875),x34431),x34432))) % 178.07/177.92 [3444]E(f329(f329(f81(a105),f329(a3,x34441)),f329(a3,x34442)),f329(a3,f329(f329(f81(a875),x34441),x34442))) % 178.07/177.92 [3445]E(f329(f329(f241(a875),f329(a118,x34451)),f329(a118,x34452)),f329(a118,f329(f329(f241(a875),x34451),x34452))) % 178.07/177.92 [3446]E(f329(f329(f242(a875),f329(a118,x34461)),f329(a118,x34462)),f329(a118,f329(f329(f242(a875),x34461),x34462))) % 178.07/177.92 [3452]E(f329(f171(a875),f138(a875,f329(f299(a875,x34521),x34522))),f329(f299(a875,x34521),x34522)) % 178.07/177.92 [3453]E(f310(x34531,f329(f329(f307(x34531),x34532),f193(f883(x34531,a869)))),x34532) % 178.07/177.92 [3458]E(f329(f260(x34581,x34582),f193(f883(f882(x34581,x34582),a869))),f193(f883(x34582,a869))) % 178.07/177.92 [3459]E(f329(f262(x34591,x34592),f193(f883(f882(x34591,x34592),a869))),f193(f883(x34591,a869))) % 178.07/177.92 [3463]E(f329(a110,f329(f329(f22(a1),x34631),x34632)),f329(f38(a1),f302(a1,x34632,x34631))) % 178.07/177.92 [3467]E(f329(f329(f81(a875),x34671),f329(f329(f82(a875),x34672),x34671)),f329(f329(f82(a875),f329(a118,x34672)),x34671)) % 178.07/177.92 [3469]E(f329(f329(f61(x34691),f193(f883(x34691,a869))),x34692),f193(f883(f883(x34691,a869),a869))) % 178.07/177.92 [3478]E(f329(f194(f876(a875)),f138(a875,f329(f299(a875,x34781),x34782))),f329(f329(f22(a875),x34782),x34781)) % 178.07/177.92 [3493]E(f329(f329(f116(f883(x34931,a869)),f193(f883(x34931,a869))),x34932),x34932) % 178.07/177.92 [3494]E(f329(f329(f107(f883(x34941,a869)),f252(f883(x34941,a869))),x34942),x34942) % 178.07/177.92 [3495]E(f329(f329(f81(a1),f329(f80(a1),x34951)),f329(f80(a1),x34952)),f329(f80(a1),f329(f329(f81(a1),x34951),x34952))) % 178.07/177.92 [3500]E(f329(f329(f82(a1),f329(f106(a1),x35001)),f329(f106(a1),x35002)),f329(f106(a1),f329(f329(f82(a875),x35001),x35002))) % 178.07/177.92 [3501]E(f329(f329(f82(a1),f329(f109(a1),x35011)),f329(f109(a1),x35012)),f329(f109(a1),f329(f329(f82(a1),x35011),x35012))) % 178.07/177.92 [3503]E(f329(f329(f81(a1),f329(f106(a1),x35031)),f329(f106(a1),x35032)),f329(f106(a1),f329(f329(f81(a875),x35031),x35032))) % 178.07/177.92 [3504]E(f329(f329(f81(a1),f329(f109(a1),x35041)),f329(f109(a1),x35042)),f329(f109(a1),f329(f329(f81(a1),x35041),x35042))) % 178.07/177.92 [3505]E(f329(f329(f39(a1),f329(f106(a1),x35051)),f329(f106(a1),x35052)),f329(f106(a1),f329(f329(f39(a875),x35051),x35052))) % 178.07/177.92 [3524]E(f329(f329(f6(x35241,a875),f329(f16(a875,x35241),f79(a875))),x35242),f329(f38(x35241),x35242)) % 178.07/177.92 [3531]E(f329(f80(a1),f45(a1,f329(f80(a1),x35311),x35312)),f45(a1,x35311,f329(f80(a1),x35312))) % 178.07/177.92 [3533]E(f329(f171(a1),f178(x35331,f329(f329(f22(a1),x35332),f79(a1)))),f329(f299(a1,x35331),x35332)) % 178.07/177.92 [3538]P24(f329(f329(f243(a875),x35381),f329(f329(f81(a875),x35382),x35381))) % 178.07/177.92 [3539]P24(f329(f329(f243(a875),x35391),f329(f329(f81(a875),x35391),x35392))) % 178.07/177.92 [3541]E(f329(f329(f116(f883(x35411,a869)),f252(f883(x35411,a869))),x35412),f252(f883(x35411,a869))) % 178.07/177.92 [3542]E(f329(f329(f22(f883(x35421,a869)),f193(f883(x35421,a869))),x35422),f193(f883(x35421,a869))) % 178.07/177.92 [3543]E(f329(f329(f107(f883(x35431,a869)),f193(f883(x35431,a869))),x35432),f193(f883(x35431,a869))) % 178.07/177.92 [3548]E(f329(f329(f264(a1,a1),x35481),f329(f80(a1),x35482)),f329(a51,f329(f329(f264(a1,a1),x35481),x35482))) % 178.07/177.92 [3549]E(f329(f299(a1,f329(f329(f81(a1),x35491),f79(a1))),x35492),f303(a1,x35491,x35492)) % 178.07/177.92 [3560]E(f329(f329(f82(a875),x35601),f329(f329(f39(a875),x35602),x35601)),f329(f329(f22(a875),x35602),f45(a875,x35602,x35601))) % 178.07/177.92 [3561]E(f329(f329(f82(a1),x35611),f329(f329(f39(a1),x35612),x35611)),f329(f329(f22(a1),x35612),f45(a1,x35612,x35611))) % 178.07/177.92 [3565]E(f329(f171(a1),f178(f329(f329(f81(a1),x35651),f79(a1)),x35652)),f302(a1,x35651,x35652)) % 178.07/177.92 [3569]P24(f329(f329(f243(f883(x35691,a869)),x35692),x35692)) % 178.07/177.92 [3572]E(f329(f329(f116(f883(x35721,a869)),x35722),f329(f80(f883(x35721,a869)),x35722)),f252(f883(x35721,a869))) % 178.07/177.92 [3573]E(f329(f329(f107(f883(x35731,a869)),x35732),f329(f80(f883(x35731,a869)),x35732)),f193(f883(x35731,a869))) % 178.07/177.92 [3579]E(f329(f329(f22(a875),f329(f329(f22(a875),x35791),f79(a875))),x35792),f329(f329(f22(a875),x35791),f329(a118,x35792))) % 178.07/177.92 [3584]E(f329(f329(f22(f883(x35841,a869)),f252(f883(x35841,a869))),x35842),f329(f80(f883(x35841,a869)),x35842)) % 178.07/177.92 [3585]E(f329(f329(f22(a1),f329(f109(a1),x35851)),f329(f109(a1),x35852)),f329(f109(a1),f329(f329(f81(a1),x35851),f329(f80(a1),x35852)))) % 178.07/177.92 [3597]E(f329(f171(a875),f138(a875,f329(f299(a875,x35971),f329(a118,x35972)))),f300(a875,x35971,x35972)) % 178.07/177.92 [3605]P24(f329(f329(f329(f329(a201,a24),x36051),x36052),x36051)) % 178.07/177.92 [3611]E(f329(f194(f876(f876(x36111))),f54(x36111,x36112)),f329(f329(f254(a875),f329(a118,f329(a118,f2(a875)))),f329(f194(f876(x36111)),x36112))) % 178.07/177.92 [3631]E(f329(f329(f188(f882(x36311,x36311),a869),f2(a875)),x36312),f305(x36311,f193(f883(f882(x36311,x36311),a869)))) % 178.07/177.92 [3635]P24(f329(f136(a875),f138(a875,f329(f299(a875,x36351),x36352)))) % 178.07/177.92 [3652]E(f329(f308(a1,a875,a110),f300(a1,f329(f106(a1),x36521),f329(f106(a1),x36522))),f300(a875,x36521,x36522)) % 178.07/177.92 [3662]E(f190(a875,f2(a875),f5(a875),f329(f329(f22(a875),x36621),x36622)),f329(f329(f22(a875),x36621),f329(a118,x36622))) % 178.07/177.92 [3663]E(f329(a110,f329(f329(f22(a1),x36631),f329(f329(f81(a1),x36632),f79(a1)))),f329(f38(a1),f303(a1,x36632,x36631))) % 178.07/177.92 [3699]E(f329(f329(f153(a875,a875),a118),f138(a875,f329(f299(a875,x36991),x36992))),f138(a875,f329(f299(a875,f329(a118,x36991)),f329(a118,x36992)))) % 178.07/177.92 [3706]E(f329(f171(a1),f178(f329(f329(f81(a1),x37061),f79(a1)),f329(f329(f22(a1),x37062),f79(a1)))),f303(a1,x37061,x37062)) % 178.07/177.92 [3717]P24(f329(f329(f243(f883(x37171,a869)),f193(f883(x37171,a869))),x37172)) % 178.07/177.92 [3722]E(f86(x37221,f329(f329(f7(x37221,x37221,a869),a326),x37222)),x37222) % 178.07/177.92 [3723]E(f91(x37231,f329(f329(f7(x37231,x37231,a869),a326),x37232)),x37232) % 178.07/177.92 [3727]E(f329(f171(a875),f138(a875,f329(f299(a875,f329(a118,x37271)),f329(a118,x37272)))),f302(a875,x37271,x37272)) % 178.07/177.92 [3751]E(f329(f329(f266(x37511,x37512),f252(f883(x37511,a869))),f329(f16(f883(x37512,a869),x37511),f252(f883(x37512,a869)))),f252(f883(f882(x37511,x37512),a869))) % 178.07/177.92 [3786]E(f329(f249(x37861),f329(f329(f8(a869,a869,x37861),a324),x37862)),f329(f80(f883(x37861,a869)),f329(f249(x37861),x37862))) % 178.07/177.92 [3789]E(f329(f249(x37891),f329(f329(f7(x37891,x37891,a869),a326),x37892)),f329(f329(f307(x37891),x37892),f193(f883(x37891,a869)))) % 178.07/177.92 [3796]E(f329(f329(f81(a1),f329(f329(f22(a1),x37961),x37962)),f329(f329(f22(a1),x37961),x37962)),f329(f329(f22(a1),f329(f329(f81(a1),x37961),x37961)),f329(f329(f81(a1),x37962),x37962))) % 178.07/177.92 [3797]E(f329(f329(f81(a1),f329(f329(f81(a1),x37971),x37971)),f329(f329(f81(a1),x37972),x37972)),f329(f329(f81(a1),f329(f329(f81(a1),x37971),x37972)),f329(f329(f81(a1),x37971),x37972))) % 178.07/177.92 [3813]P24(f329(f329(f243(a875),f329(f38(x38131),f329(f171(x38131),x38132))),f329(f194(f876(x38131)),x38132))) % 178.07/177.92 [3814]P24(f329(f329(f243(a875),f329(f194(f876(x38141)),f151(x38141,x38142))),f329(f194(f876(x38141)),x38142))) % 178.07/177.92 [3824]E(f329(f249(x38241),f329(f329(f7(x38241,f883(x38241,a869),a869),f331(x38241)),x38242)),x38242) % 178.07/177.92 [3839]E(f329(f329(f174(x38391),f329(f329(f22(a875),f329(f194(f876(x38391)),x38392)),f79(a875))),x38392),f120(x38391,x38392)) % 178.07/177.92 [3861]E(f190(a875,f2(a875),f329(f329(f8(a875,a875,a875),a118),f329(f241(a875),x38611)),x38612),f329(f329(f241(a875),f329(a118,x38611)),x38612)) % 178.07/177.92 [3865]E(f40(f883(x38651,a869),f329(f308(f883(f882(x38651,x38651),a869),f883(x38651,a869),f282(x38651)),x38652)),f329(f282(x38651),f40(f883(f882(x38651,x38651),a869),x38652))) % 178.07/177.92 [3866]E(f190(a875,f329(a118,x38661),f329(f329(f8(a875,a875,a875),a118),f329(f242(a875),x38661)),x38662),f329(f329(f242(a875),f329(a118,x38661)),x38662)) % 178.07/177.92 [3868]E(f329(f329(f264(a1,a1),f329(f329(f39(a1),f329(f76(a1),x38681)),f329(f76(a1),x38682))),f45(a1,f329(f76(a1),x38681),f329(f76(a1),x38682))),f53(x38681,x38682)) % 178.07/177.92 [3890]P24(f329(f329(f243(f883(f883(x38901,a869),a869)),x38902),f329(f306(x38901),f40(f883(x38901,a869),x38902)))) % 178.07/177.92 [3924]E(f329(f329(f43(x39241,f883(x39241,a869)),x39242),f329(f329(f7(x39241,f883(x39241,a869),f883(x39241,a869)),f307(x39241)),f193(f883(x39241,a869)))),x39242) % 178.07/177.92 [3925]E(f329(f329(f286(x39251,x39251,x39251),f329(f284(x39251,x39251),x39252)),f305(x39251,f329(f284(x39251,x39251),x39252))),f329(f284(x39251,x39251),f329(f329(f286(x39251,x39251,x39251),x39252),f305(x39251,x39252)))) % 178.07/177.92 [3994]E(f329(f171(x39941),f329(f141(f876(x39941),f876(x39941),f127(x39941),f119(x39941)),x39942)),f329(f329(f43(f876(x39941),f883(x39941,a869)),f329(f171(f876(x39941)),x39942)),f171(x39941))) % 178.07/177.92 [4026]E(f329(f329(f116(f883(f882(x40261,x40261),a869)),f305(x40261,f193(f883(f882(x40261,x40261),a869)))),f329(f329(f286(x40261,x40261,x40261),f305(x40261,x40262)),x40262)),f305(x40261,x40262)) % 178.07/177.92 [4060]E(f329(f329(f181(x40601,x40601),x40602),x40602),f329(f329(f153(x40601,f882(x40601,x40601)),f329(f329(f18(x40601,x40601,f882(x40601,x40601)),f264(x40601,x40601)),f5(x40601))),x40602)) % 178.07/177.92 [4176]E(f329(f141(a875,f876(x41761),f329(f7(f876(x41761),a875,a875),f329(f329(f8(a875,f883(a875,a875),f876(x41761)),f242(a875)),f194(f876(x41761)))),f2(a875)),f329(f168(f876(x41761)),x41762)),f329(f194(f876(f876(x41761))),f179(x41761,x41762))) % 178.07/177.92 [4254]E(f329(f329(f285(f882(a875,f876(x42541)),f876(x42541)),f321(a875,f876(x42541),a248,f144(x42541,x42542))),f329(f329(f18(f876(x42541),f876(x42541),f882(a875,f876(x42541))),f329(f329(f8(a875,f883(f876(x42541),f882(a875,f876(x42541))),f876(x42541)),f264(a875,f876(x42541))),f194(f876(x42541)))),f5(f876(x42541)))),f145(x42541,x42542)) % 178.07/177.92 [4384]E(f329(f249(x43841),f329(f329(f8(f883(f883(x43841,a869),a869),a869,x43841),f89(f883(x43841,a869))),f329(f329(f8(f883(f883(x43841,a869),a869),f883(f883(x43841,a869),a869),x43841),f329(f18(f883(x43841,a869),a869,a869),f329(f329(f8(a869,f883(a869,a869),f883(x43841,a869)),a332),f329(f329(f7(f883(x43841,a869),f883(f883(x43841,a869),a869),a869),f331(f883(x43841,a869))),x43842)))),f331(x43841)))),f41(f883(x43841,a869),x43842)) % 178.07/177.92 [4538]~P24(f329(f329(f244(a1),f329(f106(a1),x45381)),f329(f80(a1),f329(f106(a1),x45382)))) % 178.07/177.92 [4555]~P24(f329(f329(f92(a1),f329(f329(f22(a1),f329(f329(f81(a1),x45551),x45551)),a103)),f329(f329(f81(a1),x45552),x45552))) % 178.07/177.92 [3465]E(f329(f329(f22(a875),f329(f329(f81(a875),x34651),x34652)),x34652),x34651) % 178.07/177.92 [3466]E(f329(f329(f22(a875),f329(f329(f81(a875),x34661),x34662)),x34661),x34662) % 178.07/177.92 [3532]E(f329(f329(f81(a875),f329(f329(f22(a875),x35321),x35322)),x35322),f329(f329(f242(a875),x35321),x35322)) % 178.07/177.92 [3638]E(f329(f329(f82(a875),f329(f329(f39(a875),x36381),x36382)),x36382),f329(f329(f22(a875),x36381),f45(a875,x36381,x36382))) % 178.07/177.92 [3667]E(f329(f171(a875),f138(a875,f329(f299(a875,f329(a118,x36671)),x36672))),f303(a875,x36671,x36672)) % 178.07/177.92 [3674]E(f329(f106(a1),f224(f329(a110,f329(f76(a1),x36741)),f329(a110,f329(f76(a1),x36742)))),f329(f329(a225,x36741),x36742)) % 178.07/177.92 [3676]E(f329(f329(f116(f883(x36761,a869)),f329(f80(f883(x36761,a869)),x36762)),x36762),f252(f883(x36761,a869))) % 178.07/177.92 [3677]E(f329(f329(f107(f883(x36771,a869)),f329(f80(f883(x36771,a869)),x36772)),x36772),f193(f883(x36771,a869))) % 178.07/177.92 [3695]P24(f329(f329(f243(a875),f329(f329(f22(a875),x36951),x36952)),x36951)) % 178.07/177.92 [3696]P24(f329(f329(f243(a875),f329(f329(f39(a875),x36961),x36962)),x36961)) % 178.07/177.92 [3719]P24(f329(f329(f244(a875),x37191),f329(a118,f329(f329(f81(a875),x37192),x37191)))) % 178.07/177.92 [3720]P24(f329(f329(f244(a875),x37201),f329(a118,f329(f329(f81(a875),x37201),x37202)))) % 178.07/177.92 [3737]E(f329(f329(f82(a875),f329(a110,f329(f76(a1),x37371))),f329(a110,f329(f76(a1),x37372))),f329(a110,f329(f76(a1),f329(f329(f82(a1),x37371),x37372)))) % 178.07/177.92 [3747]P24(f329(f329(f243(a1),f2(a1)),f329(f329(f254(a1),f329(f76(a1),x37471)),x37472))) % 178.07/177.92 [3818]E(f329(f283(f876(x38181),f876(x38181),f157(x38181,x38182)),f329(f329(f307(f876(x38181)),f119(x38181)),f193(f883(f876(x38181),a869)))),f329(f329(f307(f876(x38181)),f119(x38181)),f193(f883(f876(x38181),a869)))) % 178.07/177.92 [3837]E(f329(f329(f116(f883(f882(x38371,x38371),a869)),f305(x38371,x38372)),f305(x38371,f193(f883(f882(x38371,x38371),a869)))),f305(x38371,x38372)) % 178.07/177.92 [3851]E(f329(f329(f39(a1),f329(f109(a1),f329(f329(f81(a1),x38511),x38511))),f329(f109(a1),f329(f329(f81(a1),x38512),x38512))),f329(f329(f39(a1),f329(f109(a1),x38511)),f329(f109(a1),x38512))) % 178.07/177.92 [3914]E(f329(f329(f254(a1),x39141),f329(f109(a875),f329(f329(f81(a1),x39142),x39142))),f329(f329(f87(a1,a1),f329(f329(f254(a1),x39141),f329(f109(a875),x39142))),f329(f329(f18(a1,a1,a1),f82(a1)),f5(a1)))) % 178.07/177.92 [3920]E(f329(f249(f883(x39201,a869)),f329(f329(f7(f883(x39201,a869),f883(x39201,a869),a869),f243(f883(x39201,a869))),x39202)),f329(f306(x39201),x39202)) % 178.07/177.92 [3935]E(f329(f329(f153(a1,a875),a110),f329(f329(f127(a1),f329(f329(f153(a875,a1),f106(a1)),x39351)),f329(f329(f153(a875,a1),f106(a1)),x39352))),f329(f329(f127(a875),x39351),x39352)) % 178.07/177.92 [3970]E(f329(f308(a1,a1,f329(f329(f7(a1,a1,a1),f81(a1)),x39701)),f329(f299(a1,f2(a1)),f329(f329(f22(a1),x39702),x39701))),f329(f299(a1,x39701),x39702)) % 178.07/177.92 [3972]P42(x39721,f329(f329(f22(f883(f882(x39721,x39721),a869)),x39722),f305(x39721,f193(f883(f882(x39721,x39721),a869))))) % 178.07/177.92 [3992]E(f329(f194(f876(x39921)),f329(f141(f876(x39921),f876(x39921),f127(x39921),f119(x39921)),x39922)),f329(f165(a875),f329(f329(f153(f876(x39921),a875),f194(f876(x39921))),x39922))) % 178.07/177.92 [3997]P40(x39971,f252(f883(x39971,a869)),f329(f329(f116(f883(f882(x39971,x39971),a869)),x39972),f305(x39971,f193(f883(f882(x39971,x39971),a869))))) % 178.07/177.92 [4040]E(f190(a875,f2(a875),f329(f329(f8(a875,a875,a875),a118),f329(f329(f7(a875,a875,a875),f241(a875)),x40401)),x40402),f329(f329(f241(a875),x40402),f329(a118,x40401))) % 178.07/177.92 [4043]E(f190(a875,f329(a118,x40431),f329(f329(f8(a875,a875,a875),a118),f329(f329(f7(a875,a875,a875),f242(a875)),x40431)),x40432),f329(f329(f242(a875),x40432),f329(a118,x40431))) % 178.07/177.92 [4046]E(f329(f308(x40461,f876(x40461),f329(f329(f7(x40461,f876(x40461),f876(x40461)),f150(x40461)),f119(x40461))),x40462),f173(x40461,x40462,f329(f329(f307(f876(x40461)),f119(x40461)),f193(f883(f876(x40461),a869))))) % 178.07/177.92 [4047]E(f329(f329(f116(f883(f882(x40471,x40471),a869)),f329(f329(f286(x40471,x40471,x40471),x40472),f305(x40471,x40472))),f305(x40471,f193(f883(f882(x40471,x40471),a869)))),f305(x40471,x40472)) % 178.07/177.92 [4055]P24(f329(f329(f243(f883(f882(x40551,x40551),a869)),f261(x40551,x40552)),f329(f329(f266(x40551,x40551),x40552),f329(f16(f883(x40551,a869),x40551),x40552)))) % 178.07/177.92 [4058]E(f329(f308(a1,a875,a110),f329(f329(f116(f883(a1,a869)),f329(f308(a875,a1,f106(a1)),x40581)),f329(f308(a875,a1,f106(a1)),x40582))),f329(f329(f116(f883(a875,a869)),x40581),x40582)) % 178.07/177.92 [4059]E(f329(f308(a1,a875,a110),f329(f329(f107(f883(a1,a869)),f329(f308(a875,a1,f106(a1)),x40591)),f329(f308(a875,a1,f106(a1)),x40592))),f329(f329(f107(f883(a875,a869)),x40591),x40592)) % 178.07/177.92 [4063]E(f329(f249(x40631),f329(f329(f8(a869,a869,x40631),a324),f329(f329(f7(x40631,f883(x40631,a869),a869),f331(x40631)),x40632))),f329(f80(f883(x40631,a869)),x40632)) % 178.07/177.92 [4090]E(f329(f141(f876(x40901),f876(x40901),f127(x40901),f119(x40901)),f329(f329(f153(f876(x40901),f876(x40901)),f168(x40901)),f329(f168(f876(x40901)),x40902))),f329(f168(x40901),f329(f141(f876(x40901),f876(x40901),f127(x40901),f119(x40901)),x40902))) % 178.07/177.92 [4119]E(f329(f329(f43(a875,f883(f882(x41191,x41191),a869)),f252(f883(a875,a869))),f329(f329(f7(a875,f883(f882(x41191,x41191),a869),f883(f882(x41191,x41191),a869)),f188(f882(x41191,x41191),a869)),x41192)),f305(x41191,x41192)) % 178.07/177.92 [4139]E(f86(x41391,f329(f329(f8(f883(x41391,a869),a869,x41391),f329(a326,x41392)),f329(f329(f7(x41391,f883(x41391,a869),f883(x41391,a869)),f307(x41391)),f193(f883(x41391,a869))))),f310(x41391,x41392)) % 178.07/177.92 [4147]E(f329(f194(f876(x41471)),f151(x41471,f329(f141(f876(x41471),f876(x41471),f127(x41471),f119(x41471)),x41472))),f329(f38(x41471),f329(f329(f43(f876(x41471),f883(x41471,a869)),f329(f171(f876(x41471)),x41472)),f171(x41471)))) % 178.07/177.92 [4163]E(f329(f329(f116(f883(f882(x41631,x41631),a869)),x41632),f329(f329(f286(x41631,x41631,x41631),f329(f329(f286(x41631,x41631,x41631),x41632),f305(x41631,x41632))),x41632)),f329(f329(f286(x41631,x41631,x41631),x41632),f305(x41631,x41632))) % 178.07/177.92 [4186]P24(f329(f329(f243(f883(f882(x41861,x41861),a869)),f329(f329(f286(x41861,x41861,x41861),x41862),f305(x41861,x41862))),f329(f329(f266(x41861,x41861),f329(f282(x41861),x41862)),f329(f16(f883(x41861,a869),x41861),f329(f282(x41861),x41862))))) % 178.07/177.92 [4229]E(f329(f249(f876(x42291)),f329(f329(f7(f876(x42291),f883(x42291,a869),a869),f329(f329(f8(f883(x42291,a869),f883(f883(x42291,a869),a869),f876(x42291)),f243(f883(x42291,a869))),f171(x42291))),x42292)),f160(x42291,x42292)) % 178.07/177.92 [4241]E(f329(f155(f876(x42411),x42411,f119(x42411),f329(f329(f8(f876(x42411),f883(f876(x42411),f876(x42411)),x42411),f329(f7(f876(x42411),f876(x42411),f876(x42411)),f127(x42411))),f329(f329(f7(x42411,f876(x42411),f876(x42411)),f150(x42411)),f119(x42411)))),x42412),f329(f167(x42411),x42412)) % 178.07/177.92 [4283]P21(f883(x42831,x42832),f883(f882(x42831,x42832),a869),f329(f329(f8(f883(f882(x42831,x42832),a869),f883(f882(x42831,x42832),a869),f883(x42831,x42832)),f249(f882(x42831,x42832))),f329(f329(f8(f883(x42831,f883(x42832,a869)),f883(f882(x42831,x42832),a869),f883(x42831,x42832)),f268(x42831,x42832,a869)),f329(f8(x42832,f883(x42832,a869),x42831),f329(f7(x42832,x42832,a869),a326)))),f252(f883(f883(x42831,x42832),a869))) % 178.07/177.92 [4288]E(f45(a1,f329(f109(a1),f329(f329(f81(a1),x42881),x42881)),f329(f109(a1),f329(f329(f81(a1),x42882),x42882))),f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f45(a1,f329(f109(a1),x42881),f329(f109(a1),x42882)))) % 178.07/177.92 [4331]E(f329(f329(f43(x43311,f883(f882(x43311,x43311),a869)),x43312),f329(f329(f7(x43311,f883(f882(x43311,x43311),a869),f883(f882(x43311,x43311),a869)),f329(f329(f8(f882(x43311,x43311),f883(f883(f882(x43311,x43311),a869),f883(f882(x43311,x43311),a869)),x43311),f307(f882(x43311,x43311))),f329(f329(f18(x43311,x43311,f882(x43311,x43311)),f264(x43311,x43311)),f5(x43311)))),f193(f883(f882(x43311,x43311),a869)))),f261(x43311,x43312)) % 178.07/177.92 [4339]E(f211(x43391,f329(f329(f264(a1,a1),f329(f80(a1),f329(f329(f74(f882(a1,a1),a1,x43391,f263(a1,a1)),f220(x43391)),x43392))),f329(f329(f74(f882(a1,a1),a1,x43391,f267(a1,a1)),f220(x43391)),x43392))),f228(x43391,x43392)) % 178.07/177.92 [4420]E(f329(f249(f883(x44201,a869)),f329(f329(f8(f883(f883(x44201,a869),a869),a869,f883(x44201,a869)),f88(f883(x44201,a869))),f329(f329(f7(f883(x44201,a869),f883(f883(x44201,a869),a869),f883(f883(x44201,a869),a869)),f329(f329(f8(f883(f883(x44201,a869),f883(a869,a869)),f883(f883(f883(x44201,a869),a869),f883(f883(x44201,a869),a869)),f883(x44201,a869)),f18(f883(x44201,a869),a869,a869)),f329(f329(f8(f883(f883(x44201,a869),a869),f883(f883(x44201,a869),f883(a869,a869)),f883(x44201,a869)),f329(f8(a869,f883(a869,a869),f883(x44201,a869)),a327)),f329(f329(f7(f883(x44201,a869),f883(f883(x44201,a869),f883(x44201,a869)),f883(f883(x44201,a869),a869)),f329(f329(f8(f883(f883(x44201,a869),a869),f883(f883(f883(x44201,a869),f883(x44201,a869)),f883(f883(x44201,a869),a869)),f883(x44201,a869)),f8(f883(x44201,a869),a869,f883(x44201,a869))),a326)),f80(f883(x44201,a869)))))),f329(f329(f8(f883(f883(x44201,a869),a869),a869,f883(x44201,a869)),f329(f331(f883(x44201,a869)),x44202)),f306(x44201))))),f329(f306(x44201),f329(f80(f883(x44201,a869)),x44202))) % 178.07/177.92 [4535]~E(f329(f329(f81(a1),x45351),x45351),f329(f329(f22(a1),f329(f329(f81(a1),x45352),x45352)),a103)) % 178.07/177.92 [4541]~P24(f329(f329(f244(a875),f329(f329(f81(a875),x45411),x45412)),x45412)) % 178.07/177.92 [4542]~P24(f329(f329(f244(a875),f329(f329(f81(a875),x45421),x45422)),x45421)) % 178.07/177.92 [3752]E(f329(f329(f22(a875),x37521),f329(f329(f82(a875),f329(f329(f39(a875),x37521),x37522)),x37522)),f45(a875,x37521,x37522)) % 178.07/177.92 [3753]E(f329(f329(f22(a1),x37531),f329(f329(f82(a1),f329(f329(f39(a1),x37531),x37532)),x37532)),f45(a1,x37531,x37532)) % 178.07/177.92 [3787]E(f329(f329(f153(a875,x37871),f329(f164(x37871),x37872)),f138(a875,f329(f299(a875,f2(a875)),f329(f194(f876(x37871)),x37872)))),x37872) % 178.07/177.92 [3847]E(f329(f283(x38471,x38471,f305(x38471,f193(f883(f882(x38471,x38471),a869)))),x38472),x38472) % 178.07/177.92 [3975]E(f305(x39751,f329(f329(f116(f883(f882(x39751,x39751),a869)),x39752),f305(x39751,f193(f883(f882(x39751,x39751),a869))))),f305(x39751,x39752)) % 178.07/177.92 [3976]E(f305(x39761,f329(f329(f22(f883(f882(x39761,x39761),a869)),x39762),f305(x39761,f193(f883(f882(x39761,x39761),a869))))),f305(x39761,x39762)) % 178.07/177.92 [4029]E(f329(f329(f22(a1),f329(f329(f22(a1),f329(f329(f81(a1),x40291),x40291)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),x40292),x40292)),a103)),f329(f329(f81(a1),f329(f329(f22(a1),x40291),x40292)),f329(f329(f22(a1),x40291),x40292))) % 178.07/177.92 [4068]E(f329(f329(f22(a1),f329(f329(f81(a1),f329(f329(f81(a1),x40681),x40682)),f329(f329(f81(a1),x40681),x40682))),a103),f329(f329(f81(a1),f329(f329(f81(a1),x40681),x40681)),f329(f329(f22(a1),f329(f329(f81(a1),x40682),x40682)),a103))) % 178.07/177.92 [4094]E(f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),x40941),x40941)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),x40942),x40942)),a103)),f329(f329(f81(a1),f329(f329(f81(a1),x40941),f329(f329(f22(a1),x40942),a103))),f329(f329(f81(a1),x40941),f329(f329(f22(a1),x40942),a103)))) % 178.07/177.92 [4104]E(f329(f329(f22(a1),f329(f329(f81(a1),f329(f329(f22(a1),x41041),x41042)),f329(f329(f22(a1),x41041),x41042))),a103),f329(f329(f22(a1),f329(f329(f22(a1),f329(f329(f81(a1),x41041),x41041)),a103)),f329(f329(f81(a1),x41042),x41042))) % 178.07/177.92 [4105]E(f329(f329(f22(a1),f329(f329(f81(a1),f329(f329(f81(a1),x41051),x41052)),f329(f329(f81(a1),x41051),x41052))),a103),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),x41051),x41051)),a103)),f329(f329(f81(a1),x41052),x41052))) % 178.07/177.92 [4160]E(f329(f106(a1),f329(f329(f39(a875),f329(f329(f82(a875),f329(a110,f329(f76(a1),x41601))),f329(a110,f329(f76(a1),x41602)))),f224(f329(a110,f329(f76(a1),x41601)),f329(a110,f329(f76(a1),x41602))))),f226(x41601,x41602)) % 178.07/177.92 [4206]E(f329(f329(f270(f882(a105,a105),a105,f882(a105,a105),f882(x42061,f882(a105,a105))),f274(f329(a3,f329(f194(f876(x42061)),x42062)))),f329(f329(f8(x42061,f883(f882(a105,a105),f882(x42061,f882(a105,a105))),a105),f264(x42061,f882(a105,a105))),f329(f329(f8(a875,x42061,a105),f329(f164(x42061),x42062)),a19))),f280(x42061,x42062)) % 178.07/177.92 [4289]E(f329(f141(a875,f876(x42891),f329(f7(f876(x42891),a875,a875),f329(f329(f8(a875,f883(a875,a875),f876(x42891)),f242(a875)),f194(f876(x42891)))),f2(a875)),f329(f168(f876(x42891)),f179(x42891,x42892))),f329(f194(f876(f876(x42891))),f329(f135(f876(x42891),f329(f329(f8(a869,a869,f876(x42891)),a324),f329(f329(f7(f876(x42891),f876(x42891),a869),a326),f119(x42891)))),x42892))) % 178.07/177.92 [4295]E(f329(f329(f43(a875,f883(x42951,a869)),f252(f883(a875,a869))),f329(f329(f7(a875,f883(a875,f883(x42951,a869)),f883(x42951,a869)),f329(f329(f8(f883(a875,a869),f883(f883(a875,f883(x42951,a869)),f883(x42951,a869)),a875),f43(a875,f883(x42951,a869))),f299(a875,f2(a875)))),x42952)),f329(f329(f43(a875,f883(x42951,a869)),f252(f883(a875,a869))),x42952)) % 178.07/177.92 [4315]P24(f329(f62(a875),f329(f249(a875),f329(f329(f18(a875,a869,a869),f329(f329(f8(a869,f883(a869,a869),a875),a327),x43151)),f329(f329(f7(a875,a875,a869),f244(a875)),x43152))))) % 178.07/177.92 [4431]E(f329(f249(f882(f876(x44311),f876(x44311))),f329(f268(f876(x44311),f876(x44311),a869),f329(f329(f18(f876(x44311),f883(f876(x44311),a869),f883(f876(x44311),a869)),f329(f329(f8(f883(f876(x44311),f883(a869,a869)),f883(f883(f876(x44311),a869),f883(f876(x44311),a869)),f876(x44311)),f18(f876(x44311),a869,a869)),f329(f329(f8(f883(f876(x44311),a869),f883(f876(x44311),f883(a869,a869)),f876(x44311)),f329(f8(a869,f883(a869,a869),f876(x44311)),a328)),f329(f329(f7(f876(x44311),f883(f876(x44311),a875),f883(f876(x44311),a869)),f329(f329(f8(f883(a875,a869),f883(f883(f876(x44311),a875),f883(f876(x44311),a869)),f876(x44311)),f8(a875,a869,f876(x44311))),f329(f329(f8(a875,f883(a875,a869),f876(x44311)),f244(a875)),f194(f876(x44311))))),f194(f876(x44311)))))),f329(f329(f18(f876(x44311),f883(f876(x44311),a869),f883(f876(x44311),a869)),f329(f329(f8(f883(f876(x44311),f883(a869,a869)),f883(f883(f876(x44311),a869),f883(f876(x44311),a869)),f876(x44311)),f18(f876(x44311),a869,a869)),f329(f329(f8(f883(f876(x44311),a869),f883(f876(x44311),f883(a869,a869)),f876(x44311)),f329(f8(a869,f883(a869,a869),f876(x44311)),a327)),f329(f329(f7(f876(x44311),f883(f876(x44311),a875),f883(f876(x44311),a869)),f329(f329(f8(f883(a875,a869),f883(f883(f876(x44311),a875),f883(f876(x44311),a869)),f876(x44311)),f8(a875,a869,f876(x44311))),f329(f329(f8(a875,f883(a875,a869),f876(x44311)),a326),f194(f876(x44311))))),f194(f876(x44311)))))),f329(f329(f7(f876(x44311),f883(f882(f876(x44311),f876(x44311)),a869),f883(f876(x44311),a869)),f329(f329(f8(f883(f876(x44311),f883(f883(f882(f876(x44311),f876(x44311)),a869),a869)),f883(f883(f882(f876(x44311),f876(x44311)),a869),f883(f876(x44311),a869)),f876(x44311)),f7(f876(x44311),f883(f882(f876(x44311),f876(x44311)),a869),a869)),f329(f329(f8(f883(f876(x44311),f882(f876(x44311),f876(x44311))),f883(f876(x44311),f883(f883(f882(f876(x44311),f876(x44311)),a869),a869)),f876(x44311)),f329(f8(f882(f876(x44311),f876(x44311)),f883(f883(f882(f876(x44311),f876(x44311)),a869),a869),f876(x44311)),f331(f882(f876(x44311),f876(x44311))))),f264(f876(x44311),f876(x44311))))),f144(x44311,x44312)))))),f145(x44311,x44312)) % 178.07/177.92 [4548]~P24(f329(f329(f92(a1),f329(f329(f81(a1),x45481),x45481)),f329(f329(f22(a1),f329(f329(f81(a1),x45482),x45482)),a103))) % 178.07/177.92 [4097]E(f329(f329(f81(a1),f329(f329(f81(a1),f329(f329(f82(a1),x40971),x40972)),f329(f329(f82(a1),x40971),x40972))),x40972),f329(f329(f82(a1),f329(f329(f22(a1),f329(f329(f81(a1),x40971),x40971)),a103)),x40972)) % 178.07/177.92 [4204]E(f329(a110,f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),x42041),x42042)),f193(f883(f882(a875,a875),a869)))))),f329(f329(f22(a875),x42041),x42042)) % 178.07/177.92 [4209]E(f329(f329(f286(x42091,x42091,x42091),f329(f329(f116(f883(f882(x42091,x42091),a869)),x42092),f305(x42091,f193(f883(f882(x42091,x42091),a869))))),f305(x42091,f329(f329(f116(f883(f882(x42091,x42091),a869)),x42092),f305(x42091,f193(f883(f882(x42091,x42091),a869)))))),f305(x42091,x42092)) % 178.07/177.92 [4247]E(f273(x42471,f329(f135(f882(a105,x42471),f329(f268(a105,x42471,a869),f329(f329(f8(a869,f883(x42471,a869),a105),f16(a869,x42471)),f329(f244(a105),f2(a105))))),x42472)),f273(x42471,x42472)) % 178.07/177.92 [4248]E(f275(x42481,f329(f135(f882(a105,x42481),f329(f268(a105,x42481,a869),f329(f329(f8(a869,f883(x42481,a869),a105),f16(a869,x42481)),f329(f244(a105),f2(a105))))),x42482)),f275(x42481,x42482)) % 178.07/177.92 [4250]E(f329(f80(a1),f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),x42501),x42502)),f193(f883(f882(a875,a875),a869)))))),f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),x42502),x42501)),f193(f883(f882(a875,a875),a869)))))) % 178.07/177.92 [4307]E(f329(f329(f285(f876(a875),x43071),f144(a875,a248)),f329(f329(f7(x43071,f876(f883(x43071,a875)),f876(a875)),f329(f329(f8(f883(f883(x43071,a875),a875),f883(f876(f883(x43071,a875)),f876(a875)),x43071),f153(f883(x43071,a875),a875)),f329(f7(f883(x43071,a875),x43071,a875),f5(f883(x43071,a875))))),x43072)),f152(x43071,x43072)) % 178.07/177.92 [4328]E(f329(f329(f87(a1,a875),f329(f109(a1),f329(f329(f81(a1),x43281),a103))),f329(f329(f18(a1,a875,a875),f329(f329(f7(a1,a875,f883(a875,a875)),f329(f329(f8(a869,f883(a875,f883(a875,a875)),a1),f102(a875)),a198)),f2(a875))),f329(f329(f8(a875,a875,a1),a118),f329(f329(f8(a875,a875,a1),f329(f241(a875),x43282)),a110)))),f329(f329(f241(a875),f329(a118,x43282)),f329(f109(a875),x43281))) % 178.07/177.92 [4329]E(f329(f329(f87(a1,a875),f329(f109(a1),f329(f329(f81(a1),x43291),a103))),f329(f329(f18(a1,a875,a875),f329(f329(f7(a1,a875,f883(a875,a875)),f329(f329(f8(a869,f883(a875,f883(a875,a875)),a1),f102(a875)),a198)),f329(a118,x43292))),f329(f329(f8(a875,a875,a1),a118),f329(f329(f8(a875,a875,a1),f329(f242(a875),x43292)),a110)))),f329(f329(f242(a875),f329(a118,x43292)),f329(f109(a875),x43291))) % 178.07/177.92 [4349]E(f329(f141(f876(x43491),f876(x43491),f127(x43491),f119(x43491)),f329(f329(f153(f876(x43491),f876(x43491)),f155(f876(x43491),x43491,f119(x43491),f329(f329(f8(f876(x43491),f883(f876(x43491),f876(x43491)),x43491),f16(f876(x43491),f876(x43491))),f329(f329(f7(x43491,f876(x43491),f876(x43491)),f150(x43491)),f119(x43491))))),x43492)),f329(f329(f153(f876(x43491),x43491),f140(x43491)),f329(f135(f876(x43491),f329(f329(f8(a869,a869,f876(x43491)),a324),f329(f329(f7(f876(x43491),f876(x43491),a869),a326),f119(x43491)))),x43492))) % 178.07/177.92 [4412]E(f329(f268(a1,a1,a869),f329(f329(f7(a1,f883(a1,a869),f883(a1,a869)),f329(f329(f8(f883(a1,f883(a869,a869)),f883(f883(a1,a869),f883(a1,a869)),a1),f18(a1,a869,a869)),f329(f329(f8(f883(a1,a869),f883(a1,f883(a869,a869)),a1),f329(f8(a869,f883(a869,a869),a1),a327)),f329(f329(f8(f883(a1,a1),f883(a1,a869),a1),f329(f8(a1,a869,a1),f329(a326,x44121))),f329(f329(f8(a1,f883(a1,a1),a1),f81(a1)),f329(f82(a1),x44122)))))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f329(f8(a869,a869,a1),f329(a332,f329(f329(f244(a1),f2(a1)),x44122))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f243(a1),f2(a1)))),f329(f329(f7(a1,a1,a869),f244(a1)),x44122))))),f329(f329(f8(a869,a869,a1),f329(a332,f329(a324,f329(f329(f244(a1),f2(a1)),x44122)))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f244(a1),x44122))),f329(f329(f7(a1,a1,a869),f243(a1)),f2(a1))))))),f49(x44121,x44122)) % 178.07/177.92 [4414]E(f329(f249(x44141),f329(f329(f8(f883(a875,a869),a869,x44141),f88(a875)),f329(f329(f7(x44141,f883(a875,a869),f883(a875,a869)),f329(f329(f8(f883(a875,f883(a869,a869)),f883(f883(a875,a869),f883(a875,a869)),x44141),f18(a875,a869,a869)),f329(f329(f8(f883(a875,a869),f883(a875,f883(a869,a869)),x44141),f329(f8(a869,f883(a869,a869),a875),a327)),f329(f329(f7(x44141,f883(a875,x44141),f883(a875,a869)),f329(f329(f8(f883(x44141,a869),f883(f883(a875,x44141),f883(a875,a869)),x44141),f8(x44141,a869,a875)),a326)),f329(f164(x44141),x44142))))),f329(f329(f7(a875,a875,a869),f244(a875)),f329(f194(f876(x44141)),x44142))))),f329(f171(x44141),x44142)) % 178.07/177.92 [4219]E(f329(f329(f22(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),x42191),a103)),x42192)),f329(f329(f22(a1),f329(f329(f81(a1),x42191),a103)),x42192))),a103),f329(f329(f22(a1),f329(f329(f81(a1),x42191),x42191)),f329(f329(f22(a1),f329(f329(f81(a1),x42192),x42192)),a103))) % 178.07/177.92 [4344]E(f329(f141(f876(f876(x43441)),f876(f876(x43441)),f127(f876(x43441)),f119(f876(x43441))),f329(f329(f153(f876(x43441),f876(f876(x43441))),f155(f876(f876(x43441)),x43441,f119(f876(x43441)),f329(f16(f883(f876(x43441),f876(f876(x43441))),x43441),f329(f329(f7(f876(x43441),f876(f876(x43441)),f876(f876(x43441))),f150(f876(x43441))),f119(f876(x43441)))))),x43442)),f329(f329(f153(f876(x43441),f876(x43441)),f170(x43441)),f329(f135(f876(x43441),f329(f329(f8(a869,a869,f876(x43441)),a324),f329(f329(f7(f876(x43441),f876(x43441),a869),a326),f119(x43441)))),x43442))) % 178.07/177.92 [4355]E(f329(f329(f87(a1,a875),f329(f109(a1),f329(f329(f81(a1),x43551),a103))),f329(f329(f18(a1,a875,a875),f329(f329(f7(a1,a875,f883(a875,a875)),f329(f329(f8(a869,f883(a875,f883(a875,a875)),a1),f102(a875)),a198)),f2(a875))),f329(f329(f8(a875,a875,a1),a118),f329(f329(f7(a1,a875,a875),f329(f329(f8(a875,f883(a875,a875),a1),f241(a875)),a110)),x43552)))),f329(f329(f241(a875),f329(f109(a875),x43551)),f329(a118,x43552))) % 178.07/177.92 [4356]E(f329(f329(f87(a1,a875),f329(f109(a1),f329(f329(f81(a1),x43561),a103))),f329(f329(f18(a1,a875,a875),f329(f329(f7(a1,a875,f883(a875,a875)),f329(f329(f8(a869,f883(a875,f883(a875,a875)),a1),f102(a875)),a198)),f329(a118,x43562))),f329(f329(f8(a875,a875,a1),a118),f329(f329(f7(a1,a875,a875),f329(f329(f8(a875,f883(a875,a875),a1),f242(a875)),a110)),x43562)))),f329(f329(f242(a875),f329(f109(a875),x43561)),f329(a118,x43562))) % 178.07/177.92 [4343]E(f329(f268(x43431,x43431,a869),f329(f329(f18(x43431,a869,f883(x43431,a869)),f329(f329(f8(f883(x43431,f883(a869,a869)),f883(a869,f883(x43431,a869)),x43431),f7(x43431,a869,a869)),f329(f329(f8(f883(x43431,a869),f883(x43431,f883(a869,a869)),x43431),f329(f8(a869,f883(a869,a869),x43431),a327)),a326))),x43432)),f261(x43431,x43432)) % 178.07/177.92 [4390]E(f329(f329(f39(a875),x43901),f329(f329(f81(a875),f329(f109(a875),f329(f329(f22(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))),a103))),x43902)),f329(f329(f39(a875),x43901),f329(a118,f329(a118,f329(a118,x43902))))) % 178.07/177.92 [4391]E(f45(a875,x43911,f329(f329(f81(a875),f329(f109(a875),f329(f329(f22(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))),a103))),x43912)),f45(a875,x43911,f329(a118,f329(a118,f329(a118,x43912))))) % 178.07/177.92 [4392]E(f45(a875,f329(f329(f81(a875),f329(f109(a875),f329(f329(f22(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))),a103))),x43921),x43922),f45(a875,f329(a118,f329(a118,f329(a118,x43921))),x43922)) % 178.07/177.92 [4405]E(f126(f329(x44051,f329(f329(f82(a105),f329(f109(a105),f329(f329(f22(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))),a103))),x44052))),f329(f209(x44051),x44052)) % 178.07/177.92 [4406]E(f329(f329(f39(a875),f329(f329(f81(a875),f329(f109(a875),f329(f329(f22(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))),a103))),x44061)),x44062),f329(f329(f39(a875),f329(a118,f329(a118,f329(a118,x44061)))),x44062)) % 178.07/177.92 [4455]~E(f34(x44551,x44552),f329(a26,x44553)) % 178.07/177.92 [4456]~E(f33(x44561,x44562),f329(a26,x44563)) % 178.07/177.92 [4457]~E(f329(a26,x44571),f34(x44572,x44573)) % 178.07/177.92 [4458]~E(f329(a26,x44581),f33(x44582,x44583)) % 178.07/177.92 [4472]~E(f29(x44721,x44722,x44723),a24) % 178.07/177.92 [4473]~E(f31(x44731,x44732,x44733),a24) % 178.07/177.92 [4474]~E(f30(x44741,x44742,x44743),a24) % 178.07/177.92 [3177]E(f329(f197(x31771,x31772),x31773),f124(x31771,x31772)) % 178.07/177.92 [3198]E(f329(f208(x31981,x31982),x31983),f329(f128(x31981),x31982)) % 178.07/177.92 [3278]E(f329(f329(f207(x32781,x32782),x32783),f206(x32781)),f206(x32782)) % 178.07/177.92 [3279]E(f329(f329(f153(x32791,x32792),x32793),f119(x32791)),f119(x32792)) % 178.07/177.92 [3299]E(f32(f29(x32991,x32992,x32993)),f2(a875)) % 178.07/177.92 [3321]E(f329(f189(x33211,x33212,x33213),f2(a875)),x33212) % 178.07/177.92 [3322]E(f329(f194(a870),f29(x33221,x33222,x33223)),f2(a875)) % 178.07/177.92 [3324]E(f329(f329(f181(x33241,x33242),x33243),f119(x33242)),f119(f882(x33241,x33242))) % 178.07/177.92 [3358]E(f86(x33581,f63(x33581,x33582,x33583)),f329(f64(x33581,x33582),x33583)) % 178.07/177.92 [3362]E(f253(x33621,x33622,f253(x33622,x33621,x33623)),x33623) % 178.07/177.92 [3410]E(f139(x34101,x34102,f151(x34101,x34103)),f151(x34101,f139(x34101,x34102,x34103))) % 178.07/177.92 [3429]E(f329(f263(f876(x34291),f876(x34291)),f166(x34291,x34292,x34293)),f329(f135(x34291,x34292),x34293)) % 178.07/177.92 [3506]E(f190(x35061,x35062,x35063,f2(a875)),x35062) % 178.07/177.92 [3507]E(f17(x35071,x35072,x35073,f2(a105)),x35072) % 178.07/177.92 [3514]E(f162(x35141,x35142,x35143,f119(x35141)),f119(x35142)) % 178.07/177.92 [3515]E(f163(x35151,x35152,x35153,f119(x35151)),f119(x35152)) % 178.07/177.92 [3522]E(f329(f329(f164(x35221),f329(f329(f150(x35221),x35222),x35223)),f2(a875)),x35222) % 178.07/177.92 [3550]E(f60(x35501,x35502,f119(x35501),x35503),f119(f882(x35501,x35502))) % 178.07/177.92 [3571]P21(x35711,x35712,x35713,f193(f883(x35711,a869))) % 178.07/177.92 [3729]E(f329(f74(x37291,x37292,x37291,x37293),f35(x37291)),x37293) % 178.07/177.92 [3905]P24(f329(f329(f331(f882(x39051,x39051)),f329(f329(f264(x39051,x39051),x39052),x39052)),f305(x39051,x39053))) % 178.07/177.92 [4549]~P24(f329(f329(f331(f882(f876(x45491),f876(x45491))),f329(f329(f264(f876(x45491),f876(x45491)),x45492),f119(x45491))),f146(x45491,x45493))) % 178.07/177.92 [4550]~P24(f329(f329(f331(f882(f876(x45501),f876(x45501))),f329(f329(f264(f876(x45501),f876(x45501)),x45502),f119(x45501))),f144(x45501,x45503))) % 178.07/177.92 [4551]~P24(f329(f329(f331(f882(f876(x45511),f876(x45511))),f329(f329(f264(f876(x45511),f876(x45511)),x45512),f119(x45511))),f156(x45511,x45513))) % 178.07/177.92 [4552]~P24(f329(f329(f331(f882(f876(x45521),f876(x45521))),f329(f329(f264(f876(x45521),f876(x45521)),f119(x45521)),x45522)),f144(x45521,x45523))) % 178.07/177.92 [4553]~P24(f329(f329(f331(f882(f876(x45531),f876(x45531))),f329(f329(f264(f876(x45531),f876(x45531)),f119(x45531)),x45532)),f156(x45531,x45533))) % 178.07/177.92 [3251]E(f329(f329(f210(x32511),x32512),x32513),f211(x32511,f223(x32512,x32513))) % 178.07/177.92 [3310]E(f329(f284(x33101,x33102),f329(f284(x33102,x33101),x33103)),x33103) % 178.07/177.92 [3334]E(f329(f329(f181(x33341,x33342),f119(x33341)),x33343),f119(f882(x33341,x33342))) % 178.07/177.92 [3337]E(f175(x33371,x33372,f329(f250(a875),x33373)),f329(f329(f174(x33371),x33373),x33372)) % 178.07/177.92 [3354]E(f151(x33541,f329(f135(x33541,x33542),x33543)),f329(f135(x33541,x33542),f151(x33541,x33543))) % 178.07/177.92 [3356]E(f329(f260(x33561,x33562),f329(f284(x33562,x33561),x33563)),f329(f262(x33562,x33561),x33563)) % 178.07/177.92 [3357]E(f329(f262(x33571,x33572),f329(f284(x33572,x33571),x33573)),f329(f260(x33572,x33571),x33573)) % 178.07/177.92 [3374]E(f329(f135(x33741,x33742),f329(f168(x33741),x33743)),f329(f168(x33741),f329(f135(x33741,x33742),x33743))) % 178.07/177.92 [3387]E(f329(f329(f137(x33871),x33872),f329(f170(x33871),x33873)),f329(f329(f137(x33871),f329(a118,x33872)),x33873)) % 178.07/177.92 [3405]E(f32(f30(x34051,x34052,x34053)),f329(f329(f81(a875),f32(x34053)),f329(a118,f2(a875)))) % 178.07/177.92 [3406]E(f329(f308(x34061,x34062,x34063),f193(f883(x34061,a869))),f193(f883(x34062,a869))) % 178.07/177.92 [3407]E(f329(f309(x34071,x34072,x34073),f193(f883(x34072,a869))),f193(f883(x34071,a869))) % 178.07/177.92 [3408]E(f329(f309(x34081,x34082,x34083),f252(f883(x34082,a869))),f252(f883(x34081,a869))) % 178.07/177.92 [3409]E(f329(f283(x34091,x34092,x34093),f193(f883(x34091,a869))),f193(f883(x34092,a869))) % 178.07/177.92 [3438]E(f329(f329(f307(x34381),x34382),f329(f171(x34381),x34383)),f329(f171(x34381),f139(x34381,x34382,x34383))) % 178.07/177.92 [3450]E(f237(x34501,x34502,f329(f236(x34501),x34503)),f329(f329(f81(a875),f329(x34502,x34503)),f329(a118,f2(a875)))) % 178.07/177.92 [3526]E(f329(f194(a870),f30(x35261,x35262,x35263)),f329(f329(f81(a875),f329(f194(a870),x35263)),f329(a118,f2(a875)))) % 178.07/177.92 [3527]E(f329(f308(f882(x35271,x35272),x35272,f267(x35271,x35272)),x35273),f329(f260(x35271,x35272),x35273)) % 178.07/177.92 [3528]E(f329(f308(f882(x35281,x35282),x35281,f263(x35281,x35282)),x35283),f329(f262(x35281,x35282),x35283)) % 178.07/177.92 [3596]E(f329(f329(f264(x35961,x35962),f329(f263(x35961,x35962),x35963)),f329(f267(x35961,x35962),x35963)),x35963) % 178.07/177.92 [3603]E(f329(f194(f877(x36031)),f129(x36031,x36032,x36033)),f329(f329(f81(a875),f329(f194(f877(x36031)),x36033)),f329(a118,f2(a875)))) % 178.07/177.92 [3606]E(f329(f329(f268(x36061,x36062,x36061),f16(x36061,x36062)),x36063),f329(f263(x36061,x36062),x36063)) % 178.07/177.92 [3626]E(f184(x36261,x36262,x36263,f329(f16(f879(x36262),x36261),f206(x36262))),x36263) % 178.07/177.92 [3627]E(f184(x36271,x36272,f329(f16(f879(x36272),x36271),f206(x36272)),x36273),x36273) % 178.07/177.92 [3683]E(f32(f31(x36831,x36832,x36833)),f329(f329(f81(a875),f329(f329(f81(a875),f32(x36832)),f32(x36833))),f329(a118,f2(a875)))) % 178.07/177.92 [3732]E(f329(f74(x37321,x37321,x37322,f35(x37321)),x37323),x37323) % 178.07/177.92 [3840]E(f329(f194(a870),f31(x38401,x38402,x38403)),f329(f329(f81(a875),f329(f329(f81(a875),f329(f194(a870),x38402)),f329(f194(a870),x38403))),f329(a118,f2(a875)))) % 178.07/177.92 [3915]P24(f329(f329(f243(f883(x39151,a869)),f329(f171(x39151),f329(f135(x39151,x39152),x39153))),f329(f171(x39151),x39153))) % 178.07/177.92 [3960]P24(f329(f329(f243(f883(x39601,a869)),f329(f171(x39601),f329(f329(f174(x39601),x39602),x39603))),f329(f171(x39601),x39603))) % 178.07/177.92 [3961]P24(f329(f329(f243(f883(x39611,a869)),f329(f171(x39611),f329(f329(f137(x39611),x39612),x39613))),f329(f171(x39611),x39613))) % 178.07/177.92 [3966]P24(f329(f329(f243(f883(x39661,a869)),f329(f171(x39661),f169(x39661,x39662,x39663))),f329(f171(x39661),x39663))) % 178.07/177.92 [3967]P24(f329(f329(f243(f883(x39671,a869)),f329(f171(x39671),f175(x39671,x39672,x39673))),f329(f171(x39671),x39672))) % 178.07/177.92 [3990]P21(f882(x39901,x39902),f882(x39902,x39901),f329(f268(x39901,x39902,f882(x39902,x39901)),f329(f7(x39902,x39901,f882(x39902,x39901)),f264(x39902,x39901))),x39903) % 178.07/177.92 [4002]E(f329(f329(f329(f188(f876(x40021),f876(x40021)),f45(a875,x40022,f329(f194(f876(x40021)),x40023))),f167(x40021)),x40023),f329(f329(f329(f188(f876(x40021),f876(x40021)),x40022),f167(x40021)),x40023)) % 178.07/177.92 [4044]P24(f329(f329(f331(f882(f876(x40441),f876(x40441))),f329(f329(f264(f876(x40441),f876(x40441)),x40442),x40442)),f157(x40441,f305(x40441,x40443)))) % 178.07/177.92 [4189]E(f86(f882(x41891,x41892),f329(f329(f18(f882(x41891,x41892),x41892,a869),f329(f329(f8(x41891,f883(x41892,a869),f882(x41891,x41892)),x41893),f263(x41891,x41892))),f267(x41891,x41892))),f86(f882(x41891,x41892),f329(f268(x41891,x41892,a869),x41893))) % 178.07/177.92 [4190]E(f91(f882(x41901,x41902),f329(f329(f18(f882(x41901,x41902),x41902,a869),f329(f329(f8(x41901,f883(x41902,a869),f882(x41901,x41902)),x41903),f263(x41901,x41902))),f267(x41901,x41902))),f91(f882(x41901,x41902),f329(f268(x41901,x41902,a869),x41903))) % 178.07/177.92 [4226]E(f329(f329(f285(f882(a875,x42261),x42261),f321(a875,x42261,a248,x42262)),f329(f329(f18(x42261,x42261,f882(a875,x42261)),f329(f329(f8(a875,f883(x42261,f882(a875,x42261)),x42261),f264(a875,x42261)),x42263)),f5(x42261))),f323(x42261,x42263,x42262)) % 178.07/177.92 [4291]E(f329(f269(x42911,x42911,x42912,x42912,f5(x42911),f5(x42912)),x42913),x42913) % 178.07/177.92 [4366]E(f329(f141(f876(f876(x43661)),f876(f876(x43661)),f127(f876(x43661)),f119(f876(x43661))),f329(f329(f153(f876(x43661),f876(f876(x43661))),f329(f329(f7(f876(x43661),f876(x43661),f876(f876(x43661))),f329(f329(f8(f883(x43661,f876(x43661)),f883(f876(x43661),f876(f876(x43661))),f876(x43661)),f153(x43661,f876(x43661))),f329(f7(x43661,f876(x43661),f876(x43661)),f150(x43661)))),x43662)),f55(x43661,x43663,x43662))),f55(x43661,f329(a118,x43663),x43662)) % 178.07/177.92 [4427]E(f329(f238(a875,f882(x44271,f877(x44271)),f2(a875),f329(f268(x44271,f877(x44271),a875),f329(f329(f7(x44271,a875,f883(f877(x44271),a875)),f329(f329(f8(f883(f877(x44271),f883(a875,a875)),f883(a875,f883(f877(x44271),a875)),x44271),f7(f877(x44271),a875,a875)),f329(f329(f8(f883(f877(x44271),a875),f883(f877(x44271),f883(a875,a875)),x44271),f329(f8(a875,f883(a875,a875),f877(x44271)),f81(a875))),f329(f329(f7(x44271,f883(f877(x44271),a875),f883(f877(x44271),a875)),f329(f329(f8(f883(a875,a875),f883(f883(f877(x44271),a875),f883(f877(x44271),a875)),x44271),f8(a875,a875,f877(x44271))),f329(f329(f8(a875,f883(a875,a875),x44271),f81(a875)),x44272))),f131(x44271,x44272))))),f79(a875)))),f329(f134(x44271),x44273)),f329(f131(x44271,x44272),x44273)) % 178.07/177.92 [4430]E(f329(f329(f87(a1,x44301),f226(f329(f329(f74(f882(a1,a1),a1,x44301,f267(a1,a1)),f220(x44301)),x44302),f329(f329(f74(f882(a1,a1),a1,x44301,f267(a1,a1)),f220(x44301)),x44303))),f329(f329(f18(a1,a1,x44301),f329(f329(f8(a1,f883(a1,x44301),a1),f210(x44301)),f329(f329(f18(a1,a1,a1),f329(f329(f8(a1,f883(a1,a1),a1),f81(a1)),f329(f329(f8(a1,a1,a1),f329(f82(a1),f329(f329(f74(f882(a1,a1),a1,x44301,f263(a1,a1)),f220(x44301)),x44302))),f329(f329(f7(a1,a1,a1),f39(a1)),f329(f329(f74(f882(a1,a1),a1,x44301,f267(a1,a1)),f220(x44301)),x44302))))),f329(f329(f8(a1,a1,a1),f329(f82(a1),f329(f329(f74(f882(a1,a1),a1,x44301,f263(a1,a1)),f220(x44301)),x44303))),f329(f329(f7(a1,a1,a1),f39(a1)),f329(f329(f74(f882(a1,a1),a1,x44301,f267(a1,a1)),f220(x44301)),x44303)))))),f5(a1))),f231(x44301,x44302,x44303)) % 178.07/177.92 [4467]~E(f329(f329(f150(x44671),x44672),x44673),x44673) % 178.07/177.92 [4476]~E(f329(f329(f150(x44761),x44762),x44763),f119(x44761)) % 178.07/177.92 [4498]~E(f329(f329(f307(x44981),x44982),x44983),f193(f883(x44981,a869))) % 178.07/177.92 [4525]~E(f329(f308(x45251,f883(x45251,a869),x45252),x45253),f329(f306(x45251),x45253)) % 178.07/177.92 [3315]E(f329(f329(f158(x33151,f119(x33151)),x33152),x33153),f119(x33151)) % 178.07/177.92 [3316]E(f329(f140(x33161),f329(f329(f150(x33161),x33162),x33163)),x33162) % 178.07/177.92 [3317]E(f329(f170(x33171),f329(f329(f150(x33171),x33172),x33173)),x33173) % 178.07/177.92 [3361]E(f329(f329(f137(x33611),f79(a875)),f329(f329(f150(x33611),x33612),x33613)),x33613) % 178.07/177.92 [3394]E(f120(x33941,f329(f329(f137(x33941),x33942),x33943)),f329(f329(f137(x33941),x33942),f120(x33941,x33943))) % 178.07/177.92 [3396]E(f329(f329(f158(x33961,x33962),x33963),f329(f329(f164(x33961),x33962),x33963)),x33962) % 178.07/177.92 [3420]E(f329(f329(f307(x34201),x34202),f329(f329(f307(x34201),x34202),x34203)),f329(f329(f307(x34201),x34202),x34203)) % 178.07/177.92 [3431]E(f329(f329(f177(x34311,x34312),f119(f882(x34311,x34312))),x34313),f206(x34312)) % 178.07/177.92 [3434]E(f329(f329(f307(x34341),x34342),f329(f171(x34341),x34343)),f329(f171(x34341),f329(f329(f150(x34341),x34342),x34343))) % 178.07/177.92 [3436]E(f329(f329(f137(x34361),x34362),f329(f170(x34361),x34363)),f329(f170(x34361),f329(f329(f137(x34361),x34362),x34363))) % 178.07/177.92 [3447]E(f329(f329(f174(x34471),f79(a875)),f329(f329(f150(x34471),x34472),x34473)),f329(f329(f150(x34471),x34472),f119(x34471))) % 178.07/177.92 [3491]E(f329(f64(x34911,x34912),f329(f329(f307(x34911),x34913),f193(f883(x34911,a869)))),x34913) % 178.07/177.92 [3534]E(f329(f329(f81(a875),x35341),f329(f329(f81(a875),x35342),x35343)),f329(f329(f81(a875),x35342),f329(f329(f81(a875),x35341),x35343))) % 178.07/177.92 [3535]E(f329(f329(f81(a1),x35351),f329(f329(f81(a1),x35352),x35353)),f329(f329(f81(a1),x35352),f329(f329(f81(a1),x35351),x35353))) % 178.07/177.92 [3540]E(f329(f329(f266(x35401,x35402),f193(f883(x35401,a869))),x35403),f193(f883(f882(x35401,x35402),a869))) % 178.07/177.92 [3563]E(f329(f329(f116(f883(x35631,a869)),x35632),x35633),f329(f329(f116(f883(x35631,a869)),x35633),x35632)) % 178.07/177.92 [3564]E(f329(f329(f107(f883(x35641,a869)),x35642),x35643),f329(f329(f107(f883(x35641,a869)),x35643),x35642)) % 178.07/177.92 [3566]E(f329(f329(f127(x35661),x35662),f329(f329(f150(x35661),x35663),f119(x35661))),f329(f167(x35661),f329(f329(f150(x35661),x35663),x35662))) % 178.07/177.92 [3567]E(f329(f329(f127(x35671),f329(f168(x35671),x35672)),f329(f168(x35671),x35673)),f329(f168(x35671),f329(f329(f127(x35671),x35673),x35672))) % 178.07/177.92 [3575]E(f329(f170(x35751),f329(f329(f174(x35751),f329(a118,x35752)),x35753)),f329(f329(f174(x35751),x35752),f329(f170(x35751),x35753))) % 178.07/177.92 [3582]P24(f329(f329(f331(x35821),x35822),f329(f329(f307(x35821),x35822),x35823))) % 178.07/177.92 [3586]E(f329(f329(f42(x35861,f883(x35862,a869)),f193(f883(x35861,a869))),x35863),f252(f883(x35862,a869))) % 178.07/177.92 [3589]E(f329(f283(x35891,x35891,f261(x35891,x35892)),x35893),f329(f329(f107(f883(x35891,a869)),x35892),x35893)) % 178.07/177.92 [3602]E(f329(f194(f876(x36021)),f329(f329(f150(x36021),x36022),x36023)),f329(f329(f81(a875),f329(f194(f876(x36021)),x36023)),f329(a118,f2(a875)))) % 178.07/177.92 [3608]E(f120(x36081,f329(f329(f127(x36081),x36082),f329(f329(f150(x36081),x36083),f119(x36081)))),x36082) % 178.07/177.92 [3609]E(f143(x36091,f329(f329(f127(x36091),x36092),f329(f329(f150(x36091),x36093),f119(x36091)))),x36093) % 178.07/177.92 [3615]E(f329(f329(f127(x36151),f329(f329(f174(x36151),x36152),x36153)),f329(f329(f137(x36151),x36152),x36153)),x36153) % 178.07/177.92 [3624]E(f329(f329(f22(a875),f329(f329(f81(a875),x36241),x36242)),f329(f329(f81(a875),x36243),x36242)),f329(f329(f22(a875),x36241),x36243)) % 178.07/177.92 [3625]E(f329(f329(f22(a875),f329(f329(f81(a875),x36251),x36252)),f329(f329(f81(a875),x36251),x36253)),f329(f329(f22(a875),x36252),x36253)) % 178.07/177.92 [3632]E(f329(f329(f127(x36321),f329(f168(x36321),x36322)),f329(f329(f150(x36321),x36323),f119(x36321))),f329(f168(x36321),f329(f329(f150(x36321),x36323),x36322))) % 178.07/177.92 [3634]E(f329(f329(f81(a875),f329(f194(f876(x36341)),x36342)),f329(f194(f876(x36341)),x36343)),f329(f194(f876(x36341)),f329(f329(f127(x36341),x36342),x36343))) % 178.07/177.92 [3637]E(f329(f329(f81(a875),f329(f194(f876(x36371)),x36372)),f329(f194(f876(x36371)),x36373)),f329(f194(f876(x36371)),f172(x36371,x36372,x36373))) % 178.07/177.92 [3645]E(f329(f329(f116(f883(x36451,a869)),f329(f171(x36451),x36452)),f329(f171(x36451),x36453)),f329(f171(x36451),f329(f329(f127(x36451),x36452),x36453))) % 178.07/177.92 [3646]E(f45(a875,f329(f329(f82(a875),x36461),x36462),f329(f329(f82(a875),x36461),x36463)),f329(f329(f82(a875),x36461),f45(a875,x36462,x36463))) % 178.07/177.92 [3659]E(f329(f329(f174(x36591),f329(f329(f22(a875),x36592),f79(a875))),f329(f170(x36591),x36593)),f329(f170(x36591),f329(f329(f174(x36591),x36592),x36593))) % 178.07/177.92 [3664]E(f329(f329(f107(f883(x36641,a869)),x36642),f329(f80(f883(x36641,a869)),x36643)),f329(f329(f22(f883(x36641,a869)),x36642),x36643)) % 178.07/177.92 [3665]E(f329(f329(f22(f883(x36651,a869)),x36652),f329(f80(f883(x36651,a869)),x36653)),f329(f329(f107(f883(x36651,a869)),x36652),x36653)) % 178.07/177.92 [3687]E(f329(f329(f266(x36871,x36872),x36873),f329(f16(f883(x36872,a869),x36871),f193(f883(x36872,a869)))),f193(f883(f882(x36871,x36872),a869))) % 178.07/177.92 [3689]E(f329(f329(f22(a875),f329(f329(f82(a875),x36891),x36892)),f329(f329(f82(a875),x36891),x36893)),f329(f329(f82(a875),x36891),f329(f329(f22(a875),x36892),x36893))) % 178.07/177.92 [3690]E(f329(f329(f81(a875),f329(f329(f82(a875),x36901),x36902)),f329(f329(f82(a875),x36901),x36903)),f329(f329(f82(a875),x36901),f329(f329(f81(a875),x36902),x36903))) % 178.07/177.92 [3691]E(f329(f329(f22(a1),f329(f329(f82(a1),x36911),x36912)),f329(f329(f82(a1),x36911),x36913)),f329(f329(f82(a1),x36911),f329(f329(f22(a1),x36912),x36913))) % 178.07/177.92 [3692]E(f329(f329(f81(a1),f329(f329(f82(a1),x36921),x36922)),f329(f329(f82(a1),x36921),x36923)),f329(f329(f82(a1),x36921),f329(f329(f81(a1),x36922),x36923))) % 178.07/177.92 [3693]E(f329(f329(f82(a1),f329(f329(f254(a1),x36931),x36932)),f329(f329(f254(a1),x36931),x36933)),f329(f329(f254(a1),x36931),f329(f329(f81(a875),x36932),x36933))) % 178.07/177.92 [3707]E(f329(f329(f43(x37071,f883(x37072,a869)),x37073),f329(f16(f883(x37072,a869),x37071),f193(f883(x37072,a869)))),f193(f883(x37072,a869))) % 178.07/177.92 [3709]E(f45(a875,f329(f329(f82(a875),x37091),x37092),f329(f329(f82(a875),x37093),x37092)),f329(f329(f82(a875),f45(a875,x37091,x37093)),x37092)) % 178.07/177.92 [3713]E(f45(a1,f329(f329(f22(a1),x37131),f45(a1,x37132,x37133)),x37133),f45(a1,f329(f329(f22(a1),x37131),x37132),x37133)) % 178.07/177.92 [3714]E(f45(a1,f329(f329(f82(a1),x37141),f45(a1,x37142,x37143)),x37143),f45(a1,f329(f329(f82(a1),x37141),x37142),x37143)) % 178.07/177.92 [3715]P24(f329(f329(f243(f883(x37151,a869)),x37152),f329(f329(f307(x37151),x37153),x37152))) % 178.07/177.92 [3718]E(f329(f308(f882(x37181,x37182),x37181,f263(x37181,x37182)),f329(f171(f882(x37181,x37182)),x37183)),f183(x37181,x37182,f329(f177(x37181,x37182),x37183))) % 178.07/177.92 [3766]P24(f329(f62(x37661),f183(x37661,x37662,f329(f177(x37661,x37662),x37663)))) % 178.07/177.92 [3791]E(f329(f329(f42(f883(x37911,a869),f883(x37911,a869)),x37912),f329(f116(f883(x37911,a869)),x37913)),f329(f329(f116(f883(x37911,a869)),x37913),f41(f883(x37911,a869),x37912))) % 178.07/177.92 [3792]E(f329(f329(f43(f883(x37921,a869),f883(x37921,a869)),x37922),f329(f107(f883(x37921,a869)),x37923)),f329(f329(f107(f883(x37921,a869)),x37923),f40(f883(x37921,a869),x37922))) % 178.07/177.92 [3803]E(f329(f171(x38031),f329(f329(f329(f188(f876(x38031),f876(x38031)),x38032),f167(x38031)),x38033)),f329(f171(x38031),x38033)) % 178.07/177.92 [3807]E(f329(f329(f174(x38071),f329(f194(f876(x38071)),f176(x38071,x38072,x38073))),x38073),f176(x38071,x38072,x38073)) % 178.07/177.92 [3808]E(f183(x38081,x38082,f329(f329(f8(x38082,f879(x38082),x38081),f236(x38082)),x38083)),f252(f883(x38081,a869))) % 178.07/177.92 [3812]E(f329(f194(f876(x38121)),f329(f329(f329(f188(f876(x38121),f876(x38121)),x38122),f167(x38121)),x38123)),f329(f194(f876(x38121)),x38123)) % 178.07/177.92 [3815]E(f329(f329(f268(x38151,x38152,x38152),f329(f16(f883(x38152,x38152),x38151),f5(x38152))),x38153),f329(f267(x38151,x38152),x38153)) % 178.07/177.92 [3821]E(f45(a1,f329(f329(f22(a1),f45(a1,x38211,x38212)),x38213),x38212),f45(a1,f329(f329(f22(a1),x38211),x38213),x38212)) % 178.07/177.92 [3822]E(f45(a1,f329(f329(f254(a1),f45(a1,x38221,x38222)),x38223),x38222),f45(a1,f329(f329(f254(a1),x38221),x38223),x38222)) % 178.07/177.92 [3825]E(f329(f329(f43(f883(f882(x38251,x38252),a869),f883(x38252,a869)),x38253),f260(x38251,x38252)),f329(f260(x38251,x38252),f40(f883(f882(x38251,x38252),a869),x38253))) % 178.07/177.92 [3826]E(f329(f329(f43(f883(f882(x38261,x38262),a869),f883(x38261,a869)),x38263),f262(x38261,x38262)),f329(f262(x38261,x38262),f40(f883(f882(x38261,x38262),a869),x38263))) % 178.07/177.92 [3852]E(f329(f74(x38521,x38521,x38521,x38522),f329(f329(f188(x38521,x38521),x38523),x38522)),f329(f329(f188(x38521,x38521),f329(a118,x38523)),x38522)) % 178.07/177.92 [3862]E(f238(f879(x38621),x38622,f206(x38621),f329(f329(f8(x38621,f879(x38621),x38622),f236(x38621)),x38623)),f329(f207(x38622,x38621),x38623)) % 178.07/177.92 [3869]E(f329(f329(f137(x38691),f329(f329(f22(a875),f329(f194(f876(x38691)),x38692)),x38693)),f329(f168(x38691),x38692)),f329(f168(x38691),f329(f329(f174(x38691),x38693),x38692))) % 178.07/177.92 [3870]E(f329(f329(f174(x38701),f329(f329(f22(a875),f329(f194(f876(x38701)),x38702)),x38703)),f329(f168(x38701),x38702)),f329(f168(x38701),f329(f329(f137(x38701),x38703),x38702))) % 178.07/177.92 [3873]E(f329(f329(f81(a875),f329(f165(a875),f329(f329(f153(x38731,a875),x38732),x38733))),f329(f194(f876(x38731)),x38733)),f154(x38731,x38732,x38733)) % 178.07/177.92 [3891]E(f329(f167(x38911),f329(f329(f329(f188(f876(x38911),f876(x38911)),x38912),f167(x38911)),x38913)),f329(f329(f329(f188(f876(x38911),f876(x38911)),f329(a118,x38912)),f167(x38911)),x38913)) % 178.07/177.92 [3906]P24(f329(f329(f243(a875),f329(f194(f876(x39061)),f329(f135(x39061,x39062),x39063))),f329(f194(f876(x39061)),x39063))) % 178.07/177.92 [3923]E(f329(f329(f116(f883(f883(x39231,a869),a869)),f329(f306(x39231),x39232)),f329(f308(f883(x39231,a869),f883(x39231,a869),f329(f307(x39231),x39233)),f329(f306(x39231),x39232))),f329(f306(x39231),f329(f329(f307(x39231),x39233),x39232))) % 178.07/177.92 [3942]P20(x39421,x39422,f329(f329(f307(f874(x39421)),f329(f329(f329(f93(x39421),x39423),a24),x39423)),f193(f883(f874(x39421),a869)))) % 178.07/177.92 [3957]P24(f329(f329(f243(a875),f329(f194(f876(x39571)),f176(x39571,x39572,x39573))),f329(f194(f876(x39571)),x39573))) % 178.07/177.92 [3965]E(f329(f262(x39651,x39652),f329(f249(f882(x39651,x39652)),f329(f268(x39651,x39652,a869),x39653))),f329(f249(x39651),f329(f329(f8(f883(x39652,a869),a869,x39651),f88(x39652)),x39653))) % 178.07/177.92 [3977]E(f329(f308(a875,a875,f329(f329(f7(a875,a875,a875),f81(a875)),x39771)),f300(a875,x39772,x39773)),f300(a875,f329(f329(f81(a875),x39772),x39771),f329(f329(f81(a875),x39773),x39771))) % 178.07/177.92 [3980]P24(f329(f62(f879(x39801)),f329(f308(x39802,f879(x39801),f329(f177(x39802,x39801),x39803)),f252(f883(x39802,a869))))) % 178.07/177.92 [3993]E(f329(f308(a875,a875,f329(f329(f7(a875,a875,a875),f81(a875)),x39931)),f329(f299(a875,x39932),x39933)),f329(f299(a875,f329(f329(f81(a875),x39932),x39931)),f329(f329(f81(a875),x39933),x39931))) % 178.07/177.92 [4011]E(f329(f329(f181(x40111,x40112),f329(f329(f153(f882(x40111,x40112),x40111),f263(x40111,x40112)),x40113)),f329(f329(f153(f882(x40111,x40112),x40112),f267(x40111,x40112)),x40113)),x40113) % 178.07/177.92 [4016]E(f329(f329(f81(a875),f329(f329(f82(a875),x40161),f45(a875,f329(f329(f39(a875),x40162),x40161),x40163))),f45(a875,x40162,x40161)),f45(a875,x40162,f329(f329(f82(a875),x40161),x40163))) % 178.07/177.92 [4030]E(f329(f329(f127(x40301),x40302),f329(f141(f876(x40301),f876(x40301),f127(x40301),f119(x40301)),x40303)),f329(f141(f876(x40301),f876(x40301),f127(x40301),x40302),x40303)) % 178.07/177.92 [4048]P24(f329(f329(f331(f882(x40481,x40481)),f329(f329(f264(x40481,x40481),x40482),x40482)),f329(f329(f188(f882(x40481,x40481),a869),f2(a875)),x40483))) % 178.07/177.92 [4054]E(f329(f249(x40541),f329(f329(f8(f883(x40542,a869),a869,x40541),f88(x40542)),f329(f7(x40542,x40541,a869),x40543))),f329(f260(x40542,x40541),f329(f249(f882(x40542,x40541)),f329(f268(x40542,x40541,a869),x40543)))) % 178.07/177.92 [4072]E(f329(f329(f116(f883(x40721,a869)),f329(f329(f43(a875,f883(x40721,a869)),f300(a875,f79(a875),x40722)),x40723)),f329(x40723,f2(a875))),f329(f329(f43(a875,f883(x40721,a869)),f329(f298(a875),x40722)),x40723)) % 178.07/177.92 [4087]E(f329(f141(f876(x40871),f876(x40871),f127(x40871),f119(x40871)),f329(f329(f153(f876(x40871),f876(x40871)),f135(x40871,x40872)),x40873)),f329(f135(x40871,x40872),f329(f141(f876(x40871),f876(x40871),f127(x40871),f119(x40871)),x40873))) % 178.07/177.92 [4092]E(f329(f267(f876(x40921),f876(x40921)),f166(x40921,x40922,x40923)),f329(f135(x40921,f329(f74(a869,a869,x40921,a324),x40922)),x40923)) % 178.07/177.92 [4110]E(f329(f329(f42(x41101,f883(x41102,a869)),f252(f883(x41101,a869))),f329(f329(f8(f883(x41102,a869),f883(x41102,a869),x41101),f249(x41102)),f329(f7(x41102,x41101,a869),x41103))),f329(f249(x41102),f329(f329(f8(f883(x41101,a869),a869,x41102),f89(x41101)),x41103))) % 178.07/177.92 [4141]E(f329(f329(f81(a1),f329(f329(f81(a1),f329(f329(f82(a1),x41411),f329(f329(f39(a1),x41412),x41411))),f45(a1,x41412,x41411))),x41413),f329(f329(f81(a1),x41412),x41413)) % 178.07/177.92 [4178]E(f329(f329(f81(a1),f329(f329(f81(a1),f329(f329(f82(a1),f329(f329(f39(a1),x41781),x41782)),x41782)),f45(a1,x41781,x41782))),x41783),f329(f329(f81(a1),x41781),x41783)) % 178.07/177.92 [4207]E(f86(f882(x42071,x42072),f329(f268(x42071,x42072,a869),f329(f329(f8(f883(x42072,f882(x42071,x42072)),f883(x42072,a869),x42071),f329(f8(f882(x42071,x42072),a869,x42072),x42073)),f264(x42071,x42072)))),f86(f882(x42071,x42072),x42073)) % 178.07/177.92 [4208]E(f91(f882(x42081,x42082),f329(f268(x42081,x42082,a869),f329(f329(f8(f883(x42082,f882(x42081,x42082)),f883(x42082,a869),x42081),f329(f8(f882(x42081,x42082),a869,x42082),x42083)),f264(x42081,x42082)))),f91(f882(x42081,x42082),x42083)) % 178.07/177.92 [4236]P24(f329(f329(f243(f883(x42361,a869)),f40(f883(x42361,a869),f329(f329(f107(f883(f883(x42361,a869),a869)),x42362),x42363))),f329(f329(f107(f883(x42361,a869)),f40(f883(x42361,a869),x42362)),f40(f883(x42361,a869),x42363)))) % 178.07/177.92 [4237]E(f329(f168(x42371),f329(f329(f329(f188(f876(x42371),f876(x42371)),f329(f329(f22(a875),f329(f194(f876(x42371)),x42372)),f45(a875,x42373,f329(f194(f876(x42371)),x42372)))),f167(x42371)),x42372)),f329(f329(f329(f188(f876(x42371),f876(x42371)),x42373),f167(x42371)),f329(f168(x42371),x42372))) % 178.07/177.92 [4251]E(f329(f249(x42511),f329(f329(f8(a869,a869,x42511),a324),f329(f329(f7(x42511,f879(x42512),a869),f329(f329(f8(f879(x42512),f883(f879(x42512),a869),x42511),a326),x42513)),f206(x42512)))),f183(x42511,x42512,x42513)) % 178.07/177.92 [4276]P24(f329(f329(f243(a875),f329(f194(f876(x42761)),f329(f329(f137(x42761),f329(f194(f876(x42761)),f176(x42761,x42762,x42763))),x42763))),f329(f194(f876(x42761)),x42763))) % 178.07/177.92 [4317]E(f329(f249(x43171),f329(f329(f8(f883(x43172,a869),a869,x43171),f88(x43172)),f329(f329(f8(f879(x43171),f883(x43172,a869),x43171),f329(f7(x43172,f879(x43171),a869),f329(f329(f8(f879(x43171),f883(f879(x43171),a869),x43172),a326),x43173))),f236(x43171)))),f185(x43172,x43171,x43173)) % 178.07/177.92 [4539]~P24(f329(f63(x45391,x45392,f193(f883(x45391,a869))),x45393)) % 178.07/177.92 [4547]~P24(f329(f329(f331(f882(x45471,x45471)),f329(f329(f264(x45471,x45471),x45472),x45473)),f152(x45471,f119(f883(x45471,a875))))) % 178.07/177.92 [3576]E(f329(f194(f876(x35761)),f329(f329(f174(x35761),x35762),x35763)),f329(f329(f241(a875),f329(f194(f876(x35761)),x35763)),x35762)) % 178.07/177.92 [3577]E(f329(f194(f876(x35771)),f329(f329(f137(x35771),x35772),x35773)),f329(f329(f22(a875),f329(f194(f876(x35771)),x35773)),x35772)) % 178.07/177.92 [3601]E(f329(f194(f876(f876(x36011))),f55(x36011,x36012,x36013)),f329(f329(f254(a875),f329(f194(f876(x36011)),x36013)),x36012)) % 178.07/177.92 [3617]E(f329(f329(f39(a875),f329(f329(f39(a875),x36171),x36172)),x36173),f329(f329(f39(a875),x36171),f329(f329(f82(a875),x36172),x36173))) % 178.07/177.92 [3618]E(f329(f329(f22(a875),f329(f329(f22(a875),x36181),x36182)),x36183),f329(f329(f22(a875),x36181),f329(f329(f81(a875),x36182),x36183))) % 178.07/177.92 [3619]E(f329(f329(f82(a875),f329(f329(f82(a875),x36191),x36192)),x36193),f329(f329(f82(a875),x36191),f329(f329(f82(a875),x36192),x36193))) % 178.07/177.92 [3620]E(f329(f329(f82(a1),f329(f329(f82(a1),x36201),x36202)),x36203),f329(f329(f82(a1),x36201),f329(f329(f82(a1),x36202),x36203))) % 178.07/177.92 [3621]E(f329(f329(f81(a875),f329(f329(f81(a875),x36211),x36212)),x36213),f329(f329(f81(a875),x36211),f329(f329(f81(a875),x36212),x36213))) % 178.07/177.92 [3622]E(f329(f329(f81(a1),f329(f329(f81(a1),x36221),x36222)),x36223),f329(f329(f81(a1),x36221),f329(f329(f81(a1),x36222),x36223))) % 178.07/177.92 [3623]E(f329(f329(f254(a1),f329(f329(f254(a1),x36231),x36232)),x36233),f329(f329(f254(a1),x36231),f329(f329(f82(a875),x36232),x36233))) % 178.07/177.92 [3643]E(f161(x36431,f329(f329(f150(f883(x36431,a869)),x36432),x36433)),f173(x36431,x36432,f161(x36431,x36433))) % 178.07/177.92 [3688]E(f329(f329(f22(a875),f329(f329(f22(a875),x36881),x36882)),x36883),f329(f329(f22(a875),f329(f329(f22(a875),x36881),x36883)),x36882)) % 178.07/177.92 [3694]E(f329(f236(f882(x36941,f877(x36941))),f329(f329(f264(x36941,f877(x36941)),x36942),x36943)),f329(f134(x36941),f129(x36941,x36942,x36943))) % 178.07/177.92 [3697]E(f329(f329(f107(f883(x36971,a869)),x36972),f329(f329(f22(f883(x36971,a869)),x36973),x36972)),f193(f883(x36971,a869))) % 178.07/177.92 [3738]E(f41(f883(x37381,a869),f329(f329(f307(f883(x37381,a869)),x37382),x37383)),f329(f329(f107(f883(x37381,a869)),x37382),f41(f883(x37381,a869),x37383))) % 178.07/177.92 [3739]E(f40(f883(x37391,a869),f329(f329(f307(f883(x37391,a869)),x37392),x37393)),f329(f329(f116(f883(x37391,a869)),x37392),f40(f883(x37391,a869),x37393))) % 178.07/177.92 [3741]E(f329(f329(f22(a875),f329(f329(f82(a875),x37411),x37412)),f329(f329(f82(a875),x37413),x37412)),f329(f329(f82(a875),f329(f329(f22(a875),x37411),x37413)),x37412)) % 178.07/177.92 [3742]E(f329(f329(f81(a875),f329(f329(f82(a875),x37421),x37422)),f329(f329(f82(a875),x37423),x37422)),f329(f329(f82(a875),f329(f329(f81(a875),x37421),x37423)),x37422)) % 178.07/177.92 [3743]E(f329(f329(f22(a1),f329(f329(f82(a1),x37431),x37432)),f329(f329(f82(a1),x37433),x37432)),f329(f329(f82(a1),f329(f329(f22(a1),x37431),x37433)),x37432)) % 178.07/177.92 [3744]E(f329(f329(f81(a1),f329(f329(f82(a1),x37441),x37442)),f329(f329(f82(a1),x37443),x37442)),f329(f329(f82(a1),f329(f329(f81(a1),x37441),x37443)),x37442)) % 178.07/177.92 [3746]E(f329(f329(f241(a875),f329(f329(f22(a875),x37461),x37462)),f329(f329(f22(a875),x37463),x37462)),f329(f329(f22(a875),f329(f329(f241(a875),x37461),x37463)),x37462)) % 178.07/177.92 [3769]E(f329(f329(f107(f883(f876(x37691),a869)),f159(x37691,x37692)),f159(x37691,x37693)),f159(x37691,f329(f329(f107(f883(x37691,a869)),x37692),x37693))) % 178.07/177.92 [3771]E(f329(f329(f116(f883(x37711,a869)),x37712),f329(f329(f116(f883(x37711,a869)),x37712),x37713)),f329(f329(f116(f883(x37711,a869)),x37712),x37713)) % 178.07/177.92 [3772]E(f329(f329(f116(f883(x37721,a869)),x37722),f329(f329(f22(f883(x37721,a869)),x37723),x37722)),f329(f329(f116(f883(x37721,a869)),x37722),x37723)) % 178.07/177.92 [3773]E(f329(f329(f107(f883(x37731,a869)),x37732),f329(f329(f107(f883(x37731,a869)),x37732),x37733)),f329(f329(f107(f883(x37731,a869)),x37732),x37733)) % 178.07/177.92 [3785]E(f329(f329(f286(x37851,x37852,x37852),x37853),f305(x37852,f193(f883(f882(x37852,x37852),a869)))),x37853) % 178.07/177.92 [3788]E(f329(f329(f116(f883(x37881,a869)),f329(f329(f307(x37881),x37882),f193(f883(x37881,a869)))),x37883),f329(f329(f307(x37881),x37882),x37883)) % 178.07/177.92 [3806]E(f329(f329(f22(a875),f329(f329(f22(a875),f329(a118,x38061)),x38062)),f329(a118,x38063)),f329(f329(f22(a875),f329(f329(f22(a875),x38061),x38062)),x38063)) % 178.07/177.92 [3834]E(f329(f329(f107(f883(f883(x38341,a869),a869)),f329(f306(x38341),x38342)),f329(f306(x38341),x38343)),f329(f306(x38341),f329(f329(f107(f883(x38341,a869)),x38342),x38343))) % 178.07/177.92 [3838]E(f329(f329(f116(f883(x38381,a869)),f329(f80(f883(x38381,a869)),x38382)),x38383),f329(f80(f883(x38381,a869)),f329(f329(f22(f883(x38381,a869)),x38382),x38383))) % 178.07/177.92 [3849]E(f329(f329(f307(x38491),x38492),f329(f329(f22(f883(x38491,a869)),x38493),f329(f329(f307(x38491),x38492),f193(f883(x38491,a869))))),f329(f329(f307(x38491),x38492),x38493)) % 178.07/177.92 [3859]P24(f329(f329(f243(f883(x38591,a869)),x38592),f329(f329(f116(f883(x38591,a869)),x38593),x38592))) % 178.07/177.92 [3860]P24(f329(f329(f243(f883(x38601,a869)),x38602),f329(f329(f116(f883(x38601,a869)),x38602),x38603))) % 178.07/177.92 [3863]E(f329(f329(f107(f883(x38631,a869)),f329(f80(f883(x38631,a869)),x38632)),f329(f80(f883(x38631,a869)),x38633)),f329(f80(f883(x38631,a869)),f329(f329(f116(f883(x38631,a869)),x38632),x38633))) % 178.07/177.92 [3864]E(f329(f329(f116(f883(x38641,a869)),f329(f80(f883(x38641,a869)),x38642)),f329(f80(f883(x38641,a869)),x38643)),f329(f80(f883(x38641,a869)),f329(f329(f107(f883(x38641,a869)),x38642),x38643))) % 178.07/177.92 [3878]P24(f329(f329(f243(f883(x38781,a869)),f329(f171(x38781),x38782)),f329(f171(x38781),f329(f329(f150(x38781),x38783),x38782)))) % 178.07/177.92 [3888]E(f329(f329(f116(f883(x38881,a869)),f329(f329(f22(f883(x38881,a869)),x38882),x38883)),f329(f329(f107(f883(x38881,a869)),x38882),x38883)),x38882) % 178.07/177.92 [3944]E(f329(f329(f6(x39441,a1),f329(f329(f8(a875,a1,x39441),f106(a1)),x39442)),x39443),f329(f106(a1),f329(f329(f6(x39441,a875),x39442),x39443))) % 178.07/177.92 [3945]E(f329(f329(f9(x39451,a1),f329(f329(f8(a875,a1,x39451),f106(a1)),x39452)),x39453),f329(f106(a1),f329(f329(f9(x39451,a875),x39452),x39453))) % 178.07/177.92 [3995]E(f329(f329(f127(x39951),f176(x39951,x39952,x39953)),f329(f329(f137(x39951),f329(f194(f876(x39951)),f176(x39951,x39952,x39953))),x39953)),x39953) % 178.07/177.92 [4000]E(f329(f80(f883(f882(x40001,x40002),a869)),f329(f329(f266(x40001,x40002),x40003),f329(f16(f883(x40002,a869),x40001),f252(f883(x40002,a869))))),f329(f329(f266(x40001,x40002),f329(f80(f883(x40001,a869)),x40003)),f329(f16(f883(x40002,a869),x40001),f252(f883(x40002,a869))))) % 178.07/177.92 [4001]E(f329(f80(f883(f882(x40011,x40012),a869)),f329(f329(f266(x40011,x40012),f252(f883(x40011,a869))),f329(f16(f883(x40012,a869),x40011),x40013))),f329(f329(f266(x40011,x40012),f252(f883(x40011,a869))),f329(f16(f883(x40012,a869),x40011),f329(f80(f883(x40012,a869)),x40013)))) % 178.07/177.92 [4049]E(f329(f329(f43(f883(x40491,a869),f883(x40491,a869)),x40492),f329(f329(f7(f883(x40491,a869),f883(x40491,a869),f883(x40491,a869)),f107(f883(x40491,a869))),x40493)),f329(f329(f107(f883(x40491,a869)),f40(f883(x40491,a869),x40492)),x40493)) % 178.07/177.92 [4056]E(f329(f141(f876(x40561),f876(x40561),f127(x40561),f119(x40561)),f329(f329(f150(f876(x40561)),x40562),x40563)),f329(f329(f127(x40561),x40562),f329(f141(f876(x40561),f876(x40561),f127(x40561),f119(x40561)),x40563))) % 178.07/177.92 [4078]E(f329(f329(f307(f883(x40781,a869)),f329(f283(x40781,x40781,x40782),f329(f329(f307(x40781),x40783),f193(f883(x40781,a869))))),f193(f883(f883(x40781,a869),a869))),f329(f329(f61(x40781),f329(f329(f307(x40781),x40783),f193(f883(x40781,a869)))),x40782)) % 178.07/177.92 [4088]E(f329(f329(f81(a875),f329(f329(f82(a875),x40881),f329(f329(f39(a875),x40882),x40883))),f329(f329(f39(a875),f329(f329(f82(a875),x40881),f45(a875,x40882,x40883))),x40883)),f329(f329(f39(a875),f329(f329(f82(a875),x40881),x40882)),x40883)) % 178.07/177.92 [4089]E(f329(f329(f81(a1),f329(f329(f82(a1),x40891),f329(f329(f39(a1),x40892),x40893))),f329(f329(f39(a1),f329(f329(f82(a1),x40891),f45(a1,x40892,x40893))),x40893)),f329(f329(f39(a1),f329(f329(f82(a1),x40891),x40892)),x40893)) % 178.07/177.92 [4126]E(f329(f329(f22(f883(x41261,a869)),f329(f171(x41261),x41262)),f329(f329(f307(x41261),x41263),f193(f883(x41261,a869)))),f329(f171(x41261),f329(f135(x41261,f329(f329(f8(a869,a869,x41261),a324),f329(a326,x41263))),x41262))) % 178.07/177.92 [4175]E(f329(f329(f127(x41751),f329(f141(f876(x41751),f876(x41751),f127(x41751),f119(x41751)),x41752)),f329(f141(f876(x41751),f876(x41751),f127(x41751),f119(x41751)),x41753)),f329(f141(f876(x41751),f876(x41751),f127(x41751),f119(x41751)),f329(f329(f127(f876(x41751)),x41752),x41753))) % 178.07/177.92 [4180]E(f329(f329(f264(f876(x41801),f876(x41801)),f329(f135(x41801,x41802),x41803)),f329(f135(x41801,f329(f74(a869,a869,x41801,a324),x41802)),x41803)),f166(x41801,x41802,x41803)) % 178.07/177.92 [4183]E(f329(f329(f81(a875),f329(f329(f81(a875),f329(f329(f39(a875),x41831),x41832)),f329(f329(f39(a875),x41833),x41832))),f329(f329(f39(a875),f329(f329(f81(a875),f45(a875,x41831,x41832)),f45(a875,x41833,x41832))),x41832)),f329(f329(f39(a875),f329(f329(f81(a875),x41831),x41833)),x41832)) % 178.07/177.92 [4184]E(f329(f329(f81(a1),f329(f329(f81(a1),f329(f329(f39(a1),x41841),x41842)),f329(f329(f39(a1),x41843),x41842))),f329(f329(f39(a1),f329(f329(f81(a1),f45(a1,x41841,x41842)),f45(a1,x41843,x41842))),x41842)),f329(f329(f39(a1),f329(f329(f81(a1),x41841),x41843)),x41842)) % 178.07/177.92 [4240]E(f329(f329(f107(f883(f876(x42401),a869)),f329(f329(f7(f876(x42401),f883(f876(x42401),a869),a869),f331(f876(x42401))),f160(x42401,x42402))),f329(f329(f7(f876(x42401),f883(f876(x42401),a869),a869),f331(f876(x42401))),f160(x42401,x42403))),f159(x42401,f329(f329(f107(f883(x42401,a869)),f329(f329(f7(x42401,f883(x42401,a869),a869),f331(x42401)),x42402)),f329(f329(f7(x42401,f883(x42401,a869),a869),f331(x42401)),x42403)))) % 178.07/177.92 [4253]E(f329(f249(x42531),f329(f329(f18(x42531,a869,a869),f329(f329(f8(a869,f883(a869,a869),x42531),a328),f329(f329(f7(x42531,x42531,a869),a326),x42532))),f329(f329(f7(x42531,f883(x42531,a869),a869),f331(x42531)),x42533))),f329(f329(f307(x42531),x42532),x42533)) % 178.07/177.92 [4273]E(f329(f329(f87(f876(f876(x42731)),f876(f876(x42731))),f54(x42731,x42732)),f329(f329(f18(f876(f876(x42731)),f876(f876(x42731)),f876(f876(x42731))),f329(f329(f8(f876(f876(x42731)),f883(f876(f876(x42731)),f876(f876(x42731))),f876(f876(x42731))),f127(f876(x42731))),f329(f153(f876(x42731),f876(x42731)),f329(f150(x42731),x42733)))),f5(f876(f876(x42731))))),f54(x42731,f329(f329(f150(x42731),x42733),x42732))) % 178.07/177.92 [4277]E(f329(f249(x42771),f329(f329(f18(x42771,a869,a869),f329(f329(f8(a869,f883(a869,a869),x42771),a328),f329(f329(f7(x42771,f883(x42771,a869),a869),f331(x42771)),x42772))),f329(f329(f7(x42771,f883(x42771,a869),a869),f331(x42771)),x42773))),f329(f329(f116(f883(x42771,a869)),x42772),x42773)) % 178.07/177.92 [4278]E(f329(f249(x42781),f329(f329(f18(x42781,a869,a869),f329(f329(f8(a869,f883(a869,a869),x42781),a327),f329(f329(f7(x42781,f883(x42781,a869),a869),f331(x42781)),x42782))),f329(f329(f7(x42781,f883(x42781,a869),a869),f331(x42781)),x42783))),f329(f329(f107(f883(x42781,a869)),x42782),x42783)) % 178.07/177.92 [4369]E(f329(f329(f43(x43691,f883(f883(x43691,a869),a869)),x43692),f329(f329(f7(x43691,f883(f883(x43691,a869),a869),f883(f883(x43691,a869),a869)),f329(f329(f8(f883(x43691,a869),f883(f883(f883(x43691,a869),a869),f883(f883(x43691,a869),a869)),x43691),f307(f883(x43691,a869))),f329(f329(f8(f883(x43691,a869),f883(x43691,a869),x43691),f283(x43691,x43691,x43693)),f329(f329(f7(x43691,f883(x43691,a869),f883(x43691,a869)),f307(x43691)),f193(f883(x43691,a869)))))),f193(f883(f883(x43691,a869),a869)))),f329(f329(f61(x43691),x43692),x43693)) % 178.07/177.92 [4371]E(f329(f329(f210(x43711),f329(f329(f82(a1),f329(f329(f74(f882(a1,a1),a1,x43711,f263(a1,a1)),f220(x43711)),x43712)),f329(f329(f74(f882(a1,a1),a1,x43711,f263(a1,a1)),f220(x43711)),x43713))),f329(f329(f82(a1),f329(f329(f74(f882(a1,a1),a1,x43711,f267(a1,a1)),f220(x43711)),x43712)),f329(f329(f74(f882(a1,a1),a1,x43711,f267(a1,a1)),f220(x43711)),x43713))),f229(x43711,x43712,x43713)) % 178.07/177.92 [4374]E(f329(f249(f876(x43741)),f329(f329(f18(f876(x43741),a869,a869),f329(f329(f8(a869,f883(a869,a869),f876(x43741)),a327),f329(f329(f7(f876(x43741),a875,a869),f329(f329(f8(a875,f883(a875,a869),f876(x43741)),a326),f194(f876(x43741)))),x43742))),f329(f329(f7(f876(x43741),f883(x43741,a869),a869),f329(f329(f8(f883(x43741,a869),f883(f883(x43741,a869),a869),f876(x43741)),f243(f883(x43741,a869))),f171(x43741))),f329(f171(x43741),x43743)))),f329(f171(f876(x43741)),f55(x43741,x43742,x43743))) % 178.07/177.92 [3759]E(f45(a875,f329(f329(f81(a875),f329(f329(f82(a875),x37591),x37592)),x37593),x37592),f45(a875,x37593,x37592)) % 178.07/177.92 [3805]E(f138(a875,f329(f299(a875,f329(f329(f81(a875),x38051),x38052)),x38053)),f329(f329(f137(a875),x38052),f138(a875,f329(f299(a875,x38051),x38053)))) % 178.07/177.92 [3848]E(f329(f329(f81(a1),f329(f106(a1),x38481)),f329(f329(f81(a1),f329(f106(a1),x38482)),x38483)),f329(f329(f81(a1),f329(f106(a1),f329(f329(f81(a875),x38481),x38482))),x38483)) % 178.07/177.92 [3855]E(f329(f329(f116(f883(x38551,a869)),f329(f329(f22(f883(x38551,a869)),x38552),x38553)),x38553),f329(f329(f116(f883(x38551,a869)),x38552),x38553)) % 178.07/177.92 [3856]E(f329(f329(f22(f883(x38561,a869)),f329(f329(f22(f883(x38561,a869)),x38562),x38563)),x38563),f329(f329(f22(f883(x38561,a869)),x38562),x38563)) % 178.07/177.92 [3879]E(f329(f329(f286(x38791,x38791,x38792),f305(x38791,f193(f883(f882(x38791,x38791),a869)))),x38793),x38793) % 178.07/177.92 [3885]E(f329(f329(f116(f883(x38851,a869)),f329(f282(x38851),x38852)),f329(f282(x38851),x38853)),f329(f282(x38851),f329(f329(f116(f883(f882(x38851,x38851),a869)),x38852),x38853))) % 178.07/177.92 [3896]E(f273(x38961,f329(f329(f150(f882(a105,x38961)),f329(f329(f264(a105,x38961),f2(a105)),x38962)),x38963)),f273(x38961,x38963)) % 178.07/177.92 [3899]E(f329(f329(f107(f883(x38991,a869)),f41(f883(x38991,a869),x38992)),f41(f883(x38991,a869),x38993)),f41(f883(x38991,a869),f329(f329(f116(f883(f883(x38991,a869),a869)),x38992),x38993))) % 178.07/177.92 [3900]E(f329(f329(f116(f883(x39001,a869)),f40(f883(x39001,a869),x39002)),f40(f883(x39001,a869),x39003)),f40(f883(x39001,a869),f329(f329(f116(f883(f883(x39001,a869),a869)),x39002),x39003))) % 178.07/177.92 [3936]E(f329(f329(f286(x39361,x39361,x39361),f329(f329(f188(f882(x39361,x39361),a869),x39362),x39363)),x39363),f329(f329(f188(f882(x39361,x39361),a869),f329(a118,x39362)),x39363)) % 178.07/177.92 [3986]P24(f329(f329(f243(f883(x39861,a869)),f329(f329(f22(f883(x39861,a869)),x39862),x39863)),x39862)) % 178.07/177.92 [3987]P24(f329(f329(f243(f883(x39871,a869)),f329(f329(f107(f883(x39871,a869)),x39872),x39873)),x39873)) % 178.07/177.92 [3988]P24(f329(f329(f243(f883(x39881,a869)),f329(f329(f107(f883(x39881,a869)),x39882),x39883)),x39882)) % 178.07/177.92 [4013]E(f305(x40131,f329(f329(f116(f883(f882(x40131,x40131),a869)),f305(x40131,x40132)),f305(x40131,x40133))),f305(x40131,f329(f329(f116(f883(f882(x40131,x40131),a869)),x40132),x40133))) % 178.07/177.92 [4017]E(f40(f883(x40171,a869),f329(f329(f307(f883(x40171,a869)),x40172),f329(f329(f307(f883(x40171,a869)),x40173),f193(f883(f883(x40171,a869),a869))))),f329(f329(f116(f883(x40171,a869)),x40172),x40173)) % 178.07/177.92 [4018]E(f41(f883(x40181,a869),f329(f329(f307(f883(x40181,a869)),x40182),f329(f329(f307(f883(x40181,a869)),x40183),f193(f883(f883(x40181,a869),a869))))),f329(f329(f107(f883(x40181,a869)),x40182),x40183)) % 178.07/177.92 [4024]E(f329(f329(f286(x40241,x40241,x40241),f329(f329(f188(f882(x40241,x40241),a869),x40242),x40243)),x40243),f329(f329(f286(x40241,x40241,x40241),x40243),f329(f329(f188(f882(x40241,x40241),a869),x40242),x40243))) % 178.07/177.92 [4093]E(f329(f329(f116(f883(x40931,a869)),f329(f249(x40931),f329(f329(f7(x40931,x40931,a869),a326),x40932))),x40933),f329(f329(f307(x40931),x40932),x40933)) % 178.07/177.92 [4095]E(f329(a110,f329(f329(f6(x40951,a1),f329(f329(f8(a875,a1,x40951),f106(a1)),x40952)),x40953)),f329(f329(f6(x40951,a875),x40952),x40953)) % 178.07/177.92 [4096]E(f329(a110,f329(f329(f9(x40961,a1),f329(f329(f8(a875,a1,x40961),f106(a1)),x40962)),x40963)),f329(f329(f9(x40961,a875),x40962),x40963)) % 178.07/177.92 [4172]E(f329(f155(f876(x41721),x41721,f329(f170(x41721),x41722),f329(f16(f883(f876(x41721),f876(x41721)),x41721),f329(f329(f7(f876(x41721),f876(x41721),f876(x41721)),f127(x41721)),x41722))),x41723),f329(f170(x41721),f329(f329(f127(x41721),x41723),x41722))) % 178.07/177.92 [4203]P24(f329(f329(f243(f883(f883(x42031,a869),a869)),f329(f329(f116(f883(f883(x42031,a869),a869)),f329(f306(x42031),x42032)),f329(f306(x42031),x42033))),f329(f306(x42031),f329(f329(f116(f883(x42031,a869)),x42032),x42033)))) % 178.07/177.92 [4296]E(f329(f249(x42961),f329(f329(f18(x42961,a869,a869),f329(f329(f8(a869,f883(a869,a869),x42961),a327),f329(f329(f7(x42961,f883(x42961,a869),a869),f331(x42961)),x42962))),f329(f329(f8(a869,a869,x42961),a324),f329(f329(f7(x42961,f883(x42961,a869),a869),f331(x42961)),x42963)))),f329(f329(f22(f883(x42961,a869)),x42962),x42963)) % 178.07/177.92 [4318]E(f329(f38(a875),f329(f249(a875),f329(f329(f18(a875,a869,a869),f329(f329(f8(a869,f883(a869,a869),a875),a327),f329(f329(f7(a875,a875,a869),f244(a875)),f329(f194(f876(x43181)),x43182)))),f329(f329(f8(x43181,a869,a875),x43183),f329(f164(x43181),x43182))))),f329(f194(f876(x43181)),f329(f135(x43181,x43183),x43182))) % 178.07/177.92 [4320]E(f329(f194(f876(x43201)),f175(x43201,x43202,x43203)),f329(f38(a875),f329(f249(a875),f329(f329(f18(a875,a869,a869),f329(f329(f8(a869,f883(a869,a869),a875),a327),f329(f329(f7(a875,a875,a869),f244(a875)),f329(f194(f876(x43201)),x43202)))),f329(f329(f7(a875,f883(a875,a869),a869),f331(a875)),x43203))))) % 178.07/177.92 [4417]E(f329(f329(f107(f883(f882(f876(x44171),f876(x44171)),a869)),f329(f308(f882(f882(x44171,f876(x44171)),f882(x44171,f876(x44171))),f882(f876(x44171),f876(x44171)),f269(f882(x44171,f876(x44171)),f876(x44171),f882(x44171,f876(x44171)),f876(x44171),f329(f268(x44171,f876(x44171),f876(x44171)),f150(x44171)),f329(f268(x44171,f876(x44171),f876(x44171)),f150(x44171)))),f321(x44171,f876(x44171),x44172,f329(f142(x44171,x44172),x44173)))),f329(f249(f882(f876(x44171),f876(x44171))),f329(f268(f876(x44171),f876(x44171),a869),f329(f329(f7(f876(x44171),f883(f876(x44171),a869),f883(f876(x44171),a869)),f329(f329(f8(f883(a869,a869),f883(f883(f876(x44171),a869),f883(f876(x44171),a869)),f876(x44171)),f8(a869,a869,f876(x44171))),f329(f329(f8(a869,f883(a869,a869),f876(x44171)),a327),f329(f329(f7(f876(x44171),a875,a869),f329(f329(f8(a875,f883(a875,a869),f876(x44171)),a326),f194(f876(x44171)))),f329(a118,x44173))))),f329(f329(f7(f876(x44171),a875,a869),f329(f329(f8(a875,f883(a875,a869),f876(x44171)),a326),f194(f876(x44171)))),f329(a118,x44173)))))),f329(f142(x44171,x44172),f329(a118,x44173))) % 178.07/177.92 [3901]E(f45(a875,f329(a118,f329(f329(f81(a875),f329(f329(f82(a875),x39011),x39012)),x39013)),x39012),f45(a875,f329(a118,x39013),x39012)) % 178.07/177.92 [4161]E(f329(f249(x41611),f329(f329(f18(x41611,a869,a869),f329(f329(f8(a869,f883(a869,a869),x41611),a327),x41612)),x41613)),f329(f329(f107(f883(x41611,a869)),f329(f249(x41611),x41612)),f329(f249(x41611),x41613))) % 178.07/177.92 [4162]E(f329(f249(x41621),f329(f329(f18(x41621,a869,a869),f329(f329(f8(a869,f883(a869,a869),x41621),a328),x41622)),x41623)),f329(f329(f116(f883(x41621,a869)),f329(f249(x41621),x41622)),f329(f249(x41621),x41623))) % 178.07/177.92 [4164]E(f329(f329(f127(x41641),f329(f329(f137(x41641),f45(a875,x41642,f329(f194(f876(x41641)),x41643))),x41643)),f329(f329(f174(x41641),f45(a875,x41642,f329(f194(f876(x41641)),x41643))),x41643)),f329(f329(f329(f188(f876(x41641),f876(x41641)),x41642),f167(x41641)),x41643)) % 178.07/177.92 [4169]E(f329(f249(x41691),f329(f329(f18(x41691,a869,a869),f329(f329(f8(a869,f883(a869,a869),x41691),a332),x41692)),x41693)),f329(f329(f116(f883(x41691,a869)),f329(f80(f883(x41691,a869)),f329(f249(x41691),x41692))),f329(f249(x41691),x41693))) % 178.07/177.92 [4185]E(f329(f329(f81(a875),f329(f194(f876(x41851)),f329(f135(x41851,x41852),x41853))),f329(f194(f876(x41851)),f329(f135(x41851,f329(f329(f8(a869,a869,x41851),a324),x41852)),x41853))),f329(f194(f876(x41851)),x41853)) % 178.07/177.92 [4210]P24(f329(f329(f243(f883(x42101,a869)),f329(f329(f116(f883(x42101,a869)),f41(f883(x42101,a869),x42102)),f41(f883(x42101,a869),x42103))),f41(f883(x42101,a869),f329(f329(f107(f883(f883(x42101,a869),a869)),x42102),x42103)))) % 178.07/177.92 [4224]E(f329(f171(x42241),f329(f135(x42241,f329(f329(f8(a869,a869,x42241),a324),f329(f329(f7(x42241,x42241,a869),a326),x42242))),x42243)),f329(f329(f22(f883(x42241,a869)),f329(f171(x42241),x42243)),f329(f329(f307(x42241),x42242),f193(f883(x42241,a869))))) % 178.07/177.92 [4233]P24(f329(f329(f243(f883(f882(x42331,x42331),a869)),f329(f329(f116(f883(f882(x42331,x42331),a869)),f305(x42331,x42332)),f305(x42331,x42333))),f305(x42331,f329(f329(f116(f883(f882(x42331,x42331),a869)),x42332),x42333)))) % 178.07/177.92 [4258]E(f329(f329(f82(a875),f329(a118,f329(a118,f2(a875)))),f329(f329(f6(a875,a875),f329(f329(f8(a875,a875,a875),f329(f81(a875),x42581)),f329(f329(f7(a875,a875,a875),f82(a875)),x42582))),f329(f250(a875),x42583))),f329(f329(f82(a875),x42583),f329(f329(f81(a875),x42581),f329(f329(f81(a875),x42581),f329(f329(f82(a875),f329(f329(f22(a875),x42583),f79(a875))),x42582))))) % 178.07/177.92 [4268]E(f329(f249(x42681),f329(f329(f18(x42681,a869,a869),f329(f329(f8(a869,f883(a869,a869),x42681),a327),f329(f329(f7(x42681,f883(x42681,a869),a869),f331(x42681)),f329(f171(x42681),x42682)))),x42683)),f329(f171(x42681),f329(f135(x42681,x42683),x42682))) % 178.07/177.92 [4416]E(f329(f249(x44161),f329(f329(f8(f883(a875,a869),a869,x44161),f88(a875)),f329(f329(f7(x44161,f883(a875,a869),f883(a875,a869)),f329(f329(f8(f883(a875,f883(a869,a869)),f883(f883(a875,a869),f883(a875,a869)),x44161),f18(a875,a869,a869)),f329(f329(f8(f883(a875,a869),f883(a875,f883(a869,a869)),x44161),f329(f8(a869,f883(a869,a869),a875),a327)),f329(f329(f7(x44161,f883(a875,x44161),f883(a875,a869)),f329(f329(f8(f883(x44161,a869),f883(f883(a875,x44161),f883(a875,a869)),x44161),f8(x44161,a869,a875)),a326)),f329(f164(x44161),x44162))))),f329(f329(f18(a875,a869,a869),f329(f329(f8(a869,f883(a869,a869),a875),a327),f329(f329(f7(a875,a875,a869),f244(a875)),f329(f194(f876(x44161)),x44162)))),f329(f329(f7(a875,f883(a875,a869),a869),f331(a875)),x44163))))),f329(f171(x44161),f175(x44161,x44162,x44163))) % 178.07/177.92 [4308]E(f329(f249(x43081),f329(f329(f18(x43081,a869,a869),f329(f329(f8(a869,f883(a869,a869),x43081),a332),f329(f329(f8(a869,a869,x43081),a324),f329(f329(f7(x43081,x43081,a869),a326),x43082)))),x43083)),f329(f329(f307(x43081),x43082),f329(f249(x43081),x43083))) % 178.07/177.92 [4340]E(f329(f329(f153(f882(x43401,a875),x43401),f263(x43401,a875)),f329(f135(f882(x43401,a875),f329(f329(f7(f882(x43401,a875),f883(a875,a869),a869),f329(f329(f8(a875,f883(f883(a875,a869),a869),f882(x43401,a875)),f331(a875)),f267(x43401,a875))),x43402)),f329(f329(f181(x43401,a875),x43403),f138(a875,f329(f299(a875,f2(a875)),f329(f194(f876(x43401)),x43403)))))),f175(x43401,x43403,x43402)) % 178.07/177.92 [4370]E(f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f329(f329(f6(a875,a1),f329(f329(f8(a1,a1,a875),f329(f81(a1),x43701)),f329(f329(f7(a875,a1,a1),f329(f329(f8(a1,f883(a1,a1),a875),f82(a1)),f106(a1))),x43702))),f329(f250(a875),x43703))),f329(f329(f82(a1),f329(f106(a1),x43703)),f329(f329(f81(a1),x43701),f329(f329(f81(a1),x43701),f329(f329(f82(a1),f329(f106(a1),f329(f329(f22(a875),x43703),f79(a875)))),x43702))))) % 178.07/177.92 [4410]E(f329(f249(f882(x44101,x44102)),f329(f268(x44101,x44102,a869),f329(f329(f7(x44101,f883(f882(x44102,x44101),a869),f883(x44102,a869)),f329(f329(f8(f883(x44102,f883(f883(f882(x44102,x44101),a869),a869)),f883(f883(f882(x44102,x44101),a869),f883(x44102,a869)),x44101),f7(x44102,f883(f882(x44102,x44101),a869),a869)),f329(f329(f8(f883(x44102,f882(x44102,x44101)),f883(x44102,f883(f883(f882(x44102,x44101),a869),a869)),x44101),f329(f8(f882(x44102,x44101),f883(f883(f882(x44102,x44101),a869),a869),x44102),f331(f882(x44102,x44101)))),f329(f7(x44102,x44101,f882(x44102,x44101)),f264(x44102,x44101))))),x44103))),f329(f284(x44102,x44101),x44103)) % 178.07/177.92 [4432]E(f329(f249(f876(x44321)),f329(f329(f8(f883(x44321,a869),a869,f876(x44321)),f88(x44321)),f329(f329(f8(f883(x44321,f883(f876(x44321),a869)),f883(x44321,a869),f876(x44321)),f329(f8(f883(f876(x44321),a869),a869,x44321),f88(f876(x44321)))),f329(f329(f7(f876(x44321),f883(x44321,f883(f876(x44321),a869)),f883(x44321,f883(f876(x44321),a869))),f329(f329(f8(f883(x44321,f883(f883(f876(x44321),a869),f883(f876(x44321),a869))),f883(f883(x44321,f883(f876(x44321),a869)),f883(x44321,f883(f876(x44321),a869))),f876(x44321)),f18(x44321,f883(f876(x44321),a869),f883(f876(x44321),a869))),f329(f329(f8(f883(x44321,f883(f876(x44321),f883(a869,a869))),f883(x44321,f883(f883(f876(x44321),a869),f883(f876(x44321),a869))),f876(x44321)),f329(f8(f883(f876(x44321),f883(a869,a869)),f883(f883(f876(x44321),a869),f883(f876(x44321),a869)),x44321),f18(f876(x44321),a869,a869))),f329(f329(f8(f883(x44321,f883(f876(x44321),a869)),f883(x44321,f883(f876(x44321),f883(a869,a869))),f876(x44321)),f329(f8(f883(f876(x44321),a869),f883(f876(x44321),f883(a869,a869)),x44321),f329(f8(a869,f883(a869,a869),f876(x44321)),a327))),f329(f329(f7(f876(x44321),f883(x44321,f883(f876(x44321),f876(x44321))),f883(x44321,f883(f876(x44321),a869))),f329(f329(f8(f883(f883(f876(x44321),f876(x44321)),f883(f876(x44321),a869)),f883(f883(x44321,f883(f876(x44321),f876(x44321))),f883(x44321,f883(f876(x44321),a869))),f876(x44321)),f8(f883(f876(x44321),f876(x44321)),f883(f876(x44321),a869),x44321)),f329(f329(f8(f883(f876(x44321),a869),f883(f883(f876(x44321),f876(x44321)),f883(f876(x44321),a869)),f876(x44321)),f8(f876(x44321),a869,f876(x44321))),a326))),f150(x44321)))))),f329(f329(f7(x44321,f883(f876(x44321),a869),f883(f876(x44321),a869)),f329(f329(f8(f883(a869,a869),f883(f883(f876(x44321),a869),f883(f876(x44321),a869)),x44321),f8(a869,a869,f876(x44321))),f329(f329(f8(a869,f883(a869,a869),x44321),a327),f329(f329(f7(x44321,f883(x44321,a869),a869),f331(x44321)),x44322)))),f329(f329(f7(f876(x44321),f883(f876(x44321),a869),a869),f331(f876(x44321))),x44323)))))),f173(x44321,x44322,x44323)) % 178.07/177.92 [4429]E(f329(f329(f87(a1,f882(a1,a1)),f329(f329(f22(a1),x44291),x44292)),f329(f329(f7(a1,f882(a1,a1),f882(a1,a1)),f329(f329(f18(a1,f882(a1,a1),f883(f882(a1,a1),f882(a1,a1))),f329(f329(f8(a869,f883(f882(a1,a1),f883(f882(a1,a1),f882(a1,a1))),a1),f102(f882(a1,a1))),f329(f243(a1),f2(a1)))),f329(f264(a1,a1),f329(f329(f81(a1),f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x44293)),f79(a1))))),f329(f329(f264(a1,a1),f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x44293)),x44291))),f329(f44(x44292),f329(f329(f264(a1,a1),x44293),x44291))) % 178.07/177.92 [4460]~E(f33(x44601,x44602),f34(x44603,x44604)) % 178.07/177.92 [4479]~E(f329(a26,x44791),f29(x44792,x44793,x44794)) % 178.07/177.92 [4480]~E(f329(a26,x44801),f31(x44802,x44803,x44804)) % 178.07/177.92 [4481]~E(f329(a26,x44811),f30(x44812,x44813,x44814)) % 178.07/177.92 [4482]~E(f29(x44821,x44822,x44823),f329(a26,x44824)) % 178.07/177.92 [4483]~E(f31(x44831,x44832,x44833),f329(a26,x44834)) % 178.07/177.92 [4484]~E(f30(x44841,x44842,x44843),f329(a26,x44844)) % 178.07/177.92 [3457]E(f329(f329(f329(f73(x34571,x34572),x34573),x34574),f329(x34573,x34574)),x34573) % 178.07/177.92 [3516]E(f329(f329(f255(x35161,x35162,x35163),x35164),f2(a875)),x35162) % 178.07/177.92 [3555]E(f190(x35551,x35552,x35553,f329(a118,x35554)),f329(x35553,x35554)) % 178.07/177.92 [3594]E(f169(x35941,x35942,f169(x35941,x35943,x35944)),f169(x35941,x35943,f169(x35941,x35942,x35944))) % 178.07/177.92 [3728]E(f329(f238(x37281,x37282,x37283,x37284),f206(x37282)),x37283) % 178.07/177.92 [3730]E(f329(f155(x37301,x37302,x37303,x37304),f119(x37302)),x37303) % 178.07/177.92 [3731]E(f329(f141(x37311,x37312,x37313,x37314),f119(x37312)),x37314) % 178.07/177.92 [3845]E(f329(f238(f879(x38451),x38452,f206(x38451),f329(f16(f879(x38451),x38452),f206(x38451))),f329(x38453,x38454)),f206(x38451)) % 178.07/177.92 [3889]E(f329(f329(f116(f883(x38891,a869)),f183(x38891,x38892,x38893)),f183(x38891,x38892,x38894)),f183(x38891,x38892,f184(x38891,x38892,x38894,x38893))) % 178.07/177.92 [3921]E(f329(f329(f270(x39211,x39212,x39213,f882(x39212,x39213)),x39214),f264(x39212,x39213)),x39214) % 178.07/177.92 [3930]E(f239(x39301,x39302,x39303,x39304,f206(x39302)),x39303) % 178.07/177.92 [3931]E(f186(x39311,x39312,x39313,x39314,f119(x39312)),x39313) % 178.07/177.92 [3932]E(f186(x39321,x39322,x39323,f119(x39321),x39324),x39323) % 178.07/177.92 [4217]P43(x42171,x42172,x42173,x42174,f193(f883(x42171,a869)),x42174) % 178.07/177.92 [3257]E(f329(f329(f16(x32571,x32572),x32573),x32574),x32573) % 178.07/177.92 [3375]E(f329(f329(f207(x33751,x33752),x33753),f329(f236(x33751),x33754)),f329(f236(x33752),f329(x33753,x33754))) % 178.07/177.92 [3546]E(f169(x35461,x35462,f329(f135(x35461,x35463),x35464)),f329(f135(x35461,x35463),f169(x35461,x35462,x35464))) % 178.07/177.92 [3578]E(f329(f329(f65(x35781,x35782,x35783),x35784),f193(f883(x35781,a869))),x35784) % 178.07/177.92 [3600]E(f329(f329(f164(x36001),f329(f329(f150(x36001),x36002),x36003)),f329(a118,x36004)),f329(f329(f164(x36001),x36003),x36004)) % 178.07/177.92 [3644]P30(x36441,f2(a875),f329(f329(f329(f93(x36441),x36442),f329(a26,x36443)),x36444)) % 178.07/177.92 [3669]E(f329(f329(x36691,x36692),f329(f189(x36693,x36694,x36691),x36692)),f329(f189(x36693,x36694,x36691),f329(a118,x36692))) % 178.07/177.92 [3764]E(f329(f329(f158(x37641,f329(f329(f150(x37641),x37642),x37643)),f2(a875)),x37644),f329(f329(f150(x37641),x37644),x37643)) % 178.07/177.92 [3775]E(f329(f329(f43(f883(x37751,a869),f883(x37752,a869)),x37753),f308(x37751,x37752,x37754)),f329(f308(x37751,x37752,x37754),f40(f883(x37751,a869),x37753))) % 178.07/177.92 [3776]E(f329(f329(f43(f883(x37761,a869),f883(x37762,a869)),x37763),f309(x37762,x37761,x37764)),f329(f309(x37762,x37761,x37764),f40(f883(x37761,a869),x37763))) % 178.07/177.92 [3872]E(f183(x38721,x38722,f187(x38721,x38722,x38723,x38724)),f329(f329(f107(f883(x38721,a869)),f183(x38721,x38722,x38723)),x38724)) % 178.07/177.92 [3876]E(f329(f131(x38761,x38762),f129(x38761,x38763,x38764)),f329(f329(f81(a875),f329(f329(f81(a875),f329(x38762,x38763)),f329(f131(x38761,x38762),x38764))),f329(a118,f2(a875)))) % 178.07/177.92 [3895]E(f329(f141(x38951,x38952,f329(f7(x38952,x38951,x38951),x38953),x38954),f329(f168(x38952),f119(x38952))),x38954) % 178.07/177.92 [3943]E(f77(x39431,x39432,x39433,x39434,f193(f883(x39431,a869))),x39433) % 178.07/177.92 [3989]E(f329(f329(f329(f329(f73(x39891,f879(x39892)),f329(f16(f879(x39892),x39891),f206(x39892))),x39893),f206(x39892)),x39894),f206(x39892)) % 178.07/177.92 [4144]E(f329(f268(x41441,x41442,x41443),f329(f329(f8(f883(x41442,f882(x41441,x41442)),f883(x41442,x41443),x41441),f329(f8(f882(x41441,x41442),x41443,x41442),x41444)),f264(x41441,x41442))),x41444) % 178.07/177.92 [3455]E(f329(f267(x34551,x34552),f329(f329(f264(x34551,x34552),x34553),x34554)),x34554) % 178.07/177.92 [3456]E(f329(f263(x34561,x34562),f329(f329(f264(x34561,x34562),x34563),x34564)),x34563) % 178.07/177.92 [3489]E(f329(f194(f876(x34891)),f329(f329(f153(x34892,x34891),x34893),x34894)),f329(f194(f876(x34892)),x34894)) % 178.07/177.92 [3490]E(f329(f194(f876(x34901)),f329(f329(f158(x34901,x34902),x34903),x34904)),f329(f194(f876(x34901)),x34902)) % 178.07/177.92 [3510]E(f329(f329(f137(x35101),f329(a118,x35102)),f329(f329(f150(x35101),x35103),x35104)),f329(f329(f137(x35101),x35102),x35104)) % 178.07/177.92 [3580]E(f329(f329(f307(x35801),x35802),f329(f329(f307(x35801),x35803),x35804)),f329(f329(f307(x35801),x35803),f329(f329(f307(x35801),x35802),x35804))) % 178.07/177.92 [3583]E(f329(f329(f153(x35831,x35832),x35833),f120(x35831,x35834)),f120(x35832,f329(f329(f153(x35831,x35832),x35833),x35834))) % 178.07/177.92 [3598]E(f329(f168(x35981),f329(f329(f153(x35982,x35981),x35983),x35984)),f329(f329(f153(x35982,x35981),x35983),f329(f168(x35982),x35984))) % 178.07/177.92 [3599]E(f329(f329(f153(x35991,x35992),x35993),f329(f170(x35991),x35994)),f329(f170(x35992),f329(f329(f153(x35991,x35992),x35993),x35994))) % 178.07/177.92 [3612]E(f329(f329(f174(x36121),f329(a118,x36122)),f329(f329(f150(x36121),x36123),x36124)),f329(f329(f150(x36121),x36123),f329(f329(f174(x36121),x36122),x36124))) % 178.07/177.92 [3616]E(f329(f171(x36161),f329(f329(f153(x36162,x36161),x36163),x36164)),f329(f308(x36162,x36161,x36163),f329(f171(x36162),x36164))) % 178.07/177.92 [3668]E(f17(x36681,x36682,x36683,f329(a3,f329(a118,f329(a19,x36684)))),f329(x36683,x36684)) % 178.07/177.92 [3671]E(f329(f329(f127(x36711),f329(f135(x36711,x36712),x36713)),f329(f135(x36711,x36712),x36714)),f329(f135(x36711,x36712),f329(f329(f127(x36711),x36713),x36714))) % 178.07/177.92 [3684]E(f151(x36841,f329(f329(f153(x36842,x36841),x36843),f151(x36842,x36844))),f151(x36841,f329(f329(f153(x36842,x36841),x36843),x36844))) % 178.07/177.92 [3700]E(f329(f284(x37001,x37001),f329(f329(f285(x37002,x37001),x37003),x37004)),f329(f329(f285(x37002,x37001),f329(f284(x37002,x37002),x37003)),x37004)) % 178.07/177.92 [3710]E(f329(f329(f286(x37101,x37102,x37103),x37104),f193(f883(f882(x37102,x37103),a869))),f193(f883(f882(x37101,x37103),a869))) % 178.07/177.92 [3711]E(f329(f329(f174(x37111),f329(f329(f22(a875),x37112),x37113)),f329(f329(f137(x37111),x37113),x37114)),f329(f329(f137(x37111),x37113),f329(f329(f174(x37111),x37112),x37114))) % 178.07/177.92 [3756]E(f41(f883(x37561,a869),f329(f308(x37562,f883(x37561,a869),x37563),x37564)),f329(f329(f42(x37562,f883(x37561,a869)),x37564),x37563)) % 178.07/177.92 [3757]E(f40(f883(x37571,a869),f329(f308(x37572,f883(x37571,a869),x37573),x37574)),f329(f329(f43(x37572,f883(x37571,a869)),x37574),x37573)) % 178.07/177.92 [3758]E(f329(f194(f876(f882(x37581,x37582))),f329(f329(f181(x37581,x37582),x37583),x37584)),f329(f329(f241(a875),f329(f194(f876(x37581)),x37583)),f329(f194(f876(x37582)),x37584))) % 178.07/177.92 [3760]E(f329(f309(x37601,x37602,x37603),f329(f80(f883(x37602,a869)),x37604)),f329(f80(f883(x37601,a869)),f329(f309(x37601,x37602,x37603),x37604))) % 178.07/177.92 [3790]E(f329(f187(x37901,x37902,x37903,f193(f883(x37901,a869))),x37904),f206(x37902)) % 178.07/177.92 [3811]E(f329(f309(x38111,x38112,x38113),f329(f249(x38112),x38114)),f329(f249(x38111),f329(f329(f8(x38112,a869,x38111),x38114),x38113))) % 178.07/177.92 [3828]E(f329(f329(f164(x38281),f329(f329(f127(x38281),x38282),f329(f329(f150(x38281),x38283),x38284))),f329(f194(f876(x38281)),x38282)),x38283) % 178.07/177.92 [3833]E(f329(f187(x38331,x38332,f329(f16(f879(x38332),x38331),f206(x38332)),x38333),x38334),f206(x38332)) % 178.07/177.92 [3853]E(f329(f308(x38531,x38532,x38533),f329(f309(x38531,x38532,x38533),x38534)),f329(f329(f107(f883(x38532,a869)),x38534),f329(f308(x38531,x38532,x38533),f252(f883(x38531,a869))))) % 178.07/177.92 [3871]P24(f329(f329(f331(x38711),f329(x38712,x38713)),f329(f308(x38714,x38711,x38712),f252(f883(x38714,a869))))) % 178.07/177.92 [3884]E(f329(f329(f266(x38841,x38842),f329(f171(x38841),x38843)),f329(f16(f883(x38842,a869),x38841),f329(f171(x38842),x38844))),f329(f171(f882(x38841,x38842)),f60(x38841,x38842,x38843,x38844))) % 178.07/177.92 [3898]E(f154(x38981,x38982,f329(f329(f150(x38981),x38983),x38984)),f329(f329(f81(a875),f329(f329(f81(a875),f329(x38982,x38983)),f154(x38981,x38982,x38984))),f329(a118,f2(a875)))) % 178.07/177.92 [3912]E(f190(f876(x39121),f329(f329(f150(x39121),x39122),x39123),f329(f329(f7(a875,f876(x39121),f876(x39121)),f137(x39121)),x39123),x39124),f329(f329(f137(x39121),x39124),f329(f329(f150(x39121),x39122),x39123))) % 178.07/177.92 [3913]P21(x39131,f882(x39132,x39131),f333(x39133,x39134,x39132,x39131),f329(f329(f43(x39132,f883(x39131,a869)),x39134),x39133)) % 178.07/177.92 [3922]E(f329(f329(f22(f883(x39221,a869)),f329(f329(f22(f883(x39221,a869)),x39222),x39223)),f329(f329(f307(x39221),x39224),f193(f883(x39221,a869)))),f329(f329(f22(f883(x39221,a869)),x39222),f329(f329(f307(x39221),x39224),x39223))) % 178.07/177.92 [3934]E(f329(f329(f188(f883(x39341,x39342),f883(x39341,x39342)),x39343),f74(x39342,x39342,x39341,x39344)),f74(x39342,x39342,x39341,f329(f329(f188(x39342,x39342),x39343),x39344))) % 178.07/177.92 [4012]E(f329(f329(f329(f188(f876(x40121),f876(x40121)),x40122),f167(x40121)),f329(f329(f329(f188(f876(x40121),f876(x40121)),x40123),f167(x40121)),x40124)),f329(f329(f329(f188(f876(x40121),f876(x40121)),f329(f329(f81(a875),x40122),x40123)),f167(x40121)),x40124)) % 178.07/177.92 [4098]P24(f329(f329(f243(f883(x40981,a869)),f329(f171(x40981),f329(f329(f158(x40981,x40982),x40983),x40984))),f329(f329(f307(x40981),x40984),f329(f171(x40981),x40982)))) % 178.07/177.92 [4134]E(f329(f329(f43(f883(x41341,a869),f883(f882(x41341,x41342),a869)),x41343),f329(f329(f7(f883(x41341,a869),f883(x41341,f883(x41342,a869)),f883(f882(x41341,x41342),a869)),f266(x41341,x41342)),x41344)),f329(f329(f266(x41341,x41342),f40(f883(x41341,a869),x41343)),x41344)) % 178.07/177.92 [4171]E(f217(x41711,x41712,x41713,f329(f74(x41712,f883(a105,f883(a105,f883(f882(a105,a105),f883(a105,f877(x41712))))),x41711,f216(x41712)),x41714)),f218(x41711,x41712,x41714,x41713)) % 178.07/177.92 [4188]E(f213(x41881,x41882,x41883,f329(f74(x41882,f883(a105,f883(a105,f883(f882(a105,a105),f883(a105,f877(f879(x41882)))))),x41881,f212(x41882)),x41884)),f214(x41881,x41882,x41884,x41883)) % 178.07/177.92 [4193]P24(f329(f67(x41931,x41932,x41933,x41934,f193(f883(x41931,a869))),x41934)) % 178.07/177.92 [4235]E(f329(f329(f43(x42351,f883(x42352,a869)),x42353),f329(f329(f7(x42351,f883(x42352,a869),f883(x42352,a869)),f329(f329(f8(x42352,f883(f883(x42352,a869),f883(x42352,a869)),x42351),f307(x42352)),x42354)),f193(f883(x42352,a869)))),f329(f308(x42351,x42352,x42354),x42353)) % 178.07/177.92 [4242]P24(f329(f329(f243(f883(x42421,a869)),f329(f260(x42422,x42421),f329(f329(f107(f883(f882(x42422,x42421),a869)),x42423),x42424))),f329(f329(f107(f883(x42421,a869)),f329(f260(x42422,x42421),x42423)),f329(f260(x42422,x42421),x42424)))) % 178.07/177.92 [4243]P24(f329(f329(f243(f883(x42431,a869)),f329(f262(x42431,x42432),f329(f329(f107(f883(f882(x42431,x42432),a869)),x42433),x42434))),f329(f329(f107(f883(x42431,a869)),f329(f262(x42431,x42432),x42433)),f329(f262(x42431,x42432),x42434)))) % 178.07/177.92 [4305]P24(f329(f329(f243(f883(f882(x43051,x43052),a869)),f329(f308(x43052,f882(x43051,x43052),f333(x43053,x43054,x43051,x43052)),f329(f329(f43(x43051,f883(x43052,a869)),x43054),x43053))),f329(f329(f266(x43051,x43052),x43054),x43053))) % 178.07/177.92 [4306]E(f329(f122(x43061,f882(x43061,x43062),x43063),f329(f329(f8(f883(x43062,f877(f882(x43061,x43062))),f877(f882(x43061,x43062)),x43061),f122(x43062,f882(x43061,x43062),x43064)),f329(f329(f8(f883(x43062,f882(x43061,x43062)),f883(x43062,f877(f882(x43061,x43062))),x43061),f329(f8(f882(x43061,x43062),f877(f882(x43061,x43062)),x43062),f128(f882(x43061,x43062)))),f264(x43061,x43062)))),f133(x43061,x43062,x43063,x43064)) % 178.07/177.92 [4346]E(f86(f882(x43461,x43462),f329(f268(x43461,x43462,a869),f329(f329(f7(x43461,f883(x43462,a869),f883(x43462,a869)),f329(f329(f8(f883(a869,a869),f883(f883(x43462,a869),f883(x43462,a869)),x43461),f8(a869,a869,x43462)),f329(f329(f8(a869,f883(a869,a869),x43461),a327),f329(a326,x43463)))),f329(a326,x43464)))),f329(f329(f264(x43461,x43462),x43463),x43464)) % 178.07/177.92 [4347]E(f91(f882(x43471,x43472),f329(f268(x43471,x43472,a869),f329(f329(f7(x43471,f883(x43472,a869),f883(x43472,a869)),f329(f329(f8(f883(a869,a869),f883(f883(x43472,a869),f883(x43472,a869)),x43471),f8(a869,a869,x43472)),f329(f329(f8(a869,f883(a869,a869),x43471),a327),f329(a326,x43473)))),f329(a326,x43474)))),f329(f329(f264(x43471,x43472),x43473),x43474)) % 178.07/177.92 [4418]E(f329(f329(f268(f876(x44181),f876(x44181),f882(f876(x44181),f876(x44181))),f329(f329(f18(f876(x44181),f883(f876(x44181),f882(f876(x44181),f876(x44181))),f883(f876(x44181),f882(f876(x44181),f876(x44181)))),f329(f329(f8(f883(f876(x44181),f883(f882(f876(x44181),f876(x44181)),f882(f876(x44181),f876(x44181)))),f883(f883(f876(x44181),f882(f876(x44181),f876(x44181))),f883(f876(x44181),f882(f876(x44181),f876(x44181)))),f876(x44181)),f18(f876(x44181),f882(f876(x44181),f876(x44181)),f882(f876(x44181),f876(x44181)))),f329(f329(f8(f883(f876(x44181),f882(f876(x44181),f876(x44181))),f883(f876(x44181),f883(f882(f876(x44181),f876(x44181)),f882(f876(x44181),f876(x44181)))),f876(x44181)),f329(f8(f882(f876(x44181),f876(x44181)),f883(f882(f876(x44181),f876(x44181)),f882(f876(x44181),f876(x44181))),f876(x44181)),f329(f102(f882(f876(x44181),f876(x44181))),f329(x44182,x44183)))),f329(f329(f8(f876(x44181),f883(f876(x44181),f882(f876(x44181),f876(x44181))),f876(x44181)),f264(f876(x44181),f876(x44181))),f329(f150(x44181),x44183))))),f329(f329(f7(f876(x44181),f883(f876(x44181),f876(x44181)),f883(f876(x44181),f882(f876(x44181),f876(x44181)))),f329(f329(f8(f883(f876(x44181),f882(f876(x44181),f876(x44181))),f883(f883(f876(x44181),f876(x44181)),f883(f876(x44181),f882(f876(x44181),f876(x44181)))),f876(x44181)),f8(f876(x44181),f882(f876(x44181),f876(x44181)),f876(x44181))),f264(f876(x44181),f876(x44181)))),f329(f150(x44181),x44183)))),f166(x44181,x44182,x44184)),f166(x44181,x44182,f329(f329(f150(x44181),x44183),x44184))) % 178.07/177.92 [4424]E(f329(f141(f883(x44241,f879(x44242)),f882(x44241,x44242),f329(f7(f882(x44241,x44242),f883(x44241,f879(x44242)),f883(x44241,f879(x44242))),f329(f268(x44241,x44242,f883(f883(x44241,f879(x44242)),f883(x44241,f879(x44242)))),f329(f329(f7(x44241,f883(x44242,f879(x44242)),f883(x44242,f883(f883(x44241,f879(x44242)),f883(x44241,f879(x44242))))),f329(f329(f8(f883(f879(x44242),f883(f883(x44241,f879(x44242)),f883(x44241,f879(x44242)))),f883(f883(x44242,f879(x44242)),f883(x44242,f883(f883(x44241,f879(x44242)),f883(x44241,f879(x44242))))),x44241),f8(f879(x44242),f883(f883(x44241,f879(x44242)),f883(x44241,f879(x44242))),x44242)),f329(f329(f8(f883(f883(x44241,f879(x44242)),f883(f879(x44242),f883(x44241,f879(x44242)))),f883(f879(x44242),f883(f883(x44241,f879(x44242)),f883(x44241,f879(x44242)))),x44241),f7(f883(x44241,f879(x44242)),f879(x44242),f883(x44241,f879(x44242)))),f329(f7(f883(x44241,f879(x44242)),x44241,f883(f879(x44242),f883(x44241,f879(x44242)))),f73(x44241,f879(x44242)))))),f236(x44242)))),x44243),f329(f168(f882(x44241,x44242)),x44244)),f184(x44241,x44242,x44243,f329(f177(x44241,x44242),x44244))) % 178.07/177.92 [3529]E(f329(f194(f874(x35291)),f329(f329(f329(f93(x35291),x35292),x35293),x35294)),f2(a875)) % 178.07/177.92 [3647]E(f329(f329(f174(x36471),x36472),f329(f329(f174(x36471),x36473),x36474)),f329(f329(f174(x36471),f329(f329(f241(a875),x36472),x36473)),x36474)) % 178.07/177.92 [3648]E(f329(f329(f137(x36481),x36482),f329(f329(f137(x36481),x36483),x36484)),f329(f329(f137(x36481),f329(f329(f81(a875),x36482),x36483)),x36484)) % 178.07/177.92 [3660]E(f329(f329(f127(x36601),f329(f329(f150(x36601),x36602),x36603)),x36604),f329(f329(f150(x36601),x36602),f329(f329(f127(x36601),x36603),x36604))) % 178.07/177.92 [3661]E(f329(f329(f127(x36611),f329(f329(f127(x36611),x36612),x36613)),x36614),f329(f329(f127(x36611),x36612),f329(f329(f127(x36611),x36613),x36614))) % 178.07/177.92 [3740]E(f329(f329(f164(x37401),f329(f329(f150(x37401),x37402),x37403)),x37404),f190(x37401,x37402,f329(f164(x37401),x37403),x37404)) % 178.07/177.92 [3749]E(f329(f329(f188(x37491,x37491),x37492),f329(f329(f188(x37491,x37491),x37493),x37494)),f329(f329(f188(x37491,x37491),f329(f329(f82(a875),x37493),x37492)),x37494)) % 178.07/177.92 [3778]E(f329(f329(f116(f883(x37781,a869)),x37782),f329(f329(f307(x37781),x37783),x37784)),f329(f329(f307(x37781),x37783),f329(f329(f116(f883(x37781,a869)),x37782),x37784))) % 178.07/177.92 [3793]E(f329(f329(f329(f188(x37931,x37931),x37932),x37933),f329(x37933,x37934)),f329(x37933,f329(f329(f329(f188(x37931,x37931),x37932),x37933),x37934))) % 178.07/177.92 [3801]E(f329(f329(f286(x38011,x38012,x38013),f193(f883(f882(x38011,x38012),a869))),x38014),f193(f883(f882(x38011,x38013),a869))) % 178.07/177.92 [3817]E(f329(f329(f116(f883(x38171,a869)),f329(f329(f307(x38171),x38172),x38173)),x38174),f329(f329(f307(x38171),x38172),f329(f329(f116(f883(x38171,a869)),x38173),x38174))) % 178.07/177.92 [3835]E(f184(x38351,x38352,f329(f177(x38351,x38352),x38353),f329(f177(x38351,x38352),x38354)),f329(f177(x38351,x38352),f329(f329(f127(f882(x38351,x38352)),x38354),x38353))) % 178.07/177.92 [3836]E(f329(f38(f882(x38361,x38362)),f329(f329(f266(x38361,x38362),x38363),f329(f16(f883(x38362,a869),x38361),x38364))),f329(f329(f82(a875),f329(f38(x38361),x38363)),f329(f38(x38362),x38364))) % 178.07/177.92 [3842]E(f329(f329(f107(f883(x38421,a869)),f329(f329(f307(x38421),x38422),x38423)),f329(f329(f307(x38421),x38422),x38424)),f329(f329(f307(x38421),x38422),f329(f329(f107(f883(x38421,a869)),x38423),x38424))) % 178.07/177.92 [3857]E(f329(f329(f116(f883(x38571,a869)),x38572),f329(f329(f116(f883(x38571,a869)),x38573),x38574)),f329(f329(f116(f883(x38571,a869)),x38573),f329(f329(f116(f883(x38571,a869)),x38572),x38574))) % 178.07/177.92 [3858]E(f329(f329(f107(f883(x38581,a869)),x38582),f329(f329(f107(f883(x38581,a869)),x38583),x38584)),f329(f329(f107(f883(x38581,a869)),x38583),f329(f329(f107(f883(x38581,a869)),x38582),x38584))) % 178.07/177.92 [3867]E(f65(x38671,x38672,f329(f329(f8(x38672,f883(x38672,x38672),x38671),x38673),x38674)),f329(f66(x38672,x38671,x38673),x38674)) % 178.07/177.92 [3877]E(f179(x38771,f329(f329(f153(f876(x38772),f876(x38771)),f329(f153(x38772,x38771),x38773)),x38774)),f329(f329(f153(f876(x38772),f876(x38771)),f329(f153(x38772,x38771),x38773)),f179(x38772,x38774))) % 178.07/177.92 [3894]E(f329(f141(f876(x38941),f876(x38941),f127(x38941),f119(x38941)),f329(f329(f153(x38942,f876(x38941)),x38943),x38944)),f163(x38942,x38941,x38943,x38944)) % 178.07/177.92 [3897]E(f187(x38971,x38972,x38973,f329(f80(f883(x38971,a869)),f329(f329(f307(x38971),x38974),f193(f883(x38971,a869))))),f329(f329(f329(f73(x38971,f879(x38972)),x38973),x38974),f206(x38972))) % 178.07/177.92 [3939]E(f329(f329(f329(f73(x39391,f879(x39392)),f329(f177(x39391,x39392),x39393)),f329(f263(x39391,x39392),x39394)),f329(f236(x39392),f329(f267(x39391,x39392),x39394))),f329(f177(x39391,x39392),f329(f329(f150(f882(x39391,x39392)),x39394),x39393))) % 178.07/177.92 [3956]E(f329(f74(x39561,x39561,x39561,f329(f329(f188(x39561,x39561),x39562),x39563)),f329(f329(f188(x39561,x39561),x39564),x39563)),f329(f329(f188(x39561,x39561),f329(f329(f81(a875),x39562),x39564)),x39563)) % 178.07/177.92 [3981]E(f329(f329(f107(f883(x39811,a869)),f329(f329(f116(f883(x39811,a869)),x39812),x39813)),f329(f329(f116(f883(x39811,a869)),x39812),x39814)),f329(f329(f116(f883(x39811,a869)),x39812),f329(f329(f107(f883(x39811,a869)),x39813),x39814))) % 178.07/177.92 [3982]E(f329(f329(f107(f883(x39821,a869)),f329(f329(f22(f883(x39821,a869)),x39822),x39823)),f329(f329(f22(f883(x39821,a869)),x39822),x39824)),f329(f329(f22(f883(x39821,a869)),x39822),f329(f329(f116(f883(x39821,a869)),x39823),x39824))) % 178.07/177.92 [3983]E(f329(f329(f116(f883(x39831,a869)),f329(f329(f22(f883(x39831,a869)),x39832),x39833)),f329(f329(f22(f883(x39831,a869)),x39832),x39834)),f329(f329(f22(f883(x39831,a869)),x39832),f329(f329(f107(f883(x39831,a869)),x39833),x39834))) % 178.07/177.92 [3984]E(f329(f329(f116(f883(x39841,a869)),f329(f329(f107(f883(x39841,a869)),x39842),x39843)),f329(f329(f107(f883(x39841,a869)),x39842),x39844)),f329(f329(f107(f883(x39841,a869)),x39842),f329(f329(f116(f883(x39841,a869)),x39843),x39844))) % 178.07/177.92 [3985]E(f329(f329(f22(f883(x39851,a869)),f329(f329(f107(f883(x39851,a869)),x39852),x39853)),f329(f329(f107(f883(x39851,a869)),x39852),x39854)),f329(f329(f107(f883(x39851,a869)),x39852),f329(f329(f22(f883(x39851,a869)),x39853),x39854))) % 178.07/177.92 [3991]E(f329(f38(f882(x39911,x39912)),f329(f329(f266(x39911,x39912),f329(f329(f307(x39911),x39913),f193(f883(x39911,a869)))),f329(f16(f883(x39912,a869),x39911),x39914))),f329(f38(x39912),x39914)) % 178.07/177.92 [4027]E(f329(f329(f43(x40271,f883(x40272,a869)),x40273),f329(f329(f8(f883(x40272,a869),f883(x40272,a869),x40271),f80(f883(x40272,a869))),x40274)),f329(f80(f883(x40272,a869)),f329(f329(f42(x40271,f883(x40272,a869)),x40273),x40274))) % 178.07/177.92 [4028]E(f329(f329(f42(x40281,f883(x40282,a869)),x40283),f329(f329(f8(f883(x40282,a869),f883(x40282,a869),x40281),f80(f883(x40282,a869))),x40284)),f329(f80(f883(x40282,a869)),f329(f329(f43(x40281,f883(x40282,a869)),x40283),x40284))) % 178.07/177.92 [4042]E(f329(f329(f286(x40421,x40421,x40421),f329(f329(f188(f882(x40421,x40421),a869),x40422),x40423)),f329(f329(f188(f882(x40421,x40421),a869),x40424),x40423)),f329(f329(f188(f882(x40421,x40421),a869),f329(f329(f81(a875),x40422),x40424)),x40423)) % 178.07/177.92 [4073]E(f329(f329(f42(x40731,f883(f883(x40732,a869),a869)),x40733),f329(f329(f8(f883(x40732,a869),f883(f883(x40732,a869),a869),x40731),f306(x40732)),x40734)),f329(f306(x40732),f329(f329(f42(x40731,f883(x40732,a869)),x40733),x40734))) % 178.07/177.92 [4102]E(f329(f329(f42(f883(x41021,a869),f883(x41022,a869)),x41023),f329(f329(f7(f883(x41021,a869),f883(x41021,f883(x41022,a869)),f883(x41022,a869)),f42(x41021,f883(x41022,a869))),x41024)),f329(f329(f42(x41021,f883(x41022,a869)),f40(f883(x41021,a869),x41023)),x41024)) % 178.07/177.92 [4103]E(f329(f329(f43(f883(x41031,a869),f883(x41032,a869)),x41033),f329(f329(f7(f883(x41031,a869),f883(x41031,f883(x41032,a869)),f883(x41032,a869)),f43(x41031,f883(x41032,a869))),x41034)),f329(f329(f43(x41031,f883(x41032,a869)),f40(f883(x41031,a869),x41033)),x41034)) % 178.07/177.92 [4108]E(f329(f329(f153(x41081,x41082),x41083),f329(f141(f876(x41081),f876(x41081),f127(x41081),f119(x41081)),x41084)),f329(f141(f876(x41082),f876(x41082),f127(x41082),f119(x41082)),f329(f329(f153(f876(x41081),f876(x41082)),f329(f153(x41081,x41082),x41083)),x41084))) % 178.07/177.92 [4112]E(f190(f876(x41121),f119(x41121),f329(f329(f8(f876(x41121),f876(x41121),a875),f329(f150(x41121),x41122)),f329(f329(f7(a875,f876(x41121),f876(x41121)),f174(x41121)),x41123)),x41124),f329(f329(f174(x41121),x41124),f329(f329(f150(x41121),x41122),x41123))) % 178.07/177.92 [4154]P24(f329(f329(f243(f883(x41541,a869)),f329(f308(x41542,x41541,x41543),f329(f309(x41542,x41541,x41543),x41544))),x41544)) % 178.07/177.92 [4157]E(f329(f308(f882(x41571,x41572),f882(x41572,x41571),f329(f268(x41571,x41572,f882(x41572,x41571)),f329(f7(x41572,x41571,f882(x41572,x41571)),f264(x41572,x41571)))),f329(f329(f266(x41571,x41572),x41573),f329(f16(f883(x41572,a869),x41571),x41574))),f329(f329(f266(x41572,x41571),x41574),f329(f16(f883(x41571,a869),x41572),x41573))) % 178.07/177.92 [4166]E(f329(f329(f43(x41661,f883(x41662,a869)),x41663),f329(f329(f8(f883(x41661,a869),f883(x41662,a869),x41661),f309(x41662,x41661,x41664)),f329(f329(f7(x41661,f883(x41661,a869),f883(x41661,a869)),f307(x41661)),f193(f883(x41661,a869))))),f329(f309(x41662,x41661,x41664),x41663)) % 178.07/177.92 [4167]E(f329(f329(f43(x41671,f883(x41672,a869)),x41673),f329(f329(f8(f883(x41671,a869),f883(x41672,a869),x41671),f283(x41671,x41672,x41674)),f329(f329(f7(x41671,f883(x41671,a869),f883(x41671,a869)),f307(x41671)),f193(f883(x41671,a869))))),f329(f283(x41671,x41672,x41674),x41673)) % 178.07/177.92 [4257]E(f329(f329(f116(f883(x42571,a869)),f329(f329(f116(f883(x42571,a869)),f329(f329(f107(f883(x42571,a869)),x42572),x42573)),f329(f329(f107(f883(x42571,a869)),x42573),x42574))),f329(f329(f107(f883(x42571,a869)),x42574),x42572)),f329(f329(f107(f883(x42571,a869)),f329(f329(f107(f883(x42571,a869)),f329(f329(f116(f883(x42571,a869)),x42572),x42573)),f329(f329(f116(f883(x42571,a869)),x42573),x42574))),f329(f329(f116(f883(x42571,a869)),x42574),x42572))) % 178.07/177.92 [4319]E(f329(f141(f876(x43191),f876(x43191),f127(x43191),f119(x43191)),f329(f329(f153(x43192,f876(x43191)),f329(f329(f7(x43192,f876(x43191),f876(x43191)),f329(f329(f8(x43191,f883(f876(x43191),f876(x43191)),x43192),f150(x43191)),x43193)),f119(x43191))),x43194)),f329(f329(f153(x43192,x43191),x43193),x43194)) % 178.07/177.92 [4330]E(f329(f329(f87(a1,x43301),f329(f109(a1),f329(f329(f81(a1),x43302),a103))),f329(f329(f18(a1,x43301,x43301),f329(f329(f7(a1,x43301,f883(x43301,x43301)),f329(f329(f8(a869,f883(x43301,f883(x43301,x43301)),a1),f102(x43301)),a198)),x43303)),f329(f329(f8(a875,x43301,a1),x43304),a110))),f190(x43301,x43303,x43304,f329(f109(a875),x43302))) % 178.07/177.92 [4544]~P24(f329(f329(f193(f883(x45441,f883(x45442,a869))),x45443),x45444)) % 178.07/177.92 [3804]E(f329(f329(f164(x38041),f329(f329(f127(x38041),x38042),x38043)),f329(f329(f81(a875),f329(f194(f876(x38041)),x38042)),x38044)),f329(f329(f164(x38041),x38043),x38044)) % 178.07/177.92 [3810]E(f329(f329(f137(x38101),x38102),f329(f329(f174(x38101),f329(f329(f81(a875),x38103),x38102)),x38104)),f329(f329(f174(x38101),x38103),f329(f329(f137(x38101),x38102),x38104))) % 178.07/177.92 [3910]E(f329(f329(f116(f883(x39101,a869)),f329(f260(x39102,x39101),x39103)),f329(f260(x39102,x39101),x39104)),f329(f260(x39102,x39101),f329(f329(f116(f883(f882(x39102,x39101),a869)),x39103),x39104))) % 178.07/177.92 [3911]E(f329(f329(f116(f883(x39111,a869)),f329(f262(x39111,x39112),x39113)),f329(f262(x39111,x39112),x39114)),f329(f262(x39111,x39112),f329(f329(f116(f883(f882(x39111,x39112),a869)),x39113),x39114))) % 178.07/177.92 [3916]E(f329(f329(f116(f883(x39161,a869)),f329(f329(f116(f883(x39161,a869)),x39162),x39163)),x39164),f329(f329(f116(f883(x39161,a869)),x39162),f329(f329(f116(f883(x39161,a869)),x39163),x39164))) % 178.07/177.92 [3917]E(f329(f329(f22(f883(x39171,a869)),f329(f329(f107(f883(x39171,a869)),x39172),x39173)),x39174),f329(f329(f107(f883(x39171,a869)),x39172),f329(f329(f22(f883(x39171,a869)),x39173),x39174))) % 178.07/177.92 [3918]E(f329(f329(f107(f883(x39181,a869)),f329(f329(f107(f883(x39181,a869)),x39182),x39183)),x39184),f329(f329(f107(f883(x39181,a869)),x39182),f329(f329(f107(f883(x39181,a869)),x39183),x39184))) % 178.07/177.92 [3958]E(f329(f329(f116(f883(f882(x39581,x39582),a869)),f329(f284(x39582,x39581),x39583)),f329(f284(x39582,x39581),x39584)),f329(f284(x39582,x39581),f329(f329(f116(f883(f882(x39582,x39581),a869)),x39583),x39584))) % 178.07/177.92 [3959]E(f329(f329(f107(f883(f882(x39591,x39592),a869)),f329(f284(x39592,x39591),x39593)),f329(f284(x39592,x39591),x39594)),f329(f284(x39592,x39591),f329(f329(f107(f883(f882(x39592,x39591),a869)),x39593),x39594))) % 178.07/177.92 [3973]E(f329(f329(f116(f883(x39731,f883(x39732,a869))),f253(x39732,x39731,x39733)),f253(x39732,x39731,x39734)),f253(x39732,x39731,f329(f329(f116(f883(x39732,f883(x39731,a869))),x39733),x39734))) % 178.07/177.92 [3974]E(f329(f329(f107(f883(x39741,f883(x39742,a869))),f253(x39742,x39741,x39743)),f253(x39742,x39741,x39744)),f253(x39742,x39741,f329(f329(f107(f883(x39742,f883(x39741,a869))),x39743),x39744))) % 178.07/177.92 [4031]E(f329(f329(f107(f883(x40311,a869)),f329(f329(f116(f883(x40311,a869)),x40312),x40313)),f329(f329(f116(f883(x40311,a869)),x40314),x40313)),f329(f329(f116(f883(x40311,a869)),f329(f329(f107(f883(x40311,a869)),x40312),x40314)),x40313)) % 178.07/177.92 [4032]E(f329(f329(f116(f883(x40321,a869)),f329(f329(f22(f883(x40321,a869)),x40322),x40323)),f329(f329(f22(f883(x40321,a869)),x40324),x40323)),f329(f329(f22(f883(x40321,a869)),f329(f329(f116(f883(x40321,a869)),x40322),x40324)),x40323)) % 178.07/177.92 [4033]E(f329(f329(f116(f883(x40331,a869)),f329(f329(f107(f883(x40331,a869)),x40332),x40333)),f329(f329(f107(f883(x40331,a869)),x40334),x40333)),f329(f329(f107(f883(x40331,a869)),f329(f329(f116(f883(x40331,a869)),x40332),x40334)),x40333)) % 178.07/177.92 [4034]E(f329(f329(f22(f883(x40341,a869)),f329(f329(f107(f883(x40341,a869)),x40342),x40343)),f329(f329(f107(f883(x40341,a869)),x40344),x40343)),f329(f329(f107(f883(x40341,a869)),f329(f329(f22(f883(x40341,a869)),x40342),x40344)),x40343)) % 178.07/177.92 [4035]E(f329(f329(f22(f883(x40351,a869)),f329(f329(f107(f883(x40351,a869)),x40352),x40353)),f329(f329(f107(f883(x40351,a869)),x40354),x40353)),f329(f329(f22(f883(x40351,a869)),f329(f329(f107(f883(x40351,a869)),x40352),x40353)),x40354)) % 178.07/177.92 [4045]E(f329(f329(f22(f883(x40451,a869)),f329(f329(f22(f883(x40451,a869)),x40452),f329(f329(f307(x40451),x40453),f193(f883(x40451,a869))))),x40454),f329(f329(f22(f883(x40451,a869)),x40452),f329(f329(f307(x40451),x40453),x40454))) % 178.07/177.92 [4099]E(f329(f329(f116(f883(x40991,a869)),f329(f329(f307(x40991),x40992),f329(f329(f307(x40991),x40993),f193(f883(x40991,a869))))),f329(f282(x40991),x40994)),f329(f282(x40991),f329(f329(f307(f882(x40991,x40991)),f329(f329(f264(x40991,x40991),x40992),x40993)),x40994))) % 178.07/177.92 [4129]E(f329(f329(f43(a875,f883(x41291,a869)),f329(f298(a875),x41292)),f329(f329(f8(a875,f883(x41291,a869),a875),x41293),f329(f329(f7(a875,a875,a875),f81(a875)),x41294))),f329(f329(f43(a875,f883(x41291,a869)),f300(a875,x41294,f329(f329(f81(a875),x41292),x41294))),x41293)) % 178.07/177.92 [4130]E(f173(x41301,f329(f283(x41301,x41301,x41302),f329(f329(f307(x41301),x41303),f193(f883(x41301,a869)))),f329(f283(f876(x41301),f876(x41301),f157(x41301,x41302)),f329(f329(f307(f876(x41301)),x41304),f193(f883(f876(x41301),a869))))),f329(f283(f876(x41301),f876(x41301),f157(x41301,x41302)),f329(f329(f307(f876(x41301)),f329(f329(f150(x41301),x41303),x41304)),f193(f883(f876(x41301),a869))))) % 178.07/177.92 [4191]E(f329(f177(x41911,x41912),f329(f329(f153(x41911,f882(x41911,x41912)),f329(f329(f18(x41911,x41912,f882(x41911,x41912)),f264(x41911,x41912)),x41913)),x41914)),f187(x41911,x41912,f329(f74(x41912,f879(x41912),x41911,f236(x41912)),x41913),f329(f171(x41911),x41914))) % 178.07/177.92 [4196]E(f329(f249(x41961),f329(f329(f7(x41961,f883(x41962,a869),a869),f329(f329(f8(x41962,f883(f883(x41962,a869),a869),x41961),f331(x41962)),x41963)),x41964)),f329(f309(x41961,x41962,x41963),x41964)) % 178.07/177.92 [4290]E(f329(f249(x42901),f329(f329(f7(x42901,f883(f882(x42902,x42901),a869),a869),f329(f329(f8(f882(x42902,x42901),f883(f883(f882(x42902,x42901),a869),a869),x42901),f331(f882(x42902,x42901))),f329(f264(x42902,x42901),x42903))),x42904)),f329(f283(x42902,x42901,x42904),f329(f329(f307(x42902),x42903),f193(f883(x42902,a869))))) % 178.07/177.92 [4304]E(f329(f329(f153(f882(x43041,a875),x43041),f263(x43041,a875)),f329(f135(f882(x43041,a875),f329(f329(f8(a875,a869,f882(x43041,a875)),x43042),f329(f329(f8(a875,a875,f882(x43041,a875)),a118),f267(x43041,a875)))),f329(f329(f181(x43041,a875),x43043),x43044))),f329(f329(f153(f882(x43041,a875),x43041),f263(x43041,a875)),f329(f135(f882(x43041,a875),f329(f329(f8(a875,a869,f882(x43041,a875)),x43042),f267(x43041,a875))),f329(f329(f181(x43041,a875),x43043),f329(f329(f153(a875,a875),a118),x43044))))) % 178.07/177.92 [4312]P24(f329(f329(f243(f883(f883(x43121,a869),a869)),f329(f329(f43(x43122,f883(f883(x43121,a869),a869)),x43123),f329(f329(f8(f883(x43121,a869),f883(f883(x43121,a869),a869),x43122),f306(x43121)),x43124))),f329(f306(x43121),f329(f329(f43(x43122,f883(x43121,a869)),x43123),x43124)))) % 178.07/177.92 [4354]E(f329(f329(f87(a1,x43541),f329(f109(a1),f329(f329(f81(a1),x43542),a103))),f329(f329(f18(a1,x43541,x43541),f329(f329(f7(a1,x43541,f883(x43541,x43541)),f329(f329(f8(a869,f883(x43541,f883(x43541,x43541)),a1),f102(x43541)),a198)),x43543)),f329(f329(f18(a1,x43541,x43541),f329(f329(f8(a875,f883(x43541,x43541),a1),x43544),a110)),f329(f329(f8(a875,x43541,a1),f189(x43541,x43543,x43544)),a110)))),f329(f189(x43541,x43543,x43544),f329(f109(a875),x43542))) % 178.07/177.92 [4357]E(f329(f329(f153(x43571,x43572),f329(f74(f879(x43572),x43572,x43571,f240(x43572)),x43573)),f329(f135(x43571,f329(f329(f8(a869,a869,x43571),a324),f329(f329(f7(x43571,f879(x43572),a869),f329(f329(f8(f879(x43572),f883(f879(x43572),a869),x43571),a326),x43573)),f206(x43572)))),x43574)),f162(x43571,x43572,x43573,x43574)) % 178.07/177.92 [4380]E(f329(f249(f882(x43801,x43802)),f329(f268(x43801,x43802,a869),f329(f329(f7(x43801,f883(x43802,a869),f883(x43802,a869)),f329(f329(f8(f883(a869,a869),f883(f883(x43802,a869),f883(x43802,a869)),x43801),f8(a869,a869,x43802)),f329(f329(f8(a869,f883(a869,a869),x43801),a327),f329(f329(f7(x43801,f883(x43801,a869),a869),f331(x43801)),x43803)))),f329(f329(f7(x43802,f883(x43802,a869),a869),f331(x43802)),x43804)))),f230(x43801,x43802,x43803,x43804)) % 178.07/177.92 [4413]E(f329(f329(f43(x44131,f883(f882(x44131,x44132),a869)),x44133),f329(f329(f18(x44131,f883(x44132,f883(f882(x44131,x44132),a869)),f883(f882(x44131,x44132),a869)),f329(f329(f8(f883(x44132,a869),f883(f883(x44132,f883(f882(x44131,x44132),a869)),f883(f882(x44131,x44132),a869)),x44131),f43(x44132,f883(f882(x44131,x44132),a869))),x44134)),f329(f329(f7(x44131,f883(f882(x44131,x44132),a869),f883(x44132,f883(f882(x44131,x44132),a869))),f329(f329(f8(f883(x44132,f883(f883(f882(x44131,x44132),a869),f883(f882(x44131,x44132),a869))),f883(f883(f882(x44131,x44132),a869),f883(x44132,f883(f882(x44131,x44132),a869))),x44131),f7(x44132,f883(f882(x44131,x44132),a869),f883(f882(x44131,x44132),a869))),f329(f329(f8(f883(x44132,f882(x44131,x44132)),f883(x44132,f883(f883(f882(x44131,x44132),a869),f883(f882(x44131,x44132),a869))),x44131),f329(f8(f882(x44131,x44132),f883(f883(f882(x44131,x44132),a869),f883(f882(x44131,x44132),a869)),x44132),f307(f882(x44131,x44132)))),f264(x44131,x44132)))),f193(f883(f882(x44131,x44132),a869))))),f329(f329(f266(x44131,x44132),x44133),x44134)) % 178.07/177.92 [3968]E(f329(f329(f127(x39681),f329(f329(f174(x39681),x39682),x39683)),f329(f329(f174(x39681),f329(f329(f22(a875),x39682),f329(f194(f876(x39681)),x39683))),x39684)),f329(f329(f174(x39681),x39682),f329(f329(f127(x39681),x39683),x39684))) % 178.07/177.92 [3969]E(f329(f329(f127(x39691),f329(f329(f137(x39691),x39692),x39693)),f329(f329(f137(x39691),f329(f329(f22(a875),x39692),f329(f194(f876(x39691)),x39693))),x39694)),f329(f329(f137(x39691),x39692),f329(f329(f127(x39691),x39693),x39694))) % 178.07/177.92 [4021]E(f329(f329(f81(a875),f329(f329(f82(a875),x40211),x40212)),f329(f329(f81(a875),f329(f329(f82(a875),x40213),x40212)),x40214)),f329(f329(f81(a875),f329(f329(f82(a875),f329(f329(f81(a875),x40211),x40213)),x40212)),x40214)) % 178.07/177.92 [4221]P24(f329(f329(f243(f883(x42211,a869)),f329(f329(f22(f883(x42211,a869)),f329(f260(x42212,x42211),x42213)),f329(f260(x42212,x42211),x42214))),f329(f260(x42212,x42211),f329(f329(f22(f883(f882(x42212,x42211),a869)),x42213),x42214)))) % 178.07/177.92 [4222]P24(f329(f329(f243(f883(x42221,a869)),f329(f329(f22(f883(x42221,a869)),f329(f262(x42221,x42222),x42223)),f329(f262(x42221,x42222),x42224))),f329(f262(x42221,x42222),f329(f329(f22(f883(f882(x42221,x42222),a869)),x42223),x42224)))) % 178.07/177.92 [4332]E(f329(f329(f81(a1),f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),x43321),x43322)),f193(f883(f882(a875,a875),a869)))))),f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),x43323),x43324)),f193(f883(f882(a875,a875),a869)))))),f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),f329(f329(f81(a875),x43321),x43323)),f329(f329(f81(a875),x43322),x43324))),f193(f883(f882(a875,a875),a869)))))) % 178.07/177.92 [4375]E(f329(f329(f82(a1),f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),x43751),x43752)),f193(f883(f882(a875,a875),a869)))))),f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),x43753),x43754)),f193(f883(f882(a875,a875),a869)))))),f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),f329(f329(f81(a875),f329(f329(f82(a875),x43751),x43753)),f329(f329(f82(a875),x43752),x43754))),f329(f329(f81(a875),f329(f329(f82(a875),x43751),x43754)),f329(f329(f82(a875),x43752),x43753)))),f193(f883(f882(a875,a875),a869)))))) % 178.07/177.92 [4395]E(f329(f249(x43951),f329(f329(f8(f883(x43952,a869),a869,x43951),f89(x43952)),f329(f329(f8(f883(x43952,a869),f883(x43952,a869),x43951),f329(f18(x43952,a869,a869),f329(f329(f8(a869,f883(a869,a869),x43952),a332),f329(f329(f7(x43952,f883(x43952,a869),a869),f331(x43952)),x43953)))),f329(f329(f7(x43951,f883(x43952,f883(x43951,a869)),f883(x43952,a869)),f329(f329(f8(f883(f883(x43951,a869),a869),f883(f883(x43952,f883(x43951,a869)),f883(x43952,a869)),x43951),f8(f883(x43951,a869),a869,x43952)),f331(x43951))),x43954)))),f329(f329(f42(x43952,f883(x43951,a869)),x43953),x43954)) % 178.07/177.92 [4428]E(f329(f329(f286(x44281,x44281,x44281),f329(f329(f307(f882(x44281,x44281)),f329(f329(f264(x44281,x44281),x44282),x44283)),x44284)),f305(x44281,f329(f329(f307(f882(x44281,x44281)),f329(f329(f264(x44281,x44281),x44282),x44283)),x44284))),f329(f329(f116(f883(f882(x44281,x44281),a869)),f329(f329(f286(x44281,x44281,x44281),x44284),f305(x44281,x44284))),f329(f249(f882(x44281,x44281)),f329(f268(x44281,x44281,a869),f329(f329(f7(x44281,f883(x44281,a869),f883(x44281,a869)),f329(f329(f8(f883(a869,a869),f883(f883(x44281,a869),f883(x44281,a869)),x44281),f8(a869,a869,x44281)),f329(f329(f8(a869,f883(a869,a869),x44281),a327),f329(f329(f7(x44281,f883(f882(x44281,x44281),a869),a869),f329(f329(f8(f882(x44281,x44281),f883(f883(f882(x44281,x44281),a869),a869),x44281),f331(f882(x44281,x44281))),f329(f329(f7(x44281,x44281,f882(x44281,x44281)),f264(x44281,x44281)),x44282))),f305(x44281,x44284))))),f329(f329(f7(x44281,f883(f882(x44281,x44281),a869),a869),f329(f329(f8(f882(x44281,x44281),f883(f883(f882(x44281,x44281),a869),a869),x44281),f331(f882(x44281,x44281))),f329(f264(x44281,x44281),x44283))),f305(x44281,x44284))))))) % 178.07/177.92 [4223]E(f329(f135(x42231,f329(f329(f18(x42231,a869,a869),f329(f329(f8(a869,f883(a869,a869),x42231),a327),x42232)),x42233)),x42234),f329(f135(x42231,x42233),f329(f135(x42231,x42232),x42234))) % 178.07/177.92 [4326]E(f329(f329(f127(x43261),f329(f329(f329(f102(f876(x43261)),f329(f329(f331(a875),f2(a875)),x43262)),f329(f329(f150(x43261),x43263),f119(x43261))),f119(x43261))),f175(x43261,x43264,f329(f249(a875),f329(f329(f7(a875,f883(a875,a869),a869),f329(f329(f8(a875,f883(f883(a875,a869),a869),a875),f331(a875)),a118)),x43262)))),f175(x43261,f329(f329(f150(x43261),x43263),x43264),x43262)) % 178.07/177.92 [4422]E(f329(f249(f882(x44221,x44222)),f329(f329(f8(f883(a875,a869),a869,f882(x44221,x44222)),f88(a875)),f329(f329(f7(f882(x44221,x44222),f883(a875,a869),f883(a875,a869)),f329(f329(f8(f883(a875,f883(a869,a869)),f883(f883(a875,a869),f883(a875,a869)),f882(x44221,x44222)),f18(a875,a869,a869)),f329(f329(f8(f883(a875,a869),f883(a875,f883(a869,a869)),f882(x44221,x44222)),f329(f8(a869,f883(a869,a869),a875),a327)),f329(f329(f7(f882(x44221,x44222),f883(a875,f882(x44221,x44222)),f883(a875,a869)),f329(f329(f8(f883(f882(x44221,x44222),a869),f883(f883(a875,f882(x44221,x44222)),f883(a875,a869)),f882(x44221,x44222)),f8(f882(x44221,x44222),a869,a875)),a326)),f329(f329(f18(a875,x44222,f882(x44221,x44222)),f329(f329(f8(x44221,f883(x44222,f882(x44221,x44222)),a875),f264(x44221,x44222)),f329(f164(x44221),x44223))),f329(f164(x44222),x44224)))))),f329(f329(f7(a875,a875,a869),f244(a875)),f329(f329(f241(a875),f329(f194(f876(x44221)),x44223)),f329(f194(f876(x44222)),x44224)))))),f329(f171(f882(x44221,x44222)),f329(f329(f181(x44221,x44222),x44223),x44224))) % 178.07/177.92 [4345]E(f329(f249(f882(x43451,x43452)),f329(f268(x43451,x43452,a869),f329(f329(f7(x43451,f883(x43452,a869),f883(x43452,a869)),f329(f329(f8(f883(a869,a869),f883(f883(x43452,a869),f883(x43452,a869)),x43451),f8(a869,a869,x43452)),f329(f329(f8(a869,f883(a869,a869),x43451),a327),x43453))),x43454))),f329(f329(f266(x43451,x43452),f329(f249(x43451),x43453)),f329(f16(f883(x43452,a869),x43451),f329(f249(x43452),x43454)))) % 178.07/177.92 [4348]E(f329(f249(f882(x43481,x43482)),f329(f268(x43481,x43482,a869),f329(f329(f18(x43481,f883(x43482,a869),f883(x43482,a869)),f329(f329(f8(f883(a869,a869),f883(f883(x43482,a869),f883(x43482,a869)),x43481),f8(a869,a869,x43482)),f329(f329(f8(a869,f883(a869,a869),x43481),a327),x43483))),x43484))),f329(f329(f266(x43481,x43482),f329(f249(x43481),x43483)),f329(f329(f8(f883(x43482,a869),f883(x43482,a869),x43481),f249(x43482)),x43484))) % 178.07/177.92 [4364]E(f329(f249(x43641),f329(f329(f8(f883(x43642,a869),a869,x43641),f89(x43642)),f329(f329(f8(f883(x43642,a869),f883(x43642,a869),x43641),f329(f18(x43642,a869,a869),f329(f329(f8(a869,f883(a869,a869),x43642),a332),f329(f329(f7(x43642,f883(x43642,a869),a869),f331(x43642)),x43643)))),x43644))),f329(f329(f42(x43642,f883(x43641,a869)),x43643),f329(f329(f8(f883(x43641,a869),f883(x43641,a869),x43642),f249(x43641)),f329(f7(x43641,x43642,a869),x43644)))) % 178.07/177.92 [4408]E(f329(f329(f153(f882(x44081,a875),x44081),f263(x44081,a875)),f329(f135(f882(x44081,a875),f329(f329(f7(f882(x44081,a875),f883(a875,a869),a869),f329(f329(f8(a875,f883(f883(a875,a869),a869),f882(x44081,a875)),f331(a875)),f267(x44081,a875))),x44082)),f329(f329(f181(x44081,a875),x44083),f138(a875,f329(f299(a875,x44084),f329(f329(f81(a875),x44084),f329(f194(f876(x44081)),x44083))))))),f329(f329(f153(f882(x44081,a875),x44081),f263(x44081,a875)),f329(f135(f882(x44081,a875),f329(f329(f7(f882(x44081,a875),f883(a875,a869),a869),f329(f329(f8(a875,f883(f883(a875,a869),a869),f882(x44081,a875)),f331(a875)),f329(f329(f7(f882(x44081,a875),a875,a875),f329(f329(f8(a875,f883(a875,a875),f882(x44081,a875)),f81(a875)),f267(x44081,a875))),x44084))),x44082)),f329(f329(f181(x44081,a875),x44083),f138(a875,f329(f299(a875,f2(a875)),f329(f194(f876(x44081)),x44083))))))) % 178.07/177.92 [4409]E(f329(a118,f329(f329(f242(a875),f329(f194(f876(x44091)),x44092)),f329(f141(a875,f876(x44093),f329(f7(f876(x44093),a875,a875),f329(f329(f8(a875,f883(a875,a875),f876(x44093)),f242(a875)),f329(f329(f7(f876(x44093),a875,a875),f329(f329(f8(a875,f883(a875,a875),f876(x44093)),f22(a875)),f194(f876(x44093)))),f329(a118,f2(a875))))),f2(a875)),f329(f168(f876(x44093)),f329(f135(f876(x44093),f329(f329(f8(a869,a869,f876(x44093)),a324),f329(f329(f7(f876(x44093),f876(x44093),a869),a326),f119(x44093)))),x44094))))),f329(f329(f242(a875),f329(a118,f329(f194(f876(x44091)),x44092))),f329(f141(a875,f876(x44093),f329(f7(f876(x44093),a875,a875),f329(f329(f8(a875,f883(a875,a875),f876(x44093)),f242(a875)),f194(f876(x44093)))),f2(a875)),f329(f168(f876(x44093)),x44094)))) % 178.07/177.92 [4363]E(f329(f329(f127(x43631),f175(x43631,x43632,x43633)),f175(x43631,x43634,f329(f249(a875),f329(f329(f7(a875,f883(a875,a869),a869),f329(f329(f8(a875,f883(f883(a875,a869),a869),a875),f331(a875)),f329(f329(f7(a875,a875,a875),f81(a875)),f329(f194(f876(x43631)),x43632)))),x43633)))),f175(x43631,f329(f329(f127(x43631),x43632),x43634),x43633)) % 178.07/177.92 [4415]E(f329(f329(f150(f876(x44151)),f329(f329(f150(x44151),x44152),f329(f141(f876(x44151),f876(x44151),f127(x44151),f119(x44151)),f329(f329(f153(f876(x44151),f876(x44151)),f155(f876(x44151),x44151,f119(x44151),f329(f329(f8(f876(x44151),f883(f876(x44151),f876(x44151)),x44151),f16(f876(x44151),f876(x44151))),f329(f329(f7(x44151,f876(x44151),f876(x44151)),f150(x44151)),f119(x44151))))),x44153)))),f179(x44151,f329(f329(f150(f876(x44151)),x44154),f329(f141(f876(f876(x44151)),f876(f876(x44151)),f127(f876(x44151)),f119(f876(x44151))),f329(f329(f153(f876(x44151),f876(f876(x44151))),f155(f876(f876(x44151)),x44151,f119(f876(x44151)),f329(f16(f883(f876(x44151),f876(f876(x44151))),x44151),f329(f329(f7(f876(x44151),f876(f876(x44151)),f876(f876(x44151))),f150(f876(x44151))),f119(f876(x44151)))))),x44153))))),f179(x44151,f329(f329(f150(f876(x44151)),f329(f329(f150(x44151),x44152),x44154)),x44153))) % 178.07/177.92 [4423]E(f329(f249(f882(x44231,x44231)),f329(f268(x44231,x44231,a869),f329(f329(f7(x44231,f883(f882(x44232,x44232),a869),f883(x44231,a869)),f329(f329(f8(f883(x44231,f883(f883(f882(x44232,x44232),a869),a869)),f883(f883(f882(x44232,x44232),a869),f883(x44231,a869)),x44231),f7(x44231,f883(f882(x44232,x44232),a869),a869)),f329(f329(f8(f883(x44231,f882(x44232,x44232)),f883(x44231,f883(f883(f882(x44232,x44232),a869),a869)),x44231),f329(f8(f882(x44232,x44232),f883(f883(f882(x44232,x44232),a869),a869),x44231),f331(f882(x44232,x44232)))),f329(f329(f7(x44231,f883(x44231,x44232),f883(x44231,f882(x44232,x44232))),f329(f329(f8(f883(x44232,f882(x44232,x44232)),f883(f883(x44231,x44232),f883(x44231,f882(x44232,x44232))),x44231),f8(x44232,f882(x44232,x44232),x44231)),f329(f329(f8(x44232,f883(x44232,f882(x44232,x44232)),x44231),f264(x44232,x44232)),x44233))),x44233)))),x44234))),f329(f329(f285(x44232,x44231),x44234),x44233)) % 178.07/177.92 [4485]~E(f34(x44851,x44852),f29(x44853,x44854,x44855)) % 178.07/177.92 [4486]~E(f34(x44861,x44862),f31(x44863,x44864,x44865)) % 178.07/177.92 [4487]~E(f34(x44871,x44872),f30(x44873,x44874,x44875)) % 178.07/177.92 [4488]~E(f33(x44881,x44882),f29(x44883,x44884,x44885)) % 178.07/177.92 [4489]~E(f33(x44891,x44892),f31(x44893,x44894,x44895)) % 178.07/177.92 [4490]~E(f33(x44901,x44902),f30(x44903,x44904,x44905)) % 178.07/177.92 [4491]~E(f29(x44911,x44912,x44913),f34(x44914,x44915)) % 178.07/177.92 [4492]~E(f29(x44921,x44922,x44923),f33(x44924,x44925)) % 178.07/177.92 [4493]~E(f31(x44931,x44932,x44933),f34(x44934,x44935)) % 178.07/177.92 [4494]~E(f31(x44941,x44942,x44943),f33(x44944,x44945)) % 178.07/177.92 [4495]~E(f30(x44951,x44952,x44953),f34(x44954,x44955)) % 178.07/177.92 [4496]~E(f30(x44961,x44962,x44963),f33(x44964,x44965)) % 178.07/177.92 [3908]E(f329(f184(x39081,x39082,x39083,x39084),x39085),f329(f238(f879(x39082),x39082,f329(x39083,x39085),f236(x39082)),f329(x39084,x39085))) % 178.07/177.92 [3996]E(f184(x39961,x39962,f184(x39961,x39962,x39963,x39964),x39965),f184(x39961,x39962,x39963,f184(x39961,x39962,x39964,x39965))) % 178.07/177.92 [4170]E(f265(x41701,x41702,x41703,f253(x41702,x41701,x41704),f253(x41703,x41702,x41705)),f253(x41703,x41701,f265(x41703,x41702,x41701,x41705,x41704))) % 178.07/177.92 [4177]E(f329(f329(f116(f883(x41771,a869)),f329(f171(x41771),f329(f329(f174(x41771),f329(f194(f876(x41772)),x41773)),x41774))),f183(x41771,x41772,x41775)),f183(x41771,x41772,f186(x41771,x41772,x41775,x41774,x41773))) % 178.07/177.92 [3736]E(f329(f329(f268(x37361,x37362,x37363),x37364),x37365),f329(f329(x37364,f329(f263(x37361,x37362),x37365)),f329(f267(x37361,x37362),x37365))) % 178.07/177.92 [3761]E(f329(f238(x37611,x37612,x37613,x37614),f329(f236(x37612),x37615)),f329(x37614,x37615)) % 178.07/177.92 [3770]E(f329(f329(f329(f66(x37701,x37702,x37703),x37704),x37705),f193(f883(x37702,a869))),x37705) % 178.07/177.92 [3940]E(f239(x39401,x39402,x39403,x39404,f329(f236(x39402),x39405)),f329(x39404,x39405)) % 178.07/177.92 [4051]E(f329(f74(f879(x40511),f879(x40512),f879(x40513),f329(f207(x40511,x40512),x40514)),f329(f207(x40513,x40511),x40515)),f329(f207(x40513,x40512),f329(f74(x40511,x40512,x40513,x40514),x40515))) % 178.07/177.92 [4053]E(f329(f74(f876(x40531),f876(x40532),f876(x40533),f329(f153(x40531,x40532),x40534)),f329(f153(x40533,x40531),x40535)),f329(f153(x40533,x40532),f329(f74(x40531,x40532,x40533,x40534),x40535))) % 178.07/177.92 [4109]E(f329(f238(x41091,f882(x41092,f877(x41092)),x41093,f329(f268(x41092,f877(x41092),x41091),x41094)),f329(f134(x41092),x41095)),f132(x41091,x41092,x41093,x41094,x41095)) % 178.07/177.92 [4133]E(f86(x41331,f67(x41332,x41331,x41333,x41334,x41335)),f329(f329(f65(x41332,x41331,x41333),x41334),x41335)) % 178.07/177.92 [4168]E(f329(f329(f81(a875),f329(f329(f81(a875),f329(x41681,f329(f263(x41682,x41683),x41684))),f329(x41685,f329(f267(x41682,x41683),x41684)))),f329(a118,f2(a875))),f272(x41682,x41683,x41681,x41685,x41684)) % 178.07/177.92 [4359]E(f162(x43591,x43592,f329(f329(f7(x43591,f879(x43592),f879(x43592)),f329(f329(f18(x43591,f879(x43592),f883(f879(x43592),f879(x43592))),f329(f329(f8(a869,f883(f879(x43592),f883(f879(x43592),f879(x43592))),x43591),f102(f879(x43592))),x43593)),f329(f329(f8(x43592,f879(x43592),x43591),f236(x43592)),x43594))),f206(x43592)),x43595),f329(f329(f153(x43591,x43592),x43594),f329(f135(x43591,x43593),x43595))) % 178.07/177.92 [4536]~E(f329(f329(f329(f73(x45361,f879(x45362)),x45363),x45364),f329(f236(x45362),x45365)),f329(f16(f879(x45362),x45361),f206(x45362))) % 178.07/177.92 [3672]E(f329(f329(f174(x36721),x36722),f329(f329(f153(x36723,x36721),x36724),x36725)),f329(f329(f153(x36723,x36721),x36724),f329(f329(f174(x36723),x36722),x36725))) % 178.07/177.92 [3673]E(f329(f329(f137(x36731),x36732),f329(f329(f153(x36733,x36731),x36734),x36735)),f329(f329(f153(x36733,x36731),x36734),f329(f329(f137(x36733),x36732),x36735))) % 178.07/177.92 [3705]E(f329(f329(f153(x37051,x37052),x37053),f329(f329(f150(x37051),x37054),x37055)),f329(f329(f150(x37052),f329(x37053,x37054)),f329(f329(f153(x37051,x37052),x37053),x37055))) % 178.07/177.92 [3765]E(f329(f308(x37651,x37652,x37653),f329(f329(f307(x37651),x37654),x37655)),f329(f329(f307(x37652),f329(x37653,x37654)),f329(f308(x37651,x37652,x37653),x37655))) % 178.07/177.92 [3794]E(f172(x37941,f329(f329(f150(x37941),x37942),x37943),f329(f329(f150(x37941),x37944),x37945)),f329(f329(f150(x37941),x37942),f329(f329(f150(x37941),x37944),f172(x37941,x37943,x37945)))) % 178.07/177.92 [3830]E(f329(f329(f181(x38301,x38302),f329(f329(f174(x38301),x38303),x38304)),f329(f329(f174(x38302),x38303),x38305)),f329(f329(f174(f882(x38301,x38302)),x38303),f329(f329(f181(x38301,x38302),x38304),x38305))) % 178.07/177.92 [3831]E(f329(f329(f181(x38311,x38312),f329(f329(f137(x38311),x38313),x38314)),f329(f329(f137(x38312),x38313),x38315)),f329(f329(f137(f882(x38311,x38312)),x38313),f329(f329(f181(x38311,x38312),x38314),x38315))) % 178.07/177.92 [3841]E(f329(f329(f158(x38411,f329(f329(f150(x38411),x38412),x38413)),f329(a118,x38414)),x38415),f329(f329(f150(x38411),x38412),f329(f329(f158(x38411,x38413),x38414),x38415))) % 178.07/177.92 [3844]E(f329(f238(f879(x38441),x38442,f206(x38441),x38443),f329(f329(f16(f879(x38442),x38444),f206(x38442)),x38445)),f206(x38441)) % 178.07/177.92 [3846]E(f329(f329(f127(x38461),f329(f329(f153(x38462,x38461),x38463),x38464)),f329(f329(f153(x38462,x38461),x38463),x38465)),f329(f329(f153(x38462,x38461),x38463),f329(f329(f127(x38462),x38464),x38465))) % 178.07/177.92 [3850]E(f329(f329(x38501,x38502),f329(f329(f255(x38503,x38504,x38501),x38502),x38505)),f329(f329(f255(x38503,x38504,x38501),x38502),f329(a118,x38505))) % 178.07/177.92 [3880]E(f163(x38801,x38802,x38803,f329(f329(f150(x38801),x38804),x38805)),f329(f329(f127(x38802),f329(x38803,x38804)),f163(x38801,x38802,x38803,x38805))) % 178.07/177.92 [3892]E(f329(f329(f286(x38921,x38922,x38923),f329(f284(x38922,x38921),x38924)),f329(f284(x38923,x38922),x38925)),f329(f284(x38923,x38921),f329(f329(f286(x38923,x38922,x38921),x38925),x38924))) % 178.07/177.92 [3926]E(f329(f329(f329(f188(f876(x39261),f876(x39261)),x39262),f167(x39261)),f329(f329(f153(x39263,x39261),x39264),x39265)),f329(f329(f153(x39263,x39261),x39264),f329(f329(f329(f188(f876(x39263),f876(x39263)),x39262),f167(x39263)),x39265))) % 178.07/177.92 [3927]E(f329(f329(f270(x39271,x39272,x39271,x39273),f329(f264(x39272,x39271),x39274)),x39275),f329(x39275,x39274)) % 178.07/177.92 [3954]E(f154(x39541,x39542,f329(f329(f153(x39543,x39541),x39544),x39545)),f154(x39543,f329(f74(x39541,a875,x39543,x39542),x39544),x39545)) % 178.07/177.92 [4019]E(f329(f329(f74(f879(x40191),f879(x40192),x40193,f329(f207(x40191,x40192),x40194)),f329(f16(f879(x40191),x40193),f206(x40191))),x40195),f206(x40192)) % 178.07/177.92 [4020]E(f176(f882(x40201,x40202),f329(f74(x40202,a869,f882(x40201,x40202),x40203),f267(x40201,x40202)),f329(f329(f181(x40201,x40202),x40204),x40205)),f329(f329(f181(x40201,x40202),x40204),f176(x40202,x40203,x40205))) % 178.07/177.92 [4025]E(f329(f308(x40251,x40252,f329(f329(f8(x40253,x40252,x40251),x40254),x40255)),f252(f883(x40251,a869))),f329(f308(x40253,x40252,x40254),f329(f308(x40251,x40253,x40255),f252(f883(x40251,a869))))) % 178.07/177.92 [4038]E(f176(f882(x40381,x40382),f329(f74(x40381,a869,f882(x40381,x40382),x40383),f263(x40381,x40382)),f329(f329(f181(x40381,x40382),x40384),x40385)),f329(f329(f181(x40381,x40382),f176(x40381,x40383,x40384)),x40385)) % 178.07/177.92 [4057]E(f329(f329(f116(f883(x40571,a869)),f329(f309(x40571,x40572,x40573),f329(f329(f307(x40572),x40574),f193(f883(x40572,a869))))),f329(f309(x40571,x40572,x40573),x40575)),f329(f309(x40571,x40572,x40573),f329(f329(f307(x40572),x40574),x40575))) % 178.07/177.92 [4117]E(f329(f329(f127(f882(x41171,x41172)),f329(f329(f153(x41172,f882(x41171,x41172)),f329(f264(x41171,x41172),x41173)),x41174)),f60(x41171,x41172,x41175,x41174)),f60(x41171,x41172,f329(f329(f150(x41171),x41173),x41175),x41174)) % 178.07/177.92 [4118]E(f329(f329(f153(x41181,x41182),x41183),f176(x41181,f329(f74(x41182,a869,x41181,x41184),x41183),x41185)),f176(x41182,x41184,f329(f329(f153(x41181,x41182),x41183),x41185))) % 178.07/177.92 [4124]E(f329(f141(x41241,x41242,f329(f7(x41242,x41241,x41241),f329(f7(x41241,x41242,x41241),x41243)),x41244),f329(f168(x41242),f329(f168(x41242),x41245))),f329(f141(x41241,x41242,x41243,x41244),x41245)) % 178.07/177.92 [4125]E(f329(f329(f329(f73(x41251,f879(x41252)),f187(x41251,x41252,x41253,x41254)),x41255),f329(x41253,x41255)),f187(x41251,x41252,x41253,f329(f329(f307(x41251),x41255),x41254))) % 178.07/177.92 [4194]E(f329(f238(f876(x41941),x41941,f162(x41942,x41941,x41943,x41944),f329(f329(f7(x41941,f876(x41941),f876(x41941)),f150(x41941)),f162(x41942,x41941,x41943,x41944))),f329(x41943,x41945)),f162(x41942,x41941,x41943,f329(f329(f150(x41942),x41945),x41944))) % 178.07/177.92 [4231]P24(f329(f329(f243(f883(x42311,a869)),f329(f308(x42312,x42311,x42313),f329(f329(f107(f883(x42312,a869)),x42314),x42315))),f329(f329(f107(f883(x42311,a869)),f329(f308(x42312,x42311,x42313),x42314)),f329(f308(x42312,x42311,x42313),x42315)))) % 178.07/177.92 [4232]P24(f329(f329(f243(f883(x42321,a869)),f329(f283(x42322,x42321,x42323),f329(f329(f107(f883(x42322,a869)),x42324),x42325))),f329(f329(f107(f883(x42321,a869)),f329(f283(x42322,x42321,x42323),x42324)),f329(f283(x42322,x42321,x42323),x42325)))) % 178.07/177.92 [4333]E(f329(f267(x43331,x43332),f329(f269(x43333,x43331,x43332,x43332,x43334,f35(x43332)),x43335)),f329(f267(x43333,x43332),x43335)) % 178.07/177.92 [4334]E(f329(f263(x43341,x43342),f329(f269(x43341,x43341,x43343,x43342,f35(x43341),x43344),x43345)),f329(f263(x43341,x43343),x43345)) % 178.07/177.92 [4419]E(f329(f141(f883(x44191,f879(x44192)),f882(x44191,x44192),f329(f329(f8(f883(x44191,f883(x44192,f883(x44191,f879(x44192)))),f883(f882(x44191,x44192),f883(x44191,f879(x44192))),f883(x44191,f879(x44192))),f268(x44191,x44192,f883(x44191,f879(x44192)))),f329(f329(f7(f883(x44191,f879(x44192)),f883(x44192,f879(x44192)),f883(x44191,f883(x44192,f883(x44191,f879(x44192))))),f329(f329(f8(f883(x44191,f883(f883(x44192,f879(x44192)),f883(x44192,f883(x44191,f879(x44192))))),f883(f883(x44192,f879(x44192)),f883(x44191,f883(x44192,f883(x44191,f879(x44192))))),f883(x44191,f879(x44192))),f7(x44191,f883(x44192,f879(x44192)),f883(x44192,f883(x44191,f879(x44192))))),f329(f329(f8(f883(x44191,f883(f879(x44192),f883(x44191,f879(x44192)))),f883(x44191,f883(f883(x44192,f879(x44192)),f883(x44192,f883(x44191,f879(x44192))))),f883(x44191,f879(x44192))),f329(f8(f883(f879(x44192),f883(x44191,f879(x44192))),f883(f883(x44192,f879(x44192)),f883(x44192,f883(x44191,f879(x44192)))),x44191),f8(f879(x44192),f883(x44191,f879(x44192)),x44192))),f73(x44191,f879(x44192))))),f236(x44192))),x44193),f329(f329(f181(x44191,x44192),x44194),x44195)),f186(x44191,x44192,x44193,x44194,x44195)) % 178.07/177.92 [4421]P20(x44211,x44212,f329(f329(f307(f874(x44211)),f329(f329(f329(f93(x44211),f329(f329(f7(x44211,f883(a871,a869),f883(a871,a869)),f329(f329(f8(f883(a871,f883(a869,a869)),f883(f883(a871,a869),f883(a871,a869)),x44211),f18(a871,a869,a869)),f329(f329(f8(f883(a871,a869),f883(a871,f883(a869,a869)),x44211),f329(f8(a869,f883(a869,a869),a871),a327)),x44213))),f329(f329(f8(a869,a869,a871),a324),x44214))),f33(x44214,x44215)),x44213)),f193(f883(f874(x44211),a869)))) % 178.07/177.92 [3517]E(f329(f329(f329(f329(f212(x35171),x35172),x35173),x35174),x35175),f197(x35171,x35172)) % 178.07/177.92 [3518]E(f329(f329(f329(f329(f216(x35181),x35182),x35183),x35184),x35185),f208(x35181,x35182)) % 178.07/177.92 [3562]E(f99(x35621,x35622,f329(f329(f329(f93(x35621),x35623),x35624),x35625)),f2(a875)) % 178.07/177.92 [3656]E(f329(f329(f329(f329(f73(x36561,x36562),x36563),x36564),x36565),x36564),x36565) % 178.07/177.92 [3881]E(f329(f329(f42(x38811,f883(x38812,a869)),f329(f329(f307(x38811),x38813),x38814)),x38815),f329(f329(f107(f883(x38812,a869)),f329(x38815,x38813)),f329(f329(f42(x38811,f883(x38812,a869)),x38814),x38815))) % 178.07/177.92 [3882]E(f329(f329(f43(x38821,f883(x38822,a869)),f329(f329(f307(x38821),x38823),x38824)),x38825),f329(f329(f116(f883(x38822,a869)),f329(x38825,x38823)),f329(f329(f43(x38821,f883(x38822,a869)),x38824),x38825))) % 178.07/177.92 [3933]E(f329(f122(x39331,x39332,f329(x39333,x39334)),f329(f329(f7(x39331,a105,f877(x39332)),x39335),x39334)),f329(f204(x39331,x39332,x39333,x39335),x39334)) % 178.07/177.92 [3947]E(f329(f329(f116(f883(x39471,a869)),f329(f308(x39472,x39471,x39473),x39474)),f329(f308(x39472,x39471,x39473),x39475)),f329(f308(x39472,x39471,x39473),f329(f329(f116(f883(x39472,a869)),x39474),x39475))) % 178.07/177.92 [3948]E(f329(f329(f116(f883(x39481,a869)),f329(f309(x39481,x39482,x39483),x39484)),f329(f309(x39481,x39482,x39483),x39485)),f329(f309(x39481,x39482,x39483),f329(f329(f116(f883(x39482,a869)),x39484),x39485))) % 178.07/177.92 [3949]E(f329(f329(f22(f883(x39491,a869)),f329(f309(x39491,x39492,x39493),x39494)),f329(f309(x39491,x39492,x39493),x39495)),f329(f309(x39491,x39492,x39493),f329(f329(f22(f883(x39492,a869)),x39494),x39495))) % 178.07/177.92 [3950]E(f329(f329(f107(f883(x39501,a869)),f329(f309(x39501,x39502,x39503),x39504)),f329(f309(x39501,x39502,x39503),x39505)),f329(f309(x39501,x39502,x39503),f329(f329(f107(f883(x39502,a869)),x39504),x39505))) % 178.07/177.92 [3951]E(f329(f329(f116(f883(x39511,a869)),f329(f283(x39512,x39511,x39513),x39514)),f329(f283(x39512,x39511,x39513),x39515)),f329(f283(x39512,x39511,x39513),f329(f329(f116(f883(x39512,a869)),x39514),x39515))) % 178.07/177.92 [3953]E(f187(x39531,x39532,f187(x39531,x39532,x39533,x39534),x39535),f187(x39531,x39532,x39533,f329(f329(f107(f883(x39531,a869)),x39534),x39535))) % 178.07/177.92 [4015]E(f329(f329(f158(x40151,f329(f329(f127(x40151),x40152),f329(f329(f150(x40151),x40153),x40154))),f329(f194(f876(x40151)),x40152)),x40155),f329(f329(f127(x40151),x40152),f329(f329(f150(x40151),x40155),x40154))) % 178.07/177.92 [4023]E(f329(f329(f42(x40231,f883(x40232,a869)),x40233),f329(f329(f8(f883(x40232,a869),f883(x40232,a869),x40231),f329(f307(x40232),x40234)),x40235)),f329(f329(f307(x40232),x40234),f329(f329(f42(x40231,f883(x40232,a869)),x40233),x40235))) % 178.07/177.92 [4091]E(f187(x40911,x40912,f329(f329(f329(f73(x40911,f879(x40912)),x40913),x40914),f329(f236(x40912),x40915)),f329(f80(f883(x40911,a869)),f329(f329(f307(x40911),x40914),f193(f883(x40911,a869))))),f187(x40911,x40912,x40913,f329(f80(f883(x40911,a869)),f329(f329(f307(x40911),x40914),f193(f883(x40911,a869)))))) % 178.07/177.92 [4181]E(f329(f329(f153(x41811,x41812),x41813),f329(f135(x41811,f329(f74(x41812,a869,x41811,x41814),x41813)),x41815)),f329(f135(x41812,x41814),f329(f329(f153(x41811,x41812),x41813),x41815))) % 178.07/177.92 [4187]E(f329(f194(f876(x41871)),f329(f135(x41871,x41872),f329(f329(f153(x41873,x41871),x41874),x41875))),f329(f194(f876(x41873)),f329(f135(x41873,f329(f74(x41871,a869,x41873,x41872),x41874)),x41875))) % 178.07/177.92 [4325]E(f329(f329(f116(f883(x43251,a869)),f329(f329(f22(f883(x43251,a869)),f183(x43251,x43252,x43253)),f329(f249(x43251),f329(f329(f7(x43251,f883(x43251,a869),a869),f331(x43251)),f329(f329(f22(f883(x43251,a869)),x43254),f183(x43251,x43252,x43255)))))),f329(f249(x43251),f329(f329(f7(x43251,f883(x43251,a869),a869),f331(x43251)),f329(f329(f107(f883(x43251,a869)),x43254),f183(x43251,x43252,x43255))))),f183(x43251,x43252,f77(x43251,f879(x43252),x43253,x43255,x43254))) % 178.07/177.92 [4400]E(f329(f155(f876(f882(x44001,x44002)),x44002,f119(f882(x44001,x44002)),f329(f329(f7(x44002,f883(f876(x44002),f876(f882(x44001,x44002))),f883(f876(x44002),f876(f882(x44001,x44002)))),f329(f329(f8(f883(f876(f882(x44001,x44002)),f876(f882(x44001,x44002))),f883(f883(f876(x44002),f876(f882(x44001,x44002))),f883(f876(x44002),f876(f882(x44001,x44002)))),x44002),f8(f876(f882(x44001,x44002)),f876(f882(x44001,x44002)),f876(x44002))),f329(f329(f8(f882(x44001,x44002),f883(f876(f882(x44001,x44002)),f876(f882(x44001,x44002))),x44002),f150(f882(x44001,x44002))),f329(f264(x44001,x44002),x44003)))),f329(f181(x44001,x44002),x44004))),x44005),f329(f329(f181(x44001,x44002),f329(f329(f150(x44001),x44003),x44004)),x44005)) % 178.07/177.92 [3875]E(f329(f329(f158(x38751,f329(f329(f158(x38751,x38752),x38753),x38754)),x38753),x38755),f329(f329(f158(x38751,x38752),x38753),x38755)) % 178.07/177.92 [3928]E(f329(f260(x39281,x39282),f329(f329(f307(f882(x39281,x39282)),f329(f329(f264(x39281,x39282),x39283),x39284)),x39285)),f329(f329(f307(x39282),x39284),f329(f260(x39281,x39282),x39285))) % 178.07/177.92 [3929]E(f329(f262(x39291,x39292),f329(f329(f307(f882(x39291,x39292)),f329(f329(f264(x39291,x39292),x39293),x39294)),x39295)),f329(f329(f307(x39291),x39293),f329(f262(x39291,x39292),x39295))) % 178.07/177.92 [3978]E(f125(x39781,x39782,f329(x39783,x39784),f329(f329(f7(x39781,a105,f877(f879(x39782))),x39785),x39784)),f329(f202(x39781,x39782,x39783,x39785),x39784)) % 178.07/177.92 [4008]E(f329(f329(f116(f883(f882(x40081,x40082),a869)),f329(f329(f266(x40081,x40082),x40083),x40084)),f329(f329(f266(x40081,x40082),x40085),x40084)),f329(f329(f266(x40081,x40082),f329(f329(f116(f883(x40081,a869)),x40083),x40085)),x40084)) % 178.07/177.92 [4009]E(f329(f329(f22(f883(f882(x40091,x40092),a869)),f329(f329(f266(x40091,x40092),x40093),x40094)),f329(f329(f266(x40091,x40092),x40095),x40094)),f329(f329(f266(x40091,x40092),f329(f329(f22(f883(x40091,a869)),x40093),x40095)),x40094)) % 178.07/177.92 [4010]E(f329(f329(f107(f883(f882(x40101,x40102),a869)),f329(f329(f266(x40101,x40102),x40103),x40104)),f329(f329(f266(x40101,x40102),x40105),x40104)),f329(f329(f266(x40101,x40102),f329(f329(f107(f883(x40101,a869)),x40103),x40105)),x40104)) % 178.07/177.92 [4069]E(f329(f329(f107(f883(x40691,a869)),f329(f329(f42(x40692,f883(x40691,a869)),x40693),x40694)),f329(f329(f42(x40692,f883(x40691,a869)),x40695),x40694)),f329(f329(f42(x40692,f883(x40691,a869)),f329(f329(f116(f883(x40692,a869)),x40693),x40695)),x40694)) % 178.07/177.92 [4070]E(f329(f329(f116(f883(x40701,a869)),f329(f329(f43(x40702,f883(x40701,a869)),x40703),x40704)),f329(f329(f43(x40702,f883(x40701,a869)),x40705),x40704)),f329(f329(f43(x40702,f883(x40701,a869)),f329(f329(f116(f883(x40702,a869)),x40703),x40705)),x40704)) % 178.07/177.92 [4084]E(f329(f329(f42(x40841,f883(x40842,a869)),x40843),f329(f329(f8(f883(x40842,a869),f883(x40842,a869),x40841),f329(f116(f883(x40842,a869)),x40844)),x40845)),f329(f329(f116(f883(x40842,a869)),x40844),f329(f329(f42(x40841,f883(x40842,a869)),x40843),x40845))) % 178.07/177.92 [4085]E(f329(f329(f43(x40851,f883(x40852,a869)),x40853),f329(f329(f8(f883(x40852,a869),f883(x40852,a869),x40851),f329(f22(f883(x40852,a869)),x40854)),x40855)),f329(f329(f22(f883(x40852,a869)),x40854),f329(f329(f42(x40851,f883(x40852,a869)),x40853),x40855))) % 178.07/177.92 [4086]E(f329(f329(f43(x40861,f883(x40862,a869)),x40863),f329(f329(f8(f883(x40862,a869),f883(x40862,a869),x40861),f329(f107(f883(x40862,a869)),x40864)),x40865)),f329(f329(f107(f883(x40862,a869)),x40864),f329(f329(f43(x40861,f883(x40862,a869)),x40863),x40865))) % 178.07/177.92 [4123]E(f184(x41231,x41232,x41233,f329(f177(x41231,x41232),f329(f168(f882(x41231,x41232)),f329(f329(f181(x41231,x41232),x41234),x41235)))),f186(x41231,x41232,x41233,x41234,x41235)) % 178.07/177.92 [4145]E(f190(f876(x41451),f329(f329(f150(x41451),x41452),x41453),f329(f329(f8(f876(x41451),f876(x41451),a875),f329(f150(x41451),x41454)),f329(f329(f7(a875,x41451,f876(x41451)),f158(x41451,x41453)),x41452)),x41455),f329(f329(f158(x41451,f329(f329(f150(x41451),x41454),x41453)),x41455),x41452)) % 178.07/177.92 [4149]E(f329(f329(f42(x41491,f883(f882(x41492,x41493),a869)),x41494),f329(f329(f8(f883(f882(x41493,x41492),a869),f883(f882(x41492,x41493),a869),x41491),f284(x41493,x41492)),x41495)),f329(f284(x41493,x41492),f329(f329(f42(x41491,f883(f882(x41493,x41492),a869)),x41494),x41495))) % 178.07/177.92 [4150]E(f329(f329(f43(x41501,f883(f882(x41502,x41503),a869)),x41504),f329(f329(f8(f883(f882(x41503,x41502),a869),f883(f882(x41502,x41503),a869),x41501),f284(x41503,x41502)),x41505)),f329(f284(x41503,x41502),f329(f329(f43(x41501,f883(f882(x41503,x41502),a869)),x41504),x41505))) % 178.07/177.92 [4205]E(f183(x42051,x42052,f329(f329(f18(x42051,f879(x42053),f879(x42052)),f329(f329(f8(f883(x42053,x42052),f883(f879(x42053),f879(x42052)),x42051),f207(x42053,x42052)),x42054)),x42055)),f183(x42051,x42053,x42055)) % 178.07/177.92 [4256]P24(f329(f329(f243(f883(x42561,a869)),f329(f329(f22(f883(x42561,a869)),f329(f308(x42562,x42561,x42563),x42564)),f329(f308(x42562,x42561,x42563),x42565))),f329(f308(x42562,x42561,x42563),f329(f329(f22(f883(x42562,a869)),x42564),x42565)))) % 178.07/177.92 [4404]E(f329(f155(f876(f882(x44041,x44042)),x44041,f119(f882(x44041,x44042)),f329(f329(f7(x44041,f883(f876(x44041),f876(f882(x44041,x44042))),f883(f876(x44041),f876(f882(x44041,x44042)))),f329(f329(f8(f883(f876(f882(x44041,x44042)),f876(f882(x44041,x44042))),f883(f883(f876(x44041),f876(f882(x44041,x44042))),f883(f876(x44041),f876(f882(x44041,x44042)))),x44041),f8(f876(f882(x44041,x44042)),f876(f882(x44041,x44042)),f876(x44041))),f329(f329(f8(f882(x44041,x44042),f883(f876(f882(x44041,x44042)),f876(f882(x44041,x44042))),x44041),f150(f882(x44041,x44042))),f329(f329(f7(x44041,x44042,f882(x44041,x44042)),f264(x44041,x44042)),x44043)))),f329(f329(f7(f876(x44041),f876(x44042),f876(f882(x44041,x44042))),f181(x44041,x44042)),x44044))),x44045),f329(f329(f181(x44041,x44042),x44045),f329(f329(f150(x44042),x44043),x44044))) % 178.07/177.92 [4111]E(f329(f329(f116(f883(x41111,a869)),f329(f283(x41112,x41111,x41113),x41114)),f329(f283(x41112,x41111,x41115),x41114)),f329(f283(x41112,x41111,f329(f329(f116(f883(f882(x41112,x41111),a869)),x41113),x41115)),x41114)) % 178.07/177.92 [4152]E(f329(f329(f127(f882(x41521,x41522)),f329(f329(f181(x41521,x41522),x41523),f329(f329(f174(x41522),f329(f194(f876(x41521)),x41523)),x41524))),f329(f329(f181(x41521,x41522),x41525),f329(f329(f137(x41522),f329(f194(f876(x41521)),x41523)),x41524))),f329(f329(f181(x41521,x41522),f329(f329(f127(x41521),x41523),x41525)),x41524)) % 178.07/177.92 [4259]E(f329(f329(f266(x42591,x42592),x42593),f329(f329(f18(x42591,f883(x42592,a869),f883(x42592,a869)),f329(f329(f8(f883(x42592,a869),f883(f883(x42592,a869),f883(x42592,a869)),x42591),f116(f883(x42592,a869))),x42594)),x42595)),f329(f329(f116(f883(f882(x42591,x42592),a869)),f329(f329(f266(x42591,x42592),x42593),x42594)),f329(f329(f266(x42591,x42592),x42593),x42595))) % 178.07/177.92 [4260]E(f329(f329(f266(x42601,x42602),x42603),f329(f329(f18(x42601,f883(x42602,a869),f883(x42602,a869)),f329(f329(f8(f883(x42602,a869),f883(f883(x42602,a869),f883(x42602,a869)),x42601),f22(f883(x42602,a869))),x42604)),x42605)),f329(f329(f22(f883(f882(x42601,x42602),a869)),f329(f329(f266(x42601,x42602),x42603),x42604)),f329(f329(f266(x42601,x42602),x42603),x42605))) % 178.07/177.92 [4261]E(f329(f329(f266(x42611,x42612),x42613),f329(f329(f18(x42611,f883(x42612,a869),f883(x42612,a869)),f329(f329(f8(f883(x42612,a869),f883(f883(x42612,a869),f883(x42612,a869)),x42611),f107(f883(x42612,a869))),x42614)),x42615)),f329(f329(f107(f883(f882(x42611,x42612),a869)),f329(f329(f266(x42611,x42612),x42613),x42614)),f329(f329(f266(x42611,x42612),x42613),x42615))) % 178.07/177.92 [4265]E(f329(f329(f42(x42651,f883(x42652,a869)),x42653),f329(f329(f7(x42651,f883(x42652,a869),f883(x42652,a869)),f329(f329(f8(f883(x42652,a869),f883(f883(x42652,a869),f883(x42652,a869)),x42651),f116(f883(x42652,a869))),x42654)),x42655)),f329(f329(f116(f883(x42652,a869)),f329(f329(f42(x42651,f883(x42652,a869)),x42653),x42654)),x42655)) % 178.07/177.92 [4266]E(f329(f329(f43(x42661,f883(x42662,a869)),x42663),f329(f329(f7(x42661,f883(x42662,a869),f883(x42662,a869)),f329(f329(f8(f883(x42662,a869),f883(f883(x42662,a869),f883(x42662,a869)),x42661),f22(f883(x42662,a869))),x42664)),x42665)),f329(f329(f22(f883(x42662,a869)),f329(f329(f43(x42661,f883(x42662,a869)),x42663),x42664)),x42665)) % 178.07/177.92 [4267]E(f329(f329(f43(x42671,f883(x42672,a869)),x42673),f329(f329(f7(x42671,f883(x42672,a869),f883(x42672,a869)),f329(f329(f8(f883(x42672,a869),f883(f883(x42672,a869),f883(x42672,a869)),x42671),f107(f883(x42672,a869))),x42674)),x42675)),f329(f329(f107(f883(x42672,a869)),f329(f329(f43(x42671,f883(x42672,a869)),x42673),x42674)),x42675)) % 178.07/177.92 [4271]E(f329(f329(f42(x42711,f883(x42712,a869)),x42713),f329(f329(f18(x42711,f883(x42712,a869),f883(x42712,a869)),f329(f329(f8(f883(x42712,a869),f883(f883(x42712,a869),f883(x42712,a869)),x42711),f107(f883(x42712,a869))),x42714)),x42715)),f329(f329(f107(f883(x42712,a869)),f329(f329(f42(x42711,f883(x42712,a869)),x42713),x42714)),f329(f329(f42(x42711,f883(x42712,a869)),x42713),x42715))) % 178.07/177.92 [4272]E(f329(f329(f43(x42721,f883(x42722,a869)),x42723),f329(f329(f18(x42721,f883(x42722,a869),f883(x42722,a869)),f329(f329(f8(f883(x42722,a869),f883(f883(x42722,a869),f883(x42722,a869)),x42721),f116(f883(x42722,a869))),x42724)),x42725)),f329(f329(f116(f883(x42722,a869)),f329(f329(f43(x42721,f883(x42722,a869)),x42723),x42724)),f329(f329(f43(x42721,f883(x42722,a869)),x42723),x42725))) % 178.07/177.92 [4286]E(f329(f329(f42(x42861,f883(x42862,a869)),x42863),f329(f329(f18(x42861,f883(x42862,a869),f883(x42862,a869)),f329(f329(f8(f883(x42862,a869),f883(f883(x42862,a869),f883(x42862,a869)),x42861),f107(f883(x42862,a869))),x42864)),x42865)),f329(f329(f107(f883(x42862,a869)),f41(f883(x42862,a869),f329(f308(x42861,f883(x42862,a869),x42864),x42863))),f41(f883(x42862,a869),f329(f308(x42861,f883(x42862,a869),x42865),x42863)))) % 178.07/177.92 [4287]E(f329(f329(f43(x42871,f883(x42872,a869)),x42873),f329(f329(f18(x42871,f883(x42872,a869),f883(x42872,a869)),f329(f329(f8(f883(x42872,a869),f883(f883(x42872,a869),f883(x42872,a869)),x42871),f116(f883(x42872,a869))),x42874)),x42875)),f329(f329(f116(f883(x42872,a869)),f40(f883(x42872,a869),f329(f308(x42871,f883(x42872,a869),x42874),x42873))),f40(f883(x42872,a869),f329(f308(x42871,f883(x42872,a869),x42875),x42873)))) % 178.07/177.92 [4321]E(f329(f329(f137(x43211),f329(f194(f876(x43211)),f176(x43211,x43212,f329(f329(f153(x43213,x43211),x43214),x43215)))),f329(f329(f153(x43213,x43211),x43214),x43215)),f329(f329(f153(x43213,x43211),x43214),f329(f329(f137(x43213),f329(f194(f876(x43213)),f176(x43213,f329(f74(x43211,a869,x43213,x43212),x43214),x43215))),x43215))) % 178.07/177.92 [4195]E(f329(f329(f127(f882(x41951,x41952)),f329(f329(f181(x41951,x41952),f329(f329(f174(x41951),f329(f194(f876(x41952)),x41953)),x41954)),x41953)),f329(f329(f181(x41951,x41952),f329(f329(f137(x41951),f329(f194(f876(x41952)),x41953)),x41954)),x41955)),f329(f329(f181(x41951,x41952),x41954),f329(f329(f127(x41952),x41953),x41955))) % 178.07/177.92 [4313]E(f86(x43131,f329(f329(f18(x43131,a869,a869),f329(f329(f8(a869,f883(a869,a869),x43131),a327),f329(f329(f7(x43131,f883(x43131,a869),a869),f331(x43131)),x43132))),f329(f329(f7(x43131,x43133,a869),f329(f329(f8(x43133,f883(x43133,a869),x43131),a326),x43134)),x43135))),f329(f78(x43131,x43133,x43132,x43134),x43135)) % 178.07/177.92 [4365]E(f329(f329(f87(a1,x43651),f329(f109(a1),f329(f329(f81(a1),x43652),a103))),f329(f329(f18(a1,x43651,x43651),f329(f329(f7(a1,x43651,f883(x43651,x43651)),f329(f329(f8(a869,f883(x43651,f883(x43651,x43651)),a1),f102(x43651)),a198)),f190(x43651,x43653,x43654,x43655))),f329(f329(f8(a875,x43651,a1),x43654),f329(f329(f7(a1,a875,a875),f329(f329(f8(a875,f883(a875,a875),a1),f81(a875)),a110)),x43655)))),f190(x43651,x43653,x43654,f329(f329(f81(a875),f329(f109(a875),x43652)),x43655))) % 178.07/177.92 [4401]E(f329(f177(x44011,x44012),f329(f329(f153(f882(x44011,x44013),f882(x44011,x44012)),f329(f268(x44011,x44013,f882(x44011,x44012)),f329(f329(f7(x44011,f883(x44013,x44012),f883(x44013,f882(x44011,x44012))),f329(f329(f8(f883(x44012,f882(x44011,x44012)),f883(f883(x44013,x44012),f883(x44013,f882(x44011,x44012))),x44011),f8(x44012,f882(x44011,x44012),x44013)),f264(x44011,x44012))),x44014))),x44015)),f329(f74(f879(x44013),f879(x44012),x44011,f329(f207(x44013,x44012),x44014)),f329(f177(x44011,x44013),x44015))) % 178.07/177.92 [4358]E(f183(x43581,x43582,f329(f329(f18(x43581,f879(x43582),f879(x43582)),f329(f329(f18(x43581,f879(x43582),f883(f879(x43582),f879(x43582))),f329(f329(f8(a869,f883(f879(x43582),f883(f879(x43582),f879(x43582))),x43581),f102(f879(x43582))),x43583)),x43584)),x43585)),f329(f329(f116(f883(x43581,a869)),f329(f329(f107(f883(x43581,a869)),f183(x43581,x43582,x43584)),f329(f249(x43581),x43583))),f329(f329(f107(f883(x43581,a869)),f183(x43581,x43582,x43585)),f329(f249(x43581),f329(f329(f8(a869,a869,x43581),a324),x43583))))) % 178.07/177.92 [4399]E(f329(f329(f87(a1,x43991),f329(f109(a1),f329(f329(f81(a1),x43992),a103))),f329(f329(f18(a1,x43991,x43991),f329(f329(f7(a1,x43991,f883(x43991,x43991)),f329(f329(f8(a869,f883(x43991,f883(x43991,x43991)),a1),f102(x43991)),a198)),f329(f189(x43991,x43993,x43994),x43995))),f329(f329(f18(a1,x43991,x43991),f329(f329(f8(a875,f883(x43991,x43991),a1),x43994),f329(f329(f7(a1,a875,a875),f329(f329(f8(a875,f883(a875,a875),a1),f81(a875)),a110)),x43995))),f329(f329(f8(a875,x43991,a1),f189(x43991,x43993,x43994)),f329(f329(f7(a1,a875,a875),f329(f329(f8(a875,f883(a875,a875),a1),f81(a875)),a110)),x43995))))),f329(f189(x43991,x43993,x43994),f329(f329(f81(a875),f329(f109(a875),x43992)),x43995))) % 178.07/177.92 [4433]E(f329(f249(f882(x44331,x44332)),f329(f268(x44331,x44332,a869),f329(f329(f8(f883(x44332,f883(x44333,a869)),f883(x44332,a869),x44331),f329(f8(f883(x44333,a869),a869,x44332),f88(x44333))),f329(f329(f7(x44331,f883(x44332,f883(x44333,a869)),f883(x44332,f883(x44333,a869))),f329(f329(f8(f883(f883(x44333,a869),f883(x44333,a869)),f883(f883(x44332,f883(x44333,a869)),f883(x44332,f883(x44333,a869))),x44331),f8(f883(x44333,a869),f883(x44333,a869),x44332)),f329(f329(f8(f883(x44333,f883(a869,a869)),f883(f883(x44333,a869),f883(x44333,a869)),x44331),f18(x44333,a869,a869)),f329(f329(f8(f883(x44333,a869),f883(x44333,f883(a869,a869)),x44331),f329(f8(a869,f883(a869,a869),x44333),a327)),f329(f329(f7(x44331,f883(f882(x44331,x44333),a869),f883(x44333,a869)),f329(f329(f8(f883(x44333,f883(f883(f882(x44331,x44333),a869),a869)),f883(f883(f882(x44331,x44333),a869),f883(x44333,a869)),x44331),f7(x44333,f883(f882(x44331,x44333),a869),a869)),f329(f329(f8(f883(x44333,f882(x44331,x44333)),f883(x44333,f883(f883(f882(x44331,x44333),a869),a869)),x44331),f329(f8(f882(x44331,x44333),f883(f883(f882(x44331,x44333),a869),a869),x44333),f331(f882(x44331,x44333)))),f264(x44331,x44333)))),x44334))))),f329(f329(f7(x44332,f883(f882(x44333,x44332),a869),f883(x44333,a869)),f329(f329(f8(f883(x44333,f883(f883(f882(x44333,x44332),a869),a869)),f883(f883(f882(x44333,x44332),a869),f883(x44333,a869)),x44332),f7(x44333,f883(f882(x44333,x44332),a869),a869)),f329(f329(f8(f883(x44333,f882(x44333,x44332)),f883(x44333,f883(f883(f882(x44333,x44332),a869),a869)),x44332),f329(f8(f882(x44333,x44332),f883(f883(f882(x44333,x44332),a869),a869),x44333),f331(f882(x44333,x44332)))),f329(f7(x44333,x44332,f882(x44333,x44332)),f264(x44333,x44332))))),x44335))))),f329(f329(f286(x44331,x44333,x44332),x44334),x44335)) % 178.07/177.92 [4517]~E(f31(x45171,x45172,x45173),f29(x45174,x45175,x45176)) % 178.07/177.92 [4520]~E(f30(x45201,x45202,x45203),f29(x45204,x45205,x45206)) % 178.07/177.92 [4521]~E(f30(x45211,x45212,x45213),f31(x45214,x45215,x45216)) % 178.07/177.92 [3963]E(f132(x39631,x39632,x39633,x39634,f129(x39632,x39635,x39636)),f329(f329(x39634,x39635),x39636)) % 178.07/177.92 [4179]E(f186(x41791,x41792,f184(x41791,x41792,x41793,x41794),x41795,x41796),f184(x41791,x41792,x41793,f186(x41791,x41792,x41794,x41795,x41796))) % 178.07/177.92 [4302]E(f329(f74(f882(x43021,x43022),x43022,f882(x43023,x43024),f267(x43021,x43022)),f269(x43023,x43021,x43024,x43022,x43025,x43026)),f329(f74(x43024,x43022,f882(x43023,x43024),x43026),f267(x43023,x43024))) % 178.07/177.92 [4303]E(f329(f74(f882(x43031,x43032),x43031,f882(x43033,x43034),f263(x43031,x43032)),f269(x43033,x43031,x43034,x43032,x43035,x43036)),f329(f74(x43033,x43031,f882(x43033,x43034),x43035),f263(x43033,x43034))) % 178.07/177.92 [3903]E(f329(f329(f74(x39031,x39032,x39033,x39034),x39035),x39036),f329(x39034,f329(x39035,x39036))) % 178.07/177.92 [3703]E(f329(f329(f268(x37031,x37032,x37033),x37034),f329(f329(f264(x37031,x37032),x37035),x37036)),f329(f329(x37034,x37035),x37036)) % 178.07/177.92 [3762]E(f329(f329(f329(f8(x37621,x37622,x37623),x37624),x37625),x37626),f329(x37624,f329(x37625,x37626))) % 178.07/177.92 [3763]E(f329(f329(f329(f7(x37631,x37632,x37633),x37634),x37635),x37636),f329(f329(x37634,x37636),x37635)) % 178.07/177.92 [3780]E(f329(f329(f329(f18(x37801,x37802,x37803),x37804),x37805),x37806),f329(f329(x37804,x37806),f329(x37805,x37806))) % 178.07/177.92 [3802]E(f329(f155(x38021,x38022,x38023,x38024),f329(f329(f150(x38022),x38025),x38026)),f329(f329(x38024,x38025),x38026)) % 178.07/177.92 [3907]E(f329(f329(f150(f882(x39071,x39072)),f329(f329(f264(x39071,x39072),x39073),x39074)),f329(f329(f181(x39071,x39072),x39075),x39076)),f329(f329(f181(x39071,x39072),f329(f329(f150(x39071),x39073),x39075)),f329(f329(f150(x39072),x39074),x39076))) % 178.07/177.92 [3909]E(f329(f329(f153(x39091,x39092),x39093),f329(f329(f158(x39091,x39094),x39095),x39096)),f329(f329(f158(x39092,f329(f329(f153(x39091,x39092),x39093),x39094)),x39095),f329(x39093,x39096))) % 178.07/177.92 [3952]E(f329(f141(x39521,x39522,x39523,x39524),f329(f329(f150(x39522),x39525),x39526)),f329(f141(x39521,x39522,x39523,f329(f329(x39523,x39524),x39525)),x39526)) % 178.07/177.92 [3979]E(f271(x39791,x39792,x39793,x39794,f329(f329(f264(x39791,x39792),x39795),x39796)),f329(f329(x39794,x39795),x39796)) % 178.07/177.92 [4062]E(f329(f329(f43(x40621,f883(x40622,a869)),x40623),f329(f74(x40624,f883(x40622,a869),x40621,x40625),x40626)),f329(f329(f43(x40624,f883(x40622,a869)),f329(f308(x40621,x40624,x40626),x40623)),x40625)) % 178.07/177.92 [4114]E(f329(f329(f207(x41141,x41142),x41143),f329(f329(f207(x41144,x41141),x41145),x41146)),f329(f329(f207(x41144,x41142),f329(f74(x41141,x41142,x41144,x41143),x41145)),x41146)) % 178.07/177.92 [4116]E(f329(f329(f153(x41161,x41162),x41163),f329(f329(f153(x41164,x41161),x41165),x41166)),f329(f329(f153(x41164,x41162),f329(f74(x41161,x41162,x41164,x41163),x41165)),x41166)) % 178.07/177.92 [4121]E(f329(f308(x41211,x41212,f329(f74(x41213,x41212,x41211,x41214),x41215)),x41216),f329(f308(x41213,x41212,x41214),f329(f308(x41211,x41213,x41215),x41216))) % 178.07/177.92 [4122]E(f329(f309(x41221,x41222,f329(f74(x41223,x41222,x41221,x41224),x41225)),x41226),f329(f309(x41221,x41223,x41225),f329(f309(x41223,x41222,x41224),x41226))) % 178.07/177.92 [4151]E(f184(x41511,x41512,x41513,f329(f329(f329(f73(x41511,f879(x41512)),x41514),x41515),f329(f236(x41512),x41516))),f329(f329(f329(f73(x41511,f879(x41512)),f184(x41511,x41512,x41513,x41514)),x41515),f329(f236(x41512),x41516))) % 178.07/177.92 [4153]E(f329(f141(x41531,x41532,x41533,f329(f141(x41531,x41532,x41533,x41534),x41535)),x41536),f329(f141(x41531,x41532,x41533,x41534),f329(f329(f127(x41532),x41535),x41536))) % 178.07/177.92 [4292]E(f329(f269(x42921,x42921,x42922,x42923,f35(x42921),x42924),f329(f329(f264(x42921,x42922),x42925),x42926)),f329(f329(f264(x42921,x42923),x42925),f329(x42924,x42926))) % 178.07/177.92 [4293]E(f329(f269(x42931,x42932,x42933,x42933,x42934,f35(x42933)),f329(f329(f264(x42931,x42933),x42935),x42936)),f329(f329(f264(x42932,x42933),f329(x42934,x42935)),x42936)) % 178.07/177.92 [4383]E(f329(f329(f153(f882(x43831,x43832),f882(x43831,x43833)),f329(f268(x43831,x43832,f882(x43831,x43833)),f329(f329(f7(x43831,f883(x43832,x43833),f883(x43832,f882(x43831,x43833))),f329(f329(f8(f883(x43833,f882(x43831,x43833)),f883(f883(x43832,x43833),f883(x43832,f882(x43831,x43833))),x43831),f8(x43833,f882(x43831,x43833),x43832)),f264(x43831,x43833))),x43834))),f329(f329(f181(x43831,x43832),x43835),x43836)),f329(f329(f181(x43831,x43833),x43835),f329(f329(f153(x43832,x43833),x43834),x43836))) % 178.07/177.92 [3767]E(f100(x37671,x37672,x37673,f329(f329(f329(f93(x37671),x37674),x37675),x37676)),f329(f329(f329(x37673,x37674),x37675),x37676)) % 178.07/177.92 [3768]E(f101(x37681,x37682,x37683,f329(f329(f329(f93(x37681),x37684),x37685),x37686)),f329(f329(f329(x37683,x37684),x37685),x37686)) % 178.07/177.92 [3962]E(f329(f329(f74(x39621,x39622,x39623,f329(f16(x39622,x39621),x39624)),x39625),x39626),x39624) % 178.07/177.92 [3998]E(f329(f308(x39981,x39982,x39983),f329(f308(x39984,x39981,x39985),x39986)),f329(f308(x39984,x39982,f329(f329(f8(x39981,x39982,x39984),x39983),x39985)),x39986)) % 178.07/177.92 [4004]E(f329(f329(f42(x40041,f883(x40042,a869)),f329(f308(x40043,x40041,x40044),x40045)),x40046),f329(f329(f42(x40043,f883(x40042,a869)),x40045),f329(f329(f8(x40041,f883(x40042,a869),x40043),x40046),x40044))) % 178.07/177.92 [4005]E(f329(f329(f43(x40051,f883(x40052,a869)),f329(f308(x40053,x40051,x40054),x40055)),x40056),f329(f329(f43(x40053,f883(x40052,a869)),x40055),f329(f329(f8(x40051,f883(x40052,a869),x40053),x40056),x40054))) % 178.07/177.92 [4006]E(f329(f329(f42(x40061,f883(x40062,a869)),x40063),f329(f329(f8(x40064,f883(x40062,a869),x40061),x40065),x40066)),f329(f329(f42(x40064,f883(x40062,a869)),f329(f308(x40061,x40064,x40066),x40063)),x40065)) % 178.07/177.92 [4007]E(f329(f329(f43(x40071,f883(x40072,a869)),x40073),f329(f329(f8(x40074,f883(x40072,a869),x40071),x40075),x40076)),f329(f329(f43(x40074,f883(x40072,a869)),f329(f308(x40071,x40074,x40076),x40073)),x40075)) % 178.07/177.92 [4064]E(f329(f329(f43(x40641,f883(x40642,a869)),x40643),f329(f329(f8(f883(x40644,a869),f883(x40642,a869),x40641),f308(x40644,x40642,x40645)),x40646)),f329(f308(x40644,x40642,x40645),f329(f329(f43(x40641,f883(x40644,a869)),x40643),x40646))) % 178.07/177.92 [4065]E(f329(f329(f42(x40651,f883(x40652,a869)),x40653),f329(f329(f8(f883(x40654,a869),f883(x40652,a869),x40651),f309(x40652,x40654,x40655)),x40656)),f329(f309(x40652,x40654,x40655),f329(f329(f42(x40651,f883(x40654,a869)),x40653),x40656))) % 178.07/177.92 [4066]E(f329(f329(f43(x40661,f883(x40662,a869)),x40663),f329(f329(f8(f883(x40664,a869),f883(x40662,a869),x40661),f309(x40662,x40664,x40665)),x40666)),f329(f309(x40662,x40664,x40665),f329(f329(f43(x40661,f883(x40664,a869)),x40663),x40666))) % 178.07/177.92 [4067]E(f329(f329(f43(x40671,f883(x40672,a869)),x40673),f329(f329(f8(f883(x40674,a869),f883(x40672,a869),x40671),f283(x40674,x40672,x40675)),x40676)),f329(f283(x40674,x40672,x40675),f329(f329(f43(x40671,f883(x40674,a869)),x40673),x40676))) % 178.07/177.92 [4159]E(f329(f141(x41591,x41592,f329(f7(x41592,x41591,x41591),x41593),x41594),f329(f168(x41592),f329(f329(f150(x41592),x41595),x41596))),f329(f329(x41593,x41595),f329(f141(x41591,x41592,f329(f7(x41592,x41591,x41591),x41593),x41594),f329(f168(x41592),x41596)))) % 178.07/177.92 [4218]E(f329(f329(f18(f882(x42181,x42182),x42182,x42183),f329(f329(f8(x42184,f883(x42182,x42183),f882(x42181,x42182)),x42185),f329(f329(f8(x42181,x42184,f882(x42181,x42182)),x42186),f263(x42181,x42182)))),f267(x42181,x42182)),f329(f268(x42181,x42182,x42183),f329(f329(f8(x42184,f883(x42182,x42183),x42181),x42185),x42186))) % 178.07/177.92 [4225]E(f329(f141(x42251,x42252,f329(f7(x42252,x42251,x42251),x42253),f329(f141(x42251,x42252,f329(f7(x42252,x42251,x42251),x42253),x42254),f329(f168(x42252),x42255))),f329(f168(x42252),x42256)),f329(f141(x42251,x42252,f329(f7(x42252,x42251,x42251),x42253),x42254),f329(f168(x42252),f329(f329(f127(x42252),x42256),x42255)))) % 178.07/177.92 [4227]E(f329(f329(f153(f882(x42271,x42272),f882(x42273,x42272)),f329(f268(x42271,x42272,f882(x42273,x42272)),f329(f329(f8(x42273,f883(x42272,f882(x42273,x42272)),x42271),f264(x42273,x42272)),x42274))),f329(f329(f181(x42271,x42272),x42275),x42276)),f329(f329(f181(x42273,x42272),f329(f329(f153(x42271,x42273),x42274),x42275)),x42276)) % 178.07/177.92 [4275]P24(f329(f329(f243(f883(x42751,a869)),f329(f283(x42752,x42751,x42753),f329(f329(f42(x42754,f883(x42752,a869)),x42755),x42756))),f329(f329(f42(x42754,f883(x42751,a869)),x42755),f329(f329(f8(f883(x42752,a869),f883(x42751,a869),x42754),f283(x42752,x42751,x42753)),x42756)))) % 178.07/177.92 [4077]E(f329(f329(f181(x40771,x40772),f329(f329(f158(x40771,x40773),x40774),f329(f263(x40771,x40772),x40775))),f329(f329(f158(x40772,x40776),x40774),f329(f267(x40771,x40772),x40775))),f329(f329(f158(f882(x40771,x40772),f329(f329(f181(x40771,x40772),x40773),x40776)),x40774),x40775)) % 178.07/177.92 [4140]E(f329(f329(f116(f883(f882(x41401,x41402),a869)),f329(f329(f286(x41401,x41403,x41402),x41404),x41405)),f329(f329(f286(x41401,x41403,x41402),x41404),x41406)),f329(f329(f286(x41401,x41403,x41402),x41404),f329(f329(f116(f883(f882(x41403,x41402),a869)),x41405),x41406))) % 178.07/177.92 [4238]E(f329(f329(f307(f882(x42381,x42382)),f329(f329(f264(x42381,x42382),x42383),x42384)),f329(f329(f116(f883(f882(x42381,x42382),a869)),f329(f329(f266(x42381,x42382),x42385),f329(f16(f883(x42382,a869),x42381),f329(f329(f307(x42382),x42384),x42386)))),f329(f329(f266(x42381,x42382),f329(f329(f307(x42381),x42383),x42385)),f329(f16(f883(x42382,a869),x42381),x42386)))),f329(f329(f266(x42381,x42382),f329(f329(f307(x42381),x42383),x42385)),f329(f16(f883(x42382,a869),x42381),f329(f329(f307(x42382),x42384),x42386)))) % 178.07/177.92 [4316]E(f329(f329(f107(f883(x43161,a869)),f329(f309(x43161,x43162,f329(f74(f882(x43162,x43163),x43162,x43161,f263(x43162,x43163)),x43164)),x43165)),f329(f309(x43161,x43163,f329(f74(f882(x43162,x43163),x43163,x43161,f267(x43162,x43163)),x43164)),x43166)),f329(f309(x43161,f882(x43162,x43163),x43164),f329(f329(f266(x43162,x43163),x43165),f329(f16(f883(x43163,a869),x43162),x43166)))) % 178.07/177.92 [4061]E(f329(f329(f329(f73(x40611,x40612),f329(f329(f329(f73(x40611,x40612),x40613),x40614),x40615)),x40614),x40616),f329(f329(f329(f73(x40611,x40612),x40613),x40614),x40616)) % 178.07/177.92 [4165]E(f329(f329(f116(f883(f882(x41651,x41652),a869)),f329(f329(f286(x41651,x41653,x41652),x41654),x41655)),f329(f329(f286(x41651,x41653,x41652),x41656),x41655)),f329(f329(f286(x41651,x41653,x41652),f329(f329(f116(f883(f882(x41651,x41653),a869)),x41654),x41656)),x41655)) % 178.07/177.92 [4300]E(f329(f329(f42(x43001,f883(x43002,a869)),x43003),f329(f329(f7(x43001,f883(x43004,f883(x43002,a869)),f883(x43002,a869)),f329(f329(f8(f883(x43004,a869),f883(f883(x43004,f883(x43002,a869)),f883(x43002,a869)),x43001),f42(x43004,f883(x43002,a869))),x43005)),x43006)),f329(f329(f42(x43004,f883(x43002,a869)),f329(f329(f43(x43001,f883(x43004,a869)),x43003),x43005)),x43006)) % 178.07/177.92 [4301]E(f329(f329(f43(x43011,f883(x43012,a869)),x43013),f329(f329(f7(x43011,f883(x43014,f883(x43012,a869)),f883(x43012,a869)),f329(f329(f8(f883(x43014,a869),f883(f883(x43014,f883(x43012,a869)),f883(x43012,a869)),x43011),f43(x43014,f883(x43012,a869))),x43015)),x43016)),f329(f329(f43(x43014,f883(x43012,a869)),f329(f329(f43(x43011,f883(x43014,a869)),x43013),x43015)),x43016)) % 178.07/177.92 [4353]E(f329(f268(x43531,x43532,f882(x43533,x43534)),f329(f329(f7(x43531,f883(x43532,x43534),f883(x43532,f882(x43533,x43534))),f329(f329(f8(f883(x43534,f882(x43533,x43534)),f883(f883(x43532,x43534),f883(x43532,f882(x43533,x43534))),x43531),f8(x43534,f882(x43533,x43534),x43532)),f329(f329(f8(x43533,f883(x43534,f882(x43533,x43534)),x43531),f264(x43533,x43534)),x43535))),x43536)),f269(x43531,x43533,x43532,x43534,x43535,x43536)) % 178.07/177.92 [4274]E(f329(f329(f329(f73(x42741,f879(x42742)),f187(x42741,x42742,x42743,f329(f329(f22(f883(x42741,a869)),x42744),f329(f329(f307(x42741),x42745),f193(f883(x42741,a869)))))),x42745),x42746),f329(f329(f329(f73(x42741,f879(x42742)),f187(x42741,x42742,x42743,x42744)),x42745),x42746)) % 178.07/177.92 [4378]E(f329(f308(x43781,x43782,f329(f329(f18(x43781,x43782,x43782),f329(f329(f18(x43781,x43782,f883(x43782,x43782)),f329(f329(f8(a869,f883(x43782,f883(x43782,x43782)),x43781),f102(x43782)),x43783)),x43784)),x43785)),x43786),f329(f329(f116(f883(x43782,a869)),f329(f308(x43781,x43782,x43784),f329(f329(f107(f883(x43781,a869)),x43786),f329(f249(x43781),x43783)))),f329(f308(x43781,x43782,x43785),f329(f329(f107(f883(x43781,a869)),x43786),f329(f249(x43781),f329(f329(f8(a869,a869,x43781),a324),x43783)))))) % 178.07/177.92 [4389]E(f329(f308(x43891,f882(x43892,x43893),f329(f329(f18(x43891,x43893,f882(x43892,x43893)),f329(f329(f8(x43892,f883(x43893,f882(x43892,x43893)),x43891),f264(x43892,x43893)),x43894)),x43895)),x43896),f329(f329(f266(x43892,x43893),f329(f308(x43891,x43892,x43894),x43896)),f329(f329(f8(f883(x43891,a869),f883(x43893,a869),x43892),f308(x43891,x43893,x43895)),f329(f329(f7(x43892,f883(x43891,a869),f883(x43891,a869)),f329(f329(f8(f883(x43891,a869),f883(f883(x43891,a869),f883(x43891,a869)),x43892),f107(f883(x43891,a869))),f329(f329(f8(f883(x43892,a869),f883(x43891,a869),x43892),f309(x43891,x43892,x43894)),f329(f329(f7(x43892,f883(x43892,a869),f883(x43892,a869)),f307(x43892)),f193(f883(x43892,a869)))))),x43896)))) % 178.07/177.92 [4335]E(f329(f267(x43351,x43352),f329(f269(x43353,x43351,x43354,x43352,x43355,x43356),x43357)),f329(x43356,f329(f267(x43353,x43354),x43357))) % 178.07/177.92 [4336]E(f329(f263(x43361,x43362),f329(f269(x43363,x43361,x43364,x43362,x43365,x43366),x43367)),f329(x43365,f329(f263(x43363,x43364),x43367))) % 178.07/177.92 [4039]E(f329(f329(f181(x40391,x40392),f329(f329(f158(x40391,x40393),x40394),x40395)),f329(f329(f158(x40392,x40396),x40394),x40397)),f329(f329(f158(f882(x40391,x40392),f329(f329(f181(x40391,x40392),x40393),x40396)),x40394),f329(f329(f264(x40391,x40392),x40395),x40397))) % 178.07/177.92 [4107]E(f329(f329(f329(f270(x41071,x41072,x41073,x41074),x41075),x41076),x41077),f329(f329(f268(x41072,x41073,x41074),x41076),f329(x41075,x41077))) % 178.07/177.92 [4120]E(f329(f329(f329(f270(x41201,x41202,x41203,x41204),x41205),x41206),x41207),f329(f329(x41206,f329(f263(x41202,x41203),f329(x41205,x41207))),f329(f267(x41202,x41203),f329(x41205,x41207)))) % 178.07/177.92 [4155]E(f186(x41551,x41552,f329(f329(f329(f73(x41551,f879(x41552)),x41553),x41554),f329(f236(x41552),x41555)),x41556,x41557),f186(x41551,x41552,x41553,f329(f329(f150(x41551),x41554),x41556),f329(f329(f150(x41552),x41555),x41557))) % 178.07/177.92 [4173]E(f329(f74(x41731,x41732,x41733,x41734),f329(f74(x41735,x41731,x41733,x41736),x41737)),f329(f74(x41735,x41732,x41733,f329(f74(x41731,x41732,x41735,x41734),x41736)),x41737)) % 178.07/177.92 [4234]E(f329(f74(f879(x42341),f879(x42342),x42343,f329(f207(x42341,x42342),x42344)),f329(f329(f329(f73(x42343,f879(x42341)),x42345),x42346),f329(f236(x42341),x42347))),f329(f329(f329(f73(x42343,f879(x42342)),f329(f74(f879(x42341),f879(x42342),x42343,f329(f207(x42341,x42342),x42344)),x42345)),x42346),f329(f236(x42342),f329(x42344,x42347)))) % 178.07/177.92 [4360]E(f329(f269(x43601,x43602,x43603,x43603,x43604,f35(x43603)),f329(f269(x43601,x43601,x43605,x43603,f35(x43601),x43606),x43607)),f329(f329(f264(x43602,x43603),f329(x43604,f329(f263(x43601,x43605),x43607))),f329(x43606,f329(f267(x43601,x43605),x43607)))) % 178.07/177.92 [4361]E(f329(f269(x43611,x43611,x43612,x43613,f35(x43611),x43614),f329(f269(x43615,x43611,x43612,x43612,x43616,f35(x43612)),x43617)),f329(f329(f264(x43611,x43613),f329(x43616,f329(f263(x43615,x43612),x43617))),f329(x43614,f329(f267(x43615,x43612),x43617)))) % 178.07/177.92 [4376]E(f329(f269(x43761,x43762,x43763,x43763,x43764,f35(x43763)),f329(f269(x43765,x43761,x43763,x43763,x43766,f35(x43763)),x43767)),f329(f269(x43765,x43762,x43763,x43763,f329(f74(x43761,x43762,x43765,x43764),x43766),f35(x43763)),x43767)) % 178.07/177.92 [4377]E(f329(f269(x43771,x43771,x43772,x43773,f35(x43771),x43774),f329(f269(x43771,x43771,x43775,x43772,f35(x43771),x43776),x43777)),f329(f269(x43771,x43771,x43775,x43773,f35(x43771),f329(f74(x43772,x43773,x43775,x43774),x43776)),x43777)) % 178.07/177.92 [4386]E(f329(f269(x43861,x43862,x43863,x43863,x43864,f35(x43863)),f329(f269(x43861,x43861,x43865,x43863,f35(x43861),x43866),x43867)),f329(f269(x43862,x43862,x43865,x43863,f35(x43862),x43866),f329(f269(x43861,x43862,x43865,x43865,x43864,f35(x43865)),x43867))) % 178.07/177.92 [4074]E(f329(f329(f286(x40741,x40742,x40743),f329(f329(f286(x40741,x40744,x40742),x40745),x40746)),x40747),f329(f329(f286(x40741,x40744,x40743),x40745),f329(f329(f286(x40744,x40742,x40743),x40746),x40747))) % 178.07/177.92 [4146]E(f329(f329(f268(x41461,x41462,x41463),f329(f74(x41464,f883(x41462,x41463),x41461,x41465),x41466)),x41467),f329(f329(x41465,f329(x41466,f329(f263(x41461,x41462),x41467))),f329(f267(x41461,x41462),x41467))) % 178.07/177.92 [4198]E(f329(f74(x41981,x41982,x41983,x41984),f329(f329(f329(f73(x41983,x41981),x41985),x41986),x41987)),f329(f329(f329(f73(x41983,x41982),f329(f74(x41981,x41982,x41983,x41984),x41985)),x41986),f329(x41984,x41987))) % 178.07/177.92 [4230]E(f329(f141(x42301,x42302,f329(f7(x42302,x42301,x42301),x42303),x42304),f329(f168(x42302),f329(f329(f153(x42305,x42302),x42306),x42307))),f329(f141(x42301,x42305,f329(f7(x42305,x42301,x42301),f329(f74(x42302,f883(x42301,x42301),x42305,x42303),x42306)),x42304),f329(f168(x42305),x42307))) % 178.07/177.92 [4174]E(f329(f329(f43(x41741,f883(f882(x41742,x41743),a869)),x41744),f329(f329(f8(f883(f882(x41745,x41743),a869),f883(f882(x41742,x41743),a869),x41741),f329(f286(x41742,x41745,x41743),x41746)),x41747)),f329(f329(f286(x41742,x41745,x41743),x41746),f329(f329(f43(x41741,f883(f882(x41745,x41743),a869)),x41744),x41747))) % 178.07/177.92 [4322]E(f329(f329(f43(x43221,f883(f882(x43222,x43223),a869)),x43224),f329(f329(f7(x43221,f883(f882(x43225,x43223),a869),f883(f882(x43222,x43223),a869)),f329(f329(f8(f883(f882(x43222,x43225),a869),f883(f883(f882(x43225,x43223),a869),f883(f882(x43222,x43223),a869)),x43221),f286(x43222,x43225,x43223)),x43226)),x43227)),f329(f329(f286(x43222,x43225,x43223),f329(f329(f43(x43221,f883(f882(x43222,x43225),a869)),x43224),x43226)),x43227)) % 178.07/177.92 [4323]E(f329(f141(x43231,x43232,f329(f329(f7(x43231,f883(x43232,x43233),f883(x43232,x43231)),f329(f329(f8(f883(x43233,x43231),f883(f883(x43232,x43233),f883(x43232,x43231)),x43231),f8(x43233,x43231,x43232)),x43234)),x43235),x43236),x43237),f329(f141(x43231,x43233,x43234,x43236),f329(f329(f153(x43232,x43233),x43235),x43237))) % 178.07/177.92 [4387]E(f329(f329(f42(x43871,f883(x43872,a869)),x43873),f329(f329(f8(f883(x43874,f883(x43872,a869)),f883(x43872,a869),x43871),f329(f42(x43874,f883(x43872,a869)),x43875)),f329(f329(f7(x43871,f883(x43874,f883(x43872,a869)),f883(x43874,f883(x43872,a869))),f329(f329(f8(f883(f883(x43872,a869),f883(x43872,a869)),f883(f883(x43874,f883(x43872,a869)),f883(x43874,f883(x43872,a869))),x43871),f8(f883(x43872,a869),f883(x43872,a869),x43874)),f329(f329(f8(f883(x43872,a869),f883(f883(x43872,a869),f883(x43872,a869)),x43871),f116(f883(x43872,a869))),x43876))),x43877))),f329(f329(f116(f883(x43872,a869)),f329(f329(f42(x43871,f883(x43872,a869)),x43873),x43876)),f329(f329(f42(x43874,f883(x43872,a869)),x43875),x43877))) % 178.07/177.92 [4388]E(f329(f329(f43(x43881,f883(x43882,a869)),x43883),f329(f329(f8(f883(x43884,f883(x43882,a869)),f883(x43882,a869),x43881),f329(f43(x43884,f883(x43882,a869)),x43885)),f329(f329(f7(x43881,f883(x43884,f883(x43882,a869)),f883(x43884,f883(x43882,a869))),f329(f329(f8(f883(f883(x43882,a869),f883(x43882,a869)),f883(f883(x43884,f883(x43882,a869)),f883(x43884,f883(x43882,a869))),x43881),f8(f883(x43882,a869),f883(x43882,a869),x43884)),f329(f329(f8(f883(x43882,a869),f883(f883(x43882,a869),f883(x43882,a869)),x43881),f107(f883(x43882,a869))),x43886))),x43887))),f329(f329(f107(f883(x43882,a869)),f329(f329(f43(x43881,f883(x43882,a869)),x43883),x43886)),f329(f329(f43(x43884,f883(x43882,a869)),x43885),x43887))) % 178.07/177.92 [4381]E(f204(x43811,x43812,f329(f329(f329(x43813,x43814),x43815),x43816),f329(f329(f7(x43811,f882(a105,a105),f883(a105,f877(x43812))),f329(f329(f7(x43811,a105,f883(f882(a105,a105),f883(a105,f877(x43812)))),f329(f329(f7(x43811,a105,f883(a105,f883(f882(a105,a105),f883(a105,f877(x43812))))),x43817),x43814)),x43815)),x43816)),f329(f329(f329(f217(x43811,x43812,x43813,x43817),x43814),x43815),x43816)) % 178.07/177.92 [4394]E(f205(x43941,x43942,f329(f329(f329(x43943,x43944),x43945),x43946),f329(f329(f7(x43941,f882(a105,a105),f883(a105,f877(x43942))),f329(f329(f7(x43941,a105,f883(f882(a105,a105),f883(a105,f877(x43942)))),f329(f329(f7(x43941,a105,f883(a105,f883(f882(a105,a105),f883(a105,f877(x43942))))),x43947),x43944)),x43945)),x43946)),f219(x43941,x43942,x43943,x43947,x43944,x43945,x43946)) % 178.07/177.92 [4385]E(f202(x43851,x43852,f329(f329(f329(x43853,x43854),x43855),x43856),f329(f329(f7(x43851,f882(a105,a105),f883(a105,f877(f879(x43852)))),f329(f329(f7(x43851,a105,f883(f882(a105,a105),f883(a105,f877(f879(x43852))))),f329(f329(f7(x43851,a105,f883(a105,f883(f882(a105,a105),f883(a105,f877(f879(x43852)))))),x43857),x43854)),x43855)),x43856)),f329(f329(f329(f213(x43851,x43852,x43853,x43857),x43854),x43855),x43856)) % 178.07/177.92 [4396]E(f203(x43961,x43962,f329(f329(f329(x43963,x43964),x43965),x43966),f329(f329(f7(x43961,f882(a105,a105),f883(a105,f877(f879(x43962)))),f329(f329(f7(x43961,a105,f883(f882(a105,a105),f883(a105,f877(f879(x43962))))),f329(f329(f7(x43961,a105,f883(a105,f883(f882(a105,a105),f883(a105,f877(f879(x43962)))))),x43967),x43964)),x43965)),x43966)),f215(x43961,x43962,x43963,x43967,x43964,x43965,x43966)) % 178.07/177.92 [4294]E(f329(f269(x42941,x42942,x42943,x42944,x42945,x42946),f329(f329(f264(x42941,x42943),x42947),x42948)),f329(f329(f264(x42942,x42944),f329(x42945,x42947)),f329(x42946,x42948))) % 178.07/177.92 [4398]E(f329(f329(f153(f882(x43981,x43982),f882(x43983,x43984)),f329(f268(x43981,x43982,f882(x43983,x43984)),f329(f329(f7(x43981,f883(x43982,x43984),f883(x43982,f882(x43983,x43984))),f329(f329(f8(f883(x43984,f882(x43983,x43984)),f883(f883(x43982,x43984),f883(x43982,f882(x43983,x43984))),x43981),f8(x43984,f882(x43983,x43984),x43982)),f329(f329(f8(x43983,f883(x43984,f882(x43983,x43984)),x43981),f264(x43983,x43984)),x43985))),x43986))),f329(f329(f181(x43981,x43982),x43987),x43988)),f329(f329(f181(x43983,x43984),f329(f329(f153(x43981,x43983),x43985),x43987)),f329(f329(f153(x43982,x43984),x43986),x43988))) % 178.07/177.92 [4402]E(f329(f329(f153(f882(x44021,x44022),x44023),f329(f268(x44021,x44022,x44023),f329(f329(f8(f883(x44022,f882(x44021,x44024)),f883(x44022,x44023),x44021),f329(f8(f882(x44021,x44024),x44023,x44022),x44025)),f329(f329(f7(x44021,f883(x44022,x44024),f883(x44022,f882(x44021,x44024))),f329(f329(f8(f883(x44024,f882(x44021,x44024)),f883(f883(x44022,x44024),f883(x44022,f882(x44021,x44024))),x44021),f8(x44024,f882(x44021,x44024),x44022)),f264(x44021,x44024))),x44026)))),f329(f329(f181(x44021,x44022),x44027),x44028)),f329(f329(f153(f882(x44021,x44024),x44023),x44025),f329(f329(f181(x44021,x44024),x44027),f329(f329(f153(x44022,x44024),x44026),x44028)))) % 178.07/177.92 [4327]E(f329(f329(f153(f882(x43271,x43272),x43273),f329(f268(x43271,x43272,x43273),f329(f329(f8(f883(x43272,f882(x43274,x43272)),f883(x43272,x43273),x43271),f329(f8(f882(x43274,x43272),x43273,x43272),x43275)),f329(f329(f8(x43274,f883(x43272,f882(x43274,x43272)),x43271),f264(x43274,x43272)),x43276)))),f329(f329(f181(x43271,x43272),x43277),x43278)),f329(f329(f153(f882(x43274,x43272),x43273),x43275),f329(f329(f181(x43274,x43272),f329(f329(f153(x43271,x43274),x43276),x43277)),x43278))) % 178.07/177.92 [4285]E(f329(f329(f268(x42851,x42852,x42853),f329(f329(f8(f883(x42852,f882(x42854,x42855)),f883(x42852,x42853),x42851),f329(f8(f882(x42854,x42855),x42853,x42852),f329(f268(x42854,x42855,x42853),x42856))),x42857)),x42858),f329(f329(f268(x42854,x42855,x42853),x42856),f329(f329(f268(x42851,x42852,f882(x42854,x42855)),x42857),x42858))) % 178.07/177.92 [4403]E(f329(f329(f43(f882(x44031,x44032),f883(f882(x44033,x44034),a869)),f329(f329(f266(x44031,x44032),x44035),f329(f16(f883(x44032,a869),x44031),x44036))),f329(f268(x44031,x44032,f883(f882(x44033,x44034),a869)),f329(f329(f7(x44031,f883(x44032,f883(x44033,f883(x44034,a869))),f883(x44032,f883(f882(x44033,x44034),a869))),f329(f329(f8(f883(f883(x44033,f883(x44034,a869)),f883(f882(x44033,x44034),a869)),f883(f883(x44032,f883(x44033,f883(x44034,a869))),f883(x44032,f883(f882(x44033,x44034),a869))),x44031),f8(f883(x44033,f883(x44034,a869)),f883(f882(x44033,x44034),a869),x44032)),f329(f329(f8(f883(x44033,a869),f883(f883(x44033,f883(x44034,a869)),f883(f882(x44033,x44034),a869)),x44031),f266(x44033,x44034)),x44037))),f329(f329(f8(f883(x44034,a869),f883(x44033,f883(x44034,a869)),x44032),f16(f883(x44034,a869),x44033)),x44038)))),f329(f329(f266(x44033,x44034),f329(f329(f43(x44031,f883(x44033,a869)),x44035),x44037)),f329(f16(f883(x44034,a869),x44033),f329(f329(f43(x44032,f883(x44034,a869)),x44036),x44038)))) % 178.07/177.92 [4341]E(f329(f329(f270(x43411,x43412,x43413,x43414),f329(f329(f270(x43411,x43415,x43416,f882(x43412,x43413)),x43417),x43418)),x43419),f329(f329(f270(x43411,x43415,x43416,x43414),x43417),f329(f329(f7(x43415,f883(x43412,f883(x43413,x43414)),f883(x43416,x43414)),f329(f329(f8(f883(x43416,f882(x43412,x43413)),f883(f883(x43412,f883(x43413,x43414)),f883(x43416,x43414)),x43415),f270(x43416,x43412,x43413,x43414)),x43418)),x43419))) % 178.07/177.92 [4373]E(f329(f74(f882(x43731,x43732),f882(x43733,x43734),f882(x43735,x43736),f269(x43731,x43733,x43732,x43734,x43737,x43738)),f269(x43735,x43731,x43736,x43732,x43739,x437310)),f269(x43735,x43733,x43736,x43734,f329(f74(x43731,x43733,x43735,x43737),x43739),f329(f74(x43732,x43734,x43736,x43738),x437310))) % 178.07/177.92 [4379]E(f329(f269(x43791,x43792,x43793,x43794,x43795,x43796),f329(f269(x43797,x43791,x43798,x43793,x43799,x437910),x437911)),f329(f269(x43797,x43792,x43798,x43794,f329(f74(x43791,x43792,x43797,x43795),x43799),f329(f74(x43793,x43794,x43798,x43796),x437910)),x437911)) % 178.07/177.92 [4556]~E(a618,a711)+~P4(a5000) % 178.07/177.92 [4558]~E(f776(x45581),x45581)+~P4(a5000) % 178.07/177.92 [4560]~P94(x45601)+E(f92(x45601),a326) % 178.07/177.92 [4561]~P26(x45611)+P26(f879(x45611)) % 178.07/177.92 [4562]~P58(x45621)+P58(f879(x45621)) % 178.07/177.92 [4565]~P140(x45651)+~E(f79(x45651),f2(x45651)) % 178.07/177.92 [4567]~E(x45671,f2(a105))+E(f329(a20,x45671),f2(a1)) % 178.07/177.92 [4568]~E(x45681,f2(a1))+E(f83(a1,x45681),f2(a1)) % 178.07/177.92 [4574]~P141(x45741)+P31(x45741,f2(x45741)) % 178.07/177.92 [4576]~P105(x45761)+P29(x45761,f119(x45761)) % 178.07/177.92 [4585]P24(x45851)+P24(f329(a324,x45851)) % 178.07/177.92 [4628]~P141(x46281)+~P31(x46281,f79(x46281)) % 178.07/177.92 [4674]~P24(x46741)+~P24(f329(a324,x46741)) % 178.07/177.92 [4697]E(f329(a110,x46971),f2(a875))+~P24(f329(a198,x46971)) % 178.07/177.92 [4761]~P99(x47611)+P11(x47611,x47611,f116(x47611)) % 178.07/177.92 [4762]~P100(x47621)+P11(x47621,x47621,f107(x47621)) % 178.07/177.92 [4763]~P95(x47631)+P11(x47631,x47631,f82(x47631)) % 178.07/177.92 [4764]~P105(x47641)+P11(x47641,x47641,f241(x47641)) % 178.07/177.92 [4765]~P105(x47651)+P11(x47651,x47651,f242(x47651)) % 178.07/177.92 [4766]~P68(x47661)+P12(x47661,x47661,f82(x47661)) % 178.07/177.92 [4571]~E(x45711,f2(a875))+E(f329(f106(a1),x45711),f2(a1)) % 178.07/177.92 [4578]~P92(x45781)+E(f329(f109(x45781),a84),f2(x45781)) % 178.07/177.92 [4581]~E(f566(x45811),f2(a875))+E(f329(f165(a875),x45811),f2(a875)) % 178.07/177.92 [4582]~P106(x45821)+E(f245(x45821,f243(x45821)),f241(x45821)) % 178.07/177.92 [4583]~P106(x45831)+E(f246(x45831,f243(x45831)),f242(x45831)) % 178.07/177.92 [4584]~P87(x45841)+E(f83(x45841,f2(x45841)),f2(x45841)) % 178.07/177.92 [4593]~P141(x45931)+E(f329(f106(x45931),f79(a875)),f79(x45931)) % 178.07/177.92 [4594]~P141(x45941)+E(f329(f106(x45941),f2(a875)),f2(x45941)) % 178.07/177.92 [4595]~P137(x45951)+E(f329(f108(x45951),f79(a1)),f79(x45951)) % 178.07/177.92 [4596]~P137(x45961)+E(f329(f108(x45961),f2(a1)),f2(x45961)) % 178.07/177.92 [4597]E(x45971,f2(a875))+~E(f329(f106(a1),x45971),f2(a1)) % 178.07/177.92 [4622]~P89(x46221)+E(f329(f80(x46221),f193(x46221)),f252(x46221)) % 178.07/177.92 [4623]~P89(x46231)+E(f329(f80(x46231),f252(x46231)),f193(x46231)) % 178.07/177.92 [4624]~P67(x46241)+E(f329(f80(x46241),f2(x46241)),f2(x46241)) % 178.07/177.92 [4625]~P117(x46251)+E(f329(f76(x46251),f79(x46251)),f79(x46251)) % 178.07/177.92 [4626]~P85(x46261)+E(f329(f76(x46261),f2(x46261)),f2(x46261)) % 178.07/177.92 [4627]~P80(x46271)+E(f329(f165(x46271),f119(x46271)),f2(x46271)) % 178.07/177.92 [4648]~P37(x46481)+P39(f329(f171(a1),x46481)) % 178.07/177.92 [4679]~P92(x46791)+E(f329(f80(x46791),f79(x46791)),f329(f109(x46791),a103)) % 178.07/177.92 [4696]~P92(x46961)+P31(x46961,f329(f109(x46961),a84)) % 178.07/177.92 [4713]~P58(x47131)+E(f329(f171(x47131),f56(x47131)),f252(f883(x47131,a869))) % 178.07/177.92 [4723]P37(x47231)+~P39(f329(f171(a1),x47231)) % 178.07/177.92 [4724]~P58(x47241)+P24(f329(f136(x47241),f56(x47241))) % 178.07/177.92 [4767]E(f329(f106(a1),f329(a110,x47671)),x47671)+P24(f329(a198,x47671)) % 178.07/177.92 [4784]~P106(x47841)+E(f95(x47841,x47841,f5(x47841)),f96(x47841)) % 178.07/177.92 [4837]~P112(x48371)+E(f255(x48371,f79(x48371),f82(x48371)),f254(x48371)) % 178.07/177.92 [4867]~P92(x48671)+~P31(x48671,f329(f109(x48671),a103)) % 178.07/177.92 [4877]E(f329(a28,x48771),f206(a870))+P24(f329(a25,f329(a26,x48771))) % 178.07/177.92 [5007]E(f329(f76(a1),x50071),x50071)+P24(f329(f329(f244(a1),x50071),f2(a1))) % 178.07/177.92 [5028]~E(f329(a110,x50281),f2(a875))+P24(f329(f329(f243(a1),x50281),f2(a1))) % 178.07/177.92 [5088]~P24(f329(a198,x50881))+P24(f329(f329(f244(a1),x50881),f2(a1))) % 178.07/177.92 [5128]~P137(x51281)+P24(f329(f329(f331(x51281),f79(x51281)),f115(x51281))) % 178.07/177.92 [5129]~P141(x51291)+P24(f329(f329(f331(x51291),f79(x51291)),f191(x51291))) % 178.07/177.92 [5130]~P137(x51301)+P24(f329(f329(f331(x51301),f2(x51301)),f115(x51301))) % 178.07/177.92 [5131]~P141(x51311)+P24(f329(f329(f331(x51311),f2(x51311)),f191(x51311))) % 178.07/177.92 [5132]~P120(x51321)+P24(f329(f329(f244(x51321),f2(x51321)),f79(x51321))) % 178.07/177.92 [5133]~P120(x51331)+P24(f329(f329(f243(x51331),f2(x51331)),f79(x51331))) % 178.07/177.92 [5136]E(f329(f236(a870),f481(x51361)),f329(a28,x51361))+~P24(f329(a25,f329(a26,x51361))) % 178.07/177.92 [5137]E(f329(f236(a870),f826(x51371)),f329(a28,x51371))+~P24(f329(a25,f329(a26,x51371))) % 178.07/177.92 [5192]E(x51921,f2(a875))+~P24(f329(f329(f243(a875),x51921),f2(a875))) % 178.07/177.92 [5236]E(f329(a110,x52361),f2(a875))+~P24(f329(f329(f243(a1),x52361),f2(a1))) % 178.07/177.92 [5299]P24(f329(a198,x52991))+~P24(f329(f329(f244(a1),x52991),f2(a1))) % 178.07/177.92 [5304]~P105(x53041)+P12(x53041,f876(x53041),f147(x53041,x53041,f5(x53041))) % 178.07/177.92 [5321]P39(x53211)+~P24(f329(f329(f243(a1),f2(a1)),f337(x53211))) % 178.07/177.92 [5327]E(f329(f76(a1),x53271),f329(f80(a1),x53271))+~P24(f329(f329(f244(a1),x53271),f2(a1))) % 178.07/177.92 [5499]~P120(x54991)+~P24(f329(f329(f244(x54991),f79(x54991)),f2(x54991))) % 178.07/177.92 [5500]~P120(x55001)+~P24(f329(f329(f243(x55001),f79(x55001)),f2(x55001))) % 178.07/177.92 [5510]~E(x55101,f2(a1))+P24(f329(f329(f244(a1),f329(f76(a1),x55101)),f79(a1))) % 178.07/177.92 [5511]~E(x55111,f2(a875))+P24(f329(f329(f243(a1),f329(f106(a1),x55111)),f2(a1))) % 178.07/177.92 [5629]~P80(x56291)+E(f141(x56291,x56291,f81(x56291),f2(x56291)),f165(x56291)) % 178.07/177.92 [5800]~P101(x58001)+P21(a875,x58001,f106(x58001),f252(f883(a875,a869))) % 178.07/177.92 [5998]E(x59981,f2(a875))+~P24(f329(f329(f243(a1),f329(f106(a1),x59981)),f2(a1))) % 178.07/177.92 [5999]E(x59991,f2(a1))+~P24(f329(f329(f244(a1),f329(f76(a1),x59991)),f79(a1))) % 178.07/177.92 [6795]~P24(f329(f329(f244(a1),x67951),f2(a1)))+P24(f329(f329(f244(a1),f329(f329(f81(a1),x67951),x67951)),f2(a1))) % 178.07/177.92 [7344]P24(f329(f329(f244(a1),x73441),f2(a1)))+~P24(f329(f329(f244(a1),f329(f329(f81(a1),x73441),x73441)),f2(a1))) % 178.07/177.92 [7899]E(x78991,f329(a3,f2(a875)))+P24(f329(f329(f244(a875),f329(f329(f22(a875),f329(a19,x78991)),f329(a118,f2(a875)))),f329(a19,x78991))) % 178.07/177.92 [8668]~P24(f329(f329(f244(a1),x86681),f2(a1)))+P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f81(a1),x86681),x86681)),a103)),f2(a1))) % 178.07/177.92 [8754]~P24(f329(f329(f244(a1),x87541),f2(a1)))+P24(f329(f329(f244(a1),f329(f329(f81(a1),f329(f329(f81(a1),f79(a1)),x87541)),x87541)),f2(a1))) % 178.07/177.92 [9077]P24(f329(f329(f244(a1),x90771),f2(a1)))+~P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f81(a1),x90771),x90771)),a103)),f2(a1))) % 178.07/177.92 [9140]P24(f329(f329(f244(a1),x91401),f2(a1)))+~P24(f329(f329(f244(a1),f329(f329(f81(a1),f329(f329(f81(a1),f79(a1)),x91401)),x91401)),f2(a1))) % 178.07/177.92 [4667]~E(a84,x46671)+E(f329(f329(f81(a1),x46671),x46671),a84) % 178.07/177.92 [4668]~E(x46681,a84)+E(f329(f329(f81(a1),x46681),x46681),a84) % 178.07/177.92 [4682]E(x46821,f2(a1))+E(f329(f329(f39(a1),x46821),x46821),f79(a1)) % 178.07/177.92 [4813]E(x48131,a84)+~E(f329(f329(f81(a1),x48131),x48131),a84) % 178.07/177.92 [4814]E(a84,x48141)+~E(f329(f329(f81(a1),x48141),x48141),a84) % 178.07/177.92 [4827]~P27(x48271)+E(f41(x48271,f193(f883(x48271,a869))),f252(x48271)) % 178.07/177.92 [4828]~P27(x48281)+E(f41(x48281,f252(f883(x48281,a869))),f193(x48281)) % 178.07/177.92 [4829]~P27(x48291)+E(f40(x48291,f193(f883(x48291,a869))),f193(x48291)) % 178.07/177.92 [4830]~P27(x48301)+E(f40(x48301,f252(f883(x48301,a869))),f252(x48301)) % 178.07/177.92 [4831]~P105(x48311)+E(f138(x48311,f193(f883(x48311,a869))),f119(x48311)) % 178.07/177.92 [4966]E(x49661,f2(a875))+P24(f329(f329(f244(a875),f2(a875)),x49661)) % 178.07/177.92 [4985]~P28(x49851)+P24(f329(f329(f243(a1),f2(a1)),x49851)) % 178.07/177.92 [5019]~E(f329(f109(a875),x50191),f2(a875))+P24(f329(f329(f243(a1),x50191),a84)) % 178.07/177.92 [5024]P39(x50241)+P24(f329(f329(f331(a1),f337(x50241)),x50241)) % 178.07/177.92 [5025]E(x50251,f329(a3,f2(a875)))+P24(f329(f329(f243(a105),f79(a105)),x50251)) % 178.07/177.92 [5062]P24(f329(a198,x50621))+P24(f329(f329(f243(a1),f2(a1)),x50621)) % 178.07/177.92 [5110]E(f329(f106(a1),f329(a110,x51101)),f2(a1))+P24(f329(f329(f243(a1),f2(a1)),x51101)) % 178.07/177.92 [5178]E(f329(f106(a1),f329(f109(a875),x51781)),f329(f109(a1),x51781))+P24(f329(a198,f329(f109(a1),x51781))) % 178.07/177.92 [5198]E(f329(f109(a875),x51981),f2(a875))+~P24(f329(a198,f329(f109(a1),x51981))) % 178.07/177.92 [5199]E(f329(f109(a875),x51991),f2(a875))+~P24(f329(f329(f243(a1),x51991),a84)) % 178.07/177.92 [5233]P28(x52331)+~P24(f329(f329(f243(a1),f2(a1)),x52331)) % 178.07/177.92 [5307]E(f329(a118,f339(x53071)),x53071)+~P24(f329(f329(f244(a875),f2(a875)),x53071)) % 178.07/177.92 [5315]E(f329(a118,f329(f109(a875),x53151)),f79(a875))+~P24(f329(a198,f329(f109(a1),x53151))) % 178.07/177.92 [5323]E(f329(f106(a1),f450(x53231)),x53231)+~P24(f329(f329(f244(a1),f2(a1)),x53231)) % 178.07/177.92 [5330]~E(x53301,f329(a3,f2(a875)))+~P24(f329(f329(f243(a105),f79(a105)),x53301)) % 178.07/177.92 [5337]E(f329(f106(a1),f329(f109(a875),x53371)),f2(a1))+~P24(f329(a198,f329(f109(a1),x53371))) % 178.07/177.92 [5363]E(f329(f165(a875),x53631),f2(a875))+P24(f329(f329(f331(a875),f566(x53631)),f329(f171(a875),x53631))) % 178.07/177.92 [5384]E(f329(f106(a1),f329(a110,x53841)),x53841)+~P24(f329(f329(f243(a1),f2(a1)),x53841)) % 178.07/177.92 [5393]~P24(f329(a198,x53931))+~P24(f329(f329(f243(a1),f2(a1)),x53931)) % 178.07/177.92 [5492]E(f329(f329(f81(a875),f79(a875)),f329(f109(a875),x54921)),f79(a875))+~P24(f329(f329(f244(a1),x54921),a84)) % 178.07/177.92 [5550]E(x55501,f2(a875))+~P24(f329(f329(f244(a875),x55501),f329(a118,f2(a875)))) % 178.07/177.92 [5588]E(f329(f329(f22(a875),f329(f109(a875),x55881)),f79(a875)),f2(a875))+~P24(f329(f329(f243(a1),x55881),a84)) % 178.07/177.92 [5589]E(f329(f329(f81(a875),f329(f109(a875),x55891)),f79(a875)),f79(a875))+~P24(f329(f329(f244(a1),x55891),a84)) % 178.07/177.92 [5599]~P39(x55991)+E(f329(f38(a875),f329(f308(a1,a875,a110),x55991)),f329(f38(a1),x55991)) % 178.07/177.92 [5630]~P105(x56301)+E(f245(x56301,f329(f7(x56301,x56301,a869),f243(x56301))),f242(x56301)) % 178.07/177.92 [5631]~P105(x56311)+E(f246(x56311,f329(f7(x56311,x56311,a869),f243(x56311))),f241(x56311)) % 178.07/177.92 [5641]E(f45(a875,f329(a118,f2(a875)),f329(f109(a875),x56411)),f329(a118,f2(a875)))+~P24(f329(a198,f329(f109(a1),x56411))) % 178.07/177.92 [5650]P24(f329(f329(f244(a1),f2(a1)),x56501))+~P24(f329(f329(f243(a1),f79(a1)),x56501)) % 178.07/177.92 [5651]~P24(f329(f329(f244(a1),f2(a1)),x56511))+P24(f329(f329(f243(a1),f79(a1)),x56511)) % 178.07/177.92 [5662]E(f329(a118,f329(f329(f22(a875),x56621),f79(a875))),x56621)+~P24(f329(f329(f244(a875),f2(a875)),x56621)) % 178.07/177.92 [5719]P24(f329(f329(f244(a875),f2(a875)),f450(x57191)))+~P24(f329(f329(f244(a1),f2(a1)),x57191)) % 178.07/177.92 [5778]E(f45(a1,f329(f109(a1),a103),x57781),f329(f329(f22(a1),x57781),f79(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x57781)) % 178.07/177.92 [5812]~P24(f329(f329(f244(a1),a84),x58121))+P24(f329(f329(f244(a875),f2(a875)),f329(f109(a875),x58121))) % 178.07/177.92 [5862]P24(f329(f329(f244(a875),f2(a875)),f329(a110,x58621)))+~P24(f329(f329(f244(a1),f2(a1)),x58621)) % 178.07/177.92 [5914]~P24(f329(f329(f244(a875),f2(a875)),x59141))+P24(f329(f329(f244(a1),f2(a1)),f329(f106(a1),x59141))) % 178.07/177.92 [5952]~P24(f329(f329(f244(a875),f2(a875)),f329(a110,x59521)))+P24(f329(f329(f244(a1),f2(a1)),x59521)) % 178.07/177.92 [5967]~P39(x59671)+E(f329(f308(a875,a1,f106(a1)),f329(f308(a1,a875,a110),x59671)),x59671) % 178.07/177.92 [5979]P24(f329(f329(f244(a1),a84),x59791))+~P24(f329(f329(f244(a875),f2(a875)),f329(f109(a875),x59791))) % 178.07/177.92 [6027]~P58(x60271)+E(f329(f329(f150(f879(x60271)),f206(x60271)),f329(f329(f153(x60271,f879(x60271)),f236(x60271)),f56(x60271))),f56(f879(x60271))) % 178.07/177.92 [6038]P24(f329(f329(f244(a875),f2(a875)),x60381))+~P24(f329(f329(f244(a1),f2(a1)),f329(f106(a1),x60381))) % 178.07/177.92 [6153]E(f329(f308(a875,a1,f106(a1)),f329(f250(a875),f329(a110,x61531))),f329(f299(a1,f2(a1)),x61531))+~P24(f329(f329(f243(a1),f2(a1)),x61531)) % 178.07/177.92 [6167]~P120(x61671)+P24(f329(f329(f244(x61671),f2(x61671)),f329(f329(f81(x61671),f79(x61671)),f79(x61671)))) % 178.07/177.92 [6218]P24(f329(f329(f244(a875),f329(a118,f2(a875))),f329(a110,x62181)))+~P24(f329(f329(f244(a1),f79(a1)),x62181)) % 178.07/177.92 [6313]E(x63131,f2(a1))+P24(f329(f49(f2(a1),x63131),f329(f329(f264(a1,a1),f2(a1)),f2(a1)))) % 178.07/177.92 [6479]~P24(f329(f329(f244(a875),f329(a118,f2(a875))),f329(a110,x64791)))+P24(f329(f329(f244(a1),f79(a1)),x64791)) % 178.07/177.92 [6907]~P113(x69071)+P38(x69071,f329(f249(f882(x69071,x69071)),f329(f268(x69071,x69071,a869),f244(x69071)))) % 178.07/177.92 [5537]E(f329(f109(a875),f329(f329(f22(a1),x55371),a103)),f329(a118,f329(f109(a875),x55371)))+P24(f329(a198,f329(f109(a1),x55371))) % 178.07/177.92 [5553]~P37(x55531)+E(f329(f329(f153(a875,a1),f106(a1)),f329(f329(f153(a1,a875),a110),x55531)),x55531) % 178.07/177.92 [5668]E(f329(f80(a1),f329(f106(a1),f329(a118,f402(x56681)))),x56681)+~P24(f329(f329(f244(a1),x56681),f2(a1))) % 178.07/177.92 [5678]E(f329(f329(f81(a875),f79(a875)),f329(f109(a875),x56781)),f329(f109(a875),f329(f329(f22(a1),x56781),a103)))+P24(f329(f329(f244(a1),x56781),a84)) % 178.07/177.92 [5721]E(f329(f329(f39(a1),f329(f109(a1),a103)),x57211),f329(f109(a1),a103))+~P24(f329(f329(f244(a1),f2(a1)),x57211)) % 178.07/177.92 [5808]E(f329(f329(f22(a875),f329(f109(a875),x58081)),f79(a875)),f329(f109(a875),f329(f329(f81(a1),x58081),a103)))+P24(f329(f329(f243(a1),x58081),a84)) % 178.07/177.92 [5809]E(f329(f329(f81(a875),f329(f109(a875),x58091)),f79(a875)),f329(f109(a875),f329(f329(f22(a1),x58091),a103)))+P24(f329(f329(f244(a1),x58091),a84)) % 178.07/177.92 [5850]E(f329(a110,f329(f329(f81(a1),f79(a1)),x58501)),f329(a118,f329(a110,x58501)))+~P24(f329(f329(f243(a1),f2(a1)),x58501)) % 178.07/177.92 [5886]E(f329(a118,f329(f329(f22(a875),x58861),f329(a118,f2(a875)))),x58861)+~P24(f329(f329(f244(a875),f2(a875)),x58861)) % 178.07/177.92 [6098]E(f45(a875,f329(a118,f2(a875)),f329(f109(a875),x60981)),f329(a110,f45(a1,f79(a1),f329(f109(a1),x60981))))+P24(f329(a198,f329(f109(a1),x60981))) % 178.07/177.92 [6143]~P24(f329(f329(f244(a1),a84),x61431))+P24(f329(f329(f244(a1),a84),f329(f329(f81(a1),x61431),x61431))) % 178.07/177.92 [6144]~P24(f329(f329(f244(a1),a103),x61441))+P24(f329(f329(f244(a1),a103),f329(f329(f81(a1),x61441),x61441))) % 178.07/177.92 [6145]~P24(f329(f329(f243(a1),a84),x61451))+P24(f329(f329(f243(a1),a84),f329(f329(f81(a1),x61451),x61451))) % 178.07/177.92 [6146]~P24(f329(f329(f244(a1),a103),x61461))+P24(f329(f329(f243(a1),a103),f329(f329(f81(a1),x61461),x61461))) % 178.07/177.92 [6147]~P24(f329(f329(f92(a1),a84),x61471))+P24(f329(f329(f92(a1),a84),f329(f329(f81(a1),x61471),x61471))) % 178.07/177.92 [6326]~P24(f329(f62(x63261),f252(f883(x63261,a869))))+P24(f329(f62(f879(x63261)),f252(f883(f879(x63261),a869)))) % 178.07/177.92 [6412]~P24(f329(f329(f243(a1),f2(a1)),x64121))+P24(f329(f329(f244(a1),f2(a1)),f329(f329(f81(a1),f79(a1)),x64121))) % 178.07/177.92 [6419]E(f329(f263(a1,a1),f47(f79(a1),f329(f109(a1),x64191))),f329(f329(f39(a1),f79(a1)),f329(f109(a1),x64191)))+~P24(f329(f329(f243(a1),f2(a1)),f329(f109(a1),x64191))) % 178.07/177.92 [6439]E(f329(f267(a1,a1),f47(f79(a1),f329(f109(a1),x64391))),f45(a1,f79(a1),f329(f109(a1),x64391)))+~P24(f329(f329(f243(a1),f2(a1)),f329(f109(a1),x64391))) % 178.07/177.92 [6451]P24(f329(f62(x64511),f252(f883(x64511,a869))))+~P24(f329(f62(f879(x64511)),f252(f883(f879(x64511),a869)))) % 178.07/177.92 [6480]P24(f329(f329(f244(a1),a84),x64801))+~P24(f329(f329(f244(a1),a84),f329(f329(f81(a1),x64801),x64801))) % 178.07/177.92 [6481]P24(f329(f329(f244(a1),a103),x64811))+~P24(f329(f329(f244(a1),a103),f329(f329(f81(a1),x64811),x64811))) % 178.07/177.92 [6482]P24(f329(f329(f244(a1),a103),x64821))+~P24(f329(f329(f243(a1),a103),f329(f329(f81(a1),x64821),x64821))) % 178.07/177.92 [6483]P24(f329(f329(f243(a1),a84),x64831))+~P24(f329(f329(f243(a1),a84),f329(f329(f81(a1),x64831),x64831))) % 178.07/177.92 [6484]P24(f329(f329(f92(a1),a84),x64841))+~P24(f329(f329(f92(a1),a84),f329(f329(f81(a1),x64841),x64841))) % 178.07/177.92 [6799]~P24(f329(f62(x67991),f252(f883(x67991,a869))))+P24(f329(f329(f244(a875),f2(a875)),f329(f38(x67991),f252(f883(x67991,a869))))) % 178.07/177.92 [7387]P24(f329(f62(a875),x73871))+~P24(f329(f62(a1),f329(f308(a875,a1,f106(a1)),x73871))) % 178.07/177.92 [5467]~E(a103,x54671)+E(f329(f329(f22(a1),f329(f329(f81(a1),x54671),x54671)),a103),a103) % 178.07/177.92 [5468]~E(x54681,a103)+E(f329(f329(f22(a1),f329(f329(f81(a1),x54681),x54681)),a103),a103) % 178.07/177.92 [5972]E(x59721,a103)+~E(f329(f329(f22(a1),f329(f329(f81(a1),x59721),x59721)),a103),a103) % 178.07/177.92 [5973]E(a103,x59731)+~E(f329(f329(f22(a1),f329(f329(f81(a1),x59731),x59731)),a103),a103) % 178.07/177.92 [6381]~E(f329(f109(a875),x63811),f2(a875))+P24(f329(a198,f329(f109(a1),f329(f329(f81(a1),x63811),a103)))) % 178.07/177.92 [6726]~P24(f329(a198,f329(f109(a1),x67261)))+P24(f329(a198,f329(f109(a1),f329(f329(f81(a1),x67261),x67261)))) % 178.07/177.92 [6727]~P24(f329(f329(f244(a1),x67271),a84))+P24(f329(f329(f244(a1),f329(f329(f81(a1),x67271),x67271)),a84)) % 178.07/177.92 [6728]~P24(f329(f329(f243(a1),x67281),a103))+P24(f329(f329(f244(a1),f329(f329(f81(a1),x67281),x67281)),a103)) % 178.07/177.92 [6729]~P24(f329(f329(f243(a1),x67291),a84))+P24(f329(f329(f243(a1),f329(f329(f81(a1),x67291),x67291)),a84)) % 178.07/177.92 [6730]~P24(f329(f329(f243(a1),x67301),a103))+P24(f329(f329(f243(a1),f329(f329(f81(a1),x67301),x67301)),a103)) % 178.07/177.92 [6731]~P24(f329(f329(f92(a1),x67311),a84))+P24(f329(f329(f92(a1),f329(f329(f81(a1),x67311),x67311)),a84)) % 178.07/177.92 [7054]E(f329(f109(a875),x70541),f2(a875))+~P24(f329(a198,f329(f109(a1),f329(f329(f81(a1),x70541),a103)))) % 178.07/177.92 [7293]~P24(f329(f329(f243(a1),f2(a1)),f329(f109(a1),x72931)))+P24(f329(f329(f243(a1),f2(a1)),f329(f109(a1),f329(f329(f81(a1),x72931),x72931)))) % 178.07/177.92 [7294]P24(f329(a198,f329(f109(a1),x72941)))+~P24(f329(a198,f329(f109(a1),f329(f329(f81(a1),x72941),x72941)))) % 178.07/177.92 [7295]P24(f329(f329(f244(a1),x72951),a84))+~P24(f329(f329(f244(a1),f329(f329(f81(a1),x72951),x72951)),a84)) % 178.07/177.92 [7296]P24(f329(f329(f243(a1),x72961),a84))+~P24(f329(f329(f243(a1),f329(f329(f81(a1),x72961),x72961)),a84)) % 178.07/177.92 [7297]P24(f329(f329(f243(a1),x72971),a103))+~P24(f329(f329(f244(a1),f329(f329(f81(a1),x72971),x72971)),a103)) % 178.07/177.92 [7298]P24(f329(f329(f243(a1),x72981),a103))+~P24(f329(f329(f243(a1),f329(f329(f81(a1),x72981),x72981)),a103)) % 178.07/177.92 [7299]P24(f329(f329(f92(a1),x72991),a84))+~P24(f329(f329(f92(a1),f329(f329(f81(a1),x72991),x72991)),a84)) % 178.07/177.92 [7668]E(f329(a112,f707(x76681)),x76681)+~P24(f329(f329(f331(f883(f882(a875,a875),a869)),x76681),a104)) % 178.07/177.92 [6299]~P92(x62991)+E(f329(f109(x62991),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f79(x62991)) % 178.07/177.92 [6778]~P24(f329(a198,f329(f109(a1),x67781)))+E(f329(f109(a875),f329(f329(f22(a1),f329(f329(f81(a1),x67781),x67781)),a103)),f2(a875)) % 178.07/177.92 [7844]~P24(f329(f329(f244(a1),f329(f109(a1),x78441)),f2(a1)))+E(f329(f263(a1,a1),f329(a51,f50(f329(f80(a1),f79(a1)),f329(f80(a1),f329(f109(a1),x78441))))),f329(f329(f39(a1),f79(a1)),f329(f109(a1),x78441))) % 178.07/177.92 [7857]~P24(f329(f329(f244(a1),f329(f109(a1),x78571)),f2(a1)))+E(f329(f267(a1,a1),f329(a51,f50(f329(f80(a1),f79(a1)),f329(f80(a1),f329(f109(a1),x78571))))),f45(a1,f79(a1),f329(f109(a1),x78571))) % 178.07/177.92 [7905]~P24(f329(f329(f243(a1),a84),x79051))+P24(f329(f329(f244(a1),a84),f329(f329(f22(a1),f329(f329(f81(a1),x79051),x79051)),a103))) % 178.07/177.92 [7906]~P24(f329(f329(f244(a1),a103),x79061))+P24(f329(f329(f244(a1),a103),f329(f329(f22(a1),f329(f329(f81(a1),x79061),x79061)),a103))) % 178.07/177.92 [7907]~P24(f329(f329(f243(a1),a84),x79071))+P24(f329(f329(f243(a1),a84),f329(f329(f22(a1),f329(f329(f81(a1),x79071),x79071)),a103))) % 178.07/177.92 [7908]~P24(f329(f329(f243(a1),a103),x79081))+P24(f329(f329(f243(a1),a103),f329(f329(f22(a1),f329(f329(f81(a1),x79081),x79081)),a103))) % 178.07/177.92 [7909]~P24(f329(f329(f92(a1),a103),x79091))+P24(f329(f329(f92(a1),a103),f329(f329(f22(a1),f329(f329(f81(a1),x79091),x79091)),a103))) % 178.07/177.92 [8217]~P92(x82171)+~P31(x82171,f329(f109(x82171),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))) % 178.07/177.92 [8396]P24(f329(f329(f244(a1),a103),x83961))+~P24(f329(f329(f244(a1),a103),f329(f329(f22(a1),f329(f329(f81(a1),x83961),x83961)),a103))) % 178.07/177.92 [8397]P24(f329(f329(f243(a1),a84),x83971))+~P24(f329(f329(f244(a1),a84),f329(f329(f22(a1),f329(f329(f81(a1),x83971),x83971)),a103))) % 178.07/177.92 [8398]P24(f329(f329(f243(a1),a84),x83981))+~P24(f329(f329(f243(a1),a84),f329(f329(f22(a1),f329(f329(f81(a1),x83981),x83981)),a103))) % 178.07/177.92 [8399]P24(f329(f329(f243(a1),a103),x83991))+~P24(f329(f329(f243(a1),a103),f329(f329(f22(a1),f329(f329(f81(a1),x83991),x83991)),a103))) % 178.07/177.92 [8400]P24(f329(f329(f92(a1),a103),x84001))+~P24(f329(f329(f92(a1),a103),f329(f329(f22(a1),f329(f329(f81(a1),x84001),x84001)),a103))) % 178.07/177.92 [8712]E(f329(f109(a875),f329(f329(f22(a1),f329(f329(f81(a1),x87121),x87121)),a103)),f329(f329(f87(a875,a875),f329(f109(a875),x87121)),f329(f329(f8(a875,a875,a875),a118),f329(f329(f18(a875,a875,a875),f81(a875)),f5(a875)))))+P24(f329(a198,f329(f109(a1),x87121))) % 178.07/177.92 [9555]E(x95551,f193(f883(f882(a875,a875),a869)))+P24(f329(f329(f331(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869))),f329(f329(f264(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),x95551),f193(f883(f882(a875,a875),a869)))),a69)) % 178.07/177.92 [8643]~P24(f329(a198,f329(f109(a1),x86431)))+P24(f329(a198,f329(f109(a1),f329(f329(f22(a1),f329(f329(f81(a1),x86431),x86431)),a103)))) % 178.07/177.92 [8644]~P24(f329(f329(f244(a1),x86441),a84))+P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f81(a1),x86441),x86441)),a103)),a84)) % 178.07/177.92 [8645]~P24(f329(f329(f244(a1),x86451),a103))+P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f81(a1),x86451),x86451)),a103)),a103)) % 178.07/177.92 [8646]~P24(f329(f329(f244(a1),x86461),a84))+P24(f329(f329(f243(a1),f329(f329(f22(a1),f329(f329(f81(a1),x86461),x86461)),a103)),a84)) % 178.07/177.92 [8647]~P24(f329(f329(f243(a1),x86471),a103))+P24(f329(f329(f243(a1),f329(f329(f22(a1),f329(f329(f81(a1),x86471),x86471)),a103)),a103)) % 178.07/177.92 [8648]~P24(f329(f329(f92(a1),x86481),a103))+P24(f329(f329(f92(a1),f329(f329(f22(a1),f329(f329(f81(a1),x86481),x86481)),a103)),a103)) % 178.07/177.92 [8747]~P24(f329(f329(f243(a1),f2(a1)),f329(f109(a1),x87471)))+P24(f329(f329(f243(a1),f2(a1)),f329(f109(a1),f329(f329(f22(a1),f329(f329(f81(a1),x87471),x87471)),a103)))) % 178.07/177.92 [8905]~P92(x89051)+E(f329(f329(f81(x89051),f79(x89051)),f79(x89051)),f329(f109(x89051),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))) % 178.07/177.92 [9061]P24(f329(a198,f329(f109(a1),x90611)))+~P24(f329(a198,f329(f109(a1),f329(f329(f22(a1),f329(f329(f81(a1),x90611),x90611)),a103)))) % 178.07/177.92 [9062]P24(f329(f329(f244(a1),x90621),a84))+~P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f81(a1),x90621),x90621)),a103)),a84)) % 178.07/177.92 [9063]P24(f329(f329(f244(a1),x90631),a84))+~P24(f329(f329(f243(a1),f329(f329(f22(a1),f329(f329(f81(a1),x90631),x90631)),a103)),a84)) % 178.07/177.92 [9064]P24(f329(f329(f244(a1),x90641),a103))+~P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f81(a1),x90641),x90641)),a103)),a103)) % 178.07/177.92 [9065]P24(f329(f329(f243(a1),x90651),a103))+~P24(f329(f329(f243(a1),f329(f329(f22(a1),f329(f329(f81(a1),x90651),x90651)),a103)),a103)) % 178.07/177.92 [9066]P24(f329(f329(f92(a1),x90661),a103))+~P24(f329(f329(f92(a1),f329(f329(f22(a1),f329(f329(f81(a1),x90661),x90661)),a103)),a103)) % 178.07/177.92 [9601]~P24(f329(f62(f882(a875,a875)),x96011))+P24(f329(f329(f331(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869))),f329(f329(f264(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),f193(f883(f882(a875,a875),a869))),x96011)),a70)) % 178.07/177.92 [9388]~P141(x93881)+E(f329(f329(f254(x93881),f79(x93881)),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f79(x93881)) % 178.07/177.92 [9389]~P141(x93891)+E(f329(f329(f254(x93891),f2(x93891)),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f2(x93891)) % 178.07/177.92 [9828]~P24(f329(f329(f244(a875),f79(a875)),x98281))+P24(f329(f329(f244(a875),f2(a875)),f329(f329(f39(a875),x98281),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))))) % 178.07/177.92 [9840]~P24(f329(f329(f244(a875),f2(a875)),x98401))+P24(f329(f329(f244(a875),f2(a875)),f329(f329(f39(a875),f329(f329(f81(a875),x98401),f79(a875))),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))))) % 178.07/177.92 [9882]~E(f45(a875,x98821,f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f79(a875))+P24(f329(f329(f244(a875),f2(a875)),f45(a875,x98821,f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))))) % 178.07/177.92 [9901]E(f45(a875,x99011,f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f79(a875))+~P24(f329(f329(f244(a875),f2(a875)),f45(a875,x99011,f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))))) % 178.07/177.92 [4601]~P38(x46011,x46012)+P53(x46011,x46012) % 178.07/177.92 [4602]~P44(x46021,x46022)+P53(x46021,x46022) % 178.07/177.92 [4563]~E(x45631,x45632)+E(f276(x45631,x45632),f79(a105)) % 178.07/177.92 [4566]E(f224(x45661,x45662),x45661)+~E(x45662,f2(a875)) % 178.07/177.92 [4573]~E(x45732,f119(x45731))+E(f151(x45731,x45732),f119(x45731)) % 178.07/177.92 [4592]~E(f151(x45922,x45921),f119(x45922))+E(x45921,f119(x45922)) % 178.07/177.92 [4606]~P25(x46062)+P25(f883(x46061,x46062)) % 178.07/177.92 [4607]~P63(x46072)+P63(f883(x46071,x46072)) % 178.07/177.92 [4608]~P96(x46082)+P64(f883(x46081,x46082)) % 178.07/177.92 [4609]~P63(x46092)+P99(f883(x46091,x46092)) % 178.07/177.92 [4610]~P65(x46102)+P65(f883(x46101,x46102)) % 178.07/177.92 [4611]~P81(x46112)+P81(f883(x46111,x46112)) % 178.07/177.92 [4612]~P89(x46122)+P89(f883(x46121,x46122)) % 178.07/177.92 [4613]~P63(x46132)+P100(f883(x46131,x46132)) % 178.07/177.92 [4614]~P97(x46142)+P97(f883(x46141,x46142)) % 178.07/177.92 [4615]~P103(x46152)+P103(f883(x46151,x46152)) % 178.07/177.92 [4616]~P96(x46162)+P98(f883(x46161,x46162)) % 178.07/177.92 [4617]~P27(x46172)+P27(f883(x46171,x46172)) % 178.07/177.92 [4618]~P104(x46182)+P104(f883(x46181,x46182)) % 178.07/177.92 [4619]~P106(x46192)+P106(f883(x46191,x46192)) % 178.07/177.92 [4620]~P107(x46202)+P107(f883(x46201,x46202)) % 178.07/177.92 [4621]~P96(x46212)+P96(f883(x46211,x46212)) % 178.07/177.92 [4633]E(x46331,x46332)+~E(f329(a26,x46331),f329(a26,x46332)) % 178.07/177.92 [4635]E(x46351,x46352)+~E(f329(a118,x46351),f329(a118,x46352)) % 178.07/177.92 [4636]E(x46361,x46362)+~E(f329(a112,x46361),f329(a112,x46362)) % 178.07/177.92 [4637]E(x46371,x46372)+~E(f329(a3,x46371),f329(a3,x46372)) % 178.07/177.92 [4639]E(x46391,x46392)+~E(f329(a19,x46391),f329(a19,x46392)) % 178.07/177.92 [4740]~P56(x47401)+E(f45(x47401,x47402,x47402),f2(x47401)) % 178.07/177.92 [4774]~P38(x47741,x47742)+P38(f876(x47741),f144(x47741,x47742)) % 178.07/177.92 [4775]~P38(x47751,x47752)+P38(f876(x47751),f145(x47751,x47752)) % 178.07/177.92 [4872]~P38(x48721,x48722)+P38(f883(x48721,a869),f322(x48721,x48722)) % 178.07/177.92 [4873]~P38(x48731,x48732)+P38(f883(x48731,a869),f320(x48731,x48732)) % 178.07/177.92 [4991]~P28(x49911)+P39(f300(a1,x49911,x49912)) % 178.07/177.92 [5091]~P38(x50911,x50912)+P55(x50911,f68(x50911,x50911,x50912)) % 178.07/177.92 [5593]~P77(x55931)+P21(x55931,x55931,f80(x55931),x55932) % 178.07/177.92 [4587]~E(x45872,f119(x45871))+E(f329(f167(x45871),x45872),f119(x45871)) % 178.07/177.92 [4588]~E(x45882,f119(x45881))+E(f329(f168(x45881),x45882),f119(x45881)) % 178.07/177.92 [4643]E(x46431,f329(a110,x46432))+~E(f329(f106(a1),x46431),x46432) % 178.07/177.92 [4646]E(x46461,f119(x46462))+~E(f329(f167(x46462),x46461),f119(x46462)) % 178.07/177.92 [4647]E(x46471,f119(x46472))+~E(f329(f168(x46472),x46471),f119(x46472)) % 178.07/177.92 [4664]~P92(x46641)+E(f329(f109(x46641),x46642),f329(f108(x46641),x46642)) % 178.07/177.92 [4671]~E(x46712,f206(x46711))+E(f235(x46711,x46712),f193(f883(x46711,a869))) % 178.07/177.92 [4673]~P26(x46731)+P24(f329(f62(x46731),x46732)) % 178.07/177.92 [4680]E(x46801,f206(x46802))+E(f329(f236(x46802),f825(x46802,x46801)),x46801) % 178.07/177.92 [4681]E(x46811,f206(x46812))+E(f329(f236(x46812),f858(x46812,x46811)),x46811) % 178.07/177.92 [4683]~E(f619(x46832,x46831),f119(x46831))+E(f179(x46831,x46832),f119(f876(x46831))) % 178.07/177.92 [4692]~E(x46922,f119(x46921))+E(f329(f171(x46921),x46922),f193(f883(x46921,a869))) % 178.07/177.92 [4693]~E(x46932,f119(x46931))+E(f193(f883(x46931,a869)),f329(f171(x46931),x46932)) % 178.07/177.92 [4695]E(x46951,x46952)+~E(f329(f106(a1),x46951),f329(f106(a1),x46952)) % 178.07/177.92 [4698]E(f222(x46981,x46982),f2(a875))+P24(f329(f62(x46981),x46982)) % 178.07/177.92 [4718]~P117(x47181)+E(f83(x47181,f83(x47181,x47182)),f83(x47181,x47182)) % 178.07/177.92 [4731]~P79(x47311)+E(f329(f329(f254(x47311),x47312),f79(a875)),x47312) % 178.07/177.92 [4732]~P114(x47321)+E(f329(f329(f254(x47321),x47322),f79(a875)),x47322) % 178.07/177.92 [4734]E(x47341,x47342)+E(f276(x47341,x47342),f329(f329(f81(a105),x47342),f79(a105))) % 178.07/177.92 [4737]E(f329(f38(x47371),x47372),f2(a875))+P24(f329(f62(x47371),x47372)) % 178.07/177.92 [4741]~E(f151(x47411,x47412),x47412)+P24(f329(f136(x47411),x47412)) % 178.07/177.92 [4744]~P64(x47441)+E(f329(f329(f116(x47441),x47442),f193(x47441)),x47442) % 178.07/177.92 [4745]~P67(x47451)+E(f329(f329(f22(x47451),x47452),f2(x47451)),x47452) % 178.07/177.92 [4746]~P98(x47461)+E(f329(f329(f107(x47461),x47462),f252(x47461)),x47462) % 178.07/177.92 [4747]~P74(x47471)+E(f329(f329(f82(x47471),x47472),f79(x47471)),x47472) % 178.07/177.92 [4748]~P79(x47481)+E(f329(f329(f82(x47481),x47482),f79(x47481)),x47482) % 178.07/177.92 [4749]~P114(x47491)+E(f329(f329(f82(x47491),x47492),f79(x47491)),x47492) % 178.07/177.92 [4750]~P70(x47501)+E(f329(f329(f81(x47501),x47502),f2(x47501)),x47502) % 178.07/177.92 [4751]~P114(x47511)+E(f329(f329(f81(x47511),x47512),f2(x47511)),x47512) % 178.07/177.92 [4752]~P80(x47521)+E(f329(f329(f81(x47521),x47522),f2(x47521)),x47522) % 178.07/177.92 [4753]~P56(x47531)+E(f329(f329(f39(x47531),x47532),f79(x47531)),x47532) % 178.07/177.92 [4754]~P115(x47541)+E(f329(f329(f287(x47541),x47542),f79(x47541)),x47542) % 178.07/177.92 [4755]~P114(x47551)+E(f329(f329(f254(x47551),x47552),f2(a875)),f79(x47551)) % 178.07/177.92 [4756]~P112(x47561)+E(f329(f329(f254(x47561),x47562),f2(a875)),f79(x47561)) % 178.07/177.92 [4757]~E(x47572,f193(f883(x47571,a869)))+E(f329(f38(x47571),x47572),f2(a875)) % 178.07/177.92 [4768]~P56(x47681)+E(f45(x47681,x47682,f2(x47681)),x47682) % 178.07/177.92 [4776]~P98(x47761)+E(f329(f329(f116(x47761),x47762),f252(x47761)),f252(x47761)) % 178.07/177.92 [4777]~P64(x47771)+E(f329(f329(f107(x47771),x47772),f193(x47771)),f193(x47771)) % 178.07/177.92 [4778]~P114(x47781)+E(f329(f329(f82(x47781),x47782),f2(x47781)),f2(x47781)) % 178.07/177.92 [4779]~P124(x47791)+E(f329(f329(f82(x47791),x47792),f2(x47791)),f2(x47791)) % 178.07/177.92 [4780]~P56(x47801)+E(f329(f329(f39(x47801),x47802),f2(x47801)),f2(x47801)) % 178.07/177.92 [4781]~P116(x47811)+E(f329(f329(f287(x47811),x47812),f2(x47811)),f2(x47811)) % 178.07/177.92 [4782]E(x47821,f206(x47822))+~E(f235(x47822,x47821),f193(f883(x47822,a869))) % 178.07/177.92 [4785]~P56(x47851)+E(f45(x47851,x47852,f79(x47851)),f2(x47851)) % 178.07/177.92 [4786]~P56(x47861)+E(f45(x47861,f2(x47861),x47862),f2(x47861)) % 178.07/177.92 [4815]E(x48151,f2(a875))+E(f55(x48152,x48151,f119(x48152)),f119(f876(x48152))) % 178.07/177.92 [4839]P38(x48391,x48392)+~E(f712(x48392,x48391),f193(f883(x48391,a869))) % 178.07/177.92 [4840]E(x48401,f119(x48402))+~E(f329(f171(x48402),x48401),f193(f883(x48402,a869))) % 178.07/177.92 [4841]E(x48411,f119(x48412))+~E(f193(f883(x48412,a869)),f329(f171(x48412),x48411)) % 178.07/177.92 [4844]~E(x48441,x48442)+P24(f329(f329(a326,x48441),x48442)) % 178.07/177.92 [4854]P24(x48541)+P24(f329(f329(a332,x48541),x48542)) % 178.07/177.92 [4855]E(x48551,f119(x48552))+E(f329(f329(f164(x48552),x48551),f2(a875)),f329(f140(x48552),x48551)) % 178.07/177.92 [4858]E(f151(x48581,x48582),x48582)+~P24(f329(f136(x48581),x48582)) % 178.07/177.92 [4863]~P24(x48632)+P24(f329(f329(a332,x48631),x48632)) % 178.07/177.92 [4864]~P24(x48642)+P24(f329(f329(a328,x48641),x48642)) % 178.07/177.92 [4865]~P24(x48651)+P24(f329(f329(a328,x48651),x48652)) % 178.07/177.92 [4875]~E(f567(x48752,x48751),f578(x48752,x48751))+P24(f329(f136(x48751),x48752)) % 178.07/177.92 [4883]E(f329(f249(x48831),x48832),f193(f883(x48831,a869)))+P24(f329(x48832,f335(x48832))) % 178.07/177.92 [4884]E(f193(f883(x48841,a869)),f329(f249(x48841),x48842))+P24(f329(x48842,f336(x48842))) % 178.07/177.92 [4948]~P117(x49481)+E(f329(f329(f82(x49481),x49482),f83(x49481,x49482)),f329(f76(x49481),x49482)) % 178.07/177.92 [4959]~E(x49591,f2(a1))+E(f46(x49591,x49592),f329(f329(f264(a1,a1),f2(a1)),f2(a1))) % 178.07/177.92 [4990]~P53(x49901,x49902)+P53(x49901,f329(f284(x49901,x49901),x49902)) % 178.07/177.92 [5008]~E(f329(a28,x50081),f329(f236(a870),x50082))+P24(f329(a25,f329(a26,x50081))) % 178.07/177.92 [5013]E(x50131,x50132)+~P24(f329(f329(a326,x50131),x50132)) % 178.07/177.92 [5017]~P24(f329(a25,x50172))+P24(f329(a25,f33(x50171,x50172))) % 178.07/177.92 [5026]P24(x50261)+~P24(f329(f329(a327,x50262),x50261)) % 178.07/177.92 [5027]P24(x50271)+~P24(f329(f329(a327,x50271),x50272)) % 178.07/177.92 [5031]~P103(x50311)+P24(f329(f329(f243(x50311),x50312),f252(x50311))) % 178.07/177.92 [5035]E(x50351,x50352)+~E(f329(x50351,f401(x50352,x50351)),f329(x50352,f401(x50352,x50351))) % 178.07/177.92 [5064]E(x50641,f2(a875))+E(f224(x50641,f45(a875,x50642,x50641)),f224(x50642,x50641)) % 178.07/177.92 [5069]~P105(x50691)+P29(x50691,f329(f329(f150(x50691),x50692),f119(x50691))) % 178.07/177.92 [5071]E(x50711,f2(a1))+P24(f329(f49(x50712,x50711),f46(x50712,x50711))) % 178.07/177.92 [5089]~E(x50891,x50892)+P24(f329(f329(f244(a875),x50891),f329(a118,x50892))) % 178.07/177.92 [5099]~E(x50991,f2(a875))+P24(f329(f329(f244(a875),x50991),f329(a118,x50992))) % 178.07/177.92 [5109]P24(f329(x51091,x51092))+P24(f329(f329(f243(a1),f2(a1)),f376(x51091))) % 178.07/177.92 [5146]P24(f329(a25,x51461))+~P24(f329(a25,f33(x51462,x51461))) % 178.07/177.92 [5148]P24(f329(a25,x51481))+~P24(f329(a25,f34(x51482,x51481))) % 178.07/177.92 [5150]P24(f329(a25,x51501))+~P24(f329(a25,f34(x51501,x51502))) % 178.07/177.92 [5182]P53(x51821,x51822)+~P53(x51821,f329(f284(x51821,x51821),x51822)) % 178.07/177.92 [5185]~E(f45(a875,x51852,x51851),f2(a875))+E(f329(f329(f82(a875),x51851),f448(x51851,x51852)),x51852) % 178.07/177.92 [5186]~E(f45(a1,x51862,x51861),f2(a1))+E(f329(f329(f82(a1),x51861),f449(x51861,x51862)),x51862) % 178.07/177.92 [5212]~P24(f329(x52121,x52122))+P24(f329(f329(f243(a1),f2(a1)),f375(x52121))) % 178.07/177.92 [5224]E(f329(f329(f22(a875),f329(a110,x52241)),f329(a110,x52242)),f329(a110,x52241))+~P24(f329(a198,x52242)) % 178.07/177.92 [5256]E(f277(x52561,x52562),f79(a105))+~P24(f329(f329(f243(a105),x52561),f79(a105))) % 178.07/177.92 [5349]E(f329(f329(f164(x53491),x53492),f567(x53492,x53491)),f329(f329(f164(x53491),x53492),f578(x53492,x53491)))+P24(f329(f136(x53491),x53492)) % 178.07/177.92 [5394]~P24(f329(x53941,f91(x53942,x53941)))+P24(f329(x53941,f582(x53942,x53941))) % 178.07/177.92 [5457]P55(x54571,x54572)+~P24(f329(f317(x54571,x54572),f679(x54572,x54571))) % 178.07/177.92 [5600]~E(f329(a118,f45(a875,x56001,x56002)),x56002)+E(f45(a875,f329(a118,x56001),x56002),f2(a875)) % 178.07/177.92 [5657]P38(x56571,x56572)+P24(f329(f329(f331(x56571),f779(x56572,x56571)),f780(x56572,x56571))) % 178.07/177.92 [5664]~P137(x56641)+P24(f329(f329(f331(x56641),f329(f106(x56641),x56642)),f115(x56641))) % 178.07/177.92 [5665]~P141(x56651)+P24(f329(f329(f331(x56651),f329(f106(x56651),x56652)),f191(x56651))) % 178.07/177.92 [5666]~P137(x56661)+P24(f329(f329(f331(x56661),f329(f108(x56661),x56662)),f115(x56661))) % 178.07/177.92 [5667]~P92(x56671)+P24(f329(f329(f331(x56671),f329(f109(x56671),x56672)),f115(x56671))) % 178.07/177.92 [5811]E(f329(a118,f45(a875,x58111,x58112)),x58112)+E(f45(a875,f329(a118,x58111),x58112),f329(a118,f45(a875,x58111,x58112))) % 178.07/177.92 [6230]P38(x62301,x62302)+~P24(f329(f329(f331(x62301),f680(x62302,x62301)),f318(x62301,x62302))) % 178.07/177.92 [6265]~P120(x62651)+~P24(f329(f329(f244(x62651),f329(f106(x62651),x62652)),f2(x62651))) % 178.07/177.92 [6266]~P85(x62661)+~P24(f329(f329(f244(x62661),f329(f76(x62661),x62662)),f2(x62661))) % 178.07/177.92 [6354]P24(f329(f329(f244(a1),x63541),f45(a1,x63542,x63541)))+~P24(f329(f329(f244(a1),x63541),f2(a1))) % 178.07/177.92 [6453]E(f329(f329(f307(a875),f329(a118,x64531)),f300(a875,x64532,x64531)),f300(a875,x64532,f329(a118,x64531)))+~P24(f329(f329(f243(a875),x64532),f329(a118,x64531))) % 178.07/177.92 [6540]~P105(x65401)+P29(x65401,f149(x65401,x65401,f5(x65401),x65402)) % 178.07/177.92 [6670]E(f329(f167(x66701),x66702),x66702)+~P24(f329(f329(f243(a875),f329(f194(f876(x66701)),x66702)),f79(a875))) % 178.07/177.92 [6690]~P85(x66901)+P24(f329(f329(f243(x66901),f329(f80(x66901),f329(f76(x66901),x66902))),f2(x66901))) % 178.07/177.92 [6723]~P38(x67231,x67232)+P38(x67231,f329(f329(f286(x67231,x67231,x67231),x67232),f305(x67231,x67232))) % 178.07/177.92 [6945]~P24(f329(f329(f244(a1),x69452),f2(a1)))+P24(f329(f329(f243(a1),f45(a1,x69451,x69452)),f2(a1))) % 178.07/177.92 [7341]~P141(x73411)+E(f195(x73411,f329(f329(f7(x73411,x73411,x73411),f81(x73411)),f79(x73411)),x73412,f2(x73411)),f329(f106(x73411),x73412)) % 178.07/177.92 [7369]~P122(x73691)+~P24(f329(f329(f244(x73691),f329(f329(f82(x73691),x73692),x73692)),f2(x73691))) % 178.07/177.92 [9991]~P117(x99911)+~P24(f329(f329(f244(x99911),f329(f329(f254(x99911),x99912),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f2(x99911))) % 178.07/177.92 [4644]~E(x46442,f119(x46441))+E(f329(f194(f876(x46441)),x46442),f2(a875)) % 178.07/177.92 [4684]~E(x46841,f2(a875))+E(f329(f329(f81(a875),x46841),x46842),x46842) % 178.07/177.92 [4685]~E(x46852,f2(a875))+E(f329(f329(f82(a875),x46851),x46852),f2(a875)) % 178.07/177.92 [4687]~E(x46871,f2(a875))+E(f329(f329(f82(a875),x46871),x46872),f2(a875)) % 178.07/177.92 [4688]~E(x46882,f2(a875))+E(f329(f329(f254(a875),x46881),x46882),f79(a875)) % 178.07/177.92 [4689]~E(x46892,f2(a1))+E(f329(f329(f39(a1),x46891),x46892),f2(a1)) % 178.07/177.92 [4699]E(x46991,f119(x46992))+~E(f329(f194(f876(x46992)),x46991),f2(a875)) % 178.07/177.92 [4700]~P63(x47001)+E(f329(f329(f116(x47001),x47002),x47002),x47002) % 178.07/177.92 [4702]~P99(x47021)+E(f329(f329(f116(x47021),x47022),x47022),x47022) % 178.07/177.92 [4703]~P63(x47031)+E(f329(f329(f107(x47031),x47032),x47032),x47032) % 178.07/177.92 [4705]~P100(x47051)+E(f329(f329(f107(x47051),x47052),x47052),x47052) % 178.07/177.92 [4707]~P95(x47071)+E(f329(f329(f82(x47071),x47072),x47072),x47072) % 178.07/177.92 [4709]~P105(x47091)+E(f329(f329(f241(x47091),x47092),x47092),x47092) % 178.07/177.92 [4711]~P105(x47111)+E(f329(f329(f242(x47111),x47112),x47112),x47112) % 178.07/177.92 [4730]~P67(x47301)+E(f329(f329(f22(x47301),x47302),x47302),f2(x47301)) % 178.07/177.92 [4742]~P89(x47421)+E(f329(f80(x47421),f329(f80(x47421),x47422)),x47422) % 178.07/177.92 [4743]~P67(x47431)+E(f329(f80(x47431),f329(f80(x47431),x47432)),x47432) % 178.07/177.92 [4760]~E(x47602,f2(a875))+E(f329(f329(f254(a875),x47601),x47602),f329(a118,f2(a875))) % 178.07/177.92 [4794]~P64(x47941)+E(f329(f329(f116(x47941),f193(x47941)),x47942),x47942) % 178.07/177.92 [4795]~P98(x47951)+E(f329(f329(f107(x47951),f252(x47951)),x47952),x47952) % 178.07/177.92 [4796]~P74(x47961)+E(f329(f329(f82(x47961),f79(x47961)),x47962),x47962) % 178.07/177.92 [4797]~P79(x47971)+E(f329(f329(f82(x47971),f79(x47971)),x47972),x47972) % 178.07/177.92 [4798]~P114(x47981)+E(f329(f329(f82(x47981),f79(x47981)),x47982),x47982) % 178.07/177.92 [4799]~P70(x47991)+E(f329(f329(f81(x47991),f2(x47991)),x47992),x47992) % 178.07/177.92 [4800]~P114(x48001)+E(f329(f329(f81(x48001),f2(x48001)),x48002),x48002) % 178.07/177.92 [4801]~P80(x48011)+E(f329(f329(f81(x48011),f2(x48011)),x48012),x48012) % 178.07/177.92 [4820]~P98(x48201)+E(f329(f329(f116(x48201),f252(x48201)),x48202),f252(x48201)) % 178.07/177.92 [4821]~P64(x48211)+E(f329(f329(f107(x48211),f193(x48211)),x48212),f193(x48211)) % 178.07/177.92 [4822]~P114(x48221)+E(f329(f329(f82(x48221),f2(x48221)),x48222),f2(x48221)) % 178.07/177.92 [4823]~P124(x48231)+E(f329(f329(f82(x48231),f2(x48231)),x48232),f2(x48231)) % 178.07/177.92 [4824]~P79(x48241)+E(f329(f329(f254(x48241),f79(x48241)),x48242),f79(x48241)) % 178.07/177.92 [4825]~P56(x48251)+E(f329(f329(f39(x48251),f2(x48251)),x48252),f2(x48251)) % 178.07/177.92 [4826]~P115(x48261)+E(f329(f329(f287(x48261),f2(x48261)),x48262),f2(x48261)) % 178.07/177.92 [4834]E(x48341,f119(x48342))+E(f143(x48342,f329(f168(x48342),x48341)),f329(f140(x48342),x48341)) % 178.07/177.92 [4835]E(x48351,f119(x48352))+E(f329(f140(x48352),f329(f168(x48352),x48351)),f143(x48352,x48351)) % 178.07/177.92 [4836]E(x48361,f2(a875))+~E(f329(f329(f81(a875),x48362),x48361),x48362) % 178.07/177.92 [4842]~P137(x48421)+E(f329(f108(x48421),f329(f106(a1),x48422)),f329(f106(x48421),x48422)) % 178.07/177.92 [4843]~P92(x48431)+E(f329(f108(x48431),f329(f109(a1),x48432)),f329(f109(x48431),x48432)) % 178.07/177.92 [4850]E(x48501,f79(a875))+~E(f329(f329(f82(a875),x48502),x48501),f79(a875)) % 178.07/177.92 [4851]E(x48511,f79(a875))+~E(f329(f329(f82(a875),x48511),x48512),f79(a875)) % 178.07/177.92 [4852]E(x48521,f2(a875))+~E(f329(f329(f81(a875),x48522),x48521),f2(a875)) % 178.07/177.92 [4853]E(x48531,f2(a875))+~E(f329(f329(f81(a875),x48531),x48532),f2(a875)) % 178.07/177.92 [4868]~P85(x48681)+E(f329(f76(x48681),f329(f80(x48681),x48682)),f329(f76(x48681),x48682)) % 178.07/177.92 [4869]~P117(x48691)+E(f329(f76(x48691),f329(f106(x48691),x48692)),f329(f106(x48691),x48692)) % 178.07/177.92 [4870]~P85(x48701)+E(f329(f76(x48701),f329(f76(x48701),x48702)),f329(f76(x48701),x48702)) % 178.07/177.92 [4871]~P70(x48711)+E(f329(f165(x48711),f329(f168(x48711),x48712)),f329(f165(x48711),x48712)) % 178.07/177.92 [4876]~E(x48761,f329(a118,f2(a875)))+E(f329(f329(f254(a875),x48761),x48762),f329(a118,f2(a875))) % 178.07/177.92 [4886]~P67(x48861)+E(f329(f329(f22(x48861),f2(x48861)),x48862),f329(f80(x48861),x48862)) % 178.07/177.92 [4887]~E(x48872,f2(a875))+E(f138(a875,f329(f299(a875,x48871),x48872)),f119(a875)) % 178.07/177.92 [4896]~P92(x48961)+E(f329(f329(f81(x48961),x48962),f329(f109(x48961),a84)),x48962) % 178.07/177.92 [4897]E(x48971,f2(a1))+E(f47(f329(f76(a1),x48972),f329(f76(a1),x48971)),f53(x48972,x48971)) % 178.07/177.92 [4911]~E(x49111,x49112)+P24(f329(f329(f243(a875),x49111),x49112)) % 178.07/177.92 [4918]~E(x49181,f2(a105))+E(f329(f329(f81(a875),f329(a19,x49181)),x49182),x49182) % 178.07/177.92 [4919]~E(f329(f109(a1),x49192),f329(f106(a1),x49191))+E(x49191,f329(a110,f329(f109(a1),x49192))) % 178.07/177.92 [4928]~P28(x49281)+P28(f329(f329(f254(a1),x49281),x49282)) % 178.07/177.92 [4929]~P89(x49291)+E(f329(f329(f116(x49291),x49292),f329(f80(x49291),x49292)),f252(x49291)) % 178.07/177.92 [4930]~P89(x49301)+E(f329(f329(f107(x49301),x49302),f329(f80(x49301),x49302)),f193(x49301)) % 178.07/177.92 [4931]~P67(x49311)+E(f329(f329(f81(x49311),x49312),f329(f80(x49311),x49312)),f2(x49311)) % 178.07/177.92 [4956]E(x49561,f2(a875))+~E(f329(f80(a1),f329(f106(a1),x49562)),f329(f106(a1),x49561)) % 178.07/177.92 [4957]E(x49571,f2(a875))+~E(f329(f80(a1),f329(f106(a1),x49571)),f329(f106(a1),x49572)) % 178.07/177.92 [4967]E(f200(x49671,x49672),f2(a1))+P24(f329(f329(f243(a1),x49672),x49671)) % 178.07/177.92 [4968]E(f178(x49681,x49682),f119(a1))+P24(f329(f329(f243(a1),x49681),x49682)) % 178.07/177.92 [4981]E(x49811,f329(a118,f2(a875)))+~E(f329(f329(f82(a875),x49812),x49811),f329(a118,f2(a875))) % 178.07/177.92 [4982]E(x49821,f329(a118,f2(a875)))+~E(f329(f329(f82(a875),x49821),x49822),f329(a118,f2(a875))) % 178.07/177.92 [4983]~P104(x49831)+P24(f329(f329(f243(x49831),x49832),x49832)) % 178.07/177.92 [4984]~P94(x49841)+P24(f329(f329(f92(x49841),x49842),x49842)) % 178.07/177.92 [4987]~P92(x49871)+E(f329(f329(f82(x49871),x49872),f329(f109(x49871),a103)),f329(f80(x49871),x49872)) % 178.07/177.92 [5005]~P137(x50051)+E(f329(f80(x50051),f329(f108(x50051),x50052)),f329(f108(x50051),f329(f80(a1),x50052))) % 178.07/177.92 [5006]~P92(x50061)+E(f329(f80(x50061),f329(f109(x50061),x50062)),f329(f109(x50061),f329(f80(a1),x50062))) % 178.07/177.92 [5036]~E(x50361,f329(a118,x50362))+P24(f329(f329(f244(a875),f2(a875)),x50361)) % 178.07/177.92 [5053]~P105(x50531)+E(f329(f80(f883(x50531,a869)),f329(f250(x50531),x50532)),f329(f251(x50531),x50532)) % 178.07/177.92 [5054]~P105(x50541)+E(f329(f80(f883(x50541,a869)),f329(f301(x50541),x50542)),f329(f298(x50541),x50542)) % 178.07/177.92 [5055]~P105(x50551)+E(f329(f80(f883(x50551,a869)),f329(f251(x50551),x50552)),f329(f250(x50551),x50552)) % 178.07/177.92 [5056]~P105(x50561)+E(f329(f80(f883(x50561,a869)),f329(f298(x50561),x50562)),f329(f301(x50561),x50562)) % 178.07/177.92 [5063]~E(f329(f106(a1),x50632),x50631)+P24(f329(f329(f243(a1),f2(a1)),x50631)) % 178.07/177.92 [5070]~E(x50702,f2(a1))+E(f53(x50701,x50702),f329(f329(f264(a1,a1),f2(a1)),f329(f76(a1),x50701))) % 178.07/177.92 [5072]~P25(x50721)+P24(f329(f329(f243(x50721),f193(x50721)),x50722)) % 178.07/177.92 [5104]E(x51041,x51042)+~E(f329(f329(f81(a1),x51041),x51041),f329(f329(f81(a1),x51042),x51042)) % 178.07/177.92 [5108]~P24(f329(x51081,x51082))+P24(f329(x51081,f329(a110,f375(x51081)))) % 178.07/177.92 [5134]~P117(x51341)+E(f329(f329(f82(x51341),f83(x51341,x51342)),f329(f76(x51341),x51342)),x51342) % 178.07/177.92 [5135]E(x51351,x51352)+~P24(f329(f329(f199(a24),x51351),x51352)) % 178.07/177.92 [5144]~E(x51442,f2(a875))+E(f86(f882(a875,a875),f48(x51441,x51442)),f329(f329(f264(a875,a875),f2(a875)),x51441)) % 178.07/177.92 [5155]~E(x51551,x51552)+~P24(f329(f329(f244(a875),x51551),x51552)) % 178.07/177.92 [5156]~E(x51561,x51562)+~P24(f329(f329(f244(a1),x51561),x51562)) % 178.07/177.92 [5159]~P141(x51591)+E(f329(f329(f81(x51591),f79(x51591)),f329(f106(x51591),x51592)),f329(f106(x51591),f329(a118,x51592))) % 178.07/177.92 [5163]~E(x51631,f2(a875))+~P24(f329(f329(f244(a875),x51632),x51631)) % 178.07/177.92 [5179]E(f151(x51791,x51792),x51792)+~E(f329(f194(f876(x51791)),f151(x51791,x51792)),f329(f194(f876(x51791)),x51792)) % 178.07/177.92 [5180]E(f329(f38(x51801),f329(f171(x51801),x51802)),f329(f194(f876(x51801)),x51802))+~P24(f329(f136(x51801),x51802)) % 178.07/177.92 [5190]~P24(f329(x51901,f377(x51901)))+P24(f329(x51901,f329(f106(a1),x51902))) % 178.07/177.92 [5201]E(f178(x52011,x52012),f119(a1))+~P24(f329(f329(f244(a1),x52012),x52011)) % 178.07/177.92 [5202]E(f277(x52021,x52022),f79(a105))+~P24(f329(f329(f244(a105),x52022),x52021)) % 178.07/177.92 [5205]~P107(x52051)+E(f300(x52051,x52052,x52052),f329(f329(f307(x52051),x52052),f193(f883(x52051,a869)))) % 178.07/177.92 [5227]~E(f329(f329(f22(a875),x52271),x52272),f2(a875))+P24(f329(f329(f243(a875),x52271),x52272)) % 178.07/177.92 [5228]~E(f329(f329(f22(a1),x52281),x52282),f2(a1))+P24(f329(f329(f92(a1),x52281),x52282)) % 178.07/177.92 [5253]~E(x52532,f2(a875))+E(f55(x52531,x52532,f119(x52531)),f329(f329(f150(f876(x52531)),f119(x52531)),f119(f876(x52531)))) % 178.07/177.92 [5257]~P104(x52571)+~P24(f329(f329(f244(x52571),x52572),x52572)) % 178.07/177.92 [5260]~E(f45(a1,x52601,x52602),f2(a1))+E(f45(a1,x52601,f329(f80(a1),x52602)),f2(a1)) % 178.07/177.92 [5262]~E(f45(a1,x52621,x52622),f2(a1))+E(f45(a1,f329(f80(a1),x52621),x52622),f2(a1)) % 178.07/177.92 [5270]E(f329(f299(a875,x52701),f329(a118,x52702)),f193(f883(a875,a869)))+P24(f329(f329(f243(a875),x52701),x52702)) % 178.07/177.92 [5290]E(f138(a875,f329(f299(a875,x52901),x52902)),f119(a875))+P24(f329(f329(f244(a875),x52901),x52902)) % 178.07/177.92 [5295]~E(f329(f38(x52951),f329(f171(x52951),x52952)),f329(f194(f876(x52951)),x52952))+P24(f329(f136(x52951),x52952)) % 178.07/177.92 [5300]~P24(f329(f136(x53001),x53002))+P24(f329(f136(x53001),f329(f167(x53001),x53002))) % 178.07/177.92 [5301]~P24(f329(f136(x53011),x53012))+P24(f329(f136(x53011),f329(f170(x53011),x53012))) % 178.07/177.92 [5302]~P24(f329(f136(x53021),x53022))+P24(f329(f136(x53021),f329(f168(x53021),x53022))) % 178.07/177.92 [5309]P24(f329(x53091,x53092))+~P24(f329(x53091,f329(a110,f376(x53091)))) % 178.07/177.92 [5310]P24(f329(f329(f243(a875),x53102),x53101))+P24(f329(f329(f243(a875),x53101),x53102)) % 178.07/177.92 [5311]P24(f329(f329(f243(a1),x53112),x53111))+P24(f329(f329(f243(a1),x53111),x53112)) % 178.07/177.92 [5313]~P85(x53131)+P24(f329(f329(f243(x53131),x53132),f329(f76(x53131),x53132))) % 178.07/177.92 [5316]P24(f329(x53161,f381(x53161)))+~P24(f329(x53161,f329(f106(a1),x53162))) % 178.07/177.92 [5341]E(f329(f329(f22(a875),x53411),x53412),f2(a875))+~P24(f329(f329(f243(a875),x53411),x53412)) % 178.07/177.92 [5342]E(f329(f329(f22(a1),x53421),x53422),f2(a1))+~P24(f329(f329(f92(a1),x53421),x53422)) % 178.07/177.92 [5343]E(f329(f329(f39(a875),x53431),x53432),f2(a875))+~P24(f329(f329(f244(a875),x53431),x53432)) % 178.07/177.92 [5361]E(f45(a875,x53611,x53612),x53611)+~P24(f329(f329(f244(a875),x53611),x53612)) % 178.07/177.92 [5370]E(f45(a1,x53701,f329(f80(a1),x53702)),f288(x53701,x53702))+P24(f329(f329(f243(a1),f2(a1)),x53702)) % 178.07/177.92 [5382]E(f329(f329(f22(a1),x53821),x53822),f200(x53821,x53822))+~P24(f329(f329(f243(a1),x53822),x53821)) % 178.07/177.92 [5401]P24(f329(f329(f243(a1),f2(a1)),f377(x54011)))+P24(f329(x54011,f329(f106(a1),x54012))) % 178.07/177.92 [5413]~P58(x54131)+P24(f329(f329(f331(x54131),x54132),f329(f171(x54131),f56(x54131)))) % 178.07/177.92 [5415]~P120(x54151)+P24(f329(f329(f243(x54151),f2(x54151)),f329(f106(x54151),x54152))) % 178.07/177.92 [5416]~P85(x54161)+P24(f329(f329(f243(x54161),f2(x54161)),f329(f76(x54161),x54162))) % 178.07/177.92 [5443]E(f329(f329(f81(a875),x54431),f859(x54432,x54431)),x54432)+~P24(f329(f329(f243(a875),x54431),x54432)) % 178.07/177.92 [5455]~E(f329(f109(a1),x54551),f329(f106(a1),x54552))+P24(f329(f329(f243(a1),f2(a1)),f329(f109(a1),x54551))) % 178.07/177.92 [5458]E(f300(a1,x54581,x54582),f193(f883(a1,a869)))+~P24(f329(f329(f244(a1),x54582),x54581)) % 178.07/177.92 [5461]~P117(x54611)+E(f329(f329(f82(x54611),f329(f76(x54611),x54612)),f329(f76(x54611),x54612)),f329(f329(f82(x54611),x54612),x54612)) % 178.07/177.92 [5466]E(f138(a875,f329(f299(a875,x54661),f329(a118,x54662))),f119(a875))+P24(f329(f329(f243(a875),x54661),x54662)) % 178.07/177.92 [5470]E(f329(f329(f39(a1),x54701),x54702),f289(x54701,x54702))+~P24(f329(f329(f243(a1),f2(a1)),x54702)) % 178.07/177.92 [5490]P24(f329(f136(x54901),x54902))+~P24(f329(f136(x54901),f329(f167(x54901),x54902))) % 178.07/177.92 [5491]P24(f329(f136(x54911),x54912))+~P24(f329(f136(x54911),f329(f168(x54911),x54912))) % 178.07/177.92 [5512]P24(f329(f62(a875),x55121))+P24(f329(f329(f331(a875),f340(x55121,x55122)),x55121)) % 178.07/177.92 [5513]P24(f329(f62(a875),x55131))+P24(f329(f329(f331(a875),f356(x55131,x55132)),x55131)) % 178.07/177.92 [5514]P24(f329(f329(f244(a875),x55142),f329(a118,x55141)))+P24(f329(f329(f244(a875),x55141),x55142)) % 178.07/177.92 [5515]E(f45(a1,x55151,x55152),f288(x55151,x55152))+~P24(f329(f329(f243(a1),f2(a1)),x55152)) % 178.07/177.92 [5518]E(f138(a875,f329(f299(a875,x55181),x55182)),f119(a875))+~P24(f329(f329(f243(a875),x55182),x55181)) % 178.07/177.92 [5519]~P77(x55191)+E(f329(f308(x55191,x55191,f80(x55191)),f329(f250(x55191),x55192)),f329(f301(x55191),f329(f80(x55191),x55192))) % 178.07/177.92 [5520]~P77(x55201)+E(f329(f308(x55201,x55201,f80(x55201)),f329(f301(x55201),x55202)),f329(f250(x55201),f329(f80(x55201),x55202))) % 178.07/177.92 [5521]~P77(x55211)+E(f329(f308(x55211,x55211,f80(x55211)),f329(f251(x55211),x55212)),f329(f298(x55211),f329(f80(x55211),x55212))) % 178.07/177.92 [5522]~P77(x55221)+E(f329(f308(x55221,x55221,f80(x55221)),f329(f298(x55221),x55222)),f329(f251(x55221),f329(f80(x55221),x55222))) % 178.07/177.92 [5533]E(x55331,f193(f883(x55332,a869)))+P24(f329(f329(f331(x55332),f482(x55331,x55332)),x55331)) % 178.07/177.92 [5534]E(x55341,f193(f883(x55342,a869)))+P24(f329(f329(f331(x55342),f524(x55341,x55342)),x55341)) % 178.07/177.92 [5545]~P24(f329(f329(f244(a875),x55451),x55452))+P24(f329(f329(f243(a875),x55451),x55452)) % 178.07/177.92 [5546]~P24(f329(f329(f244(a1),x55461),x55462))+P24(f329(f329(f243(a1),x55461),x55462)) % 178.07/177.92 [5562]E(f47(x55621,x55622),f329(f329(f264(a1,a1),f2(a1)),x55621))+~P24(f329(f329(f244(a1),x55621),x55622)) % 178.07/177.92 [5563]E(f223(f329(f80(a1),x55631),f329(f80(a1),x55632)),f223(x55631,x55632))+~P24(f329(f329(f244(a1),x55632),f2(a1))) % 178.07/177.92 [5574]E(x55741,x55742)+~E(f329(a3,f329(a118,f329(a19,x55741))),f329(a3,f329(a118,f329(a19,x55742)))) % 178.07/177.92 [5579]E(f47(x55791,x55792),f329(f329(f264(a1,a1),f2(a1)),x55791))+~P24(f329(f329(f243(a1),x55792),f2(a1))) % 178.07/177.92 [5606]E(f45(a875,f329(f109(a875),x56061),f329(f109(a875),x56062)),f2(a875))+~P24(f329(a198,f329(f109(a1),x56061))) % 178.07/177.92 [5621]P24(f329(f329(f243(a1),f2(a1)),f381(x56211)))+~P24(f329(x56211,f329(f106(a1),x56212))) % 178.07/177.92 [5655]P39(f300(a1,x56551,x56552))+~P24(f329(f329(f243(a1),f2(a1)),x56551)) % 178.07/177.92 [5660]~P24(f329(f62(x56601),x56602))+P24(f329(f62(f883(x56601,a869)),f329(f306(x56601),x56602))) % 178.07/177.92 [5673]E(f329(f329(f81(a1),x56731),f329(f106(a1),f386(x56732,x56731))),x56732)+~P24(f329(f329(f243(a1),x56731),x56732)) % 178.07/177.92 [5681]P24(f329(f329(f243(a875),x56811),x56812))+P24(f329(f329(f243(a875),f329(a118,x56812)),x56811)) % 178.07/177.92 [5725]E(f329(f329(f39(a875),f329(f109(a875),x57251)),f329(f109(a875),x57252)),f2(a875))+~P24(f329(a198,f329(f109(a1),x57251))) % 178.07/177.92 [5726]E(f329(f329(f82(a875),f329(f109(a875),x57261)),f329(f109(a875),x57262)),f2(a875))+~P24(f329(f329(f244(a1),x57261),a84)) % 178.07/177.92 [5728]P24(f329(f329(f244(a875),x57281),f329(a118,x57282)))+~P24(f329(f329(f244(a875),x57281),x57282)) % 178.07/177.92 [5730]P24(f329(f329(f244(a875),x57301),f329(a118,x57302)))+~P24(f329(f329(f243(a875),x57301),x57302)) % 178.07/177.92 [5732]P24(f329(f329(f243(a875),x57321),f329(a118,x57322)))+~P24(f329(f329(f243(a875),x57321),x57322)) % 178.07/177.92 [5735]~E(x57351,x57352)+P24(f329(f329(f244(a1),x57351),f329(f329(f81(a1),x57352),f79(a1)))) % 178.07/177.92 [5738]E(f45(a1,x57381,x57382),f2(a1))+E(f329(f329(f22(a1),x57382),f45(a1,x57381,x57382)),f45(a1,f329(f80(a1),x57381),x57382)) % 178.07/177.92 [5747]E(x57471,f119(x57472))+P24(f329(f329(f331(x57472),f143(x57472,x57471)),f329(f171(x57472),x57471))) % 178.07/177.92 [5759]E(f86(f882(a875,a875),f48(x57591,x57592)),f329(f329(f264(a875,a875),f2(a875)),x57591))+~P24(f329(f329(f244(a875),x57591),x57592)) % 178.07/177.92 [5792]E(f329(f329(f22(a875),f329(f109(a875),x57921)),f329(f109(a875),x57922)),f329(f109(a875),x57921))+~P24(f329(f329(f244(a1),x57922),a84)) % 178.07/177.92 [5793]E(f329(f329(f81(a875),f329(f109(a875),x57931)),f329(f109(a875),x57932)),f329(f109(a875),x57932))+~P24(f329(f329(f244(a1),x57931),a84)) % 178.07/177.92 [5798]E(f329(a118,f329(f329(f81(a875),x57981),f860(x57982,x57981))),x57982)+~P24(f329(f329(f244(a875),x57981),x57982)) % 178.07/177.92 [5821]P24(f329(x58211,x58212))+~P24(f329(x58211,f329(a90,f714(x58212,x58211)))) % 178.07/177.92 [5829]~P24(f329(f329(f244(a875),x58291),f329(a118,x58292)))+P24(f329(f329(f243(a875),x58291),x58292)) % 178.07/177.92 [5875]E(f329(f329(f307(a875),x58751),f329(f299(a875,x58752),x58751)),f329(f299(a875,x58752),f329(a118,x58751)))+~P24(f329(f329(f243(a875),x58752),x58751)) % 178.07/177.92 [5879]E(x58791,f119(x58792))+E(f329(f329(f127(x58792),f120(x58792,x58791)),f329(f329(f150(x58792),f143(x58792,x58791)),f119(x58792))),x58791) % 178.07/177.92 [5893]P24(f329(f62(x58931),x58932))+~P24(f329(f329(f244(a875),f2(a875)),f329(f38(x58931),x58932))) % 178.07/177.92 [5895]~E(x58951,f193(f883(x58952,a869)))+~P24(f329(f329(f244(a875),f2(a875)),f329(f38(x58952),x58951))) % 178.07/177.92 [5907]~P24(f329(f329(f244(a875),x59071),x59072))+P24(f329(f329(f243(a875),f329(a118,x59071)),x59072)) % 178.07/177.92 [5915]~P105(x59151)+E(f149(x59151,x59151,f5(x59151),f151(x59151,x59152)),f138(x59151,f329(f171(x59151),x59152))) % 178.07/177.92 [5918]E(x59181,f119(x59182))+P24(f329(f329(f331(x59182),f329(f140(x59182),x59181)),f329(f171(x59182),x59181))) % 178.07/177.92 [5924]~P120(x59241)+P24(f329(f329(f244(x59241),x59242),f329(f329(f81(x59241),x59242),f79(x59241)))) % 178.07/177.92 [5926]~P85(x59261)+P24(f329(f329(f243(x59261),f329(f80(x59261),x59262)),f329(f76(x59261),x59262))) % 178.07/177.92 [5959]P24(f329(f62(a875),x59591))+~P24(f329(f329(f244(a875),f340(x59591,x59592)),x59592)) % 178.07/177.92 [5960]P24(f329(f62(a875),x59601))+~P24(f329(f329(f243(a875),f356(x59601,x59602)),x59602)) % 178.07/177.92 [5964]~P24(f329(f62(f882(x59641,x59641)),x59642))+P24(f329(f62(x59641),f329(f282(x59641),x59642))) % 178.07/177.92 [6019]~P24(f329(f329(f244(a875),x60192),f329(a118,x60191)))+~P24(f329(f329(f244(a875),x60191),x60192)) % 178.07/177.92 [6020]~P107(x60201)+E(f329(f329(f107(f883(x60201,a869)),f329(f298(x60201),x60202)),f329(f251(x60201),x60202)),f329(f329(f307(x60201),x60202),f193(f883(x60201,a869)))) % 178.07/177.92 [6033]P24(f329(f62(x60331),x60332))+~P24(f329(f62(f883(x60331,a869)),f329(f306(x60331),x60332))) % 178.07/177.92 [6058]P24(f329(f329(f244(a875),f329(a118,x60581)),f329(a118,x60582)))+~P24(f329(f329(f244(a875),x60581),x60582)) % 178.07/177.92 [6059]P24(f329(f329(f244(a875),f329(a19,x60591)),f329(a19,x60592)))+~P24(f329(f329(f244(a105),x60591),x60592)) % 178.07/177.92 [6060]P24(f329(f329(f244(a105),f329(a3,x60601)),f329(a3,x60602)))+~P24(f329(f329(f244(a875),x60601),x60602)) % 178.07/177.92 [6061]P24(f329(f329(f243(a875),f329(a118,x60611)),f329(a118,x60612)))+~P24(f329(f329(f243(a875),x60611),x60612)) % 178.07/177.92 [6062]P24(f329(f329(f243(a875),f329(a19,x60621)),f329(a19,x60622)))+~P24(f329(f329(f243(a105),x60621),x60622)) % 178.07/177.92 [6063]P24(f329(f329(f243(a105),f329(a3,x60631)),f329(a3,x60632)))+~P24(f329(f329(f243(a875),x60631),x60632)) % 178.07/177.92 [6066]E(x60661,x60662)+~E(f329(f308(a875,a1,f106(a1)),x60661),f329(f308(a875,a1,f106(a1)),x60662)) % 178.07/177.92 [6082]P24(f329(f329(f244(a875),x60821),x60822))+~P24(f329(f329(f244(a875),f329(a118,x60821)),x60822)) % 178.07/177.92 [6085]P24(f329(f329(f244(a875),x60851),x60852))+~P24(f329(f329(f243(a875),f329(a118,x60851)),x60852)) % 178.07/177.92 [6086]P24(f329(f329(f243(a875),x60861),x60862))+~P24(f329(f329(f243(a875),f329(a118,x60861)),x60862)) % 178.07/177.92 [6101]E(f45(a1,x61011,x61012),f2(a1))+E(f329(f329(f22(a1),f45(a1,x61011,x61012)),x61012),f45(a1,x61011,f329(f80(a1),x61012))) % 178.07/177.92 [6170]E(f329(f38(f883(x61701,a869)),f329(f306(x61701),x61702)),f329(f329(f254(a875),f329(a118,f329(a118,f2(a875)))),f329(f38(x61701),x61702)))+~P24(f329(f62(x61701),x61702)) % 178.07/177.92 [6173]E(x61731,f119(x61732))+E(f329(f329(f164(x61732),x61731),f329(f329(f22(a875),f329(f194(f876(x61732)),x61731)),f79(a875))),f143(x61732,x61731)) % 178.07/177.92 [6198]E(x61981,f119(x61982))+E(f329(f329(f127(x61982),f329(f170(x61982),x61981)),f329(f329(f150(x61982),f329(f140(x61982),x61981)),f119(x61982))),f329(f167(x61982),x61981)) % 178.07/177.92 [6227]~P24(f329(f62(x62271),f40(f883(x62271,a869),x62272)))+P24(f329(f62(f883(x62271,a869)),x62272)) % 178.07/177.92 [6250]P24(f329(f329(f243(a875),f329(f109(a875),x62501)),f329(f109(a875),x62502)))+~P24(f329(f329(f243(a1),x62501),a84)) % 178.07/177.92 [6267]~P24(f329(f329(f244(a1),x62671),x62672))+P24(f329(f329(f244(a1),x62671),f329(f329(f81(a1),x62672),f79(a1)))) % 178.07/177.92 [6268]~P24(f329(f329(f243(a1),x62681),x62682))+P24(f329(f329(f244(a1),x62681),f329(f329(f81(a1),x62682),f79(a1)))) % 178.07/177.92 [6269]~P24(f329(f329(f244(a1),x62691),x62692))+P24(f329(f329(f243(a1),x62691),f329(f329(f22(a1),x62692),f79(a1)))) % 178.07/177.92 [6272]~P24(f329(f329(f244(a875),x62721),x62722))+P24(f329(f329(f244(a1),f329(f106(a1),x62721)),f329(f106(a1),x62722))) % 178.07/177.92 [6273]~P24(f329(f329(f244(a1),x62731),x62732))+P24(f329(f329(f244(a1),f329(f109(a1),x62731)),f329(f109(a1),x62732))) % 178.07/177.92 [6274]~P24(f329(f329(f243(a1),x62741),x62742))+P24(f329(f329(f243(a875),f329(f109(a875),x62741)),f329(f109(a875),x62742))) % 178.07/177.92 [6276]~P24(f329(f329(f243(a875),x62761),x62762))+P24(f329(f329(f243(a1),f329(f106(a1),x62761)),f329(f106(a1),x62762))) % 178.07/177.92 [6277]~P24(f329(f329(f243(a1),x62771),x62772))+P24(f329(f329(f243(a1),f329(f109(a1),x62771)),f329(f109(a1),x62772))) % 178.07/177.92 [6278]~P24(f329(f329(f92(a1),x62781),x62782))+P24(f329(f329(f92(a1),f329(f109(a1),x62781)),f329(f109(a1),x62782))) % 178.07/177.92 [6296]~P24(f329(f329(f243(a875),x62961),x62962))+~P24(f329(f329(f243(a875),f329(a118,x62962)),x62961)) % 178.07/177.92 [6341]~P24(f329(f329(f244(a875),f329(a118,x63411)),f329(a118,x63412)))+P24(f329(f329(f244(a875),x63411),x63412)) % 178.07/177.92 [6342]~P24(f329(f329(f244(a105),f329(a3,x63421)),f329(a3,x63422)))+P24(f329(f329(f244(a875),x63421),x63422)) % 178.07/177.92 [6343]~P24(f329(f329(f244(a875),f329(a110,x63431)),f329(a110,x63432)))+P24(f329(f329(f244(a1),x63431),x63432)) % 178.07/177.92 [6344]~P24(f329(f329(f244(a875),f329(a19,x63441)),f329(a19,x63442)))+P24(f329(f329(f244(a105),x63441),x63442)) % 178.07/177.92 [6345]~P24(f329(f329(f243(a875),f329(a118,x63451)),f329(a118,x63452)))+P24(f329(f329(f243(a875),x63451),x63452)) % 178.07/177.92 [6346]~P24(f329(f329(f243(a105),f329(a3,x63461)),f329(a3,x63462)))+P24(f329(f329(f243(a875),x63461),x63462)) % 178.07/177.92 [6347]~P24(f329(f329(f243(a875),f329(a19,x63471)),f329(a19,x63472)))+P24(f329(f329(f243(a105),x63471),x63472)) % 178.07/177.92 [6387]~P24(f329(f329(f244(a875),f329(a110,x63872)),f329(a110,x63871)))+P24(f329(f329(f244(a1),f2(a1)),x63871)) % 178.07/177.92 [6418]P24(f329(f329(f243(a1),f2(a1)),f45(a1,x64181,x64182)))+~P24(f329(f329(f244(a1),f2(a1)),x64182)) % 178.07/177.92 [6576]P38(x65761,x65762)+~E(f329(f329(f286(x65761,x65761,x65761),x65762),x65762),f193(f883(f882(x65761,x65761),a869))) % 178.07/177.92 [6588]~P38(x65881,x65882)+P38(x65881,f329(f329(f286(x65881,x65881,x65881),x65882),x65882)) % 178.07/177.92 [6600]P24(f329(f329(f244(a1),x66001),x66002))+~P24(f329(f329(f243(a1),x66001),f329(f329(f22(a1),x66002),f79(a1)))) % 178.07/177.92 [6601]P24(f329(f329(f243(a1),x66011),x66012))+~P24(f329(f329(f244(a1),x66011),f329(f329(f81(a1),x66012),f79(a1)))) % 178.07/177.92 [6604]P24(f329(f329(f244(a875),x66041),x66042))+~P24(f329(f329(f244(a1),f329(f106(a1),x66041)),f329(f106(a1),x66042))) % 178.07/177.92 [6605]P24(f329(f329(f244(a1),x66051),x66052))+~P24(f329(f329(f244(a875),f329(f109(a875),x66051)),f329(f109(a875),x66052))) % 178.07/177.92 [6606]P24(f329(f329(f244(a1),x66061),x66062))+~P24(f329(f329(f244(a1),f329(f109(a1),x66061)),f329(f109(a1),x66062))) % 178.07/177.92 [6608]P24(f329(f329(f243(a875),x66081),x66082))+~P24(f329(f329(f243(a1),f329(f106(a1),x66081)),f329(f106(a1),x66082))) % 178.07/177.92 [6609]P24(f329(f329(f243(a1),x66091),x66092))+~P24(f329(f329(f243(a1),f329(f109(a1),x66091)),f329(f109(a1),x66092))) % 178.07/177.92 [6610]P24(f329(f329(f92(a1),x66101),x66102))+~P24(f329(f329(f92(a1),f329(f109(a1),x66101)),f329(f109(a1),x66102))) % 178.07/177.92 [6703]~E(f654(x67032,x67031),f119(x67031))+E(f329(f141(f876(x67031),f876(x67031),f127(x67031),f119(x67031)),x67032),f119(x67031)) % 178.07/177.92 [6704]~E(f655(x67042,x67041),f119(x67041))+E(f329(f141(f876(x67041),f876(x67041),f127(x67041),f119(x67041)),x67042),f119(x67041)) % 178.07/177.92 [6711]~P27(x67111)+E(f329(f141(x67111,x67111,f107(x67111),f252(x67111)),x67112),f41(x67111,f329(f171(x67111),x67112))) % 178.07/177.92 [6712]~P27(x67121)+E(f329(f141(x67121,x67121,f116(x67121),f193(x67121)),x67122),f40(x67121,f329(f171(x67121),x67122))) % 178.07/177.92 [6724]E(x67241,f2(a105))+E(f329(f329(f81(a875),f329(a19,f329(f329(f22(a105),x67241),f79(a105)))),f329(a118,x67242)),f329(f329(f81(a875),f329(a19,x67241)),x67242)) % 178.07/177.92 [6774]P24(f329(f329(f244(a1),f329(f329(f22(a1),x67741),x67742)),f2(a1)))+~P24(f329(f329(f244(a1),x67741),x67742)) % 178.07/177.92 [6801]~P105(x68011)+E(f329(f329(f116(f883(x68011,a869)),f329(f329(f307(x68011),x68012),f193(f883(x68011,a869)))),f329(f301(x68011),x68012)),f329(f251(x68011),x68012)) % 178.07/177.92 [6876]~P55(x68761,x68762)+P38(x68761,f329(f249(f882(x68761,x68761)),f329(f268(x68761,x68761,a869),x68762))) % 178.07/177.92 [6877]~P55(x68771,x68772)+P53(x68771,f329(f249(f882(x68771,x68771)),f329(f268(x68771,x68771,a869),x68772))) % 178.07/177.92 [6878]E(x68781,f193(f883(x68782,a869)))+~P24(f329(f329(f243(f883(x68782,a869)),x68781),f193(f883(x68782,a869)))) % 178.07/177.92 [6961]~P24(f329(f329(f244(a875),f2(a875)),x69612))+P24(f329(f329(f244(a875),f45(a875,x69611,x69612)),x69612)) % 178.07/177.92 [6963]~P24(f329(f329(f244(a1),f2(a1)),x69632))+P24(f329(f329(f244(a1),f45(a1,x69631,x69632)),x69632)) % 178.07/177.92 [6964]~P24(f329(f329(f244(a875),f2(a875)),x69642))+P24(f329(f329(f243(a875),f45(a875,x69641,x69642)),x69642)) % 178.07/177.92 [6965]~P24(f329(f329(f243(a1),f2(a1)),x69651))+P24(f329(f329(f243(a1),f45(a1,x69651,x69652)),x69651)) % 178.07/177.92 [7043]~P107(x70431)+E(f329(f329(f22(f883(x70431,a869)),f329(f329(f307(x70431),x70432),f193(f883(x70431,a869)))),f329(f250(x70431),x70432)),f329(f329(f307(x70431),x70432),f193(f883(x70431,a869)))) % 178.07/177.92 [7116]~P49(x71161,x71162)+P40(x71161,f252(f883(x71161,a869)),f329(f249(f882(x71161,x71161)),f329(f268(x71161,x71161,a869),x71162))) % 178.07/177.92 [7117]P24(f329(x71171,x71172))+P24(f329(f329(f331(f883(f882(a875,a875),a869)),f714(x71172,x71171)),a104)) % 178.07/177.92 [7162]E(f329(f329(f127(a875),f138(a875,f329(f299(a875,x71621),x71622))),f329(f329(f150(a875),x71622),f119(a875))),f138(a875,f329(f299(a875,x71621),f329(a118,x71622))))+~P24(f329(f329(f243(a875),x71621),x71622)) % 178.07/177.92 [7303]E(x73031,f2(a875))+~E(f329(f141(a875,a875,f81(a875),x73031),x73032),f2(a875)) % 178.07/177.92 [7331]~P24(f329(f329(f244(a1),f329(f329(f22(a1),x73311),x73312)),f2(a1)))+P24(f329(f329(f244(a1),x73311),x73312)) % 178.07/177.92 [7360]P38(x73601,x73602)+~P38(x73601,f329(f329(f286(x73601,x73601,x73601),x73602),x73602)) % 178.07/177.93 [7390]~P24(f329(f329(f243(a875),f329(a118,x73901)),x73902))+P24(f190(a869,a247,f329(f243(a875),x73901),x73902)) % 178.07/177.93 [7548]P21(a875,a875,f329(f329(f7(a875,a875,a875),f22(a875)),x75481),x75482)+P24(f329(f329(f331(a875),f486(x75481,x75482)),x75482)) % 178.07/177.93 [7604]E(f329(f329(f329(f66(a875,x76041,f81(a875)),f329(f16(a875,x76041),f79(a875))),f2(a875)),x76042),f329(f38(x76041),x76042))+~P24(f329(f62(x76041),x76042)) % 178.07/177.93 [7646]P21(a875,a875,f329(f329(f7(a875,a875,a875),f22(a875)),x76461),x76462)+~P24(f329(f329(f243(a875),x76461),f486(x76461,x76462))) % 178.07/177.93 [7704]P38(x77041,x77042)+P24(f329(f329(f243(f883(x77041,a869)),f712(x77042,x77041)),f329(f283(x77041,x77041,x77042),f712(x77042,x77041)))) % 178.07/177.93 [7709]P55(x77091,x77092)+~P38(x77091,f329(f249(f882(x77091,x77091)),f329(f268(x77091,x77091,a869),x77092))) % 178.07/177.93 [7778]P24(f329(f329(f243(a875),f329(a118,x77781)),x77782))+~P24(f190(a869,a247,f329(f243(a875),x77781),x77782)) % 178.07/177.93 [7832]P24(f329(f329(f331(f882(a875,a875)),f329(f329(f264(a875,a875),x78321),x78322)),f305(a875,a319)))+~P24(f329(f329(f243(a875),x78321),x78322)) % 178.07/177.93 [7929]P49(x79291,x79292)+~P40(x79291,f252(f883(x79291,a869)),f329(f249(f882(x79291,x79291)),f329(f268(x79291,x79291,a869),x79292))) % 178.07/177.93 [7989]~P24(f329(f136(x79891),x79892))+P24(f329(f136(f883(x79891,a869)),f329(f329(f153(f876(x79891),f883(x79891,a869)),f171(x79891)),f54(x79891,x79892)))) % 178.07/177.93 [8194]~P38(x81941,f329(f284(x81941,x81941),x81942))+P38(x81941,f329(f284(x81941,x81941),f329(f329(f286(x81941,x81941,x81941),x81942),f305(x81941,x81942)))) % 178.07/177.93 [8315]P24(f329(f62(f882(x83151,x83151)),f329(f329(f286(x83151,x83151,x83151),x83152),f305(x83151,x83152))))+~P24(f329(f62(f882(x83151,x83151)),x83152)) % 178.07/177.93 [8346]E(x83461,f2(a1))+P24(f329(f49(x83462,x83461),f329(f329(f264(a1,a1),f329(f329(f39(a1),x83462),x83461)),f45(a1,x83462,x83461)))) % 178.07/177.93 [8357]~P24(f329(f329(f331(f882(a875,a875)),f329(f329(f264(a875,a875),x83571),x83572)),f305(a875,a319)))+P24(f329(f329(f243(a875),x83571),x83572)) % 178.07/177.93 [8374]~P80(x83741)+E(f329(f141(x83741,x83741,f329(f7(x83741,x83741,x83741),f81(x83741)),f2(x83741)),f329(f168(x83741),x83742)),f329(f141(x83741,x83741,f81(x83741),f2(x83741)),x83742)) % 178.07/177.93 [8551]~P105(x85511)+E(f329(f141(f876(x85511),x85511,f329(f7(x85511,f876(x85511),f876(x85511)),f147(x85511,x85511,f5(x85511))),f119(x85511)),x85512),f149(x85511,x85511,f5(x85511),x85512)) % 178.07/177.93 [8653]~P53(x86531,f329(f249(f882(x86531,x86531)),f329(f268(x86531,x86531,a869),x86532)))+P53(x86531,f329(f249(f882(x86531,x86531)),f329(f268(x86531,x86531,a869),f253(x86531,x86531,x86532)))) % 178.07/177.93 [8667]P24(f329(f329(f331(f882(a875,a875)),f329(f329(f264(a875,a875),x86671),x86672)),f329(f329(f286(a875,a875,a875),a319),f305(a875,a319))))+~P24(f329(f329(f244(a875),x86671),x86672)) % 178.07/177.93 [8710]~P24(f329(f62(f882(x87101,x87101)),f329(f329(f286(x87101,x87101,x87101),x87102),f305(x87101,x87102))))+P24(f329(f62(f882(x87101,x87101)),x87102)) % 178.07/177.93 [8761]~P53(x87611,f329(f249(f882(x87611,x87611)),f329(f268(x87611,x87611,a869),f253(x87611,x87611,x87612))))+P53(x87611,f329(f249(f882(x87611,x87611)),f329(f268(x87611,x87611,a869),x87612))) % 178.07/177.93 [8962]P53(x89621,x89622)+P24(f329(f329(f331(f882(x89621,x89621)),f329(f329(f264(x89621,x89621),f748(x89622,x89621)),f748(x89622,x89621))),f329(f329(f286(x89621,x89621,x89621),x89622),f305(x89621,x89622)))) % 178.07/177.93 [8963]P53(x89631,x89632)+P24(f329(f329(f331(f882(x89631,x89631)),f329(f329(f264(x89631,x89631),f758(x89632,x89631)),f758(x89632,x89631))),f329(f329(f286(x89631,x89631,x89631),x89632),f305(x89631,x89632)))) % 178.07/177.93 [9080]~P24(f329(f329(f331(f882(a875,a875)),f329(f329(f264(a875,a875),x90801),x90802)),f329(f329(f286(a875,a875,a875),a319),f305(a875,a319))))+P24(f329(f329(f244(a875),x90801),x90802)) % 178.07/177.93 [5049]~P92(x50491)+E(f329(f329(f81(x50491),f329(f109(x50491),a84)),x50492),x50492) % 178.07/177.93 [5077]~P89(x50771)+E(f329(f329(f116(x50771),f329(f80(x50771),x50772)),x50772),f252(x50771)) % 178.07/177.93 [5078]~P89(x50781)+E(f329(f329(f107(x50781),f329(f80(x50781),x50782)),x50782),f193(x50781)) % 178.07/177.93 [5079]~P66(x50791)+E(f329(f329(f81(x50791),f329(f80(x50791),x50792)),x50792),f2(x50791)) % 178.07/177.93 [5080]~P67(x50801)+E(f329(f329(f81(x50801),f329(f80(x50801),x50802)),x50802),f2(x50801)) % 178.07/177.93 [5112]~P92(x51121)+E(f329(f329(f82(x51121),f329(f109(x51121),a103)),x51122),f329(f80(x51121),x51122)) % 178.07/177.93 [5284]~P111(x52841)+E(f329(f329(f82(x52841),f329(f80(x52841),f79(x52841))),x52842),f329(f80(x52841),x52842)) % 178.07/177.93 [5326]E(f329(f76(a1),x53261),f79(a1))+~E(f329(f76(a1),f329(f329(f82(a1),x53261),x53262)),f79(a1)) % 178.07/177.93 [5418]~P92(x54181)+E(f329(f329(f81(x54181),f79(x54181)),f329(f109(x54181),x54182)),f329(f109(x54181),f329(f329(f22(a1),x54182),a103))) % 178.07/177.93 [5471]~P63(x54711)+E(f13(x54711,f329(f329(f307(x54711),x54712),f193(f883(x54711,a869)))),x54712) % 178.07/177.93 [5472]~P63(x54721)+E(f10(x54721,f329(f329(f307(x54721),x54722),f193(f883(x54721,a869)))),x54722) % 178.07/177.93 [5473]~P27(x54731)+E(f41(x54731,f329(f329(f307(x54731),x54732),f193(f883(x54731,a869)))),x54732) % 178.07/177.93 [5474]~P27(x54741)+E(f40(x54741,f329(f329(f307(x54741),x54742),f193(f883(x54741,a869)))),x54742) % 178.07/177.93 [5475]~P105(x54751)+E(f14(x54751,f329(f329(f307(x54751),x54752),f193(f883(x54751,a869)))),x54752) % 178.07/177.93 [5476]~P105(x54761)+E(f15(x54761,f329(f329(f307(x54761),x54762),f193(f883(x54761,a869)))),x54762) % 178.07/177.93 [5498]E(f329(f329(f81(a875),x54981),f329(f329(f22(a875),x54982),x54981)),x54982)+P24(f329(f329(f244(a875),x54982),x54981)) % 178.07/177.93 [5528]E(x55281,f119(x55282))+P24(f329(f329(f244(a875),f2(a875)),f329(f194(f876(x55282)),x55281))) % 178.07/177.93 [5652]~P105(x56521)+E(f11(x56521,f242(x56521),f329(f329(f307(x56521),x56522),f193(f883(x56521,a869)))),x56522) % 178.07/177.93 [5653]~P105(x56531)+E(f12(x56531,f241(x56531),f329(f329(f307(x56531),x56532),f193(f883(x56531,a869)))),x56532) % 178.07/177.93 [5715]E(f329(f329(f22(a875),x57151),f329(f329(f22(a875),x57151),x57152)),x57152)+~P24(f329(f329(f243(a875),x57152),x57151)) % 178.07/177.93 [5716]E(f329(f329(f81(a875),x57161),f329(f329(f22(a875),x57162),x57161)),x57162)+~P24(f329(f329(f243(a875),x57161),x57162)) % 178.07/177.93 [5737]E(f45(a875,f329(f329(f22(a875),x57371),x57372),x57372),f45(a875,x57371,x57372))+P24(f329(f329(f244(a875),x57371),x57372)) % 178.07/177.93 [5748]E(f329(f80(a1),f329(f329(f39(a1),x57481),f329(f80(a1),x57482))),f289(x57481,x57482))+P24(f329(f329(f243(a1),f2(a1)),x57482)) % 178.07/177.93 [5750]~E(x57502,f2(a875))+P24(f329(f329(f244(a875),f2(a875)),f329(f329(f254(a875),x57501),x57502))) % 178.07/177.93 [5801]~P92(x58011)+E(f329(f329(f81(x58011),f329(f80(x58011),f79(x58011))),f329(f109(x58011),x58012)),f329(f109(x58011),f329(f329(f81(a1),x58012),a103))) % 178.07/177.93 [5802]E(f329(f329(f254(a875),f329(f109(a875),x58021)),x58022),f329(f329(f254(a875),f2(a875)),x58022))+~P24(f329(a198,f329(f109(a1),x58021))) % 178.07/177.93 [5899]E(f329(f140(a875),f138(a875,f329(f299(a875,x58991),x58992))),x58991)+~P24(f329(f329(f244(a875),x58991),x58992)) % 178.07/177.93 [5919]E(f329(f329(f82(a875),f329(f109(a875),x59191)),f329(f109(a875),x59192)),f329(f109(a875),f329(f329(f82(a1),x59191),x59192)))+P24(f329(f329(f244(a1),x59191),a84)) % 178.07/177.93 [5925]~P122(x59251)+P24(f329(f329(f243(x59251),f2(x59251)),f329(f329(f82(x59251),x59252),x59252))) % 178.07/177.93 [5937]E(f329(f329(f22(a875),f329(a118,x59371)),x59372),f329(a118,f329(f329(f22(a875),x59371),x59372)))+~P24(f329(f329(f243(a875),x59372),x59371)) % 178.07/177.93 [5940]E(f45(a875,f329(f329(f22(a875),x59401),x59402),x59402),f45(a875,x59401,x59402))+~P24(f329(f329(f243(a875),x59402),x59401)) % 178.07/177.93 [5994]E(f329(f329(f254(a875),f329(a110,x59941)),x59942),f329(a110,f329(f329(f254(a1),x59941),x59942)))+~P24(f329(f329(f243(a1),f2(a1)),x59941)) % 178.07/177.93 [6010]P24(f329(f136(x60101),x60102))+P24(f329(f329(f244(a875),f567(x60102,x60101)),f329(f194(f876(x60101)),x60102))) % 178.07/177.93 [6011]P24(f329(f136(x60111),x60112))+P24(f329(f329(f244(a875),f578(x60112,x60111)),f329(f194(f876(x60111)),x60112))) % 178.07/177.93 [6026]~E(x60261,f119(x60262))+~P24(f329(f329(f244(a875),f2(a875)),f329(f194(f876(x60262)),x60261))) % 178.07/177.93 [6040]E(f143(a875,f138(a875,f329(f299(a875,x60401),x60402))),f329(f329(f22(a875),x60402),f79(a875)))+~P24(f329(f329(f244(a875),x60401),x60402)) % 178.07/177.93 [6043]E(f329(f329(f81(a1),x60431),f329(f106(a1),f329(a118,f378(x60432,x60431)))),x60432)+~P24(f329(f329(f244(a1),x60431),x60432)) % 178.07/177.93 [6050]E(x60501,f2(a875))+E(f329(f329(f82(a875),x60502),f329(f329(f254(a875),x60502),f329(f329(f22(a875),x60501),f79(a875)))),f329(f329(f254(a875),x60502),x60501)) % 178.07/177.93 [6076]E(f329(f329(f82(a875),f329(a110,x60761)),f329(a110,x60762)),f329(a110,f329(f329(f82(a1),x60761),x60762)))+~P24(f329(f329(f243(a1),f2(a1)),x60761)) % 178.07/177.93 [6077]E(f329(f329(f39(a875),f329(a110,x60771)),f329(a110,x60772)),f329(a110,f329(f329(f39(a1),x60771),x60772)))+~P24(f329(f329(f243(a1),f2(a1)),x60771)) % 178.07/177.93 [6091]~P114(x60911)+E(f329(f329(f81(x60911),x60912),x60912),f329(f329(f82(x60911),f329(f329(f81(x60911),f79(x60911)),f79(x60911))),x60912)) % 178.07/177.93 [6108]E(f329(f329(f22(a1),f329(f106(a1),x61081)),f329(f106(a1),x61082)),f329(f106(a1),f329(f329(f22(a875),x61081),x61082)))+~P24(f329(f329(f243(a875),x61082),x61081)) % 178.07/177.93 [6110]E(f329(f329(f264(a1,a1),f329(f109(a1),a103)),f329(f329(f81(a1),x61101),x61102)),f50(x61101,x61102))+~P24(f329(f329(f243(a1),x61102),f2(a1))) % 178.07/177.93 [6150]E(f179(x61501,x61502),f119(f876(x61501)))+P24(f329(f329(f331(f876(x61501)),f619(x61502,x61501)),f329(f171(f876(x61501)),x61502))) % 178.07/177.93 [6233]E(f329(f329(f150(a1),x62331),f178(f329(f329(f81(a1),x62331),f79(a1)),x62332)),f178(x62331,x62332))+~P24(f329(f329(f243(a1),x62331),x62332)) % 178.07/177.93 [6270]~P24(f329(f329(f244(a875),x62702),x62701))+P24(f329(f329(f244(a875),f2(a875)),f329(f329(f22(a875),x62701),x62702))) % 178.07/177.93 [6301]~P24(f329(f329(f244(a875),x63011),f329(a110,x63012)))+P24(f329(f329(f244(a1),f329(f106(a1),x63011)),x63012)) % 178.07/177.93 [6332]~P105(x63321)+E(f329(f329(f116(f883(x63321,a869)),f329(f250(x63321),x63322)),f329(f329(f307(x63321),x63322),f193(f883(x63321,a869)))),f329(f298(x63321),x63322)) % 178.07/177.93 [6335]~P24(f329(f329(f244(a875),f2(a875)),x63351))+P24(f329(f329(f244(a875),f2(a875)),f329(f329(f254(a875),x63351),x63352))) % 178.07/177.93 [6336]~P24(f329(f329(f243(a1),f2(a1)),x63361))+P24(f329(f329(f243(a1),f2(a1)),f329(f329(f254(a1),x63361),x63362))) % 178.07/177.93 [6363]~E(f329(x63631,f2(a875)),f2(a875))+E(f329(f329(f6(a875,a875),x63631),f300(a875,f329(a118,f2(a875)),x63632)),f329(f329(f6(a875,a875),x63631),f300(a875,f2(a875),x63632))) % 178.07/177.93 [6426]~P92(x64261)+E(f329(f329(f82(x64261),f329(f329(f81(x64261),f79(x64261)),f79(x64261))),f329(f109(x64261),x64262)),f329(f109(x64261),f329(f329(f81(a1),x64262),x64262))) % 178.07/177.93 [6442]E(f329(f329(f307(a1),x64421),f300(a1,f329(f329(f81(a1),x64421),f79(a1)),x64422)),f300(a1,x64421,x64422))+P24(f329(f329(f244(a1),x64422),x64421)) % 178.07/177.93 [6443]P24(f329(f329(f244(a875),x64431),f329(a110,x64432)))+~P24(f329(f329(f244(a1),f329(f106(a1),x64431)),x64432)) % 178.07/177.93 [6544]E(f329(a110,f329(f329(f39(a1),f329(f109(a1),x65441)),f329(f109(a1),x65442))),f329(f329(f39(a875),f329(f109(a875),x65441)),f329(f109(a875),x65442)))+P24(f329(a198,f329(f109(a1),x65441))) % 178.07/177.93 [6602]P24(f329(f329(f244(a875),x66021),x66022))+~P24(f329(f329(f244(a875),f2(a875)),f329(f329(f22(a875),x66022),x66021))) % 178.07/177.93 [6646]P24(f329(f329(f244(a875),f2(a875)),x66461))+~P24(f329(f329(f244(a875),f2(a875)),f329(f329(f82(a875),x66462),x66461))) % 178.07/177.93 [6647]P24(f329(f329(f244(a875),f2(a875)),x66471))+~P24(f329(f329(f244(a875),f2(a875)),f329(f329(f82(a875),x66471),x66472))) % 178.07/177.93 [6664]~P24(f329(f329(f243(a1),x66641),f2(a1)))+E(f329(f329(f82(a875),f329(a110,f329(f80(a1),x66641))),f329(a110,f329(f80(a1),x66642))),f329(a110,f329(f329(f82(a1),x66641),x66642))) % 178.07/177.93 [6722]~E(x67222,f193(f883(x67221,a869)))+P24(f329(f329(f243(f883(x67221,a869)),x67222),f329(f80(f883(x67221,a869)),x67222))) % 178.07/177.93 [6785]~P92(x67851)+E(f329(f329(f81(x67851),f329(f329(f81(x67851),f2(x67851)),f329(f109(x67851),x67852))),f329(f109(x67851),x67852)),f329(f109(x67851),f329(f329(f81(a1),x67852),x67852))) % 178.07/177.93 [6841]~P24(f329(f329(f244(a1),x68411),x68412))+P24(f329(f329(f243(a1),f329(f329(f81(a1),x68411),f79(a1))),x68412)) % 178.07/177.93 [6908]E(x69081,f2(a875))+~P24(f329(f329(f243(a1),f329(f106(a1),x69082)),f329(f80(a1),f329(f106(a1),x69081)))) % 178.07/177.93 [6909]E(x69091,f2(a875))+~P24(f329(f329(f243(a1),f329(f106(a1),x69091)),f329(f80(a1),f329(f106(a1),x69092)))) % 178.07/177.93 [7014]E(f329(f329(f264(a1,a1),f329(f109(a1),a103)),f329(f329(f81(a1),x70141),x70142)),f50(x70141,x70142))+~P24(f329(f329(f243(a1),f2(a1)),f329(f329(f81(a1),x70141),x70142))) % 178.07/177.93 [7056]~P22(x70561,x70562)+P38(x70561,f329(f263(f883(f882(x70561,x70561),a869),f883(f882(x70561,x70561),a869)),x70562)) % 178.07/177.93 [7074]~P24(f329(f329(f243(a875),f329(a118,f2(a875))),x70741))+P24(f329(f329(f243(a875),f329(a118,f2(a875))),f329(f329(f254(a875),x70741),x70742))) % 178.07/177.93 [7237]~P24(f329(f329(f244(a1),x72371),x72372))+P24(f329(f329(f244(a1),f329(f329(f81(a1),x72371),x72371)),f329(f329(f81(a1),x72372),x72372))) % 178.07/177.93 [7249]~P24(f329(f329(f243(a1),x72491),x72492))+P24(f329(f329(f243(a1),f329(f329(f81(a1),x72491),x72491)),f329(f329(f81(a1),x72492),x72492))) % 178.07/177.93 [7250]~P24(f329(f329(f92(a1),x72501),x72502))+P24(f329(f329(f92(a1),f329(f329(f81(a1),x72501),x72501)),f329(f329(f81(a1),x72502),x72502))) % 178.07/177.93 [7305]~P24(f329(f329(f244(a875),f2(a875)),x73051))+P24(f329(f329(f244(a875),f329(f329(f22(a875),x73051),f329(a118,x73052))),x73051)) % 178.07/177.93 [7342]P24(f329(f329(f243(a875),f329(a118,f2(a875))),x73421))+~P24(f329(f329(f243(a875),f329(a118,f2(a875))),f329(f329(f82(a875),x73422),x73421))) % 178.07/177.93 [7343]P24(f329(f329(f243(a875),f329(a118,f2(a875))),x73431))+~P24(f329(f329(f243(a875),f329(a118,f2(a875))),f329(f329(f82(a875),x73431),x73432))) % 178.07/177.93 [7347]P24(f329(f329(f243(a875),f329(f329(f164(a875),x73471),x73472)),f329(f165(a875),x73471)))+~P24(f329(f329(f244(a875),x73472),f329(f194(f876(a875)),x73471))) % 178.07/177.93 [7389]P24(f329(f329(f244(a1),x73891),x73892))+~P24(f329(f329(f243(a1),f329(f329(f81(a1),x73891),f79(a1))),x73892)) % 178.07/177.93 [7434]P24(f329(f62(x74341),f252(f883(x74341,a869))))+~P24(f329(f62(f883(x74342,x74341)),f252(f883(f883(x74342,x74341),a869)))) % 178.07/177.93 [7435]P24(f329(f62(x74351),f252(f883(x74351,a869))))+~P24(f329(f62(f881(x74352,x74351)),f252(f883(f881(x74352,x74351),a869)))) % 178.07/177.93 [7436]P24(f329(f62(x74361),f252(f883(x74361,a869))))+~P24(f329(f62(f881(x74361,x74362)),f252(f883(f881(x74361,x74362),a869)))) % 178.07/177.93 [7478]E(x74781,f193(f883(x74782,a869)))+~P24(f329(f329(f243(f883(x74782,a869)),x74781),f329(f80(f883(x74782,a869)),x74781))) % 178.07/177.93 [7614]E(f329(f141(f876(x76141),f876(x76141),f127(x76141),f119(x76141)),x76142),f119(x76141))+P24(f329(f329(f331(f876(x76141)),f654(x76142,x76141)),f329(f171(f876(x76141)),x76142))) % 178.07/177.93 [7615]E(f329(f141(f876(x76151),f876(x76151),f127(x76151),f119(x76151)),x76152),f119(x76151))+P24(f329(f329(f331(f876(x76151)),f655(x76152,x76151)),f329(f171(f876(x76151)),x76152))) % 178.07/177.93 [7851]P24(f329(f329(f244(a1),x78511),x78512))+~P24(f329(f329(f244(a1),f329(f329(f81(a1),x78511),x78511)),f329(f329(f81(a1),x78512),x78512))) % 178.07/177.93 [7854]P24(f329(f329(f243(a1),x78541),x78542))+~P24(f329(f329(f243(a1),f329(f329(f81(a1),x78541),x78541)),f329(f329(f81(a1),x78542),x78542))) % 178.07/177.93 [7855]P24(f329(f329(f92(a1),x78551),x78552))+~P24(f329(f329(f92(a1),f329(f329(f81(a1),x78551),x78551)),f329(f329(f81(a1),x78552),x78552))) % 178.07/177.93 [7949]~P114(x79491)+E(f329(f329(f82(x79491),f329(f329(f81(x79491),f79(x79491)),f79(x79491))),f329(f329(f6(a875,x79491),f106(x79491)),f300(a875,f79(a875),x79492))),f329(f329(f82(x79491),f329(f106(x79491),x79492)),f329(f329(f81(x79491),f329(f106(x79491),x79492)),f79(x79491)))) % 178.07/177.93 [8005]P24(f329(f329(f331(a875),x80051),x80052))+~P24(f329(f329(f331(a1),f329(f106(a1),x80051)),f329(f308(a875,a1,f106(a1)),x80052))) % 178.07/177.93 [8165]~P24(f329(f62(x81651),x81652))+E(f329(f308(a875,x81651,f488(x81652,x81651)),f329(f249(a875),f329(f329(f7(a875,a875,a869),f244(a875)),f489(x81652,x81651)))),x81652) % 178.07/177.93 [8453]P42(x84531,x84532)+P24(f329(f329(f331(f882(x84531,x84531)),f329(f329(f264(x84531,x84531),f549(x84532,x84531)),f549(x84532,x84531))),x84532)) % 178.07/177.93 [8592]~P92(x85921)+E(f329(f329(f22(x85921),f79(x85921)),f329(f109(x85921),x85922)),f329(f109(x85921),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f80(a1),x85922)))) % 178.07/177.93 [8706]~P24(f329(f329(f244(f883(a875,a869)),x87061),x87062))+P24(f329(f329(f244(f883(a1,a869)),f329(f308(a875,a1,f106(a1)),x87061)),f329(f308(a875,a1,f106(a1)),x87062))) % 178.07/177.93 [8735]~P24(f329(f329(f244(a1),x87351),x87352))+P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f81(a1),x87351),x87351)),a103)),f329(f329(f81(a1),x87352),x87352))) % 178.07/177.93 [8737]~P24(f329(f329(f244(a1),x87371),x87372))+P24(f329(f329(f243(a1),f329(f329(f22(a1),f329(f329(f81(a1),x87371),x87371)),a103)),f329(f329(f81(a1),x87372),x87372))) % 178.07/177.93 [8807]~P24(f329(f329(f331(a875),x88071),f329(f171(a875),x88072)))+P24(f329(f329(f243(a875),x88071),f329(f141(a875,a875,f81(a875),f2(a875)),x88072))) % 178.07/177.93 [8899]P46(x88991,x88992)+~P24(f329(f329(f331(f882(x88991,x88991)),f329(f329(f264(x88991,x88991),f542(x88992,x88991)),f542(x88992,x88991))),x88992)) % 178.07/177.93 [8978]P20(a871,x89781,f329(f329(f307(f874(a871)),f329(a94,f329(a26,x89782))),f193(f883(f874(a871),a869))))+~P20(a871,f329(f329(f307(f874(a871)),f329(a94,f329(a26,x89782))),x89781),f329(f329(f307(f874(a871)),f329(a94,f329(f240(a870),f329(a28,x89782)))),f193(f883(f874(a871),a869)))) % 178.07/177.93 [9046]~P24(f329(f329(f244(f883(a1,a869)),f329(f308(a875,a1,f106(a1)),x90461)),f329(f308(a875,a1,f106(a1)),x90462)))+P24(f329(f329(f244(f883(a875,a869)),x90461),x90462)) % 178.07/177.93 [9047]~P24(f329(f329(f243(f883(a1,a869)),f329(f308(a875,a1,f106(a1)),x90471)),f329(f308(a875,a1,f106(a1)),x90472)))+P24(f329(f329(f243(f883(a875,a869)),x90471),x90472)) % 178.07/177.93 [9127]P24(f329(f329(f244(a1),x91271),x91272))+~P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f81(a1),x91271),x91271)),a103)),f329(f329(f81(a1),x91272),x91272))) % 178.07/177.93 [9129]P24(f329(f329(f244(a1),x91291),x91292))+~P24(f329(f329(f243(a1),f329(f329(f22(a1),f329(f329(f81(a1),x91291),x91291)),a103)),f329(f329(f81(a1),x91292),x91292))) % 178.07/177.93 [10032]~P24(f329(f62(x100321),x100322))+E(f329(f194(f876(x100321)),f91(f876(x100321),f329(f329(f18(f876(x100321),a869,a869),f329(f329(f8(a869,f883(a869,a869),f876(x100321)),a327),f329(f329(f7(f876(x100321),f883(x100321,a869),a869),f329(f329(f8(f883(x100321,a869),f883(f883(x100321,a869),a869),f876(x100321)),a326),f171(x100321))),x100322))),f136(x100321)))),f222(x100321,x100322)) % 178.07/177.93 [10168]~P20(a871,x101681,f329(f329(f307(f874(a871)),f329(a94,x101682)),f193(f883(f874(a871),a869))))+P20(a871,x101681,f329(f329(f307(f874(a871)),f329(f329(f329(f93(a871),f329(f329(f8(f883(a871,f883(a871,a869)),f883(a871,a869),a871),f329(f8(f883(a871,a869),a869,a871),f89(a871))),f329(f329(f8(f883(a871,a869),f883(a871,f883(a871,a869)),a871),f329(f7(a871,f883(a871,a869),f883(a871,a869)),f329(f329(f8(f883(a871,f883(a869,a869)),f883(f883(a871,a869),f883(a871,a869)),a871),f18(a871,a869,a869)),f329(f329(f8(f883(a871,a869),f883(a871,f883(a869,a869)),a871),f329(f8(a869,f883(a869,a869),a871),a332)),f199(x101682))))),a326))),x101682),a326)),f193(f883(f874(a871),a869)))) % 178.07/177.93 [6039]E(f329(f329(f81(a875),f329(f329(f22(a875),x60391),x60392)),x60392),x60391)+~P24(f329(f329(f243(a875),x60392),x60391)) % 178.07/177.93 [6104]E(f329(f329(f39(a875),f329(f329(f82(a875),x61041),x61042)),x61042),x61041)+~P24(f329(f329(f244(a875),f2(a875)),x61042)) % 178.07/177.93 [6105]E(f329(f329(f39(a875),f329(f329(f82(a875),x61051),x61052)),x61051),x61052)+~P24(f329(f329(f244(a875),f2(a875)),x61051)) % 178.07/177.93 [6109]~P70(x61091)+E(f329(f329(f6(a875,x61091),f329(f164(x61091),x61092)),f329(f299(a875,f2(a875)),f329(f194(f876(x61091)),x61092))),f329(f165(x61091),x61092)) % 178.07/177.93 [6225]E(f45(a875,f329(a118,f329(f329(f82(a875),x62251),x62252)),x62251),f79(a875))+~P24(f329(f329(f244(a875),f79(a875)),x62251)) % 178.07/177.93 [6231]E(f329(a118,f329(f329(f81(a875),f329(f109(a875),x62311)),x62312)),f329(f329(f81(a875),f79(a875)),x62312))+~P24(f329(a198,f329(f109(a1),x62311))) % 178.07/177.93 [6259]E(f329(a110,f329(f329(f254(a1),f329(f109(a1),x62591)),x62592)),f329(f329(f254(a875),f329(f109(a875),x62591)),x62592))+P24(f329(a198,f329(f109(a1),x62591))) % 178.07/177.93 [6496]E(f329(f329(f22(a875),x64961),f329(f109(a875),f329(f329(f81(a1),x64962),a103))),f329(f329(f22(a875),f329(a118,x64961)),f329(f109(a875),x64962)))+~P24(f329(f329(f244(a1),a84),x64962)) % 178.07/177.93 [6575]E(x65751,f2(a875))+E(f329(a118,f329(f329(f81(a875),f329(f329(f22(a875),x65751),f79(a875))),x65752)),f329(f329(f81(a875),x65751),x65752)) % 178.07/177.93 [6616]E(x66161,f2(a1))+P24(f329(f329(f244(a1),f2(a1)),f329(f329(f254(a1),f329(f76(a1),x66161)),x66162))) % 178.07/177.93 [6631]~E(x66312,f2(a875))+P24(f329(f329(f244(a1),f2(a1)),f329(f329(f254(a1),f329(f76(a1),x66311)),x66312))) % 178.07/177.93 [6668]E(x66681,f2(a875))+E(f329(f329(f81(a875),x66682),f329(f329(f82(a875),f329(f329(f22(a875),x66681),f79(a875))),x66682)),f329(f329(f82(a875),x66681),x66682)) % 178.07/177.93 [6716]~P24(f329(f329(f243(a1),x67161),x67162))+P24(f329(f329(f244(a1),f329(f329(f81(a1),x67161),a103)),x67162)) % 178.07/177.93 [6844]E(f329(f329(f150(a875),x68441),f138(a875,f329(f299(a875,f329(a118,x68441)),x68442))),f138(a875,f329(f299(a875,x68441),x68442)))+~P24(f329(f329(f244(a875),x68441),x68442)) % 178.07/177.93 [7047]E(x70471,x70472)+~E(f329(f329(f22(a1),f329(f329(f81(a1),x70471),x70471)),a103),f329(f329(f22(a1),f329(f329(f81(a1),x70472),x70472)),a103)) % 178.07/177.93 [7050]E(x70501,f119(x70502))+E(f273(x70502,f329(f329(f153(x70502,f882(a105,x70502)),f329(f264(a105,x70502),f79(a105))),x70501)),f280(x70502,x70501)) % 178.07/177.93 [7274]P24(f329(f329(f243(a1),x72741),x72742))+~P24(f329(f329(f244(a1),f329(f329(f81(a1),x72741),a103)),x72742)) % 178.07/177.93 [7755]~P24(f329(f329(f244(a875),x77551),x77552))+P24(f329(f329(f331(f882(a875,a875)),f329(f329(f264(a875,a875),x77551),x77552)),a248)) % 178.07/177.93 [7977]~P24(f329(f329(f244(a105),f2(a105)),x79771))+P24(f329(f329(f244(a105),f329(f263(a105,f882(a105,a105)),f329(f274(x79771),x79772))),x79771)) % 178.07/177.93 [8293]~P85(x82931)+P24(f329(f329(f243(x82931),f329(f76(x82931),f329(f165(x82931),x82932))),f329(f165(x82931),f329(f329(f153(x82931,x82931),f76(x82931)),x82932)))) % 178.07/177.93 [8317]P24(f329(f329(f244(a875),x83171),x83172))+~P24(f329(f329(f331(f882(a875,a875)),f329(f329(f264(a875,a875),x83171),x83172)),a248)) % 178.07/177.93 [8476]E(f329(f329(f264(x84761,x84761),f757(x84762,x84761)),f757(x84762,x84761)),x84762)+~P24(f329(f329(f331(f882(x84761,x84761)),x84762),f305(x84761,f193(f883(f882(x84761,x84761),a869))))) % 178.07/177.93 [8517]E(f329(f299(a875,x85171),f329(f329(f81(a875),x85171),f329(f38(a875),x85172))),x85172)+~P24(f329(f329(f243(f883(a875,a869)),x85172),f329(f299(a875,x85171),f329(f329(f81(a875),x85171),f329(f38(a875),x85172))))) % 178.07/177.93 [8846]E(f329(f329(f39(a1),f329(f109(a1),f329(f329(f22(a1),f329(f329(f81(a1),x88461),x88461)),a103))),f329(f109(a1),f329(f329(f81(a1),x88462),x88462))),f329(f329(f39(a1),f329(f109(a1),x88461)),f329(f109(a1),x88462)))+~P24(f329(f329(f243(a1),f2(a1)),f329(f109(a1),x88462))) % 178.07/177.93 [8973]E(f176(f876(x89731),f329(f329(f8(a869,a869,f876(x89731)),a324),f329(f329(f7(f876(x89731),f876(x89731),a869),a326),f119(x89731))),x89732),f179(x89731,f179(x89731,x89732)))+~P29(a875,f329(f168(a875),f329(f329(f153(f876(x89731),a875),f194(f876(x89731))),x89732))) % 178.07/177.93 [8976]E(f329(f329(f39(a1),f329(f109(a1),f329(f329(f22(a1),f329(f329(f81(a1),x89761),x89761)),a103))),f329(f109(a1),f329(f329(f81(a1),x89762),x89762))),f329(f329(f39(a1),f329(f329(f81(a1),f329(f109(a1),x89761)),f79(a1))),f329(f109(a1),x89762)))+P24(f329(f329(f243(a1),f2(a1)),f329(f109(a1),x89762))) % 178.07/177.93 [9808]P24(f329(a198,x98082))+E(f329(f329(f87(a1,a875),f329(f329(f22(a1),x98081),x98082)),f329(f329(f18(a1,a875,a875),f329(f329(f7(a1,a875,f883(a875,a875)),f329(f329(f8(a869,f883(a875,f883(a875,a875)),a1),f102(a875)),a198)),f2(a875))),a110)),f329(f329(f22(a875),f329(a110,x98081)),f329(a110,x98082))) % 178.07/177.93 [9816]E(f329(f329(f87(a1,a875),f329(f109(a1),f329(f329(f81(a1),x98161),f329(f80(a1),x98162)))),f329(f329(f18(a1,a875,a875),f329(f329(f7(a1,a875,f883(a875,a875)),f329(f329(f8(a869,f883(a875,f883(a875,a875)),a1),f102(a875)),a198)),f2(a875))),a110)),f329(f329(f22(a875),f329(f109(a875),x98161)),f329(f109(a875),x98162)))+P24(f329(f329(f244(a1),x98162),a84)) % 178.07/177.93 [9817]~P22(x98171,x98172)+P24(f329(f329(f243(f883(f882(x98171,x98171),a869)),f329(f329(f286(x98171,x98171,x98171),f329(f263(f883(f882(x98171,x98171),a869),f883(f882(x98171,x98171),a869)),x98172)),f329(f267(f883(f882(x98171,x98171),a869),f883(f882(x98171,x98171),a869)),x98172))),f329(f263(f883(f882(x98171,x98171),a869),f883(f882(x98171,x98171),a869)),x98172))) % 178.07/177.93 [9883]~E(f329(f38(a875),f329(f249(a875),f329(f329(f18(a875,a869,a869),f329(f329(f8(a869,f883(a869,a869),a875),a327),f329(f329(f7(a875,f883(a875,a869),a869),f331(a875)),x98831))),f329(f329(f7(a875,a875,a869),f244(a875)),f329(a118,x98832))))),f2(a875))+~P24(f329(f329(f331(a875),f2(a875)),x98831)) % 178.07/177.93 [9939]E(f45(a1,f329(f109(a1),f329(f329(f22(a1),f329(f329(f81(a1),x99391),x99391)),a103)),f329(f109(a1),f329(f329(f81(a1),x99392),x99392))),f329(f329(f81(a1),f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f45(a1,f329(f109(a1),x99391),f329(f109(a1),x99392)))),f79(a1)))+~P24(f329(f329(f243(a1),f2(a1)),f329(f109(a1),x99392))) % 178.07/177.93 [9948]E(f45(a1,f329(f109(a1),f329(f329(f22(a1),f329(f329(f81(a1),x99481),x99481)),a103)),f329(f109(a1),f329(f329(f81(a1),x99482),x99482))),f329(f329(f22(a1),f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f45(a1,f329(f329(f81(a1),f329(f109(a1),x99481)),f79(a1)),f329(f109(a1),x99482)))),f79(a1)))+P24(f329(f329(f243(a1),f2(a1)),f329(f109(a1),x99482))) % 178.07/177.93 [10000]~P27(x100001)+E(f40(x100001,f329(f249(x100001),f329(f329(f8(f883(x100001,a869),a869,x100001),f89(x100001)),f329(f329(f8(f883(x100001,a869),f883(x100001,a869),x100001),f329(f18(x100001,a869,a869),f329(f329(f8(a869,f883(a869,a869),x100001),a332),f329(f329(f7(x100001,f883(x100001,a869),a869),f331(x100001)),x100002)))),f243(x100001))))),f41(x100001,x100002)) % 178.07/177.93 [10025]~P38(x100251,x100252)+P55(x100251,f329(f329(f7(x100251,f883(f882(x100251,x100251),a869),f883(x100251,a869)),f329(f329(f8(f883(x100251,f883(f883(f882(x100251,x100251),a869),a869)),f883(f883(f882(x100251,x100251),a869),f883(x100251,a869)),x100251),f7(x100251,f883(f882(x100251,x100251),a869),a869)),f329(f329(f8(f883(x100251,f882(x100251,x100251)),f883(x100251,f883(f883(f882(x100251,x100251),a869),a869)),x100251),f329(f8(f882(x100251,x100251),f883(f883(f882(x100251,x100251),a869),a869),x100251),f331(f882(x100251,x100251)))),f264(x100251,x100251)))),x100252)) % 178.07/177.93 [10026]~P6(x100261,f252(f883(x100261,a869)),x100262)+P5(x100261,f329(f329(f7(x100261,f883(f882(x100261,x100261),a869),f883(x100261,a869)),f329(f329(f8(f883(x100261,f883(f883(f882(x100261,x100261),a869),a869)),f883(f883(f882(x100261,x100261),a869),f883(x100261,a869)),x100261),f7(x100261,f883(f882(x100261,x100261),a869),a869)),f329(f329(f8(f883(x100261,f882(x100261,x100261)),f883(x100261,f883(f883(f882(x100261,x100261),a869),a869)),x100261),f329(f8(f882(x100261,x100261),f883(f883(f882(x100261,x100261),a869),a869),x100261),f331(f882(x100261,x100261)))),f264(x100261,x100261)))),x100262)) % 178.07/177.93 [10063]P38(x100631,x100632)+~P55(x100631,f329(f329(f7(x100631,f883(f882(x100631,x100631),a869),f883(x100631,a869)),f329(f329(f8(f883(x100631,f883(f883(f882(x100631,x100631),a869),a869)),f883(f883(f882(x100631,x100631),a869),f883(x100631,a869)),x100631),f7(x100631,f883(f882(x100631,x100631),a869),a869)),f329(f329(f8(f883(x100631,f882(x100631,x100631)),f883(x100631,f883(f883(f882(x100631,x100631),a869),a869)),x100631),f329(f8(f882(x100631,x100631),f883(f883(f882(x100631,x100631),a869),a869),x100631),f331(f882(x100631,x100631)))),f264(x100631,x100631)))),x100632)) % 178.07/177.93 [10064]P6(x100641,f252(f883(x100641,a869)),x100642)+~P5(x100641,f329(f329(f7(x100641,f883(f882(x100641,x100641),a869),f883(x100641,a869)),f329(f329(f8(f883(x100641,f883(f883(f882(x100641,x100641),a869),a869)),f883(f883(f882(x100641,x100641),a869),f883(x100641,a869)),x100641),f7(x100641,f883(f882(x100641,x100641),a869),a869)),f329(f329(f8(f883(x100641,f882(x100641,x100641)),f883(x100641,f883(f883(f882(x100641,x100641),a869),a869)),x100641),f329(f8(f882(x100641,x100641),f883(f883(f882(x100641,x100641),a869),a869),x100641),f331(f882(x100641,x100641)))),f264(x100641,x100641)))),x100642)) % 178.07/177.93 [7225]E(f329(f329(f81(a875),f329(f109(a875),f329(f329(f22(a1),x72251),a103))),x72252),f329(a118,f329(f329(f81(a875),f329(f109(a875),x72251)),x72252)))+P24(f329(a198,f329(f109(a1),x72251))) % 178.07/177.93 [7672]~P92(x76721)+E(f329(f329(f81(x76721),f329(f329(f81(x76721),f79(x76721)),f329(f109(x76721),x76722))),f329(f109(x76721),x76722)),f329(f109(x76721),f329(f329(f22(a1),f329(f329(f81(a1),x76722),x76722)),a103))) % 178.07/177.93 [8319]~P24(f329(f329(f243(a1),x83191),x83192))+P24(f329(f329(f244(a1),f329(f329(f81(a1),x83191),x83191)),f329(f329(f22(a1),f329(f329(f81(a1),x83192),x83192)),a103))) % 178.07/177.93 [8321]~P24(f329(f329(f243(a1),x83211),x83212))+P24(f329(f329(f243(a1),f329(f329(f81(a1),x83211),x83211)),f329(f329(f22(a1),f329(f329(f81(a1),x83212),x83212)),a103))) % 178.07/177.93 [8739]P24(f329(f329(f243(a1),x87391),x87392))+~P24(f329(f329(f244(a1),f329(f329(f81(a1),x87391),x87391)),f329(f329(f22(a1),f329(f329(f81(a1),x87392),x87392)),a103))) % 178.07/177.93 [8741]P24(f329(f329(f243(a1),x87411),x87412))+~P24(f329(f329(f243(a1),f329(f329(f81(a1),x87411),x87411)),f329(f329(f22(a1),f329(f329(f81(a1),x87412),x87412)),a103))) % 178.07/177.93 [9034]~P24(f329(f329(f244(a1),x90341),x90342))+P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f81(a1),x90341),x90341)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),x90342),x90342)),a103))) % 178.07/177.93 [9036]~P24(f329(f329(f243(a1),x90361),x90362))+P24(f329(f329(f243(a1),f329(f329(f22(a1),f329(f329(f81(a1),x90361),x90361)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),x90362),x90362)),a103))) % 178.07/177.93 [9037]~P24(f329(f329(f92(a1),x90371),x90372))+P24(f329(f329(f92(a1),f329(f329(f22(a1),f329(f329(f81(a1),x90371),x90371)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),x90372),x90372)),a103))) % 178.07/177.93 [9301]P24(f329(f329(f244(a1),x93011),x93012))+~P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f81(a1),x93011),x93011)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),x93012),x93012)),a103))) % 178.07/177.93 [9303]P24(f329(f329(f243(a1),x93031),x93032))+~P24(f329(f329(f243(a1),f329(f329(f22(a1),f329(f329(f81(a1),x93031),x93031)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),x93032),x93032)),a103))) % 178.07/177.93 [9304]P24(f329(f329(f92(a1),x93041),x93042))+~P24(f329(f329(f92(a1),f329(f329(f22(a1),f329(f329(f81(a1),x93041),x93041)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),x93042),x93042)),a103))) % 178.07/177.93 [9336]~P24(f329(f62(x93361),x93362))+P24(f329(f62(f883(x93361,a869)),f329(f249(f883(x93361,a869)),f329(f329(f7(f883(x93361,a869),f883(x93361,a869),a869),f243(f883(x93361,a869))),x93362)))) % 178.07/177.93 [9383]~E(f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),x93831),f193(f883(f882(a875,a875),a869)))),f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),x93832),f193(f883(f882(a875,a875),a869)))))+P24(f329(f329(f331(f882(f882(a875,a875),f882(a875,a875))),f329(f329(f264(f882(a875,a875),f882(a875,a875)),x93831),x93832)),a114)) % 178.07/177.93 [9467]E(f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),x94671),f193(f883(f882(a875,a875),a869)))),f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),x94672),f193(f883(f882(a875,a875),a869)))))+~P24(f329(f329(f331(f882(f882(a875,a875),f882(a875,a875))),f329(f329(f264(f882(a875,a875),f882(a875,a875)),x94671),x94672)),a114)) % 178.07/177.93 [9503]P24(f329(f329(f243(a1),f2(a1)),f793(x95031,x95032)))+E(f329(f249(a1),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f243(a1),f2(a1)))),x95031)),f329(f249(a1),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f243(a1),f2(a1)))),x95032))) % 178.07/177.93 [10010]~P27(x100101)+E(f41(x100101,f329(f249(x100101),f329(f329(f8(f883(x100101,a869),a869,x100101),f89(x100101)),f329(f329(f8(f883(x100101,a869),f883(x100101,a869),x100101),f329(f18(x100101,a869,a869),f329(f329(f8(a869,f883(a869,a869),x100101),a332),f329(f329(f7(x100101,f883(x100101,a869),a869),f331(x100101)),x100102)))),f329(f7(x100101,x100101,a869),f243(x100101)))))),f40(x100101,x100102)) % 178.07/177.93 [10031]P24(f329(f329(f331(a875),f2(a875)),x100311))+E(f329(f38(a875),f329(f249(a875),f329(f329(f18(a875,a869,a869),f329(f329(f8(a869,f883(a869,a869),a875),a327),f329(f329(f7(a875,f883(a875,a869),a869),f329(f329(f8(a875,f883(f883(a875,a869),a869),a875),f331(a875)),a118)),x100311))),f329(f329(f7(a875,a875,a869),f244(a875)),x100312)))),f329(f38(a875),f329(f249(a875),f329(f329(f18(a875,a869,a869),f329(f329(f8(a869,f883(a869,a869),a875),a327),f329(f329(f7(a875,f883(a875,a869),a869),f331(a875)),x100311))),f329(f329(f7(a875,a875,a869),f244(a875)),f329(a118,x100312)))))) % 178.07/177.93 [7542]~P92(x75421)+E(f329(f329(f82(x75421),x75422),f329(f109(x75421),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))),x75422) % 178.07/177.93 [7802]~P92(x78021)+E(f329(f329(f81(x78021),f329(f109(x78021),x78022)),f79(x78021)),f329(f109(x78021),f329(f329(f81(a1),x78022),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))) % 178.07/177.93 [7947]P24(f329(f329(f243(a1),f2(a1)),f329(f109(a1),x79472)))+E(f329(f329(f254(a1),x79471),f329(f109(a875),f329(f329(f22(a1),f329(f329(f81(a1),x79472),x79472)),a103))),f79(a1)) % 178.07/177.93 [9361]~P24(f329(f329(f243(a1),f2(a1)),f329(f109(a1),x93612)))+E(f329(f329(f254(a1),x93611),f329(f109(a875),f329(f329(f22(a1),f329(f329(f81(a1),x93612),x93612)),a103))),f329(f329(f87(a1,a1),f329(f329(f254(a1),x93611),f329(f109(a875),x93612))),f329(f329(f18(a1,a1,a1),f329(f329(f8(a1,f883(a1,a1),a1),f82(a1)),f329(f82(a1),x93611))),f5(a1)))) % 178.07/177.93 [9723]~P24(f329(f329(f243(a875),f811(x97232,x97231)),f329(x97231,f811(x97232,x97231))))+P24(f329(f62(a875),f329(f249(a875),f329(f329(f7(a875,a875,a869),f329(f329(f8(a875,f883(a875,a869),a875),f243(a875)),x97231)),x97232)))) % 178.07/177.93 [9873]~P24(f329(f329(f244(a875),f329(f109(a875),x98731)),f329(a118,x98732)))+P24(f329(f329(f87(a1,a869),f329(f109(a1),f329(f329(f81(a1),x98731),a103))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f7(a1,a875,a869),f329(f329(f8(a875,f883(a875,a869),a1),f244(a875)),a110)),x98732)))) % 178.07/177.93 [9874]~P24(f329(f329(f243(a875),f329(f109(a875),x98741)),f329(a118,x98742)))+P24(f329(f329(f87(a1,a869),f329(f109(a1),f329(f329(f81(a1),x98741),a103))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f7(a1,a875,a869),f329(f329(f8(a875,f883(a875,a869),a1),f243(a875)),a110)),x98742)))) % 178.07/177.93 [9923]P24(f329(f329(f244(a875),f329(f109(a875),x99231)),f329(a118,x99232)))+~P24(f329(f329(f87(a1,a869),f329(f109(a1),f329(f329(f81(a1),x99231),a103))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f7(a1,a875,a869),f329(f329(f8(a875,f883(a875,a869),a1),f244(a875)),a110)),x99232)))) % 178.07/177.93 [9924]P24(f329(f329(f243(a875),f329(f109(a875),x99241)),f329(a118,x99242)))+~P24(f329(f329(f87(a1,a869),f329(f109(a1),f329(f329(f81(a1),x99241),a103))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f7(a1,a875,a869),f329(f329(f8(a875,f883(a875,a869),a1),f243(a875)),a110)),x99242)))) % 178.07/177.93 [9954]~P24(f329(f329(f244(a875),f329(a118,x99542)),f329(f109(a875),x99541)))+P24(f329(f329(f87(a1,a869),f329(f109(a1),f329(f329(f81(a1),x99541),a103))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f8(a875,a869,a1),f329(f244(a875),x99542)),a110))))) % 178.07/177.93 [9955]~P24(f329(f329(f243(a875),f329(a118,x99552)),f329(f109(a875),x99551)))+P24(f329(f329(f87(a1,a869),f329(f109(a1),f329(f329(f81(a1),x99551),a103))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f8(a875,a869,a1),f329(f243(a875),x99552)),a110))))) % 178.07/177.93 [9998]P24(f329(f329(f244(a875),f329(a118,x99981)),f329(f109(a875),x99982)))+~P24(f329(f329(f87(a1,a869),f329(f109(a1),f329(f329(f81(a1),x99982),a103))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f8(a875,a869,a1),f329(f244(a875),x99981)),a110))))) % 178.07/177.93 [9999]P24(f329(f329(f243(a875),f329(a118,x99991)),f329(f109(a875),x99992)))+~P24(f329(f329(f87(a1,a869),f329(f109(a1),f329(f329(f81(a1),x99992),a103))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f8(a875,a869,a1),f329(f243(a875),x99991)),a110))))) % 178.07/177.93 [10071]~P24(f329(f329(f331(a875),f2(a875)),x100711))+E(f329(a118,f329(f38(a875),f329(f249(a875),f329(f329(f18(a875,a869,a869),f329(f329(f8(a869,f883(a869,a869),a875),a327),f329(f329(f7(a875,f883(a875,a869),a869),f329(f329(f8(a875,f883(f883(a875,a869),a869),a875),f331(a875)),a118)),x100711))),f329(f329(f7(a875,a875,a869),f244(a875)),x100712))))),f329(f38(a875),f329(f249(a875),f329(f329(f18(a875,a869,a869),f329(f329(f8(a869,f883(a869,a869),a875),a327),f329(f329(f7(a875,f883(a875,a869),a869),f331(a875)),x100711))),f329(f329(f7(a875,a875,a869),f244(a875)),f329(a118,x100712)))))) % 178.07/177.93 [8501]~P92(x85011)+E(f329(f329(f82(x85011),f329(f109(x85011),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))),x85012),x85012) % 178.07/177.93 [8560]~P92(x85601)+E(f329(f329(f81(x85601),f79(x85601)),f329(f109(x85601),x85602)),f329(f109(x85601),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),x85602))) % 178.07/177.93 [8618]~P92(x86181)+E(f329(f329(f22(x86181),f329(f109(x86181),x86182)),f79(x86181)),f329(f109(x86181),f329(f329(f81(a1),x86182),f329(f80(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))) % 178.07/177.93 [8757]~P24(f329(f329(f244(a875),f329(f109(a875),a84)),x87572))+E(f329(f329(f22(a875),x87571),f329(f329(f22(a875),x87572),f329(f109(a875),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f329(f329(f22(a875),f329(a118,x87571)),x87572)) % 178.07/177.93 [9399]~P114(x93991)+E(f329(f329(f82(x93991),x93992),x93992),f329(f329(f254(x93991),x93992),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))) % 178.07/177.93 [9400]~P79(x94001)+E(f329(f329(f254(x94001),x94002),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f329(f329(f82(x94001),x94002),x94002)) % 178.07/177.93 [9402]~P92(x94021)+E(f329(f329(f82(x94021),x94022),f329(f109(x94021),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f329(f329(f81(x94021),x94022),x94022)) % 178.07/177.93 [9642]~P137(x96421)+E(f329(f329(f254(x96421),f329(f80(x96421),x96422)),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f329(f329(f254(x96421),x96422),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))) % 178.07/177.93 [9643]~P117(x96431)+E(f329(f329(f254(x96431),f329(f76(x96431),x96432)),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f329(f329(f254(x96431),x96432),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))) % 178.07/177.93 [9639]~P92(x96391)+E(f329(f329(f82(x96391),f329(f109(x96391),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x96392),f329(f329(f81(x96391),x96392),x96392)) % 178.07/177.93 [9763]~P117(x97631)+E(f329(f76(x97631),f329(f329(f254(x97631),x97632),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f329(f329(f254(x97631),x97632),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))) % 178.07/177.93 [9825]~P117(x98251)+P24(f329(f329(f243(x98251),f2(x98251)),f329(f329(f254(x98251),x98252),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))))) % 178.07/177.93 [9989]~E(f329(a118,x99892),f329(f109(a875),x99891))+P24(f329(f329(f87(a1,a869),f329(f109(a1),f329(f329(f81(a1),x99891),a103))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f7(a1,a875,a869),f329(f329(f8(a875,f883(a875,a869),a1),a326),a110)),x99892))))) % 178.07/177.93 [9990]~E(f329(f109(a875),x99901),f329(a118,x99902))+P24(f329(f329(f87(a1,a869),f329(f109(a1),f329(f329(f81(a1),x99901),a103))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f7(a1,a875,a869),f329(f329(f8(a875,f883(a875,a869),a1),a326),a110)),x99902))))) % 178.07/177.93 [10034]E(f329(a118,x100341),f329(f109(a875),x100342))+~P24(f329(f329(f87(a1,a869),f329(f109(a1),f329(f329(f81(a1),x100342),a103))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f7(a1,a875,a869),f329(f329(f8(a875,f883(a875,a869),a1),a326),a110)),x100341))))) % 178.07/177.93 [10035]E(f329(f109(a875),x100351),f329(a118,x100352))+~P24(f329(f329(f87(a1,a869),f329(f109(a1),f329(f329(f81(a1),x100351),a103))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f7(a1,a875,a869),f329(f329(f8(a875,f883(a875,a869),a1),a326),a110)),x100352))))) % 178.07/177.93 [9822]~P92(x98221)+E(f329(f329(f254(x98221),f329(f109(x98221),a103)),f329(f329(f82(a875),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x98222)),f79(x98221)) % 178.07/177.93 [9823]~P137(x98231)+E(f329(f329(f254(x98231),f329(f80(x98231),f79(x98231))),f329(f329(f82(a875),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x98232)),f79(x98231)) % 178.07/177.93 [9827]~P79(x98271)+E(f329(f329(f254(x98271),x98272),f329(f109(a875),f329(f329(f22(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))),a103))),f329(f329(f82(x98271),f329(f329(f82(x98271),x98272),x98272)),x98272)) % 178.07/177.93 [10013]~P24(f329(f329(f243(a1),f2(a1)),x100132))+E(f45(a1,f329(f329(f81(a1),f79(a1)),f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x100131)),f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x100132)),f329(f329(f81(a1),f79(a1)),f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f45(a1,x100131,x100132)))) % 178.07/177.93 [10037]~P24(f329(f329(f243(a1),f2(a1)),x100372))+E(f329(f329(f39(a1),f329(f329(f81(a1),f79(a1)),f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x100371))),f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x100372)),f329(f329(f39(a1),x100371),x100372)) % 178.07/177.93 [10039]~P24(f329(f329(f243(a1),x100392),f2(a1)))+E(f329(f329(f39(a1),f329(f329(f81(a1),f79(a1)),f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x100391))),f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x100392)),f329(f329(f39(a1),f329(f329(f81(a1),x100391),f79(a1))),x100392)) % 178.07/177.93 [10040]~P24(f329(f329(f243(a1),x100402),f2(a1)))+E(f45(a1,f329(f329(f81(a1),f79(a1)),f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x100401)),f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x100402)),f329(f329(f22(a1),f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f45(a1,f329(f329(f81(a1),x100401),f79(a1)),x100402))),f79(a1))) % 178.07/177.93 [9914]~P92(x99141)+E(f329(f329(f254(x99141),f329(f109(x99141),a103)),f329(a118,f329(f329(f82(a875),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x99142))),f329(f109(x99141),a103)) % 178.07/177.93 [9916]~P137(x99161)+E(f329(f329(f254(x99161),f329(f80(x99161),f79(x99161))),f329(a118,f329(f329(f82(a875),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x99162))),f329(f80(x99161),f79(x99161))) % 178.07/177.93 [5085]~P20(x50851,x50852,x50853)+P23(x50851,x50852,x50853) % 178.07/177.93 [8020]~E(x80202,x80203)+P35(x80201,x80201,a326,x80202,x80203) % 178.07/177.93 [8573]E(x85731,x85732)+~P35(x85733,x85733,a326,x85731,x85732) % 178.07/177.93 [5090]~P38(x50901,x50903)+P38(x50901,f323(x50901,x50902,x50903)) % 178.07/177.93 [5265]P30(x52651,x52652,x52653)+~P30(x52651,f329(a118,x52652),x52653) % 178.07/177.93 [5350]~P6(x53501,x53502,x53503)+P6(f876(x53501),f160(x53501,x53502),f157(x53501,x53503)) % 178.07/177.93 [5351]~P40(x53511,x53512,x53513)+P40(f876(x53511),f160(x53511,x53512),f157(x53511,x53513)) % 178.07/177.93 [5463]P50(x54631,x54632,x54633)+~E(f727(x54633,x54632,x54631),f728(x54633,x54632,x54631)) % 178.07/177.93 [5464]P51(x54641,x54642,x54643)+~E(f752(x54643,x54642,x54641),f753(x54643,x54642,x54641)) % 178.07/177.93 [6401]P23(x64011,x64012,x64013)+~P30(x64011,f592(x64013,x64012,x64011),f601(x64013,x64012,x64011)) % 178.07/177.93 [4641]~E(x46411,f206(x46412))+~E(x46411,f329(f236(x46412),x46413)) % 178.07/177.93 [4690]~E(f329(f168(x46902),x46901),x46903)+E(x46901,f329(f168(x46902),x46903)) % 178.07/177.93 [4691]~E(x46912,f329(f168(x46911),x46913))+E(f329(f168(x46911),x46912),x46913) % 178.07/177.93 [4738]E(x47381,x47382)+~E(f329(f236(x47383),x47381),f329(f236(x47383),x47382)) % 178.07/177.93 [4739]E(x47391,x47392)+~E(f329(f168(x47393),x47391),f329(f168(x47393),x47392)) % 178.07/177.93 [4944]~P5(x49443,x49441)+P24(f329(f329(x49441,x49442),x49442)) % 178.07/177.93 [4945]~P49(x49453,x49451)+P24(f329(f329(x49451,x49452),x49452)) % 178.07/177.93 [4947]~P55(x49471,x49472)+P24(f329(f317(x49471,x49472),x49473)) % 178.07/177.93 [5009]~P38(x50091,x50092)+P38(f876(x50091),f329(f142(x50091,x50092),x50093)) % 178.07/177.93 [5014]~P24(f329(x50142,x50143))+~E(f329(f249(x50141),x50142),f193(f883(x50141,a869))) % 178.07/177.93 [5015]~P24(f329(x50152,x50153))+~E(f193(f883(x50151,a869)),f329(f249(x50151),x50152)) % 178.07/177.93 [5046]~P24(f329(x50461,x50463))+P24(f329(x50461,f91(x50462,x50461))) % 178.07/177.93 [5171]~E(x51712,x51713)+P24(f329(f329(f331(x51711),x51712),f329(a326,x51713))) % 178.07/177.93 [5183]P24(f329(x51831,x51832))+~P24(f329(x51831,f581(x51831,x51833))) % 178.07/177.93 [5229]E(f329(f168(x52291),x52292),f329(f329(f150(x52291),x52293),f119(x52291)))+~E(x52292,f329(f329(f150(x52291),x52293),f119(x52291))) % 178.07/177.93 [5230]~E(x52303,f329(f329(f150(x52301),x52302),f119(x52301)))+E(f329(f329(f150(x52301),x52302),f119(x52301)),f329(f168(x52301),x52303)) % 178.07/177.93 [5258]~E(x52583,f329(f16(f879(x52582),x52581),f206(x52582)))+E(f183(x52581,x52582,x52583),f193(f883(x52581,a869))) % 178.07/177.93 [5279]~P34(x52791,x52792,x52793)+P34(x52791,x52792,f329(f168(x52791),x52793)) % 178.07/177.93 [5280]~P32(x52801,x52802,x52803)+P32(x52801,x52802,f329(f168(x52801),x52803)) % 178.07/177.93 [5283]E(f329(f38(x52831),f338(x52832,x52833,x52831)),x52832)+~E(f329(f38(x52831),x52833),f329(a118,x52832)) % 178.07/177.93 [5289]~P38(x52891,x52893)+P24(f329(f329(f331(x52891),x52892),f318(x52891,x52893))) % 178.07/177.93 [5292]~E(f329(f168(x52922),x52921),f329(f329(f150(x52922),x52923),f119(x52922)))+E(x52921,f329(f329(f150(x52922),x52923),f119(x52922))) % 178.07/177.93 [5293]~E(f329(f329(f150(x52932),x52933),f119(x52932)),f329(f168(x52932),x52931))+E(x52931,f329(f329(f150(x52932),x52933),f119(x52932))) % 178.07/177.93 [5308]E(x53081,f329(f16(f879(x53082),x53083),f206(x53082)))+~E(f183(x53083,x53082,x53081),f193(f883(x53083,a869))) % 178.07/177.93 [5314]E(f86(f882(a875,a875),f48(x53141,x53142)),x53143)+~P24(f329(f48(x53141,x53142),x53143)) % 178.07/177.93 [5322]~E(x53223,f329(f236(x53221),x53222))+P24(f329(f329(f331(x53221),x53222),f235(x53221,x53223))) % 178.07/177.93 [5354]P34(x53541,x53542,x53543)+~P34(x53541,x53542,f329(f168(x53541),x53543)) % 178.07/177.93 [5355]P32(x53551,x53552,x53553)+~P32(x53551,x53552,f329(f168(x53551),x53553)) % 178.07/177.93 [5417]~E(x54172,f119(x54171))+P24(f329(f329(f331(f876(x54171)),x54172),f160(x54171,x54173))) % 178.07/177.93 [5424]~P40(x54241,x54242,x54243)+P40(x54241,x54242,f329(f284(x54241,x54241),x54243)) % 178.07/177.93 [5425]~P51(x54251,x54252,x54253)+P51(x54251,x54252,f329(f284(x54251,x54251),x54253)) % 178.07/177.93 [5444]~P56(x54441)+E(f45(x54441,f45(x54441,x54442,x54443),x54443),f45(x54441,x54442,x54443)) % 178.07/177.93 [5539]E(x55391,x55392)+~P24(f329(f329(f331(x55393),x55391),f329(a326,x55392))) % 178.07/177.93 [5584]~P141(x55841)+E(f195(x55841,x55842,f2(a875),x55843),x55843) % 178.07/177.93 [5604]P40(x56041,x56042,x56043)+~P40(x56041,x56042,f329(f284(x56041,x56041),x56043)) % 178.07/177.93 [5605]P51(x56051,x56052,x56053)+~P51(x56051,x56052,f329(f284(x56051,x56051),x56053)) % 178.07/177.93 [5609]~P105(x56092)+E(f149(x56091,x56092,x56093,f119(x56091)),f119(x56091)) % 178.07/177.93 [5622]E(f169(x56221,x56222,f151(x56221,x56223)),f151(x56221,f169(x56221,x56222,x56223)))+~P24(f329(f136(x56221),x56223)) % 178.07/177.93 [5628]E(x56281,f329(f236(x56282),x56283))+~P24(f329(f329(f331(x56282),x56283),f235(x56282,x56281))) % 178.07/177.93 [5713]~P24(f329(a25,x57133))+P24(f329(a25,f30(x57131,x57132,x57133))) % 178.07/177.93 [5724]E(f329(f135(x57241,x57242),x57243),f119(x57241))+P24(f329(x57242,f620(x57243,x57242,x57241))) % 178.07/177.93 [5867]~P24(f329(f136(x58671),x58673))+P24(f329(f136(x58671),f169(x58671,x58672,x58673))) % 178.07/177.93 [5868]~P24(f329(f136(x58681),x58682))+P24(f329(f136(x58681),f175(x58681,x58682,x58683))) % 178.07/177.93 [5869]~P24(f329(f136(x58691),x58693))+P24(f329(f136(x58691),f176(x58691,x58692,x58693))) % 178.07/177.93 [5870]~P24(f329(f136(x58701),x58703))+P24(f329(f136(x58701),f139(x58701,x58702,x58703))) % 178.07/177.93 [5871]~P143(x58711,x58713,x58712)+P24(f329(x58711,f45(a1,x58712,x58713))) % 178.07/177.93 [5890]~P34(x58903,x58901,x58902)+P24(f329(x58901,f745(x58902,x58901,x58903))) % 178.07/177.93 [5891]~P36(x58913,x58911,x58912)+P24(f329(x58911,f805(x58912,x58911,x58913))) % 178.07/177.93 [5913]E(f329(f135(x59131,x59132),x59133),f176(x59131,x59132,x59133))+P24(f329(x59132,f671(x59133,x59132,x59131))) % 178.07/177.93 [5955]~P24(f329(f136(x59551),x59553))+P24(f329(f136(f876(x59551)),f55(x59551,x59552,x59553))) % 178.07/177.93 [5977]P24(f329(a25,f29(x59771,x59772,x59773)))+~P24(f329(a25,f329(a26,x59772))) % 178.07/177.93 [5989]~P107(x59891)+E(f329(f329(f107(f883(x59891,a869)),f329(f250(x59891),x59892)),f300(x59891,x59892,x59893)),f193(f883(x59891,a869))) % 178.07/177.93 [5990]~P107(x59901)+E(f329(f329(f107(f883(x59901,a869)),f329(f298(x59901),x59902)),f303(x59901,x59902,x59903)),f193(f883(x59901,a869))) % 178.07/177.93 [5991]~P107(x59911)+E(f329(f329(f107(f883(x59911,a869)),f329(f298(x59911),x59912)),f302(x59911,x59912,x59913)),f193(f883(x59911,a869))) % 178.07/177.93 [6138]P24(f329(a25,x61381))+~P24(f329(a25,f30(x61382,x61383,x61381))) % 178.07/177.93 [6140]P24(f329(a25,x61401))+~P24(f329(a25,f31(x61402,x61403,x61401))) % 178.07/177.93 [6142]P24(f329(a25,x61421))+~P24(f329(a25,f31(x61422,x61421,x61423))) % 178.07/177.93 [6221]E(f329(f135(x62211,x62212),x62213),x62213)+~P24(f329(x62212,f644(x62213,x62212,x62211))) % 178.07/177.93 [6223]E(f329(f329(f307(x62231),f367(x62232,x62233,x62231)),f338(x62232,x62233,x62231)),x62233)+~E(f329(f38(x62231),x62233),f329(a118,x62232)) % 178.07/177.93 [6239]P143(x62391,x62392,x62393)+~P24(f329(x62391,f45(a1,x62393,x62392))) % 178.07/177.93 [6286]P32(x62861,x62862,x62863)+~P24(f329(x62862,f788(x62863,x62862,x62861))) % 178.07/177.93 [6287]P32(x62871,x62872,x62873)+~P24(f329(x62872,f802(x62872,x62873,x62871))) % 178.07/177.93 [6288]P32(x62881,x62882,x62883)+~P24(f329(x62882,f803(x62883,x62882,x62881))) % 178.07/177.93 [6290]E(f176(x62901,x62902,x62903),x62903)+~P24(f329(x62902,f653(x62903,x62902,x62901))) % 178.07/177.93 [6328]~P24(f329(a25,f29(x63282,x63281,x63283)))+P24(f329(a25,f329(a26,x63281))) % 178.07/177.93 [6370]~P24(f329(x63702,f584(x63703,x63702,x63701)))+P24(f329(f257(x63701,x63702),x63703)) % 178.07/177.93 [6371]~P24(f329(x63712,f673(x63713,x63712,x63711)))+P24(f329(f159(x63711,x63712),x63713)) % 178.07/177.93 [6617]~P24(f329(f317(x66171,x66172),f535(x66173,x66172,x66171)))+P24(f329(f317(x66171,x66172),x66173)) % 178.07/177.93 [6618]~P24(f329(f317(x66181,x66182),f547(x66183,x66182,x66181)))+P24(f329(f317(x66181,x66182),x66183)) % 178.07/177.93 [7226]~P56(x72261)+E(f329(f329(f81(x72261),f329(f329(f82(x72261),x72262),f329(f329(f39(x72261),x72263),x72262))),f45(x72261,x72263,x72262)),x72263) % 178.07/177.93 [7696]E(f329(f329(f264(x76961,x76961),f563(x76962,x76963,x76961)),f563(x76962,x76963,x76961)),x76963)+~P24(f329(f329(f331(f882(x76961,x76961)),x76963),f261(x76961,x76962))) % 178.07/177.93 [7810]~P24(f329(f329(f331(x78101),f681(x78103,x78102,x78101)),f318(x78101,x78103)))+P24(f329(f329(f331(x78101),x78102),f318(x78101,x78103))) % 178.07/177.93 [7811]~P24(f329(f329(f331(x78111),f736(x78113,x78112,x78111)),f318(x78111,x78113)))+P24(f329(f329(f331(x78111),x78112),f318(x78111,x78113))) % 178.07/177.93 [7812]~P24(f329(f329(f331(x78121),f740(x78123,x78122,x78121)),f318(x78121,x78123)))+P24(f329(f329(f331(x78121),x78122),f318(x78121,x78123))) % 178.07/177.93 [8001]~P56(x80011)+E(f329(f329(f81(x80011),f329(f329(f82(x80011),f329(f329(f39(x80011),x80012),x80013)),x80013)),f45(x80011,x80012,x80013)),x80012) % 178.07/177.93 [8046]~E(f329(f38(x80461),x80462),f329(a118,x80463))+~P24(f329(f329(f331(x80461),f367(x80463,x80462,x80461)),f338(x80463,x80462,x80461))) % 178.07/177.93 [8669]P24(f329(f329(f243(f883(f882(x86691,x86691),a869)),f305(x86691,x86692)),f305(x86691,x86693)))+~P24(f329(f329(f243(f883(f882(x86691,x86691),a869)),x86692),f305(x86691,x86693))) % 178.07/177.93 [8942]E(x89421,f119(x89422))+~P24(f329(f329(f331(f882(f876(x89422),f876(x89422))),f329(f329(f264(f876(x89422),f876(x89422)),x89421),f119(x89422))),f157(x89422,x89423))) % 178.07/177.93 [8967]E(x89671,f119(x89672))+~P24(f329(f329(f331(f882(f876(x89672),f876(x89672))),f329(f329(f264(f876(x89672),f876(x89672)),f119(x89672)),x89671)),f157(x89672,x89673))) % 178.07/177.93 [9091]E(f329(f329(f150(x90911),f641(x90912,x90913,x90911)),f642(x90912,x90913,x90911)),x90913)+~P24(f329(f329(f331(f882(f876(x90911),f876(x90911))),f329(f329(f264(f876(x90911),f876(x90911)),f119(x90911)),x90913)),f146(x90911,x90912))) % 178.07/177.93 [9329]~P122(x93291)+~P24(f329(f329(f244(x93291),f329(f329(f81(x93291),f329(f329(f82(x93291),x93292),x93292)),f329(f329(f82(x93291),x93293),x93293))),f2(x93291))) % 178.07/177.93 [9378]P24(f329(f62(x93781),x93782))+~P24(f329(f329(f331(f882(f883(x93781,a869),f883(x93781,a869))),f329(f329(f264(f883(x93781,a869),f883(x93781,a869)),x93783),x93782)),f304(x93781))) % 178.07/177.93 [9664]~P47(x96641,x96642,x96643)+P24(f329(f329(f244(a1),f329(f329(f74(f882(a1,a1),a1,x96641,f263(a1,a1)),f220(x96641)),f231(x96641,x96642,f228(x96641,x96643)))),f2(a1))) % 178.07/177.93 [9665]~P48(x96651,x96652,x96653)+P24(f329(f329(f243(a1),f329(f329(f74(f882(a1,a1),a1,x96651,f263(a1,a1)),f220(x96651)),f231(x96651,x96652,f228(x96651,x96653)))),f2(a1))) % 178.07/177.93 [9792]P47(x97921,x97922,x97923)+~P24(f329(f329(f244(a1),f329(f329(f74(f882(a1,a1),a1,x97921,f263(a1,a1)),f220(x97921)),f231(x97921,x97922,f228(x97921,x97923)))),f2(a1))) % 178.07/177.93 [9793]P48(x97931,x97932,x97933)+~P24(f329(f329(f243(a1),f329(f329(f74(f882(a1,a1),a1,x97931,f263(a1,a1)),f220(x97931)),f231(x97931,x97932,f228(x97931,x97933)))),f2(a1))) % 178.07/177.93 [10114]~P117(x101141)+~P24(f329(f329(f244(x101141),f329(f329(f81(x101141),f329(f329(f254(x101141),x101142),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f329(f329(f254(x101141),x101143),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))))),f2(x101141))) % 178.07/177.93 [4721]~E(x47213,f119(x47211))+E(f329(f329(f127(x47211),x47212),x47213),x47212) % 178.07/177.93 [4722]~E(x47222,f119(x47221))+E(f329(f329(f127(x47221),x47222),x47223),x47223) % 178.07/177.93 [4729]~E(x47292,f2(a875))+E(f329(f329(f174(x47291),x47292),x47293),f119(x47291)) % 178.07/177.93 [4733]~E(x47333,f119(x47331))+E(f329(f329(f174(x47331),x47332),x47333),f119(x47331)) % 178.07/177.93 [4773]~E(x47731,x47733)+E(x47731,f329(f329(f127(x47732),f119(x47732)),x47733)) % 178.07/177.93 [4861]~P25(x48612)+E(f329(f193(f883(x48611,x48612)),x48613),f193(x48612)) % 178.07/177.93 [4862]~P103(x48622)+E(f329(f252(f883(x48621,x48622)),x48623),f252(x48622)) % 178.07/177.93 [4881]E(x48811,f119(x48812))+~E(f329(f329(f127(x48812),x48813),x48811),x48813) % 178.07/177.93 [4882]E(x48821,f119(x48822))+~E(f329(f329(f127(x48822),x48821),x48823),x48823) % 178.07/177.93 [4890]E(x48901,f119(x48902))+~E(f329(f329(f127(x48902),x48903),x48901),f119(x48902)) % 178.07/177.93 [4891]E(x48911,f119(x48912))+~E(f329(f329(f127(x48912),x48911),x48913),f119(x48912)) % 178.07/177.93 [4914]~E(x49142,f2(a875))+E(f329(f329(f82(a875),x49141),x49142),f329(f329(f82(a875),x49143),x49142)) % 178.07/177.93 [4916]~E(x49161,f2(a875))+E(f329(f329(f82(a875),x49161),x49162),f329(f329(f82(a875),x49161),x49163)) % 178.07/177.93 [4969]~P63(x49691)+E(f329(f329(f116(x49691),x49692),x49693),f329(f329(f116(x49691),x49693),x49692)) % 178.07/177.93 [4971]~P99(x49711)+E(f329(f329(f116(x49711),x49712),x49713),f329(f329(f116(x49711),x49713),x49712)) % 178.07/177.93 [4972]~P63(x49721)+E(f329(f329(f107(x49721),x49722),x49723),f329(f329(f107(x49721),x49723),x49722)) % 178.07/177.93 [4974]~P100(x49741)+E(f329(f329(f107(x49741),x49742),x49743),f329(f329(f107(x49741),x49743),x49742)) % 178.07/177.93 [4975]~P114(x49751)+E(f329(f329(f82(x49751),x49752),x49753),f329(f329(f82(x49751),x49753),x49752)) % 178.07/177.93 [4976]~P114(x49761)+E(f329(f329(f81(x49761),x49762),x49763),f329(f329(f81(x49761),x49763),x49762)) % 178.07/177.93 [4978]~P105(x49781)+E(f329(f329(f241(x49781),x49782),x49783),f329(f329(f241(x49781),x49783),x49782)) % 178.07/177.93 [4980]~P105(x49801)+E(f329(f329(f242(x49801),x49802),x49803),f329(f329(f242(x49801),x49803),x49802)) % 178.07/177.93 [5041]E(f45(a875,x50411,x50412),f2(a875))+~E(x50411,f329(f329(f82(a875),x50412),x50413)) % 178.07/177.93 [5042]E(f45(a1,x50421,x50422),f2(a1))+~E(x50421,f329(f329(f82(a1),x50422),x50423)) % 178.07/177.93 [5102]E(x51021,x51022)+~E(f329(f329(f81(a875),x51023),x51021),f329(f329(f81(a875),x51023),x51022)) % 178.07/177.93 [5103]E(x51031,x51032)+~E(f329(f329(f81(a875),x51031),x51033),f329(f329(f81(a875),x51032),x51033)) % 178.07/177.93 [5113]~P89(x51131)+E(f329(f329(f107(x51131),x51132),f329(f80(x51131),x51133)),f329(f329(f22(x51131),x51132),x51133)) % 178.07/177.93 [5114]~P66(x51141)+E(f329(f329(f81(x51141),x51142),f329(f80(x51141),x51143)),f329(f329(f22(x51141),x51142),x51143)) % 178.07/177.93 [5115]~P67(x51151)+E(f329(f329(f81(x51151),x51152),f329(f80(x51151),x51153)),f329(f329(f22(x51151),x51152),x51153)) % 178.07/177.93 [5116]~P111(x51161)+E(f329(f329(f81(x51161),x51162),f329(f80(x51161),x51163)),f329(f329(f22(x51161),x51162),x51163)) % 178.07/177.93 [5117]~P67(x51171)+E(f329(f329(f22(x51171),x51172),f329(f80(x51171),x51173)),f329(f329(f81(x51171),x51172),x51173)) % 178.07/177.93 [5164]~P24(f329(x51643,x51642))+P24(f329(f329(f331(x51641),x51642),x51643)) % 178.07/177.93 [5166]~P70(x51662)+E(f329(f329(f6(x51661,x51662),x51663),f193(f883(x51661,a869))),f2(x51662)) % 178.07/177.93 [5168]~P74(x51682)+E(f329(f329(f9(x51681,x51682),x51683),f193(f883(x51681,a869))),f79(x51682)) % 178.07/177.93 [5217]~E(x52172,f329(f329(f81(a875),x52171),x52173))+P24(f329(f329(f243(a875),x52171),x52172)) % 178.07/177.93 [5220]~E(x52202,f193(f883(x52201,a869)))+E(f329(f329(f61(x52201),x52202),x52203),f193(f883(f883(x52201,a869),a869))) % 178.07/177.93 [5221]~E(x52212,f193(f883(x52211,a869)))+E(f193(f883(f883(x52211,a869),a869)),f329(f329(f61(x52211),x52212),x52213)) % 178.07/177.93 [5297]~E(f329(f260(x52972,x52973),x52971),f193(f883(x52973,a869)))+E(x52971,f193(f883(f882(x52972,x52973),a869))) % 178.07/177.93 [5298]~E(f329(f262(x52982,x52983),x52981),f193(f883(x52982,a869)))+E(x52981,f193(f883(f882(x52982,x52983),a869))) % 178.07/177.93 [5328]E(f329(f260(x53281,x53282),x53283),f193(f883(x53282,a869)))+~E(x53283,f193(f883(f882(x53281,x53282),a869))) % 178.07/177.93 [5329]E(f329(f262(x53291,x53292),x53293),f193(f883(x53291,a869)))+~E(x53293,f193(f883(f882(x53291,x53292),a869))) % 178.07/177.93 [5332]E(f279(x53321,x53322,x53323),f329(f329(f22(a105),x53322),x53323))+P24(f329(f329(f244(a105),x53322),x53323)) % 178.07/177.93 [5348]P24(f329(x53481,x53482))+~P24(f329(f329(f331(x53483),x53482),x53481)) % 178.07/177.93 [5387]E(x53871,x53872)+~E(f329(f80(f883(x53873,a869)),x53871),f329(f80(f883(x53873,a869)),x53872)) % 178.07/177.93 [5392]E(f311(x53921,x53922,x53923),f206(f876(a325)))+~P24(f329(f329(f244(a1),x53922),x53923)) % 178.07/177.93 [5397]~E(x53971,f193(f883(x53972,a869)))+~P24(f329(f329(f331(x53972),x53973),x53971)) % 178.07/177.93 [5426]~E(x54262,f329(f329(f81(a1),x54261),f329(f106(a1),x54263)))+P24(f329(f329(f243(a1),x54261),x54262)) % 178.07/177.93 [5442]E(f329(f329(f307(x54421),x54422),x54423),x54423)+~P24(f329(f329(f331(x54421),x54422),x54423)) % 178.07/177.93 [5453]E(x54531,f193(f883(x54532,a869)))+~E(f329(f329(f61(x54532),x54531),x54533),f193(f883(f883(x54532,a869),a869))) % 178.07/177.93 [5454]E(x54541,f193(f883(x54542,a869)))+~E(f193(f883(f883(x54542,a869),a869)),f329(f329(f61(x54542),x54541),x54543)) % 178.07/177.93 [5460]~P108(x54601)+E(f329(f329(f82(x54601),f329(f80(x54601),x54602)),f329(f80(x54601),x54603)),f329(f329(f82(x54601),x54602),x54603)) % 178.07/177.93 [5462]~P59(x54621)+E(f329(f329(f287(x54621),f329(f80(x54621),x54622)),f329(f80(x54621),x54623)),f329(f329(f287(x54621),x54622),x54623)) % 178.07/177.93 [5494]~P24(f329(x54943,x54942))+P24(f329(f329(f331(x54941),x54942),f329(f249(x54941),x54943))) % 178.07/177.93 [5532]E(f169(x55321,x55322,x55323),x55323)+P24(f329(f329(f331(x55321),x55322),f329(f171(x55321),x55323))) % 178.07/177.93 [5613]~P24(f329(f136(x56131),x56133))+P24(f329(f136(x56131),f329(f135(x56131,x56132),x56133))) % 178.07/177.93 [5658]~P56(x56581)+E(f329(f329(f39(x56581),f45(x56581,x56582,x56583)),x56583),f2(x56581)) % 178.07/177.93 [5677]E(f175(x56771,f329(f329(f150(x56771),x56772),f119(x56771)),x56773),f119(x56771))+P24(f329(f329(f331(a875),f2(a875)),x56773)) % 178.07/177.93 [5734]E(f329(f329(f150(x57341),x57342),x57343),f139(x57341,x57342,x57343))+P24(f329(f329(f331(x57341),x57342),f329(f171(x57341),x57343))) % 178.07/177.93 [5743]E(x57431,x57432)+~E(f329(f329(f82(a875),f329(a118,x57433)),x57431),f329(f329(f82(a875),f329(a118,x57433)),x57432)) % 178.07/177.93 [5744]~E(x57442,f329(f329(f81(a1),x57441),f329(f106(a1),f329(a118,x57443))))+P24(f329(f329(f244(a1),x57441),x57442)) % 178.07/177.93 [5849]~E(x58493,f119(x58491))+E(f329(f329(f329(f188(f876(x58491),f876(x58491)),x58492),f167(x58491)),x58493),f119(x58491)) % 178.07/177.93 [5853]P24(f329(x58531,x58532))+~P24(f329(f329(f331(x58533),x58532),f329(f249(x58533),x58531))) % 178.07/177.93 [5885]E(x58851,x58852)+~E(f329(f329(f307(x58853),x58851),f193(f883(x58853,a869))),f329(f329(f307(x58853),x58852),f193(f883(x58853,a869)))) % 178.07/177.93 [5896]~P107(x58961)+E(f329(f329(f107(f883(x58961,a869)),f329(f250(x58961),x58962)),f329(f299(x58961,x58962),x58963)),f193(f883(x58961,a869))) % 178.07/177.93 [5939]E(f139(x59391,x59392,x59393),x59393)+~P24(f329(f329(f331(x59391),x59392),f329(f171(x59391),x59393))) % 178.07/177.93 [5963]~P77(x59631)+E(f329(f308(x59631,x59631,f80(x59631)),f329(f299(x59631,x59632),x59633)),f302(x59631,f329(f80(x59631),x59633),f329(f80(x59631),x59632))) % 178.07/177.93 [5971]E(f329(f194(f876(x59711)),f169(x59711,x59712,x59713)),f329(f194(f876(x59711)),x59713))+P24(f329(f329(f331(x59711),x59712),f329(f171(x59711),x59713))) % 178.07/177.93 [6025]~P107(x60251)+E(f329(f329(f107(f883(x60251,a869)),f329(f299(x60251,x60252),x60253)),f329(f251(x60251),x60253)),f193(f883(x60251,a869))) % 178.07/177.93 [6048]~P77(x60481)+E(f329(f308(x60481,x60481,f80(x60481)),f303(x60481,x60482,x60483)),f303(x60481,f329(f80(x60481),x60483),f329(f80(x60481),x60482))) % 178.07/177.93 [6049]~P77(x60491)+E(f329(f308(x60491,x60491,f80(x60491)),f300(x60491,x60492,x60493)),f300(x60491,f329(f80(x60491),x60493),f329(f80(x60491),x60492))) % 178.07/177.93 [6106]E(f175(x61061,f329(f329(f150(x61061),x61062),f119(x61061)),x61063),f329(f329(f150(x61061),x61062),f119(x61061)))+~P24(f329(f329(f331(a875),f2(a875)),x61063)) % 178.07/177.93 [6113]~P77(x61131)+E(f329(f308(x61131,x61131,f80(x61131)),f302(x61131,x61132,x61133)),f329(f299(x61131,f329(f80(x61131),x61133)),f329(f80(x61131),x61132))) % 178.07/177.93 [6133]~P57(x61331)+E(f45(x61331,f329(f80(x61331),f45(x61331,x61332,x61333)),x61333),f45(x61331,f329(f80(x61331),x61332),x61333)) % 178.07/177.93 [6236]~P24(f329(f62(f882(x62362,x62361)),x62363))+P24(f329(f62(x62361),f329(f260(x62362,x62361),x62363))) % 178.07/177.93 [6237]~P24(f329(f62(f882(x62371,x62372)),x62373))+P24(f329(f62(x62371),f329(f262(x62371,x62372),x62373))) % 178.07/177.93 [6243]~P107(x62431)+E(f329(f329(f107(f883(x62431,a869)),f303(x62431,x62432,x62433)),f329(f251(x62431),x62433)),f193(f883(x62431,a869))) % 178.07/177.93 [6244]~P107(x62441)+E(f329(f329(f107(f883(x62441,a869)),f302(x62441,x62442,x62443)),f329(f301(x62441),x62443)),f193(f883(x62441,a869))) % 178.07/177.93 [6245]~P107(x62451)+E(f329(f329(f107(f883(x62451,a869)),f300(x62451,x62452,x62453)),f329(f301(x62451),x62453)),f193(f883(x62451,a869))) % 178.07/177.93 [6311]E(f329(f329(f164(x63111),x63112),f580(x63112,x63113,x63111)),x63113)+~P24(f329(f329(f331(x63111),x63113),f329(f171(x63111),x63112))) % 178.07/177.93 [6452]E(x64521,f119(x64522))+~E(f329(f329(f329(f188(f876(x64522),f876(x64522)),x64523),f167(x64522)),x64521),f119(x64522)) % 178.07/177.93 [6554]~P24(f329(f62(f882(x65542,x65541)),x65543))+P24(f329(f62(f882(x65541,x65542)),f329(f284(x65542,x65541),x65543))) % 178.07/177.93 [6705]P51(x67051,x67052,x67053)+P24(f329(f329(f331(x67051),f753(x67053,x67052,x67051)),x67052)) % 178.07/177.93 [6706]P51(x67061,x67062,x67063)+P24(f329(f329(f331(x67061),f752(x67063,x67062,x67061)),x67062)) % 178.07/177.93 [6718]P24(f329(f317(x67181,x67182),x67183))+P24(f329(f329(x67182,f535(x67183,x67182,x67181)),x67183)) % 178.07/177.93 [6719]P24(f329(f317(x67191,x67192),x67193))+P24(f329(f329(x67192,f547(x67193,x67192,x67191)),x67193)) % 178.07/177.93 [6750]E(f329(f194(f876(x67501)),f169(x67501,x67502,x67503)),f329(f329(f22(a875),f329(f194(f876(x67501)),x67503)),f79(a875)))+~P24(f329(f329(f331(x67501),x67502),f329(f171(x67501),x67503))) % 178.07/177.93 [6790]P24(f329(f257(x67901,x67902),x67903))+P24(f329(f329(f331(x67901),f584(x67903,x67902,x67901)),x67903)) % 178.07/177.93 [6800]~P24(f329(f62(f882(x68002,x68001)),f329(f284(x68001,x68002),x68003)))+P24(f329(f62(f882(x68001,x68002)),x68003)) % 178.07/177.93 [6856]~P24(f329(f329(f331(x68561),x68562),f329(f171(x68561),f120(x68561,x68563))))+P24(f329(f329(f331(x68561),x68562),f329(f171(x68561),x68563))) % 178.07/177.93 [6861]P23(x68611,x68612,x68613)+P24(f329(f329(f331(f874(x68611)),f601(x68613,x68612,x68611)),x68613)) % 178.07/177.93 [6891]E(f329(f135(x68911,x68912),x68913),x68913)+P24(f329(f329(f331(x68911),f644(x68913,x68912,x68911)),f329(f171(x68911),x68913))) % 178.07/177.93 [6906]E(f329(f135(x69061,x69062),x69063),f119(x69061))+P24(f329(f329(f331(x69061),f620(x69063,x69062,x69061)),f329(f171(x69061),x69063))) % 178.07/177.93 [6929]P32(x69291,x69292,x69293)+P24(f329(f329(f331(x69291),f788(x69293,x69292,x69291)),f329(f171(x69291),x69293))) % 178.07/177.93 [6930]P32(x69301,x69302,x69303)+P24(f329(f329(f331(x69301),f803(x69303,x69302,x69301)),f329(f171(x69301),x69303))) % 178.07/177.93 [6931]P32(x69311,x69312,x69313)+P24(f329(f329(f331(x69311),f802(x69312,x69313,x69311)),f329(f171(x69311),x69313))) % 178.07/177.93 [6934]E(f176(x69341,x69342,x69343),x69343)+P24(f329(f329(f331(x69341),f653(x69343,x69342,x69341)),f329(f171(x69341),x69343))) % 178.07/177.93 [7015]P24(f329(f159(x70151,x70152),x70153))+P24(f329(f329(f331(x70151),f673(x70153,x70152,x70151)),f329(f171(x70151),x70153))) % 178.07/177.93 [7024]~P34(x70241,x70243,x70242)+P24(f329(f329(f331(x70241),f745(x70242,x70243,x70241)),f329(f171(x70241),x70242))) % 178.07/177.93 [7025]~P36(x70251,x70253,x70252)+P24(f329(f329(f331(x70251),f805(x70252,x70253,x70251)),f329(f171(x70251),x70252))) % 178.07/177.93 [7060]P24(f329(f329(f331(x70601),x70602),f790(x70603,x70602,x70601)))+~P24(f329(f329(f331(x70601),x70602),f40(f883(x70601,a869),x70603))) % 178.07/177.93 [7061]~P70(x70611)+E(f329(f329(f81(x70611),f329(f329(f6(a875,x70611),x70612),f329(f250(a875),x70613))),f329(x70612,x70613)),f329(f329(f6(a875,x70611),x70612),f329(f250(a875),f329(a118,x70613)))) % 178.07/177.93 [7150]~P34(x71502,x71501,x71503)+P24(f329(x71501,f329(f329(f164(x71502),x71503),f746(x71503,x71501,x71502)))) % 178.07/177.93 [7163]~P24(f329(f329(f331(x71631),x71632),f529(x71632,x71633,x71631)))+P24(f329(f329(f331(x71631),x71632),f41(f883(x71631,a869),x71633))) % 178.07/177.93 [7193]~P70(x71931)+E(f329(f329(f81(x71931),f329(f329(f6(a875,x71931),x71932),f329(f298(a875),x71933))),f329(x71932,f329(a118,x71933))),f329(f329(f6(a875,x71931),x71932),f329(f298(a875),f329(a118,x71933)))) % 178.07/177.93 [7328]P24(f329(f329(f331(f876(x73281)),x73282),f160(x73281,x73283)))+P24(f329(f329(f331(x73281),f640(x73283,x73282,x73281)),f329(f171(x73281),x73282))) % 178.07/177.93 [7345]~P24(f329(f329(f331(f876(x73451)),x73452),f160(x73451,f318(x73451,x73453))))+P24(f329(f329(f331(f876(x73451)),x73452),f318(f876(x73451),f156(x73451,x73453)))) % 178.07/177.93 [7371]~P24(f329(f329(f331(f876(x73711)),x73712),f318(f876(x73711),f156(x73711,x73713))))+P24(f329(f329(f331(f876(x73711)),x73712),f160(x73711,f318(x73711,x73713)))) % 178.07/177.93 [7407]E(f329(f329(f329(f188(f876(x74071),f876(x74071)),x74072),f167(x74071)),x74073),x74073)+~P24(f329(f329(f243(a875),f329(f194(f876(x74071)),x74073)),f79(a875))) % 178.07/177.93 [7443]E(f329(f329(f127(x74431),f782(x74432,x74433,x74431)),f329(f329(f150(x74431),x74433),f787(x74432,x74433,x74431))),x74432)+~P24(f329(f329(f331(x74431),x74433),f329(f171(x74431),x74432))) % 178.07/177.93 [7444]E(f329(f329(f127(x74441),f783(x74442,x74443,x74441)),f329(f329(f150(x74441),x74443),f784(x74442,x74443,x74441))),x74442)+~P24(f329(f329(f331(x74441),x74443),f329(f171(x74441),x74442))) % 178.07/177.93 [7445]E(f329(f329(f127(x74451),f785(x74452,x74453,x74451)),f329(f329(f150(x74451),x74453),f786(x74452,x74453,x74451))),x74452)+~P24(f329(f329(f331(x74451),x74453),f329(f171(x74451),x74452))) % 178.07/177.93 [7469]~P21(x74691,x74692,x74693,f252(f883(x74691,a869)))+P21(f876(x74691),f876(x74692),f329(f153(x74691,x74692),x74693),f252(f883(f876(x74691),a869))) % 178.07/177.93 [7617]E(x76171,f329(f329(f81(a875),f329(f329(f82(a875),f329(f263(a875,a875),x76172)),x76173)),f329(f267(a875,a875),x76172)))+~P24(f329(f48(x76171,x76173),x76172)) % 178.07/177.93 [7625]P21(x76251,x76252,x76253,f252(f883(x76251,a869)))+~P21(f876(x76251),f876(x76252),f329(f153(x76251,x76252),x76253),f252(f883(f876(x76251),a869))) % 178.07/177.93 [7663]~P24(f329(f329(f199(x76631),x76632),x76633))+P24(f329(f329(f329(f329(a201,x76631),x76632),f487(x76633,x76632,x76631)),x76633)) % 178.07/177.93 [7667]P24(f329(f329(f331(f883(x76671,a869)),f529(x76672,x76673,x76671)),x76673))+P24(f329(f329(f331(x76671),x76672),f41(f883(x76671,a869),x76673))) % 178.07/177.93 [7759]P24(f329(f329(f331(f876(x77591)),x77592),f160(x77591,x77593)))+~P24(f329(f329(f331(x77591),f640(x77593,x77592,x77591)),x77593)) % 178.07/177.93 [7859]P32(x78591,x78592,x78593)+~P24(f329(x78592,f329(f329(f164(x78591),x78593),f789(x78593,x78592,x78591)))) % 178.07/177.93 [7884]E(x78841,x78842)+~E(f329(f329(f7(x78843,f883(x78843,a869),a869),f331(x78843)),x78841),f329(f329(f7(x78843,f883(x78843,a869),a869),f331(x78843)),x78842)) % 178.07/177.93 [7890]~P24(f329(f329(f331(f882(x78901,x78901)),x78903),f261(x78901,x78902)))+P24(f329(f329(f331(x78901),f563(x78902,x78903,x78901)),x78902)) % 178.07/177.93 [7892]~P24(f329(f329(f331(x78921),x78923),f40(f883(x78921,a869),x78922)))+P24(f329(f329(f331(f883(x78921,a869)),f790(x78922,x78923,x78921)),x78922)) % 178.07/177.93 [8074]~P24(f329(f329(f331(x80741),x80742),f329(f171(x80741),f783(x80743,x80742,x80741))))+~P24(f329(f329(f331(x80741),x80742),f329(f171(x80741),x80743))) % 178.07/177.93 [8075]~P24(f329(f329(f331(x80751),x80752),f329(f171(x80751),f786(x80753,x80752,x80751))))+~P24(f329(f329(f331(x80751),x80752),f329(f171(x80751),x80753))) % 178.07/177.93 [8164]E(f329(f238(f879(f876(a325)),f876(a325),f311(x81641,x81642,f329(f329(f81(a1),x81643),f79(a1))),f236(f876(a325))),f329(x81641,x81643)),f311(x81641,x81642,x81643))+P24(f329(f329(f244(a1),x81642),x81643)) % 178.07/177.93 [8266]E(x82661,f119(x82662))+P24(f329(f329(f331(x82662),f329(f263(x82662,f882(a105,a105)),f329(f280(x82662,x82661),x82663))),f329(f171(x82662),x82661))) % 178.07/177.93 [8362]~P69(x83621)+E(f329(f141(x83621,x83621,f329(f7(x83621,x83621,x83621),f81(x83621)),x83622),f329(f168(x83621),x83623)),f329(f141(x83621,x83621,f81(x83621),x83622),x83623)) % 178.07/177.93 [8852]~P105(x88521)+E(f329(f171(x88521),f148(x88521,x88521,f5(x88521),x88522,x88523)),f329(f329(f307(x88521),x88522),f329(f171(x88521),x88523))) % 178.07/177.93 [8863]P24(f329(f329(f244(a875),f2(a875)),f756(x88631,x88632,x88633)))+~P24(f329(f329(f331(f882(x88633,x88633)),x88632),f329(f329(f286(x88633,x88633,x88633),x88631),f305(x88633,x88631)))) % 178.07/177.93 [9151]~P53(x91511,x91512)+~P24(f329(f329(f331(f882(x91511,x91511)),f329(f329(f264(x91511,x91511),x91513),x91513)),f329(f329(f286(x91511,x91511,x91511),x91512),f305(x91511,x91512)))) % 178.07/177.93 [9284]~E(f329(f329(f107(f883(f882(x92841,x92841),a869)),f329(f284(x92841,x92841),x92842)),f305(x92841,x92842)),f193(f883(f882(x92841,x92841),a869)))+~P24(f329(f329(f331(f882(x92841,x92841)),f329(f329(f264(x92841,x92841),x92843),x92843)),f329(f329(f286(x92841,x92841,x92841),x92842),f305(x92841,x92842)))) % 178.07/177.93 [9462]~P24(f329(f62(x94621),x94622))+P24(f329(f329(f243(a875),f329(f38(x94621),f329(f329(f22(f883(x94621,a869)),x94622),f329(f329(f307(x94621),x94623),f193(f883(x94621,a869)))))),f329(f38(x94621),x94622))) % 178.07/177.93 [5030]~E(x50303,f119(x50301))+E(f143(x50301,f329(f329(f150(x50301),x50302),x50303)),x50302) % 178.07/177.93 [5038]~E(x50383,f119(x50381))+E(f120(x50381,f329(f329(f150(x50381),x50382),x50383)),f119(x50381)) % 178.07/177.93 [5066]E(x50661,f119(x50662))+E(f143(x50662,f329(f329(f150(x50662),x50663),x50661)),f143(x50662,x50661)) % 178.07/177.93 [5068]E(x50681,f119(x50682))+E(f143(x50682,f329(f329(f127(x50682),x50683),x50681)),f143(x50682,x50681)) % 178.07/177.93 [5073]~E(x50733,f119(x50731))+E(f120(x50731,f329(f329(f127(x50731),x50732),x50733)),f120(x50731,x50732)) % 178.07/177.93 [5075]~E(x50753,f119(x50751))+E(f143(x50751,f329(f329(f127(x50751),x50752),x50753)),f143(x50751,x50752)) % 178.07/177.93 [5107]E(x51071,f119(x51072))+E(f329(f140(x51072),f329(f329(f127(x51072),x51071),x51073)),f329(f140(x51072),x51071)) % 178.07/177.93 [5138]~E(x51382,f119(x51381))+E(f329(f140(x51381),f329(f329(f127(x51381),x51382),x51383)),f329(f140(x51381),x51383)) % 178.07/177.93 [5193]~P63(x51931)+E(f329(f329(f116(x51931),x51932),f329(f329(f107(x51931),x51932),x51933)),x51932) % 178.07/177.93 [5194]~P63(x51941)+E(f329(f329(f107(x51941),x51942),f329(f329(f116(x51941),x51942),x51943)),x51942) % 178.07/177.93 [5195]~P105(x51951)+E(f329(f329(f241(x51951),x51952),f329(f329(f242(x51951),x51952),x51953)),x51952) % 178.07/177.93 [5196]~P105(x51961)+E(f329(f329(f242(x51961),x51962),f329(f329(f241(x51961),x51962),x51963)),x51962) % 178.07/177.93 [5215]~P56(x52151)+E(f45(x52151,f329(f329(f82(x52151),x52152),x52153),x52153),f2(x52151)) % 178.07/177.93 [5216]~P56(x52161)+E(f45(x52161,f329(f329(f82(x52161),x52162),x52163),x52162),f2(x52161)) % 178.07/177.93 [5291]~P66(x52911)+E(f329(f80(x52911),f329(f329(f22(x52911),x52912),x52913)),f329(f329(f22(x52911),x52913),x52912)) % 178.07/177.93 [5352]E(x53521,f119(x53522))+E(f120(x53522,f329(f329(f150(x53522),x53523),x53521)),f329(f329(f150(x53522),x53523),f120(x53522,x53521))) % 178.07/177.93 [5353]E(x53531,f119(x53532))+E(f120(x53532,f329(f329(f127(x53532),x53533),x53531)),f329(f329(f127(x53532),x53533),f120(x53532,x53531))) % 178.07/177.93 [5356]~P27(x53561)+E(f41(x53561,f329(f329(f307(x53561),x53562),x53563)),f329(f329(f107(x53561),x53562),f41(x53561,x53563))) % 178.07/177.93 [5357]~P27(x53571)+E(f40(x53571,f329(f329(f307(x53571),x53572),x53573)),f329(f329(f116(x53571),x53572),f40(x53571,x53573))) % 178.07/177.93 [5402]~P63(x54021)+E(f329(f329(f116(x54021),x54022),f329(f329(f116(x54021),x54022),x54023)),f329(f329(f116(x54021),x54022),x54023)) % 178.07/177.93 [5404]~P99(x54041)+E(f329(f329(f116(x54041),x54042),f329(f329(f116(x54041),x54042),x54043)),f329(f329(f116(x54041),x54042),x54043)) % 178.07/177.93 [5405]~P63(x54051)+E(f329(f329(f107(x54051),x54052),f329(f329(f107(x54051),x54052),x54053)),f329(f329(f107(x54051),x54052),x54053)) % 178.07/177.93 [5407]~P100(x54071)+E(f329(f329(f107(x54071),x54072),f329(f329(f107(x54071),x54072),x54073)),f329(f329(f107(x54071),x54072),x54073)) % 178.07/177.93 [5408]~P95(x54081)+E(f329(f329(f82(x54081),x54082),f329(f329(f82(x54081),x54082),x54083)),f329(f329(f82(x54081),x54082),x54083)) % 178.07/177.93 [5410]~P105(x54101)+E(f329(f329(f241(x54101),x54102),f329(f329(f241(x54101),x54102),x54103)),f329(f329(f241(x54101),x54102),x54103)) % 178.07/177.93 [5412]~P105(x54121)+E(f329(f329(f242(x54121),x54122),f329(f329(f242(x54121),x54122),x54123)),f329(f329(f242(x54121),x54122),x54123)) % 178.07/177.93 [5420]~P56(x54201)+E(f45(x54201,f329(f329(f81(x54201),x54202),x54203),x54203),f45(x54201,x54202,x54203)) % 178.07/177.93 [5421]~P56(x54211)+E(f45(x54211,f329(f329(f81(x54211),x54212),x54213),x54212),f45(x54211,x54213,x54212)) % 178.07/177.93 [5427]~P108(x54271)+E(f329(f329(f82(x54271),x54272),f329(f80(x54271),x54273)),f329(f80(x54271),f329(f329(f82(x54271),x54272),x54273))) % 178.07/177.93 [5428]~P59(x54281)+E(f329(f329(f287(x54281),x54282),f329(f80(x54281),x54283)),f329(f80(x54281),f329(f329(f287(x54281),x54282),x54283))) % 178.07/177.93 [5429]~P80(x54291)+E(f329(f329(f81(x54291),x54292),f329(f165(x54291),x54293)),f329(f165(x54291),f329(f329(f150(x54291),x54292),x54293))) % 178.07/177.93 [5459]~P108(x54591)+E(f329(f329(f82(x54591),f329(f80(x54591),x54592)),x54593),f329(f329(f82(x54591),x54592),f329(f80(x54591),x54593))) % 178.07/177.93 [5465]~P6(x54651,x54652,x54653)+E(f40(f883(x54651,a869),f329(f329(f61(x54651),x54652),x54653)),x54652) % 178.07/177.93 [5524]~P112(x55241)+E(f329(f329(f82(x55241),x55242),f329(f329(f254(x55241),x55242),x55243)),f329(f329(f254(x55241),x55242),f329(a118,x55243))) % 178.07/177.93 [5525]~P114(x55251)+E(f329(f329(f82(x55251),x55252),f329(f329(f254(x55251),x55252),x55253)),f329(f329(f254(x55251),x55252),f329(a118,x55253))) % 178.07/177.93 [5535]~P67(x55351)+E(f329(f329(f81(x55351),f329(f80(x55351),x55352)),f329(f329(f81(x55351),x55352),x55353)),x55353) % 178.07/177.93 [5558]~P141(x55581)+E(f329(f329(f254(x55581),f329(f106(x55581),x55582)),x55583),f329(f106(x55581),f329(f329(f254(a875),x55582),x55583))) % 178.07/177.93 [5559]~P137(x55591)+E(f329(f329(f254(x55591),f329(f108(x55591),x55592)),x55593),f329(f108(x55591),f329(f329(f254(a1),x55592),x55593))) % 178.07/177.93 [5564]~P85(x55641)+E(f329(f76(x55641),f329(f329(f22(x55641),x55642),x55643)),f329(f76(x55641),f329(f329(f22(x55641),x55643),x55642))) % 178.07/177.93 [5566]~P117(x55661)+E(f329(f329(f82(x55661),f83(x55661,x55662)),f83(x55661,x55663)),f83(x55661,f329(f329(f82(x55661),x55662),x55663))) % 178.07/177.93 [5570]E(x55701,f119(x55702))+E(f329(f329(f127(x55702),f329(f170(x55702),x55701)),x55703),f329(f170(x55702),f329(f329(f127(x55702),x55701),x55703))) % 178.07/177.93 [5575]~E(x55752,f329(a118,f329(f329(f81(a875),x55751),x55753)))+P24(f329(f329(f244(a875),x55751),x55752)) % 178.07/177.93 [5576]~P108(x55761)+E(f329(f329(f82(x55761),f329(f80(x55761),x55762)),x55763),f329(f80(x55761),f329(f329(f82(x55761),x55762),x55763))) % 178.07/177.93 [5577]~P115(x55771)+E(f329(f329(f287(x55771),f329(f80(x55771),x55772)),x55773),f329(f80(x55771),f329(f329(f287(x55771),x55772),x55773))) % 178.07/177.93 [5578]~P117(x55781)+E(f329(f329(f254(x55781),f329(f76(x55781),x55782)),x55783),f329(f76(x55781),f329(f329(f254(x55781),x55782),x55783))) % 178.07/177.93 [5676]E(f729(x56761,x56762,x56763),f754(x56761,x56762,x56763))+E(f329(f329(f107(f883(x56763,a869)),x56762),x56761),f193(f883(x56763,a869))) % 178.07/177.93 [5690]~P70(x56902)+E(f329(f329(f6(x56901,x56902),f329(f16(x56902,x56901),f2(x56902))),x56903),f2(x56902)) % 178.07/177.93 [5691]~P74(x56912)+E(f329(f329(f9(x56911,x56912),f329(f16(x56912,x56911),f79(x56912))),x56913),f79(x56912)) % 178.07/177.93 [5693]~P141(x56931)+E(f329(f329(f82(x56931),f329(f106(x56931),x56932)),f329(f106(x56931),x56933)),f329(f106(x56931),f329(f329(f82(a875),x56932),x56933))) % 178.07/177.93 [5694]~P141(x56941)+E(f329(f329(f81(x56941),f329(f106(x56941),x56942)),f329(f106(x56941),x56943)),f329(f106(x56941),f329(f329(f81(a875),x56942),x56943))) % 178.07/177.93 [5695]~P137(x56951)+E(f329(f329(f22(x56951),f329(f108(x56951),x56952)),f329(f108(x56951),x56953)),f329(f108(x56951),f329(f329(f22(a1),x56952),x56953))) % 178.07/177.93 [5696]~P137(x56961)+E(f329(f329(f82(x56961),f329(f108(x56961),x56962)),f329(f108(x56961),x56963)),f329(f108(x56961),f329(f329(f82(a1),x56962),x56963))) % 178.07/177.93 [5697]~P137(x56971)+E(f329(f329(f81(x56971),f329(f108(x56971),x56972)),f329(f108(x56971),x56973)),f329(f108(x56971),f329(f329(f81(a1),x56972),x56973))) % 178.07/177.93 [5698]~P92(x56981)+E(f329(f329(f22(x56981),f329(f109(x56981),x56982)),f329(f109(x56981),x56983)),f329(f109(x56981),f329(f329(f22(a1),x56982),x56983))) % 178.07/177.93 [5701]~P92(x57011)+E(f329(f329(f82(x57011),f329(f109(x57011),x57012)),f329(f109(x57011),x57013)),f329(f109(x57011),f329(f329(f82(a1),x57012),x57013))) % 178.07/177.93 [5702]~P92(x57021)+E(f329(f329(f81(x57021),f329(f109(x57021),x57022)),f329(f109(x57021),x57023)),f329(f109(x57021),f329(f329(f81(a1),x57022),x57023))) % 178.07/177.93 [5751]~E(x57513,x57512)+P24(f329(f329(f243(f883(x57511,a869)),x57512),x57513)) % 178.07/177.93 [5757]~E(x57572,x57573)+P24(f329(f329(f243(f883(x57571,a869)),x57572),x57573)) % 178.07/177.93 [5762]~P89(x57621)+E(f329(f329(f107(x57621),f329(f80(x57621),x57622)),f329(f80(x57621),x57623)),f329(f80(x57621),f329(f329(f116(x57621),x57622),x57623))) % 178.07/177.93 [5763]~P89(x57631)+E(f329(f329(f116(x57631),f329(f80(x57631),x57632)),f329(f80(x57631),x57633)),f329(f80(x57631),f329(f329(f107(x57631),x57632),x57633))) % 178.07/177.93 [5764]~P67(x57641)+E(f329(f329(f81(x57641),f329(f80(x57641),x57642)),f329(f80(x57641),x57643)),f329(f80(x57641),f329(f329(f81(x57641),x57643),x57642))) % 178.07/177.93 [5765]~P66(x57651)+E(f329(f329(f81(x57651),f329(f80(x57651),x57652)),f329(f80(x57651),x57653)),f329(f80(x57651),f329(f329(f81(x57651),x57652),x57653))) % 178.07/177.93 [5766]~P75(x57661)+E(f329(f329(f242(x57661),f329(f80(x57661),x57662)),f329(f80(x57661),x57663)),f329(f80(x57661),f329(f329(f241(x57661),x57662),x57663))) % 178.07/177.93 [5767]~P75(x57671)+E(f329(f329(f241(x57671),f329(f80(x57671),x57672)),f329(f80(x57671),x57673)),f329(f80(x57671),f329(f329(f242(x57671),x57672),x57673))) % 178.07/177.93 [5768]~P117(x57681)+E(f329(f329(f82(x57681),f329(f76(x57681),x57682)),f329(f76(x57681),x57683)),f329(f76(x57681),f329(f329(f82(x57681),x57682),x57683))) % 178.07/177.93 [5769]~P61(x57691)+E(f329(f329(f287(x57691),f329(f76(x57691),x57692)),f329(f76(x57691),x57693)),f329(f76(x57691),f329(f329(f287(x57691),x57692),x57693))) % 178.07/177.93 [5770]~P80(x57701)+E(f329(f329(f81(x57701),f329(f165(x57701),x57702)),f329(f165(x57701),x57703)),f329(f165(x57701),f329(f329(f127(x57701),x57702),x57703))) % 178.07/177.93 [5771]E(x57711,f193(f883(x57712,a869)))+~E(f329(f329(f116(f883(x57712,a869)),x57713),x57711),f193(f883(x57712,a869))) % 178.07/177.93 [5772]E(x57721,f193(f883(x57722,a869)))+~E(f329(f329(f116(f883(x57722,a869)),x57721),x57723),f193(f883(x57722,a869))) % 178.07/177.93 [5773]~P144(x57731,x57733,x57732)+P24(f329(x57731,f329(f329(f39(a1),x57732),x57733))) % 178.07/177.93 [5823]~P24(f329(f62(x58231),x58233))+P24(f329(f62(x58231),f329(f329(f307(x58231),x58232),x58233))) % 178.07/177.93 [5824]~P24(f329(f136(x58241),x58243))+P24(f329(f136(x58241),f329(f329(f174(x58241),x58242),x58243))) % 178.07/177.93 [5825]~P24(f329(f136(x58251),x58253))+P24(f329(f136(x58251),f329(f329(f137(x58251),x58252),x58253))) % 178.07/177.93 [5854]~P63(x58541)+P24(f329(f329(f243(x58541),x58542),f329(f329(f116(x58541),x58543),x58542))) % 178.07/177.93 [5855]~P99(x58551)+P24(f329(f329(f243(x58551),x58552),f329(f329(f116(x58551),x58553),x58552))) % 178.07/177.93 [5856]~P63(x58561)+P24(f329(f329(f243(x58561),x58562),f329(f329(f116(x58561),x58562),x58563))) % 178.07/177.93 [5857]~P99(x58571)+P24(f329(f329(f243(x58571),x58572),f329(f329(f116(x58571),x58572),x58573))) % 178.07/177.93 [5858]~P105(x58581)+P24(f329(f329(f243(x58581),x58582),f329(f329(f242(x58581),x58583),x58582))) % 178.07/177.93 [5859]~P105(x58591)+P24(f329(f329(f243(x58591),x58592),f329(f329(f242(x58591),x58592),x58593))) % 178.07/177.93 [5873]~E(x58731,f2(a875))+E(f329(f329(f39(a875),f329(f329(f82(a875),x58731),x58732)),f329(f329(f82(a875),x58731),x58733)),f2(a875)) % 178.07/177.93 [5942]P24(f329(x59421,x59422))+P24(f329(f329(f199(f33(x59421,x59423)),x59422),x59422)) % 178.07/177.93 [5957]~P92(x59571)+E(f329(f329(f22(x59571),f329(f109(x59571),x59572)),f329(f109(x59571),x59573)),f329(f109(x59571),f329(f329(f81(a1),x59572),f329(f80(a1),x59573)))) % 178.07/177.93 [6012]E(x60121,f2(a875))+E(f329(f329(f39(a875),f329(f329(f82(a875),x60121),x60122)),f329(f329(f82(a875),x60121),x60123)),f329(f329(f39(a875),x60122),x60123)) % 178.07/177.93 [6046]E(f151(x60461,f329(f329(f150(x60461),x60462),x60463)),f329(f329(f150(x60461),x60462),f151(x60461,x60463)))+P24(f329(f329(f331(x60461),x60462),f329(f171(x60461),x60463))) % 178.07/177.93 [6080]P144(x60801,x60802,x60803)+~P24(f329(x60801,f329(f329(f39(a1),x60803),x60802))) % 178.07/177.93 [6155]E(x61551,f119(x61552))+E(f329(f329(f150(x61552),f329(f140(x61552),x61551)),f329(f329(f174(x61552),x61553),f329(f170(x61552),x61551))),f329(f329(f174(x61552),f329(a118,x61553)),x61551)) % 178.07/177.93 [6161]E(f329(f329(f22(f883(x61611,a869)),x61612),x61613),x61612)+~E(f329(f329(f107(f883(x61611,a869)),x61612),x61613),f193(f883(x61611,a869))) % 178.07/177.93 [6174]E(f151(x61741,f329(f329(f150(x61741),x61742),x61743)),f151(x61741,x61743))+~P24(f329(f329(f331(x61741),x61742),f329(f171(x61741),x61743))) % 178.07/177.93 [6206]~P24(f329(f329(f244(a875),x62061),x62063))+P24(f329(f329(f244(a875),x62061),f329(f329(f81(a875),x62062),x62063))) % 178.07/177.93 [6208]~P24(f329(f329(f244(a875),x62081),x62082))+P24(f329(f329(f244(a875),x62081),f329(f329(f81(a875),x62082),x62083))) % 178.07/177.93 [6210]~P24(f329(f329(f243(a875),x62101),x62103))+P24(f329(f329(f243(a875),x62101),f329(f329(f81(a875),x62102),x62103))) % 178.07/177.93 [6212]~P24(f329(f329(f243(a875),x62121),x62122))+P24(f329(f329(f243(a875),x62121),f329(f329(f81(a875),x62122),x62123))) % 178.07/177.93 [6251]P24(f329(f62(x62511),x62512))+~P24(f329(f62(x62511),f329(f329(f307(x62511),x62513),x62512))) % 178.07/177.93 [6252]P24(f329(f136(x62521),x62522))+~P24(f329(f136(x62521),f329(f329(f150(x62521),x62523),x62522))) % 178.07/177.93 [6253]P24(f329(f136(x62531),x62532))+~P24(f329(f136(x62531),f329(f329(f127(x62531),x62533),x62532))) % 178.07/177.93 [6254]P24(f329(f136(x62541),x62542))+~P24(f329(f136(x62541),f329(f329(f127(x62541),x62542),x62543))) % 178.07/177.93 [6300]~P114(x63001)+E(f329(f329(f81(x63001),x63002),f329(f329(f82(x63001),x63003),x63002)),f329(f329(f82(x63001),f329(f329(f81(x63001),x63003),f79(x63001))),x63002)) % 178.07/177.93 [6348]~E(x63481,x63482)+~P24(f329(f329(f244(f883(x63483,a869)),x63481),x63482)) % 178.07/177.93 [6392]P24(f329(f329(f331(x63921),x63922),x63923))+P24(f329(f329(f331(x63921),x63922),f329(f80(f883(x63921,a869)),x63923))) % 178.07/177.93 [6398]E(f143(x63981,f329(f329(f137(x63981),x63982),x63983)),f143(x63981,x63983))+~P24(f329(f329(f244(a875),x63982),f329(f194(f876(x63981)),x63983))) % 178.07/177.93 [6399]E(f329(f329(f174(x63991),x63992),f120(x63991,x63993)),f329(f329(f174(x63991),x63992),x63993))+~P24(f329(f329(f244(a875),x63992),f329(f194(f876(x63991)),x63993))) % 178.07/177.93 [6454]E(f329(f329(f329(f188(f876(x64541),f876(x64541)),x64542),f167(x64541)),x64543),x64543)+~E(f45(a875,x64542,f329(f194(f876(x64541)),x64543)),f2(a875)) % 178.07/177.93 [6461]~P6(x64611,x64613,x64612)+E(f329(f329(f286(x64611,x64611,x64611),f329(f284(x64611,x64611),x64612)),x64612),x64612) % 178.07/177.93 [6503]~E(f329(f329(f116(f883(x65031,a869)),x65032),x65033),x65033)+P24(f329(f329(f243(f883(x65031,a869)),x65032),x65033)) % 178.07/177.93 [6508]~P50(x65081,x65081,x65083)+P50(x65081,x65081,f329(f329(f188(f882(x65081,x65081),a869),x65082),x65083)) % 178.07/177.93 [6510]~P24(f329(f329(f331(x65101),x65103),f329(f171(x65101),x65102)))+P24(f329(f329(f244(a875),f2(a875)),f329(f194(f876(x65101)),x65102))) % 178.07/177.93 [6536]~P85(x65361)+E(f329(f76(x65361),f329(f329(f81(x65361),f329(f76(x65361),x65362)),f329(f76(x65361),x65363))),f329(f329(f81(x65361),f329(f76(x65361),x65362)),f329(f76(x65361),x65363))) % 178.07/177.93 [6547]E(f329(f329(f39(a875),f329(f329(f82(a875),x65471),x65472)),f329(f329(f82(a875),x65471),x65473)),f329(f329(f39(a875),x65472),x65473))+~P24(f329(f329(f244(a875),f2(a875)),x65471)) % 178.07/177.93 [6595]E(x65951,x65952)+~P24(f329(f329(f329(f329(a201,a24),x65951),x65953),x65952)) % 178.07/177.93 [6684]~P24(f329(f62(x66841),x66843))+E(f329(f329(f65(x66841,f883(x66841,a869),f307(x66841)),x66842),x66843),f329(f329(f116(f883(x66841,a869)),x66843),x66842)) % 178.07/177.93 [6743]E(f329(f329(f116(f883(x67431,a869)),x67432),x67433),x67432)+~P24(f329(f329(f243(f883(x67431,a869)),x67433),x67432)) % 178.07/177.93 [6745]E(f329(f329(f116(f883(x67451,a869)),x67452),x67453),x67453)+~P24(f329(f329(f243(f883(x67451,a869)),x67452),x67453)) % 178.07/177.93 [6746]E(f329(f329(f107(f883(x67461,a869)),x67462),x67463),x67463)+~P24(f329(f329(f243(f883(x67461,a869)),x67463),x67462)) % 178.07/177.93 [6747]E(f329(f329(f107(f883(x67471,a869)),x67472),x67473),x67472)+~P24(f329(f329(f243(f883(x67471,a869)),x67472),x67473)) % 178.07/177.93 [6798]~P24(f329(f136(x67981),x67982))+E(f329(f329(f22(f883(x67981,a869)),f329(f171(x67981),x67982)),f329(f329(f307(x67981),x67983),f193(f883(x67981,a869)))),f329(f171(x67981),f169(x67981,x67983,x67982))) % 178.07/177.93 [6851]P38(x68511,x68512)+~P38(x68511,f329(f329(f188(f882(x68511,x68511),a869),x68513),x68512)) % 178.07/177.93 [6917]P24(f329(f49(x69171,x69172),f329(a51,x69173)))+~P24(f329(f49(f329(f80(a1),x69171),f329(f80(a1),x69172)),x69173)) % 178.07/177.93 [6922]E(f329(f329(f22(f883(x69221,a869)),f329(f329(f307(x69221),x69222),x69223)),f329(f329(f307(x69221),x69222),f193(f883(x69221,a869)))),x69223)+P24(f329(f329(f331(x69221),x69222),x69223)) % 178.07/177.93 [6943]E(f329(f329(f107(f883(x69431,a869)),f329(f171(x69431),x69432)),f329(f171(x69431),x69433)),f193(f883(x69431,a869)))+~P24(f329(f136(x69431),f329(f329(f127(x69431),x69432),x69433))) % 178.07/177.93 [6959]~P24(f329(f329(f331(x69591),x69592),f329(f171(x69591),x69593)))+~P24(f329(f136(x69591),f329(f329(f150(x69591),x69592),x69593))) % 178.07/177.93 [7031]P32(x70311,x70312,x70313)+P24(f329(f329(f244(a875),f789(x70313,x70312,x70311)),f329(f194(f876(x70311)),x70313))) % 178.07/177.93 [7041]E(f329(f329(f107(f883(x70411,a869)),x70412),x70413),f193(f883(x70411,a869)))+P24(f329(f329(f331(x70411),f729(x70413,x70412,x70411)),x70412)) % 178.07/177.93 [7042]E(f329(f329(f107(f883(x70421,a869)),x70422),x70423),f193(f883(x70421,a869)))+P24(f329(f329(f331(x70421),f754(x70423,x70422,x70421)),x70423)) % 178.07/177.93 [7046]E(f120(x70461,f329(f329(f174(x70461),x70462),x70463)),f329(f329(f174(x70461),f329(f329(f22(a875),x70462),f79(a875))),x70463))+~P24(f329(f329(f243(a875),x70462),f329(f194(f876(x70461)),x70463))) % 178.07/177.93 [7105]~P34(x71053,x71052,x71051)+P24(f329(f329(f244(a875),f746(x71051,x71052,x71053)),f329(f194(f876(x71053)),x71051))) % 178.07/177.93 [7123]P24(f329(f329(f244(a875),f2(a875)),x71231))+P24(f329(f329(f243(a875),f329(f329(f82(a875),x71232),x71231)),f329(f329(f82(a875),x71233),x71231))) % 178.07/177.93 [7124]P24(f329(f329(f244(a875),f2(a875)),x71241))+P24(f329(f329(f243(a875),f329(f329(f82(a875),x71241),x71242)),f329(f329(f82(a875),x71241),x71243))) % 178.07/177.93 [7127]~P24(f329(f329(f331(x71271),x71272),x71273))+~P24(f329(f329(f331(x71271),x71272),f329(f80(f883(x71271,a869)),x71273))) % 178.07/177.93 [7134]~P24(f329(f329(f244(f883(x71341,a869)),x71342),x71343))+P24(f329(f329(f243(f883(x71341,a869)),x71342),x71343)) % 178.07/177.93 [7233]~P24(f329(f329(f244(a875),x72332),x72333))+P24(f329(f329(f244(a875),f329(f329(f81(a875),x72331),x72332)),f329(f329(f81(a875),x72331),x72333))) % 178.07/177.93 [7234]~P24(f329(f329(f244(a875),x72341),x72343))+P24(f329(f329(f244(a875),f329(f329(f81(a875),x72341),x72342)),f329(f329(f81(a875),x72343),x72342))) % 178.07/177.93 [7235]~P24(f329(f329(f244(a1),x72351),x72353))+P24(f329(f329(f244(a1),f329(f329(f81(a1),x72351),x72352)),f329(f329(f81(a1),x72353),x72352))) % 178.07/177.93 [7238]~P24(f329(f329(f243(a875),x72383),x72382))+P24(f329(f329(f243(a875),f329(f329(f22(a875),x72381),x72382)),f329(f329(f22(a875),x72381),x72383))) % 178.07/177.93 [7239]~P24(f329(f329(f243(a875),x72391),x72393))+P24(f329(f329(f243(a875),f329(f329(f22(a875),x72391),x72392)),f329(f329(f22(a875),x72393),x72392))) % 178.07/177.93 [7241]~P24(f329(f329(f243(a875),x72412),x72413))+P24(f329(f329(f243(a875),f329(f329(f82(a875),x72411),x72412)),f329(f329(f82(a875),x72411),x72413))) % 178.07/177.93 [7243]~P24(f329(f329(f243(a875),x72431),x72433))+P24(f329(f329(f243(a875),f329(f329(f82(a875),x72431),x72432)),f329(f329(f82(a875),x72433),x72432))) % 178.07/177.93 [7244]~P24(f329(f329(f243(a875),x72442),x72443))+P24(f329(f329(f243(a875),f329(f329(f81(a875),x72441),x72442)),f329(f329(f81(a875),x72441),x72443))) % 178.07/177.93 [7245]~P24(f329(f329(f243(a875),x72451),x72453))+P24(f329(f329(f243(a875),f329(f329(f81(a875),x72451),x72452)),f329(f329(f81(a875),x72453),x72452))) % 178.07/177.93 [7246]~P24(f329(f329(f243(a875),x72461),x72463))+P24(f329(f329(f243(a875),f329(f329(f39(a875),x72461),x72462)),f329(f329(f39(a875),x72463),x72462))) % 178.07/177.93 [7247]~P24(f329(f329(f243(a1),x72472),x72473))+P24(f329(f329(f243(a1),f329(f329(f81(a1),x72471),x72472)),f329(f329(f81(a1),x72471),x72473))) % 178.07/177.93 [7327]E(x73271,x73272)+~P24(f329(f329(f331(x73273),x73271),f329(f329(f307(x73273),x73272),f193(f883(x73273,a869))))) % 178.07/177.93 [7329]~E(f329(f329(f107(f883(x73291,a869)),x73292),x73293),f193(f883(x73291,a869)))+P24(f329(f329(f243(f883(x73291,a869)),x73292),f329(f80(f883(x73291,a869)),x73293))) % 178.07/177.93 [7337]P24(f329(f329(f331(f883(x73371,a869)),x73372),f329(f306(x73371),x73373)))+~P24(f329(f329(f243(f883(x73371,a869)),x73372),x73373)) % 178.07/177.93 [7391]E(f329(f329(f150(x73911),f329(f329(f164(x73911),x73912),x73913)),f329(f329(f137(x73911),f329(a118,x73913)),x73912)),f329(f329(f137(x73911),x73913),x73912))+~P24(f329(f329(f244(a875),x73913),f329(f194(f876(x73911)),x73912))) % 178.07/177.93 [7418]P24(f329(f329(f331(f882(x74181,x74181)),x74182),f305(x74181,x74183)))+~P24(f329(f329(f331(f882(x74181,x74181)),x74182),x74183)) % 178.07/177.93 [7429]~P24(f329(f329(f331(f883(x74291,a869)),x74292),f329(f306(x74291),x74293)))+P24(f329(f329(f243(f883(x74291,a869)),x74292),x74293)) % 178.07/177.93 [7475]P24(f329(f329(f243(f883(x74751,a869)),x74752),f40(f883(x74751,a869),x74753)))+~P24(f329(f329(f331(f883(x74751,a869)),x74752),x74753)) % 178.07/177.93 [7500]~P137(x75001)+E(f329(f329(f82(x75001),f329(f329(f254(x75001),f329(f80(x75001),f79(x75001))),x75002)),f329(f329(f254(x75001),x75003),x75002)),f329(f329(f254(x75001),f329(f80(x75001),x75003)),x75002)) % 178.07/177.93 [7521]E(f329(f329(f164(x75211),x75212),f329(f329(f22(a875),f329(f194(f876(x75211)),x75212)),f329(a118,x75213))),f329(f329(f164(x75211),f329(f168(x75211),x75212)),x75213))+~P24(f329(f329(f244(a875),x75213),f329(f194(f876(x75211)),x75212))) % 178.07/177.93 [7538]~E(f329(f329(f107(f883(x75381,a869)),f838(x75383,x75382,x75381)),x75383),f193(f883(x75381,a869)))+E(f329(f329(f107(f883(x75381,a869)),f40(f883(x75381,a869),x75382)),x75383),f193(f883(x75381,a869))) % 178.07/177.93 [7599]~P24(f329(f329(f331(x75993),x75992),f329(f171(x75993),x75991)))+P24(f329(f329(f244(a875),f580(x75991,x75992,x75993)),f329(f194(f876(x75993)),x75991))) % 178.07/177.93 [7607]P24(f329(f329(f331(x76071),f329(f329(f164(x76071),x76072),x76073)),f329(f171(x76071),x76072)))+~P24(f329(f329(f244(a875),x76073),f329(f194(f876(x76071)),x76072))) % 178.07/177.93 [7707]~P24(f329(x77072,f660(x77073,x77072,x77071)))+E(f329(f329(f137(x77071),f329(f194(f876(x77071)),f176(x77071,x77072,x77073))),x77073),f119(x77071)) % 178.07/177.93 [7717]P24(f329(f329(f243(f883(f876(x77171),a869)),f160(x77171,x77172)),f160(x77171,x77173)))+~P24(f329(f329(f243(f883(x77171,a869)),x77172),x77173)) % 178.07/177.93 [7718]P24(f329(f329(f243(f883(f876(x77181),a869)),f159(x77181,x77182)),f159(x77181,x77183)))+~P24(f329(f329(f243(f883(x77181,a869)),x77182),x77183)) % 178.07/177.93 [7746]E(f329(f329(f107(f883(x77461,a869)),f40(f883(x77461,a869),x77462)),x77463),f193(f883(x77461,a869)))+P24(f329(f329(f331(f883(x77461,a869)),f838(x77463,x77462,x77461)),x77462)) % 178.07/177.93 [7749]~P24(f329(f329(f331(f883(x77491,a869)),x77493),x77492))+P24(f329(f329(f243(f883(x77491,a869)),f41(f883(x77491,a869),x77492)),x77493)) % 178.07/177.93 [7751]E(f329(f329(f107(f883(x77511,a869)),x77512),x77513),f193(f883(x77511,a869)))+~P24(f329(f329(f243(f883(x77511,a869)),x77512),f329(f80(f883(x77511,a869)),x77513))) % 178.07/177.93 [7798]E(f329(f329(f22(a875),f329(f329(f81(a875),f329(f165(a875),x77981)),x77982)),f329(f329(f164(a875),x77981),x77983)),f329(f165(a875),f329(f329(f158(a875,x77981),x77983),x77982)))+~P24(f329(f329(f244(a875),x77983),f329(f194(f876(a875)),x77981))) % 178.07/177.93 [7847]P24(f329(f329(f244(a875),x78471),x78472))+~P24(f329(f329(f244(a875),f329(f329(f81(a875),x78473),x78471)),f329(f329(f81(a875),x78473),x78472))) % 178.07/177.93 [7848]P24(f329(f329(f244(a875),x78481),x78482))+~P24(f329(f329(f244(a875),f329(f329(f82(a875),x78483),x78481)),f329(f329(f82(a875),x78483),x78482))) % 178.07/177.93 [7849]P24(f329(f329(f244(a875),x78491),x78492))+~P24(f329(f329(f244(a875),f329(f329(f82(a875),x78491),x78493)),f329(f329(f82(a875),x78492),x78493))) % 178.07/177.93 [7852]P24(f329(f329(f243(a875),x78521),x78522))+~P24(f329(f329(f243(a875),f329(f329(f81(a875),x78523),x78521)),f329(f329(f81(a875),x78523),x78522))) % 178.07/177.93 [7882]P24(f329(f329(f244(a875),f2(a875)),x78821))+~P24(f329(f329(f244(a875),f329(f329(f82(a875),x78822),x78821)),f329(f329(f82(a875),x78823),x78821))) % 178.07/177.93 [7883]P24(f329(f329(f244(a875),f2(a875)),x78831))+~P24(f329(f329(f244(a875),f329(f329(f82(a875),x78831),x78832)),f329(f329(f82(a875),x78831),x78833))) % 178.07/177.93 [7956]E(f256(x79561,x79562,x79563),x79562)+~P24(f329(f329(f243(f883(x79561,a869)),x79563),f329(f329(f307(x79561),x79562),f193(f883(x79561,a869))))) % 178.07/177.93 [8014]~P24(f329(f136(x80141),x80143))+E(f329(f135(x80141,f329(f329(f8(a869,a869,x80141),a324),f329(a326,x80142))),x80143),f169(x80141,x80142,x80143)) % 178.07/177.93 [8037]E(f329(f329(f137(x80371),f329(f194(f876(x80371)),f176(x80371,x80372,x80373))),x80373),f119(x80371))+P24(f329(f329(f331(x80371),f660(x80373,x80372,x80371)),f329(f171(x80371),x80373))) % 178.07/177.93 [8041]E(f329(f329(f127(x80411),f329(f329(f174(x80411),x80412),x80413)),f329(f329(f150(x80411),f329(f329(f164(x80411),x80413),x80412)),f119(x80411))),f329(f329(f174(x80411),f329(a118,x80412)),x80413))+~P24(f329(f329(f244(a875),x80412),f329(f194(f876(x80411)),x80413))) % 178.07/177.93 [8103]E(f329(f135(x81031,f329(f329(f8(a869,a869,x81031),a324),f329(a326,x81032))),x81033),x81033)+P24(f329(f329(f331(x81031),x81032),f329(f171(x81031),x81033))) % 178.07/177.93 [8111]P24(f329(f329(f243(f883(f883(x81111,a869),a869)),f257(x81111,x81112)),f257(x81111,x81113)))+~P24(f329(f329(f243(f883(x81111,a869)),x81112),x81113)) % 178.07/177.93 [8155]~P24(f329(f136(x81551),x81553))+P24(f329(f136(x81551),f329(f329(f329(f188(f876(x81551),f876(x81551)),x81552),f167(x81551)),x81553))) % 178.07/177.93 [8160]~P24(f329(f329(f244(a875),x81602),x81603))+P24(f329(f329(f244(a875),f329(f329(f82(a875),f329(a118,x81601)),x81602)),f329(f329(f82(a875),f329(a118,x81601)),x81603))) % 178.07/177.93 [8183]P24(f329(f329(f243(f883(f883(x81831,a869),a869)),f329(f306(x81831),x81832)),f329(f306(x81831),x81833)))+~P24(f329(f329(f243(f883(x81831,a869)),x81832),x81833)) % 178.07/177.93 [8345]~P24(f329(f329(f243(f883(x83451,a869)),x83453),x83452))+P24(f329(f329(f243(f883(x83451,a869)),f329(f80(f883(x83451,a869)),x83452)),f329(f80(f883(x83451,a869)),x83453))) % 178.07/177.93 [8377]E(f329(f308(a875,a875,f329(f329(f7(a875,a875,a875),f22(a875)),x83771)),f329(f299(a875,x83772),x83773)),f329(f299(a875,f329(f329(f22(a875),x83772),x83771)),f329(f329(f22(a875),x83773),x83771)))+~P24(f329(f329(f244(a875),x83771),x83773)) % 178.07/177.93 [8405]~P80(x84051)+E(f329(f329(f81(x84051),x84052),f329(f141(x84051,x84051,f81(x84051),f2(x84051)),x84053)),f329(f141(x84051,x84051,f81(x84051),x84052),x84053)) % 178.07/177.93 [8488]~P85(x84881)+P24(f329(f329(f243(x84881),f329(f76(x84881),f329(f329(f22(x84881),x84882),x84883))),f329(f329(f81(x84881),f329(f76(x84881),x84882)),f329(f76(x84881),x84883)))) % 178.07/177.93 [8489]~P85(x84891)+P24(f329(f329(f243(x84891),f329(f76(x84891),f329(f329(f81(x84891),x84892),x84893))),f329(f329(f81(x84891),f329(f76(x84891),x84892)),f329(f76(x84891),x84893)))) % 178.07/177.93 [8499]E(f329(f329(f81(a1),f329(f329(f82(a1),x84991),f45(a1,f329(f329(f39(a1),x84992),x84991),x84993))),f45(a1,x84992,x84991)),f45(a1,x84992,f329(f329(f82(a1),x84991),x84993)))+~P24(f329(f329(f244(a1),f2(a1)),x84993)) % 178.07/177.93 [8505]E(f329(f329(f127(x85051),f329(f329(f174(x85051),x85052),x85053)),f329(f329(f150(x85051),f329(f140(x85051),f329(f329(f137(x85051),x85052),x85053))),f119(x85051))),f329(f329(f174(x85051),f329(a118,x85052)),x85053))+~P24(f329(f329(f244(a875),x85052),f329(f194(f876(x85051)),x85053))) % 178.07/177.93 [8524]E(f329(f275(x85241,f329(f329(f153(x85241,f882(a105,x85241)),f329(f264(a105,x85241),f79(a105))),x85242)),f329(a3,x85243)),f329(f329(f164(x85241),x85242),x85243))+~P24(f329(f329(f244(a875),x85243),f329(f194(f876(x85241)),x85242))) % 178.07/177.93 [8589]P24(f329(f329(f331(f882(x85891,x85891)),x85892),f329(f329(f286(x85891,x85891,x85891),x85893),f305(x85891,x85893))))+~P24(f329(f329(f331(f882(x85891,x85891)),x85892),x85893)) % 178.07/177.93 [8609]P24(f329(f329(f243(a875),x86091),x86092))+~P24(f329(f329(f243(a875),f329(f329(f82(a875),f329(a118,x86093)),x86091)),f329(f329(f82(a875),f329(a118,x86093)),x86092))) % 178.07/177.93 [8623]P24(f329(f329(f243(f883(x86231,a869)),x86232),x86233))+~P24(f329(f329(f243(f883(x86231,a869)),f329(f80(f883(x86231,a869)),x86233)),f329(f80(f883(x86231,a869)),x86232))) % 178.07/177.93 [8642]P24(f329(f136(x86421),x86422))+~P24(f329(f136(x86421),f329(f329(f329(f188(f876(x86421),f876(x86421)),x86423),f167(x86421)),x86422))) % 178.07/177.93 [8702]E(f329(f308(f882(x87021,x87022),x87022,f267(x87021,x87022)),f329(f171(f882(x87021,x87022)),x87023)),f185(x87021,x87022,f329(f177(x87021,x87022),x87023)))+~P24(f329(f136(x87021),f329(f329(f153(f882(x87021,x87022),x87021),f263(x87021,x87022)),x87023))) % 178.07/177.93 [8711]E(f329(f283(x87111,x87111,f305(x87111,x87112)),x87113),x87113)+~P24(f329(f329(f243(f883(x87111,a869)),f329(f283(x87111,x87111,x87112),x87113)),x87113)) % 178.07/177.93 [8753]~P105(x87531)+P29(x87531,f329(f135(x87531,f329(f329(f7(x87531,x87531,a869),a326),f329(x87532,x87533))),x87533)) % 178.07/177.93 [8759]~P24(f329(f329(f243(a875),x87591),x87592))+P24(f329(f329(f243(a875),x87591),f329(f141(a875,a875,f81(a875),x87592),x87593))) % 178.07/177.93 [8836]~P24(f329(f329(f331(f882(x88361,x88361)),x88362),f305(x88361,x88363)))+P24(f329(f329(f331(f882(x88361,x88361)),x88362),f329(f329(f188(f882(x88361,x88361),a869),f755(x88363,x88362,x88361)),x88363))) % 178.07/177.93 [8928]~P80(x89281)+E(f329(f329(f81(x89281),x89282),f329(f141(x89281,x89281,f329(f7(x89281,x89281,x89281),f81(x89281)),f2(x89281)),f329(f168(x89281),x89283))),f329(f141(x89281,x89281,f81(x89281),x89282),x89283)) % 178.07/177.93 [9197]P50(x91971,x91972,x91973)+P24(f329(f329(f331(f882(x91971,x91972)),f329(f329(f264(x91971,x91972),f750(x91973,x91972,x91971)),f728(x91973,x91972,x91971))),x91973)) % 178.07/177.93 [9198]P50(x91981,x91982,x91983)+P24(f329(f329(f331(f882(x91981,x91982)),f329(f329(f264(x91981,x91982),f750(x91983,x91982,x91981)),f727(x91983,x91982,x91981))),x91983)) % 178.07/177.93 [9269]~P24(f329(f329(f331(f882(x92691,x92691)),x92692),f329(f329(f286(x92691,x92691,x92691),x92693),f305(x92691,x92693))))+P24(f329(f329(f331(f882(x92691,x92691)),x92692),f329(f329(f188(f882(x92691,x92691),a869),f756(x92693,x92692,x92691)),x92693))) % 178.07/177.93 [9270]~P24(f329(x92701,f329(f329(f164(x92702),x92703),f329(f194(f876(x92702)),f176(x92702,x92701,x92703)))))+~P24(f329(f329(f244(a875),f329(f194(f876(x92702)),f176(x92702,x92701,x92703))),f329(f194(f876(x92702)),x92703))) % 178.07/177.93 [9359]~P24(f329(f329(f243(f883(x93591,a869)),x93592),x93593))+P24(f329(f329(f243(f883(x93591,a869)),f329(f329(f7(x93591,f883(x93591,a869),a869),f331(x93591)),x93592)),f329(f329(f7(x93591,f883(x93591,a869),a869),f331(x93591)),x93593))) % 178.07/177.93 [9411]~P24(f329(f329(f331(f882(f883(x94111,a869),f883(x94111,a869))),f329(f329(f264(f883(x94111,a869),f883(x94111,a869)),x94112),x94113)),f304(x94111)))+P24(f329(f329(f244(f883(x94111,a869)),x94112),x94113)) % 178.07/177.93 [9436]P51(x94361,x94362,x94363)+~P24(f329(f329(f331(f882(x94361,x94361)),f329(f329(f264(x94361,x94361),f753(x94363,x94362,x94361)),f752(x94363,x94362,x94361))),x94363)) % 178.07/177.93 [9437]P51(x94371,x94372,x94373)+~P24(f329(f329(f331(f882(x94371,x94371)),f329(f329(f264(x94371,x94371),f752(x94373,x94372,x94371)),f753(x94373,x94372,x94371))),x94373)) % 178.07/177.93 [9473]~P24(f329(f329(f331(f882(f876(x94731),f876(x94731))),f329(f329(f264(f876(x94731),f876(x94731)),x94732),x94732)),f146(x94731,x94733)))+P24(f329(f329(f331(f882(x94731,x94731)),f329(f329(f264(x94731,x94731),f608(x94732,x94733,x94731)),f608(x94732,x94733,x94731))),x94733)) % 178.07/177.93 [9524]P24(f329(f329(f243(f883(x95241,a869)),x95242),x95243))+~P24(f329(f329(f243(f883(x95241,a869)),f329(f329(f7(x95241,f883(x95241,a869),a869),f331(x95241)),x95242)),f329(f329(f7(x95241,f883(x95241,a869),a869),f331(x95241)),x95243))) % 178.07/177.93 [9605]E(f329(f329(f22(a875),f329(f329(f6(a875,a875),x96051),f329(f250(a875),x96052))),f329(f329(f6(a875,a875),x96053),f329(f250(a875),x96052))),f329(f329(f6(a875,a875),f329(f329(f18(a875,a875,a875),f329(f329(f8(a875,f883(a875,a875),a875),f22(a875)),x96051)),x96053)),f329(f250(a875),x96052)))+~P24(f329(f329(f243(a875),f329(x96053,f410(x96052,x96051,x96053))),f329(x96051,f410(x96052,x96051,x96053)))) % 178.07/177.93 [9908]E(f329(f249(f882(x99081,x99082)),f329(f268(x99081,x99082,a869),f329(f329(f7(x99081,f883(x99082,f879(x99082)),f883(x99082,a869)),f329(f329(f8(f883(f879(x99082),a869),f883(f883(x99082,f879(x99082)),f883(x99082,a869)),x99081),f8(f879(x99082),a869,x99082)),f329(f329(f8(f879(x99082),f883(f879(x99082),a869),x99081),a326),f329(f177(x99081,x99082),x99083)))),f236(x99082)))),f329(f171(f882(x99081,x99082)),x99083))+~P24(f329(f136(x99081),f329(f329(f153(f882(x99081,x99082),x99081),f263(x99081,x99082)),x99083))) % 178.07/177.93 [5610]~P67(x56101)+E(f329(f329(f22(x56101),f329(f329(f81(x56101),x56102),x56103)),x56103),x56102) % 178.07/177.93 [5611]~P67(x56111)+E(f329(f329(f81(x56111),f329(f329(f22(x56111),x56112),x56113)),x56113),x56112) % 178.07/177.93 [5831]~P67(x58311)+E(f329(f329(f81(x58311),x58312),f329(f329(f81(x58311),f329(f80(x58311),x58312)),x58313)),x58313) % 178.07/177.93 [5916]~P79(x59161)+E(f329(f329(f82(x59161),f329(f329(f254(x59161),x59162),x59163)),x59162),f329(f329(f254(x59161),x59162),f329(a118,x59163))) % 178.07/177.93 [5917]~P114(x59171)+E(f329(f329(f82(x59171),f329(f329(f254(x59171),x59172),x59173)),x59172),f329(f329(f254(x59171),x59172),f329(a118,x59173))) % 178.07/177.93 [6130]~P117(x61301)+E(f329(f76(x61301),f329(f329(f254(x61301),f329(f80(x61301),x61302)),x61303)),f329(f76(x61301),f329(f329(f254(x61301),x61302),x61303))) % 178.07/177.93 [6186]~P79(x61861)+E(f329(f329(f82(x61861),f329(f329(f254(x61861),x61862),x61863)),x61862),f329(f329(f82(x61861),x61862),f329(f329(f254(x61861),x61862),x61863))) % 178.07/177.93 [6242]E(f329(f329(f22(a105),f329(f329(f81(a105),x62421),x62422)),x62423),f279(x62421,x62422,x62423))+~P24(f329(f329(f244(a105),x62422),x62423)) % 178.07/177.93 [6263]~E(f329(f329(f137(x62631),x62633),x62632),f119(x62631))+P24(f329(f329(f243(a875),f329(f194(f876(x62631)),x62632)),x62633)) % 178.07/177.93 [6397]E(f329(f329(f82(a875),f329(f109(a875),x63971)),f329(f329(f82(a875),f329(f109(a875),x63972)),x63973)),f2(a875))+~P24(f329(f329(f244(a1),x63971),a84)) % 178.07/177.93 [6413]~P59(x64131)+E(f329(f329(f254(x64131),f329(f329(f287(x64131),f79(x64131)),x64132)),x64133),f329(f329(f287(x64131),f79(x64131)),f329(f329(f254(x64131),x64132),x64133))) % 178.07/177.93 [6490]E(f329(f329(f22(a875),f329(f329(f81(a875),x64901),x64902)),x64903),f329(f329(f22(a875),x64901),f329(f329(f22(a875),x64903),x64902)))+~P24(f329(f329(f243(a875),x64902),x64903)) % 178.07/177.93 [6492]E(f329(f329(f22(a875),f329(f329(f81(a875),x64921),x64922)),x64923),f329(f329(f81(a875),x64921),f329(f329(f22(a875),x64922),x64923)))+~P24(f329(f329(f243(a875),x64923),x64922)) % 178.07/177.93 [6527]~P63(x65271)+P24(f329(f329(f243(x65271),f329(f329(f107(x65271),x65272),x65273)),x65273)) % 178.07/177.93 [6528]~P100(x65281)+P24(f329(f329(f243(x65281),f329(f329(f107(x65281),x65282),x65283)),x65283)) % 178.07/177.93 [6529]~P63(x65291)+P24(f329(f329(f243(x65291),f329(f329(f107(x65291),x65292),x65293)),x65292)) % 178.07/177.93 [6530]~P100(x65301)+P24(f329(f329(f243(x65301),f329(f329(f107(x65301),x65302),x65303)),x65302)) % 178.07/177.93 [6531]~P105(x65311)+P24(f329(f329(f243(x65311),f329(f329(f241(x65311),x65312),x65313)),x65313)) % 178.07/177.93 [6532]~P105(x65321)+P24(f329(f329(f243(x65321),f329(f329(f241(x65321),x65322),x65323)),x65322)) % 178.07/177.93 [6546]E(f329(f329(f39(a1),f329(f329(f39(a1),x65461),x65462)),x65463),f329(f329(f39(a1),x65461),f329(f329(f82(a1),x65462),x65463)))+~P24(f329(f329(f244(a1),f2(a1)),x65463)) % 178.07/177.93 [6598]~P114(x65981)+E(f329(f329(f81(x65981),f329(f329(f82(x65981),x65982),x65983)),x65983),f329(f329(f82(x65981),f329(f329(f81(x65981),x65982),f79(x65981))),x65983)) % 178.07/177.93 [6599]~P92(x65991)+E(f329(f329(f82(x65991),f329(f80(x65991),f329(f109(x65991),x65992))),x65993),f329(f329(f82(x65991),f329(f109(x65991),f329(f80(a1),x65992))),x65993)) % 178.07/177.93 [6671]~P80(x66711)+E(f329(f165(x66711),f329(f329(f153(x66712,x66711),f329(f16(x66711,x66712),f2(x66711))),x66713)),f2(x66711)) % 178.07/177.93 [6687]E(f329(f329(f81(a875),f329(f109(a875),x66871)),f329(f329(f81(a875),f329(f109(a875),x66872)),x66873)),f329(f329(f81(a875),f329(f109(a875),x66872)),x66873))+~P24(f329(a198,f329(f109(a1),x66871))) % 178.07/177.93 [6701]~P27(x67011)+E(f41(x67011,f329(f329(f307(x67011),x67012),f329(f329(f307(x67011),x67013),f193(f883(x67011,a869))))),f329(f329(f107(x67011),x67012),x67013)) % 178.07/177.93 [6702]~P27(x67021)+E(f40(x67021,f329(f329(f307(x67021),x67022),f329(f329(f307(x67021),x67023),f193(f883(x67021,a869))))),f329(f329(f116(x67021),x67022),x67023)) % 178.07/177.93 [6725]E(f329(f329(f174(x67251),x67252),x67253),x67253)+~P24(f329(f329(f243(a875),f329(f194(f876(x67251)),x67253)),x67252)) % 178.07/177.93 [6738]E(f329(f329(f137(x67381),x67382),x67383),f119(x67381))+~P24(f329(f329(f243(a875),f329(f194(f876(x67381)),x67383)),x67382)) % 178.07/177.93 [6749]E(f329(f329(f81(a875),f329(f329(f22(a875),x67491),x67492)),x67493),f329(f329(f22(a875),f329(f329(f81(a875),x67491),x67493)),x67492))+~P24(f329(f329(f243(a875),x67492),x67491)) % 178.07/177.93 [6763]~P24(f329(f329(f244(a875),x67631),x67633))+P24(f329(f329(f244(a875),f329(f329(f22(a875),x67631),x67632)),x67633)) % 178.07/177.93 [6791]~P105(x67911)+E(f169(x67911,x67912,f329(f329(f147(x67911,x67911,f5(x67911)),x67912),x67913)),x67913) % 178.07/177.93 [6879]E(f329(f329(f22(a875),f329(f329(f81(a875),x68791),x68792)),f329(a118,x68793)),f329(f329(f22(a875),x68791),f329(a118,f329(f329(f22(a875),x68793),x68792))))+~P24(f329(f329(f243(a875),x68792),x68793)) % 178.07/177.93 [6880]~P117(x68801)+P24(f329(f329(f243(x68801),f2(x68801)),f329(f329(f254(x68801),f329(f76(x68801),x68802)),x68803))) % 178.07/177.93 [6927]P20(x69271,x69272,x69273)+~P24(f329(f329(f243(f883(f874(x69271),a869)),x69273),x69272)) % 178.07/177.93 [6970]~P24(f329(f62(x69701),x69702))+P24(f329(f62(x69701),f329(f329(f22(f883(x69701,a869)),x69702),x69703))) % 178.07/177.93 [6971]~P24(f329(f62(x69711),x69713))+P24(f329(f62(x69711),f329(f329(f107(f883(x69711,a869)),x69712),x69713))) % 178.07/177.93 [6972]~P24(f329(f62(x69721),x69722))+P24(f329(f62(x69721),f329(f329(f107(f883(x69721,a869)),x69722),x69723))) % 178.07/177.93 [7113]~P38(x71131,x71133)+P38(x71131,f329(f329(f107(f883(f882(x71131,x71131),a869)),x71132),x71133)) % 178.07/177.93 [7114]~P38(x71141,x71142)+P38(x71141,f329(f329(f107(f883(f882(x71141,x71141),a869)),x71142),x71143)) % 178.07/177.93 [7229]~P63(x72291)+E(f13(x72291,f329(f171(x72291),f329(f329(f150(x72291),x72292),x72293))),f329(f141(x72291,x72291,f116(x72291),x72292),x72293)) % 178.07/177.93 [7230]~P63(x72301)+E(f10(x72301,f329(f171(x72301),f329(f329(f150(x72301),x72302),x72303))),f329(f141(x72301,x72301,f107(x72301),x72302),x72303)) % 178.07/177.93 [7231]~P105(x72311)+E(f14(x72311,f329(f171(x72311),f329(f329(f150(x72311),x72312),x72313))),f329(f141(x72311,x72311,f241(x72311),x72312),x72313)) % 178.07/177.93 [7232]~P105(x72321)+E(f15(x72321,f329(f171(x72321),f329(f329(f150(x72321),x72322),x72323))),f329(f141(x72321,x72321,f242(x72321),x72322),x72323)) % 178.07/177.93 [7292]~P24(f329(f62(x72921),x72922))+P24(f329(f329(f243(a875),f329(f38(x72921),x72922)),f329(f38(x72921),f329(f329(f307(x72921),x72923),x72922)))) % 178.07/177.93 [7300]E(f329(f329(f116(f883(a875,a869)),f329(f299(a875,x73001),x73002)),f329(f299(a875,x73002),f329(f329(f81(a875),x73002),x73003))),f329(f299(a875,x73001),f329(f329(f81(a875),x73002),x73003)))+~P24(f329(f329(f243(a875),x73001),x73002)) % 178.07/177.93 [7308]P24(f329(f329(f244(a875),x73081),x73082))+~P24(f329(f329(f244(a875),f329(f329(f81(a875),x73081),x73083)),x73082)) % 178.07/177.93 [7311]P24(f329(f329(f243(a875),x73111),x73112))+~P24(f329(f329(f243(a875),f329(f329(f81(a875),x73113),x73111)),x73112)) % 178.07/177.93 [7312]P24(f329(f329(f243(a875),x73121),x73122))+~P24(f329(f329(f243(a875),f329(f329(f81(a875),x73121),x73123)),x73122)) % 178.07/177.93 [7354]~P105(x73541)+E(f11(x73541,f242(x73541),f329(f171(x73541),f329(f329(f150(x73541),x73542),x73543))),f329(f141(x73541,x73541,f242(x73541),x73542),x73543)) % 178.07/177.93 [7355]~P105(x73551)+E(f12(x73551,f241(x73551),f329(f171(x73551),f329(f329(f150(x73551),x73552),x73553))),f329(f141(x73551,x73551,f241(x73551),x73552),x73553)) % 178.07/177.93 [7359]~E(x73592,f193(f883(f882(x73591,x73591),a869)))+P24(f329(f329(f243(f883(f882(x73591,x73591),a869)),x73592),x73593)) % 178.07/177.93 [7470]E(f329(f329(f116(f883(x74701,a869)),x74702),f329(f329(f22(f883(x74701,a869)),x74703),x74702)),x74703)+~P24(f329(f329(f243(f883(x74701,a869)),x74702),x74703)) % 178.07/177.93 [7471]~P24(f329(f329(f244(a875),x74711),f329(f329(f22(a875),x74713),x74712)))+P24(f329(f329(f244(a875),f329(f329(f81(a875),x74711),x74712)),x74713)) % 178.07/177.93 [7472]~P24(f329(f329(f243(a875),x74721),f329(f329(f81(a875),x74723),x74722)))+P24(f329(f329(f243(a875),f329(f329(f22(a875),x74721),x74722)),x74723)) % 178.07/177.93 [7528]E(x75281,f119(x75282))+E(f329(f140(x75282),f329(f329(f329(f188(f876(x75282),f876(x75282)),x75283),f167(x75282)),x75281)),f329(f329(f164(x75282),x75281),f45(a875,x75283,f329(f194(f876(x75282)),x75281)))) % 178.07/177.93 [7537]E(f329(f329(f307(x75371),x75372),f329(f329(f22(f883(x75371,a869)),x75373),f329(f329(f307(x75371),x75372),f193(f883(x75371,a869))))),x75373)+~P24(f329(f329(f331(x75371),x75372),x75373)) % 178.07/177.93 [7698]P24(f329(f329(f244(a875),x76981),f329(f329(f22(a875),x76982),x76983)))+~P24(f329(f329(f244(a875),f329(f329(f81(a875),x76981),x76983)),x76982)) % 178.07/177.93 [7699]P24(f329(f329(f243(a875),x76991),f329(f329(f81(a875),x76992),x76993)))+~P24(f329(f329(f243(a875),f329(f329(f22(a875),x76991),x76993)),x76992)) % 178.07/177.93 [7721]P24(f329(f62(x77211),x77212))+~P24(f329(f62(x77211),f329(f329(f116(f883(x77211,a869)),x77213),x77212))) % 178.07/177.93 [7722]P24(f329(f62(x77221),x77222))+~P24(f329(f62(x77221),f329(f329(f116(f883(x77221,a869)),x77222),x77223))) % 178.07/177.93 [7797]~P46(x77971,x77973)+P24(f329(f329(f331(f882(x77971,x77971)),f329(f329(f264(x77971,x77971),x77972),x77972)),x77973)) % 178.07/177.93 [7930]E(f329(f329(f164(a875),f138(a875,f329(f299(a875,x79301),x79302))),x79303),f329(f329(f81(a875),x79301),x79303))+~P24(f329(f329(f244(a875),f329(f329(f81(a875),x79301),x79303)),x79302)) % 178.07/177.93 [7998]~P24(f329(f329(f199(f329(a26,x79981)),x79982),x79983))+P24(f329(f329(f199(f329(f240(a870),f329(a28,x79981))),x79982),x79983)) % 178.07/177.93 [8003]E(f329(f329(f174(a875),x80031),f138(a875,f329(f299(a875,x80032),x80033))),f138(a875,f329(f299(a875,x80032),f329(f329(f81(a875),x80032),x80031))))+~P24(f329(f329(f243(a875),f329(f329(f81(a875),x80032),x80031)),x80033)) % 178.07/177.93 [8056]~P92(x80561)+E(f329(f329(f254(x80561),x80562),f329(f109(a875),f329(f329(f81(a1),x80563),x80563))),f329(f329(f87(x80561,x80561),f329(f329(f254(x80561),x80562),f329(f109(a875),x80563))),f329(f329(f18(x80561,x80561,x80561),f82(x80561)),f5(x80561)))) % 178.07/177.93 [8265]P24(f329(f329(f199(f329(a26,x82651)),x82652),x82653))+~P24(f329(f329(f199(f329(f240(a870),f329(a28,x82651))),x82652),x82653)) % 178.07/177.93 [8325]E(f329(f329(f127(x83251),f329(f329(f174(x83251),x83252),x83253)),f329(f329(f150(x83251),f329(f329(f164(x83251),x83253),x83252)),f329(f329(f137(x83251),f329(a118,x83252)),x83253))),x83253)+~P24(f329(f329(f244(a875),x83252),f329(f194(f876(x83251)),x83253))) % 178.07/177.93 [8332]P24(f329(f329(f243(f883(x83321,a869)),f317(x83321,x83322)),f317(x83321,x83323)))+~P24(f329(f329(f243(f883(x83321,f883(x83321,a869))),x83323),x83322)) % 178.07/177.93 [8334]~P51(x83341,x83342,x83343)+P51(x83341,x83342,f329(f329(f22(f883(f882(x83341,x83341),a869)),x83343),f305(x83341,f193(f883(f882(x83341,x83341),a869))))) % 178.07/177.93 [8351]P24(f329(f329(f243(f883(x83511,a869)),f318(x83511,x83512)),f318(x83511,x83513)))+~P24(f329(f329(f243(f883(f882(x83511,x83511),a869)),x83513),x83512)) % 178.07/177.93 [8358]~P122(x83581)+P24(f329(f329(f243(x83581),f2(x83581)),f329(f329(f81(x83581),f329(f329(f82(x83581),x83582),x83582)),f329(f329(f82(x83581),x83583),x83583)))) % 178.07/177.93 [8393]P24(f329(f329(f243(f883(x83931,a869)),f329(f282(x83931),x83932)),f329(f282(x83931),x83933)))+~P24(f329(f329(f243(f883(f882(x83931,x83931),a869)),x83932),x83933)) % 178.07/177.93 [8426]~P42(x84261,x84262)+~P24(f329(f329(f331(f882(x84261,x84261)),f329(f329(f264(x84261,x84261),x84263),x84263)),x84262)) % 178.07/177.93 [8428]~P38(x84281,x84282)+~P24(f329(f329(f331(f882(x84281,x84281)),f329(f329(f264(x84281,x84281),x84283),x84283)),x84282)) % 178.07/177.93 [8490]P24(f329(f329(f243(f883(x84901,a869)),f41(f883(x84901,a869),x84902)),f41(f883(x84901,a869),x84903)))+~P24(f329(f329(f243(f883(f883(x84901,a869),a869)),x84903),x84902)) % 178.07/177.93 [8491]P24(f329(f329(f243(f883(x84911,a869)),f40(f883(x84911,a869),x84912)),f40(f883(x84911,a869),x84913)))+~P24(f329(f329(f243(f883(f883(x84911,a869),a869)),x84912),x84913)) % 178.07/177.93 [8543]~P6(x85431,x85433,x85432)+P24(f329(f329(f243(f883(f882(x85431,x85431),a869)),x85432),f329(f329(f266(x85431,x85431),x85433),f329(f16(f883(x85431,a869),x85431),x85433)))) % 178.07/177.93 [8544]~P40(x85441,x85443,x85442)+P24(f329(f329(f243(f883(f882(x85441,x85441),a869)),x85442),f329(f329(f266(x85441,x85441),x85443),f329(f16(f883(x85441,a869),x85441),x85443)))) % 178.07/177.93 [8590]~P85(x85901)+P24(f329(f329(f243(x85901),f329(f329(f22(x85901),f329(f76(x85901),x85902)),f329(f76(x85901),x85903))),f329(f76(x85901),f329(f329(f22(x85901),x85903),x85902)))) % 178.07/177.93 [8591]~P85(x85911)+P24(f329(f329(f243(x85911),f329(f329(f22(x85911),f329(f76(x85911),x85912)),f329(f76(x85911),x85913))),f329(f76(x85911),f329(f329(f22(x85911),x85912),x85913)))) % 178.07/177.93 [8621]P24(f329(f329(f243(f883(f882(x86211,x86211),a869)),f305(x86211,x86212)),f305(x86211,x86213)))+~P24(f329(f329(f243(f883(f882(x86211,x86211),a869)),x86212),x86213)) % 178.07/177.93 [8777]P51(x87771,x87772,x87773)+~P51(x87771,x87772,f329(f329(f22(f883(f882(x87771,x87771),a869)),x87773),f305(x87771,f193(f883(f882(x87771,x87771),a869))))) % 178.07/177.93 [8795]P24(f329(f329(f243(f883(f882(f876(x87951),f876(x87951)),a869)),f157(x87951,x87952)),f157(x87951,x87953)))+~P24(f329(f329(f243(f883(f882(x87951,x87951),a869)),x87952),x87953)) % 178.07/177.93 [8796]P24(f329(f329(f243(f883(f882(f876(x87961),f876(x87961)),a869)),f156(x87961,x87962)),f156(x87961,x87963)))+~P24(f329(f329(f243(f883(f882(x87961,x87961),a869)),x87962),x87963)) % 178.07/177.93 [8815]~P40(x88151,x88153,x88152)+P24(f329(f329(f243(f883(f882(x88151,x88151),a869)),x88152),f329(f329(f286(x88151,x88151,x88151),f329(f284(x88151,x88151),x88152)),x88152))) % 178.07/177.93 [8864]~P24(f329(f136(x88641),x88642))+E(f329(f135(x88641,f329(f329(f7(x88641,f883(x88641,a869),a869),f331(x88641)),f329(f171(x88641),f175(x88641,x88642,x88643)))),x88642),f175(x88641,x88642,x88643)) % 178.07/177.93 [8926]E(x89261,x89262)+~P24(f329(f329(f331(f882(x89263,x89263)),f329(f329(f264(x89263,x89263),x89261),x89262)),f305(x89263,f193(f883(f882(x89263,x89263),a869))))) % 178.07/177.93 [9012]P24(f329(f329(f331(x90121),x90122),f318(x90121,x90123)))+P24(f329(f329(f331(f882(x90121,x90121)),f329(f329(f264(x90121,x90121),f681(x90123,x90122,x90121)),x90122)),x90123)) % 178.07/177.93 [9013]P24(f329(f329(f331(x90131),x90132),f318(x90131,x90133)))+P24(f329(f329(f331(f882(x90131,x90131)),f329(f329(f264(x90131,x90131),f736(x90133,x90132,x90131)),x90132)),x90133)) % 178.07/177.93 [9014]P24(f329(f329(f331(x90141),x90142),f318(x90141,x90143)))+P24(f329(f329(f331(f882(x90141,x90141)),f329(f329(f264(x90141,x90141),f740(x90143,x90142,x90141)),x90142)),x90143)) % 178.07/177.93 [9100]~P24(f329(f329(f331(f876(x91001)),x91003),f160(x91001,x91002)))+P24(f329(f159(x91001,f329(f329(f7(x91001,f883(x91001,a869),a869),f331(x91001)),x91002)),x91003)) % 178.07/177.93 [9121]P24(f329(x91213,x91212))+E(f329(f249(x91211),f329(f329(f18(x91211,a869,a869),f329(f329(f8(a869,f883(a869,a869),x91211),a327),f329(a326,x91212))),x91213)),f193(f883(x91211,a869))) % 178.07/177.93 [9142]~P85(x91421)+P24(f329(f329(f243(x91421),f329(f76(x91421),f329(f329(f22(x91421),f329(f76(x91421),x91422)),f329(f76(x91421),x91423)))),f329(f76(x91421),f329(f329(f22(x91421),x91422),x91423)))) % 178.07/177.93 [9156]~P24(f329(x91563,x91562))+E(f329(f249(x91561),f329(f329(f18(x91561,a869,a869),f329(f329(f8(a869,f883(a869,a869),x91561),a327),f329(a326,x91562))),x91563)),f329(f329(f307(x91561),x91562),f193(f883(x91561,a869)))) % 178.07/177.93 [9163]~P24(f329(f329(f331(f883(x91631,a869)),x91633),f329(f306(x91631),x91632)))+P24(f329(f257(x91631,f329(f329(f7(x91631,f883(x91631,a869),a869),f331(x91631)),x91632)),x91633)) % 178.07/177.93 [9196]P38(x91961,x91962)+P24(f329(f329(f331(f882(x91961,x91961)),f329(f329(f264(x91961,x91961),f329(f696(x91962,x91961),f329(a118,x91963))),f329(f696(x91962,x91961),x91963))),x91962)) % 178.07/177.93 [9338]P24(f329(f329(f331(f876(x93381)),x93382),f160(x93381,x93383)))+~P24(f329(f159(x93381,f329(f329(f7(x93381,f883(x93381,a869),a869),f331(x93381)),x93383)),x93382)) % 178.07/177.93 [9351]P24(f329(f329(f331(f883(x93511,a869)),x93512),f329(f306(x93511),x93513)))+~P24(f329(f257(x93511,f329(f329(f7(x93511,f883(x93511,a869),a869),f331(x93511)),x93513)),x93512)) % 178.07/177.93 [9407]P24(f329(f329(f331(x94071),f329(f275(x94071,x94072),x94073)),f329(f171(x94071),f329(f329(f153(f882(a105,x94071),x94071),f267(a105,x94071)),x94072))))+~P24(f329(f329(f244(a105),x94073),f329(f165(a105),f329(f329(f153(f882(a105,x94071),a105),f263(a105,x94071)),x94072)))) % 178.07/177.93 [9455]P24(f329(f329(f243(f883(f882(f876(x94551),f876(x94551)),a869)),f157(x94551,x94552)),f329(f329(f266(f876(x94551),f876(x94551)),f160(x94551,x94553)),f329(f16(f883(f876(x94551),a869),f876(x94551)),f160(x94551,x94553)))))+~P24(f329(f329(f243(f883(f882(x94551,x94551),a869)),x94552),f329(f329(f266(x94551,x94551),x94553),f329(f16(f883(x94551,a869),x94551),x94553)))) % 178.07/177.93 [9476]P24(f329(f329(f331(x94761),f329(f263(x94761,f882(a105,a105)),f329(f273(x94761,x94762),x94763))),f329(f171(x94761),f329(f329(f153(f882(a105,x94761),x94761),f267(a105,x94761)),x94762))))+~P24(f329(f329(f244(a105),f2(a105)),f329(f165(a105),f329(f329(f153(f882(a105,x94761),a105),f263(a105,x94761)),x94762)))) % 178.07/177.93 [9493]~P24(f329(f329(f243(f883(f882(x94931,x94931),a869)),x94932),f329(f329(f266(x94931,x94931),x94933),f329(f16(f883(x94931,a869),x94931),x94933))))+P24(f329(f329(f243(f883(f882(x94931,x94931),a869)),f329(f329(f286(x94931,x94931,x94931),x94932),f305(x94931,x94932))),f329(f329(f266(x94931,x94931),x94933),f329(f16(f883(x94931,a869),x94931),x94933)))) % 178.07/177.93 [9795]~P38(x97951,x97952)+~P24(f329(f329(f331(f882(x97951,x97951)),f329(f329(f264(x97951,x97951),f329(x97953,f329(a118,f698(x97952,x97951,x97953)))),f329(x97953,f698(x97952,x97951,x97953)))),x97952)) % 178.07/177.93 [9796]~P38(x97961,x97962)+~P24(f329(f329(f331(f882(x97961,x97961)),f329(f329(f264(x97961,x97961),f329(x97963,f329(a118,f744(x97963,x97962,x97961)))),f329(x97963,f744(x97963,x97962,x97961)))),x97962)) % 178.07/177.93 [10048]P24(f329(f329(f243(f883(f882(f883(x100481,a869),f883(x100481,a869)),a869)),f329(f329(f286(f883(x100481,a869),f883(x100481,a869),f883(x100481,a869)),f322(x100481,x100482)),f329(f329(f116(f883(f882(f883(x100481,a869),f883(x100481,a869)),a869)),f322(x100481,x100483)),f329(f329(f307(f882(f883(x100481,a869),f883(x100481,a869))),f329(f329(f264(f883(x100481,a869),f883(x100481,a869)),f193(f883(x100481,a869))),f193(f883(x100481,a869)))),f193(f883(f882(f883(x100481,a869),f883(x100481,a869)),a869)))))),f322(x100481,x100482)))+~P24(f329(f329(f243(f883(f882(x100481,x100481),a869)),f329(f329(f286(x100481,x100481,x100481),x100482),x100483)),x100482)) % 178.07/177.93 [10049]P24(f329(f329(f243(f883(f882(f883(x100491,a869),f883(x100491,a869)),a869)),f329(f329(f286(f883(x100491,a869),f883(x100491,a869),f883(x100491,a869)),f320(x100491,x100492)),f329(f329(f116(f883(f882(f883(x100491,a869),f883(x100491,a869)),a869)),f320(x100491,x100493)),f329(f329(f307(f882(f883(x100491,a869),f883(x100491,a869))),f329(f329(f264(f883(x100491,a869),f883(x100491,a869)),f193(f883(x100491,a869))),f193(f883(x100491,a869)))),f193(f883(f882(f883(x100491,a869),f883(x100491,a869)),a869)))))),f320(x100491,x100492)))+~P24(f329(f329(f243(f883(f882(x100491,x100491),a869)),f329(f329(f286(x100491,x100491,x100491),x100492),x100493)),x100492)) % 178.07/177.93 [7228]~P24(f329(f329(f243(a875),x72282),x72281))+E(f329(f329(f22(a875),f329(a118,f329(f329(f22(a875),x72281),x72282))),x72283),f329(f329(f22(a875),f329(a118,x72281)),f329(f329(f81(a875),x72282),x72283))) % 178.07/177.93 [7267]~P56(x72671)+E(f329(f329(f81(x72671),f45(x72671,x72672,x72673)),f329(f329(f82(x72671),f329(f329(f39(x72671),x72672),x72673)),x72673)),x72672) % 178.07/177.93 [7476]E(f329(f329(f82(a875),f329(f109(a875),x74761)),f329(f329(f82(a875),f329(f109(a875),x74762)),x74763)),f329(f329(f82(a875),f329(f109(a875),f329(f329(f82(a1),x74761),x74762))),x74763))+P24(f329(f329(f244(a1),x74761),a84)) % 178.07/177.93 [7939]~P24(f329(f329(f243(a875),x79393),x79392))+P24(f329(f329(f243(a875),x79391),f329(f329(f22(a875),f329(f329(f81(a875),x79392),x79391)),x79393))) % 178.07/177.93 [8145]~P24(f329(f329(f243(a875),x81451),x81452))+E(f329(f329(f127(a875),f138(a875,f329(f299(a875,x81451),x81452))),f138(a875,f329(f299(a875,x81452),f329(f329(f81(a875),x81452),x81453)))),f138(a875,f329(f299(a875,x81451),f329(f329(f81(a875),x81452),x81453)))) % 178.07/177.93 [8402]~P24(f329(f62(x84021),x84022))+E(f329(a118,f329(f38(x84021),f329(f329(f22(f883(x84021,a869)),x84022),f329(f329(f307(x84021),x84023),f193(f883(x84021,a869)))))),f329(f38(x84021),f329(f329(f307(x84021),x84023),x84022))) % 178.07/177.93 [8450]~P24(f329(f62(x84501),x84502))+E(f329(f329(f81(a875),f79(a875)),f329(f38(x84501),f329(f329(f22(f883(x84501,a869)),x84502),f329(f329(f307(x84501),x84503),f193(f883(x84501,a869)))))),f329(f38(x84501),f329(f329(f307(x84501),x84503),x84502))) % 178.07/177.93 [8630]E(f329(f329(f22(a875),f329(f38(x86301),x86302)),f329(f38(x86301),f329(f329(f107(f883(x86301,a869)),x86302),x86303))),f329(f38(x86301),f329(f329(f22(f883(x86301,a869)),x86302),x86303)))+~P24(f329(f62(x86301),f329(f329(f107(f883(x86301,a869)),x86302),x86303))) % 178.07/177.93 [8860]~P28(f329(x88602,f404(x88602,x88603,x88601)))+E(f329(f106(a1),f329(f329(f6(x88601,a875),f329(f329(f8(a1,a875,x88601),a110),x88602)),x88603)),f329(f329(f6(x88601,a1),x88602),x88603)) % 178.07/177.93 [8861]~P28(f329(x88612,f405(x88612,x88613,x88611)))+E(f329(f106(a1),f329(f329(f9(x88611,a875),f329(f329(f8(a1,a875,x88611),a110),x88612)),x88613)),f329(f329(f9(x88611,a1),x88612),x88613)) % 178.07/177.93 [8908]~P24(f329(f62(x89081),x89083))+P24(f329(f329(f243(a875),f329(f329(f22(a875),f329(f38(x89081),x89082)),f329(f38(x89081),x89083))),f329(f38(x89081),f329(f329(f22(f883(x89081,a869)),x89082),x89083)))) % 178.07/177.93 [8934]P24(f329(f329(f331(x89341),f404(x89342,x89343,x89341)),x89343))+E(f329(f106(a1),f329(f329(f6(x89341,a875),f329(f329(f8(a1,a875,x89341),a110),x89342)),x89343)),f329(f329(f6(x89341,a1),x89342),x89343)) % 178.07/177.93 [8935]P24(f329(f329(f331(x89351),f405(x89352,x89353,x89351)),x89353))+E(f329(f106(a1),f329(f329(f9(x89351,a875),f329(f329(f8(a1,a875,x89351),a110),x89352)),x89353)),f329(f329(f9(x89351,a1),x89352),x89353)) % 178.07/177.93 [9004]E(f86(x90041,f329(f329(f7(x90041,f883(x90041,a869),a869),f331(x90041)),f329(f329(f22(f883(x90041,a869)),x90042),f329(f329(f307(x90041),x90043),f193(f883(x90041,a869)))))),f256(x90041,x90043,x90042))+P24(f329(f329(f243(f883(x90041,a869)),x90042),f329(f329(f307(x90041),x90043),f193(f883(x90041,a869))))) % 178.07/177.93 [9352]E(f329(f329(f153(f876(x93521),x93521),f329(f329(f7(f876(x93521),a875,x93521),f164(x93521)),x93522)),f329(f135(f876(x93521),f329(f329(f8(a875,a869,f876(x93521)),f329(f244(a875),x93522)),f194(f876(x93521)))),x93523)),f329(f329(f164(f876(x93521)),f179(x93521,x93523)),x93522))+~P24(f329(f329(f244(a875),x93522),f329(f194(f876(f876(x93521))),f179(x93521,x93523)))) % 178.07/177.93 [9424]E(f329(f135(x94241,x94242),x94243),f176(x94241,x94242,x94243))+P24(f329(f329(f331(x94241),f671(x94243,x94242,x94241)),f329(f171(x94241),f329(f329(f137(x94241),f329(f194(f876(x94241)),f176(x94241,x94242,x94243))),x94243)))) % 178.07/177.93 [9564]E(f329(f329(f137(x95641),f329(f194(f876(x95641)),f176(x95641,x95642,x95643))),x95643),f119(x95641))+~P24(f329(x95642,f329(f140(x95641),f329(f329(f137(x95641),f329(f194(f876(x95641)),f176(x95641,x95642,x95643))),x95643)))) % 178.07/177.93 [9657]~P24(f329(f329(f331(f882(x96571,x96571)),x96572),f305(x96571,x96573)))+P24(f329(f329(f331(f882(x96571,x96571)),x96572),f329(f329(f43(a875,f883(f882(x96571,x96571),a869)),f252(f883(a875,a869))),f329(f329(f7(a875,f883(f882(x96571,x96571),a869),f883(f882(x96571,x96571),a869)),f188(f882(x96571,x96571),a869)),x96573)))) % 178.07/177.93 [9713]~P24(f329(f329(f243(f883(x97131,a869)),f329(f329(f43(a875,f883(x97131,a869)),f329(f299(a875,f2(a875)),f393(x97133,x97132,x97131))),x97132)),x97133))+P24(f329(f329(f243(f883(x97131,a869)),f329(f329(f43(a875,f883(x97131,a869)),f252(f883(a875,a869))),x97132)),x97133)) % 178.07/177.93 [9771]~P24(f329(f329(f244(a1),f2(a1)),x97713))+P24(f329(f329(f244(a1),x97711),f329(f329(f81(a1),x97712),f329(f329(f82(a1),f329(f329(f81(a1),f329(f76(a1),f329(f329(f22(a1),x97712),x97711))),f79(a1))),x97713)))) % 178.07/177.93 [9782]~P38(x97821,f329(f329(f116(f883(f882(x97821,x97821),a869)),x97822),x97823))+P38(x97821,f329(f329(f116(f883(f882(x97821,x97821),a869)),f329(f329(f116(f883(f882(x97821,x97821),a869)),f329(f329(f286(x97821,x97821,x97821),x97822),x97822)),f329(f329(f286(x97821,x97821,x97821),x97823),x97822))),x97823)) % 178.07/177.93 [9864]P38(x98641,f329(f329(f116(f883(f882(x98641,x98641),a869)),x98642),x98643))+~P38(x98641,f329(f329(f116(f883(f882(x98641,x98641),a869)),f329(f329(f116(f883(f882(x98641,x98641),a869)),f329(f329(f286(x98641,x98641,x98641),x98642),x98642)),f329(f329(f286(x98641,x98641,x98641),x98643),x98642))),x98643)) % 178.07/177.93 [9428]~P137(x94281)+E(f329(f108(x94281),f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),x94282),x94283)),f193(f883(f882(a875,a875),a869)))))),f329(f329(f22(x94281),f329(f106(x94281),x94282)),f329(f106(x94281),x94283))) % 178.07/177.93 [9511]P24(f329(x95113,x95112))+E(f329(f249(x95111),f329(f329(f18(x95111,a869,a869),f329(f329(f8(a869,f883(a869,a869),x95111),a327),f329(f329(f7(x95111,x95111,a869),a326),x95112))),x95113)),f193(f883(x95111,a869))) % 178.07/177.93 [9513]~P24(f329(x95133,x95132))+E(f329(f249(x95131),f329(f329(f18(x95131,a869,a869),f329(f329(f8(a869,f883(a869,a869),x95131),a327),f329(f329(f7(x95131,x95131,a869),a326),x95132))),x95133)),f329(f329(f307(x95131),x95132),f193(f883(x95131,a869)))) % 178.07/177.93 [9749]E(x97491,x97492)+P24(f329(f329(f253(x97493,x97493,f329(f329(f8(f883(x97493,a869),f883(x97493,a869),x97493),f329(f8(a869,a869,x97493),a324)),a326)),x97491),x97492)) % 178.07/177.93 [9842]~E(x98421,x98422)+~P24(f329(f329(f253(x98423,x98423,f329(f329(f8(f883(x98423,a869),f883(x98423,a869),x98423),f329(f8(a869,a869,x98423),a324)),a326)),x98421),x98422)) % 178.07/177.93 [9856]~P24(f329(f62(x98561),x98563))+E(f329(f329(f65(x98561,f883(x98561,a869),f329(f329(f8(f883(x98561,a869),f883(f883(x98561,a869),f883(x98561,a869)),x98561),f329(f7(f883(x98561,a869),f883(x98561,a869),f883(x98561,a869)),f22(f883(x98561,a869)))),f329(f329(f7(x98561,f883(x98561,a869),f883(x98561,a869)),f307(x98561)),f193(f883(x98561,a869))))),x98562),x98563),f329(f329(f22(f883(x98561,a869)),x98562),x98563)) % 178.07/177.93 [9888]~P24(f329(f329(f244(a1),f2(a1)),x98883))+P24(f329(f329(f244(a1),f329(f329(f22(a1),x98881),f329(f329(f82(a1),f329(f329(f81(a1),f329(f76(a1),f329(f329(f22(a1),x98881),x98882))),f79(a1))),x98883))),x98882)) % 178.07/177.93 [10110]~P24(f329(f329(f331(x101101),x101103),f318(x101101,x101102)))+P24(f329(f317(x101101,f329(f329(f7(x101101,f883(f882(x101101,x101101),a869),f883(x101101,a869)),f329(f329(f8(f883(x101101,f883(f883(f882(x101101,x101101),a869),a869)),f883(f883(f882(x101101,x101101),a869),f883(x101101,a869)),x101101),f7(x101101,f883(f882(x101101,x101101),a869),a869)),f329(f329(f8(f883(x101101,f882(x101101,x101101)),f883(x101101,f883(f883(f882(x101101,x101101),a869),a869)),x101101),f329(f8(f882(x101101,x101101),f883(f883(f882(x101101,x101101),a869),a869),x101101),f331(f882(x101101,x101101)))),f264(x101101,x101101)))),x101102)),x101103)) % 178.07/177.93 [10122]P24(f329(f329(f331(x101221),x101222),f318(x101221,x101223)))+~P24(f329(f317(x101221,f329(f329(f7(x101221,f883(f882(x101221,x101221),a869),f883(x101221,a869)),f329(f329(f8(f883(x101221,f883(f883(f882(x101221,x101221),a869),a869)),f883(f883(f882(x101221,x101221),a869),f883(x101221,a869)),x101221),f7(x101221,f883(f882(x101221,x101221),a869),a869)),f329(f329(f8(f883(x101221,f882(x101221,x101221)),f883(x101221,f883(f883(f882(x101221,x101221),a869),a869)),x101221),f329(f8(f882(x101221,x101221),f883(f883(f882(x101221,x101221),a869),a869),x101221),f331(f882(x101221,x101221)))),f264(x101221,x101221)))),x101223)),x101222)) % 178.07/177.93 [9711]~P24(f329(f62(x97111),f329(f249(x97111),x97113)))+P24(f329(f62(x97111),f329(f249(x97111),f329(f329(f18(x97111,a869,a869),f329(f329(f8(a869,f883(a869,a869),x97111),a327),x97112)),x97113)))) % 178.07/177.93 [9712]~P24(f329(f62(x97121),f329(f249(x97121),x97122)))+P24(f329(f62(x97121),f329(f249(x97121),f329(f329(f18(x97121,a869,a869),f329(f329(f8(a869,f883(a869,a869),x97121),a327),x97122)),x97123)))) % 178.07/177.93 [9814]P24(f329(f62(x98141),f329(f249(x98141),x98142)))+~P24(f329(f62(x98141),f329(f249(x98141),f329(f329(f18(x98141,a869,a869),f329(f329(f8(a869,f883(a869,a869),x98141),a328),x98143)),x98142)))) % 178.07/177.93 [9815]P24(f329(f62(x98151),f329(f249(x98151),x98152)))+~P24(f329(f62(x98151),f329(f249(x98151),f329(f329(f18(x98151,a869,a869),f329(f329(f8(a869,f883(a869,a869),x98151),a328),x98152)),x98153)))) % 178.07/177.93 [10097]~P24(f329(f62(x100971),x100972))+P24(f329(f62(f876(x100971)),f329(f249(f876(x100971)),f329(f329(f18(f876(x100971),a869,a869),f329(f329(f8(a869,f883(a869,a869),f876(x100971)),a327),f329(f329(f7(f876(x100971),f883(x100971,a869),a869),f329(f329(f8(f883(x100971,a869),f883(f883(x100971,a869),a869),f876(x100971)),f243(f883(x100971,a869))),f171(x100971))),x100972))),f329(f329(f7(f876(x100971),a875,a869),f329(f329(f8(a875,f883(a875,a869),f876(x100971)),a326),f194(f876(x100971)))),x100973))))) % 178.07/177.93 [10098]~P24(f329(f62(x100981),x100982))+P24(f329(f62(f876(x100981)),f329(f249(f876(x100981)),f329(f329(f18(f876(x100981),a869,a869),f329(f329(f8(a869,f883(a869,a869),f876(x100981)),a327),f329(f329(f7(f876(x100981),f883(x100981,a869),a869),f329(f329(f8(f883(x100981,a869),f883(f883(x100981,a869),a869),f876(x100981)),f243(f883(x100981,a869))),f171(x100981))),x100982))),f329(f329(f7(f876(x100981),a875,a869),f329(f329(f8(a875,f883(a875,a869),f876(x100981)),f243(a875)),f194(f876(x100981)))),x100983))))) % 178.07/177.93 [9829]~P114(x98291)+E(f329(f329(f254(x98291),x98292),f329(f329(f82(a875),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x98293)),f329(f329(f82(x98291),f329(f329(f254(x98291),x98292),x98293)),f329(f329(f254(x98291),x98292),x98293))) % 178.07/177.93 [9869]~P79(x98691)+E(f329(f329(f254(x98691),f329(f329(f254(x98691),x98692),x98693)),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f329(f329(f254(x98691),x98692),f329(f329(f82(a875),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x98693))) % 178.07/177.93 [9915]~P137(x99151)+E(f329(f329(f254(x99151),f329(f80(x99151),x99152)),f329(f329(f82(a875),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x99153)),f329(f329(f254(x99151),x99152),f329(f329(f82(a875),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x99153))) % 178.07/177.93 [10055]~P117(x100551)+P24(f329(f329(f243(x100551),f2(x100551)),f329(f329(f81(x100551),f329(f329(f254(x100551),x100552),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f329(f329(f254(x100551),x100553),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))))) % 178.07/177.93 [9925]~P114(x99251)+E(f329(f329(f254(x99251),x99252),f329(a118,f329(f329(f82(a875),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x99253))),f329(f329(f82(x99251),x99252),f329(f329(f82(x99251),f329(f329(f254(x99251),x99252),x99253)),f329(f329(f254(x99251),x99252),x99253)))) % 178.07/177.93 [9974]~P79(x99741)+E(f329(f329(f82(x99741),x99742),f329(f329(f254(x99741),f329(f329(f254(x99741),x99742),x99743)),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f329(f329(f254(x99741),x99742),f329(a118,f329(f329(f82(a875),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x99743)))) % 178.07/177.93 [10012]~P117(x100121)+P24(f329(f329(f243(x100121),f2(x100121)),f329(f329(f254(x100121),x100122),f329(f329(f82(a875),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x100123)))) % 178.07/177.93 [10078]~P92(x100781)+E(f329(f329(f22(x100781),f329(f329(f81(x100781),f329(f329(f254(x100781),x100782),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f329(f329(f254(x100781),x100783),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))))),f329(f329(f82(x100781),f329(f329(f82(x100781),f329(f109(x100781),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x100782)),x100783)),f329(f329(f254(x100781),f329(f329(f22(x100781),x100782),x100783)),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))) % 178.07/177.93 [10079]~P92(x100791)+E(f329(f329(f81(x100791),f329(f329(f81(x100791),f329(f329(f254(x100791),x100792),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f329(f329(f254(x100791),x100793),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))))),f329(f329(f82(x100791),f329(f329(f82(x100791),f329(f109(x100791),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x100792)),x100793)),f329(f329(f254(x100791),f329(f329(f81(x100791),x100792),x100793)),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))) % 178.07/177.93 [10177]~P30(x101771,x101772,x101773)+P24(f101(x101771,a869,f329(f329(f8(f883(a870,f883(f883(x101771,f883(a871,a869)),f883(x101771,a869))),f883(a870,f883(f883(x101771,f883(a871,a869)),a869)),f883(x101771,f883(a871,a869))),f329(f8(f883(f883(x101771,f883(a871,a869)),f883(x101771,a869)),f883(f883(x101771,f883(a871,a869)),a869),a870),f329(f8(f883(x101771,a869),a869,f883(x101771,f883(a871,a869))),f89(x101771)))),f329(f329(f8(f883(a870,f883(f883(x101771,f883(a871,a869)),f883(x101771,f883(a871,a869)))),f883(a870,f883(f883(x101771,f883(a871,a869)),f883(x101771,a869))),f883(x101771,f883(a871,a869))),f329(f8(f883(f883(x101771,f883(a871,a869)),f883(x101771,f883(a871,a869))),f883(f883(x101771,f883(a871,a869)),f883(x101771,a869)),a870),f329(f8(f883(x101771,f883(a871,a869)),f883(x101771,a869),f883(x101771,f883(a871,a869))),f329(f8(f883(a871,a869),a869,x101771),f89(a871))))),f329(f329(f7(f883(x101771,f883(a871,a869)),f883(a870,f883(f883(x101771,f883(a871,a869)),f883(x101771,f883(a871,a869)))),f883(a870,f883(f883(x101771,f883(a871,a869)),f883(x101771,f883(a871,a869))))),f329(f329(f8(f883(f883(f883(x101771,f883(a871,a869)),f883(x101771,f883(a871,a869))),f883(f883(x101771,f883(a871,a869)),f883(x101771,f883(a871,a869)))),f883(f883(a870,f883(f883(x101771,f883(a871,a869)),f883(x101771,f883(a871,a869)))),f883(a870,f883(f883(x101771,f883(a871,a869)),f883(x101771,f883(a871,a869))))),f883(x101771,f883(a871,a869))),f8(f883(f883(x101771,f883(a871,a869)),f883(x101771,f883(a871,a869))),f883(f883(x101771,f883(a871,a869)),f883(x101771,f883(a871,a869))),a870)),f329(f329(f8(f883(f883(x101771,f883(a871,a869)),f883(x101771,f883(a871,a869))),f883(f883(f883(x101771,f883(a871,a869)),f883(x101771,f883(a871,a869))),f883(f883(x101771,f883(a871,a869)),f883(x101771,f883(a871,a869)))),f883(x101771,f883(a871,a869))),f8(f883(x101771,f883(a871,a869)),f883(x101771,f883(a871,a869)),f883(x101771,f883(a871,a869)))),f329(f329(f8(f883(x101771,f883(f883(a871,a869),f883(a871,a869))),f883(f883(x101771,f883(a871,a869)),f883(x101771,f883(a871,a869))),f883(x101771,f883(a871,a869))),f18(x101771,f883(a871,a869),f883(a871,a869))),f329(f329(f8(f883(x101771,f883(a871,f883(a869,a869))),f883(x101771,f883(f883(a871,a869),f883(a871,a869))),f883(x101771,f883(a871,a869))),f329(f8(f883(a871,f883(a869,a869)),f883(f883(a871,a869),f883(a871,a869)),x101771),f18(a871,a869,a869))),f329(f8(f883(a871,a869),f883(a871,f883(a869,a869)),x101771),f329(f8(a869,f883(a869,a869),a871),a332))))))),f329(f329(f8(f883(f883(x101771,f883(a871,a869)),f883(x101771,f883(a871,f883(a871,a869)))),f883(f883(x101771,f883(a871,a869)),f883(x101771,f883(a871,a869))),a870),f329(f8(f883(x101771,f883(a871,f883(a871,a869))),f883(x101771,f883(a871,a869)),f883(x101771,f883(a871,a869))),f329(f8(f883(a871,f883(a871,a869)),f883(a871,a869),x101771),f329(f8(f883(a871,a869),a869,a871),f89(a871))))),f329(f329(f8(f883(f883(a871,a869),f883(a871,f883(a871,a869))),f883(f883(x101771,f883(a871,a869)),f883(x101771,f883(a871,f883(a871,a869)))),a870),f8(f883(a871,a869),f883(a871,f883(a871,a869)),x101771)),f329(f329(f8(f883(a871,f883(f883(a871,a869),f883(a871,a869))),f883(f883(a871,a869),f883(a871,f883(a871,a869))),a870),f7(a871,f883(a871,a869),f883(a871,a869))),f329(f329(f8(f883(a871,f883(a871,f883(a869,a869))),f883(a871,f883(f883(a871,a869),f883(a871,a869))),a870),f329(f8(f883(a871,f883(a869,a869)),f883(f883(a871,a869),f883(a871,a869)),a871),f18(a871,a869,a869))),f329(f329(f8(f883(a871,f883(a871,a869)),f883(a871,f883(a871,f883(a869,a869))),a870),f329(f8(f883(a871,a869),f883(a871,f883(a869,a869)),a871),f329(f8(a869,f883(a869,a869),a871),a332))),f329(f329(f7(a870,a875,f883(a871,f883(a871,a869))),f329(f329(f8(f883(a871,f883(a875,f883(a871,a869))),f883(a875,f883(a871,f883(a871,a869))),a870),f7(a871,a875,f883(a871,a869))),a201)),x101772))))))))),x101773)) % 178.07/177.93 [10179]P30(x101791,x101792,x101793)+~P24(f101(x101791,a869,f329(f329(f8(f883(a870,f883(f883(x101791,f883(a871,a869)),f883(x101791,a869))),f883(a870,f883(f883(x101791,f883(a871,a869)),a869)),f883(x101791,f883(a871,a869))),f329(f8(f883(f883(x101791,f883(a871,a869)),f883(x101791,a869)),f883(f883(x101791,f883(a871,a869)),a869),a870),f329(f8(f883(x101791,a869),a869,f883(x101791,f883(a871,a869))),f89(x101791)))),f329(f329(f8(f883(a870,f883(f883(x101791,f883(a871,a869)),f883(x101791,f883(a871,a869)))),f883(a870,f883(f883(x101791,f883(a871,a869)),f883(x101791,a869))),f883(x101791,f883(a871,a869))),f329(f8(f883(f883(x101791,f883(a871,a869)),f883(x101791,f883(a871,a869))),f883(f883(x101791,f883(a871,a869)),f883(x101791,a869)),a870),f329(f8(f883(x101791,f883(a871,a869)),f883(x101791,a869),f883(x101791,f883(a871,a869))),f329(f8(f883(a871,a869),a869,x101791),f89(a871))))),f329(f329(f7(f883(x101791,f883(a871,a869)),f883(a870,f883(f883(x101791,f883(a871,a869)),f883(x101791,f883(a871,a869)))),f883(a870,f883(f883(x101791,f883(a871,a869)),f883(x101791,f883(a871,a869))))),f329(f329(f8(f883(f883(f883(x101791,f883(a871,a869)),f883(x101791,f883(a871,a869))),f883(f883(x101791,f883(a871,a869)),f883(x101791,f883(a871,a869)))),f883(f883(a870,f883(f883(x101791,f883(a871,a869)),f883(x101791,f883(a871,a869)))),f883(a870,f883(f883(x101791,f883(a871,a869)),f883(x101791,f883(a871,a869))))),f883(x101791,f883(a871,a869))),f8(f883(f883(x101791,f883(a871,a869)),f883(x101791,f883(a871,a869))),f883(f883(x101791,f883(a871,a869)),f883(x101791,f883(a871,a869))),a870)),f329(f329(f8(f883(f883(x101791,f883(a871,a869)),f883(x101791,f883(a871,a869))),f883(f883(f883(x101791,f883(a871,a869)),f883(x101791,f883(a871,a869))),f883(f883(x101791,f883(a871,a869)),f883(x101791,f883(a871,a869)))),f883(x101791,f883(a871,a869))),f8(f883(x101791,f883(a871,a869)),f883(x101791,f883(a871,a869)),f883(x101791,f883(a871,a869)))),f329(f329(f8(f883(x101791,f883(f883(a871,a869),f883(a871,a869))),f883(f883(x101791,f883(a871,a869)),f883(x101791,f883(a871,a869))),f883(x101791,f883(a871,a869))),f18(x101791,f883(a871,a869),f883(a871,a869))),f329(f329(f8(f883(x101791,f883(a871,f883(a869,a869))),f883(x101791,f883(f883(a871,a869),f883(a871,a869))),f883(x101791,f883(a871,a869))),f329(f8(f883(a871,f883(a869,a869)),f883(f883(a871,a869),f883(a871,a869)),x101791),f18(a871,a869,a869))),f329(f8(f883(a871,a869),f883(a871,f883(a869,a869)),x101791),f329(f8(a869,f883(a869,a869),a871),a332))))))),f329(f329(f8(f883(f883(x101791,f883(a871,a869)),f883(x101791,f883(a871,f883(a871,a869)))),f883(f883(x101791,f883(a871,a869)),f883(x101791,f883(a871,a869))),a870),f329(f8(f883(x101791,f883(a871,f883(a871,a869))),f883(x101791,f883(a871,a869)),f883(x101791,f883(a871,a869))),f329(f8(f883(a871,f883(a871,a869)),f883(a871,a869),x101791),f329(f8(f883(a871,a869),a869,a871),f89(a871))))),f329(f329(f8(f883(f883(a871,a869),f883(a871,f883(a871,a869))),f883(f883(x101791,f883(a871,a869)),f883(x101791,f883(a871,f883(a871,a869)))),a870),f8(f883(a871,a869),f883(a871,f883(a871,a869)),x101791)),f329(f329(f8(f883(a871,f883(f883(a871,a869),f883(a871,a869))),f883(f883(a871,a869),f883(a871,f883(a871,a869))),a870),f7(a871,f883(a871,a869),f883(a871,a869))),f329(f329(f8(f883(a871,f883(a871,f883(a869,a869))),f883(a871,f883(f883(a871,a869),f883(a871,a869))),a870),f329(f8(f883(a871,f883(a869,a869)),f883(f883(a871,a869),f883(a871,a869)),a871),f18(a871,a869,a869))),f329(f329(f8(f883(a871,f883(a871,a869)),f883(a871,f883(a871,f883(a869,a869))),a870),f329(f8(f883(a871,a869),f883(a871,f883(a869,a869)),a871),f329(f8(a869,f883(a869,a869),a871),a332))),f329(f329(f7(a870,a875,f883(a871,f883(a871,a869))),f329(f329(f8(f883(a871,f883(a875,f883(a871,a869))),f883(a875,f883(a871,f883(a871,a869))),a870),f7(a871,a875,f883(a871,a869))),a201)),x101792))))))))),x101793)) % 178.07/177.93 [4660]E(x46601,x46602)+~E(f34(x46603,x46601),f34(x46604,x46602)) % 178.07/177.93 [4661]E(x46611,x46612)+~E(f34(x46611,x46613),f34(x46612,x46614)) % 178.07/177.93 [4662]E(x46621,x46622)+~E(f33(x46623,x46621),f33(x46624,x46622)) % 178.07/177.93 [4663]E(x46631,x46632)+~E(f33(x46631,x46633),f33(x46632,x46634)) % 178.07/177.93 [7740]P21(x77401,x77402,x77403,x77404)+~E(f715(x77404,x77403,x77402,x77401),f731(x77404,x77403,x77402,x77401)) % 178.07/177.93 [8035]P35(x80351,x80352,x80353,x80354,f119(x80352))+~E(x80354,f119(x80351)) % 178.07/177.93 [8036]P35(x80361,x80362,x80363,f119(x80361),x80364)+~E(x80364,f119(x80362)) % 178.07/177.93 [8250]~P21(x82501,f879(x82502),x82504,f183(x82501,x82502,x82504))+P21(x82501,f879(x82502),f184(x82501,x82502,x82503,x82504),f183(x82501,x82502,x82504)) % 178.07/177.93 [8464]~P21(x84641,f879(x84642),f184(x84641,x84642,x84644,x84643),f183(x84641,x84642,x84643))+P21(x84641,f879(x84642),x84643,f183(x84641,x84642,x84643)) % 178.07/177.93 [8580]~P35(x85802,x85803,x85804,x85801,f119(x85803))+E(x85801,f119(x85802)) % 178.07/177.93 [8581]~P35(x85813,x85812,x85814,f119(x85813),x85811)+E(x85811,f119(x85812)) % 178.07/177.93 [5034]~P13(x50343,x50341,x50344)+E(f329(f329(x50341,x50342),x50342),x50342) % 178.07/177.93 [5325]~E(x53254,f193(f883(x53251,a869)))+E(f329(f308(x53251,x53252,x53253),x53254),f193(f883(x53252,a869))) % 178.07/177.93 [5591]~E(f329(f308(x55912,x55913,x55914),x55911),f193(f883(x55913,a869)))+E(x55911,f193(f883(x55912,a869))) % 178.07/177.93 [5874]~P105(x58742)+E(f329(f329(f147(x58741,x58742,x58743),x58744),f119(x58741)),f329(f329(f150(x58741),x58744),f119(x58741))) % 178.07/177.93 [5912]E(f329(x59121,x59122),f206(x59123))+P24(f329(f329(f331(x59124),x59122),f183(x59124,x59123,x59121))) % 178.07/177.93 [6235]~E(x62351,f193(f883(x62352,a869)))+~P24(f329(f63(x62352,x62353,x62351),x62354)) % 178.07/177.93 [6257]~P54(x62571,x62573,x62574,x62572)+P24(f329(f62(x62571),x62572)) % 178.07/177.93 [6258]~P54(x62581,x62583,x62582,x62584)+P24(f329(f62(x62581),x62582)) % 178.07/177.93 [6264]~P54(x62642,x62643,x62644,x62641)+~E(x62641,f193(f883(x62642,a869))) % 178.07/177.93 [6295]~P107(x62951)+E(f329(f329(f107(f883(x62951,a869)),f329(f299(x62951,x62952),x62953)),f300(x62951,x62953,x62954)),f193(f883(x62951,a869))) % 178.07/177.93 [6322]~P24(f329(f329(x63223,x63224),x63222))+P24(f329(f329(f331(x63221),x63222),f290(x63221,x63223,x63224))) % 178.07/177.93 [6323]~P24(f329(f329(x63233,x63234),x63232))+P24(f329(f329(f331(x63231),x63232),f291(x63231,x63233,x63234))) % 178.07/177.93 [6324]~P24(f329(f329(x63243,x63242),x63244))+P24(f329(f329(f331(x63241),x63242),f295(x63241,x63243,x63244))) % 178.07/177.93 [6325]~P24(f329(f329(x63253,x63252),x63254))+P24(f329(f329(f331(x63251),x63252),f292(x63251,x63253,x63254))) % 178.07/177.93 [6465]~P107(x64651)+E(f329(f329(f107(f883(x64651,a869)),f303(x64651,x64652,x64653)),f300(x64651,x64653,x64654)),f193(f883(x64651,a869))) % 178.07/177.93 [6466]~P107(x64661)+E(f329(f329(f107(f883(x64661,a869)),f302(x64661,x64662,x64663)),f303(x64661,x64663,x64664)),f193(f883(x64661,a869))) % 178.07/177.93 [6467]~P107(x64671)+E(f329(f329(f107(f883(x64671,a869)),f302(x64671,x64672,x64673)),f302(x64671,x64673,x64674)),f193(f883(x64671,a869))) % 178.07/177.93 [6468]~P107(x64681)+E(f329(f329(f107(f883(x64681,a869)),f300(x64681,x64682,x64683)),f303(x64681,x64683,x64684)),f193(f883(x64681,a869))) % 178.07/177.93 [6469]~P107(x64691)+E(f329(f329(f107(f883(x64691,a869)),f300(x64691,x64692,x64693)),f302(x64691,x64693,x64694)),f193(f883(x64691,a869))) % 178.07/177.93 [6506]P24(f329(f329(x65061,x65062),f693(x65062,x65061)))+~P24(f329(f258(x65063,x65064,x65061),x65062)) % 178.07/177.93 [6555]~E(f329(x65551,x65552),f206(x65553))+~P24(f329(f329(f331(x65554),x65552),f183(x65554,x65553,x65551))) % 178.07/177.93 [6584]~P105(x65842)+E(f329(f171(x65841),f149(x65841,x65842,x65843,x65844)),f329(f171(x65841),x65844)) % 178.07/177.93 [6636]~P141(x66361)+E(f195(x66361,x66362,f329(a118,x66363),x66364),f195(x66361,x66362,x66363,f329(x66362,x66364))) % 178.07/177.93 [6696]~P24(f329(f329(f331(x66964),x66963),f290(x66964,x66961,x66962)))+P24(f329(f329(x66961,x66962),x66963)) % 178.07/177.93 [6697]~P24(f329(f329(f331(x66974),x66973),f291(x66974,x66971,x66972)))+P24(f329(f329(x66971,x66972),x66973)) % 178.07/177.93 [6698]~P24(f329(f329(f331(x66984),x66982),f295(x66984,x66981,x66983)))+P24(f329(f329(x66981,x66982),x66983)) % 178.07/177.93 [6699]~P24(f329(f329(f331(x66994),x66992),f292(x66994,x66991,x66993)))+P24(f329(f329(x66991,x66992),x66993)) % 178.07/177.93 [6776]E(f329(f38(f881(x67761,x67762)),f316(x67761,x67762,x67763,x67764)),f2(a875))+P24(f329(f62(x67762),x67764)) % 178.07/177.93 [6777]E(f329(f38(f881(x67771,x67772)),f316(x67771,x67772,x67773,x67774)),f2(a875))+P24(f329(f62(x67771),x67773)) % 178.07/177.93 [6979]~P11(x69794,x69791,x69792)+E(f329(f74(x69791,x69791,x69791,f329(x69792,x69793)),f329(x69792,x69793)),f329(x69792,x69793)) % 178.07/177.93 [7777]~P24(f329(x77771,x77774))+P24(f329(x77771,f97(x77772,a875,x77773,x77771))) % 178.07/177.93 [7860]~E(x78602,x78603)+P24(f329(f329(f331(f882(x78601,x78601)),f329(f329(f264(x78601,x78601),x78602),x78603)),f305(x78601,x78604))) % 178.07/177.93 [7889]~P21(x78891,x78892,x78893,f252(f883(x78891,a869)))+E(f329(f78(x78891,x78892,f252(f883(x78891,a869)),x78893),f329(x78893,x78894)),x78894) % 178.07/177.93 [7981]~P24(f329(f329(f331(f876(x79811)),f329(f329(f150(x79811),x79814),x79812)),f160(x79811,x79813)))+P24(f329(f329(f331(f876(x79811)),x79812),f160(x79811,x79813))) % 178.07/177.93 [7982]~P24(f329(f329(f331(f876(x79821)),f329(f329(f127(x79821),x79824),x79822)),f160(x79821,x79823)))+P24(f329(f329(f331(f876(x79821)),x79822),f160(x79821,x79823))) % 178.07/177.93 [7983]~P24(f329(f329(f331(f876(x79831)),f329(f329(f127(x79831),x79832),x79834)),f160(x79831,x79833)))+P24(f329(f329(f331(f876(x79831)),x79832),f160(x79831,x79833))) % 178.07/177.93 [7999]~P105(x79991)+P29(x79991,f329(f329(f153(x79992,x79991),x79993),f149(x79992,x79991,x79993,x79994))) % 178.07/177.93 [8097]P21(x80974,x80973,x80971,x80972)+E(f329(x80971,f715(x80972,x80971,x80973,x80974)),f329(x80971,f731(x80972,x80971,x80973,x80974))) % 178.07/177.93 [8110]E(f184(x81101,x81102,x81103,x81104),f184(x81101,x81102,x81104,x81103))+~E(f329(f329(f107(f883(x81101,a869)),f183(x81101,x81102,x81103)),f183(x81101,x81102,x81104)),f193(f883(x81101,a869))) % 178.07/177.93 [8213]~P21(x82132,x82131,x82134,x82133)+P21(x82131,x82132,f78(x82132,x82131,x82133,x82134),f329(f308(x82132,x82131,x82134),x82133)) % 178.07/177.93 [8349]P38(f882(x83492,x83494),f281(x83492,x83494,x83491,x83493))+P24(f329(x83491,f695(x83492,x83493,x83494,x83491))) % 178.07/177.93 [8471]E(x84711,x84712)+~P24(f329(f329(f331(f882(x84713,x84713)),f329(f329(f264(x84713,x84713),x84711),x84712)),f261(x84713,x84714))) % 178.07/177.93 [8535]~P24(f329(f62(f881(x85353,x85351)),f316(x85353,x85351,x85354,x85352)))+P24(f329(f62(x85351),x85352)) % 178.07/177.93 [8536]~P24(f329(f62(f881(x85361,x85363)),f316(x85361,x85363,x85362,x85364)))+P24(f329(f62(x85361),x85362)) % 178.07/177.93 [8714]P38(f882(x87141,x87142),f281(x87141,x87142,x87143,x87144))+~P38(x87142,f329(x87144,f695(x87141,x87144,x87142,x87143))) % 178.07/177.93 [9274]E(f329(f329(f158(x92741,x92742),f605(x92743,x92744,x92742,x92741)),f606(x92743,x92744,x92742,x92741)),x92744)+~P24(f329(f329(f331(f882(f876(x92741),f876(x92741))),f329(f329(f264(f876(x92741),f876(x92741)),x92742),x92744)),f156(x92741,x92743))) % 178.07/177.93 [9275]~P24(f329(x92753,x92754))+P24(f329(f329(f243(a875),f329(x92751,f97(x92752,a875,x92751,x92753))),f329(x92751,x92754))) % 178.07/177.93 [9281]~P24(f329(f329(f331(f882(f876(x92811),f876(x92811))),f329(f329(f264(f876(x92811),f876(x92811)),x92812),x92813)),f144(x92811,x92814)))+P24(f329(f329(f331(f882(f876(x92811),f876(x92811))),f329(f329(f264(f876(x92811),f876(x92811)),x92812),x92813)),f146(x92811,x92814))) % 178.07/177.93 [9386]P24(f329(f62(x93861),x93862))+~P24(f329(f329(f331(f882(f883(x93861,a869),f883(x93861,a869))),f329(f329(f264(f883(x93861,a869),f883(x93861,a869)),x93863),x93862)),f320(x93861,x93864))) % 178.07/177.93 [9387]P24(f329(f62(x93871),x93872))+~P24(f329(f329(f331(f882(f883(x93871,a869),f883(x93871,a869))),f329(f329(f264(f883(x93871,a869),f883(x93871,a869)),x93872),x93873)),f320(x93871,x93874))) % 178.07/177.93 [9390]~E(x93901,f193(f883(x93902,a869)))+~P24(f329(f329(f331(f882(f883(x93902,a869),f883(x93902,a869))),f329(f329(f264(f883(x93902,a869),f883(x93902,a869)),x93903),x93901)),f320(x93902,x93904))) % 178.07/177.93 [10024]P9(x100241,x100242,x100243,x100244)+~P24(f329(f329(f268(x100241,x100241,a869),f329(f329(f7(x100241,f883(x100241,x100242),f883(x100241,a869)),f329(f329(f8(f883(x100242,a869),f883(f883(x100241,x100242),f883(x100241,a869)),x100241),f8(x100242,a869,x100241)),f329(f329(f8(x100242,f883(x100242,a869),x100241),a326),x100244))),x100244)),f595(x100244,x100243,x100242,x100241))) % 178.07/177.93 [4935]~E(x49354,f206(x49351))+E(f329(f329(f207(x49351,x49352),x49353),x49354),f206(x49352)) % 178.07/177.93 [4936]~E(x49364,f119(x49361))+E(f329(f329(f153(x49361,x49362),x49363),x49364),f119(x49362)) % 178.07/177.93 [4937]~E(x49372,f119(x49371))+E(f329(f329(f158(x49371,x49372),x49373),x49374),f119(x49371)) % 178.07/177.93 [5173]E(x51731,f206(x51732))+~E(f329(f329(f207(x51732,x51733),x51734),x51731),f206(x51733)) % 178.07/177.93 [5174]E(x51741,f119(x51742))+~E(f329(f329(f153(x51742,x51743),x51744),x51741),f119(x51743)) % 178.07/177.93 [5175]E(x51751,f119(x51752))+~E(f329(f329(f158(x51752,x51751),x51753),x51754),f119(x51752)) % 178.07/177.93 [5207]E(x52071,x52072)+~E(f329(f329(f127(x52073),x52074),x52071),f329(f329(f127(x52073),x52074),x52072)) % 178.07/177.93 [5208]E(x52081,x52082)+~E(f329(f329(f127(x52083),x52081),x52084),f329(f329(f127(x52083),x52082),x52084)) % 178.07/177.93 [5362]P24(f329(x53623,x53622))+E(f169(x53621,x53622,f329(f135(x53621,x53623),x53624)),f329(f135(x53621,x53623),x53624)) % 178.07/177.93 [5365]~P24(f329(x53652,x53653))+P34(x53651,x53652,f329(f329(f150(x53651),x53653),x53654)) % 178.07/177.93 [5374]E(x53741,x53742)+~E(f138(a875,f329(f299(a875,x53741),x53743)),f329(f329(f150(a875),x53742),x53744)) % 178.07/177.93 [5422]~P22(x54222,x54223)+P22(x54221,f329(f329(f75(x54222,x54221),x54223),x54224)) % 178.07/177.93 [5423]~P38(x54232,x54233)+P38(x54231,f329(f329(f285(x54232,x54231),x54233),x54234)) % 178.07/177.93 [5547]~P34(x55471,x55472,x55474)+P34(x55471,x55472,f329(f329(f150(x55471),x55473),x55474)) % 178.07/177.93 [5548]~P34(x55481,x55482,x55484)+P34(x55481,x55482,f329(f329(f127(x55481),x55483),x55484)) % 178.07/177.93 [5549]~P34(x55491,x55492,x55493)+P34(x55491,x55492,f329(f329(f127(x55491),x55493),x55494)) % 178.07/177.93 [5634]~E(x56341,f119(x56342))+~E(f329(f329(f127(x56342),x56343),f329(f329(f150(x56342),x56344),f119(x56342))),x56341) % 178.07/177.93 [5659]~P32(x56593,x56591,f329(f329(f150(x56593),x56592),x56594))+P24(f329(x56591,x56592)) % 178.07/177.93 [5669]E(f120(x56691,x56692),x56693)+~E(f329(f329(f127(x56691),x56693),f329(f329(f150(x56691),x56694),f119(x56691))),x56692) % 178.07/177.93 [5670]E(f143(x56701,x56702),x56703)+~E(f329(f329(f127(x56701),x56704),f329(f329(f150(x56701),x56703),f119(x56701))),x56702) % 178.07/177.93 [5779]~E(f138(a875,f329(f299(a875,x57791),x57792)),f329(f329(f150(a875),x57793),x57794))+P24(f329(f329(f244(a875),x57791),x57792)) % 178.07/177.93 [5787]P32(x57871,x57872,x57873)+~P32(x57871,x57872,f329(f329(f150(x57871),x57874),x57873)) % 178.07/177.93 [5788]P32(x57881,x57882,x57883)+~P32(x57881,x57882,f329(f329(f127(x57881),x57884),x57883)) % 178.07/177.93 [5789]P32(x57891,x57892,x57893)+~P32(x57891,x57892,f329(f329(f127(x57891),x57893),x57894)) % 178.07/177.93 [5980]E(x59801,f329(f329(f127(x59802),f329(f168(x59802),x59803)),f329(f329(f150(x59802),x59804),f119(x59802))))+~E(f329(f168(x59802),x59801),f329(f329(f150(x59802),x59804),x59803)) % 178.07/177.93 [6157]~P107(x61571)+E(f329(f329(f107(f883(x61571,a869)),f329(f299(x61571,x61572),x61573)),f329(f299(x61571,x61573),x61574)),f193(f883(x61571,a869))) % 178.07/177.93 [6193]~P70(x61931)+E(f329(f165(x61931),f329(f329(f153(a1,x61931),x61932),f178(x61933,x61934))),f329(f329(f6(a1,x61931),x61932),f329(f171(a1),f178(x61933,x61934)))) % 178.07/177.93 [6194]~P70(x61941)+E(f329(f329(f6(a1,x61941),x61942),f329(f171(a1),f178(x61943,x61944))),f329(f165(x61941),f329(f329(f153(a1,x61941),x61942),f178(x61943,x61944)))) % 178.07/177.93 [6337]~E(x63372,f329(f329(f127(x63371),f329(f168(x63371),x63374)),f329(f329(f150(x63371),x63373),f119(x63371))))+E(f329(f168(x63371),x63372),f329(f329(f150(x63371),x63373),x63374)) % 178.07/177.93 [6352]~P15(x63522,x63523,x63524,x63521)+E(f329(x63521,f193(f883(x63522,a869))),f35(x63523)) % 178.07/177.93 [6378]~P107(x63781)+E(f329(f329(f107(f883(x63781,a869)),f303(x63781,x63782,x63783)),f329(f299(x63781,x63783),x63784)),f193(f883(x63781,a869))) % 178.07/177.93 [6585]E(x65851,f193(f883(x65852,a869)))+~E(f316(x65853,x65852,x65854,x65851),f193(f883(f881(x65853,x65852),a869))) % 178.07/177.93 [6586]E(x65861,f193(f883(x65862,a869)))+~E(f316(x65862,x65863,x65861,x65864),f193(f883(f881(x65862,x65863),a869))) % 178.07/177.93 [6655]~P105(x66552)+E(f329(f194(f876(x66551)),f149(x66551,x66552,x66553,x66554)),f329(f194(f876(x66551)),x66554)) % 178.07/177.93 [6667]~P24(f329(f259(x66673,x66674,x66671),x66672))+P24(f329(f329(x66671,f694(x66672,x66671)),x66672)) % 178.07/177.93 [6707]~P24(f329(f62(x67072),x67074))+P24(f329(f62(x67071),f329(f308(x67072,x67071,x67073),x67074))) % 178.07/177.93 [6939]~P21(x69392,x69391,x69393,x69394)+E(f329(f38(x69391),f329(f308(x69392,x69391,x69393),x69394)),f329(f38(x69392),x69394)) % 178.07/177.93 [6958]E(f329(f308(x69581,x69582,x69583),f329(f309(x69581,x69582,x69583),x69584)),x69584)+~E(f329(f308(x69581,x69582,x69583),f252(f883(x69581,a869))),f252(f883(x69582,a869))) % 178.07/177.93 [7368]~P21(x73681,x73682,x73683,f252(f883(x73681,a869)))+E(f329(f309(x73681,x73682,x73683),f329(f308(x73681,x73682,x73683),x73684)),x73684) % 178.07/177.93 [7701]P24(f329(x77011,x77012))+~P24(f329(f329(f331(x77013),x77012),f329(f171(x77013),f176(x77013,x77011,x77014)))) % 178.07/177.93 [7807]~P24(f329(f329(f331(f876(x78071)),f329(f329(f150(x78071),x78072),x78074)),f160(x78071,x78073)))+P24(f329(f329(f331(x78071),x78072),x78073)) % 178.07/177.93 [7935]~P24(f329(f329(f331(x79351),x79352),f329(f171(x79351),f169(x79351,x79354,x79353))))+P24(f329(f329(f331(x79351),x79352),f329(f171(x79351),x79353))) % 178.07/177.93 [7937]~P24(f329(f329(f331(x79371),x79372),f329(f171(x79371),f175(x79371,x79373,x79374))))+P24(f329(f329(f331(x79371),x79372),f329(f171(x79371),x79373))) % 178.07/177.93 [7938]~P24(f329(f329(f331(x79381),x79382),f329(f171(x79381),f176(x79381,x79384,x79383))))+P24(f329(f329(f331(x79381),x79382),f329(f171(x79381),x79383))) % 178.07/177.93 [7948]E(f329(f194(f876(x79481)),x79482),x79483)+~P24(f329(f329(f331(f876(x79481)),x79482),f329(f171(f876(x79481)),f55(x79481,x79483,x79484)))) % 178.07/177.93 [8047]P24(f329(x80473,x80472))+E(f329(f135(x80471,f329(f329(f8(a869,a869,x80471),a324),f329(a326,x80472))),f329(f135(x80471,x80473),x80474)),f329(f135(x80471,x80473),x80474)) % 178.07/177.93 [8162]E(f329(f329(f164(x81621),f176(x81621,x81622,x81623)),x81624),f329(f329(f164(x81621),x81623),x81624))+~P24(f329(f329(f244(a875),x81624),f329(f194(f876(x81621)),f176(x81621,x81622,x81623)))) % 178.07/177.93 [8248]~P70(x82481)+E(f329(f329(f6(a875,x82481),f329(f329(f8(a875,x82481,a875),x82482),a118)),f329(f299(a875,x82483),x82484)),f329(f329(f6(a875,x82481),x82482),f329(f299(a875,f329(a118,x82483)),f329(a118,x82484)))) % 178.07/177.93 [8257]~P70(x82571)+E(f329(f329(f6(a875,x82571),f329(f329(f8(a875,x82571,a875),x82572),a118)),f300(a875,x82573,x82574)),f329(f329(f6(a875,x82571),x82572),f300(a875,f329(a118,x82573),f329(a118,x82574)))) % 178.07/177.93 [8386]~P21(x83861,x83863,x83864,f252(f883(x83861,a869)))+P21(x83861,f883(x83862,x83863),f329(f329(f8(x83863,f883(x83862,x83863),x83861),f16(x83863,x83862)),x83864),f252(f883(x83861,a869))) % 178.07/177.93 [8479]~P21(x84792,x84791,x84794,x84793)+E(f329(f308(x84791,x84792,f78(x84792,x84791,x84793,x84794)),f329(f308(x84792,x84791,x84794),x84793)),x84793) % 178.07/177.93 [8537]~P24(f329(f329(f331(f882(x85371,x85371)),f329(f329(f264(x85371,x85371),x85372),x85374)),f261(x85371,x85373)))+P24(f329(f329(f331(x85371),x85372),x85373)) % 178.07/177.93 [8626]E(f329(f329(f329(f73(x86261,f879(x86262)),f329(f16(f879(x86262),x86261),f206(x86262))),x86263),f329(f236(x86262),f349(x86263,x86264,x86262,x86261))),x86264)+~E(f183(x86261,x86262,x86264),f329(f329(f307(x86261),x86263),f193(f883(x86261,a869)))) % 178.07/177.93 [8749]~E(f329(f329(f6(x87491,a875),x87494),x87493),f329(a118,x87492))+P24(f329(f329(f331(x87491),f503(x87492,x87493,x87494,x87491)),x87493)) % 178.07/177.93 [8769]~E(f329(f329(f6(x87694,a875),x87691),x87693),f329(a118,x87692))+P24(f329(f329(f244(a875),f2(a875)),f329(x87691,f503(x87692,x87693,x87691,x87694)))) % 178.07/177.93 [8780]~P24(f329(f62(x87802),x87804))+P24(f329(f329(f243(a875),f329(f38(x87801),f329(f308(x87802,x87801,x87803),x87804))),f329(f38(x87802),x87804))) % 178.07/177.93 [8781]E(f329(f329(f264(x87811,x87812),f795(x87813,x87814,x87812,x87811)),f796(x87813,x87814,x87812,x87811)),x87814)+~P24(f329(f329(f331(f882(x87811,x87812)),x87814),f329(f284(x87812,x87811),x87813))) % 178.07/177.93 [8789]P21(x87891,x87892,x87893,x87894)+P24(f329(f329(f331(x87891),f715(x87894,x87893,x87892,x87891)),x87894)) % 178.07/177.93 [8790]P21(x87901,x87902,x87903,x87904)+P24(f329(f329(f331(x87901),f731(x87904,x87903,x87902,x87901)),x87904)) % 178.07/177.93 [8851]P9(x88511,x88512,x88513,x88514)+P24(f329(f329(f331(f882(x88511,x88511)),f595(x88514,x88513,x88512,x88511)),x88513)) % 178.07/177.93 [8912]P24(f329(x89121,x89122))+~P24(f329(x89121,f329(f329(f264(x89123,x89124),f543(x89124,x89123,x89121)),f544(x89124,x89123,x89121)))) % 178.07/177.93 [8931]E(f329(f194(f876(x89311)),x89312),f329(f194(f876(x89311)),x89313))+~P24(f329(f329(f331(f882(f876(x89311),f876(x89311))),f329(f329(f264(f876(x89311),f876(x89311)),x89312),x89313)),f157(x89311,x89314))) % 178.07/177.93 [8932]E(f329(f194(f876(x89321)),x89322),f329(f194(f876(x89321)),x89323))+~P24(f329(f329(f331(f882(f876(x89321),f876(x89321))),f329(f329(f264(f876(x89321),f876(x89321)),x89322),x89323)),f144(x89321,x89324))) % 178.07/177.93 [8933]E(f329(f194(f876(x89331)),x89332),f329(f194(f876(x89331)),x89333))+~P24(f329(f329(f331(f882(f876(x89331),f876(x89331))),f329(f329(f264(f876(x89331),f876(x89331)),x89332),x89333)),f156(x89331,x89334))) % 178.07/177.93 [9008]P24(f329(f329(f243(a875),f154(x90081,x90082,x90083)),f154(x90081,x90084,x90083)))+P24(f329(f329(f331(x90081),f586(x90084,x90082,x90083,x90081)),f329(f171(x90081),x90083))) % 178.07/177.93 [9011]E(f329(f194(f876(x90111)),x90112),f329(f194(f876(x90111)),x90113))+~P24(f329(f329(f331(f882(f876(x90111),f876(x90111))),f329(f329(f264(f876(x90111),f876(x90111)),x90112),x90113)),f305(f876(x90111),f156(x90111,x90114)))) % 178.07/177.93 [9246]~P21(x92461,x92462,x92463,x92464)+~P24(f329(f329(f244(a875),f329(f38(x92462),f329(f308(x92461,x92462,x92463),x92464))),f329(f38(x92461),x92464))) % 178.07/177.93 [9292]~P24(f329(f329(f331(f882(f876(x92921),f876(x92921))),f329(f329(f264(f876(x92921),f876(x92921)),x92922),x92923)),f156(x92921,x92924)))+P24(f329(f329(f331(f882(f876(x92921),f876(x92921))),f329(f329(f264(f876(x92921),f876(x92921)),x92922),x92923)),f157(x92921,f305(x92921,x92924)))) % 178.07/177.93 [9296]~P24(f329(f329(f331(f882(f876(x92961),f876(x92961))),f329(f329(f264(f876(x92961),f876(x92961)),x92962),x92963)),f157(x92961,x92964)))+P24(f329(f329(f331(f882(f876(x92961),f876(x92961))),f329(f329(f264(f876(x92961),f876(x92961)),x92962),x92963)),f305(f876(x92961),f156(x92961,x92964)))) % 178.07/177.93 [9313]P24(f329(f329(f331(f882(x93131,x93131)),f329(f329(f264(x93131,x93131),x93132),x93133)),f305(x93131,x93134)))+~P24(f329(f329(f331(f882(x93131,x93131)),f329(f329(f264(x93131,x93131),x93132),x93133)),f329(f329(f286(x93131,x93131,x93131),x93134),f305(x93131,x93134)))) % 178.07/177.93 [9494]E(f329(f329(f127(x94941),f633(x94942,x94943,x94944,x94941)),f329(f329(f150(x94941),f634(x94942,x94943,x94944,x94941)),f636(x94942,x94943,x94944,x94941))),x94944)+~P24(f329(f329(f331(f882(f876(x94941),f876(x94941))),f329(f329(f264(f876(x94941),f876(x94941)),x94944),x94943)),f156(x94941,x94942))) % 178.07/177.93 [9495]E(f329(f329(f127(x94951),f633(x94952,x94953,x94954,x94951)),f329(f329(f150(x94951),f635(x94952,x94953,x94954,x94951)),f636(x94952,x94953,x94954,x94951))),x94953)+~P24(f329(f329(f331(f882(f876(x94951),f876(x94951))),f329(f329(f264(f876(x94951),f876(x94951)),x94954),x94953)),f156(x94951,x94952))) % 178.07/177.93 [9571]P24(f329(f329(f331(f882(x95711,x95711)),f329(f329(f264(x95711,x95711),x95712),f772(x95713,x95714,x95712,x95711))),f305(x95711,x95713)))+~P24(f329(f329(f331(f882(x95711,x95711)),f329(f329(f264(x95711,x95711),x95712),x95714)),f329(f329(f286(x95711,x95711,x95711),x95713),f305(x95711,x95713)))) % 178.07/177.93 [9640]P24(f329(f329(f243(a875),f154(x96401,x96402,x96403)),f154(x96401,x96404,x96403)))+~P24(f329(f329(f244(a875),f329(x96402,f586(x96404,x96402,x96403,x96401))),f329(x96404,f586(x96404,x96402,x96403,x96401)))) % 178.07/177.93 [9707]P24(f329(f329(f331(f882(x97071,x97071)),f329(f329(f264(x97071,x97071),f766(x97072,x97073,x97074,x97071)),x97073)),f305(x97071,x97072)))+~P24(f329(f329(f331(f882(x97071,x97071)),f329(f329(f264(x97071,x97071),x97074),x97073)),f329(f329(f286(x97071,x97071,x97071),x97072),f305(x97071,x97072)))) % 178.07/177.93 [5189]~E(x51892,x51893)+E(f169(x51891,x51892,f329(f329(f150(x51891),x51893),x51894)),x51894) % 178.07/177.93 [5317]P24(f329(x53172,x53173))+E(f176(x53171,x53172,f329(f329(f150(x53171),x53173),x53174)),f119(x53171)) % 178.07/177.93 [5386]~P81(x53862)+E(f329(f329(f80(f883(x53861,x53862)),x53863),x53864),f329(f80(x53862),f329(x53863,x53864))) % 178.07/177.93 [5398]~E(x53982,f2(a875))+E(f329(f329(f137(x53981),x53982),f329(f329(f150(x53981),x53983),x53984)),f329(f329(f150(x53981),x53983),x53984)) % 178.07/177.93 [5399]P24(f329(x53992,x53993))+E(f329(f135(x53991,x53992),f329(f329(f150(x53991),x53993),x53994)),f329(f135(x53991,x53992),x53994)) % 178.07/177.93 [5530]~E(x55302,x55304)+P24(f329(f329(f329(f307(x55301),x55302),x55303),x55304)) % 178.07/177.93 [5538]E(x55381,f119(x55382))+E(f143(x55383,f329(f329(f153(x55382,x55383),x55384),x55381)),f329(x55384,f143(x55382,x55381))) % 178.07/177.93 [5552]~E(x55521,f64(x55522,x55524))+E(f329(x55521,f329(f329(f307(x55522),x55523),f193(f883(x55522,a869)))),x55523) % 178.07/177.93 [5586]E(x55861,f119(x55862))+E(f329(f140(x55863),f329(f329(f153(x55862,x55863),x55864),x55861)),f329(x55864,f329(f140(x55862),x55861))) % 178.07/177.93 [5688]~P24(f329(x56883,x56884))+P24(f329(f329(f329(f307(x56881),x56882),x56883),x56884)) % 178.07/177.93 [5804]~P14(x58042,x58044,x58041)+E(f329(x58041,f329(f329(f307(x58042),x58043),f193(f883(x58042,a869)))),x58043) % 178.07/177.93 [5828]~E(x58282,x58283)+P24(f329(f329(f331(x58281),x58282),f329(f329(f307(x58281),x58283),x58284))) % 178.07/177.93 [5832]~P63(x58321)+E(f329(f329(f116(x58321),x58322),f329(f329(f116(x58321),x58323),x58324)),f329(f329(f116(x58321),x58323),f329(f329(f116(x58321),x58322),x58324))) % 178.07/177.93 [5834]~P99(x58341)+E(f329(f329(f116(x58341),x58342),f329(f329(f116(x58341),x58343),x58344)),f329(f329(f116(x58341),x58343),f329(f329(f116(x58341),x58342),x58344))) % 178.07/177.93 [5835]~P63(x58351)+E(f329(f329(f107(x58351),x58352),f329(f329(f107(x58351),x58353),x58354)),f329(f329(f107(x58351),x58353),f329(f329(f107(x58351),x58352),x58354))) % 178.07/177.93 [5837]~P100(x58371)+E(f329(f329(f107(x58371),x58372),f329(f329(f107(x58371),x58373),x58374)),f329(f329(f107(x58371),x58373),f329(f329(f107(x58371),x58372),x58374))) % 178.07/177.93 [5838]~P114(x58381)+E(f329(f329(f82(x58381),x58382),f329(f329(f82(x58381),x58383),x58384)),f329(f329(f82(x58381),x58383),f329(f329(f82(x58381),x58382),x58384))) % 178.07/177.93 [5839]~P114(x58391)+E(f329(f329(f81(x58391),x58392),f329(f329(f81(x58391),x58393),x58394)),f329(f329(f81(x58391),x58393),f329(f329(f81(x58391),x58392),x58394))) % 178.07/177.93 [5841]~P105(x58411)+E(f329(f329(f241(x58411),x58412),f329(f329(f241(x58411),x58413),x58414)),f329(f329(f241(x58411),x58413),f329(f329(f241(x58411),x58412),x58414))) % 178.07/177.93 [5843]~P105(x58431)+E(f329(f329(f242(x58431),x58432),f329(f329(f242(x58431),x58433),x58434)),f329(f329(f242(x58431),x58433),f329(f329(f242(x58431),x58432),x58434))) % 178.07/177.93 [5848]E(x58481,x58482)+E(f169(x58483,x58481,f329(f329(f150(x58483),x58482),x58484)),f329(f329(f150(x58483),x58482),f169(x58483,x58481,x58484))) % 178.07/177.93 [5861]~P24(f329(x58612,x58613))+E(f329(f135(x58611,x58612),f329(f329(f150(x58611),x58613),x58614)),f329(f329(f150(x58611),x58613),f329(f135(x58611,x58612),x58614))) % 178.07/177.93 [6000]~P24(f329(x60002,x60003))+E(f176(x60001,x60002,f329(f329(f150(x60001),x60003),x60004)),f329(f329(f150(x60001),x60003),f176(x60001,x60002,x60004))) % 178.07/177.93 [6051]P20(x60511,x60512,x60513)+~P20(x60511,x60512,f329(f329(f307(f874(x60511)),x60514),x60513)) % 178.07/177.93 [6064]E(x60641,f193(f883(x60642,a869)))+E(f329(f329(f42(x60642,f883(x60643,a869)),x60641),f329(f16(f883(x60643,a869),x60642),x60644)),x60644) % 178.07/177.93 [6065]E(x60651,f193(f883(x60652,a869)))+E(f329(f329(f43(x60652,f883(x60653,a869)),x60651),f329(f16(f883(x60653,a869),x60652),x60654)),x60654) % 178.07/177.93 [6074]~E(x60744,f193(f883(x60742,a869)))+E(f329(f329(f266(x60741,x60742),x60743),f329(f16(f883(x60742,a869),x60741),x60744)),f193(f883(f882(x60741,x60742),a869))) % 178.07/177.93 [6075]~E(x60753,f193(f883(x60751,a869)))+E(f329(f329(f266(x60751,x60752),x60753),f329(f16(f883(x60752,a869),x60751),x60754)),f193(f883(f882(x60751,x60752),a869))) % 178.07/177.93 [6121]E(x61211,f2(a875))+E(f329(f329(f137(x61212),x61211),f329(f329(f150(x61212),x61213),x61214)),f329(f329(f137(x61212),f329(f329(f22(a875),x61211),f79(a875))),x61214)) % 178.07/177.93 [6151]E(x61511,f193(f883(x61512,a869)))+E(f329(f308(x61512,x61513,f329(f16(x61513,x61512),x61514)),x61511),f329(f329(f307(x61513),x61514),f193(f883(x61513,a869)))) % 178.07/177.93 [6154]E(f329(f309(x61541,x61542,f329(f16(x61542,x61541),x61543)),x61544),f193(f883(x61541,a869)))+P24(f329(f329(f331(x61542),x61543),x61544)) % 178.07/177.93 [6219]~E(x62193,f193(f883(x62191,a869)))+E(f329(f329(f42(x62191,f883(x62192,a869)),x62193),f329(f16(f883(x62192,a869),x62191),x62194)),f252(f883(x62192,a869))) % 178.07/177.93 [6220]~E(x62203,f193(f883(x62201,a869)))+E(f329(f329(f43(x62201,f883(x62202,a869)),x62203),f329(f16(f883(x62202,a869),x62201),x62204)),f193(f883(x62202,a869))) % 178.07/177.93 [6222]~P56(x62221)+E(f45(x62221,f329(f329(f82(x62221),x62222),x62223),f329(f329(f82(x62221),x62222),x62224)),f329(f329(f82(x62221),x62222),f45(x62221,x62223,x62224))) % 178.07/177.93 [6388]E(f329(f309(x63881,x63882,f329(f16(x63882,x63881),x63883)),x63884),f252(f883(x63881,a869)))+~P24(f329(f329(f331(x63882),x63883),x63884)) % 178.07/177.93 [6411]~P24(f329(f329(f331(x64111),x64112),x64114))+P24(f329(f329(f331(x64111),x64112),f329(f329(f307(x64111),x64113),x64114))) % 178.07/177.93 [6416]P24(f329(x64161,x64162))+~P24(f329(f159(x64163,x64161),f329(f329(f150(x64163),x64162),x64164))) % 178.07/177.93 [6425]~E(x64253,f329(f329(f22(a875),f329(f194(f876(x64251)),x64252)),f79(a875)))+E(f120(x64251,f329(f329(f158(x64251,x64252),x64253),x64254)),f120(x64251,x64252)) % 178.07/177.93 [6444]~P105(x64441)+E(f329(f329(f107(f883(x64441,a869)),f329(f298(x64441),x64442)),f300(x64441,x64443,x64444)),f300(x64441,x64443,f329(f329(f241(x64441),x64442),x64444))) % 178.07/177.93 [6445]~P105(x64451)+E(f329(f329(f107(f883(x64451,a869)),f329(f251(x64451),x64452)),f300(x64451,x64453,x64454)),f300(x64451,f329(f329(f242(x64451),x64452),x64453),x64454)) % 178.07/177.93 [6460]E(f329(f329(f107(f883(x64601,a869)),x64602),f329(f329(f307(x64601),x64603),x64604)),f329(f329(f107(f883(x64601,a869)),x64602),x64604))+P24(f329(f329(f331(x64601),x64603),x64602)) % 178.07/177.93 [6472]E(f169(x64721,x64722,f329(f329(f127(x64721),x64723),x64724)),f329(f329(f127(x64721),x64723),f169(x64721,x64722,x64724)))+P24(f329(f329(f331(x64721),x64722),f329(f171(x64721),x64723))) % 178.07/177.93 [6476]~P79(x64761)+E(f329(f329(f82(x64761),f329(f329(f254(x64761),x64762),x64763)),f329(f329(f254(x64761),x64762),x64764)),f329(f329(f254(x64761),x64762),f329(f329(f81(a875),x64763),x64764))) % 178.07/177.93 [6477]~P114(x64771)+E(f329(f329(f82(x64771),f329(f329(f254(x64771),x64772),x64773)),f329(f329(f254(x64771),x64772),x64774)),f329(f329(f254(x64771),x64772),f329(f329(f81(a875),x64773),x64774))) % 178.07/177.93 [6513]~P97(x65131)+E(f329(f329(f107(x65131),f329(f329(f116(x65131),x65132),x65133)),f329(f329(f116(x65131),x65132),x65134)),f329(f329(f116(x65131),x65132),f329(f329(f107(x65131),x65133),x65134))) % 178.07/177.93 [6514]~P97(x65141)+E(f329(f329(f116(x65141),f329(f329(f107(x65141),x65142),x65143)),f329(f329(f107(x65141),x65142),x65144)),f329(f329(f107(x65141),x65142),f329(f329(f116(x65141),x65143),x65144))) % 178.07/177.93 [6515]~P114(x65151)+E(f329(f329(f81(x65151),f329(f329(f82(x65151),x65152),x65153)),f329(f329(f82(x65151),x65152),x65154)),f329(f329(f82(x65151),x65152),f329(f329(f81(x65151),x65153),x65154))) % 178.07/177.93 [6516]~P105(x65161)+E(f329(f329(f242(x65161),f329(f329(f241(x65161),x65162),x65163)),f329(f329(f241(x65161),x65162),x65164)),f329(f329(f241(x65161),x65162),f329(f329(f242(x65161),x65163),x65164))) % 178.07/177.93 [6517]~P105(x65171)+E(f329(f329(f241(x65171),f329(f329(f242(x65171),x65172),x65173)),f329(f329(f242(x65171),x65172),x65174)),f329(f329(f242(x65171),x65172),f329(f329(f241(x65171),x65173),x65174))) % 178.07/177.93 [6549]~P56(x65491)+E(f45(x65491,f329(f329(f82(x65491),x65492),x65493),f329(f329(f82(x65491),x65494),x65493)),f329(f329(f82(x65491),f45(x65491,x65492,x65494)),x65493)) % 178.07/177.93 [6552]~E(f329(f194(f876(x65521)),x65523),f329(f194(f876(x65522)),x65524))+E(f329(f329(f153(f882(x65521,x65522),x65522),f267(x65521,x65522)),f329(f329(f181(x65521,x65522),x65523),x65524)),x65524) % 178.07/177.93 [6553]~E(f329(f194(f876(x65531)),x65533),f329(f194(f876(x65532)),x65534))+E(f329(f329(f153(f882(x65531,x65532),x65531),f263(x65531,x65532)),f329(f329(f181(x65531,x65532),x65533),x65534)),x65533) % 178.07/177.93 [6559]P24(f329(f159(x65591,x65592),x65593))+~P24(f329(f159(x65591,x65592),f329(f329(f150(x65591),x65594),x65593))) % 178.07/177.93 [6560]P24(f329(f159(x65601,x65602),x65603))+~P24(f329(f159(x65601,x65602),f329(f329(f127(x65601),x65604),x65603))) % 178.07/177.93 [6561]P24(f329(f159(x65611,x65612),x65613))+~P24(f329(f159(x65611,x65612),f329(f329(f127(x65611),x65613),x65614))) % 178.07/177.93 [6566]~P57(x65661)+E(f45(x65661,f329(f329(f22(x65661),x65662),f45(x65661,x65663,x65664)),x65664),f45(x65661,f329(f329(f22(x65661),x65662),x65663),x65664)) % 178.07/177.93 [6567]~P56(x65671)+E(f45(x65671,f329(f329(f82(x65671),x65672),f45(x65671,x65673,x65674)),x65674),f45(x65671,f329(f329(f82(x65671),x65672),x65673),x65674)) % 178.07/177.93 [6569]~P56(x65691)+E(f45(x65691,f329(f329(f81(x65691),x65692),f45(x65691,x65693,x65694)),x65694),f45(x65691,f329(f329(f81(x65691),x65692),x65693),x65694)) % 178.07/177.93 [6649]~P105(x66491)+E(f329(f329(f107(f883(x66491,a869)),f300(x66491,x66492,x66493)),f329(f298(x66491),x66494)),f300(x66491,x66492,f329(f329(f241(x66491),x66493),x66494))) % 178.07/177.93 [6650]~P105(x66501)+E(f329(f329(f107(f883(x66501,a869)),f300(x66501,x66502,x66503)),f329(f251(x66501),x66504)),f300(x66501,f329(f329(f242(x66501),x66502),x66504),x66503)) % 178.07/177.93 [6653]~E(f329(f194(f876(x66531)),x66533),f329(f194(f876(x66532)),x66534))+E(f329(f329(f181(x66531,x66532),f329(f168(x66531),x66533)),f329(f168(x66532),x66534)),f329(f168(f882(x66531,x66532)),f329(f329(f181(x66531,x66532),x66533),x66534))) % 178.07/177.93 [6663]E(x66631,f329(f329(f22(a875),f329(f194(f876(x66632)),x66633)),f79(a875)))+E(f120(x66632,f329(f329(f158(x66632,x66633),x66631),x66634)),f329(f329(f158(x66632,f120(x66632,x66633)),x66631),x66634)) % 178.07/177.93 [6678]~P24(f329(f136(x66782),x66784))+P24(f329(f136(f882(x66781,x66782)),f329(f329(f181(x66781,x66782),x66783),x66784))) % 178.07/177.93 [6679]~P24(f329(f136(x66791),x66793))+P24(f329(f136(f882(x66791,x66792)),f329(f329(f181(x66791,x66792),x66793),x66794))) % 178.07/177.93 [6942]E(f329(f329(f39(a875),x69421),x69422),x69423)+~P24(f329(f48(x69421,x69422),f329(f329(f264(a875,a875),x69423),x69424))) % 178.07/177.93 [6966]E(f45(a875,x69661,x69662),x69663)+~P24(f329(f48(x69661,x69662),f329(f329(f264(a875,a875),x69664),x69663))) % 178.07/177.93 [6969]P24(f329(f136(x69691),x69692))+~P24(f329(f136(x69693),f329(f329(f153(x69691,x69693),x69694),x69692))) % 178.07/177.93 [6977]~P20(x69771,x69772,f329(f329(f307(f874(x69771)),x69773),x69774))+P20(x69771,x69772,f329(f329(f307(f874(x69771)),x69773),f193(f883(f874(x69771),a869)))) % 178.07/177.93 [6983]P24(f329(f329(f199(x69831),x69832),x69833))+~P24(f329(f329(f329(f329(a201,x69831),x69832),x69834),x69833)) % 178.07/177.93 [7055]E(f169(x70551,x70552,f329(f329(f127(x70551),x70553),x70554)),f329(f329(f127(x70551),f169(x70551,x70552,x70553)),x70554))+~P24(f329(f329(f331(x70551),x70552),f329(f171(x70551),x70553))) % 178.07/177.93 [7145]~P57(x71451)+E(f45(x71451,f329(f329(f22(x71451),f45(x71451,x71452,x71453)),x71454),x71453),f45(x71451,f329(f329(f22(x71451),x71452),x71454),x71453)) % 178.07/177.93 [7148]~P56(x71481)+E(f45(x71481,f329(f329(f82(x71481),f45(x71481,x71482,x71483)),x71484),x71483),f45(x71481,f329(f329(f82(x71481),x71482),x71484),x71483)) % 178.07/177.93 [7149]~P56(x71491)+E(f45(x71491,f329(f329(f81(x71491),f45(x71491,x71492,x71493)),x71494),x71493),f45(x71491,f329(f329(f81(x71491),x71492),x71494),x71493)) % 178.07/177.93 [7339]~E(x73391,f329(f329(f150(x73392),x73393),x73394))+~P24(f329(f329(f243(a875),f329(f194(f876(x73392)),x73391)),f329(f194(f876(x73392)),x73394))) % 178.07/177.93 [7415]~E(f329(f177(x74151,x74152),x74153),f329(f177(x74151,x74152),x74154))+E(f329(f308(f882(x74151,x74152),x74151,f263(x74151,x74152)),f329(f171(f882(x74151,x74152)),x74153)),f329(f308(f882(x74151,x74152),x74151,f263(x74151,x74152)),f329(f171(f882(x74151,x74152)),x74154))) % 178.07/177.93 [7549]P21(x75491,x75492,x75493,f329(f171(x75491),x75494))+~P24(f329(f136(x75492),f329(f329(f153(x75491,x75492),x75493),x75494))) % 178.07/177.93 [7623]~P24(f329(f329(f243(f883(x76231,a869)),x76232),x76234))+P24(f329(f329(f243(f883(x76231,a869)),x76232),f329(f329(f307(x76231),x76233),x76234))) % 178.07/177.93 [7656]~P57(x76561)+E(f45(x76561,f329(f329(f22(x76561),f45(x76561,x76562,x76563)),f45(x76561,x76564,x76563)),x76563),f45(x76561,f329(f329(f22(x76561),x76562),x76564),x76563)) % 178.07/177.93 [7657]~P56(x76571)+E(f45(x76571,f329(f329(f82(x76571),f45(x76571,x76572,x76573)),f45(x76571,x76574,x76573)),x76573),f45(x76571,f329(f329(f82(x76571),x76572),x76574),x76573)) % 178.07/177.93 [7658]~P56(x76581)+E(f45(x76581,f329(f329(f81(x76581),f45(x76581,x76582,x76583)),f45(x76581,x76584,x76583)),x76583),f45(x76581,f329(f329(f81(x76581),x76582),x76584),x76583)) % 178.07/177.93 [7756]P24(f329(f329(f329(f329(a201,x77561),x77562),f329(a118,x77563)),x77564))+~P24(f329(f329(f329(f329(a201,x77561),x77562),x77563),x77564)) % 178.07/177.93 [7763]~E(f329(x77634,f839(x77634,x77633,x77631,x77632)),f193(f883(x77632,a869)))+E(f329(f329(f43(x77631,f883(x77632,a869)),x77633),x77634),f193(f883(x77632,a869))) % 178.07/177.93 [7764]~E(f329(x77644,f828(x77644,x77643,x77641,x77642)),f252(f883(x77642,a869)))+E(f329(f329(f42(x77641,f883(x77642,a869)),x77643),x77644),f252(f883(x77642,a869))) % 178.07/177.93 [7765]~E(f329(x77654,f835(x77654,x77653,x77652,x77651)),f252(f883(x77652,a869)))+E(f329(f329(f42(x77651,f883(x77652,a869)),x77653),x77654),f252(f883(x77652,a869))) % 178.07/177.93 [7766]~E(f329(x77664,f840(x77664,x77663,x77662,x77661)),f193(f883(x77662,a869)))+E(f329(f329(f43(x77661,f883(x77662,a869)),x77663),x77664),f193(f883(x77662,a869))) % 178.07/177.93 [8163]P24(f329(x81631,x81632))+~P24(f329(f329(f331(x81633),x81632),f329(f329(f107(f883(x81633,a869)),x81634),f329(f249(x81633),x81631)))) % 178.07/177.93 [8202]~P24(f329(f329(f243(f883(x82021,a869)),x82023),x82024))+P24(f329(f329(f243(f883(x82021,a869)),f329(f329(f307(x82021),x82022),x82023)),f329(f329(f307(x82021),x82022),x82024))) % 178.07/177.93 [8369]P24(f329(f329(f199(x83691),x83692),f600(x83693,x83692,x83694,x83691)))+~P24(f329(f329(f199(f34(x83691,x83694)),x83692),x83693)) % 178.07/177.93 [8378]P24(f329(x83782,x83783))+E(f329(f329(f137(x83781),f329(f194(f876(x83781)),f176(x83781,x83782,f329(f329(f150(x83781),x83783),x83784)))),f329(f329(f150(x83781),x83783),x83784)),f329(f329(f150(x83781),x83783),x83784)) % 178.07/177.93 [8493]~P24(f329(f329(f244(a875),f329(x84934,x84932)),f329(x84934,x84933)))+P24(f329(f329(f331(f882(x84931,x84931)),f329(f329(f264(x84931,x84931),x84932),x84933)),f329(f329(f285(a875,x84931),a248),x84934))) % 178.07/177.93 [8583]~P24(f329(x85832,f725(x85834,x85832,x85833,x85831)))+E(f176(x85831,x85832,f329(f329(f127(x85831),x85833),x85834)),f329(f329(f127(x85831),x85833),f176(x85831,x85832,x85834))) % 178.07/177.93 [8654]P21(f876(x86541),f876(x86542),f329(f153(x86541,x86542),x86543),x86544)+~P21(x86541,x86542,x86543,f40(f883(x86541,a869),f329(f308(f876(x86541),f883(x86541,a869),f171(x86541)),x86544))) % 178.07/177.93 [8721]~P24(f329(x87212,x87213))+E(f329(f329(f137(x87211),f329(f194(f876(x87211)),f176(x87211,x87212,f329(f329(f150(x87211),x87213),x87214)))),f329(f329(f150(x87211),x87213),x87214)),f329(f329(f137(x87211),f329(f194(f876(x87211)),f176(x87211,x87212,x87214))),x87214)) % 178.07/177.93 [8760]~E(x87602,x87603)+E(f329(f135(x87601,f329(f329(f8(a869,a869,x87601),a324),f329(a326,x87602))),f329(f329(f150(x87601),x87603),x87604)),f329(f135(x87601,f329(f329(f8(a869,a869,x87601),a324),f329(a326,x87602))),x87604)) % 178.07/177.93 [8770]E(f329(f329(f43(x87701,f883(x87702,a869)),x87703),x87704),f193(f883(x87702,a869)))+P24(f329(f329(f331(x87701),f839(x87704,x87703,x87701,x87702)),x87703)) % 178.07/177.93 [8771]E(f329(f329(f42(x87711,f883(x87712,a869)),x87713),x87714),f252(f883(x87712,a869)))+P24(f329(f329(f331(x87711),f828(x87714,x87713,x87711,x87712)),x87713)) % 178.07/177.93 [8772]E(f329(f329(f42(x87721,f883(x87722,a869)),x87723),x87724),f252(f883(x87722,a869)))+P24(f329(f329(f331(x87721),f835(x87724,x87723,x87722,x87721)),x87723)) % 178.07/177.93 [8773]E(f329(f329(f43(x87731,f883(x87732,a869)),x87733),x87734),f193(f883(x87732,a869)))+P24(f329(f329(f331(x87731),f840(x87734,x87733,x87732,x87731)),x87733)) % 178.07/177.93 [8809]P24(f329(f329(f244(a875),f329(x88091,x88092)),f329(x88091,x88093)))+~P24(f329(f329(f331(f882(x88094,x88094)),f329(f329(f264(x88094,x88094),x88092),x88093)),f329(f329(f285(a875,x88094),a248),x88091))) % 178.07/177.93 [8830]E(f176(x88301,x88302,f329(f329(f127(x88301),x88303),x88304)),f329(f329(f127(x88301),x88303),f176(x88301,x88302,x88304)))+P24(f329(f329(f331(x88301),f725(x88304,x88302,x88303,x88301)),f329(f171(x88301),x88303))) % 178.07/177.93 [8867]P24(f329(f329(f199(x88671),f600(x88672,x88673,x88671,x88674)),x88672))+~P24(f329(f329(f199(f34(x88674,x88671)),x88673),x88672)) % 178.07/177.93 [8997]P24(f329(f329(f331(x89971),f506(x89972,x89973,x89974,x89971)),x89973))+~P24(f329(f329(f331(f883(x89971,a869)),x89974),f329(f329(f61(x89971),x89973),x89972))) % 178.07/177.93 [9000]E(x90001,x90002)+~P24(f329(f329(f331(f882(x90003,x90003)),f329(f329(f264(x90003,x90003),x90001),x90002)),f329(f329(f188(f882(x90003,x90003),a869),f2(a875)),x90004))) % 178.07/177.93 [9079]E(f329(f283(x90791,x90791,x90792),f329(f329(f307(x90791),f506(x90792,x90793,x90794,x90791)),f193(f883(x90791,a869)))),x90794)+~P24(f329(f329(f331(f883(x90791,a869)),x90794),f329(f329(f61(x90791),x90793),x90792))) % 178.07/177.93 [9084]~P24(f329(f329(f331(f882(x90841,x90841)),f329(f329(f264(x90841,x90841),x90843),x90842)),f305(x90841,x90844)))+P24(f329(f329(f331(f882(x90841,x90841)),f329(f329(f264(x90841,x90841),x90842),x90843)),f305(x90841,f329(f284(x90841,x90841),x90844)))) % 178.07/177.93 [9096]~P56(x90961)+E(f329(f329(f81(x90961),f329(f329(f81(x90961),f329(f329(f82(x90961),x90962),f329(f329(f39(x90961),x90963),x90962))),f45(x90961,x90963,x90962))),x90964),f329(f329(f81(x90961),x90963),x90964)) % 178.07/177.93 [9106]~P24(f329(f329(f331(x91061),x91063),x91064))+P24(f329(f329(f331(f883(x91061,a869)),f329(f283(x91061,x91061,x91062),f329(f329(f307(x91061),x91063),f193(f883(x91061,a869))))),f329(f329(f61(x91061),x91064),x91062))) % 178.07/177.93 [9117]P24(f329(f329(f331(f882(x91171,x91171)),f329(f329(f264(x91171,x91171),x91172),x91173)),f305(x91171,x91174)))+~P24(f329(f329(f331(f882(x91171,x91171)),f329(f329(f264(x91171,x91171),x91173),x91172)),f305(x91171,f329(f284(x91171,x91171),x91174)))) % 178.07/177.93 [9209]E(f329(f329(f158(x92091,f329(f168(x92091),x92092)),f329(f329(f22(a875),f329(f329(f22(a875),f329(f194(f876(x92091)),x92092)),x92093)),f79(a875))),x92094),f329(f168(x92091),f329(f329(f158(x92091,x92092),x92093),x92094)))+~P24(f329(f329(f244(a875),x92093),f329(f194(f876(x92091)),x92092))) % 178.07/177.93 [9212]~P24(f329(x92122,f719(x92124,x92122,x92123,x92121)))+E(f329(f329(f137(x92121),f329(f194(f876(x92121)),f176(x92121,x92122,f329(f329(f127(x92121),x92123),x92124)))),f329(f329(f127(x92121),x92123),x92124)),f329(f329(f137(x92121),f329(f194(f876(x92121)),f176(x92121,x92122,x92124))),x92124)) % 178.07/177.93 [9252]~P21(x92522,x92521,x92523,f252(f883(x92522,a869)))+P24(f329(f329(f243(f883(x92521,a869)),f329(f308(x92522,x92521,x92523),f329(f80(f883(x92522,a869)),x92524))),f329(f80(f883(x92521,a869)),f329(f308(x92522,x92521,x92523),x92524)))) % 178.07/177.93 [9265]~P27(x92651)+E(f329(f141(x92651,x92652,f329(f7(x92652,x92651,x92651),f329(f329(f8(x92651,f883(x92651,x92651),x92652),f107(x92651)),x92653)),f252(x92651)),x92654),f329(f329(f42(x92652,x92651),f329(f171(x92652),x92654)),x92653)) % 178.07/177.93 [9266]~P27(x92661)+E(f329(f141(x92661,x92662,f329(f7(x92662,x92661,x92661),f329(f329(f8(x92661,f883(x92661,x92661),x92662),f116(x92661)),x92663)),f193(x92661)),x92664),f329(f329(f43(x92662,x92661),f329(f171(x92662),x92664)),x92663)) % 178.07/177.93 [9278]E(f329(f329(f137(x92781),f329(f194(f876(x92781)),f176(x92781,x92782,f329(f329(f127(x92781),x92783),x92784)))),f329(f329(f127(x92781),x92783),x92784)),f329(f329(f137(x92781),f329(f194(f876(x92781)),f176(x92781,x92782,x92784))),x92784))+P24(f329(f329(f331(x92781),f719(x92784,x92782,x92783,x92781)),f329(f171(x92781),x92783))) % 178.07/177.93 [9346]~P24(f329(f329(f331(f882(f876(x93464),f876(x93464))),f329(f329(f264(f876(x93464),f876(x93464)),x93463),x93462)),f156(x93464,x93461)))+P24(f329(f329(f244(a875),f605(x93461,x93462,x93463,x93464)),f329(f194(f876(x93464)),x93463))) % 178.07/177.93 [9347]~P56(x93471)+E(f329(f329(f81(x93471),f329(f329(f81(x93471),f329(f329(f82(x93471),f329(f329(f39(x93471),x93472),x93473)),x93473)),f45(x93471,x93472,x93473))),x93474),f329(f329(f81(x93471),x93472),x93474)) % 178.07/177.93 [9374]~P24(f329(f329(f331(f882(f876(x93741),f876(x93741))),f329(f329(f264(f876(x93741),f876(x93741)),x93742),x93743)),f329(f284(f876(x93741),f876(x93741)),f156(x93741,x93744))))+P24(f329(f329(f331(f882(f876(x93741),f876(x93741))),f329(f329(f264(f876(x93741),f876(x93741)),x93742),x93743)),f156(x93741,f329(f284(x93741,x93741),x93744)))) % 178.07/177.93 [9375]P24(f329(f329(f331(f882(f876(x93751),f876(x93751))),f329(f329(f264(f876(x93751),f876(x93751)),x93752),x93753)),f329(f284(f876(x93751),f876(x93751)),f156(x93751,x93754))))+~P24(f329(f329(f331(f882(f876(x93751),f876(x93751))),f329(f329(f264(f876(x93751),f876(x93751)),x93752),x93753)),f156(x93751,f329(f284(x93751,x93751),x93754)))) % 178.07/177.93 [9409]~P24(f329(f329(f331(x94091),x94093),f329(f262(x94091,x94092),x94094)))+P24(f329(f329(f331(f882(x94091,x94092)),f329(f329(f264(x94091,x94092),x94093),f703(x94094,x94092,x94093,x94091))),x94094)) % 178.07/177.93 [9410]~P24(f329(f329(f331(x94101),x94103),f329(f262(x94101,x94102),x94104)))+P24(f329(f329(f331(f882(x94101,x94102)),f329(f329(f264(x94101,x94102),x94103),f705(x94104,x94102,x94103,x94101))),x94104)) % 178.07/177.93 [9519]~P24(f329(f62(f879(x95191)),f329(f308(x95192,f879(x95191),x95193),f252(f883(x95192,a869)))))+P24(f329(f62(f879(x95191)),f329(f308(x95192,f879(x95191),f184(x95192,x95191,x95193,f329(f177(x95192,x95191),x95194))),f252(f883(x95192,a869))))) % 178.07/177.93 [9566]~P24(f329(f329(f331(f882(x95661,x95661)),f329(f329(f264(x95661,x95661),x95662),x95664)),f329(f329(f286(x95661,x95661,x95661),x95663),f305(x95661,x95663))))+P24(f329(f329(f331(f882(x95661,x95661)),f329(f329(f264(x95661,x95661),x95662),f766(x95663,x95664,x95662,x95661))),x95663)) % 178.07/177.93 [9734]~P24(f329(f329(f331(f882(x97342,x97341)),x97344),f329(f284(x97341,x97342),x97343)))+P24(f329(f329(f331(f882(x97341,x97342)),f329(f329(f264(x97341,x97342),f796(x97343,x97344,x97341,x97342)),f795(x97343,x97344,x97341,x97342))),x97343)) % 178.07/177.93 [9762]~P24(f329(f329(f331(f882(f876(x97621),f876(x97621))),f329(f329(f264(f876(x97621),f876(x97621)),x97624),x97623)),f156(x97621,x97622)))+P24(f329(f329(f331(f882(x97621,x97621)),f329(f329(f264(x97621,x97621),f634(x97622,x97623,x97624,x97621)),f635(x97622,x97623,x97624,x97621))),x97622)) % 178.07/177.93 [9858]~P24(f329(f329(f331(f882(f876(x98581),f876(x98581))),f329(f329(f264(f876(x98581),f876(x98581)),x98582),x98584)),f156(x98581,x98583)))+P24(f329(f329(f331(f882(x98581,x98581)),f329(f329(f264(x98581,x98581),f329(f329(f164(x98581),x98582),f605(x98583,x98584,x98582,x98581))),f606(x98583,x98584,x98582,x98581))),x98583)) % 178.07/177.93 [9880]~P24(f329(f62(x98802),x98804))+E(f329(f329(f329(f66(f883(x98801,a869),x98802,f116(f883(x98801,a869))),f329(f329(f7(x98802,f883(x98801,a869),f883(x98801,a869)),f329(f329(f8(x98801,f883(f883(x98801,a869),f883(x98801,a869)),x98802),f307(x98801)),x98803)),f193(f883(x98801,a869)))),f193(f883(x98801,a869))),x98804),f329(f308(x98802,x98801,x98803),x98804)) % 178.07/177.93 [9975]~P21(x99751,x99752,x99753,f252(f883(x99751,a869)))+P24(f329(f329(f243(f883(x99751,a869)),f329(f309(x99751,x99752,x99753),f329(f329(f307(x99752),x99754),f193(f883(x99752,a869))))),f329(f329(f307(x99751),f86(x99751,f329(f329(f7(x99751,x99752,a869),f329(f329(f8(x99752,f883(x99752,a869),x99751),a326),x99753)),x99754))),f193(f883(x99751,a869))))) % 178.07/177.93 [5595]~E(f329(f329(f127(x55951),x55952),x55954),x55953)+E(f329(f329(f174(x55951),f329(f194(f876(x55951)),x55952)),x55953),x55952) % 178.07/177.93 [5596]~E(f329(f329(f127(x55962),x55963),x55961),x55964)+E(x55961,f329(f329(f137(x55962),f329(f194(f876(x55962)),x55963)),x55964)) % 178.07/177.93 [5607]~E(x56074,f2(a875))+E(f329(f329(f164(x56071),f329(f329(f150(x56071),x56072),x56073)),x56074),x56072) % 178.07/177.93 [6134]~P114(x61341)+E(f329(f329(f254(x61341),f329(f329(f254(x61341),x61342),x61343)),x61344),f329(f329(f254(x61341),x61342),f329(f329(f82(a875),x61343),x61344))) % 178.07/177.93 [6135]~P79(x61351)+E(f329(f329(f254(x61351),f329(f329(f254(x61351),x61352),x61353)),x61354),f329(f329(f254(x61351),x61352),f329(f329(f82(a875),x61353),x61354))) % 178.07/177.93 [6152]E(x61521,f2(a875))+E(f329(f329(f164(x61522),f329(f329(f150(x61522),x61523),x61524)),x61521),f329(f329(f164(x61522),x61524),f329(f329(f22(a875),x61521),f79(a875)))) % 178.07/177.93 [6176]~P115(x61761)+E(f329(f329(f287(x61761),f329(f329(f82(x61761),x61762),x61763)),x61764),f329(f329(f82(x61761),x61762),f329(f329(f287(x61761),x61763),x61764))) % 178.07/177.93 [6178]~P63(x61781)+E(f329(f329(f116(x61781),f329(f329(f116(x61781),x61782),x61783)),x61784),f329(f329(f116(x61781),x61782),f329(f329(f116(x61781),x61783),x61784))) % 178.07/177.93 [6180]~P99(x61801)+E(f329(f329(f116(x61801),f329(f329(f116(x61801),x61802),x61803)),x61804),f329(f329(f116(x61801),x61802),f329(f329(f116(x61801),x61803),x61804))) % 178.07/177.93 [6181]~P63(x61811)+E(f329(f329(f107(x61811),f329(f329(f107(x61811),x61812),x61813)),x61814),f329(f329(f107(x61811),x61812),f329(f329(f107(x61811),x61813),x61814))) % 178.07/177.93 [6183]~P100(x61831)+E(f329(f329(f107(x61831),f329(f329(f107(x61831),x61832),x61833)),x61834),f329(f329(f107(x61831),x61832),f329(f329(f107(x61831),x61833),x61834))) % 178.07/177.93 [6184]~P68(x61841)+E(f329(f329(f82(x61841),f329(f329(f82(x61841),x61842),x61843)),x61844),f329(f329(f82(x61841),x61842),f329(f329(f82(x61841),x61843),x61844))) % 178.07/177.93 [6185]~P114(x61851)+E(f329(f329(f82(x61851),f329(f329(f82(x61851),x61852),x61853)),x61854),f329(f329(f82(x61851),x61852),f329(f329(f82(x61851),x61853),x61854))) % 178.07/177.93 [6187]~P69(x61871)+E(f329(f329(f81(x61871),f329(f329(f81(x61871),x61872),x61873)),x61874),f329(f329(f81(x61871),x61872),f329(f329(f81(x61871),x61873),x61874))) % 178.07/177.93 [6188]~P114(x61881)+E(f329(f329(f81(x61881),f329(f329(f81(x61881),x61882),x61883)),x61884),f329(f329(f81(x61881),x61882),f329(f329(f81(x61881),x61883),x61884))) % 178.07/177.93 [6190]~P105(x61901)+E(f329(f329(f241(x61901),f329(f329(f241(x61901),x61902),x61903)),x61904),f329(f329(f241(x61901),x61902),f329(f329(f241(x61901),x61903),x61904))) % 178.07/177.93 [6192]~P105(x61921)+E(f329(f329(f242(x61921),f329(f329(f242(x61921),x61922),x61923)),x61924),f329(f329(f242(x61921),x61922),f329(f329(f242(x61921),x61923),x61924))) % 178.07/177.93 [6203]~P56(x62031)+E(f45(x62031,f329(f329(f81(x62031),x62032),f329(f329(f82(x62031),x62033),x62034)),x62034),f45(x62031,x62032,x62034)) % 178.07/177.93 [6204]~P56(x62041)+E(f45(x62041,f329(f329(f81(x62041),x62042),f329(f329(f82(x62041),x62043),x62044)),x62043),f45(x62041,x62042,x62043)) % 178.07/177.93 [6338]E(f329(f329(f164(x63381),f329(f329(f174(x63381),x63382),x63383)),x63384),f329(f329(f164(x63381),x63383),x63384))+~P24(f329(f329(f244(a875),x63384),x63382)) % 178.07/177.93 [6511]~P114(x65111)+E(f329(f329(f82(x65111),f329(f329(f82(x65111),x65112),x65113)),x65114),f329(f329(f82(x65111),f329(f329(f82(x65111),x65112),x65114)),x65113)) % 178.07/177.93 [6512]~P114(x65121)+E(f329(f329(f81(x65121),f329(f329(f81(x65121),x65122),x65123)),x65124),f329(f329(f81(x65121),f329(f329(f81(x65121),x65122),x65124)),x65123)) % 178.07/177.93 [6572]~P141(x65722)+E(f329(f329(f6(x65721,x65722),f329(f16(x65722,x65721),x65723)),x65724),f329(f329(f82(x65722),f329(f106(x65722),f329(f38(x65721),x65724))),x65723)) % 178.07/177.93 [6741]E(f329(f329(f107(f883(x67411,a869)),f329(f329(f307(x67411),x67412),x67413)),x67414),f329(f329(f107(f883(x67411,a869)),x67413),x67414))+P24(f329(f329(f331(x67411),x67412),x67414)) % 178.07/177.93 [6810]~P97(x68101)+E(f329(f329(f107(x68101),f329(f329(f116(x68101),x68102),x68103)),f329(f329(f116(x68101),x68104),x68103)),f329(f329(f116(x68101),f329(f329(f107(x68101),x68102),x68104)),x68103)) % 178.07/177.93 [6811]~P77(x68111)+E(f329(f329(f241(x68111),f329(f329(f22(x68111),x68112),x68113)),f329(f329(f22(x68111),x68114),x68113)),f329(f329(f22(x68111),f329(f329(f241(x68111),x68112),x68114)),x68113)) % 178.07/177.93 [6812]~P77(x68121)+E(f329(f329(f242(x68121),f329(f329(f22(x68121),x68122),x68123)),f329(f329(f22(x68121),x68124),x68123)),f329(f329(f22(x68121),f329(f329(f242(x68121),x68122),x68124)),x68123)) % 178.07/177.93 [6813]~P97(x68131)+E(f329(f329(f116(x68131),f329(f329(f107(x68131),x68132),x68133)),f329(f329(f107(x68131),x68134),x68133)),f329(f329(f107(x68131),f329(f329(f116(x68131),x68132),x68134)),x68133)) % 178.07/177.93 [6814]~P110(x68141)+E(f329(f329(f81(x68141),f329(f329(f82(x68141),x68142),x68143)),f329(f329(f82(x68141),x68144),x68143)),f329(f329(f82(x68141),f329(f329(f81(x68141),x68142),x68144)),x68143)) % 178.07/177.93 [6816]~P83(x68161)+E(f329(f329(f241(x68161),f329(f329(f81(x68161),x68162),x68163)),f329(f329(f81(x68161),x68164),x68163)),f329(f329(f81(x68161),f329(f329(f241(x68161),x68162),x68164)),x68163)) % 178.07/177.93 [6817]~P83(x68171)+E(f329(f329(f242(x68171),f329(f329(f81(x68171),x68172),x68173)),f329(f329(f81(x68171),x68174),x68173)),f329(f329(f81(x68171),f329(f329(f242(x68171),x68172),x68174)),x68173)) % 178.07/177.93 [6818]~P74(x68181)+E(f329(f329(f82(x68181),f329(f329(f254(x68181),x68182),x68183)),f329(f329(f254(x68181),x68184),x68183)),f329(f329(f254(x68181),f329(f329(f82(x68181),x68182),x68184)),x68183)) % 178.07/177.93 [6819]~P114(x68191)+E(f329(f329(f82(x68191),f329(f329(f254(x68191),x68192),x68193)),f329(f329(f254(x68191),x68194),x68193)),f329(f329(f254(x68191),f329(f329(f82(x68191),x68192),x68194)),x68193)) % 178.07/177.93 [6820]~P59(x68201)+E(f329(f329(f287(x68201),f329(f329(f254(x68201),x68202),x68203)),f329(f329(f254(x68201),x68204),x68203)),f329(f329(f254(x68201),f329(f329(f287(x68201),x68202),x68204)),x68203)) % 178.07/177.93 [6821]~P115(x68211)+E(f329(f329(f22(x68211),f329(f329(f287(x68211),x68212),x68213)),f329(f329(f287(x68211),x68214),x68213)),f329(f329(f287(x68211),f329(f329(f22(x68211),x68212),x68214)),x68213)) % 178.07/177.93 [6822]~P115(x68221)+E(f329(f329(f81(x68221),f329(f329(f287(x68221),x68222),x68223)),f329(f329(f287(x68221),x68224),x68223)),f329(f329(f287(x68221),f329(f329(f81(x68221),x68222),x68224)),x68223)) % 178.07/177.93 [6823]~P105(x68231)+E(f329(f329(f242(x68231),f329(f329(f241(x68231),x68232),x68233)),f329(f329(f241(x68231),x68234),x68233)),f329(f329(f241(x68231),f329(f329(f242(x68231),x68232),x68234)),x68233)) % 178.07/177.93 [6824]~P105(x68241)+E(f329(f329(f241(x68241),f329(f329(f242(x68241),x68242),x68243)),f329(f329(f242(x68241),x68244),x68243)),f329(f329(f242(x68241),f329(f329(f241(x68241),x68242),x68244)),x68243)) % 178.07/177.93 [6825]~P114(x68251)+E(f329(f329(f81(x68251),f329(f329(f82(x68251),x68252),x68253)),f329(f329(f82(x68251),x68254),x68253)),f329(f329(f82(x68251),f329(f329(f81(x68251),x68252),x68254)),x68253)) % 178.07/177.93 [6857]E(f329(f329(f158(x68571,x68572),x68573),x68574),x68572)+~P24(f329(f329(f243(a875),f329(f194(f876(x68571)),x68572)),x68573)) % 178.07/177.93 [6882]~P24(f329(x68823,x68824))+P24(f329(f329(f329(f116(f883(x68821,a869)),x68822),x68823),x68824)) % 178.07/177.93 [6884]~P24(f329(x68842,x68844))+P24(f329(f329(f329(f116(f883(x68841,a869)),x68842),x68843),x68844)) % 178.07/177.93 [6905]E(f329(f329(f164(x69051),f329(f329(f127(x69051),x69052),x69053)),x69054),f329(f329(f164(x69051),x69052),x69054))+~P24(f329(f329(f244(a875),x69054),f329(f194(f876(x69051)),x69052))) % 178.07/177.93 [6915]E(f329(f329(f22(f883(x69151,a869)),f329(f329(f307(x69151),x69152),x69153)),x69154),f329(f329(f22(f883(x69151,a869)),x69153),x69154))+~P24(f329(f329(f331(x69151),x69152),x69154)) % 178.07/177.93 [6956]~E(f138(a875,f329(f299(a875,x69561),x69562)),f329(f329(f150(a875),x69564),x69563))+E(f138(a875,f329(f299(a875,f329(f329(f81(a875),x69561),f79(a875))),x69562)),x69563) % 178.07/177.93 [7029]E(x70291,f2(a875))+E(f329(f329(f150(x70292),x70293),f329(f329(f174(x70292),f329(f329(f22(a875),x70291),f79(a875))),x70294)),f329(f329(f174(x70292),x70291),f329(f329(f150(x70292),x70293),x70294))) % 178.07/177.93 [7129]E(f329(f329(f164(x71291),x71292),f329(f329(f22(a875),x71293),f329(f194(f876(x71291)),x71294))),f329(f329(f164(x71291),f329(f329(f127(x71291),x71294),x71292)),x71293))+P24(f329(f329(f244(a875),x71293),f329(f194(f876(x71291)),x71294))) % 178.07/177.93 [7159]E(f329(f329(f107(f883(x71591,a869)),x71592),f329(f329(f307(x71591),x71593),x71594)),f329(f329(f307(x71591),x71593),f329(f329(f107(f883(x71591,a869)),x71592),x71594)))+~P24(f329(f329(f331(x71591),x71593),x71592)) % 178.07/177.93 [7194]E(f329(f329(f164(x71941),f329(f329(f158(x71941,x71942),x71943),x71944)),x71943),x71944)+~P24(f329(f329(f244(a875),x71943),f329(f194(f876(x71941)),x71942))) % 178.07/177.93 [7215]E(x72151,f193(f883(x72152,a869)))+E(f329(f308(f882(x72153,x72152),x72153,f263(x72153,x72152)),f329(f329(f266(x72153,x72152),x72154),f329(f16(f883(x72152,a869),x72153),x72151))),x72154) % 178.07/177.93 [7216]E(x72161,f193(f883(x72162,a869)))+E(f329(f308(f882(x72162,x72163),x72163,f267(x72162,x72163)),f329(f329(f266(x72162,x72163),x72161),f329(f16(f883(x72163,a869),x72162),x72164))),x72164) % 178.07/177.93 [7283]E(f329(f329(f22(f883(x72831,a869)),f329(f329(f307(x72831),x72832),x72833)),x72834),f329(f329(f307(x72831),x72832),f329(f329(f22(f883(x72831,a869)),x72833),x72834)))+P24(f329(f329(f331(x72831),x72832),x72834)) % 178.07/177.93 [7315]P24(f329(x73151,x73152))+P24(f329(f329(f329(f329(a201,f33(x73151,x73153)),x73152),x73154),x73152)) % 178.07/177.93 [7322]~E(x73224,f193(f883(x73222,a869)))+E(f329(f308(f882(x73221,x73222),x73221,f263(x73221,x73222)),f329(f329(f266(x73221,x73222),x73223),f329(f16(f883(x73222,a869),x73221),x73224))),f193(f883(x73221,a869))) % 178.07/177.93 [7323]~E(x73233,f193(f883(x73231,a869)))+E(f329(f308(f882(x73231,x73232),x73232,f267(x73231,x73232)),f329(f329(f266(x73231,x73232),x73233),f329(f16(f883(x73232,a869),x73231),x73234))),f193(f883(x73232,a869))) % 178.07/177.93 [7380]~P24(f329(f329(f331(x73801),x73802),x73804))+P24(f329(f329(f331(x73801),x73802),f329(f329(f116(f883(x73801,a869)),x73803),x73804))) % 178.07/177.93 [7383]~P24(f329(f329(f331(x73831),x73832),x73833))+P24(f329(f329(f331(x73831),x73832),f329(f329(f116(f883(x73831,a869)),x73833),x73834))) % 178.07/177.93 [7402]E(f329(f329(f107(f883(x74021,a869)),f329(f329(f307(x74021),x74022),x74023)),x74024),f329(f329(f307(x74021),x74022),f329(f329(f107(f883(x74021,a869)),x74023),x74024)))+~P24(f329(f329(f331(x74021),x74022),x74024)) % 178.07/177.93 [7679]P24(f329(x76791,x76792))+~P24(f329(f329(f329(f107(f883(x76793,a869)),x76794),x76791),x76792)) % 178.07/177.93 [7680]P24(f329(x76801,x76802))+~P24(f329(f329(f329(f107(f883(x76803,a869)),x76801),x76804),x76802)) % 178.07/177.93 [7683]E(f329(f329(f6(x76831,a875),x76832),f329(f329(f22(f883(x76831,a869)),x76833),f329(f329(f307(x76831),x76834),f193(f883(x76831,a869))))),f329(f329(f6(x76831,a875),x76832),x76833))+P24(f329(f329(f331(x76831),x76834),x76833)) % 178.07/177.93 [7689]~P70(x76891)+E(f329(f165(x76891),f329(f329(f153(a875,x76891),x76892),f138(a875,f329(f299(a875,x76893),x76894)))),f329(f329(f6(a875,x76891),x76892),f329(f171(a875),f138(a875,f329(f299(a875,x76893),x76894))))) % 178.07/177.93 [7690]~P70(x76901)+E(f329(f329(f6(a875,x76901),x76902),f329(f171(a875),f138(a875,f329(f299(a875,x76903),x76904)))),f329(f165(x76901),f329(f329(f153(a875,x76901),x76902),f138(a875,f329(f299(a875,x76903),x76904))))) % 178.07/177.93 [7800]~E(x78003,x78004)+P24(f329(f63(x78001,x78002,f329(f329(f307(x78001),x78003),f193(f883(x78001,a869)))),x78004)) % 178.07/177.93 [7897]P24(f329(f329(f331(x78971),x78972),f329(f171(x78971),x78973)))+~P24(f329(f329(f331(x78971),x78972),f329(f171(x78971),f329(f329(f174(x78971),x78974),x78973)))) % 178.07/177.93 [7898]P24(f329(f329(f331(x78981),x78982),f329(f171(x78981),x78983)))+~P24(f329(f329(f331(x78981),x78982),f329(f171(x78981),f329(f329(f137(x78981),x78984),x78983)))) % 178.07/177.93 [7971]P24(f329(f329(f331(x79711),x79712),x79713))+~P24(f329(f329(f331(x79711),x79712),f329(f329(f22(f883(x79711,a869)),x79713),x79714))) % 178.07/177.93 [7973]P24(f329(f329(f331(x79731),x79732),x79733))+~P24(f329(f329(f331(x79731),x79732),f329(f329(f107(f883(x79731,a869)),x79734),x79733))) % 178.07/177.93 [7976]P24(f329(f329(f331(x79761),x79762),x79763))+~P24(f329(f329(f331(x79761),x79762),f329(f329(f107(f883(x79761,a869)),x79763),x79764))) % 178.07/177.93 [7994]E(f329(f329(f127(x79941),f329(f329(f174(x79941),x79942),x79943)),f329(f329(f150(x79941),x79944),f329(f329(f137(x79941),f329(a118,x79942)),x79943))),f329(f329(f158(x79941,x79943),x79942),x79944))+~P24(f329(f329(f244(a875),x79942),f329(f194(f876(x79941)),x79943))) % 178.07/177.93 [8019]P24(f329(f329(f331(x80191),x80192),x80193))+~P24(f329(f329(f243(f883(x80191,a869)),f329(f329(f307(x80191),x80192),x80194)),x80193)) % 178.07/177.93 [8052]~P24(f329(f329(f331(x80521),x80522),x80523))+~P24(f329(f329(f331(x80521),x80522),f329(f329(f22(f883(x80521,a869)),x80524),x80523))) % 178.07/177.93 [8085]~P24(f329(f329(f244(a875),x80854),f329(f194(f876(x80851)),x80853)))+P24(f329(f329(f331(x80851),x80852),f329(f171(x80851),f329(f329(f158(x80851,x80853),x80854),x80852)))) % 178.07/177.93 [8140]E(f329(f329(f164(x81401),f329(f329(f137(x81401),x81402),x81403)),x81404),f329(f329(f164(x81401),x81403),f329(f329(f81(a875),x81402),x81404)))+~P24(f329(f329(f243(a875),f329(f329(f81(a875),x81402),x81404)),f329(f194(f876(x81401)),x81403))) % 178.07/177.93 [8150]~P141(x81502)+E(f329(f329(f6(x81501,x81502),f329(f329(f8(a875,x81502,x81501),f106(x81502)),x81503)),x81504),f329(f106(x81502),f329(f329(f6(x81501,a875),x81503),x81504))) % 178.07/177.93 [8151]~P137(x81512)+E(f329(f329(f6(x81511,x81512),f329(f329(f8(a1,x81512,x81511),f108(x81512)),x81513)),x81514),f329(f108(x81512),f329(f329(f6(x81511,a1),x81513),x81514))) % 178.07/177.93 [8204]~P62(x82042)+E(f329(f329(f9(x82041,x82042),f329(f329(f8(x82042,x82042,x82041),f76(x82042)),x82043)),x82044),f329(f76(x82042),f329(f329(f9(x82041,x82042),x82043),x82044))) % 178.07/177.93 [8205]~P66(x82052)+E(f329(f329(f6(x82051,x82052),f329(f329(f8(x82052,x82052,x82051),f80(x82052)),x82053)),x82054),f329(f80(x82052),f329(f329(f6(x82051,x82052),x82053),x82054))) % 178.07/177.93 [8207]E(f329(f329(f6(x82071,a875),x82072),f329(f329(f22(f883(x82071,a869)),x82073),f329(f329(f307(x82071),x82074),f193(f883(x82071,a869))))),f329(f329(f22(a875),f329(f329(f6(x82071,a875),x82072),x82073)),f329(x82072,x82074)))+~P24(f329(f329(f331(x82071),x82074),x82073)) % 178.07/177.93 [8227]P24(f329(f329(f243(f883(x82271,a869)),x82272),x82273))+~P24(f329(f329(f243(f883(x82271,a869)),f329(f329(f307(x82271),x82274),x82272)),x82273)) % 178.07/177.93 [8434]E(f329(a118,f490(x84341,x84342,x84343,x84344)),x84342)+~P24(f329(f329(f329(f329(a201,f329(a26,x84344)),x84343),x84342),x84341)) % 178.07/177.93 [8436]E(f329(f329(f177(x84361,x84362),x84363),x84364),f206(x84362))+P24(f329(f329(f331(x84361),x84364),f329(f308(f882(x84361,x84362),x84361,f263(x84361,x84362)),f329(f171(f882(x84361,x84362)),x84363)))) % 178.07/177.93 [8437]P38(x84371,x84372)+~P38(x84371,f329(f329(f307(f882(x84371,x84371)),f329(f329(f264(x84371,x84371),x84373),x84374)),x84372)) % 178.07/177.93 [8438]P53(x84381,x84382)+~P53(x84381,f329(f329(f307(f882(x84381,x84381)),f329(f329(f264(x84381,x84381),x84383),x84384)),x84382)) % 178.07/177.93 [8447]~P105(x84471)+E(f329(f329(f147(x84471,x84471,f5(x84471)),x84472),f329(f329(f147(x84471,x84471,f5(x84471)),x84473),x84474)),f329(f329(f147(x84471,x84471,f5(x84471)),x84473),f329(f329(f147(x84471,x84471,f5(x84471)),x84472),x84474))) % 178.07/177.93 [8457]E(x84571,x84572)+~P24(f329(f63(x84573,x84574,f329(f329(f307(x84573),x84571),f193(f883(x84573,a869)))),x84572)) % 178.07/177.93 [8467]E(f329(f329(f127(x84671),f329(f329(f174(x84671),x84672),x84673)),f329(f329(f174(x84671),x84674),f329(f329(f137(x84671),x84672),x84673))),f329(f329(f174(x84671),f329(f329(f81(a875),x84672),x84674)),x84673))+~P24(f329(f329(f243(a875),f329(f329(f81(a875),x84672),x84674)),f329(f194(f876(x84671)),x84673))) % 178.07/177.93 [8507]P24(f329(f62(x85071),x85072))+~E(x85072,f329(f308(a875,x85071,x85073),f329(f249(a875),f329(f329(f7(a875,a875,a869),f244(a875)),x85074)))) % 178.07/177.93 [8527]~P88(x85271)+E(f329(f141(x85271,x85271,f81(x85271),f329(f329(f81(x85271),x85272),x85273)),x85274),f329(f329(f81(x85271),x85272),f329(f141(x85271,x85271,f81(x85271),x85273),x85274))) % 178.07/177.93 [8561]P24(f329(f329(f243(f883(x85611,a869)),f329(f262(x85611,x85612),x85613)),f329(f262(x85611,x85612),x85614)))+~P24(f329(f329(f243(f883(f882(x85611,x85612),a869)),x85613),x85614)) % 178.07/177.93 [8574]~P24(f329(f329(f243(a875),x85742),x85744))+P24(f329(f329(f243(f883(x85741,a869)),f329(f171(x85741),f329(f329(f174(x85741),x85742),x85743))),f329(f171(x85741),f329(f329(f174(x85741),x85744),x85743)))) % 178.07/177.93 [8575]~P24(f329(f329(f243(a875),x85754),x85752))+P24(f329(f329(f243(f883(x85751,a869)),f329(f171(x85751),f329(f329(f137(x85751),x85752),x85753))),f329(f171(x85751),f329(f329(f137(x85751),x85754),x85753)))) % 178.07/177.93 [8628]~P24(f329(f62(x86281),f329(f329(f22(f883(x86281,a869)),x86282),x86284)))+P24(f329(f62(x86281),f329(f329(f22(f883(x86281,a869)),x86282),f329(f329(f307(x86281),x86283),x86284)))) % 178.07/177.93 [8665]P24(f329(f329(f331(f882(x86651,x86651)),x86652),f305(x86651,x86653)))+~P24(f329(f329(f331(f882(x86651,x86651)),x86652),f329(f329(f188(f882(x86651,x86651),a869),x86654),x86653))) % 178.07/177.93 [8742]~P24(f329(f62(x87421),f329(f329(f22(f883(x87421,a869)),x87422),f329(f329(f307(x87421),x87424),x87423))))+P24(f329(f62(x87421),f329(f329(f22(f883(x87421,a869)),x87422),x87423))) % 178.07/177.93 [8889]~E(f329(f329(f177(x88891,x88892),x88893),x88894),f206(x88892))+~P24(f329(f329(f331(x88891),x88894),f329(f308(f882(x88891,x88892),x88891,f263(x88891,x88892)),f329(f171(f882(x88891,x88892)),x88893)))) % 178.07/177.93 [8955]~P63(x89551)+P24(f329(f329(f243(x89551),f329(f329(f116(x89551),x89552),f329(f329(f107(x89551),x89553),x89554))),f329(f329(f107(x89551),f329(f329(f116(x89551),x89552),x89553)),f329(f329(f116(x89551),x89552),x89554)))) % 178.07/177.93 [8956]~P105(x89561)+P24(f329(f329(f243(x89561),f329(f329(f242(x89561),x89562),f329(f329(f241(x89561),x89563),x89564))),f329(f329(f241(x89561),f329(f329(f242(x89561),x89562),x89563)),f329(f329(f242(x89561),x89562),x89564)))) % 178.07/177.93 [9102]E(x91021,x91022)+~P24(f329(f329(f331(f882(x91023,x91023)),f329(f329(f264(x91023,x91023),x91021),x91022)),f329(f171(f882(x91023,x91023)),f329(f329(f181(x91023,x91023),x91024),x91024)))) % 178.07/177.93 [9135]~P24(f329(f329(f331(f882(x91351,x91351)),f329(f329(f264(x91351,x91351),x91353),x91352)),f305(x91351,x91354)))+~P38(x91351,f329(f329(f307(f882(x91351,x91351)),f329(f329(f264(x91351,x91351),x91352),x91353)),x91354)) % 178.07/177.93 [9136]~P24(f329(f329(f331(f882(x91361,x91361)),f329(f329(f264(x91361,x91361),x91363),x91362)),f305(x91361,x91364)))+~P53(x91361,f329(f329(f307(f882(x91361,x91361)),f329(f329(f264(x91361,x91361),x91362),x91363)),x91364)) % 178.07/177.93 [9141]E(x91411,x91412)+E(f329(f135(x91413,f329(f329(f8(a869,a869,x91413),a324),f329(a326,x91411))),f329(f329(f150(x91413),x91412),x91414)),f329(f329(f150(x91413),x91412),f329(f135(x91413,f329(f329(f8(a869,a869,x91413),a324),f329(a326,x91411))),x91414))) % 178.07/177.93 [9185]~P63(x91851)+P24(f329(f329(f243(x91851),f329(f329(f116(x91851),f329(f329(f107(x91851),x91852),x91853)),f329(f329(f107(x91851),x91852),x91854))),f329(f329(f107(x91851),x91852),f329(f329(f116(x91851),x91853),x91854)))) % 178.07/177.93 [9186]~P105(x91861)+P24(f329(f329(f243(x91861),f329(f329(f242(x91861),f329(f329(f241(x91861),x91862),x91863)),f329(f329(f241(x91861),x91862),x91864))),f329(f329(f241(x91861),x91862),f329(f329(f242(x91861),x91863),x91864)))) % 178.07/177.93 [9261]~E(f329(f308(x92612,x92611,x92613),f252(f883(x92612,a869))),f252(f883(x92611,a869)))+P24(f329(f329(f243(f883(x92611,a869)),f329(f80(f883(x92611,a869)),f329(f308(x92612,x92611,x92613),x92614))),f329(f308(x92612,x92611,x92613),f329(f80(f883(x92612,a869)),x92614)))) % 178.07/177.93 [9339]P24(f329(f329(f329(f329(a201,f329(f240(a870),f329(a28,x93391))),x93392),f490(x93393,x93394,x93392,x93391)),x93393))+~P24(f329(f329(f329(f329(a201,f329(a26,x93391)),x93392),x93394),x93393)) % 178.07/177.93 [9580]P24(f329(f329(f331(f882(x95801,x95801)),f329(f329(f264(x95801,x95801),x95802),x95803)),f329(f284(x95801,x95801),f329(f329(f286(x95801,x95801,x95801),x95804),f305(x95801,x95804)))))+~P24(f329(f329(f331(f882(x95801,x95801)),f329(f329(f264(x95801,x95801),x95802),x95803)),f329(f329(f286(x95801,x95801,x95801),f329(f284(x95801,x95801),x95804)),f305(x95801,f329(f284(x95801,x95801),x95804))))) % 178.07/177.93 [9581]~P24(f329(f329(f331(f882(x95811,x95811)),f329(f329(f264(x95811,x95811),x95812),x95813)),f329(f284(x95811,x95811),f329(f329(f286(x95811,x95811,x95811),x95814),f305(x95811,x95814)))))+P24(f329(f329(f331(f882(x95811,x95811)),f329(f329(f264(x95811,x95811),x95812),x95813)),f329(f329(f286(x95811,x95811,x95811),f329(f284(x95811,x95811),x95814)),f305(x95811,f329(f284(x95811,x95811),x95814))))) % 178.07/177.93 [9602]~P24(f329(f329(f331(x96022),x96024),f329(f260(x96021,x96022),x96023)))+P24(f329(f329(f331(f882(x96021,x96022)),f329(f329(f264(x96021,x96022),f701(x96023,x96021,x96024,x96022)),x96024)),x96023)) % 178.07/177.93 [9603]~P24(f329(f329(f331(x96032),x96034),f329(f260(x96031,x96032),x96033)))+P24(f329(f329(f331(f882(x96031,x96032)),f329(f329(f264(x96031,x96032),f704(x96033,x96031,x96034,x96032)),x96034)),x96033)) % 178.07/177.93 [9628]~P24(f329(f329(f331(x96281),x96284),f329(f329(f116(f883(x96281,a869)),x96282),x96283)))+P24(f329(f329(f329(f116(f883(x96281,a869)),f329(f329(f7(x96281,f883(x96281,a869),a869),f331(x96281)),x96282)),f329(f329(f7(x96281,f883(x96281,a869),a869),f331(x96281)),x96283)),x96284)) % 178.07/177.93 [9629]~P24(f329(f329(f331(x96291),x96294),f329(f329(f107(f883(x96291,a869)),x96292),x96293)))+P24(f329(f329(f329(f107(f883(x96291,a869)),f329(f329(f7(x96291,f883(x96291,a869),a869),f331(x96291)),x96292)),f329(f329(f7(x96291,f883(x96291,a869),a869),f331(x96291)),x96293)),x96294)) % 178.07/177.93 [9705]~P24(f329(f329(f331(f882(x97051,x97051)),f329(f329(f264(x97051,x97051),x97054),x97053)),f329(f329(f286(x97051,x97051,x97051),x97052),f305(x97051,x97052))))+P24(f329(f329(f331(f882(x97051,x97051)),f329(f329(f264(x97051,x97051),f772(x97052,x97053,x97054,x97051)),x97053)),x97052)) % 178.07/177.93 [9750]P24(f329(f329(f331(x97501),x97502),f329(f329(f116(f883(x97501,a869)),x97503),x97504)))+~P24(f329(f329(f329(f116(f883(x97501,a869)),f329(f329(f7(x97501,f883(x97501,a869),a869),f331(x97501)),x97503)),f329(f329(f7(x97501,f883(x97501,a869),a869),f331(x97501)),x97504)),x97502)) % 178.07/177.93 [9751]P24(f329(f329(f331(x97511),x97512),f329(f329(f107(f883(x97511,a869)),x97513),x97514)))+~P24(f329(f329(f329(f107(f883(x97511,a869)),f329(f329(f7(x97511,f883(x97511,a869),a869),f331(x97511)),x97513)),f329(f329(f7(x97511,f883(x97511,a869),a869),f331(x97511)),x97514)),x97512)) % 178.07/177.93 [10029]P33(x100291,f329(f329(f7(x100291,f883(f882(x100291,x100291),a869),f883(x100291,a869)),f329(f329(f8(f883(x100291,f883(f883(f882(x100291,x100291),a869),a869)),f883(f883(f882(x100291,x100291),a869),f883(x100291,a869)),x100291),f7(x100291,f883(f882(x100291,x100291),a869),a869)),f329(f329(f8(f883(x100291,f882(x100291,x100291)),f883(x100291,f883(f883(f882(x100291,x100291),a869),a869)),x100291),f329(f8(f882(x100291,x100291),f883(f883(f882(x100291,x100291),a869),a869),x100291),f331(f882(x100291,x100291)))),f264(x100291,x100291)))),x100292),x100293,x100294)+~P24(f329(f329(f331(f882(f876(x100291),f876(x100291))),f329(f329(f264(f876(x100291),f876(x100291)),x100293),x100294)),f157(x100291,x100292))) % 178.07/177.93 [10033]P54(x100331,f329(f329(f7(x100331,f883(f882(x100331,x100331),a869),f883(x100331,a869)),f329(f329(f8(f883(x100331,f883(f883(f882(x100331,x100331),a869),a869)),f883(f883(f882(x100331,x100331),a869),f883(x100331,a869)),x100331),f7(x100331,f883(f882(x100331,x100331),a869),a869)),f329(f329(f8(f883(x100331,f882(x100331,x100331)),f883(x100331,f883(f883(f882(x100331,x100331),a869),a869)),x100331),f329(f8(f882(x100331,x100331),f883(f883(f882(x100331,x100331),a869),a869),x100331),f331(f882(x100331,x100331)))),f264(x100331,x100331)))),x100332),x100333,x100334)+~P24(f329(f329(f331(f882(f883(x100331,a869),f883(x100331,a869))),f329(f329(f264(f883(x100331,a869),f883(x100331,a869)),x100333),x100334)),f320(x100331,x100332))) % 178.07/177.93 [10062]E(x100621,x100622)+~E(f329(f329(f7(x100623,f883(f882(x100623,x100624),a869),f883(x100624,a869)),f329(f329(f8(f883(x100624,f883(f883(f882(x100623,x100624),a869),a869)),f883(f883(f882(x100623,x100624),a869),f883(x100624,a869)),x100623),f7(x100624,f883(f882(x100623,x100624),a869),a869)),f329(f329(f8(f883(x100624,f882(x100623,x100624)),f883(x100624,f883(f883(f882(x100623,x100624),a869),a869)),x100623),f329(f8(f882(x100623,x100624),f883(f883(f882(x100623,x100624),a869),a869),x100624),f331(f882(x100623,x100624)))),f264(x100623,x100624)))),x100621),f329(f329(f7(x100623,f883(f882(x100623,x100624),a869),f883(x100624,a869)),f329(f329(f8(f883(x100624,f883(f883(f882(x100623,x100624),a869),a869)),f883(f883(f882(x100623,x100624),a869),f883(x100624,a869)),x100623),f7(x100624,f883(f882(x100623,x100624),a869),a869)),f329(f329(f8(f883(x100624,f882(x100623,x100624)),f883(x100624,f883(f883(f882(x100623,x100624),a869),a869)),x100623),f329(f8(f882(x100623,x100624),f883(f883(f882(x100623,x100624),a869),a869),x100624),f331(f882(x100623,x100624)))),f264(x100623,x100624)))),x100622)) % 178.07/177.93 [10066]~P33(x100661,f329(f329(f7(x100661,f883(f882(x100661,x100661),a869),f883(x100661,a869)),f329(f329(f8(f883(x100661,f883(f883(f882(x100661,x100661),a869),a869)),f883(f883(f882(x100661,x100661),a869),f883(x100661,a869)),x100661),f7(x100661,f883(f882(x100661,x100661),a869),a869)),f329(f329(f8(f883(x100661,f882(x100661,x100661)),f883(x100661,f883(f883(f882(x100661,x100661),a869),a869)),x100661),f329(f8(f882(x100661,x100661),f883(f883(f882(x100661,x100661),a869),a869),x100661),f331(f882(x100661,x100661)))),f264(x100661,x100661)))),x100664),x100662,x100663)+P24(f329(f329(f331(f882(f876(x100661),f876(x100661))),f329(f329(f264(f876(x100661),f876(x100661)),x100662),x100663)),f157(x100661,x100664))) % 178.07/177.93 [10067]~P54(x100671,f329(f329(f7(x100671,f883(f882(x100671,x100671),a869),f883(x100671,a869)),f329(f329(f8(f883(x100671,f883(f883(f882(x100671,x100671),a869),a869)),f883(f883(f882(x100671,x100671),a869),f883(x100671,a869)),x100671),f7(x100671,f883(f882(x100671,x100671),a869),a869)),f329(f329(f8(f883(x100671,f882(x100671,x100671)),f883(x100671,f883(f883(f882(x100671,x100671),a869),a869)),x100671),f329(f8(f882(x100671,x100671),f883(f883(f882(x100671,x100671),a869),a869),x100671),f331(f882(x100671,x100671)))),f264(x100671,x100671)))),x100674),x100672,x100673)+P24(f329(f329(f331(f882(f883(x100671,a869),f883(x100671,a869))),f329(f329(f264(f883(x100671,a869),f883(x100671,a869)),x100672),x100673)),f320(x100671,x100674))) % 178.07/177.93 [7454]~P92(x74541)+E(f329(f329(f82(x74541),f329(f109(x74541),x74542)),f329(f329(f82(x74541),f329(f109(x74541),x74543)),x74544)),f329(f329(f82(x74541),f329(f109(x74541),f329(f329(f82(a1),x74542),x74543))),x74544)) % 178.07/177.93 [7455]~P92(x74551)+E(f329(f329(f81(x74551),f329(f109(x74551),x74552)),f329(f329(f22(x74551),f329(f109(x74551),x74553)),x74554)),f329(f329(f22(x74551),f329(f109(x74551),f329(f329(f81(a1),x74552),x74553))),x74554)) % 178.07/177.93 [7456]~P92(x74561)+E(f329(f329(f81(x74561),f329(f109(x74561),x74562)),f329(f329(f81(x74561),f329(f109(x74561),x74563)),x74564)),f329(f329(f81(x74561),f329(f109(x74561),f329(f329(f81(a1),x74562),x74563))),x74564)) % 178.07/177.93 [7501]~P141(x75011)+E(f329(f165(x75011),f329(f329(f153(x75012,x75011),f329(f16(x75011,x75012),x75013)),x75014)),f329(f329(f82(x75011),f329(f106(x75011),f329(f194(f876(x75012)),x75014))),x75013)) % 178.07/177.93 [7734]E(f329(f275(x77341,f329(f329(f150(f882(a105,x77341)),x77342),x77343)),x77344),f329(f267(a105,x77341),x77342))+~P24(f329(f329(f244(a105),x77344),f329(f263(a105,x77341),x77342))) % 178.07/177.93 [7779]~P92(x77791)+E(f329(f329(f81(x77791),f329(f109(x77791),x77792)),f329(f329(f22(x77791),x77793),f329(f109(x77791),x77794))),f329(f329(f81(x77791),f329(f109(x77791),f329(f329(f81(a1),x77792),f329(f80(a1),x77794)))),x77793)) % 178.07/177.93 [7910]E(f329(f275(x79101,x79102),f329(f329(f22(a105),x79103),f329(f263(a105,x79101),x79104))),f329(f275(x79101,f329(f329(f150(f882(a105,x79101)),x79104),x79102)),x79103))+P24(f329(f329(f244(a105),x79103),f329(f263(a105,x79101),x79104))) % 178.07/177.93 [8353]~P24(f329(f329(f331(x83531),x83532),f329(f171(x83531),f120(x83531,x83534))))+P24(f329(f329(f331(x83531),x83532),f329(f171(x83531),f120(x83531,f329(f329(f127(x83531),x83533),x83534))))) % 178.07/177.93 [8354]~P24(f329(f329(f331(x83541),x83542),f329(f171(x83541),f120(x83541,x83543))))+P24(f329(f329(f331(x83541),x83542),f329(f171(x83541),f120(x83541,f329(f329(f127(x83541),x83543),x83544))))) % 178.07/177.93 [8373]E(f329(f329(f116(f883(x83731,a869)),f329(f329(f107(f883(x83731,a869)),x83732),x83733)),x83734),f329(f329(f107(f883(x83731,a869)),x83732),f329(f329(f116(f883(x83731,a869)),x83733),x83734)))+~P24(f329(f329(f243(f883(x83731,a869)),x83734),x83732)) % 178.07/177.93 [8678]~E(f329(f329(f116(f883(x86781,a869)),f329(f329(f107(f883(x86781,a869)),x86783),x86784)),x86782),f329(f329(f107(f883(x86781,a869)),x86783),f329(f329(f116(f883(x86781,a869)),x86784),x86782)))+P24(f329(f329(f243(f883(x86781,a869)),x86782),x86783)) % 178.07/177.93 [8961]~P24(f329(f329(f243(f883(x89611,a869)),x89612),f329(f329(f116(f883(x89611,a869)),x89613),x89614)))+P24(f329(f329(f243(f883(x89611,a869)),f329(f329(f22(f883(x89611,a869)),x89612),x89613)),x89614)) % 178.07/177.93 [9021]~P24(f329(f329(f329(f329(a201,f329(a26,x90211)),x90212),f329(a118,x90213)),x90214))+P24(f329(f329(f329(f329(a201,f329(f240(a870),f329(a28,x90211))),x90212),x90213),x90214)) % 178.07/177.93 [9081]P24(f329(f329(f243(f883(x90811,a869)),x90812),f329(f329(f116(f883(x90811,a869)),x90813),x90814)))+~P24(f329(f329(f243(f883(x90811,a869)),f329(f329(f22(f883(x90811,a869)),x90812),x90813)),x90814)) % 178.07/177.93 [9134]P24(f329(f329(f329(f329(a201,f329(a26,x91341)),x91342),f329(a118,x91343)),x91344))+~P24(f329(f329(f329(f329(a201,f329(f240(a870),f329(a28,x91341))),x91342),x91343),x91344)) % 178.07/177.93 [9166]~P85(x91661)+E(f329(f76(x91661),f329(f329(f6(x91662,x91661),f329(f329(f8(x91661,x91661,x91662),f76(x91661)),x91663)),x91664)),f329(f329(f6(x91662,x91661),f329(f329(f8(x91661,x91661,x91662),f76(x91661)),x91663)),x91664)) % 178.07/177.93 [9337]~P85(x93371)+P24(f329(f329(f243(x93371),f2(x93371)),f329(f329(f6(x93372,x93371),f329(f329(f8(x93371,x93371,x93372),f76(x93371)),x93373)),x93374))) % 178.07/177.93 [9342]~P66(x93421)+E(f329(f165(x93421),f329(f329(f153(x93422,x93421),f329(f74(x93421,x93421,x93422,f80(x93421)),x93423)),x93424)),f329(f80(x93421),f329(f165(x93421),f329(f329(f153(x93422,x93421),x93423),x93424)))) % 178.07/177.93 [9475]~P85(x94751)+P24(f329(f329(f243(x94751),f329(f76(x94751),f329(f329(f6(x94752,x94751),x94753),x94754))),f329(f329(f6(x94752,x94751),f329(f329(f8(x94751,x94751,x94752),f76(x94751)),x94753)),x94754))) % 178.07/177.93 [9505]~E(f329(f329(f81(a875),x95051),x95054),f329(f329(f81(a875),x95053),x95052))+P24(f329(f329(f331(f882(f882(a875,a875),f882(a875,a875))),f329(f329(f264(f882(a875,a875),f882(a875,a875)),f329(f329(f264(a875,a875),x95051),x95052)),f329(f329(f264(a875,a875),x95053),x95054))),a114)) % 178.07/177.93 [9506]~P24(f329(f329(f244(a875),x95061),x95063))+P24(f329(f329(f331(f882(f882(a875,a875),f882(a875,a875))),f329(f329(f264(f882(a875,a875),f882(a875,a875)),f329(f329(f264(a875,a875),x95061),x95062)),f329(f329(f264(a875,a875),x95063),x95064))),a36)) % 178.07/177.93 [9507]~P24(f329(f329(f244(a875),x95071),x95073))+P24(f329(f329(f331(f882(f882(a875,a875),f882(a875,a875))),f329(f329(f264(f882(a875,a875),f882(a875,a875)),f329(f329(f264(a875,a875),x95071),x95072)),f329(f329(f264(a875,a875),x95073),x95074))),a71)) % 178.07/177.93 [9653]E(f329(f329(f81(a875),x96531),x96532),f329(f329(f81(a875),x96533),x96534))+~P24(f329(f329(f331(f882(f882(a875,a875),f882(a875,a875))),f329(f329(f264(f882(a875,a875),f882(a875,a875)),f329(f329(f264(a875,a875),x96531),x96534)),f329(f329(f264(a875,a875),x96533),x96532))),a114)) % 178.07/177.93 [9679]E(f329(f329(f164(x96791),f329(f329(f137(x96791),f329(f194(f876(x96791)),f176(x96791,x96792,x96793))),x96793)),x96794),f329(f329(f164(x96791),x96793),f329(f329(f81(a875),x96794),f329(f194(f876(x96791)),f176(x96791,x96792,x96793)))))+~P24(f329(f329(f244(a875),x96794),f329(f194(f876(x96791)),f329(f329(f137(x96791),f329(f194(f876(x96791)),f176(x96791,x96792,x96793))),x96793)))) % 178.07/177.93 [9696]~P24(f329(f329(f331(x96962),x96964),f329(f329(f42(x96961,f883(x96962,a869)),f252(f883(x96961,a869))),x96963)))+P24(f329(f329(f329(f42(x96961,f883(x96962,a869)),f252(f883(x96961,a869))),f329(f329(f8(f883(x96962,a869),f883(x96962,a869),x96961),f329(f7(x96962,f883(x96962,a869),a869),f331(x96962))),x96963)),x96964)) % 178.07/177.93 [9697]~P24(f329(f329(f331(x96972),x96974),f329(f329(f43(x96971,f883(x96972,a869)),f252(f883(x96971,a869))),x96973)))+P24(f329(f329(f329(f43(x96971,f883(x96972,a869)),f252(f883(x96971,a869))),f329(f329(f8(f883(x96972,a869),f883(x96972,a869),x96971),f329(f7(x96972,f883(x96972,a869),a869),f331(x96972))),x96973)),x96974)) % 178.07/177.93 [9778]~P24(f329(f49(x97781,x97782),f329(f329(f264(a1,a1),x97784),x97783)))+P24(f329(f49(f329(f80(a1),x97781),x97782),f329(f329(f264(a1,a1),f329(f329(f329(f102(a1),f329(f329(a326,x97783),f2(a1))),f329(f80(a1),x97784)),f329(f329(f22(a1),f329(f80(a1),x97784)),f79(a1)))),f329(f329(f329(f102(a1),f329(f329(a326,x97783),f2(a1))),f2(a1)),f329(f329(f22(a1),x97782),x97783))))) % 178.07/177.93 [9787]P24(f329(f329(f331(x97871),x97872),f329(f329(f42(x97873,f883(x97871,a869)),f252(f883(x97873,a869))),x97874)))+~P24(f329(f329(f329(f42(x97873,f883(x97871,a869)),f252(f883(x97873,a869))),f329(f329(f8(f883(x97871,a869),f883(x97871,a869),x97873),f329(f7(x97871,f883(x97871,a869),a869),f331(x97871))),x97874)),x97872)) % 178.07/177.93 [9788]P24(f329(f329(f331(x97881),x97882),f329(f329(f43(x97883,f883(x97881,a869)),f252(f883(x97883,a869))),x97884)))+~P24(f329(f329(f329(f43(x97883,f883(x97881,a869)),f252(f883(x97883,a869))),f329(f329(f8(f883(x97881,a869),f883(x97881,a869),x97883),f329(f7(x97881,f883(x97881,a869),a869),f331(x97881))),x97884)),x97882)) % 178.07/177.93 [9800]E(f329(f329(f43(a875,f883(x98001,a869)),f252(f883(a875,a869))),x98002),f329(f329(f43(a875,f883(x98001,a869)),f252(f883(a875,a869))),x98003))+~E(f329(f329(f43(a875,f883(x98001,a869)),f329(f299(a875,f2(a875)),f394(x98002,x98004,x98003,x98001))),x98003),f329(f329(f43(a875,f883(x98001,a869)),f329(f299(a875,f2(a875)),f329(f329(f81(a875),f394(x98002,x98004,x98003,x98001)),x98004))),x98002)) % 178.07/177.93 [10120]~P24(f329(f329(f243(f883(f882(x101201,x101202),a869)),x101203),x101204))+P24(f329(f329(f243(f883(x101201,f883(x101202,a869))),f329(f329(f7(x101201,f883(f882(x101201,x101202),a869),f883(x101202,a869)),f329(f329(f8(f883(x101202,f883(f883(f882(x101201,x101202),a869),a869)),f883(f883(f882(x101201,x101202),a869),f883(x101202,a869)),x101201),f7(x101202,f883(f882(x101201,x101202),a869),a869)),f329(f329(f8(f883(x101202,f882(x101201,x101202)),f883(x101202,f883(f883(f882(x101201,x101202),a869),a869)),x101201),f329(f8(f882(x101201,x101202),f883(f883(f882(x101201,x101202),a869),a869),x101202),f331(f882(x101201,x101202)))),f264(x101201,x101202)))),x101203)),f329(f329(f7(x101201,f883(f882(x101201,x101202),a869),f883(x101202,a869)),f329(f329(f8(f883(x101202,f883(f883(f882(x101201,x101202),a869),a869)),f883(f883(f882(x101201,x101202),a869),f883(x101202,a869)),x101201),f7(x101202,f883(f882(x101201,x101202),a869),a869)),f329(f329(f8(f883(x101202,f882(x101201,x101202)),f883(x101202,f883(f883(f882(x101201,x101202),a869),a869)),x101201),f329(f8(f882(x101201,x101202),f883(f883(f882(x101201,x101202),a869),a869),x101202),f331(f882(x101201,x101202)))),f264(x101201,x101202)))),x101204))) % 178.07/177.93 [10137]P24(f329(f329(f243(f883(f882(x101371,x101372),a869)),x101373),x101374))+~P24(f329(f329(f243(f883(x101371,f883(x101372,a869))),f329(f329(f7(x101371,f883(f882(x101371,x101372),a869),f883(x101372,a869)),f329(f329(f8(f883(x101372,f883(f883(f882(x101371,x101372),a869),a869)),f883(f883(f882(x101371,x101372),a869),f883(x101372,a869)),x101371),f7(x101372,f883(f882(x101371,x101372),a869),a869)),f329(f329(f8(f883(x101372,f882(x101371,x101372)),f883(x101372,f883(f883(f882(x101371,x101372),a869),a869)),x101371),f329(f8(f882(x101371,x101372),f883(f883(f882(x101371,x101372),a869),a869),x101372),f331(f882(x101371,x101372)))),f264(x101371,x101372)))),x101373)),f329(f329(f7(x101371,f883(f882(x101371,x101372),a869),f883(x101372,a869)),f329(f329(f8(f883(x101372,f883(f883(f882(x101371,x101372),a869),a869)),f883(f883(f882(x101371,x101372),a869),f883(x101372,a869)),x101371),f7(x101372,f883(f882(x101371,x101372),a869),a869)),f329(f329(f8(f883(x101372,f882(x101371,x101372)),f883(x101372,f883(f883(f882(x101371,x101372),a869),a869)),x101371),f329(f8(f882(x101371,x101372),f883(f883(f882(x101371,x101372),a869),a869),x101372),f331(f882(x101371,x101372)))),f264(x101371,x101372)))),x101374))) % 178.07/177.93 [9215]~P24(f329(f329(f331(f882(x92151,x92151)),x92152),f305(x92151,x92154)))+P24(f329(f329(f331(f882(x92151,x92151)),x92152),f305(x92151,f329(f329(f116(f883(f882(x92151,x92151),a869)),x92153),x92154)))) % 178.07/177.93 [9216]~P24(f329(f329(f331(f882(x92161,x92161)),x92162),f305(x92161,x92163)))+P24(f329(f329(f331(f882(x92161,x92161)),x92162),f305(x92161,f329(f329(f116(f883(f882(x92161,x92161),a869)),x92163),x92164)))) % 178.07/177.93 [9572]~E(f329(f171(x95721),x95724),f183(x95721,x95722,x95723))+E(f329(f177(x95721,x95722),f329(f329(f153(x95721,f882(x95721,x95722)),f329(f329(f18(x95721,x95722,f882(x95721,x95722)),f264(x95721,x95722)),f329(f329(f8(f879(x95722),x95722,x95721),f240(x95722)),x95723))),x95724)),x95723) % 178.07/177.93 [9894]~P24(f329(f329(f244(a875),f329(f329(f81(a875),x98941),x98944)),f329(f329(f81(a875),x98943),x98942)))+P24(f329(f329(f244(a1),f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),x98941),x98942)),f193(f883(f882(a875,a875),a869)))))),f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),x98943),x98944)),f193(f883(f882(a875,a875),a869))))))) % 178.07/177.93 [9895]~P24(f329(f329(f243(a875),f329(f329(f81(a875),x98951),x98954)),f329(f329(f81(a875),x98953),x98952)))+P24(f329(f329(f243(a1),f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),x98951),x98952)),f193(f883(f882(a875,a875),a869)))))),f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),x98953),x98954)),f193(f883(f882(a875,a875),a869))))))) % 178.07/177.93 [9972]P24(f329(f329(f244(a875),f329(f329(f81(a875),x99721),x99722)),f329(f329(f81(a875),x99723),x99724)))+~P24(f329(f329(f244(a1),f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),x99721),x99724)),f193(f883(f882(a875,a875),a869)))))),f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),x99723),x99722)),f193(f883(f882(a875,a875),a869))))))) % 178.07/177.93 [9973]P24(f329(f329(f243(a875),f329(f329(f81(a875),x99731),x99732)),f329(f329(f81(a875),x99733),x99734)))+~P24(f329(f329(f243(a1),f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),x99731),x99734)),f193(f883(f882(a875,a875),a869)))))),f329(a90,f329(f283(f882(a875,a875),f882(a875,a875),a114),f329(f329(f307(f882(a875,a875)),f329(f329(f264(a875,a875),x99733),x99732)),f193(f883(f882(a875,a875),a869))))))) % 178.07/177.93 [10014]P24(f329(f329(f243(f883(x100141,a869)),f329(f329(f43(a875,f883(x100141,a869)),f252(f883(a875,a869))),x100142)),f329(f329(f43(a875,f883(x100141,a869)),f252(f883(a875,a869))),x100143)))+~P24(f329(f329(f243(f883(x100141,a869)),f329(f329(f43(a875,f883(x100141,a869)),f329(f299(a875,f2(a875)),f395(x100143,x100144,x100142,x100141))),x100142)),f329(f329(f43(a875,f883(x100141,a869)),f329(f299(a875,f2(a875)),f329(f329(f81(a875),f395(x100143,x100144,x100142,x100141)),x100144))),x100143))) % 178.07/177.93 [10111]~P24(f329(f329(f331(x101112),x101114),f329(f260(x101111,x101112),x101113)))+P24(f329(f259(x101111,x101112,f329(f329(f7(x101111,f883(f882(x101111,x101112),a869),f883(x101112,a869)),f329(f329(f8(f883(x101112,f883(f883(f882(x101111,x101112),a869),a869)),f883(f883(f882(x101111,x101112),a869),f883(x101112,a869)),x101111),f7(x101112,f883(f882(x101111,x101112),a869),a869)),f329(f329(f8(f883(x101112,f882(x101111,x101112)),f883(x101112,f883(f883(f882(x101111,x101112),a869),a869)),x101111),f329(f8(f882(x101111,x101112),f883(f883(f882(x101111,x101112),a869),a869),x101112),f331(f882(x101111,x101112)))),f264(x101111,x101112)))),x101113)),x101114)) % 178.07/177.93 [10112]~P24(f329(f329(f331(x101121),x101124),f329(f262(x101121,x101122),x101123)))+P24(f329(f258(x101121,x101122,f329(f329(f7(x101121,f883(f882(x101121,x101122),a869),f883(x101122,a869)),f329(f329(f8(f883(x101122,f883(f883(f882(x101121,x101122),a869),a869)),f883(f883(f882(x101121,x101122),a869),f883(x101122,a869)),x101121),f7(x101122,f883(f882(x101121,x101122),a869),a869)),f329(f329(f8(f883(x101122,f882(x101121,x101122)),f883(x101122,f883(f883(f882(x101121,x101122),a869),a869)),x101121),f329(f8(f882(x101121,x101122),f883(f883(f882(x101121,x101122),a869),a869),x101122),f331(f882(x101121,x101122)))),f264(x101121,x101122)))),x101123)),x101124)) % 178.07/177.93 [10123]P24(f329(f329(f331(x101231),x101232),f329(f260(x101233,x101231),x101234)))+~P24(f329(f259(x101233,x101231,f329(f329(f7(x101233,f883(f882(x101233,x101231),a869),f883(x101231,a869)),f329(f329(f8(f883(x101231,f883(f883(f882(x101233,x101231),a869),a869)),f883(f883(f882(x101233,x101231),a869),f883(x101231,a869)),x101233),f7(x101231,f883(f882(x101233,x101231),a869),a869)),f329(f329(f8(f883(x101231,f882(x101233,x101231)),f883(x101231,f883(f883(f882(x101233,x101231),a869),a869)),x101233),f329(f8(f882(x101233,x101231),f883(f883(f882(x101233,x101231),a869),a869),x101231),f331(f882(x101233,x101231)))),f264(x101233,x101231)))),x101234)),x101232)) % 178.07/177.93 [10124]P24(f329(f329(f331(x101241),x101242),f329(f262(x101241,x101243),x101244)))+~P24(f329(f258(x101241,x101243,f329(f329(f7(x101241,f883(f882(x101241,x101243),a869),f883(x101243,a869)),f329(f329(f8(f883(x101243,f883(f883(f882(x101241,x101243),a869),a869)),f883(f883(f882(x101241,x101243),a869),f883(x101243,a869)),x101241),f7(x101243,f883(f882(x101241,x101243),a869),a869)),f329(f329(f8(f883(x101243,f882(x101241,x101243)),f883(x101243,f883(f883(f882(x101241,x101243),a869),a869)),x101241),f329(f8(f882(x101241,x101243),f883(f883(f882(x101241,x101243),a869),a869),x101243),f331(f882(x101241,x101243)))),f264(x101241,x101243)))),x101244)),x101242)) % 178.07/177.93 [9810]P24(f329(f159(x98101,x98102),x98103))+~P24(f329(f159(x98101,f329(f329(f18(x98101,a869,a869),f329(f329(f8(a869,f883(a869,a869),x98101),a327),x98104)),x98102)),x98103)) % 178.07/177.93 [9811]P24(f329(f159(x98111,x98112),x98113))+~P24(f329(f159(x98111,f329(f329(f18(x98111,a869,a869),f329(f329(f8(a869,f883(a869,a869),x98111),a327),x98112)),x98114)),x98113)) % 178.07/177.93 [9896]~P114(x98961)+E(f329(f329(f82(x98961),f329(f329(f81(x98961),f79(x98961)),f79(x98961))),f329(f329(f6(a875,x98961),f329(f329(f8(x98961,x98961,a875),f329(f81(x98961),x98962)),f329(f329(f7(a875,x98961,x98961),f329(f329(f8(x98961,f883(x98961,x98961),a875),f82(x98961)),f106(x98961))),x98963))),f329(f250(a875),x98964))),f329(f329(f82(x98961),f329(f106(x98961),x98964)),f329(f329(f81(x98961),x98962),f329(f329(f81(x98961),x98962),f329(f329(f82(x98961),f329(f106(x98961),f329(f329(f22(a875),x98964),f79(a875)))),x98963))))) % 178.07/177.93 [10036]P24(f329(x100361,f700(x100362,x100363,x100364,x100361)))+P38(x100362,f329(f249(f882(x100362,x100362)),f329(f268(x100362,x100362,a869),f329(f329(f8(f883(x100362,a869),f883(x100362,a869),x100362),f329(f18(x100362,a869,a869),f329(f329(f8(a869,f883(a869,a869),x100362),a327),x100361))),f329(f329(f7(x100362,f883(x100362,x100362),f883(x100362,a869)),f329(f329(f8(f883(x100362,a869),f883(f883(x100362,x100362),f883(x100362,a869)),x100362),f8(x100362,a869,x100362)),a326)),x100363))))) % 178.07/177.93 [10050]~P24(f329(f329(f244(a875),f329(x100504,f329(x100503,f700(x100501,x100503,x100504,x100502)))),f329(x100504,f700(x100501,x100503,x100504,x100502))))+P38(x100501,f329(f249(f882(x100501,x100501)),f329(f268(x100501,x100501,a869),f329(f329(f8(f883(x100501,a869),f883(x100501,a869),x100501),f329(f18(x100501,a869,a869),f329(f329(f8(a869,f883(a869,a869),x100501),a327),x100502))),f329(f329(f7(x100501,f883(x100501,x100501),f883(x100501,a869)),f329(f329(f8(f883(x100501,a869),f883(f883(x100501,x100501),f883(x100501,a869)),x100501),f8(x100501,a869,x100501)),a326)),x100503))))) % 178.07/177.93 [10150]~P24(f329(f329(f331(f882(x101501,x101501)),f329(f329(f264(x101501,x101501),x101503),x101504)),f329(f329(f116(f883(f882(x101501,x101501),a869)),x101502),f305(x101501,f193(f883(f882(x101501,x101501),a869))))))+P24(f329(f329(f329(f329(f116(f883(x101501,f883(x101501,a869))),f329(f329(f7(x101501,f883(f882(x101501,x101501),a869),f883(x101501,a869)),f329(f329(f8(f883(x101501,f883(f883(f882(x101501,x101501),a869),a869)),f883(f883(f882(x101501,x101501),a869),f883(x101501,a869)),x101501),f7(x101501,f883(f882(x101501,x101501),a869),a869)),f329(f329(f8(f883(x101501,f882(x101501,x101501)),f883(x101501,f883(f883(f882(x101501,x101501),a869),a869)),x101501),f329(f8(f882(x101501,x101501),f883(f883(f882(x101501,x101501),a869),a869),x101501),f331(f882(x101501,x101501)))),f264(x101501,x101501)))),x101502)),a326),x101503),x101504)) % 178.07/177.93 [10160]P24(f329(f329(f331(f882(x101601,x101601)),f329(f329(f264(x101601,x101601),x101602),x101603)),f329(f329(f116(f883(f882(x101601,x101601),a869)),x101604),f305(x101601,f193(f883(f882(x101601,x101601),a869))))))+~P24(f329(f329(f329(f329(f116(f883(x101601,f883(x101601,a869))),f329(f329(f7(x101601,f883(f882(x101601,x101601),a869),f883(x101601,a869)),f329(f329(f8(f883(x101601,f883(f883(f882(x101601,x101601),a869),a869)),f883(f883(f882(x101601,x101601),a869),f883(x101601,a869)),x101601),f7(x101601,f883(f882(x101601,x101601),a869),a869)),f329(f329(f8(f883(x101601,f882(x101601,x101601)),f883(x101601,f883(f883(f882(x101601,x101601),a869),a869)),x101601),f329(f8(f882(x101601,x101601),f883(f883(f882(x101601,x101601),a869),a869),x101601),f331(f882(x101601,x101601)))),f264(x101601,x101601)))),x101604)),a326),x101602),x101603)) % 178.07/177.93 [10022]~P106(x100223)+E(f91(x100221,f329(f329(f18(x100221,a869,a869),f329(f329(f8(a869,f883(a869,a869),x100221),a327),x100222)),f329(f329(f8(f883(x100221,a869),a869,x100221),f89(x100221)),f329(f329(f8(f883(x100221,a869),f883(x100221,a869),x100221),f329(f18(x100221,a869,a869),f329(f329(f8(a869,f883(a869,a869),x100221),a332),x100222))),f329(f329(f8(x100223,f883(x100221,a869),x100221),f329(f7(x100221,x100223,a869),f329(f329(f8(x100223,f883(x100223,a869),x100221),f243(x100223)),x100224))),x100224))))),f329(f95(x100221,x100223,x100224),x100222)) % 178.07/177.93 [10065]~P106(x100653)+E(f91(x100651,f329(f329(f18(x100651,a869,a869),f329(f329(f8(a869,f883(a869,a869),x100651),a327),x100652)),f329(f329(f8(f883(x100651,a869),a869,x100651),f89(x100651)),f329(f329(f8(f883(x100651,a869),f883(x100651,a869),x100651),f329(f18(x100651,a869,a869),f329(f329(f8(a869,f883(a869,a869),x100651),a332),x100652))),f329(f329(f7(x100651,f883(x100651,x100653),f883(x100651,a869)),f329(f329(f8(f883(x100653,a869),f883(f883(x100651,x100653),f883(x100651,a869)),x100651),f8(x100653,a869,x100651)),f329(f329(f8(x100653,f883(x100653,a869),x100651),f243(x100653)),x100654))),x100654))))),f97(x100651,x100653,x100654,x100652)) % 178.07/177.93 [10109]E(f329(f329(f150(f876(x101091)),f329(f329(f150(x101091),x101092),f329(f141(f876(x101091),f876(x101091),f127(x101091),f119(x101091)),f329(f329(f153(f876(x101091),f876(x101091)),f155(f876(x101091),x101091,f119(x101091),f329(f329(f8(f876(x101091),f883(f876(x101091),f876(x101091)),x101091),f16(f876(x101091),f876(x101091))),f329(f329(f7(x101091,f876(x101091),f876(x101091)),f150(x101091)),f119(x101091))))),x101093)))),f179(x101091,f329(f329(f150(f876(x101091)),x101094),f329(f141(f876(f876(x101091)),f876(f876(x101091)),f127(f876(x101091)),f119(f876(x101091))),f329(f329(f153(f876(x101091),f876(f876(x101091))),f155(f876(f876(x101091)),x101091,f119(f876(x101091)),f329(f16(f883(f876(x101091),f876(f876(x101091))),x101091),f329(f329(f7(f876(x101091),f876(f876(x101091)),f876(f876(x101091))),f150(f876(x101091))),f119(f876(x101091)))))),x101093))))),f179(x101091,f329(f329(f150(f876(x101091)),f329(f329(f150(x101091),x101092),x101094)),x101093)))+~P24(f329(f317(f876(f876(x101091)),f180(x101091)),f329(f329(f150(f876(x101091)),f329(f329(f150(x101091),x101092),x101094)),x101093))) % 178.07/177.93 [10149]~P24(f329(f62(x101492),f329(f249(x101492),x101494)))+P24(f329(f62(x101491),f329(f249(x101491),f329(f329(f8(f883(x101492,a869),a869,x101491),f88(x101492)),f329(f329(f7(x101491,f883(x101492,a869),f883(x101492,a869)),f329(f329(f8(f883(x101492,f883(a869,a869)),f883(f883(x101492,a869),f883(x101492,a869)),x101491),f18(x101492,a869,a869)),f329(f329(f8(f883(x101492,a869),f883(x101492,f883(a869,a869)),x101491),f329(f8(a869,f883(a869,a869),x101492),a327)),f329(f329(f7(x101491,f883(x101492,x101491),f883(x101492,a869)),f329(f329(f8(f883(x101491,a869),f883(f883(x101492,x101491),f883(x101492,a869)),x101491),f8(x101491,a869,x101492)),a326)),x101493)))),x101494))))) % 178.07/177.93 [5246]E(x52461,x52462)+~E(f129(x52463,x52464,x52461),f129(x52463,x52465,x52462)) % 178.07/177.93 [5247]E(x52471,x52472)+~E(f129(x52473,x52471,x52474),f129(x52473,x52472,x52475)) % 178.07/177.93 [5620]E(f329(f329(f307(x56201),x56202),f183(x56201,x56203,x56204)),f183(x56201,x56203,x56204))+~E(f329(x56204,x56202),f329(f236(x56203),x56205)) % 178.07/177.93 [6030]P24(f329(f259(x60301,x60302,x60303),x60304))+~P24(f329(f329(x60303,x60305),x60304)) % 178.07/177.93 [6032]P24(f329(f258(x60321,x60322,x60323),x60324))+~P24(f329(f329(x60323,x60324),x60325)) % 178.07/177.93 [6035]~E(f329(x60354,x60352),f329(f236(x60353),x60355))+P24(f329(f329(f331(x60351),x60352),f183(x60351,x60353,x60354))) % 178.07/177.93 [6036]~E(f329(x60364,x60365),f329(f236(x60361),x60362))+P24(f329(f329(f331(x60361),x60362),f185(x60363,x60361,x60364))) % 178.07/177.93 [6501]~E(x65015,f2(a105))+E(f329(f203(x65011,x65012,x65013,x65014),x65015),f130(x65012)) % 178.07/177.93 [6502]~E(x65025,f2(a105))+E(f329(f205(x65021,x65022,x65023,x65024),x65025),f121(x65022)) % 178.07/177.93 [6638]~E(x66383,f2(a105))+E(f329(f278(x66381,x66382,x66383,x66384),x66385),f329(f264(x66381,x66382),x66385)) % 178.07/177.93 [6710]~E(f329(x67104,x67105),f206(x67102))+E(f329(f238(f879(x67101),x67102,f206(x67101),x67103),f329(x67104,x67105)),f206(x67101)) % 178.07/177.93 [7334]E(f329(x73341,x73342),f206(x73343))+~E(f329(f184(x73344,x73343,x73345,x73341),x73342),f206(x73343)) % 178.07/177.93 [7335]E(f329(x73351,x73352),f206(x73353))+~E(f329(f184(x73354,x73353,x73351,x73355),x73352),f206(x73353)) % 178.07/177.93 [7372]E(f329(f184(x73721,x73722,x73723,x73724),x73725),f329(x73723,x73725))+P24(f329(f329(f331(x73721),x73725),f183(x73721,x73722,x73724))) % 178.07/177.93 [7373]E(f329(f184(x73731,x73732,x73733,x73734),x73735),f329(x73734,x73735))+P24(f329(f329(f331(x73731),x73735),f183(x73731,x73732,x73733))) % 178.07/177.93 [7694]~P16(x76944,x76941,x76942,x76945)+E(f329(f74(x76941,x76941,x76941,f329(x76942,x76943)),f329(x76942,x76943)),f329(x76942,x76943)) % 178.07/177.93 [7738]E(f329(f184(x77381,x77382,x77383,x77384),x77385),f329(x77384,x77385))+~P24(f329(f329(f331(x77381),x77385),f183(x77381,x77382,x77384))) % 178.07/177.93 [8086]~P12(x80865,x80861,x80862)+E(f329(f74(x80861,x80861,x80861,f329(x80862,x80863)),f329(x80862,x80864)),f329(f74(x80861,x80861,x80861,f329(x80862,x80864)),f329(x80862,x80863))) % 178.07/177.93 [8415]P24(f329(f329(f331(f882(x84151,x84151)),f329(f329(f264(x84151,x84151),x84152),x84153)),f323(x84151,x84154,x84155)))+~P24(f329(f329(f244(a875),f329(x84154,x84152)),f329(x84154,x84153))) % 178.07/177.93 [8513]~P24(f329(f329(f331(x85134),x85133),f296(x85134,x85131,x85132,x85135)))+P24(f329(f329(x85131,x85132),x85133)) % 178.07/177.93 [8514]~P24(f329(f329(f331(x85144),x85143),f293(x85144,x85141,x85142,x85145)))+P24(f329(f329(x85141,x85142),x85143)) % 178.07/177.93 [8515]~P24(f329(f329(f331(x85154),x85152),f296(x85154,x85151,x85155,x85153)))+P24(f329(f329(x85151,x85152),x85153)) % 178.07/177.93 [8516]~P24(f329(f329(f331(x85164),x85162),f293(x85164,x85161,x85165,x85163)))+P24(f329(f329(x85161,x85162),x85163)) % 178.07/177.93 [8655]~P52(x86552,x86551,x86555,x86553,x86554)+E(f329(f308(x86551,x86552,x86553),x86554),f252(f883(x86552,a869))) % 178.07/177.93 [9092]~P35(x90921,x90922,x90923,x90924,x90925)+P35(x90921,x90922,x90923,f329(f168(x90921),x90924),f329(f168(x90922),x90925)) % 178.07/177.93 [9094]~P35(x90941,x90942,x90943,f329(f168(x90941),x90944),x90945)+P35(x90941,x90942,x90943,x90944,f329(f168(x90942),x90945)) % 178.07/177.93 [9095]~P35(x90951,x90952,x90953,x90954,f329(f168(x90952),x90955))+P35(x90951,x90952,x90953,f329(f168(x90951),x90954),x90955) % 178.07/177.93 [9101]P35(x91011,x91012,x91013,x91014,x91015)+~P35(x91011,x91012,x91013,f329(f168(x91011),x91014),f329(f168(x91012),x91015)) % 178.07/177.93 [9496]P24(f329(f329(f331(f882(f876(x94961),f876(x94961))),f329(f329(f264(f876(x94961),f876(x94961)),f329(f329(f150(x94961),x94962),x94963)),f329(f329(f150(x94961),x94962),x94964))),f156(x94961,x94965)))+~P24(f329(f329(f331(f882(f876(x94961),f876(x94961))),f329(f329(f264(f876(x94961),f876(x94961)),x94963),x94964)),f156(x94961,x94965))) % 178.07/177.93 [9497]P24(f329(f329(f331(f882(f876(x94971),f876(x94971))),f329(f329(f264(f876(x94971),f876(x94971)),f329(f329(f127(x94971),x94972),x94973)),f329(f329(f127(x94971),x94972),x94974))),f146(x94971,x94975)))+~P24(f329(f329(f331(f882(f876(x94971),f876(x94971))),f329(f329(f264(f876(x94971),f876(x94971)),x94973),x94974)),f146(x94971,x94975))) % 178.07/177.93 [9686]E(f329(f329(f150(x96861),f613(x96862,x96863,x96864,x96865,x96861)),f614(x96862,x96863,x96864,x96865,x96861)),x96865)+~P24(f329(f329(f331(f882(f876(x96861),f876(x96861))),f329(f329(f264(f876(x96861),f876(x96861)),x96865),f329(f329(f150(x96861),x96864),x96863))),f157(x96861,x96862))) % 178.07/177.93 [9708]E(f329(f329(f150(x97081),f609(x97082,x97083,x97084,x97085,x97081)),f610(x97082,x97083,x97084,x97085,x97081)),x97083)+~P24(f329(f329(f331(f882(f876(x97081),f876(x97081))),f329(f329(f264(f876(x97081),f876(x97081)),f329(f329(f150(x97081),x97085),x97084)),x97083)),f157(x97081,x97082))) % 178.07/177.93 [9870]~P24(f329(f329(f331(f882(f876(x98701),f876(x98701))),f329(f329(f264(f876(x98701),f876(x98701)),f329(f329(f150(x98701),x98705),x98702)),x98704)),f157(x98701,x98703)))+P24(f329(f329(f331(f882(f876(x98701),f876(x98701))),f329(f329(f264(f876(x98701),f876(x98701)),x98702),f610(x98703,x98704,x98702,x98705,x98701))),f157(x98701,x98703))) % 178.07/177.93 [9940]~P24(f329(f329(f331(f882(f876(x99401),f876(x99401))),f329(f329(f264(f876(x99401),f876(x99401)),x99405),f329(f329(f150(x99401),x99404),x99403))),f157(x99401,x99402)))+P24(f329(f329(f331(f882(f876(x99401),f876(x99401))),f329(f329(f264(f876(x99401),f876(x99401)),f614(x99402,x99403,x99404,x99405,x99401)),x99403)),f157(x99401,x99402))) % 178.07/177.93 [10104]P24(f329(f329(f331(f882(x101041,x101041)),f329(f329(f264(x101041,x101041),f329(x101042,f329(f329(f81(a875),x101043),x101044))),f329(x101042,x101043))),f305(x101041,x101045)))+~P24(f329(f329(f331(f882(x101041,x101041)),f329(f329(f264(x101041,x101041),f329(x101042,f329(a118,f751(x101044,x101043,x101045,x101042,x101041)))),f329(x101042,f751(x101044,x101043,x101045,x101042,x101041)))),f305(x101041,x101045))) % 178.07/177.93 [5209]E(x52091,x52092)+~E(f329(f329(f150(x52093),x52094),x52091),f329(f329(f150(x52093),x52095),x52092)) % 178.07/177.93 [5210]E(x52101,x52102)+~E(f329(f329(f150(x52103),x52101),x52104),f329(f329(f150(x52103),x52102),x52105)) % 178.07/177.93 [5263]P24(f329(x52631,x52632))+~E(f329(f135(x52633,x52631),x52634),f329(f329(f150(x52633),x52632),x52635)) % 178.07/177.93 [5264]P24(f329(x52641,x52642))+~E(f329(f329(f150(x52643),x52642),x52644),f329(f135(x52643,x52641),x52645)) % 178.07/177.93 [5419]~E(f329(f329(f137(x54191),x54193),x54192),f329(f329(f150(x54191),x54194),x54195))+E(f329(f329(f164(x54191),x54192),x54193),x54194) % 178.07/177.93 [5551]~P11(x55514,x55515,x55511)+E(f329(f329(x55511,x55512),f329(f329(x55511,x55512),x55513)),f329(f329(x55511,x55512),x55513)) % 178.07/177.93 [6088]~E(x60884,f2(a105))+E(f329(f329(f123(x60881,x60882,x60883),x60884),x60885),f329(f329(f264(f876(x60882),x60881),f119(x60882)),x60885)) % 178.07/177.93 [6160]~P105(x61602)+~E(f329(f329(f147(x61601,x61602,x61603),x61604),x61605),f119(x61601)) % 178.07/177.93 [6538]E(x65381,x65382)+~E(f329(f329(f127(x65383),x65384),f329(f329(f150(x65383),x65381),f119(x65383))),f329(f329(f127(x65383),x65385),f329(f329(f150(x65383),x65382),f119(x65383)))) % 178.07/177.93 [6539]E(x65391,x65392)+~E(f329(f329(f127(x65393),x65391),f329(f329(f150(x65393),x65394),f119(x65393))),f329(f329(f127(x65393),x65392),f329(f329(f150(x65393),x65395),f119(x65393)))) % 178.07/177.93 [6793]E(f329(f187(x67931,x67932,x67933,x67934),x67935),f206(x67932))+P24(f329(f329(f331(x67931),x67935),x67934)) % 178.07/177.93 [6855]E(f329(f329(f307(x68551),f329(x68552,x68553)),f329(f308(x68554,x68551,x68552),x68555)),f329(f308(x68554,x68551,x68552),x68555))+~P24(f329(f329(f331(x68554),x68553),x68555)) % 178.07/177.93 [6862]~P24(f329(x68624,f329(x68623,x68625)))+P24(f329(f329(f309(x68621,x68622,x68623),x68624),x68625)) % 178.07/177.93 [6865]~P24(f329(f329(x68653,x68655),x68654))+P24(f329(f329(f253(x68651,x68652,x68653),x68654),x68655)) % 178.07/177.93 [6960]~E(f329(f308(x69601,x69602,x69603),x69604),x69605)+E(f329(f308(f883(x69601,a869),f883(x69602,a869),f308(x69601,x69602,x69603)),f329(f306(x69601),x69604)),f329(f306(x69602),x69605)) % 178.07/177.93 [6992]E(f329(f187(x69921,x69922,x69923,x69924),x69925),f329(x69923,x69925))+~P24(f329(f329(f331(x69921),x69925),x69924)) % 178.07/177.93 [7291]P21(x72911,x72912,x72913,x72914)+~P21(x72911,x72912,x72913,f329(f329(f307(x72911),x72915),x72914)) % 178.07/177.93 [7361]P24(f329(x73611,x73612))+~P24(f329(f329(f98(x73613,x73614,x73611),x73615),x73612)) % 178.07/177.93 [7406]~P24(f329(f329(f331(x74064),x74063),x74065))+P24(f329(f329(f331(x74061),f329(x74062,x74063)),f329(f308(x74064,x74061,x74062),x74065))) % 178.07/177.93 [7430]~P105(x74302)+E(f149(x74301,x74302,x74303,f329(f135(x74301,x74304),x74305)),f329(f135(x74301,x74304),f149(x74301,x74302,x74303,x74305))) % 178.07/177.93 [7463]P24(f329(x74631,f329(x74632,x74633)))+~P24(f329(f329(f309(x74634,x74635,x74632),x74631),x74633)) % 178.07/177.93 [7466]P24(f329(f329(x74661,x74662),x74663))+~P24(f329(f329(f253(x74664,x74665,x74661),x74663),x74662)) % 178.07/177.93 [7467]P24(f329(f329(x74671,x74672),x74673))+~P24(f329(f329(f98(x74674,x74671,x74675),x74672),x74673)) % 178.07/177.93 [7530]~P24(f329(f329(f331(x75303),f329(x75304,x75302)),x75305))+P24(f329(f329(f331(x75301),x75302),f329(f309(x75301,x75303,x75304),x75305))) % 178.07/177.93 [7924]~P24(f329(f329(f331(x79245),x79243),f329(f309(x79245,x79241,x79242),x79244)))+P24(f329(f329(f331(x79241),f329(x79242,x79243)),x79244)) % 178.07/177.93 [8152]~E(x81523,f329(f329(f329(f73(x81521,f879(x81522)),f329(f16(f879(x81522),x81521),f206(x81522))),x81524),f329(f236(x81522),x81525)))+E(f183(x81521,x81522,x81523),f329(f329(f307(x81521),x81524),f193(f883(x81521,a869)))) % 178.07/177.93 [8232]~P12(x82322,x82321,x82323)+E(f329(f141(x82321,x82322,f329(f7(x82322,x82321,x82321),x82323),x82324),f151(x82322,x82325)),f329(f329(f65(x82322,x82321,x82323),x82324),f329(f171(x82322),x82325))) % 178.07/177.93 [8251]E(f329(x82511,f541(x82512,x82511,x82513,x82514)),x82514)+~P24(f329(f329(f331(x82515),x82514),f329(f308(x82513,x82515,x82511),x82512))) % 178.07/177.93 [8559]~E(x85592,f329(f329(f150(x85591),x85594),x85595))+P24(f329(f329(f331(f882(f876(x85591),f876(x85591))),f329(f329(f264(f876(x85591),f876(x85591)),f119(x85591)),x85592)),f146(x85591,x85593))) % 178.07/177.93 [8612]~P35(x86121,x86123,x86125,x86122,x86124)+E(f329(f194(f876(x86121)),x86122),f329(f194(f876(x86123)),x86124)) % 178.07/177.93 [8622]P24(f329(f329(f243(f883(x86221,a869)),f329(f329(f42(x86222,f883(x86221,a869)),x86223),x86224)),f329(x86224,x86225)))+~P24(f329(f329(f331(x86222),x86225),x86223)) % 178.07/177.93 [8671]~P52(x86711,x86712,x86713,x86715,x86714)+E(f329(f308(x86711,x86712,x86713),f252(f883(x86711,a869))),x86714) % 178.07/177.93 [8875]E(f329(f329(f329(f73(x88751,f879(x88752)),f187(x88751,x88752,x88753,x88754)),x88755),f206(x88752)),f187(x88751,x88752,x88753,x88754))+P24(f329(f329(f331(x88751),x88755),x88754)) % 178.07/177.93 [8880]E(f329(f135(x88801,x88802),f732(x88803,x88804,x88805,x88802,x88801)),x88803)+~E(f329(f135(x88801,x88802),x88805),f329(f329(f150(x88801),x88804),x88803)) % 178.07/177.93 [8881]E(f329(f135(x88811,x88812),f737(x88813,x88812,x88814,x88815,x88811)),x88814)+~E(f329(f329(f150(x88811),x88815),x88814),f329(f135(x88811,x88812),x88813)) % 178.07/177.93 [8882]E(f329(x88821,f676(x88822,x88823,x88821,x88824,x88825)),x88822)+~E(f329(f329(f207(x88825,x88824),x88821),x88823),f329(f236(x88824),x88822)) % 178.07/177.93 [8886]E(f329(f236(x88861),f676(x88862,x88863,x88864,x88865,x88861)),x88863)+~E(f329(f329(f207(x88861,x88865),x88864),x88863),f329(f236(x88865),x88862)) % 178.07/177.93 [8984]E(f329(f194(f876(x89841)),x89842),x89843)+~P24(f329(f329(f331(f882(f876(x89841),f876(x89841))),f329(f329(f264(f876(x89841),f876(x89841)),x89844),x89842)),f329(f142(x89841,x89845),x89843))) % 178.07/177.93 [8985]E(f329(f194(f876(x89851)),x89852),x89853)+~P24(f329(f329(f331(f882(f876(x89851),f876(x89851))),f329(f329(f264(f876(x89851),f876(x89851)),x89852),x89854)),f329(f142(x89851,x89855),x89853))) % 178.07/177.93 [9052]P24(f329(f329(f331(x90521),f541(x90522,x90523,x90521,x90524)),x90522))+~P24(f329(f329(f331(x90525),x90524),f329(f308(x90521,x90525,x90523),x90522))) % 178.07/177.93 [9213]E(f329(f308(x92131,x92132,x92133),f350(x92134,x92133,x92131,x92135,x92132)),x92135)+~P24(f329(f329(f243(f883(x92132,a869)),x92135),f329(f308(x92131,x92132,x92133),x92134))) % 178.07/177.93 [9466]E(f329(x94661,f710(x94662,x94661,x94663,x94664,x94665)),f329(f236(x94665),x94664))+~P24(f329(f329(f331(x94665),x94664),f185(x94663,x94665,f187(x94663,x94665,x94661,x94662)))) % 178.07/177.93 [9512]P24(f329(f329(f331(f882(f876(x95121),f876(x95121))),f329(f329(f264(f876(x95121),f876(x95121)),f329(f329(f150(x95121),x95122),x95123)),f329(f329(f150(x95121),x95122),x95124))),f305(f876(x95121),f156(x95121,x95125))))+~P24(f329(f329(f331(f882(f876(x95121),f876(x95121))),f329(f329(f264(f876(x95121),f876(x95121)),x95123),x95124)),f305(f876(x95121),f156(x95121,x95125)))) % 178.07/177.93 [9543]~E(f329(x95433,f572(x95435,x95434,x95433,x95432,x95431)),f329(x95435,f572(x95435,x95434,x95433,x95432,x95431)))+E(f329(f329(f153(x95431,x95432),x95433),x95434),f329(f329(f153(x95431,x95432),x95435),x95434)) % 178.07/177.93 [9619]~E(f329(f135(x96191,x96195),x96194),f329(f329(f150(x96191),x96193),x96192))+E(f329(f329(f127(x96191),f733(x96192,x96193,x96194,x96195,x96191)),f329(f329(f150(x96191),x96193),f732(x96192,x96193,x96194,x96195,x96191))),x96194) % 178.07/177.93 [9620]~E(f329(f329(f150(x96201),x96205),x96204),f329(f135(x96201,x96203),x96202))+E(f329(f329(f127(x96201),f734(x96202,x96203,x96204,x96205,x96201)),f329(f329(f150(x96201),x96205),f737(x96202,x96203,x96204,x96205,x96201))),x96202) % 178.07/177.93 [9624]E(f329(f329(f153(x96241,x96242),x96243),x96244),f329(f329(f153(x96241,x96242),x96245),x96244))+P24(f329(f329(f331(x96241),f572(x96243,x96244,x96245,x96242,x96241)),f329(f171(x96241),x96244))) % 178.07/177.93 [9654]~P24(f329(f329(f331(x96545),x96544),f329(f283(x96541,x96545,x96543),x96542)))+P24(f329(f329(f331(x96541),f537(x96542,x96543,x96541,x96544,x96545)),x96542)) % 178.07/177.93 [9655]~P24(f329(f329(f331(x96555),x96554),f329(f283(x96551,x96555,x96553),x96552)))+P24(f329(f329(f331(x96551),f564(x96552,x96553,x96551,x96554,x96555)),x96552)) % 178.07/177.93 [9680]~P24(f329(f329(f243(f883(x96805,a869)),x96804),f329(f308(x96801,x96805,x96803),x96802)))+P24(f329(f329(f243(f883(x96801,a869)),f350(x96802,x96803,x96801,x96804,x96805)),x96802)) % 178.07/177.93 [9731]~P24(f329(f329(f331(x97315),x97314),f185(x97311,x97315,f187(x97311,x97315,x97313,x97312))))+P24(f329(f329(f331(x97311),f710(x97312,x97313,x97311,x97314,x97315)),x97312)) % 178.07/177.93 [10126]E(x101261,f2(a105))+E(f329(f238(f882(f876(x101262),x101263),f882(x101262,x101263),f329(f329(f264(f876(x101262),x101263),f119(x101262)),x101264),f329(f268(x101262,x101263,f882(f876(x101262),x101263)),f329(f329(f7(x101262,f883(x101263,f882(f876(x101262),x101263)),f883(x101263,f882(f876(x101262),x101263))),f329(f329(f8(f883(f882(f876(x101262),x101263),f882(f876(x101262),x101263)),f883(f883(x101263,f882(f876(x101262),x101263)),f883(x101263,f882(f876(x101262),x101263))),x101262),f8(f882(f876(x101262),x101263),f882(f876(x101262),x101263),x101263)),f329(f329(f8(f883(f876(x101262),f883(x101263,f882(f876(x101262),x101263))),f883(f882(f876(x101262),x101263),f882(f876(x101262),x101263)),x101262),f268(f876(x101262),x101263,f882(f876(x101262),x101263))),f329(f329(f8(f883(f876(x101262),f876(x101262)),f883(f876(x101262),f883(x101263,f882(f876(x101262),x101263))),x101262),f329(f8(f876(x101262),f883(x101263,f882(f876(x101262),x101263)),f876(x101262)),f264(f876(x101262),x101263))),f150(x101262))))),f329(f123(x101263,x101262,x101265),f329(f329(f22(a105),x101261),f79(a105)))))),f329(x101265,x101264)),f329(f329(f123(x101263,x101262,x101265),x101261),x101264)) % 178.07/177.93 [5432]~E(f329(x54323,x54324),x54325)+E(f329(f329(f329(f73(x54321,x54322),x54323),x54324),x54325),x54323) % 178.07/177.93 [5872]E(f329(x58721,x58722),x58723)+~E(f329(f329(f329(f73(x58724,x58725),x58721),x58722),x58723),x58721) % 178.07/177.93 [5968]E(x59681,x59682)+~E(f329(f267(x59683,x59684),f329(f329(f264(x59683,x59684),x59685),x59681)),x59682) % 178.07/177.93 [5969]E(x59691,x59692)+~E(f329(f263(x59693,x59694),f329(f329(f264(x59693,x59694),x59691),x59695)),x59692) % 178.07/177.93 [6234]~E(x62343,f329(f329(f127(x62341),x62344),f329(f329(f150(x62341),x62342),x62345)))+P24(f329(f329(f331(x62341),x62342),f329(f171(x62341),x62343))) % 178.07/177.93 [6625]E(f329(f308(x66251,x66252,f329(f16(x66252,x66251),x66253)),x66254),f329(f329(f307(x66252),x66253),f193(f883(x66252,a869))))+~P24(f329(f329(f331(x66251),x66255),x66254)) % 178.07/177.93 [6695]E(f329(f329(f116(f883(x66951,a869)),f329(f171(x66951),x66952)),f329(f171(x66951),x66953)),f329(f171(x66951),x66954))+~E(f166(x66951,x66955,x66954),f329(f329(f264(f876(x66951),f876(x66951)),x66952),x66953)) % 178.07/177.93 [6797]~P105(x67972)+E(f329(f194(f876(x67971)),f329(f329(f147(x67971,x67972,x67973),x67974),x67975)),f329(a118,f329(f194(f876(x67971)),x67975))) % 178.07/177.93 [6809]~P105(x68092)+E(f329(f171(x68091),f329(f329(f147(x68091,x68092,x68093),x68094),x68095)),f329(f329(f307(x68091),x68094),f329(f171(x68091),x68095))) % 178.07/177.93 [7083]~P114(x70831)+E(f329(f329(f82(x70831),f329(f329(f82(x70831),x70832),x70833)),f329(f329(f82(x70831),x70834),x70835)),f329(f329(f82(x70831),f329(f329(f82(x70831),x70832),x70834)),f329(f329(f82(x70831),x70833),x70835))) % 178.07/177.93 [7084]~P114(x70841)+E(f329(f329(f81(x70841),f329(f329(f81(x70841),x70842),x70843)),f329(f329(f81(x70841),x70844),x70845)),f329(f329(f81(x70841),f329(f329(f81(x70841),x70842),x70844)),f329(f329(f81(x70841),x70843),x70845))) % 178.07/177.93 [7085]~P59(x70851)+E(f329(f329(f287(x70851),f329(f329(f82(x70851),x70852),x70853)),f329(f329(f82(x70851),x70854),x70855)),f329(f329(f82(x70851),f329(f329(f287(x70851),x70852),x70854)),f329(f329(f287(x70851),x70853),x70855))) % 178.07/177.93 [7099]~P105(x70991)+E(f303(x70991,f329(f329(f242(x70991),x70992),x70993),f329(f329(f241(x70991),x70994),x70995)),f329(f329(f107(f883(x70991,a869)),f303(x70991,x70992,x70994)),f303(x70991,x70993,x70995))) % 178.07/177.93 [7100]~P105(x71001)+E(f302(x71001,f329(f329(f242(x71001),x71002),x71003),f329(f329(f241(x71001),x71004),x71005)),f329(f329(f107(f883(x71001,a869)),f302(x71001,x71002,x71004)),f302(x71001,x71003,x71005))) % 178.07/177.93 [7101]~P105(x71011)+E(f300(x71011,f329(f329(f242(x71011),x71012),x71013),f329(f329(f241(x71011),x71014),x71015)),f329(f329(f107(f883(x71011,a869)),f300(x71011,x71012,x71014)),f300(x71011,x71013,x71015))) % 178.07/177.93 [7102]~P105(x71021)+E(f329(f329(f107(f883(x71021,a869)),f329(f299(x71021,x71022),x71023)),f329(f299(x71021,x71024),x71025)),f329(f299(x71021,f329(f329(f242(x71021),x71022),x71024)),f329(f329(f241(x71021),x71023),x71025))) % 178.07/177.93 [7217]~P24(f329(x72171,f536(x72173,x72172,x72171)))+P24(f329(x72171,f329(f329(f264(x72172,x72173),x72174),x72175))) % 178.07/177.93 [7304]~E(f329(x73043,x73044),f206(x73042))+E(f185(x73041,x73042,f329(f329(f329(f73(x73041,f879(x73042)),x73043),x73044),f329(f236(x73042),x73045))),f329(f329(f307(x73042),x73045),f185(x73041,x73042,x73043))) % 178.07/177.93 [7325]~E(x73252,f329(x73254,x73255))+P24(f329(f329(f331(x73251),x73252),f329(f308(x73253,x73251,x73254),f252(f883(x73253,a869))))) % 178.07/177.93 [7384]~E(f329(x73843,x73844),f206(x73842))+E(f329(f329(f22(f883(x73841,a869)),f183(x73841,x73842,x73843)),f329(f329(f307(x73841),x73844),x73845)),f329(f329(f22(f883(x73841,a869)),f183(x73841,x73842,x73843)),x73845)) % 178.07/177.93 [7403]~P11(x74033,x74032,x74034)+P11(x74031,x74032,f329(f329(f8(x74033,f883(x74032,x74032),x74031),x74034),x74035)) % 178.07/177.93 [7404]~P12(x74043,x74042,x74044)+P12(x74041,x74042,f329(f329(f8(x74043,f883(x74042,x74042),x74041),x74044),x74045)) % 178.07/177.93 [7546]~P21(x75461,x75462,x75463,x75464)+P21(x75461,x75462,x75463,f329(f329(f22(f883(x75461,a869)),x75464),x75465)) % 178.07/177.93 [7703]~P24(f329(f329(x77033,x77034),x77035))+P24(f329(f329(f268(x77031,x77032,a869),x77033),f329(f329(f264(x77031,x77032),x77034),x77035))) % 178.07/177.93 [7813]~P24(f329(x78132,x78134))+~E(f329(f329(f137(x78131),f329(f194(f876(x78131)),f176(x78131,x78132,x78133))),x78133),f329(f329(f150(x78131),x78134),x78135)) % 178.07/177.93 [7833]P21(x78331,x78332,x78333,x78334)+~P21(x78331,x78332,x78333,f329(f329(f116(f883(x78331,a869)),x78335),x78334)) % 178.07/177.93 [7834]P21(x78341,x78342,x78343,x78344)+~P21(x78341,x78342,x78343,f329(f329(f116(f883(x78341,a869)),x78344),x78345)) % 178.07/177.93 [7881]~P105(x78812)+E(f329(f329(f147(x78811,x78812,x78813),x78814),f149(x78811,x78812,x78813,x78815)),f149(x78811,x78812,x78813,f329(f329(f150(x78811),x78814),x78815))) % 178.07/177.93 [8045]~P30(x80451,f329(a118,x80452),f329(f329(f329(f93(x80451),x80453),f329(a26,x80454)),x80455))+P30(x80451,x80452,f329(f329(f329(f93(x80451),x80453),f329(f240(a870),f329(a28,x80454))),x80455)) % 178.07/177.93 [8179]P30(x81791,f329(a118,x81792),f329(f329(f329(f93(x81791),x81793),f329(a26,x81794)),x81795))+~P30(x81791,x81792,f329(f329(f329(f93(x81791),x81793),f329(f240(a870),f329(a28,x81794))),x81795)) % 178.07/177.93 [8208]~P11(x82082,x82081,x82083)+E(f329(f141(x82081,x82082,f329(f7(x82082,x82081,x82081),x82083),x82084),x82085),f329(f329(f65(x82082,x82081,x82083),x82084),f329(f171(x82082),x82085))) % 178.07/177.93 [8237]~E(f329(f329(f137(x82371),f329(f194(f876(x82371)),f176(x82371,x82372,x82373))),x82373),f329(f329(f150(x82371),x82374),x82375))+E(f329(f329(f127(x82371),f176(x82371,x82372,x82373)),f329(f329(f150(x82371),x82374),x82375)),x82373) % 178.07/177.93 [8261]P24(f329(f329(x82611,x82612),x82613))+~P24(f329(f329(f268(x82614,x82615,a869),x82611),f329(f329(f264(x82614,x82615),x82612),x82613))) % 178.07/177.93 [8324]~E(f329(f329(f177(x83241,x83242),x83245),x83243),f329(f236(x83242),x83244))+P24(f329(f329(f331(f882(x83241,x83242)),f329(f329(f264(x83241,x83242),x83243),x83244)),f329(f171(f882(x83241,x83242)),x83245))) % 178.07/177.93 [8726]P24(f329(f329(f243(f883(x87261,a869)),f329(f308(x87262,x87261,x87263),x87264)),f329(f308(x87262,x87261,x87263),x87265)))+~P24(f329(f329(f243(f883(x87262,a869)),x87264),x87265)) % 178.07/177.93 [8727]P24(f329(f329(f243(f883(x87271,a869)),f329(f309(x87271,x87272,x87273),x87274)),f329(f309(x87271,x87272,x87273),x87275)))+~P24(f329(f329(f243(f883(x87272,a869)),x87274),x87275)) % 178.07/177.93 [8802]E(x88021,f2(a105))+E(f329(f329(f270(x88022,x88023,x88022,f882(x88023,x88022)),f329(x88024,x88025)),f278(x88023,x88022,f329(f329(f22(a105),x88021),f79(a105)),x88024)),f329(f278(x88023,x88022,x88021,x88024),x88025)) % 178.07/177.93 [9122]P30(x91221,x91222,f329(f329(f329(f93(x91221),x91223),x91224),x91225))+P24(f329(f329(x91223,f493(x91225,x91224,x91223,x91222)),f494(x91225,x91224,x91223,x91222))) % 178.07/177.93 [9323]E(f329(f236(x93231),f571(x93232,x93233,x93234,x93231,x93235)),f329(f329(f177(x93235,x93231),x93232),x93234))+~P24(f329(f329(f331(f882(x93235,x93231)),f329(f329(f264(x93235,x93231),x93234),x93233)),f329(f171(f882(x93235,x93231)),x93232))) % 178.07/177.93 [9367]P30(x93671,x93672,f329(f329(f329(f93(x93671),x93673),x93674),x93675))+~P24(f329(f329(x93675,f493(x93675,x93674,x93673,x93672)),f495(x93675,x93674,x93673,x93672))) % 178.07/177.93 [9426]P30(x94261,x94262,f329(f329(f329(f93(x94261),x94263),x94264),x94265))+P24(f329(f329(f329(f329(a201,x94264),f494(x94265,x94264,x94263,x94262)),x94262),f495(x94265,x94264,x94263,x94262))) % 178.07/177.93 [9429]~P20(x94291,x94292,f329(f329(f307(f874(x94291)),f329(f329(f329(f93(x94291),x94293),f329(f240(a870),f329(a28,x94294))),x94295)),f193(f883(f874(x94291),a869))))+P20(x94291,x94292,f329(f329(f307(f874(x94291)),f329(f329(f329(f93(x94291),x94293),f329(a26,x94294)),x94295)),f193(f883(f874(x94291),a869)))) % 178.07/177.93 [9457]~P24(f329(f62(x94573),f329(f308(x94572,x94573,x94575),f252(f883(x94572,a869)))))+P24(f329(f62(x94571),f329(f308(x94572,x94571,f329(f329(f8(x94573,x94571,x94572),x94574),x94575)),f252(f883(x94572,a869))))) % 178.07/177.93 [9479]P24(f329(f329(f243(f883(f883(x94791,a869),a869)),f329(f308(f883(x94792,a869),f883(x94791,a869),f308(x94792,x94791,x94793)),f329(f306(x94792),x94794))),f329(f306(x94791),x94795)))+~P24(f329(f329(f243(f883(x94791,a869)),f329(f308(x94792,x94791,x94793),x94794)),x94795)) % 178.07/177.93 [9492]~P24(f329(f62(f879(x94921)),f329(f308(x94922,f879(x94921),x94923),f252(f883(x94922,a869)))))+P24(f329(f62(f879(x94921)),f329(f308(x94922,f879(x94921),f329(f329(f329(f73(x94922,f879(x94921)),x94923),x94924),f329(f236(x94921),x94925))),f252(f883(x94922,a869))))) % 178.07/177.93 [9552]E(x95521,x95522)+~P24(f329(f67(x95523,x95524,x95525,x95521,f193(f883(x95523,a869))),x95522)) % 178.07/177.93 [9567]E(f329(f329(f264(x95671,x95672),f686(x95673,x95674,x95675,x95672,x95671)),f689(x95673,x95674,x95675,x95672,x95671)),x95675)+~P24(f329(f329(f331(f882(x95671,x95672)),x95675),f329(f329(f266(x95671,x95672),x95674),x95673))) % 178.07/177.93 [9659]P24(f329(f329(f331(x96591),f686(x96592,x96593,x96594,x96595,x96591)),x96593))+~P24(f329(f329(f331(f882(x96591,x96595)),x96594),f329(f329(f266(x96591,x96595),x96593),x96592))) % 178.07/177.93 [9767]P20(x97675,x97674,f329(f329(f307(f874(x97675)),f329(f329(f329(f93(x97675),x97671),x97673),x97672)),f193(f883(f874(x97675),a869))))+P24(f329(f329(x97671,f373(x97672,x97673,x97674,x97675,x97671)),f384(x97672,x97673,x97674,x97675,x97671))) % 178.07/177.93 [9818]P24(f329(f329(f331(x98181),f689(x98182,x98183,x98184,x98181,x98185)),f329(x98182,f686(x98182,x98183,x98184,x98181,x98185))))+~P24(f329(f329(f331(f882(x98185,x98181)),x98184),f329(f329(f266(x98185,x98181),x98183),x98182))) % 178.07/177.93 [9846]P24(f329(f329(f331(f882(x98461,x98461)),f329(f329(f264(x98461,x98461),x98462),f769(x98463,x98464,x98465,x98462,x98461))),x98463))+~P24(f329(f329(f331(f882(x98461,x98461)),f329(f329(f264(x98461,x98461),x98462),x98465)),f329(f329(f188(f882(x98461,x98461),a869),f329(a118,x98464)),x98463))) % 178.07/177.93 [9847]P24(f329(f329(f331(f882(x98471,x98471)),f329(f329(f264(x98471,x98471),x98472),f770(x98473,x98474,x98475,x98472,x98471))),x98473))+~P24(f329(f329(f331(f882(x98471,x98471)),f329(f329(f264(x98471,x98471),x98472),x98475)),f329(f329(f188(f882(x98471,x98471),a869),f329(a118,x98474)),x98473))) % 178.07/177.93 [9865]~P24(f329(f329(f331(f882(f876(x98651),f876(x98651))),f329(f329(f264(f876(x98651),f876(x98651)),f329(f329(f150(x98651),x98652),x98655)),x98654)),f157(x98651,x98653)))+P24(f329(f329(f331(f882(x98651,x98651)),f329(f329(f264(x98651,x98651),x98652),f609(x98653,x98654,x98655,x98652,x98651))),x98653)) % 178.07/177.93 [9867]~P20(x98671,x98672,f329(f329(f307(f874(x98671)),f329(f329(f329(f93(x98671),f98(x98671,x98673,x98674)),x98675),x98673)),f193(f883(f874(x98671),a869))))+P20(x98671,x98672,f329(f329(f307(f874(x98671)),f329(f329(f329(f93(x98671),x98673),f33(x98674,x98675)),f98(x98671,x98673,f329(f74(a869,a869,a871,a324),x98674)))),f193(f883(f874(x98671),a869)))) % 178.07/177.93 [9868]~P23(x98681,x98682,f329(f329(f307(f874(x98681)),f329(f329(f329(f93(x98681),f98(x98681,x98683,x98684)),x98685),x98683)),f193(f883(f874(x98681),a869))))+P23(x98681,x98682,f329(f329(f307(f874(x98681)),f329(f329(f329(f93(x98681),x98683),f33(x98684,x98685)),f98(x98681,x98683,f329(f74(a869,a869,a871,a324),x98684)))),f193(f883(f874(x98681),a869)))) % 178.07/177.93 [10127]P20(x101271,x101272,f329(f329(f307(f874(x101271)),f329(f329(f329(f93(x101271),x101273),x101274),x101275)),f193(f883(f874(x101271),a869))))+~P20(x101271,x101272,f329(f329(f307(f874(x101271)),f329(f329(f329(f93(x101271),f329(f16(f883(a871,a869),x101271),f329(f329(f7(a871,a871,a869),a326),f384(x101275,x101274,x101272,x101271,x101273)))),x101274),f329(f16(f883(a871,a869),x101271),f329(x101275,f373(x101275,x101274,x101272,x101271,x101273))))),f193(f883(f874(x101271),a869)))) % 178.07/177.93 [6308]P24(f329(x63082,x63084))+E(f176(x63081,x63082,f329(f329(f127(x63081),x63083),f329(f329(f150(x63081),x63084),x63085))),f176(x63081,x63082,x63083)) % 178.07/177.93 [6357]~P63(x63572)+E(f329(f329(f329(f116(f883(x63571,x63572)),x63573),x63574),x63575),f329(f329(f116(x63572),f329(x63573,x63575)),f329(x63574,x63575))) % 178.07/177.93 [6359]~P65(x63592)+E(f329(f329(f329(f22(f883(x63591,x63592)),x63593),x63594),x63595),f329(f329(f22(x63592),f329(x63593,x63595)),f329(x63594,x63595))) % 178.07/177.93 [6361]~P63(x63612)+E(f329(f329(f329(f107(f883(x63611,x63612)),x63613),x63614),x63615),f329(f329(f107(x63612),f329(x63613,x63615)),f329(x63614,x63615))) % 178.07/177.93 [6379]E(x63791,x63792)+E(f329(f329(f164(x63793),f329(f329(f158(x63793,x63794),x63791),x63795)),x63792),f329(f329(f164(x63793),x63794),x63792)) % 178.07/177.93 [6643]~E(x66434,f193(f883(x66433,a869)))+E(f329(f329(f116(f883(x66431,a869)),x66432),f329(f329(f43(x66433,f883(x66431,a869)),x66434),x66435)),x66432) % 178.07/177.93 [6644]~E(x66444,f193(f883(x66443,a869)))+E(f329(f329(f22(f883(x66441,a869)),x66442),f329(f329(f43(x66443,f883(x66441,a869)),x66444),x66445)),x66442) % 178.07/177.93 [6645]~E(x66454,f193(f883(x66453,a869)))+E(f329(f329(f107(f883(x66451,a869)),x66452),f329(f329(f42(x66453,f883(x66451,a869)),x66454),x66455)),x66452) % 178.07/177.93 [6659]~E(x66594,f193(f883(x66593,a869)))+E(f329(f329(f307(x66591),x66592),f329(f329(f43(x66593,f883(x66591,a869)),x66594),x66595)),f329(f329(f307(x66591),x66592),f193(f883(x66591,a869)))) % 178.07/177.93 [7452]E(f329(f329(f164(x74521),f329(f329(f153(x74522,x74521),x74523),x74524)),x74525),f329(x74523,f329(f329(f164(x74522),x74524),x74525)))+~P24(f329(f329(f244(a875),x74525),f329(f194(f876(x74522)),x74524))) % 178.07/177.93 [7518]E(f329(f329(f116(f883(x75181,a869)),f329(x75182,x75183)),f329(f329(f43(x75184,f883(x75181,a869)),x75185),x75182)),f329(f329(f43(x75184,f883(x75181,a869)),x75185),x75182))+~P24(f329(f329(f331(x75184),x75183),x75185)) % 178.07/177.93 [7519]E(f329(f329(f107(f883(x75191,a869)),f329(x75192,x75193)),f329(f329(f42(x75194,f883(x75191,a869)),x75195),x75192)),f329(f329(f42(x75194,f883(x75191,a869)),x75195),x75192))+~P24(f329(f329(f331(x75194),x75193),x75195)) % 178.07/177.93 [8124]~E(x81243,f193(f883(x81241,a869)))+E(f329(f329(f43(x81241,f883(x81242,a869)),x81243),f329(f329(f8(f883(x81242,a869),f883(x81242,a869),x81241),f329(f307(x81242),x81244)),x81245)),f193(f883(x81242,a869))) % 178.07/177.93 [8130]~P24(f329(f329(f331(x81304),x81303),x81305))+P24(f329(f329(f243(f883(x81301,a869)),f329(x81302,x81303)),f329(f329(f43(x81304,f883(x81301,a869)),x81305),x81302))) % 178.07/177.93 [8260]~E(f329(x82604,x82602),x82605)+P24(f329(f329(f331(x82601),x82602),f329(f309(x82601,x82603,x82604),f329(f329(f307(x82603),x82605),f193(f883(x82603,a869)))))) % 178.07/177.93 [8306]~P50(x83061,x83062,f329(f284(x83062,x83061),x83063))+E(f329(f329(f107(f883(x83061,a869)),f329(f283(x83062,x83061,x83063),x83064)),f329(f283(x83062,x83061,x83063),x83065)),f329(f283(x83062,x83061,x83063),f329(f329(f107(f883(x83062,a869)),x83064),x83065))) % 178.07/177.93 [8382]E(x83821,f2(a105))+E(f329(f122(x83822,x83823,f329(x83824,f329(f329(f22(a105),x83821),f79(a105)))),f329(f329(f7(x83822,a105,f877(x83823)),x83825),x83821)),f329(f205(x83822,x83823,x83824,x83825),x83821)) % 178.07/177.93 [8425]E(x84251,f193(f883(x84252,a869)))+E(f329(f329(f43(x84252,f883(x84253,a869)),x84251),f329(f329(f8(f883(x84253,a869),f883(x84253,a869),x84252),f329(f307(x84253),x84254)),x84255)),f329(f329(f307(x84253),x84254),f329(f329(f43(x84252,f883(x84253,a869)),x84251),x84255))) % 178.07/177.93 [8480]~P21(x84802,x84801,x84803,f252(f883(x84802,a869)))+E(f329(f329(f22(f883(x84801,a869)),f329(f308(x84802,x84801,x84803),x84804)),f329(f308(x84802,x84801,x84803),x84805)),f329(f308(x84802,x84801,x84803),f329(f329(f22(f883(x84802,a869)),x84804),x84805))) % 178.07/177.93 [8481]~P21(x84812,x84811,x84813,f252(f883(x84812,a869)))+E(f329(f329(f107(f883(x84811,a869)),f329(f308(x84812,x84811,x84813),x84814)),f329(f308(x84812,x84811,x84813),x84815)),f329(f308(x84812,x84811,x84813),f329(f329(f107(f883(x84812,a869)),x84814),x84815))) % 178.07/177.93 [8545]~P24(f329(f329(f68(x85451,x85452,x85455),x85453),x85454))+P24(f329(f329(f331(f882(x85451,x85452)),f329(f329(f264(x85451,x85452),x85453),x85454)),x85455)) % 178.07/177.93 [8577]P24(f329(f329(f331(x85771),x85772),f329(f260(x85773,x85771),x85774)))+~P24(f329(f329(f331(f882(x85773,x85771)),f329(f329(f264(x85773,x85771),x85775),x85772)),x85774)) % 178.07/177.93 [8579]P24(f329(f329(f331(x85791),x85792),f329(f262(x85791,x85793),x85794)))+~P24(f329(f329(f331(f882(x85791,x85793)),f329(f329(f264(x85791,x85793),x85792),x85795)),x85794)) % 178.07/177.93 [8713]P24(f329(f329(f68(x87131,x87132,x87133),x87134),x87135))+~P24(f329(f329(f331(f882(x87131,x87132)),f329(f329(f264(x87131,x87132),x87134),x87135)),x87133)) % 178.07/177.93 [8748]E(f329(x87481,x87482),x87483)+~P24(f329(f329(f331(x87484),x87482),f329(f309(x87484,x87485,x87481),f329(f329(f307(x87485),x87483),f193(f883(x87485,a869)))))) % 178.07/177.93 [8981]P24(f329(f329(f331(f882(x89811,x89812)),f329(f329(f264(x89811,x89812),x89813),x89814)),f329(f284(x89812,x89811),x89815)))+~P24(f329(f329(f331(f882(x89812,x89811)),f329(f329(f264(x89812,x89811),x89814),x89813)),x89815)) % 178.07/177.93 [8999]~P24(f329(f329(x89991,x89995),x89994))+P24(f329(f329(x89991,f329(f267(x89992,x89993),f329(f329(f264(x89992,x89993),x89994),x89995))),f329(f263(x89992,x89993),f329(f329(f264(x89992,x89993),x89994),x89995)))) % 178.07/177.93 [9029]~P24(f329(f329(f331(f882(x90292,x90291)),f329(f329(f264(x90292,x90291),x90294),x90293)),f329(f284(x90291,x90292),x90295)))+P24(f329(f329(f331(f882(x90291,x90292)),f329(f329(f264(x90291,x90292),x90293),x90294)),x90295)) % 178.07/177.93 [9059]~P24(f329(f329(f331(f882(x90593,x90591)),f329(f329(f264(x90593,x90591),x90595),x90592)),x90594))+P24(f329(f329(f331(x90591),x90592),f329(f283(x90593,x90591,x90594),f329(f329(f307(x90593),x90595),f193(f883(x90593,a869)))))) % 178.07/177.93 [9104]P24(f329(f329(f331(f882(x91041,x91042)),f329(f329(f264(x91041,x91042),x91043),x91044)),x91045))+~P24(f329(f329(f331(x91042),x91044),f329(f283(x91041,x91042,x91045),f329(f329(f307(x91041),x91043),f193(f883(x91041,a869)))))) % 178.07/177.93 [9125]E(f329(f329(f329(f73(x91251,f879(x91252)),f187(x91251,x91252,x91253,x91254)),x91255),f206(x91252)),f187(x91251,x91252,x91253,f329(f329(f22(f883(x91251,a869)),x91254),f329(f329(f307(x91251),x91255),f193(f883(x91251,a869))))))+~P24(f329(f329(f331(x91251),x91255),x91254)) % 178.07/177.93 [9193]~P70(x91931)+E(f329(f329(f6(a875,x91931),x91932),f300(a875,f329(f329(f81(a875),x91933),x91934),f329(f329(f81(a875),x91935),x91934))),f329(f329(f6(a875,x91931),f329(f329(f8(a875,x91931,a875),x91932),f329(f329(f7(a875,a875,a875),f81(a875)),x91934))),f300(a875,x91933,x91935))) % 178.07/177.93 [9217]~P70(x92171)+E(f329(f329(f6(a875,x92171),x92172),f329(f299(a875,f329(f329(f81(a875),x92173),x92174)),f329(f329(f81(a875),x92175),x92174))),f329(f329(f6(a875,x92171),f329(f329(f8(a875,x92171,a875),x92172),f329(f329(f7(a875,a875,a875),f81(a875)),x92174))),f329(f299(a875,x92173),x92175))) % 178.07/177.93 [9271]~P21(x92711,x92712,x92713,f252(f883(x92711,a869)))+E(f329(f329(f153(x92711,x92712),x92713),f329(f135(x92711,f329(f329(f8(a869,a869,x92711),a324),f329(a326,x92714))),x92715)),f329(f135(x92712,f329(f329(f8(a869,a869,x92712),a324),f329(a326,f329(x92713,x92714)))),f329(f329(f153(x92711,x92712),x92713),x92715))) % 178.07/177.93 [9289]~P21(x92891,x92892,x92893,f329(f329(f307(x92891),x92894),f329(f171(x92891),x92895)))+E(f329(f329(f153(x92891,x92892),x92893),f329(f135(x92891,f329(f329(f8(a869,a869,x92891),a324),f329(a326,x92894))),x92895)),f329(f135(x92892,f329(f329(f8(a869,a869,x92892),a324),f329(a326,f329(x92893,x92894)))),f329(f329(f153(x92891,x92892),x92893),x92895))) % 178.07/177.93 [9444]P24(f329(f329(f331(f882(f876(x94441),f876(x94441))),f329(f329(f264(f876(x94441),f876(x94441)),f329(f329(f150(x94441),x94442),x94443)),f329(f329(f150(x94441),x94444),x94443))),f156(x94441,x94445)))+~P24(f329(f329(f331(f882(x94441,x94441)),f329(f329(f264(x94441,x94441),x94442),x94444)),x94445)) % 178.07/177.93 [9480]P24(f329(f329(f329(f329(a201,x94801),x94802),x94803),f480(x94804,x94803,x94802,x94805,x94801)))+~P24(f329(f329(f329(f329(a201,f34(x94801,x94805)),x94802),x94803),x94804)) % 178.07/177.93 [9550]P20(x95501,x95502,f329(f329(f307(f874(x95501)),f329(f329(f329(f93(x95501),x95503),f329(a26,x95504)),x95505)),f193(f883(f874(x95501),a869))))+~P20(x95501,f329(f329(f307(f874(x95501)),f329(f329(f329(f93(x95501),x95503),f329(a26,x95504)),x95505)),x95502),f329(f329(f307(f874(x95501)),f329(f329(f329(f93(x95501),x95503),f329(f240(a870),f329(a28,x95504))),x95505)),f193(f883(f874(x95501),a869)))) % 178.07/177.93 [9562]E(f329(f329(f307(x95621),f823(x95622,x95623,x95624,x95625,x95621)),f824(x95622,x95623,x95624,x95625,x95621)),f329(f329(f307(x95621),x95624),x95623))+~P24(f329(f63(x95621,x95625,f329(f329(f307(x95621),x95624),x95623)),x95622)) % 178.07/177.93 [9563]E(f329(f329(f307(x95631),f829(x95632,x95633,x95634,x95635,x95631)),f830(x95632,x95633,x95634,x95635,x95631)),f329(f329(f307(x95631),x95634),x95633))+~P24(f329(f63(x95631,x95635,f329(f329(f307(x95631),x95634),x95633)),x95632)) % 178.07/177.93 [9645]P24(f329(f329(f331(x96451),f831(x96452,x96453,x96454,x96455,x96451)),x96454))+P24(f329(f329(f329(f42(x96451,f883(x96455,a869)),x96454),x96453),x96452)) % 178.07/177.93 [9650]P24(f329(f329(f331(x96501),f833(x96502,x96503,x96501,x96504,x96505)),x96503))+P24(f329(f329(f331(x96505),x96504),f329(f329(f42(x96501,f883(x96505,a869)),x96503),x96502))) % 178.07/177.93 [9658]P24(f329(f329(f331(x96581),f353(x96582,x96583,x96581,x96584,x96585)),x96583))+P24(f329(f329(f243(f883(x96585,a869)),x96584),f329(f329(f42(x96581,f883(x96585,a869)),x96583),x96582))) % 178.07/177.93 [9660]P24(f329(f329(x96601,f849(x96602,x96601,x96603,x96604,x96605)),x96602))+~P24(f329(f329(f329(f43(x96605,f883(x96604,a869)),x96603),x96601),x96602)) % 178.07/177.93 [9663]P24(f329(f329(f331(x96631),f849(x96632,x96633,x96634,x96635,x96631)),x96634))+~P24(f329(f329(f329(f43(x96631,f883(x96635,a869)),x96634),x96633),x96632)) % 178.07/177.93 [9673]P24(f329(f329(f331(x96731),f841(x96732,x96733,x96731,x96734,x96735)),x96733))+~P24(f329(f329(f331(x96735),x96734),f329(f329(f43(x96731,f883(x96735,a869)),x96733),x96732))) % 178.07/177.93 [9678]P24(f329(f329(f331(x96781),x96782),f329(x96783,f841(x96783,x96784,x96785,x96782,x96781))))+~P24(f329(f329(f331(x96781),x96782),f329(f329(f43(x96785,f883(x96781,a869)),x96784),x96783))) % 178.07/177.93 [9772]~P24(f329(f329(x97724,f831(x97725,x97724,x97723,x97722,x97721)),x97725))+P24(f329(f329(f329(f42(x97721,f883(x97722,a869)),x97723),x97724),x97725)) % 178.07/177.93 [9775]~P24(f329(f329(f331(x97751),x97752),f329(x97755,f833(x97755,x97754,x97753,x97752,x97751))))+P24(f329(f329(f331(x97751),x97752),f329(f329(f42(x97753,f883(x97751,a869)),x97754),x97755))) % 178.07/177.93 [9779]~P24(f329(f329(f243(f883(x97791,a869)),x97792),f329(x97795,f353(x97795,x97794,x97793,x97792,x97791))))+P24(f329(f329(f243(f883(x97791,a869)),x97792),f329(f329(f42(x97793,f883(x97791,a869)),x97794),x97795))) % 178.07/177.93 [9824]P24(f329(f329(f329(f329(a201,x98241),f480(x98242,x98243,x98244,x98241,x98245)),x98243),x98242))+~P24(f329(f329(f329(f329(a201,f34(x98245,x98241)),x98244),x98243),x98242)) % 178.07/177.93 [9850]~P24(f329(f329(f331(x98501),f823(x98505,x98504,x98503,x98502,x98501)),f824(x98505,x98504,x98503,x98502,x98501)))+~P24(f329(f63(x98501,x98502,f329(f329(f307(x98501),x98503),x98504)),x98505)) % 178.07/177.93 [9851]~P24(f329(f329(f331(x98511),f829(x98515,x98514,x98513,x98512,x98511)),f830(x98515,x98514,x98513,x98512,x98511)))+~P24(f329(f63(x98511,x98512,f329(f329(f307(x98511),x98513),x98514)),x98515)) % 178.07/177.93 [9852]~P24(f329(f329(f331(f882(x98521,x98521)),f329(f329(f264(x98521,x98521),x98522),x98525)),f329(f329(f188(f882(x98521,x98521),a869),f329(a118,x98524)),x98523)))+P24(f329(f329(f331(f882(x98521,x98521)),f329(f329(f264(x98521,x98521),x98522),f771(x98523,x98524,x98525,x98522,x98521))),f329(f329(f188(f882(x98521,x98521),a869),x98524),x98523))) % 178.07/177.93 [9859]P24(f329(f67(x98591,x98591,x98592,f823(x98593,x98594,x98595,x98592,x98591),f824(x98593,x98594,x98595,x98592,x98591)),x98593))+~P24(f329(f63(x98591,x98592,f329(f329(f307(x98591),x98595),x98594)),x98593)) % 178.07/177.93 [9860]P24(f329(f67(x98601,x98601,x98602,f829(x98603,x98604,x98605,x98602,x98601),f830(x98603,x98604,x98605,x98602,x98601)),x98603))+~P24(f329(f63(x98601,x98602,f329(f329(f307(x98601),x98605),x98604)),x98603)) % 178.07/177.93 [9872]~P105(x98721)+P29(x98721,f329(f329(f153(x98722,x98721),x98723),f329(f135(x98722,f329(f329(f7(x98722,x98721,a869),f329(f329(f8(x98721,f883(x98721,a869),x98722),a326),x98723)),f329(x98724,x98725))),x98725))) % 178.07/177.93 [9912]~P24(f329(f329(f331(x99122),x99125),f329(f283(x99121,x99122,x99124),x99123)))+P24(f329(f329(f331(f882(x99121,x99122)),f329(f329(f264(x99121,x99122),f537(x99123,x99124,x99121,x99125,x99122)),x99125)),x99124)) % 178.07/177.93 [9913]~P24(f329(f329(f331(x99132),x99135),f329(f283(x99131,x99132,x99134),x99133)))+P24(f329(f329(f331(f882(x99131,x99132)),f329(f329(f264(x99131,x99132),f564(x99133,x99134,x99131,x99135,x99132)),x99135)),x99134)) % 178.07/177.93 [9933]~P24(f329(f329(f331(f882(x99331,x99331)),f329(f329(f264(x99331,x99331),x99335),x99334)),f329(f329(f188(f882(x99331,x99331),a869),f329(a118,x99333)),x99332)))+P24(f329(f329(f331(f882(x99331,x99331)),f329(f329(f264(x99331,x99331),f771(x99332,x99333,x99334,x99335,x99331)),x99334)),x99332)) % 178.07/177.93 [9936]~P24(f329(f329(f331(f882(x99361,x99361)),f329(f329(f264(x99361,x99361),x99365),x99364)),f329(f329(f188(f882(x99361,x99361),a869),f329(a118,x99363)),x99362)))+P24(f329(f329(f331(f882(x99361,x99361)),f329(f329(f264(x99361,x99361),f769(x99362,x99363,x99364,x99365,x99361)),x99364)),f329(f329(f188(f882(x99361,x99361),a869),x99363),x99362))) % 178.07/177.93 [9937]~P24(f329(f329(f331(f882(x99371,x99371)),f329(f329(f264(x99371,x99371),x99375),x99374)),f329(f329(f188(f882(x99371,x99371),a869),f329(a118,x99373)),x99372)))+P24(f329(f329(f331(f882(x99371,x99371)),f329(f329(f264(x99371,x99371),f770(x99372,x99373,x99374,x99375,x99371)),x99374)),f329(f329(f188(f882(x99371,x99371),a869),x99373),x99372))) % 178.07/177.93 [9938]~P24(f329(f329(f331(f882(f876(x99381),f876(x99381))),f329(f329(f264(f876(x99381),f876(x99381)),x99385),f329(f329(f150(x99381),x99384),x99383))),f157(x99381,x99382)))+P24(f329(f329(f331(f882(x99381,x99381)),f329(f329(f264(x99381,x99381),f613(x99382,x99383,x99384,x99385,x99381)),x99384)),x99382)) % 178.07/177.93 [7045]E(x70451,f206(x70452))+E(f183(x70453,x70452,f329(f329(f329(f73(x70453,f879(x70452)),x70454),x70455),x70451)),f329(f329(f307(x70453),x70455),f183(x70453,x70452,x70454))) % 178.07/177.93 [7539]~E(x75393,f193(f883(x75392,a869)))+E(f329(f329(f116(f883(x75391,a869)),f329(f329(f43(x75392,f883(x75391,a869)),x75393),x75394)),x75395),x75395) % 178.07/177.93 [7540]~E(x75403,f193(f883(x75402,a869)))+E(f329(f329(f107(f883(x75401,a869)),f329(f329(f42(x75402,f883(x75401,a869)),x75403),x75404)),x75405),x75405) % 178.07/177.93 [7896]~E(x78965,f206(x78962))+E(f183(x78961,x78962,f329(f329(f329(f73(x78961,f879(x78962)),x78963),x78964),x78965)),f329(f329(f22(f883(x78961,a869)),f183(x78961,x78962,x78963)),f329(f329(f307(x78961),x78964),f193(f883(x78961,a869))))) % 178.07/177.93 [7965]~E(x79653,f193(f883(x79652,a869)))+E(f329(f329(f22(f883(x79651,a869)),f329(f329(f42(x79652,f883(x79651,a869)),x79653),x79654)),x79655),f329(f329(f22(f883(x79651,a869)),f252(f883(x79651,a869))),x79655)) % 178.07/177.93 [8096]E(f329(f329(f158(x80961,f329(f329(f127(x80961),x80962),x80963)),x80964),x80965),f329(f329(f127(x80961),f329(f329(f158(x80961,x80962),x80964),x80965)),x80963))+~P24(f329(f329(f244(a875),x80964),f329(f194(f876(x80961)),x80962))) % 178.07/177.93 [8212]P24(f329(f329(f331(x82121),x82125),f329(f171(x82121),x82123)))+E(f329(f329(f177(x82121,x82122),f329(f329(f181(x82121,x82122),x82123),f329(f329(f153(x82121,x82122),x82124),x82123))),x82125),f206(x82122)) % 178.07/177.93 [8333]~P24(f329(f329(f331(x83331),x83335),f329(f171(x83331),x83333)))+E(f329(f329(f177(x83331,x83332),f329(f329(f181(x83331,x83332),x83333),f329(f329(f153(x83331,x83332),x83334),x83333))),x83335),f329(f236(x83332),f329(x83334,x83335))) % 178.07/177.93 [8372]E(f329(f329(f164(x83721),f329(f329(f153(a875,x83721),x83722),f138(a875,f329(f299(a875,x83723),x83724)))),x83725),f329(x83722,f329(f329(f81(a875),x83723),x83725)))+~P24(f329(f329(f244(a875),x83725),f329(f329(f22(a875),x83724),x83723))) % 178.07/177.93 [8387]E(x83871,f2(a105))+E(f125(x83872,x83873,f329(x83874,f329(f329(f22(a105),x83871),f79(a105))),f329(f329(f7(x83872,a105,f877(f879(x83873))),x83875),x83871)),f329(f203(x83872,x83873,x83874,x83875),x83871)) % 178.07/177.93 [8412]~E(x84123,f193(f883(x84121,a869)))+E(f329(f329(f42(x84121,f883(x84122,a869)),x84123),f329(f329(f8(f883(x84122,a869),f883(x84122,a869),x84121),f329(f22(f883(x84122,a869)),x84124)),x84125)),f252(f883(x84122,a869))) % 178.07/177.93 [8413]~E(x84133,f193(f883(x84131,a869)))+E(f329(f329(f42(x84131,f883(x84132,a869)),x84133),f329(f329(f8(f883(x84132,a869),f883(x84132,a869),x84131),f329(f107(f883(x84132,a869)),x84134)),x84135)),f252(f883(x84132,a869))) % 178.07/177.93 [8414]~E(x84143,f193(f883(x84141,a869)))+E(f329(f329(f43(x84141,f883(x84142,a869)),x84143),f329(f329(f8(f883(x84142,a869),f883(x84142,a869),x84141),f329(f116(f883(x84142,a869)),x84144)),x84145)),f193(f883(x84142,a869))) % 178.07/177.93 [8419]~P134(x84192)+E(f329(f329(f6(x84191,x84192),f329(f329(f8(x84192,x84192,x84191),f329(f82(x84192),x84193)),x84194)),x84195),f329(f329(f82(x84192),x84193),f329(f329(f6(x84191,x84192),x84194),x84195))) % 178.07/177.93 [8698]E(x86981,f193(f883(x86982,a869)))+E(f329(f329(f42(x86982,f883(x86983,a869)),x86981),f329(f329(f8(f883(x86983,a869),f883(x86983,a869),x86982),f329(f22(f883(x86983,a869)),x86984)),x86985)),f329(f329(f22(f883(x86983,a869)),x86984),f329(f329(f43(x86982,f883(x86983,a869)),x86981),x86985))) % 178.07/177.93 [8699]E(x86991,f193(f883(x86992,a869)))+E(f329(f329(f42(x86992,f883(x86993,a869)),x86991),f329(f329(f8(f883(x86993,a869),f883(x86993,a869),x86992),f329(f107(f883(x86993,a869)),x86994)),x86995)),f329(f329(f107(f883(x86993,a869)),x86994),f329(f329(f42(x86992,f883(x86993,a869)),x86991),x86995))) % 178.07/177.93 [8700]E(x87001,f193(f883(x87002,a869)))+E(f329(f329(f43(x87002,f883(x87003,a869)),x87001),f329(f329(f8(f883(x87003,a869),f883(x87003,a869),x87002),f329(f116(f883(x87003,a869)),x87004)),x87005)),f329(f329(f116(f883(x87003,a869)),x87004),f329(f329(f43(x87002,f883(x87003,a869)),x87001),x87005))) % 178.07/177.93 [8894]~P24(f329(f329(f244(a875),f329(x88944,x88942)),f329(x88944,x88943)))+P24(f329(f329(f331(f882(x88941,x88941)),f329(f329(f264(x88941,x88941),x88942),x88943)),f152(x88941,f329(f329(f150(f883(x88941,a875)),x88944),x88945)))) % 178.07/177.93 [9160]~P21(x91602,x91601,x91603,f329(f329(f116(f883(x91602,a869)),x91604),x91605))+E(f329(f329(f107(f883(x91601,a869)),f329(f308(x91602,x91601,x91603),f329(f329(f22(f883(x91602,a869)),x91604),x91605))),f329(f308(x91602,x91601,x91603),f329(f329(f22(f883(x91602,a869)),x91605),x91604))),f193(f883(x91601,a869))) % 178.07/177.93 [9440]~P24(f329(f329(f243(f883(x94403,a869)),f329(f283(x94401,x94403,x94404),x94402)),x94405))+P24(f329(f329(f243(f883(x94401,a869)),x94402),f329(f80(f883(x94401,a869)),f329(f283(x94403,x94401,f329(f284(x94401,x94403),x94404)),f329(f80(f883(x94403,a869)),x94405))))) % 178.07/177.93 [9465]~P21(x94651,x94652,x94653,f329(f329(f307(x94651),x94654),x94655))+~P24(f329(f329(f331(x94652),f329(x94653,x94654)),f329(f308(x94651,x94652,x94653),f329(f329(f22(f883(x94651,a869)),x94655),f329(f329(f307(x94651),x94654),f193(f883(x94651,a869))))))) % 178.07/177.93 [9516]P24(f329(f329(f243(f883(x95161,a869)),f329(f283(x95162,x95161,x95163),x95164)),x95165))+~P24(f329(f329(f243(f883(x95162,a869)),x95164),f329(f80(f883(x95162,a869)),f329(f283(x95161,x95162,f329(f284(x95162,x95161),x95163)),f329(f80(f883(x95161,a869)),x95165))))) % 178.07/177.93 [9590]~P85(x95901)+P24(f329(f329(f243(x95901),f329(f76(x95901),f329(f329(f22(x95901),f329(f329(f81(x95901),x95902),x95903)),f329(f329(f81(x95901),x95904),x95905)))),f329(f329(f81(x95901),f329(f76(x95901),f329(f329(f22(x95901),x95902),x95904))),f329(f76(x95901),f329(f329(f22(x95901),x95903),x95905))))) % 178.07/177.93 [9693]P24(f329(f329(f331(x96931),f354(x96932,x96933,x96934,x96931,x96935)),x96934))+P24(f329(f329(f243(f883(x96935,a869)),f329(f329(f43(x96931,f883(x96935,a869)),x96934),x96933)),x96932)) % 178.07/177.93 [9890]~P24(f329(f329(f243(f883(x98901,a869)),f329(x98904,f354(x98905,x98904,x98903,x98902,x98901))),x98905))+P24(f329(f329(f243(f883(x98901,a869)),f329(f329(f43(x98902,f883(x98901,a869)),x98903),x98904)),x98905)) % 178.07/177.93 [8526]E(f329(f329(f127(x85261),x85262),f329(f329(f158(x85261,x85263),f329(f329(f22(a875),x85264),f329(f194(f876(x85261)),x85262))),x85265)),f329(f329(f158(x85261,f329(f329(f127(x85261),x85262),x85263)),x85264),x85265))+P24(f329(f329(f244(a875),x85264),f329(f194(f876(x85261)),x85262))) % 178.07/177.93 [8553]~P135(x85531)+E(f329(f329(f81(x85531),f329(f329(f82(x85531),x85532),x85533)),f329(f329(f81(x85531),f329(f329(f82(x85531),x85534),x85533)),x85535)),f329(f329(f81(x85531),f329(f329(f82(x85531),f329(f329(f81(x85531),x85532),x85534)),x85533)),x85535)) % 178.07/177.93 [9114]~P134(x91141)+E(f329(f165(x91141),f329(f329(f153(x91142,x91141),f329(f329(f8(x91141,x91141,x91142),f329(f82(x91141),x91143)),x91144)),x91145)),f329(f329(f82(x91141),x91143),f329(f165(x91141),f329(f329(f153(x91142,x91141),x91144),x91145)))) % 178.07/177.93 [9288]E(f329(f194(f876(x92881)),f329(f329(f174(x92881),f329(f329(f241(a875),f329(f194(f876(x92881)),x92882)),f329(f194(f876(x92883)),x92884))),x92882)),f329(f194(f876(x92883)),f329(f329(f174(x92883),f329(f329(f241(a875),f329(f194(f876(x92881)),x92882)),f329(f194(f876(x92883)),x92884))),x92884)))+P24(f329(x92885,f329(f329(f181(x92881,x92883),x92882),x92884))) % 178.07/177.93 [9527]~P134(x95272)+E(f329(f329(f6(x95271,x95272),f329(f329(f7(x95271,x95272,x95272),f329(f329(f8(x95272,f883(x95272,x95272),x95271),f82(x95272)),x95273)),x95274)),x95275),f329(f329(f82(x95272),f329(f329(f6(x95271,x95272),x95273),x95275)),x95274)) % 178.07/177.93 [9528]~P60(x95282)+E(f329(f329(f6(x95281,x95282),f329(f329(f7(x95281,x95282,x95282),f329(f329(f8(x95282,f883(x95282,x95282),x95281),f287(x95282)),x95283)),x95284)),x95285),f329(f329(f287(x95282),f329(f329(f6(x95281,x95282),x95283),x95285)),x95284)) % 178.07/177.93 [9535]~P66(x95352)+E(f329(f329(f6(x95351,x95352),f329(f329(f18(x95351,x95352,x95352),f329(f329(f8(x95352,f883(x95352,x95352),x95351),f22(x95352)),x95353)),x95354)),x95355),f329(f329(f22(x95352),f329(f329(f6(x95351,x95352),x95353),x95355)),f329(f329(f6(x95351,x95352),x95354),x95355))) % 178.07/177.93 [9536]~P70(x95362)+E(f329(f329(f6(x95361,x95362),f329(f329(f18(x95361,x95362,x95362),f329(f329(f8(x95362,f883(x95362,x95362),x95361),f81(x95362)),x95363)),x95364)),x95365),f329(f329(f81(x95362),f329(f329(f6(x95361,x95362),x95363),x95365)),f329(f329(f6(x95361,x95362),x95364),x95365))) % 178.07/177.93 [9537]~P74(x95372)+E(f329(f329(f9(x95371,x95372),f329(f329(f18(x95371,x95372,x95372),f329(f329(f8(x95372,f883(x95372,x95372),x95371),f82(x95372)),x95373)),x95374)),x95375),f329(f329(f82(x95372),f329(f329(f9(x95371,x95372),x95373),x95375)),f329(f329(f9(x95371,x95372),x95374),x95375))) % 178.07/177.93 [9575]~E(x95753,f193(f883(x95751,a869)))+E(f329(f329(f42(x95751,f883(x95752,a869)),x95753),f329(f329(f7(x95751,f883(x95752,a869),f883(x95752,a869)),f329(f329(f8(f883(x95752,a869),f883(f883(x95752,a869),f883(x95752,a869)),x95751),f22(f883(x95752,a869))),x95754)),x95755)),f252(f883(x95752,a869))) % 178.07/177.93 [9576]~E(x95763,f193(f883(x95761,a869)))+E(f329(f329(f42(x95761,f883(x95762,a869)),x95763),f329(f329(f7(x95761,f883(x95762,a869),f883(x95762,a869)),f329(f329(f8(f883(x95762,a869),f883(f883(x95762,a869),f883(x95762,a869)),x95761),f107(f883(x95762,a869))),x95764)),x95765)),f252(f883(x95762,a869))) % 178.07/177.93 [9577]~E(x95773,f193(f883(x95771,a869)))+E(f329(f329(f43(x95771,f883(x95772,a869)),x95773),f329(f329(f7(x95771,f883(x95772,a869),f883(x95772,a869)),f329(f329(f8(f883(x95772,a869),f883(f883(x95772,a869),f883(x95772,a869)),x95771),f116(f883(x95772,a869))),x95774)),x95775)),f193(f883(x95772,a869))) % 178.07/177.93 [9598]E(x95981,f193(f883(x95982,a869)))+E(f329(f329(f42(x95982,f883(x95983,a869)),x95981),f329(f329(f7(x95982,f883(x95983,a869),f883(x95983,a869)),f329(f329(f8(f883(x95983,a869),f883(f883(x95983,a869),f883(x95983,a869)),x95982),f22(f883(x95983,a869))),x95984)),x95985)),f329(f329(f22(f883(x95983,a869)),f329(f329(f42(x95982,f883(x95983,a869)),x95981),x95984)),x95985)) % 178.07/177.93 [9599]E(x95991,f193(f883(x95992,a869)))+E(f329(f329(f42(x95992,f883(x95993,a869)),x95991),f329(f329(f7(x95992,f883(x95993,a869),f883(x95993,a869)),f329(f329(f8(f883(x95993,a869),f883(f883(x95993,a869),f883(x95993,a869)),x95992),f107(f883(x95993,a869))),x95994)),x95995)),f329(f329(f107(f883(x95993,a869)),f329(f329(f42(x95992,f883(x95993,a869)),x95991),x95994)),x95995)) % 178.07/177.93 [9600]E(x96001,f193(f883(x96002,a869)))+E(f329(f329(f43(x96002,f883(x96003,a869)),x96001),f329(f329(f7(x96002,f883(x96003,a869),f883(x96003,a869)),f329(f329(f8(f883(x96003,a869),f883(f883(x96003,a869),f883(x96003,a869)),x96002),f116(f883(x96003,a869))),x96004)),x96005)),f329(f329(f116(f883(x96003,a869)),f329(f329(f43(x96002,f883(x96003,a869)),x96001),x96004)),x96005)) % 178.07/177.93 [9167]~P24(f329(f329(f243(a875),x91671),x91674))+E(f329(f329(f22(a875),f329(f329(f81(a875),f329(f329(f82(a875),x91671),x91672)),x91673)),f329(f329(f81(a875),f329(f329(f82(a875),x91674),x91672)),x91675)),f329(f329(f22(a875),x91673),f329(f329(f81(a875),f329(f329(f82(a875),f329(f329(f22(a875),x91674),x91671)),x91672)),x91675))) % 178.07/177.93 [9753]~P134(x97531)+E(f329(f165(x97531),f329(f329(f153(x97532,x97531),f329(f329(f7(x97532,x97531,x97531),f329(f329(f8(x97531,f883(x97531,x97531),x97532),f82(x97531)),x97533)),x97534)),x97535)),f329(f329(f82(x97531),f329(f165(x97531),f329(f329(f153(x97532,x97531),x97533),x97535))),x97534)) % 178.07/177.93 [9759]~P66(x97591)+E(f329(f165(x97591),f329(f329(f153(x97592,x97591),f329(f329(f18(x97592,x97591,x97591),f329(f329(f8(x97591,f883(x97591,x97591),x97592),f22(x97591)),x97593)),x97594)),x97595)),f329(f329(f22(x97591),f329(f165(x97591),f329(f329(f153(x97592,x97591),x97593),x97595))),f329(f165(x97591),f329(f329(f153(x97592,x97591),x97594),x97595)))) % 178.07/177.93 [9760]~P70(x97601)+E(f329(f165(x97601),f329(f329(f153(x97602,x97601),f329(f329(f18(x97602,x97601,x97601),f329(f329(f8(x97601,f883(x97601,x97601),x97602),f81(x97601)),x97603)),x97604)),x97605)),f329(f329(f81(x97601),f329(f165(x97601),f329(f329(f153(x97602,x97601),x97603),x97605))),f329(f165(x97601),f329(f329(f153(x97602,x97601),x97604),x97605)))) % 178.07/177.93 [9903]P24(f329(x99031,f329(f329(f181(x99032,x99033),x99034),x99035)))+~P24(f329(x99031,f329(f329(f181(x99032,x99033),f329(f329(f174(x99032),f329(f329(f241(a875),f329(f194(f876(x99032)),x99034)),f329(f194(f876(x99033)),x99035))),x99034)),f329(f329(f174(x99033),f329(f329(f241(a875),f329(f194(f876(x99032)),x99034)),f329(f194(f876(x99033)),x99035))),x99035)))) % 178.07/177.93 [10136]~P24(f329(f329(f331(f882(x101362,x101361)),f329(f329(f264(x101362,x101361),x101364),x101365)),f329(f284(x101361,x101362),x101363)))+P24(f329(f329(f253(x101361,x101362,f329(f329(f7(x101361,f883(f882(x101361,x101362),a869),f883(x101362,a869)),f329(f329(f8(f883(x101362,f883(f883(f882(x101361,x101362),a869),a869)),f883(f883(f882(x101361,x101362),a869),f883(x101362,a869)),x101361),f7(x101362,f883(f882(x101361,x101362),a869),a869)),f329(f329(f8(f883(x101362,f882(x101361,x101362)),f883(x101362,f883(f883(f882(x101361,x101362),a869),a869)),x101361),f329(f8(f882(x101361,x101362),f883(f883(f882(x101361,x101362),a869),a869),x101362),f331(f882(x101361,x101362)))),f264(x101361,x101362)))),x101363)),x101364),x101365)) % 178.07/177.93 [10145]P24(f329(f329(f331(f882(x101451,x101452)),f329(f329(f264(x101451,x101452),x101453),x101454)),f329(f284(x101452,x101451),x101455)))+~P24(f329(f329(f253(x101452,x101451,f329(f329(f7(x101452,f883(f882(x101452,x101451),a869),f883(x101451,a869)),f329(f329(f8(f883(x101451,f883(f883(f882(x101452,x101451),a869),a869)),f883(f883(f882(x101452,x101451),a869),f883(x101451,a869)),x101452),f7(x101451,f883(f882(x101452,x101451),a869),a869)),f329(f329(f8(f883(x101451,f882(x101452,x101451)),f883(x101451,f883(f883(f882(x101452,x101451),a869),a869)),x101452),f329(f8(f882(x101452,x101451),f883(f883(f882(x101452,x101451),a869),a869),x101451),f331(f882(x101452,x101451)))),f264(x101452,x101451)))),x101455)),x101453),x101454)) % 178.07/177.93 [9408]~P24(f329(f329(f243(a875),x94084),x94081))+E(f329(f329(f22(a875),f329(f329(f81(a875),f329(f329(f82(a875),x94081),x94082)),x94083)),f329(f329(f81(a875),f329(f329(f82(a875),x94084),x94082)),x94085)),f329(f329(f22(a875),f329(f329(f81(a875),f329(f329(f82(a875),f329(f329(f22(a875),x94081),x94084)),x94082)),x94083)),x94085)) % 178.07/177.93 [10154]P20(x101541,x101542,f329(f308(a872,f874(x101541),f329(f329(f18(a872,f883(x101541,f883(a871,a869)),f874(x101541)),f329(f329(f18(a872,a870,f883(f883(x101541,f883(a871,a869)),f874(x101541))),f329(f329(f8(f883(x101541,f883(a871,a869)),f883(a870,f883(f883(x101541,f883(a871,a869)),f874(x101541))),a872),f93(x101541)),x101543)),a26)),x101544)),x101545))+~P20(x101541,f329(f329(f116(f883(f874(x101541),a869)),x101542),f329(f308(a872,f874(x101541),f329(f329(f18(a872,f883(x101541,f883(a871,a869)),f874(x101541)),f329(f329(f18(a872,a870,f883(f883(x101541,f883(a871,a869)),f874(x101541))),f329(f329(f8(f883(x101541,f883(a871,a869)),f883(a870,f883(f883(x101541,f883(a871,a869)),f874(x101541))),a872),f93(x101541)),x101543)),a26)),x101544)),x101545)),f329(f308(a872,f874(x101541),f329(f329(f18(a872,f883(x101541,f883(a871,a869)),f874(x101541)),f329(f329(f18(a872,a870,f883(f883(x101541,f883(a871,a869)),f874(x101541))),f329(f329(f8(f883(x101541,f883(a871,a869)),f883(a870,f883(f883(x101541,f883(a871,a869)),f874(x101541))),a872),f93(x101541)),x101543)),f329(f329(f8(f879(a870),a870,a872),f240(a870)),a28))),x101544)),x101545)) % 178.07/177.93 [10155]P23(x101551,x101552,f329(f308(a872,f874(x101551),f329(f329(f18(a872,f883(x101551,f883(a871,a869)),f874(x101551)),f329(f329(f18(a872,a870,f883(f883(x101551,f883(a871,a869)),f874(x101551))),f329(f329(f8(f883(x101551,f883(a871,a869)),f883(a870,f883(f883(x101551,f883(a871,a869)),f874(x101551))),a872),f93(x101551)),x101553)),a26)),x101554)),x101555))+~P23(x101551,f329(f329(f116(f883(f874(x101551),a869)),x101552),f329(f308(a872,f874(x101551),f329(f329(f18(a872,f883(x101551,f883(a871,a869)),f874(x101551)),f329(f329(f18(a872,a870,f883(f883(x101551,f883(a871,a869)),f874(x101551))),f329(f329(f8(f883(x101551,f883(a871,a869)),f883(a870,f883(f883(x101551,f883(a871,a869)),f874(x101551))),a872),f93(x101551)),x101553)),a26)),x101554)),x101555)),f329(f308(a872,f874(x101551),f329(f329(f18(a872,f883(x101551,f883(a871,a869)),f874(x101551)),f329(f329(f18(a872,a870,f883(f883(x101551,f883(a871,a869)),f874(x101551))),f329(f329(f8(f883(x101551,f883(a871,a869)),f883(a870,f883(f883(x101551,f883(a871,a869)),f874(x101551))),a872),f93(x101551)),x101553)),f329(f329(f8(f879(a870),a870,a872),f240(a870)),a28))),x101554)),x101555)) % 178.07/177.93 [5237]E(x52371,x52372)+~E(f29(x52373,x52374,x52371),f29(x52375,x52376,x52372)) % 178.07/177.93 [5238]E(x52381,x52382)+~E(f29(x52383,x52381,x52384),f29(x52385,x52382,x52386)) % 178.07/177.93 [5239]E(x52391,x52392)+~E(f29(x52391,x52393,x52394),f29(x52392,x52395,x52396)) % 178.07/177.93 [5240]E(x52401,x52402)+~E(f31(x52403,x52404,x52401),f31(x52405,x52406,x52402)) % 178.07/177.93 [5241]E(x52411,x52412)+~E(f31(x52413,x52411,x52414),f31(x52415,x52412,x52416)) % 178.07/177.93 [5242]E(x52421,x52422)+~E(f31(x52421,x52423,x52424),f31(x52422,x52425,x52426)) % 178.07/177.93 [5243]E(x52431,x52432)+~E(f30(x52433,x52434,x52431),f30(x52435,x52436,x52432)) % 178.07/177.93 [5244]E(x52441,x52442)+~E(f30(x52443,x52441,x52444),f30(x52445,x52442,x52446)) % 178.07/177.93 [5245]E(x52451,x52452)+~E(f30(x52451,x52453,x52454),f30(x52452,x52455,x52456)) % 178.07/177.93 [6686]E(f329(f184(x66861,x66862,x66863,x66864),x66865),f329(f236(x66862),x66866))+~E(f329(x66864,x66865),f329(f236(x66862),x66866)) % 178.07/177.93 [6829]E(f329(f238(f879(x68291),x68292,f206(x68291),x68293),f329(x68294,x68295)),f329(x68293,x68296))+~E(f329(x68294,x68295),f329(f236(x68292),x68296)) % 178.07/177.93 [8356]~P15(x83565,x83561,x83562,x83566)+E(f329(f74(x83561,x83561,x83561,f329(x83562,x83563)),f329(x83562,x83564)),f329(f74(x83561,x83561,x83561,f329(x83562,x83564)),f329(x83562,x83563))) % 178.07/177.93 [8594]~P52(x85944,x85945,x85942,x85941,x85946)+E(f329(x85941,f329(x85942,x85943)),x85943) % 178.07/177.93 [8746]P21(x87461,x87462,x87463,x87464)+~P21(x87461,x87465,f329(f74(x87462,x87465,x87461,x87466),x87463),x87464) % 178.07/177.93 [8829]~P21(x88294,x88292,f329(f74(x88291,x88292,x88294,x88293),x88295),x88296)+P21(x88291,x88292,x88293,f329(f308(x88294,x88291,x88295),x88296)) % 178.07/177.93 [9538]P24(f329(f62(x95381),x95382))+~P24(f329(f67(x95381,x95383,x95384,x95385,x95382),x95386)) % 178.07/177.93 [9546]~P24(f329(f329(f331(x95464),x95463),f297(x95464,x95465,x95461,x95462,x95466)))+P24(f329(f329(x95461,x95462),x95463)) % 178.07/177.93 [9547]~P24(f329(f329(f331(x95474),x95473),f294(x95474,x95471,x95475,x95472,x95476)))+P24(f329(f329(x95471,x95472),x95473)) % 178.07/177.93 [9548]~P24(f329(f329(f331(x95484),x95482),f297(x95484,x95481,x95485,x95486,x95483)))+P24(f329(f329(x95481,x95482),x95483)) % 178.07/177.93 [9549]~P24(f329(f329(f331(x95494),x95492),f294(x95494,x95495,x95491,x95496,x95493)))+P24(f329(f329(x95491,x95492),x95493)) % 178.07/177.93 [5740]E(x57401,x57402)+~E(f329(f329(f264(x57403,x57404),x57405),x57401),f329(f329(f264(x57403,x57404),x57406),x57402)) % 178.07/177.93 [5742]E(x57421,x57422)+~E(f329(f329(f264(x57423,x57424),x57421),x57425),f329(f329(f264(x57423,x57424),x57422),x57426)) % 178.07/177.93 [5866]~P12(x58665,x58666,x58661)+E(f329(f329(x58661,x58662),f329(f329(x58661,x58663),x58664)),f329(f329(x58661,x58663),f329(f329(x58661,x58662),x58664))) % 178.07/177.93 [7285]~P33(x72854,x72851,f329(f329(f150(x72854),x72852),x72855),f329(f329(f150(x72854),x72853),x72856))+P24(f329(f329(x72851,x72852),x72853)) % 178.07/177.93 [7653]P33(x76531,x76532,x76533,x76534)+~P33(x76531,x76532,f329(f329(f150(x76531),x76535),x76533),f329(f329(f150(x76531),x76536),x76534)) % 178.07/177.93 [8689]~P52(x86895,x86891,x86892,x86896,x86894)+P24(f329(f329(f331(x86891),f329(x86892,x86893)),x86894)) % 178.07/177.93 [8857]E(f329(f77(x88571,x88572,x88573,x88574,x88575),x88576),f329(x88573,x88576))+P24(f329(f329(f331(x88571),x88576),x88575)) % 178.07/177.93 [8878]~E(x88783,f329(f329(f150(x88781),x88785),x88786))+P24(f329(f329(f331(f882(f876(x88781),f876(x88781))),f329(f329(f264(f876(x88781),f876(x88781)),x88782),f329(f329(f127(x88781),x88782),x88783))),f146(x88781,x88784))) % 178.07/177.93 [8885]E(f329(f77(x88851,x88852,x88853,x88854,x88855),x88856),f329(x88854,x88856))+~P24(f329(f329(f331(x88851),x88856),x88855)) % 178.07/177.93 [8890]E(f329(f186(x88901,x88902,x88903,x88904,x88905),x88906),f329(x88903,x88906))+P24(f329(f329(f331(x88901),x88906),f329(f171(x88901),x88904))) % 178.07/177.93 [9118]~P35(x91181,x91182,x91183,x91185,x91186)+P35(x91181,x91182,x91183,f329(f329(f174(x91181),x91184),x91185),f329(f329(f174(x91182),x91184),x91186)) % 178.07/177.93 [9119]~P35(x91191,x91192,x91193,x91195,x91196)+P35(x91191,x91192,x91193,f329(f329(f137(x91191),x91194),x91195),f329(f329(f137(x91192),x91194),x91196)) % 178.07/177.93 [9610]~P19(x96104,x96102,x96105,x96103,x96106,x96101)+E(f329(x96101,f193(f883(x96102,a869))),x96103) % 178.07/177.93 [9853]~E(f329(x98534,f329(f263(x98531,x98533),x98535)),f329(x98536,f329(f263(x98531,x98533),x98535)))+E(f329(f269(x98531,x98532,x98533,x98533,x98534,f35(x98533)),x98535),f329(f269(x98531,x98532,x98533,x98533,x98536,f35(x98533)),x98535)) % 178.07/177.93 [9854]~E(f329(x98544,f329(f267(x98541,x98542),x98545)),f329(x98546,f329(f267(x98541,x98542),x98545)))+E(f329(f269(x98541,x98541,x98542,x98543,f35(x98541),x98544),x98545),f329(f269(x98541,x98541,x98542,x98543,f35(x98541),x98546),x98545)) % 178.07/177.93 [9899]~E(f329(f269(x98992,x98996,x98993,x98993,x98991,f35(x98993)),x98994),f329(f269(x98992,x98996,x98993,x98993,x98995,f35(x98993)),x98994))+E(f329(x98991,f329(f263(x98992,x98993),x98994)),f329(x98995,f329(f263(x98992,x98993),x98994))) % 178.07/177.93 [9900]~E(f329(f269(x99002,x99002,x99003,x99006,f35(x99002),x99001),x99004),f329(f269(x99002,x99002,x99003,x99006,f35(x99002),x99005),x99004))+E(f329(x99001,f329(f267(x99002,x99003),x99004)),f329(x99005,f329(f267(x99002,x99003),x99004))) % 178.07/177.93 [8785]P24(f329(f329(f331(x87851),x87852),x87853))+~P24(f329(f329(f331(f882(x87851,x87854)),f329(f329(f264(x87851,x87854),x87852),x87855)),f329(f329(f266(x87851,x87854),x87853),x87856))) % 178.07/177.93 [8799]P24(f329(f329(f331(x87991),x87992),f329(x87993,x87994)))+~P24(f329(f329(f331(f882(x87995,x87991)),f329(f329(f264(x87995,x87991),x87994),x87992)),f329(f329(f266(x87995,x87991),x87996),x87993))) % 178.07/177.93 [8887]~E(f329(f194(f876(x88871)),x88874),f329(f194(f876(x88872)),x88875))+E(f186(x88871,x88872,x88873,x88874,f329(f329(f127(x88872),x88875),x88876)),f186(x88871,x88872,x88873,x88874,x88875)) % 178.07/177.93 [8888]~E(f329(f194(f876(x88881)),x88884),f329(f194(f876(x88882)),x88886))+E(f186(x88881,x88882,x88883,f329(f329(f127(x88881),x88884),x88885),x88886),f186(x88881,x88882,x88883,x88884,x88886)) % 178.07/177.93 [9139]P24(f329(f329(f331(x91391),x91394),f183(x91391,x91392,x91396)))+E(f184(x91391,x91392,f329(f329(f329(f73(x91391,f879(x91392)),x91393),x91394),f329(f236(x91392),x91395)),x91396),f329(f329(f329(f73(x91391,f879(x91392)),f184(x91391,x91392,x91393,x91396)),x91394),f329(f236(x91392),x91395))) % 178.07/177.93 [9239]P24(f329(f329(f331(f882(x92391,x92391)),f329(f329(f264(x92391,x92391),f329(x92392,x92393)),f329(x92392,x92394))),x92395))+~P24(f329(f329(f331(f882(x92396,x92396)),f329(f329(f264(x92396,x92396),x92393),x92394)),f329(f329(f285(x92391,x92396),x92395),x92392))) % 178.07/177.93 [9259]~P24(f329(f329(f331(f882(x92594,x92594)),f329(f329(f264(x92594,x92594),f329(x92596,x92592)),f329(x92596,x92593))),x92595))+P24(f329(f329(f331(f882(x92591,x92591)),f329(f329(f264(x92591,x92591),x92592),x92593)),f329(f329(f285(x92594,x92591),x92595),x92596))) % 178.07/177.93 [9902]E(f329(f329(f264(x99021,x99022),f797(x99023,x99024,x99025,x99026,x99022,x99021)),f798(x99023,x99024,x99025,x99026,x99022,x99021)),x99026)+~P24(f329(f329(f331(f882(x99021,x99022)),x99026),f329(f329(f286(x99021,x99025,x99022),x99024),x99023))) % 178.07/177.93 [10102]~P24(f329(f329(f331(f882(x101021,x101026)),x101025),f329(f329(f286(x101021,x101022,x101026),x101024),x101023)))+P24(f329(f329(f331(f882(x101021,x101022)),f329(f329(f264(x101021,x101022),f797(x101023,x101024,x101022,x101025,x101026,x101021)),f799(x101023,x101024,x101022,x101025,x101026,x101021))),x101024)) % 178.07/177.93 [10103]~P24(f329(f329(f331(f882(x101036,x101032)),x101035),f329(f329(f286(x101036,x101031,x101032),x101034),x101033)))+P24(f329(f329(f331(f882(x101031,x101032)),f329(f329(f264(x101031,x101032),f799(x101033,x101034,x101031,x101035,x101032,x101036)),f798(x101033,x101034,x101031,x101035,x101032,x101036))),x101033)) % 178.07/177.93 [6149]~E(x61496,x61494)+E(f329(f329(f329(f329(f73(x61491,x61492),x61493),x61494),x61495),x61496),x61495) % 178.07/177.93 [6197]E(x61971,x61972)+E(f329(f329(f329(f329(f73(x61973,x61974),x61975),x61972),x61976),x61971),f329(x61975,x61971)) % 178.07/177.93 [7723]~P27(x77232)+E(f329(f329(f42(x77231,x77232),x77233),f329(f329(f7(x77231,x77234,x77232),x77235),x77236)),f329(f329(f329(f42(x77231,f883(x77234,x77232)),x77233),x77235),x77236)) % 178.07/177.93 [7724]~P27(x77242)+E(f329(f329(f43(x77241,x77242),x77243),f329(f329(f7(x77241,x77244,x77242),x77245),x77246)),f329(f329(f329(f43(x77241,f883(x77244,x77242)),x77243),x77245),x77246)) % 178.07/177.93 [8509]E(f329(f329(f43(x85091,f883(x85092,a869)),x85093),f329(f329(f8(f883(x85092,a869),f883(x85092,a869),x85091),f329(f307(x85092),x85094)),x85095)),f329(f329(f307(x85092),x85094),f329(f329(f43(x85091,f883(x85092,a869)),x85093),x85095)))+~P24(f329(f329(f331(x85091),x85096),x85093)) % 178.07/177.93 [8940]~P27(x89402)+E(f329(f329(f42(x89401,x89402),x89403),f329(f329(f8(f883(x89404,x89402),x89402,x89401),f329(f42(x89404,x89402),x89405)),f329(f7(x89404,x89401,x89402),x89406))),f329(f329(f42(x89404,x89402),x89405),f329(f329(f8(f883(x89401,x89402),x89402,x89404),f329(f42(x89401,x89402),x89403)),x89406))) % 178.07/177.93 [8941]~P27(x89412)+E(f329(f329(f43(x89411,x89412),x89413),f329(f329(f8(f883(x89414,x89412),x89412,x89411),f329(f43(x89414,x89412),x89415)),f329(f7(x89414,x89411,x89412),x89416))),f329(f329(f43(x89414,x89412),x89415),f329(f329(f8(f883(x89411,x89412),x89412,x89414),f329(f43(x89411,x89412),x89413)),x89416))) % 178.07/177.93 [9148]P24(f329(f329(f331(x91481),x91482),f329(f171(x91481),x91483)))+~P24(f329(f329(f331(f882(x91484,x91481)),f329(f329(f264(x91484,x91481),x91485),x91482)),f329(f171(f882(x91484,x91481)),f329(f329(f181(x91484,x91481),x91486),x91483)))) % 178.07/177.93 [9149]P24(f329(f329(f331(x91491),x91492),f329(f171(x91491),x91493)))+~P24(f329(f329(f331(f882(x91491,x91494)),f329(f329(f264(x91491,x91494),x91492),x91495)),f329(f171(f882(x91491,x91494)),f329(f329(f181(x91491,x91494),x91493),x91496)))) % 178.07/177.93 [9253]P24(f329(f329(f243(f883(x92531,a869)),f329(f283(x92532,x92531,x92533),x92534)),x92535))+~P24(f329(f329(f243(f883(f882(x92532,x92531),a869)),x92533),f329(f329(f266(x92532,x92531),x92536),f329(f16(f883(x92531,a869),x92532),x92535)))) % 178.07/177.93 [9443]P24(f329(f329(f331(f882(f876(x94431),f876(x94431))),f329(f329(f264(f876(x94431),f876(x94431)),f329(f329(f150(x94431),x94432),x94433)),f329(f329(f150(x94431),x94434),x94435))),f146(x94431,x94436)))+~P24(f329(f329(f331(f882(x94431,x94431)),f329(f329(f264(x94431,x94431),x94432),x94434)),x94436)) % 178.07/177.93 [9898]E(f329(f329(f264(x98981,x98982),f721(x98983,x98984,x98985,x98982,x98981,x98986)),f722(x98983,x98984,x98985,x98982,x98981,x98986)),x98986)+P24(f329(f329(f331(x98985),x98984),f329(f329(f268(x98981,x98982,f883(x98985,a869)),x98983),x98986))) % 178.07/177.93 [9904]E(f329(f329(f264(x99041,x99042),f723(x99043,x99044,x99042,x99041,x99045,x99046)),f724(x99043,x99044,x99042,x99041,x99045,x99046)),x99043)+~P24(f329(f329(f331(x99046),x99045),f329(f329(f268(x99041,x99042,f883(x99046,a869)),x99044),x99043))) % 178.07/177.93 [10061]P24(f329(f329(f331(x100611),x100612),f329(f329(x100613,f723(x100614,x100613,x100615,x100616,x100612,x100611)),f724(x100614,x100613,x100615,x100616,x100612,x100611))))+~P24(f329(f329(f331(x100611),x100612),f329(f329(f268(x100616,x100615,f883(x100611,a869)),x100613),x100614))) % 178.07/177.93 [10080]~P24(f329(f329(f331(x100801),x100802),f329(f329(x100805,f721(x100805,x100802,x100801,x100804,x100803,x100806)),f722(x100805,x100802,x100801,x100804,x100803,x100806))))+P24(f329(f329(f331(x100801),x100802),f329(f329(f268(x100803,x100804,f883(x100801,a869)),x100805),x100806))) % 178.07/177.93 [7842]P24(f329(f329(f331(x78421),x78424),x78426))+E(f187(x78421,x78422,f329(f329(f329(f73(x78421,f879(x78422)),x78423),x78424),x78425),x78426),f187(x78421,x78422,x78423,x78426)) % 178.07/177.93 [7919]P24(f329(f329(f331(x79191),x79194),x79196))+E(f329(f308(x79191,x79192,f329(f329(f329(f73(x79191,x79192),x79193),x79194),x79195)),x79196),f329(f308(x79191,x79192,x79193),x79196)) % 178.07/177.93 [7946]P24(f329(f329(f331(x79461),x79464),f329(f171(x79461),x79466)))+E(f329(f329(f153(x79461,x79462),f329(f329(f329(f73(x79461,x79462),x79463),x79464),x79465)),x79466),f329(f329(f153(x79461,x79462),x79463),x79466)) % 178.07/177.93 [8404]E(x84041,x84042)+E(f329(f329(f158(x84043,f329(f329(f158(x84043,x84044),x84041),x84045)),x84042),x84046),f329(f329(f158(x84043,f329(f329(f158(x84043,x84044),x84042),x84046)),x84041),x84045)) % 178.07/177.93 [8946]~P24(f329(f329(f331(x89463),x89466),x89465))+E(f329(f329(f307(x89461),x89462),f329(f308(x89463,x89461,x89464),f329(f329(f22(f883(x89463,a869)),x89465),f329(f329(f307(x89463),x89466),f193(f883(x89463,a869)))))),f329(f308(x89463,x89461,f329(f329(f329(f73(x89463,x89461),x89464),x89466),x89462)),x89465)) % 178.07/177.93 [9715]E(f186(x97151,x97152,x97153,f329(f329(f127(x97151),x97154),f329(f329(f150(x97151),x97155),f119(x97151))),x97156),f329(f329(f329(f73(x97151,f879(x97152)),f186(x97151,x97152,x97153,x97154,x97156)),x97155),f329(f236(x97152),f329(f329(f164(x97152),x97156),f329(f194(f876(x97151)),x97154)))))+~P24(f329(f329(f244(a875),f329(f194(f876(x97151)),x97154)),f329(f194(f876(x97152)),x97156))) % 178.07/177.93 [8728]~E(x87283,x87286)+E(f329(f329(f177(x87281,x87282),f329(f329(f150(f882(x87281,x87282)),f329(f329(f264(x87281,x87282),x87283),x87284)),x87285)),x87286),f329(f236(x87282),x87284)) % 178.07/177.93 [8755]E(x87551,x87552)+E(f329(f329(f177(x87553,x87554),f329(f329(f150(f882(x87553,x87554)),f329(f329(f264(x87553,x87554),x87551),x87555)),x87556)),x87552),f329(f329(f177(x87553,x87554),x87556),x87552)) % 178.07/177.93 [9023]~P24(f329(f329(x90234,x90235),x90236))+P24(f329(f329(f329(f329(f116(f883(x90231,f883(x90232,a869))),x90233),x90234),x90235),x90236)) % 178.07/177.93 [9025]~P24(f329(f329(x90253,x90255),x90256))+P24(f329(f329(f329(f329(f116(f883(x90251,f883(x90252,a869))),x90253),x90254),x90255),x90256)) % 178.07/177.93 [9310]P24(f329(f329(x93101,x93102),x93103))+~P24(f329(f329(f329(f329(f107(f883(x93104,f883(x93105,a869))),x93106),x93101),x93102),x93103)) % 178.07/177.93 [9311]P24(f329(f329(x93111,x93112),x93113))+~P24(f329(f329(f329(f329(f107(f883(x93114,f883(x93115,a869))),x93111),x93116),x93112),x93113)) % 178.07/177.93 [9737]~P70(x97372)+E(f329(f329(f6(x97371,x97372),f329(f329(f7(x97371,f883(x97373,a869),x97372),f329(f329(f8(f883(x97373,x97372),f883(f883(x97373,a869),x97372),x97371),f6(x97373,x97372)),x97374)),x97375)),x97376),f329(f329(f6(f882(x97371,x97373),x97372),f329(f268(x97371,x97373,x97372),x97374)),f329(f329(f266(x97371,x97373),x97376),f329(f16(f883(x97373,a869),x97371),x97375)))) % 178.07/177.93 [9738]~P74(x97382)+E(f329(f329(f9(x97381,x97382),f329(f329(f7(x97381,f883(x97383,a869),x97382),f329(f329(f8(f883(x97383,x97382),f883(f883(x97383,a869),x97382),x97381),f9(x97383,x97382)),x97384)),x97385)),x97386),f329(f329(f9(f882(x97381,x97383),x97382),f329(f268(x97381,x97383,x97382),x97384)),f329(f329(f266(x97381,x97383),x97386),f329(f16(f883(x97383,a869),x97381),x97385)))) % 178.07/177.93 [9881]~P70(x98812)+E(f329(f329(f6(x98811,x98812),f329(f329(f7(x98811,f883(x98813,a869),x98812),f329(f329(f8(f883(x98813,x98812),f883(f883(x98813,a869),x98812),x98811),f6(x98813,x98812)),f329(f7(x98813,x98811,x98812),x98814))),x98815)),x98816),f329(f329(f6(x98813,x98812),f329(f329(f7(x98813,f883(x98811,a869),x98812),f329(f329(f8(f883(x98811,x98812),f883(f883(x98811,a869),x98812),x98813),f6(x98811,x98812)),x98814)),x98816)),x98815)) % 178.07/177.93 [9579]~P24(f329(f329(f331(x95791),x95795),x95794))+E(f329(f329(f329(f73(x95791,f879(x95792)),f187(x95791,x95792,x95793,f329(f329(f22(f883(x95791,a869)),x95794),f329(f329(f307(x95791),x95795),f193(f883(x95791,a869)))))),x95795),x95796),f187(x95791,x95792,f329(f329(f329(f73(x95791,f879(x95792)),x95793),x95795),x95796),x95794)) % 178.07/177.93 [10158]~P24(f329(f329(f331(f882(x101581,x101582)),f329(f329(f264(x101581,x101582),x101585),x101586)),f329(f329(f116(f883(f882(x101581,x101582),a869)),x101583),x101584)))+P24(f329(f329(f329(f329(f116(f883(x101581,f883(x101582,a869))),f329(f329(f7(x101581,f883(f882(x101581,x101582),a869),f883(x101582,a869)),f329(f329(f8(f883(x101582,f883(f883(f882(x101581,x101582),a869),a869)),f883(f883(f882(x101581,x101582),a869),f883(x101582,a869)),x101581),f7(x101582,f883(f882(x101581,x101582),a869),a869)),f329(f329(f8(f883(x101582,f882(x101581,x101582)),f883(x101582,f883(f883(f882(x101581,x101582),a869),a869)),x101581),f329(f8(f882(x101581,x101582),f883(f883(f882(x101581,x101582),a869),a869),x101582),f331(f882(x101581,x101582)))),f264(x101581,x101582)))),x101583)),f329(f329(f7(x101581,f883(f882(x101581,x101582),a869),f883(x101582,a869)),f329(f329(f8(f883(x101582,f883(f883(f882(x101581,x101582),a869),a869)),f883(f883(f882(x101581,x101582),a869),f883(x101582,a869)),x101581),f7(x101582,f883(f882(x101581,x101582),a869),a869)),f329(f329(f8(f883(x101582,f882(x101581,x101582)),f883(x101582,f883(f883(f882(x101581,x101582),a869),a869)),x101581),f329(f8(f882(x101581,x101582),f883(f883(f882(x101581,x101582),a869),a869),x101582),f331(f882(x101581,x101582)))),f264(x101581,x101582)))),x101584)),x101585),x101586)) % 178.07/177.93 [10159]~P24(f329(f329(f331(f882(x101591,x101592)),f329(f329(f264(x101591,x101592),x101595),x101596)),f329(f329(f107(f883(f882(x101591,x101592),a869)),x101593),x101594)))+P24(f329(f329(f329(f329(f107(f883(x101591,f883(x101592,a869))),f329(f329(f7(x101591,f883(f882(x101591,x101592),a869),f883(x101592,a869)),f329(f329(f8(f883(x101592,f883(f883(f882(x101591,x101592),a869),a869)),f883(f883(f882(x101591,x101592),a869),f883(x101592,a869)),x101591),f7(x101592,f883(f882(x101591,x101592),a869),a869)),f329(f329(f8(f883(x101592,f882(x101591,x101592)),f883(x101592,f883(f883(f882(x101591,x101592),a869),a869)),x101591),f329(f8(f882(x101591,x101592),f883(f883(f882(x101591,x101592),a869),a869),x101592),f331(f882(x101591,x101592)))),f264(x101591,x101592)))),x101593)),f329(f329(f7(x101591,f883(f882(x101591,x101592),a869),f883(x101592,a869)),f329(f329(f8(f883(x101592,f883(f883(f882(x101591,x101592),a869),a869)),f883(f883(f882(x101591,x101592),a869),f883(x101592,a869)),x101591),f7(x101592,f883(f882(x101591,x101592),a869),a869)),f329(f329(f8(f883(x101592,f882(x101591,x101592)),f883(x101592,f883(f883(f882(x101591,x101592),a869),a869)),x101591),f329(f8(f882(x101591,x101592),f883(f883(f882(x101591,x101592),a869),a869),x101592),f331(f882(x101591,x101592)))),f264(x101591,x101592)))),x101594)),x101595),x101596)) % 178.07/177.93 [10165]P24(f329(f329(f331(f882(x101651,x101652)),f329(f329(f264(x101651,x101652),x101653),x101654)),f329(f329(f116(f883(f882(x101651,x101652),a869)),x101655),x101656)))+~P24(f329(f329(f329(f329(f116(f883(x101651,f883(x101652,a869))),f329(f329(f7(x101651,f883(f882(x101651,x101652),a869),f883(x101652,a869)),f329(f329(f8(f883(x101652,f883(f883(f882(x101651,x101652),a869),a869)),f883(f883(f882(x101651,x101652),a869),f883(x101652,a869)),x101651),f7(x101652,f883(f882(x101651,x101652),a869),a869)),f329(f329(f8(f883(x101652,f882(x101651,x101652)),f883(x101652,f883(f883(f882(x101651,x101652),a869),a869)),x101651),f329(f8(f882(x101651,x101652),f883(f883(f882(x101651,x101652),a869),a869),x101652),f331(f882(x101651,x101652)))),f264(x101651,x101652)))),x101655)),f329(f329(f7(x101651,f883(f882(x101651,x101652),a869),f883(x101652,a869)),f329(f329(f8(f883(x101652,f883(f883(f882(x101651,x101652),a869),a869)),f883(f883(f882(x101651,x101652),a869),f883(x101652,a869)),x101651),f7(x101652,f883(f882(x101651,x101652),a869),a869)),f329(f329(f8(f883(x101652,f882(x101651,x101652)),f883(x101652,f883(f883(f882(x101651,x101652),a869),a869)),x101651),f329(f8(f882(x101651,x101652),f883(f883(f882(x101651,x101652),a869),a869),x101652),f331(f882(x101651,x101652)))),f264(x101651,x101652)))),x101656)),x101653),x101654)) % 178.07/177.93 [10166]P24(f329(f329(f331(f882(x101661,x101662)),f329(f329(f264(x101661,x101662),x101663),x101664)),f329(f329(f107(f883(f882(x101661,x101662),a869)),x101665),x101666)))+~P24(f329(f329(f329(f329(f107(f883(x101661,f883(x101662,a869))),f329(f329(f7(x101661,f883(f882(x101661,x101662),a869),f883(x101662,a869)),f329(f329(f8(f883(x101662,f883(f883(f882(x101661,x101662),a869),a869)),f883(f883(f882(x101661,x101662),a869),f883(x101662,a869)),x101661),f7(x101662,f883(f882(x101661,x101662),a869),a869)),f329(f329(f8(f883(x101662,f882(x101661,x101662)),f883(x101662,f883(f883(f882(x101661,x101662),a869),a869)),x101661),f329(f8(f882(x101661,x101662),f883(f883(f882(x101661,x101662),a869),a869),x101662),f331(f882(x101661,x101662)))),f264(x101661,x101662)))),x101665)),f329(f329(f7(x101661,f883(f882(x101661,x101662),a869),f883(x101662,a869)),f329(f329(f8(f883(x101662,f883(f883(f882(x101661,x101662),a869),a869)),f883(f883(f882(x101661,x101662),a869),f883(x101662,a869)),x101661),f7(x101662,f883(f882(x101661,x101662),a869),a869)),f329(f329(f8(f883(x101662,f882(x101661,x101662)),f883(x101662,f883(f883(f882(x101661,x101662),a869),a869)),x101661),f329(f8(f882(x101661,x101662),f883(f883(f882(x101661,x101662),a869),a869),x101662),f331(f882(x101661,x101662)))),f264(x101661,x101662)))),x101666)),x101663),x101664)) % 178.07/177.93 [10152]~P24(f329(f329(f331(f882(x101522,x101523)),f329(f329(f264(x101522,x101523),x101525),x101526)),f329(f329(f42(x101521,f883(f882(x101522,x101523),a869)),f252(f883(x101521,a869))),x101524)))+P24(f329(f329(f329(f329(f42(x101521,f883(x101522,f883(x101523,a869))),f252(f883(x101521,a869))),f329(f329(f8(f883(f882(x101522,x101523),a869),f883(x101522,f883(x101523,a869)),x101521),f329(f7(x101522,f883(f882(x101522,x101523),a869),f883(x101523,a869)),f329(f329(f8(f883(x101523,f883(f883(f882(x101522,x101523),a869),a869)),f883(f883(f882(x101522,x101523),a869),f883(x101523,a869)),x101522),f7(x101523,f883(f882(x101522,x101523),a869),a869)),f329(f329(f8(f883(x101523,f882(x101522,x101523)),f883(x101523,f883(f883(f882(x101522,x101523),a869),a869)),x101522),f329(f8(f882(x101522,x101523),f883(f883(f882(x101522,x101523),a869),a869),x101523),f331(f882(x101522,x101523)))),f264(x101522,x101523))))),x101524)),x101525),x101526)) % 178.07/177.93 [10153]~P24(f329(f329(f331(f882(x101532,x101533)),f329(f329(f264(x101532,x101533),x101535),x101536)),f329(f329(f43(x101531,f883(f882(x101532,x101533),a869)),f252(f883(x101531,a869))),x101534)))+P24(f329(f329(f329(f329(f43(x101531,f883(x101532,f883(x101533,a869))),f252(f883(x101531,a869))),f329(f329(f8(f883(f882(x101532,x101533),a869),f883(x101532,f883(x101533,a869)),x101531),f329(f7(x101532,f883(f882(x101532,x101533),a869),f883(x101533,a869)),f329(f329(f8(f883(x101533,f883(f883(f882(x101532,x101533),a869),a869)),f883(f883(f882(x101532,x101533),a869),f883(x101533,a869)),x101532),f7(x101533,f883(f882(x101532,x101533),a869),a869)),f329(f329(f8(f883(x101533,f882(x101532,x101533)),f883(x101533,f883(f883(f882(x101532,x101533),a869),a869)),x101532),f329(f8(f882(x101532,x101533),f883(f883(f882(x101532,x101533),a869),a869),x101533),f331(f882(x101532,x101533)))),f264(x101532,x101533))))),x101534)),x101535),x101536)) % 178.07/177.93 [10162]P24(f329(f329(f331(f882(x101621,x101622)),f329(f329(f264(x101621,x101622),x101623),x101624)),f329(f329(f42(x101625,f883(f882(x101621,x101622),a869)),f252(f883(x101625,a869))),x101626)))+~P24(f329(f329(f329(f329(f42(x101625,f883(x101621,f883(x101622,a869))),f252(f883(x101625,a869))),f329(f329(f8(f883(f882(x101621,x101622),a869),f883(x101621,f883(x101622,a869)),x101625),f329(f7(x101621,f883(f882(x101621,x101622),a869),f883(x101622,a869)),f329(f329(f8(f883(x101622,f883(f883(f882(x101621,x101622),a869),a869)),f883(f883(f882(x101621,x101622),a869),f883(x101622,a869)),x101621),f7(x101622,f883(f882(x101621,x101622),a869),a869)),f329(f329(f8(f883(x101622,f882(x101621,x101622)),f883(x101622,f883(f883(f882(x101621,x101622),a869),a869)),x101621),f329(f8(f882(x101621,x101622),f883(f883(f882(x101621,x101622),a869),a869),x101622),f331(f882(x101621,x101622)))),f264(x101621,x101622))))),x101626)),x101623),x101624)) % 178.07/177.93 [10163]P24(f329(f329(f331(f882(x101631,x101632)),f329(f329(f264(x101631,x101632),x101633),x101634)),f329(f329(f43(x101635,f883(f882(x101631,x101632),a869)),f252(f883(x101635,a869))),x101636)))+~P24(f329(f329(f329(f329(f43(x101635,f883(x101631,f883(x101632,a869))),f252(f883(x101635,a869))),f329(f329(f8(f883(f882(x101631,x101632),a869),f883(x101631,f883(x101632,a869)),x101635),f329(f7(x101631,f883(f882(x101631,x101632),a869),f883(x101632,a869)),f329(f329(f8(f883(x101632,f883(f883(f882(x101631,x101632),a869),a869)),f883(f883(f882(x101631,x101632),a869),f883(x101632,a869)),x101631),f7(x101632,f883(f882(x101631,x101632),a869),a869)),f329(f329(f8(f883(x101632,f882(x101631,x101632)),f883(x101632,f883(f883(f882(x101631,x101632),a869),a869)),x101631),f329(f8(f882(x101631,x101632),f883(f883(f882(x101631,x101632),a869),a869),x101632),f331(f882(x101631,x101632)))),f264(x101631,x101632))))),x101636)),x101633),x101634)) % 178.07/177.93 [7399]E(f329(x73991,f329(x73992,x73993)),f329(x73994,x73993))+~E(f329(f74(x73995,x73996,x73997,x73991),x73992),x73994) % 178.07/177.93 [9609]~P18(x96093,x96094,x96091,x96095,x96096,x96097)+E(f329(f329(x96091,x96092),x96092),x96092) % 178.07/177.93 [9978]~E(f329(f238(f879(x99787),x99781,f206(x99787),x99785),f329(x99784,x99783)),f329(f236(x99787),x99782))+E(f329(f236(x99781),f590(x99782,x99783,x99784,x99785,x99786,x99787,x99781)),f329(x99784,x99783)) % 178.07/177.93 [9979]~E(f329(f238(f879(x99796),x99797,f206(x99796),x99791),f329(x99794,x99793)),f329(f236(x99796),x99792))+E(f329(x99791,f590(x99792,x99793,x99794,x99791,x99795,x99796,x99797)),f329(f236(x99796),x99792)) % 178.07/177.93 [5970]~E(f329(f329(f153(x59701,x59705),x59706),x59702),f329(f329(f153(x59703,x59705),x59707),x59704))+E(f329(f194(f876(x59701)),x59702),f329(f194(f876(x59703)),x59704)) % 178.07/177.93 [7477]E(x74771,x74772)+~E(f329(f329(f329(f73(x74773,f879(x74774)),x74775),x74776),f329(f236(x74774),x74771)),f329(f329(f329(f73(x74773,f879(x74774)),x74777),x74776),f329(f236(x74774),x74772))) % 178.07/177.93 [8443]E(f329(x84431,f329(x84432,x84433)),f329(x84434,x84433))+~E(f329(f74(x84435,x84436,x84437,x84431),x84432),f329(f74(x84436,x84436,x84437,f35(x84436)),x84434)) % 178.07/177.93 [8774]~P35(x87744,x87745,x87741,f329(f329(f150(x87744),x87742),x87746),f329(f329(f150(x87745),x87743),x87747))+P24(f329(f329(x87741,x87742),x87743)) % 178.07/177.93 [9155]P35(x91551,x91552,x91553,x91554,x91555)+~P35(x91551,x91552,x91553,f329(f329(f150(x91551),x91556),x91554),f329(f329(f150(x91552),x91557),x91555)) % 178.07/177.93 [9776]P24(f329(f329(x97761,x97762),f697(x97763,x97762,x97764,x97761)))+~P24(f329(f329(f265(x97765,x97766,x97767,x97761,x97764),x97762),x97763)) % 178.07/177.93 [9797]P24(f329(f329(x97971,f697(x97972,x97973,x97971,x97974)),x97972))+~P24(f329(f329(f265(x97975,x97976,x97977,x97974,x97971),x97973),x97972)) % 178.07/177.93 [6015]E(x60151,x60152)+~E(f329(f329(f329(f93(x60153),x60154),x60155),x60151),f329(f329(f329(f93(x60153),x60156),x60157),x60152)) % 178.07/177.93 [6016]E(x60161,x60162)+~E(f329(f329(f329(f93(x60163),x60164),x60161),x60165),f329(f329(f329(f93(x60163),x60166),x60162),x60167)) % 178.07/177.93 [6017]E(x60171,x60172)+~E(f329(f329(f329(f93(x60173),x60171),x60174),x60175),f329(f329(f329(f93(x60173),x60172),x60176),x60177)) % 178.07/177.93 [8892]~P16(x88926,x88921,x88923,x88927)+E(f329(f74(x88921,x88921,x88922,f329(x88923,x88924)),f329(f74(x88921,x88921,x88922,f329(x88923,x88924)),x88925)),f329(f74(x88921,x88921,x88922,f329(x88923,x88924)),x88925)) % 178.07/177.93 [9262]~P35(x92623,x92622,x92624,f329(f329(f153(x92621,x92623),x92625),x92626),x92627)+P35(x92621,x92622,f329(f329(f8(x92623,f883(x92622,a869),x92621),x92624),x92625),x92626,x92627) % 178.07/177.93 [9285]P35(x92851,x92852,x92853,f329(f329(f153(x92854,x92851),x92855),x92856),x92857)+~P35(x92854,x92852,f329(f329(f8(x92851,f883(x92852,a869),x92854),x92853),x92855),x92856,x92857) % 178.07/177.93 [9695]E(f186(x96951,x96952,f329(f329(f329(f73(x96951,f879(x96952)),x96953),x96954),f329(f236(x96952),x96955)),x96956,x96957),f329(f329(f329(f73(x96951,f879(x96952)),f186(x96951,x96952,x96953,x96956,x96957)),x96954),f329(f236(x96952),x96955)))+P24(f329(f329(f331(x96951),x96954),f329(f171(x96951),x96956))) % 178.07/177.93 [8891]~P24(f329(f329(f331(x88911),x88912),f329(f329(x88915,x88916),x88917)))+P24(f329(f329(f331(x88911),x88912),f329(f329(f268(x88913,x88914,f883(x88911,a869)),x88915),f329(f329(f264(x88913,x88914),x88916),x88917)))) % 178.07/177.93 [9181]P24(f329(f329(f329(x91811,x91812),x91813),x91814))+~P24(f329(f329(f329(f268(x91815,x91816,f883(x91817,a869)),x91811),f329(f329(f264(x91815,x91816),x91812),x91813)),x91814)) % 178.07/177.93 [9324]P24(f329(f329(f331(x93241),f329(f329(x93242,x93243),x93244)),f329(f308(f882(x93245,x93246),x93241,f329(f268(x93245,x93246,x93241),x93242)),x93247)))+~P24(f329(f329(f331(f882(x93245,x93246)),f329(f329(f264(x93245,x93246),x93243),x93244)),x93247)) % 178.07/177.93 [9656]P24(f329(f329(f331(f882(f876(x96561),f876(x96561))),f329(f329(f264(f876(x96561),f876(x96561)),f329(f329(f127(x96561),x96562),f329(f329(f150(x96561),x96563),x96564))),f329(f329(f127(x96561),x96562),f329(f329(f150(x96561),x96565),x96566)))),f146(x96561,x96567)))+~P24(f329(f329(f331(f882(x96561,x96561)),f329(f329(f264(x96561,x96561),x96563),x96565)),x96567)) % 178.07/177.93 [9717]~P35(x97171,x97173,x97174,x97176,f329(f329(f153(x97172,x97173),x97175),x97177))+P35(x97171,x97172,f329(f329(f7(x97171,f883(x97172,x97173),f883(x97172,a869)),f329(f329(f8(f883(x97173,a869),f883(f883(x97172,x97173),f883(x97172,a869)),x97171),f8(x97173,a869,x97172)),x97174)),x97175),x97176,x97177) % 178.07/177.93 [9801]P35(x98011,x98012,x98013,x98014,f329(f329(f153(x98015,x98012),x98016),x98017))+~P35(x98011,x98015,f329(f329(f7(x98011,f883(x98015,x98012),f883(x98015,a869)),f329(f329(f8(f883(x98012,a869),f883(f883(x98015,x98012),f883(x98015,a869)),x98011),f8(x98012,a869,x98015)),x98013)),x98016),x98014,x98017) % 178.07/177.93 [9173]E(x91731,x91732)+E(f329(f329(f329(f73(x91733,x91734),f329(f329(f329(f73(x91733,x91734),x91735),x91731),x91736)),x91732),x91737),f329(f329(f329(f73(x91733,x91734),f329(f329(f329(f73(x91733,x91734),x91735),x91732),x91737)),x91731),x91736)) % 178.07/177.93 [9417]E(f186(x94171,x94172,f329(f329(f329(f73(x94171,f879(x94172)),x94173),x94174),f329(f236(x94172),x94175)),x94176,x94177),f186(x94171,x94172,x94173,x94176,x94177))+~P24(f329(f329(f331(x94171),x94174),f329(f171(x94171),f329(f329(f174(x94171),f329(f194(f876(x94172)),x94177)),x94176)))) % 178.07/177.93 [9728]E(f186(x97281,x97282,f329(f329(f329(f73(x97281,f879(x97282)),x97283),x97284),f329(f236(x97282),x97285)),x97286,x97287),f329(f329(f329(f73(x97281,f879(x97282)),f186(x97281,x97282,x97283,x97286,x97287)),x97284),f329(f236(x97282),x97285)))+P24(f329(f329(f331(x97281),x97284),f329(f171(x97281),f329(f329(f174(x97281),f329(f194(f876(x97282)),x97287)),x97286)))) % 178.07/177.93 [10091]P24(f329(f329(f331(x100911),f834(x100912,x100913,x100914,x100915,x100916,x100917,x100911)),x100915))+P24(f329(f329(f329(f329(f42(x100911,f883(x100917,f883(x100916,a869))),x100915),x100914),x100913),x100912)) % 178.07/177.93 [10092]P24(f329(f329(f331(x100921),f850(x100922,x100923,x100924,x100925,x100926,x100927,x100921)),x100925))+~P24(f329(f329(f329(f329(f43(x100921,f883(x100927,f883(x100926,a869))),x100925),x100924),x100923),x100922)) % 178.07/177.93 [10117]P24(f329(f329(f329(x101171,f850(x101172,x101173,x101171,x101174,x101175,x101176,x101177)),x101173),x101172))+~P24(f329(f329(f329(f329(f43(x101177,f883(x101176,f883(x101175,a869))),x101174),x101171),x101173),x101172)) % 178.07/177.93 [10134]~P24(f329(f329(f329(x101345,f834(x101347,x101346,x101345,x101344,x101343,x101342,x101341)),x101346),x101347))+P24(f329(f329(f329(f329(f42(x101341,f883(x101342,f883(x101343,a869))),x101344),x101345),x101346),x101347)) % 178.07/177.93 [10151]~P24(f329(f329(f331(f882(x101511,x101513)),f329(f329(f264(x101511,x101513),x101516),x101517)),f329(f329(f286(x101511,x101512,x101513),x101514),x101515)))+P24(f329(f329(f265(x101511,x101512,x101513,f329(f329(f7(x101511,f883(f882(x101511,x101512),a869),f883(x101512,a869)),f329(f329(f8(f883(x101512,f883(f883(f882(x101511,x101512),a869),a869)),f883(f883(f882(x101511,x101512),a869),f883(x101512,a869)),x101511),f7(x101512,f883(f882(x101511,x101512),a869),a869)),f329(f329(f8(f883(x101512,f882(x101511,x101512)),f883(x101512,f883(f883(f882(x101511,x101512),a869),a869)),x101511),f329(f8(f882(x101511,x101512),f883(f883(f882(x101511,x101512),a869),a869),x101512),f331(f882(x101511,x101512)))),f264(x101511,x101512)))),x101514),f329(f329(f7(x101512,f883(f882(x101512,x101513),a869),f883(x101513,a869)),f329(f329(f8(f883(x101513,f883(f883(f882(x101512,x101513),a869),a869)),f883(f883(f882(x101512,x101513),a869),f883(x101513,a869)),x101512),f7(x101513,f883(f882(x101512,x101513),a869),a869)),f329(f329(f8(f883(x101513,f882(x101512,x101513)),f883(x101513,f883(f883(f882(x101512,x101513),a869),a869)),x101512),f329(f8(f882(x101512,x101513),f883(f883(f882(x101512,x101513),a869),a869),x101513),f331(f882(x101512,x101513)))),f264(x101512,x101513)))),x101515)),x101516),x101517)) % 178.07/177.93 [10161]P24(f329(f329(f331(f882(x101611,x101612)),f329(f329(f264(x101611,x101612),x101613),x101614)),f329(f329(f286(x101611,x101615,x101612),x101616),x101617)))+~P24(f329(f329(f265(x101611,x101615,x101612,f329(f329(f7(x101611,f883(f882(x101611,x101615),a869),f883(x101615,a869)),f329(f329(f8(f883(x101615,f883(f883(f882(x101611,x101615),a869),a869)),f883(f883(f882(x101611,x101615),a869),f883(x101615,a869)),x101611),f7(x101615,f883(f882(x101611,x101615),a869),a869)),f329(f329(f8(f883(x101615,f882(x101611,x101615)),f883(x101615,f883(f883(f882(x101611,x101615),a869),a869)),x101611),f329(f8(f882(x101611,x101615),f883(f883(f882(x101611,x101615),a869),a869),x101615),f331(f882(x101611,x101615)))),f264(x101611,x101615)))),x101616),f329(f329(f7(x101615,f883(f882(x101615,x101612),a869),f883(x101612,a869)),f329(f329(f8(f883(x101612,f883(f883(f882(x101615,x101612),a869),a869)),f883(f883(f882(x101615,x101612),a869),f883(x101612,a869)),x101615),f7(x101612,f883(f882(x101615,x101612),a869),a869)),f329(f329(f8(f883(x101612,f882(x101615,x101612)),f883(x101612,f883(f883(f882(x101615,x101612),a869),a869)),x101615),f329(f8(f882(x101615,x101612),f883(f883(f882(x101615,x101612),a869),a869),x101612),f331(f882(x101615,x101612)))),f264(x101615,x101612)))),x101617)),x101613),x101614)) % 178.07/177.93 [10101]~P134(x101012)+E(f329(f329(f6(x101011,x101012),f329(f329(f7(x101011,f883(x101013,a869),x101012),f329(f329(f8(f883(x101013,x101012),f883(f883(x101013,a869),x101012),x101011),f6(x101013,x101012)),f329(f329(f7(x101011,f883(x101013,x101012),f883(x101013,x101012)),f329(f329(f8(f883(x101012,x101012),f883(f883(x101013,x101012),f883(x101013,x101012)),x101011),f8(x101012,x101012,x101013)),f329(f329(f8(x101012,f883(x101012,x101012),x101011),f82(x101012)),x101014))),x101015))),x101016)),x101017),f329(f329(f82(x101012),f329(f329(f6(x101011,x101012),x101014),x101017)),f329(f329(f6(x101013,x101012),x101015),x101016))) % 178.07/177.93 [9214]~P15(x92147,x92141,x92143,x92148)+E(f329(f74(x92141,x92141,x92142,f329(x92143,x92144)),f329(f74(x92141,x92141,x92142,f329(x92143,x92145)),x92146)),f329(f74(x92141,x92141,x92142,f329(x92143,x92145)),f329(f74(x92141,x92141,x92142,f329(x92143,x92144)),x92146))) % 178.07/177.93 [10156]E(f329(f329(f264(x101561,x101562),f329(x101563,f615(x101564,x101565,x101563,x101566,x101567,x101568,x101562,x101561))),f329(x101565,f616(x101564,x101565,x101563,x101566,x101567,x101568,x101562,x101561))),x101568)+~P24(f329(f329(f331(f882(x101561,x101562)),x101568),f329(f308(f882(x101567,x101566),f882(x101561,x101562),f269(x101567,x101561,x101566,x101562,x101563,x101565)),x101564))) % 178.07/177.93 [10172]~P24(f329(f329(f331(f882(x101728,x101727)),x101726),f329(f308(f882(x101721,x101722),f882(x101728,x101727),f269(x101721,x101728,x101722,x101727,x101725,x101724)),x101723)))+P24(f329(f329(f331(f882(x101721,x101722)),f329(f329(f264(x101721,x101722),f615(x101723,x101724,x101725,x101722,x101721,x101726,x101727,x101728)),f616(x101723,x101724,x101725,x101722,x101721,x101726,x101727,x101728))),x101723)) % 178.07/177.93 [9646]P24(f329(f329(f331(f882(f882(x96461,x96462),f882(x96461,x96462))),f329(f329(f264(f882(x96461,x96462),f882(x96461,x96462)),f329(f329(f264(x96461,x96462),x96463),x96464)),f329(f329(f264(x96461,x96462),x96465),x96466))),f321(x96461,x96462,x96467,x96468)))+~P24(f329(f329(f331(f882(x96461,x96461)),f329(f329(f264(x96461,x96461),x96463),x96465)),x96467)) % 178.07/177.93 [10144]E(f329(f141(x101441,x101442,f329(f7(x101442,x101441,x101441),x101443),f329(x101444,x101445)),x101446),f329(x101444,f329(f141(x101447,x101442,f329(f7(x101442,x101447,x101447),x101448),x101445),x101446)))+P24(f329(f329(f331(x101442),f706(x101445,x101448,x101444,x101443,x101447,x101441,x101446,x101442)),f329(f171(x101442),x101446))) % 178.07/177.93 [10164]~E(f329(f74(x101641,x101641,x101647,f329(x101643,f706(x101645,x101648,x101644,x101643,x101647,x101641,x101646,x101642))),x101644),f329(f74(x101647,x101641,x101647,x101644),f329(x101648,f706(x101645,x101648,x101644,x101643,x101647,x101641,x101646,x101642))))+E(f329(f141(x101641,x101642,f329(f7(x101642,x101641,x101641),x101643),f329(x101644,x101645)),x101646),f329(x101644,f329(f141(x101647,x101642,f329(f7(x101642,x101647,x101647),x101648),x101645),x101646))) % 178.07/177.93 [8449]E(f329(x84491,f329(x84492,x84493)),f329(x84494,f329(x84495,x84493)))+~E(f329(f74(x84496,x84497,x84498,x84491),x84492),f329(f74(x84499,x84497,x84498,x84494),x84495)) % 178.07/177.93 [10030]P24(f329(f329(f331(f882(x100301,x100302)),f329(f329(f264(x100301,x100302),f329(x100303,x100304)),f329(x100305,x100306))),f329(f308(f882(x100307,x100308),f882(x100301,x100302),f269(x100307,x100301,x100308,x100302,x100303,x100305)),x100309)))+~P24(f329(f329(f331(f882(x100307,x100308)),f329(f329(f264(x100307,x100308),x100304),x100306)),x100309)) % 178.07/177.93 [8722]~E(f329(x87224,f329(x87225,x87226)),f329(x87229,f329(x872210,x872211)))+E(f329(f329(f74(x87221,x87222,x87223,x87224),x87225),x87226),f329(f329(f74(x87227,x87222,x87228,x87229),x872210),x872211)) % 178.07/177.93 [4569]~P100(x45691)+~P105(x45691)+E(f107(x45691),f241(x45691)) % 178.07/177.93 [4570]~P99(x45701)+~P105(x45701)+E(f116(x45701),f242(x45701)) % 178.07/177.93 [4812]~P117(x48121)+~P92(x48121)+E(f329(f76(x48121),f329(f109(x48121),a103)),f79(x48121)) % 178.07/177.93 [5087]E(x50871,f2(a1))+E(f83(a1,x50871),f329(f80(a1),f79(a1)))+P24(f329(f329(f244(a1),f2(a1)),x50871)) % 178.07/177.93 [5303]E(x53031,f2(a1))+E(f83(a1,x53031),f79(a1))+~P24(f329(f329(f244(a1),f2(a1)),x53031)) % 178.07/177.93 [7289]~P39(x72891)+P24(f329(f62(a1),x72891))+~P24(f329(f62(a875),f329(f308(a1,a875,a110),x72891))) % 178.07/177.93 [8550]~P1(a5000)+~P24(f329(f329(f331(f882(a872,a870)),x85501),f329(f171(f882(a872,a870)),a27)))+P24(f329(f329(f268(a872,a870,a869),f329(f16(f883(a870,a869),a872),a25)),x85501)) % 178.07/177.93 [9608]E(x96081,f193(f883(f882(a875,a875),a869)))+~P24(f329(f62(f882(a875,a875)),x96081))+P24(f329(f329(f331(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869))),f329(f329(f264(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),f193(f883(f882(a875,a875),a869))),x96081)),a37)) % 178.07/177.93 [9777]E(x97771,f2(a875))+E(x97771,f329(a118,f2(a875)))+~P24(f329(f329(f244(a875),x97771),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))) % 178.07/177.93 [10058]E(x100581,f2(a105))+E(f329(f329(f81(a1),f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f329(a20,f329(f329(f39(a105),x100581),f329(f109(a105),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))))),f79(a1)),f329(a20,x100581))+E(f45(a105,x100581,f329(f109(a105),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f2(a105)) % 178.07/177.93 [9909]E(x99091,f2(a105))+~E(f45(a105,x99091,f329(f109(a105),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f2(a105))+E(f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f329(a20,f329(f329(f39(a105),x99091),f329(f109(a105),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))))),f329(a20,x99091)) % 178.07/177.93 [4642]~P53(x46421,x46422)+P44(x46421,x46422)+~P45(a869) % 178.07/177.93 [4579]~P141(x45791)+P31(x45791,x45792)+~E(x45792,f2(x45791)) % 178.07/177.93 [4580]~P105(x45801)+P29(x45801,x45802)+~E(x45802,f119(x45801)) % 178.07/177.93 [4589]~P117(x45891)+~E(x45892,f2(x45891))+E(f83(x45891,x45892),f2(x45891)) % 178.07/177.93 [4590]~P87(x45901)+~E(x45902,f2(x45901))+E(f83(x45901,x45902),f2(x45901)) % 178.07/177.93 [4598]~P141(x45982)+~P31(x45982,x45981)+E(x45981,f2(x45982)) % 178.07/177.93 [4632]~P117(x46322)+~E(f83(x46322,x46321),f2(x46322))+E(x46321,f2(x46322)) % 178.07/177.93 [4649]~P26(x46492)+~P26(x46491)+P26(f883(x46491,x46492)) % 178.07/177.93 [4650]~P26(x46502)+~P26(x46501)+P26(f881(x46501,x46502)) % 178.07/177.93 [4651]~P26(x46512)+~P26(x46511)+P26(f882(x46511,x46512)) % 178.07/177.93 [4652]~P28(x46522)+~P28(x46521)+P28(f200(x46521,x46522)) % 178.07/177.93 [4653]~P142(x46532)+~P142(x46531)+P142(f882(x46531,x46532)) % 178.07/177.93 [4654]~P58(x46542)+~P58(x46541)+P58(f883(x46541,x46542)) % 178.07/177.93 [4655]~P58(x46552)+~P58(x46551)+P58(f881(x46551,x46552)) % 178.07/177.93 [4656]~P58(x46562)+~P58(x46561)+P58(f882(x46561,x46562)) % 178.07/177.93 [4657]~P58(x46571)+~P94(x46572)+P94(f883(x46571,x46572)) % 178.07/177.93 [4783]~P105(x47831)+~P29(x47831,x47832)+P29(x47831,f151(x47831,x47832)) % 178.07/177.93 [5020]~P28(x50202)+~P28(x50201)+P28(f45(a1,x50201,x50202)) % 178.07/177.93 [4600]~P75(x46001)+~E(x46002,f2(x46001))+E(f329(f80(x46001),x46002),x46002) % 178.07/177.93 [4604]~P137(x46041)+~E(x46042,f2(a1))+E(f329(f108(x46041),x46042),f2(x46041)) % 178.07/177.93 [4605]~P91(x46051)+~E(x46052,f2(a1))+E(f329(f108(x46051),x46052),f2(x46051)) % 178.07/177.93 [4629]~P67(x46291)+~E(f2(x46291),x46292)+E(f329(f80(x46291),x46292),f2(x46291)) % 178.07/177.93 [4630]~P67(x46301)+~E(x46302,f2(x46301))+E(f329(f80(x46301),x46302),f2(x46301)) % 178.07/177.93 [4631]~P85(x46311)+~E(x46312,f2(x46311))+E(f329(f76(x46311),x46312),f2(x46311)) % 178.07/177.93 [4659]~P75(x46592)+E(x46591,f2(x46592))+~E(f329(f80(x46592),x46591),x46591) % 178.07/177.93 [4665]E(x46651,f329(a110,x46652))+~E(x46651,f2(a875))+~E(x46652,f329(f106(a1),x46651)) % 178.07/177.93 [4666]E(f329(a110,x46661),x46662)+~E(x46662,f2(a875))+~E(x46661,f329(f106(a1),x46662)) % 178.07/177.93 [4670]~P91(x46702)+E(x46701,f2(a1))+~E(f329(f108(x46702),x46701),f2(x46702)) % 178.07/177.93 [4675]~P67(x46752)+E(x46751,f2(x46752))+~E(f329(f80(x46752),x46751),f2(x46752)) % 178.07/177.93 [4676]~P85(x46762)+E(x46761,f2(x46762))+~E(f329(f76(x46762),x46761),f2(x46762)) % 178.07/177.93 [4677]~P67(x46771)+E(f2(x46771),x46772)+~E(f329(f80(x46771),x46772),f2(x46771)) % 178.07/177.93 [4817]~P1(a5000)+~E(f329(a28,x48172),f329(f236(a870),x48171))+P24(f329(a25,x48171)) % 178.07/177.93 [4859]~P105(x48591)+~P29(x48591,x48592)+P29(x48591,f329(f170(x48591),x48592)) % 178.07/177.93 [4885]~P24(x48852)+~P24(x48851)+P24(f329(f329(a327,x48851),x48852)) % 178.07/177.93 [4917]~E(f79(a875),f2(a875))+E(f329(f38(x49171),x49172),f2(a875))+~P24(f329(f62(x49171),x49172)) % 178.07/177.93 [4950]~P134(x49501)+~P112(x49501)+E(f329(f329(f254(x49501),f2(x49501)),f329(a118,x49502)),f2(x49501)) % 178.07/177.93 [4988]~P105(x49881)+P29(x49881,f138(x49881,x49882))+~P24(f329(f62(x49881),x49882)) % 178.07/177.93 [4989]~P105(x49891)+P29(x49891,f713(x49892,x49891))+~P24(f329(f62(x49891),x49892)) % 178.07/177.93 [5010]~P105(x50101)+E(f329(f171(x50101),f138(x50101,x50102)),x50102)+~P24(f329(f62(x50101),x50102)) % 178.07/177.93 [5011]~P105(x50111)+E(f329(f171(x50111),f713(x50112,x50111)),x50112)+~P24(f329(f62(x50111),x50112)) % 178.07/177.93 [5040]P24(x50401)+P24(x50402)+~P24(f329(f329(a328,x50402),x50401)) % 178.07/177.93 [5052]E(x50521,f193(f883(x50522,a869)))+~E(f329(f38(x50522),x50521),f2(a875))+~P24(f329(f62(x50522),x50521)) % 178.07/177.93 [5057]P24(x50571)+~P24(x50572)+~P24(f329(f329(a332,x50572),x50571)) % 178.07/177.93 [5105]~P73(x51051)+E(f329(f76(x51051),x51052),x51052)+P24(f329(f329(f244(x51051),x51052),f2(x51051))) % 178.07/177.93 [5176]~P58(x51762)+~P24(f329(f58(x51762),x51761))+P24(f329(x51761,f667(x51761,x51762))) % 178.07/177.93 [5177]~P58(x51772)+~P24(f329(f58(x51772),x51771))+P24(f329(x51771,f668(x51771,x51772))) % 178.07/177.93 [5204]~P24(f329(a25,x52042))+~P24(f329(a25,x52041))+P24(f329(a25,f34(x52041,x52042))) % 178.07/177.93 [5213]E(x52131,f119(x52132))+P24(f329(f136(x52132),f120(x52132,x52131)))+~P24(f329(f136(x52132),x52131)) % 178.07/177.93 [5218]~P105(x52181)+~P24(f329(f62(x52181),x52182))+P24(f329(f136(x52181),f138(x52181,x52182))) % 178.07/177.93 [5219]~P105(x52191)+~P24(f329(f62(x52191),x52192))+P24(f329(f136(x52191),f713(x52192,x52191))) % 178.07/177.93 [5225]~P137(x52251)+E(f329(f106(x52251),f329(a110,x52252)),f329(f108(x52251),x52252))+P24(f329(f329(f244(a1),x52252),f2(a1))) % 178.07/177.93 [5255]P5(x52552,x52551)+E(f329(x52551,f557(x52551)),f329(x52551,f562(x52551)))+P24(f329(f329(x52551,f557(x52551)),f562(x52551))) % 178.07/177.93 [5269]E(f329(f106(a1),f399(x52691,x52692)),x52691)+P24(f329(x52692,f329(a110,x52691)))+~P24(f329(x52692,f2(a875))) % 178.07/177.93 [5281]~P58(x52811)+~P24(f329(x52812,f669(x52812,x52811)))+P24(f329(f59(x52811),x52812)) % 178.07/177.93 [5282]~P58(x52821)+~P24(f329(x52822,f670(x52822,x52821)))+P24(f329(f59(x52821),x52822)) % 178.07/177.93 [5296]~P58(x52962)+~P36(x52962,x52961,f56(x52962))+P24(f329(x52961,f777(x52961,x52962))) % 178.07/177.93 [5312]~P117(x53121)+~E(f83(x53121,x53122),f329(f80(x53121),f79(x53121)))+P24(f329(f329(f244(x53121),x53122),f2(x53121))) % 178.07/177.93 [5388]~E(x53882,f2(a1))+E(f223(x53881,x53882),f329(f329(f264(a1,a1),f2(a1)),f79(a1)))+P24(f329(f329(f244(a1),x53882),f2(a1))) % 178.07/177.93 [5389]~E(x53891,f2(a1))+E(f223(x53891,x53892),f329(f329(f264(a1,a1),f2(a1)),f79(a1)))+P24(f329(f329(f244(a1),x53892),f2(a1))) % 178.07/177.93 [5441]E(f329(f106(a1),f399(x54411,x54412)),x54411)+P24(f329(x54412,f329(a110,x54411)))+P24(f329(f329(f244(a1),x54411),f2(a1))) % 178.07/177.93 [5504]~P117(x55041)+E(f83(x55041,x55042),f329(f80(x55041),f79(x55041)))+~P24(f329(f329(f244(x55041),x55042),f2(x55041))) % 178.07/177.93 [5505]~P85(x55051)+E(f329(f76(x55051),x55052),f329(f80(x55051),x55052))+~P24(f329(f329(f244(x55051),x55052),f2(x55051))) % 178.07/177.93 [5506]~P85(x55061)+E(f329(f76(x55061),x55062),f329(f80(x55061),x55062))+~P24(f329(f329(f243(x55061),x55062),f2(x55061))) % 178.07/177.93 [5507]~P73(x55071)+E(f329(f76(x55071),x55072),f329(f80(x55071),x55072))+~P24(f329(f329(f244(x55071),x55072),f2(x55071))) % 178.07/177.93 [5601]~P24(f329(x56011,f399(x56012,x56011)))+P24(f329(x56011,f329(a110,x56012)))+~P24(f329(x56011,f2(a875))) % 178.07/177.93 [5608]E(x56081,f2(a875))+E(f329(a118,f358(x56082,x56081)),x56081)+~P24(f329(f329(f244(a875),x56081),f329(a118,x56082))) % 178.07/177.93 [5612]P5(x56121,x56122)+~E(f329(x56122,f557(x56122)),f329(x56122,f562(x56122)))+~P24(f329(f329(x56122,f557(x56122)),f562(x56122))) % 178.07/177.93 [5632]~P105(x56321)+P29(x56321,x56322)+P24(f329(f329(f243(a875),f646(x56322,x56321)),f647(x56322,x56321))) % 178.07/177.93 [5633]~P105(x56331)+P29(x56331,x56332)+P24(f329(f329(f243(a875),f652(x56332,x56331)),f662(x56332,x56331))) % 178.07/177.93 [5720]~P85(x57201)+~E(x57202,f2(x57201))+P24(f329(f329(f243(x57201),f329(f76(x57201),x57202)),f2(x57201))) % 178.07/177.93 [5799]~P58(x57992)+~P58(x57991)+E(f60(x57991,x57992,f56(x57991),f56(x57992)),f56(f882(x57991,x57992))) % 178.07/177.93 [5803]~P24(f329(x58031,f399(x58032,x58031)))+P24(f329(x58031,f329(a110,x58032)))+P24(f329(f329(f244(a1),x58032),f2(a1))) % 178.07/177.93 [5826]~P24(f329(x58261,f329(a110,x58262)))+P24(f329(x58261,f2(a875)))+~P24(f329(f329(f244(a1),x58262),f2(a1))) % 178.07/177.93 [6169]~P117(x61691)+~P24(f329(f329(f244(x61691),x61692),f2(x61691)))+P24(f329(f329(f244(x61691),f83(x61691,x61692)),f2(x61691))) % 178.07/177.93 [6283]~P117(x62831)+P24(f329(f329(f244(x62831),f329(f108(x62831),x62832)),f2(x62831)))+~P24(f329(f329(f244(a1),x62832),f2(a1))) % 178.07/177.93 [6284]~P117(x62841)+P24(f329(f329(f243(x62841),f329(f108(x62841),x62842)),f2(x62841)))+~P24(f329(f329(f243(a1),x62842),f2(a1))) % 178.07/177.93 [6291]~P85(x62912)+E(x62911,f2(x62912))+~P24(f329(f329(f243(x62912),f329(f76(x62912),x62911)),f2(x62912))) % 178.07/177.93 [6368]~P137(x63681)+~P24(f329(f329(f331(x63681),x63682),f115(x63681)))+P24(f329(f329(f331(x63681),f329(f80(x63681),x63682)),f115(x63681))) % 178.07/177.93 [6400]~P117(x64001)+~P24(f329(f329(f244(x64001),f83(x64001,x64002)),f2(x64001)))+P24(f329(f329(f244(x64001),x64002),f2(x64001))) % 178.07/177.93 [6570]~P117(x65702)+~P24(f329(f329(f244(x65702),f329(f108(x65702),x65701)),f2(x65702)))+P24(f329(f329(f244(a1),x65701),f2(a1))) % 178.07/177.93 [6571]~P117(x65712)+~P24(f329(f329(f243(x65712),f329(f108(x65712),x65711)),f2(x65712)))+P24(f329(f329(f243(a1),x65711),f2(a1))) % 178.07/177.93 [7076]~P117(x70761)+~P24(f329(f329(f244(x70761),x70762),f2(x70761)))+P24(f329(f329(f244(x70761),f329(f329(f81(x70761),x70762),x70762)),f2(x70761))) % 178.07/177.93 [7077]~P75(x70771)+~P24(f329(f329(f244(x70771),x70772),f2(x70771)))+P24(f329(f329(f244(x70771),f329(f329(f81(x70771),x70772),x70772)),f2(x70771))) % 178.07/177.93 [7078]~P75(x70781)+~P24(f329(f329(f243(x70781),x70782),f2(x70781)))+P24(f329(f329(f243(x70781),f329(f329(f81(x70781),x70782),x70782)),f2(x70781))) % 178.07/177.93 [7647]~P117(x76471)+~P24(f329(f329(f244(x76471),f329(f329(f81(x76471),x76472),x76472)),f2(x76471)))+P24(f329(f329(f244(x76471),x76472),f2(x76471))) % 178.07/177.93 [7648]~P75(x76481)+~P24(f329(f329(f244(x76481),f329(f329(f81(x76481),x76482),x76482)),f2(x76481)))+P24(f329(f329(f244(x76481),x76482),f2(x76481))) % 178.07/177.93 [7649]~P75(x76491)+~P24(f329(f329(f243(x76491),f329(f329(f81(x76491),x76492),x76492)),f2(x76491)))+P24(f329(f329(f243(x76491),x76492),f2(x76491))) % 178.07/177.93 [4715]~E(x47152,f79(a875))+~E(x47151,f79(a875))+E(f329(f329(f82(a875),x47151),x47152),f79(a875)) % 178.07/177.93 [4716]~E(x47162,f79(a1))+~E(x47161,f79(a1))+E(f329(f329(f82(a1),x47161),x47162),f79(a1)) % 178.07/177.93 [4717]~E(x47172,f2(a875))+~E(x47171,f2(a875))+E(f329(f329(f81(a875),x47171),x47172),f2(a875)) % 178.07/177.93 [4769]~P56(x47692)+E(x47691,f2(x47692))+E(f329(f329(f39(x47692),x47691),x47691),f79(x47692)) % 178.07/177.93 [4770]~P115(x47702)+E(x47701,f2(x47702))+E(f329(f329(f287(x47702),x47701),x47701),f79(x47702)) % 178.07/177.93 [4771]~P116(x47712)+E(x47711,f2(x47712))+E(f329(f329(f287(x47712),x47711),x47711),f79(x47712)) % 178.07/177.93 [4790]~P136(x47901)+~E(x47902,f79(x47901))+E(f329(f329(f82(x47901),x47902),x47902),f79(x47901)) % 178.07/177.93 [4791]~P75(x47911)+~E(x47912,f2(x47911))+E(f329(f329(f81(x47911),x47912),x47912),f2(x47911)) % 178.07/177.93 [4792]~P116(x47921)+~E(x47922,f2(x47921))+E(f329(f329(f287(x47921),x47922),x47922),f2(x47921)) % 178.07/177.93 [4838]~E(x48382,f2(a875))+~E(x48381,f2(a875))+E(f329(f80(a1),f329(f106(a1),x48381)),f329(f106(a1),x48382)) % 178.07/177.93 [4856]E(x48561,f79(a875))+E(x48562,f2(a875))+~E(f329(f329(f82(a875),x48562),x48561),x48562) % 178.07/177.93 [4866]E(x48661,f2(a875))+E(x48662,f2(a875))+~E(f329(f329(f82(a875),x48662),x48661),f2(a875)) % 178.07/177.93 [4894]~E(x48942,f2(a875))+~E(x48941,f329(a118,f2(a875)))+E(f329(f329(f81(a875),x48941),x48942),f329(a118,f2(a875))) % 178.07/177.93 [4895]~E(x48951,f2(a875))+~E(x48952,f329(a118,f2(a875)))+E(f329(f329(f81(a875),x48951),x48952),f329(a118,f2(a875))) % 178.07/177.93 [4900]E(x49001,f79(a1))+E(x49002,f329(f109(a1),a103))+~E(f329(f329(f82(a1),x49001),x49002),f79(a1)) % 178.07/177.93 [4901]E(x49011,f79(a1))+E(x49012,f329(f109(a1),a103))+~E(f329(f329(f82(a1),x49012),x49011),f79(a1)) % 178.07/177.93 [4902]E(x49021,f79(a1))+E(x49021,f329(f109(a1),a103))+~E(f329(f329(f82(a1),x49022),x49021),f79(a1)) % 178.07/177.93 [4904]E(x49041,f79(a1))+E(x49041,f329(f109(a1),a103))+~E(f329(f329(f82(a1),x49041),x49042),f79(a1)) % 178.07/177.93 [4921]~P75(x49212)+E(x49211,f2(x49212))+~E(f329(f329(f81(x49212),x49211),x49211),f2(x49212)) % 178.07/177.93 [4927]~E(x49271,f329(f109(a1),a103))+~E(x49272,f329(f109(a1),a103))+E(f329(f329(f82(a1),x49271),x49272),f79(a1)) % 178.07/177.93 [4939]E(x49391,f2(a875))+E(x49392,f2(a875))+~E(f329(f329(f81(a875),x49392),x49391),f329(a118,f2(a875))) % 178.07/177.93 [4949]~P59(x49491)+~P92(x49491)+E(f329(f329(f287(x49491),x49492),f329(f109(x49491),a84)),f2(x49491)) % 178.07/177.93 [4955]~P136(x49551)+~E(x49552,f329(f80(x49551),f79(x49551)))+E(f329(f329(f82(x49551),x49552),x49552),f79(x49551)) % 178.07/177.93 [4960]~P28(x49602)+~P28(x49601)+P28(f329(f329(f82(a1),x49601),x49602)) % 178.07/177.93 [4961]~P28(x49612)+~P28(x49611)+P28(f329(f329(f81(a1),x49611),x49612)) % 178.07/177.93 [4962]~P28(x49622)+~P28(x49621)+P28(f329(f329(f39(a1),x49621),x49622)) % 178.07/177.93 [4964]~E(x49642,f2(a1))+E(x49641,f2(a1))+E(f46(x49641,x49642),f329(f329(f264(a1,a1),f2(a1)),x49641)) % 178.07/177.93 [4986]~E(x49862,f329(a118,f2(a875)))+~E(x49861,f329(a118,f2(a875)))+E(f329(f329(f82(a875),x49861),x49862),f329(a118,f2(a875))) % 178.07/177.93 [5001]E(x50011,f2(a875))+E(x50012,f329(a118,f2(a875)))+~E(f329(f329(f254(a875),x50012),x50011),f329(a118,f2(a875))) % 178.07/177.93 [5002]E(x50021,f2(a875))+E(x50021,f329(a118,f2(a875)))+~E(f329(f329(f81(a875),x50022),x50021),f329(a118,f2(a875))) % 178.07/177.93 [5003]E(x50031,f2(a875))+E(x50031,f329(a118,f2(a875)))+~E(f329(f329(f81(a875),x50031),x50032),f329(a118,f2(a875))) % 178.07/177.93 [5012]~P59(x50121)+~P92(x50121)+E(f329(f329(f287(x50121),x50122),f329(f109(x50121),a103)),f329(f80(x50121),x50122)) % 178.07/177.93 [5032]E(x50321,f329(a110,x50322))+~E(x50321,f2(a875))+P24(f329(f329(f243(a1),f2(a1)),x50322)) % 178.07/177.93 [5033]E(f329(a110,x50331),x50332)+~E(x50332,f2(a875))+P24(f329(f329(f243(a1),f2(a1)),x50331)) % 178.07/177.93 [5048]E(x50481,f329(a118,f2(a875)))+E(x50482,f329(a118,f2(a875)))+~E(f329(f329(f81(a875),x50481),x50482),f329(a118,f2(a875))) % 178.07/177.93 [5058]~E(x50581,f329(a110,x50582))+E(x50581,f2(a875))+P24(f329(f329(f243(a1),f2(a1)),x50582)) % 178.07/177.93 [5059]~E(f329(a110,x50592),x50591)+E(x50591,f2(a875))+P24(f329(f329(f243(a1),f2(a1)),x50592)) % 178.07/177.93 [5081]~P63(x50811)+E(f329(f64(x50811,f116(x50811)),x50812),f13(x50811,x50812))+~P24(f329(f62(x50811),x50812)) % 178.07/177.93 [5082]~P63(x50821)+E(f329(f64(x50821,f107(x50821)),x50822),f10(x50821,x50822))+~P24(f329(f62(x50821),x50822)) % 178.07/177.93 [5083]~P105(x50831)+E(f329(f64(x50831,f241(x50831)),x50832),f14(x50831,x50832))+~P24(f329(f62(x50831),x50832)) % 178.07/177.93 [5084]~P105(x50841)+E(f329(f64(x50841,f242(x50841)),x50842),f15(x50841,x50842))+~P24(f329(f62(x50841),x50842)) % 178.07/177.93 [5086]~P58(x50861)+~P24(f329(x50862,f206(x50861)))+P24(f329(f58(f879(x50861)),x50862)) % 178.07/177.93 [5169]~P58(x51692)+P24(f329(x51691,f206(x51692)))+~P24(f329(f59(f879(x51692)),x51691)) % 178.07/177.93 [5170]E(x51701,x51702)+~E(f329(f329(f22(a875),x51702),x51701),f2(a875))+~E(f329(f329(f22(a875),x51701),x51702),f2(a875)) % 178.07/177.93 [5184]P28(x51841)+~P39(x51842)+~P24(f329(f329(f331(a1),x51841),x51842)) % 178.07/177.93 [5214]~P117(x52141)+~E(f83(x52141,x52142),f79(x52141))+P24(f329(f329(f244(x52141),f2(x52141)),x52142)) % 178.07/177.93 [5226]~P92(x52261)+E(f329(f106(x52261),f329(f109(a875),x52262)),f329(f109(x52261),x52262))+P24(f329(a198,f329(f109(a1),x52262))) % 178.07/177.93 [5232]~P44(x52321,x52322)+P45(a869)+P24(f329(f62(f882(x52321,x52321)),x52322)) % 178.07/177.93 [5305]~P105(x53051)+E(f329(f64(x53051,f242(x53051)),x53052),f11(x53051,f242(x53051),x53052))+~P24(f329(f62(x53051),x53052)) % 178.07/177.93 [5306]~P105(x53061)+E(f329(f64(x53061,f241(x53061)),x53062),f12(x53061,f241(x53061),x53062))+~P24(f329(f62(x53061),x53062)) % 178.07/177.93 [5319]E(x53191,x53192)+P24(f329(f329(f244(a875),x53192),x53191))+P24(f329(f329(f244(a875),x53191),x53192)) % 178.07/177.93 [5320]E(x53201,x53202)+P24(f329(f329(f244(a1),x53202),x53201))+P24(f329(f329(f244(a1),x53201),x53202)) % 178.07/177.93 [5375]~P92(x53751)+E(f329(f106(x53751),f329(f109(a875),x53752)),f2(x53751))+~P24(f329(a198,f329(f109(a1),x53752))) % 178.07/177.93 [5378]~E(x53782,f329(a110,x53781))+E(x53781,f329(f106(a1),x53782))+~P24(f329(f329(f243(a1),f2(a1)),x53781)) % 178.07/177.93 [5379]~E(f329(a110,x53791),x53792)+E(x53791,f329(f106(a1),x53792))+~P24(f329(f329(f243(a1),f2(a1)),x53791)) % 178.07/177.93 [5380]~E(x53801,f329(a110,x53802))+E(f329(f106(a1),x53801),x53802)+~P24(f329(f329(f243(a1),f2(a1)),x53802)) % 178.07/177.93 [5390]E(x53901,f329(a110,x53902))+~E(x53902,f329(f106(a1),x53901))+~P24(f329(f329(f243(a1),f2(a1)),x53902)) % 178.07/177.93 [5391]E(f329(a110,x53911),x53912)+~E(x53911,f329(f106(a1),x53912))+~P24(f329(f329(f243(a1),f2(a1)),x53911)) % 178.07/177.93 [5430]~P85(x54302)+E(x54301,f2(x54302))+P24(f329(f329(f244(x54302),f2(x54302)),f329(f76(x54302),x54301))) % 178.07/177.93 [5497]~P117(x54971)+E(f83(x54971,x54972),f79(x54971))+~P24(f329(f329(f244(x54971),f2(x54971)),x54972)) % 178.07/177.93 [5501]~P92(x55011)+E(f329(f106(x55011),f329(f109(a875),x55012)),f2(x55011))+P24(f329(f329(f243(a1),f2(a1)),f329(f109(a1),x55012))) % 178.07/177.93 [5508]~P85(x55081)+E(f329(f76(x55081),x55082),x55082)+~P24(f329(f329(f244(x55081),f2(x55081)),x55082)) % 178.07/177.93 [5509]~P85(x55091)+E(f329(f76(x55091),x55092),x55092)+~P24(f329(f329(f243(x55091),f2(x55091)),x55092)) % 178.07/177.93 [5516]E(x55161,f2(a875))+~E(f138(a875,f329(f299(a875,x55162),x55161)),f119(a875))+P24(f329(f329(f243(a875),x55161),x55162)) % 178.07/177.93 [5526]~P70(x55261)+E(f329(f329(f6(x55261,x55261),f5(x55261)),f329(f171(x55261),x55262)),f329(f165(x55261),x55262))+~P24(f329(f136(x55261),x55262)) % 178.07/177.93 [5529]~P137(x55291)+E(f329(f106(x55291),f329(a110,x55292)),f329(f108(x55291),x55292))+~P24(f329(f329(f243(a1),f2(a1)),x55292)) % 178.07/177.93 [5556]E(x55561,x55562)+P24(f329(f329(f244(a875),x55561),x55562))+~P24(f329(f329(f243(a875),x55561),x55562)) % 178.07/177.93 [5557]E(x55571,x55572)+P24(f329(f329(f244(a1),x55571),x55572))+~P24(f329(f329(f243(a1),x55571),x55572)) % 178.07/177.93 [5560]E(x55601,f79(a1))+~E(f329(f329(f82(a1),x55602),x55601),f79(a1))+~P24(f329(f329(f244(a1),f2(a1)),x55602)) % 178.07/177.93 [5561]E(x55611,f79(a1))+~E(f329(f329(f82(a1),x55611),x55612),f79(a1))+~P24(f329(f329(f244(a1),f2(a1)),x55611)) % 178.07/177.93 [5598]~P39(x55982)+P24(f329(f329(f243(a1),f2(a1)),x55981))+~P24(f329(f329(f331(a1),x55981),x55982)) % 178.07/177.93 [5617]~P53(x56171,x56172)+P38(x56171,x56172)+~P24(f329(f62(f882(x56171,x56171)),x56172)) % 178.07/177.93 [5619]~P53(x56191,x56192)+P44(x56191,x56192)+~P24(f329(f62(f882(x56191,x56191)),x56192)) % 178.07/177.93 [5663]E(x56631,f193(f883(x56632,a869)))+~P24(f329(f62(x56632),x56631))+P24(f329(f329(f244(a875),f2(a875)),f329(f38(x56632),x56631))) % 178.07/177.93 [5689]~P24(f329(x56891,x56892))+P24(f329(x56891,f2(a875)))+P24(f329(f329(f244(a875),f412(x56892,x56891)),x56892)) % 178.07/177.93 [5714]E(x57141,f2(a875))+~E(f329(f165(a875),x57142),f2(a875))+~P24(f329(f329(f331(a875),x57141),f329(f171(a875),x57142))) % 178.07/177.93 [5780]E(x57801,x57802)+~P24(f329(f329(f243(a875),x57802),x57801))+~P24(f329(f329(f243(a875),x57801),x57802)) % 178.07/177.93 [5781]E(x57811,x57812)+~P24(f329(f329(f243(a1),x57812),x57811))+~P24(f329(f329(f243(a1),x57811),x57812)) % 178.07/177.93 [5782]E(f329(f38(x57821),x57822),f2(a875))+~P24(f329(f62(x57821),x57822))+P24(f329(f329(f331(x57821),f525(x57822,x57821)),x57822)) % 178.07/177.93 [5791]E(f50(x57911,x57912),f46(x57911,x57912))+P24(f329(f329(f243(a1),f2(a1)),x57911))+~P24(f329(f329(f244(a1),f2(a1)),x57912)) % 178.07/177.93 [5815]~P24(f329(x58151,f389(x58151)))+P24(f329(x58151,f329(a110,x58152)))+~P24(f329(f329(f243(a1),f2(a1)),x58152)) % 178.07/177.93 [5817]P24(f329(f329(f244(a875),x58171),f341(x58172)))+~P24(f329(f62(a875),x58172))+~P24(f329(f329(f331(a875),x58171),x58172)) % 178.07/177.93 [5818]P24(f329(f329(f243(a875),x58181),f357(x58182)))+~P24(f329(f62(a875),x58182))+~P24(f329(f329(f331(a875),x58181),x58182)) % 178.07/177.93 [5847]E(x58471,x58472)+~P24(f329(f329(f244(a875),x58471),f329(a118,x58472)))+P24(f329(f329(f244(a875),x58471),x58472)) % 178.07/177.93 [5881]E(x58811,f329(a118,x58812))+~P24(f329(f329(f243(a875),x58811),f329(a118,x58812)))+P24(f329(f329(f243(a875),x58811),x58812)) % 178.07/177.93 [5894]P24(f329(x58941,f400(x58941)))+~P24(f329(x58941,f329(a110,x58942)))+~P24(f329(f329(f243(a1),f2(a1)),x58942)) % 178.07/177.93 [5908]~P24(f329(x59081,x59082))+~P24(f329(f329(f243(a1),f2(a1)),x59082))+P24(f329(x59081,f329(f106(a1),f382(x59081)))) % 178.07/177.93 [5923]~P85(x59232)+~E(x59231,f2(x59232))+~P24(f329(f329(f244(x59232),f2(x59232)),f329(f76(x59232),x59231))) % 178.07/177.93 [5950]~P53(x59501,x59502)+P38(x59501,f329(f284(x59501,x59501),x59502))+~P24(f329(f62(f882(x59501,x59501)),x59502)) % 178.07/177.93 [5958]~P92(x59581)+E(f329(f106(x59581),f329(f109(a875),x59582)),f329(f109(x59581),x59582))+~P24(f329(f329(f243(a1),f2(a1)),f329(f109(a1),x59582))) % 178.07/177.93 [5962]E(f329(a118,x59621),x59622)+~P24(f329(f329(f244(a875),x59621),x59622))+P24(f329(f329(f244(a875),f329(a118,x59621)),x59622)) % 178.07/177.93 [5975]E(f329(f329(f39(a1),x59751),x59752),f2(a1))+~P24(f329(f329(f243(a1),x59751),f2(a1)))+~P24(f329(f329(f244(a1),x59752),x59751)) % 178.07/177.93 [5988]E(f45(a1,x59881,x59882),x59881)+~P24(f329(f329(f243(a1),x59881),f2(a1)))+~P24(f329(f329(f244(a1),x59882),x59881)) % 178.07/177.93 [6001]E(f47(x60011,x60012),f46(x60011,x60012))+~P24(f329(f329(f243(a1),f2(a1)),x60011))+~P24(f329(f329(f243(a1),f2(a1)),x60012)) % 178.07/177.93 [6009]E(f329(f329(f39(a1),x60091),x60092),f2(a1))+~P24(f329(f329(f243(a1),f2(a1)),x60091))+~P24(f329(f329(f244(a1),x60091),x60092)) % 178.07/177.93 [6021]E(f45(a875,f329(f109(a875),x60211),f329(f109(a875),x60212)),f329(f109(a875),x60211))+P24(f329(a198,f329(f109(a1),x60211)))+~P24(f329(a198,f329(f109(a1),x60212))) % 178.07/177.93 [6023]E(f45(a1,x60231,x60232),x60231)+~P24(f329(f329(f243(a1),f2(a1)),x60231))+~P24(f329(f329(f244(a1),x60231),x60232)) % 178.07/177.93 [6024]E(x60241,x60242)+~P24(f329(f329(f244(a875),x60241),f329(a118,x60242)))+~P24(f329(f329(f243(a875),x60242),x60241)) % 178.07/177.93 [6041]~P117(x60411)+~P24(f329(f329(f244(x60411),x60412),f2(x60411)))+P24(f329(f329(f244(x60411),x60412),f329(f80(x60411),x60412))) % 178.07/177.93 [6042]~P75(x60421)+~P24(f329(f329(f243(x60421),x60422),f2(x60421)))+P24(f329(f329(f243(x60421),x60422),f329(f80(x60421),x60422))) % 178.07/177.93 [6052]~P27(x60521)+E(f329(f329(f65(x60521,x60521,f107(x60521)),f252(x60521)),x60522),f41(x60521,x60522))+~P24(f329(f62(x60521),x60522)) % 178.07/177.93 [6053]~P27(x60531)+E(f329(f329(f65(x60531,x60531,f116(x60531)),f193(x60531)),x60532),f40(x60531,x60532))+~P24(f329(f62(x60531),x60532)) % 178.07/177.93 [6067]~P120(x60671)+~P24(f329(f329(f244(a875),f2(a875)),x60672))+P24(f329(f329(f244(x60671),f2(x60671)),f329(f106(x60671),x60672))) % 178.07/177.93 [6068]~P117(x60681)+~P24(f329(f329(f244(a1),f2(a1)),x60682))+P24(f329(f329(f244(x60681),f2(x60681)),f329(f108(x60681),x60682))) % 178.07/177.93 [6069]~P117(x60691)+~P24(f329(f329(f243(a1),f2(a1)),x60692))+P24(f329(f329(f243(x60691),f2(x60691)),f329(f108(x60691),x60692))) % 178.07/177.93 [6072]~P28(x60722)+~P28(x60721)+E(f329(f308(a875,a1,f106(a1)),f300(a875,f329(a110,x60721),f329(a110,x60722))),f300(a1,x60721,x60722)) % 178.07/177.93 [6078]P24(f329(x60781,x60782))+~P24(f329(f329(f243(a1),f2(a1)),x60782))+~P24(f329(x60781,f329(f106(a1),f383(x60781)))) % 178.07/177.93 [6103]E(f329(f329(f81(a875),f329(f109(a875),x61031)),f329(f109(a875),x61032)),f329(f109(a875),x61031))+P24(f329(f329(f244(a1),x61031),a84))+~P24(f329(f329(f244(a1),x61032),a84)) % 178.07/177.93 [6107]~P117(x61071)+P24(f329(f329(f244(x61071),f2(x61071)),f83(x61071,x61072)))+~P24(f329(f329(f244(x61071),f2(x61071)),x61072)) % 178.07/177.93 [6118]~P77(x61181)+~P24(f329(f329(f244(x61181),x61182),f2(x61181)))+P24(f329(f329(f244(x61181),f2(x61181)),f329(f80(x61181),x61182))) % 178.07/177.93 [6119]~P77(x61191)+~P24(f329(f329(f243(x61191),x61192),f2(x61191)))+P24(f329(f329(f243(x61191),f2(x61191)),f329(f80(x61191),x61192))) % 178.07/177.93 [6122]E(x61221,f252(f883(x61222,a869)))+~E(f329(f38(x61222),x61221),f329(f38(x61222),f252(f883(x61222,a869))))+~P24(f329(f62(x61222),f252(f883(x61222,a869)))) % 178.07/177.93 [6162]~P117(x61621)+P24(f329(f329(f244(x61621),x61622),f2(x61621)))+~P24(f329(f329(f244(x61621),x61622),f329(f80(x61621),x61622))) % 178.07/177.93 [6163]~P75(x61631)+P24(f329(f329(f243(x61631),x61632),f2(x61631)))+~P24(f329(f329(f243(x61631),x61632),f329(f80(x61631),x61632))) % 178.07/177.93 [6171]~P92(x61711)+P24(f329(f329(f331(x61711),f329(f109(x61711),x61712)),f191(x61711)))+~P24(f329(f329(f243(a1),a84),x61712)) % 178.07/177.93 [6202]E(x62021,f2(a875))+~P24(f329(f329(f244(a875),x62021),f329(a118,x62022)))+P24(f329(f329(f244(a875),f358(x62022,x62021)),x62022)) % 178.07/177.93 [6224]~P117(x62241)+~P24(f329(f329(f244(x62241),f2(x62241)),f83(x62241,x62242)))+P24(f329(f329(f244(x62241),f2(x62241)),x62242)) % 178.07/177.93 [6226]~E(f329(f109(a875),x62262),f329(f109(a875),x62261))+P24(f329(f329(f243(a1),f329(f109(a1),x62261)),f2(a1)))+~P24(f329(a198,f329(f109(a1),x62262))) % 178.07/177.93 [6256]E(f329(f263(a1,a1),f50(x62561,x62562)),f329(f329(f39(a1),x62561),x62562))+~P24(f329(f329(f244(a1),x62561),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x62562)) % 178.07/177.93 [6289]E(f329(f267(a1,a1),f50(x62891,x62892)),f45(a1,x62891,x62892))+~P24(f329(f329(f244(a1),x62891),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x62892)) % 178.07/177.93 [6292]~P120(x62922)+~P24(f329(f329(f244(x62922),f2(x62922)),f329(f106(x62922),x62921)))+P24(f329(f329(f244(a875),f2(a875)),x62921)) % 178.07/177.93 [6293]~P117(x62932)+~P24(f329(f329(f244(x62932),f2(x62932)),f329(f108(x62932),x62931)))+P24(f329(f329(f244(a1),f2(a1)),x62931)) % 178.07/177.93 [6294]~P117(x62942)+~P24(f329(f329(f243(x62942),f2(x62942)),f329(f108(x62942),x62941)))+P24(f329(f329(f243(a1),f2(a1)),x62941)) % 178.07/177.93 [6297]E(f329(f263(a1,a1),f47(x62971,x62972)),f329(f329(f39(a1),x62971),x62972))+~P24(f329(f329(f244(a1),f2(a1)),x62971))+~P24(f329(f329(f243(a1),f2(a1)),x62972)) % 178.07/177.93 [6312]E(f329(f267(a1,a1),f47(x63121,x63122)),f45(a1,x63121,x63122))+~P24(f329(f329(f244(a1),f2(a1)),x63121))+~P24(f329(f329(f243(a1),f2(a1)),x63122)) % 178.07/177.93 [6329]~P77(x63291)+P24(f329(f329(f244(x63291),x63292),f2(x63291)))+~P24(f329(f329(f244(x63291),f2(x63291)),f329(f80(x63291),x63292))) % 178.07/177.93 [6330]~P77(x63301)+P24(f329(f329(f243(x63301),x63302),f2(x63301)))+~P24(f329(f329(f243(x63301),f2(x63301)),f329(f80(x63301),x63302))) % 178.07/177.93 [6355]P24(f329(f49(x63551,x63552),f50(x63551,x63552)))+~P24(f329(f329(f244(a1),x63551),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x63552)) % 178.07/177.93 [6380]P24(f329(f49(x63801,x63802),f47(x63801,x63802)))+~P24(f329(f329(f244(a1),f2(a1)),x63802))+~P24(f329(f329(f243(a1),f2(a1)),x63801)) % 178.07/177.93 [6423]~P77(x64231)+P24(f329(f329(f244(x64231),f329(f80(x64231),x64232)),f2(x64231)))+~P24(f329(f329(f244(x64231),f2(x64231)),x64232)) % 178.07/177.93 [6424]~P77(x64241)+P24(f329(f329(f243(x64241),f329(f80(x64241),x64242)),f2(x64241)))+~P24(f329(f329(f243(x64241),f2(x64241)),x64242)) % 178.07/177.93 [6441]E(f329(f329(f22(a875),f329(a110,x64411)),f329(a110,x64412)),f329(a110,f200(x64411,x64412)))+~P24(f329(f329(f243(a1),f2(a1)),x64412))+~P24(f329(f329(f243(a1),f2(a1)),x64411)) % 178.07/177.93 [6458]P24(f329(f329(f243(a1),f2(a1)),f200(x64581,x64582)))+~P24(f329(f329(f243(a1),f2(a1)),x64582))+~P24(f329(f329(f243(a1),f2(a1)),x64581)) % 178.07/177.93 [6495]~P24(f329(x64951,x64952))+P24(f329(x64951,f2(a875)))+P24(f329(x64951,f329(f329(f81(a875),f412(x64952,x64951)),f79(a875)))) % 178.07/177.93 [6577]E(f329(f109(a875),x65771),f329(f109(a875),x65772))+~P24(f329(f329(f243(a1),f329(f109(a1),x65772)),f2(a1)))+~P24(f329(a198,f329(f109(a1),x65771))) % 178.07/177.93 [6587]~E(x65871,f2(a875))+~E(f621(x65872,x65871),f2(a875))+E(f329(f141(a875,a875,f81(a875),x65871),x65872),f2(a875)) % 178.07/177.93 [6613]~P24(f329(f62(x66131),f848(x66132,x66131)))+~P24(f329(f62(f883(x66131,a869)),x66132))+P24(f329(f62(x66131),f40(f883(x66131,a869),x66132))) % 178.07/177.93 [6619]E(x66191,x66192)+P24(f329(f329(f244(a1),x66191),x66192))+~P24(f329(f329(f244(a1),x66191),f329(f329(f81(a1),x66192),f79(a1)))) % 178.07/177.93 [6621]P24(f329(f329(f244(a875),f329(a110,x66211)),f329(a110,x66212)))+~P24(f329(f329(f244(a1),f2(a1)),x66212))+~P24(f329(f329(f244(a1),x66211),x66212)) % 178.07/177.93 [6622]P24(f329(f329(f244(a875),f329(a110,x66221)),f329(a110,x66222)))+~P24(f329(f329(f243(a1),f2(a1)),x66221))+~P24(f329(f329(f244(a1),x66221),x66222)) % 178.07/177.93 [6623]P24(f329(f329(f243(a875),f329(a110,x66231)),f329(a110,x66232)))+~P24(f329(f329(f244(a1),f2(a1)),x66231))+~P24(f329(f329(f243(a1),x66231),x66232)) % 178.07/177.93 [6624]P24(f329(f329(f243(a875),f329(a110,x66241)),f329(a110,x66242)))+~P24(f329(f329(f243(a1),f2(a1)),x66242))+~P24(f329(f329(f243(a1),x66241),x66242)) % 178.07/177.93 [6635]E(f45(a875,f329(a110,x66351),f329(a110,x66352)),f329(a110,f45(a1,x66351,x66352)))+~P24(f329(f329(f243(a1),f2(a1)),x66352))+~P24(f329(f329(f243(a1),f2(a1)),x66351)) % 178.07/177.93 [6657]~P77(x66571)+~P24(f329(f329(f244(x66571),f329(f80(x66571),x66572)),f2(x66571)))+P24(f329(f329(f244(x66571),f2(x66571)),x66572)) % 178.07/177.93 [6658]~P77(x66581)+~P24(f329(f329(f243(x66581),f329(f80(x66581),x66582)),f2(x66581)))+P24(f329(f329(f243(x66581),f2(x66581)),x66582)) % 178.07/177.93 [6673]~P24(f329(f329(f244(a1),a84),x66732))+~P24(f329(f329(f244(a1),x66731),x66732))+P24(f329(f329(f244(a875),f329(f109(a875),x66731)),f329(f109(a875),x66732))) % 178.07/177.93 [6764]~P24(f329(f329(f243(a1),f2(a1)),x67641))+P24(f329(f329(f244(a875),f329(a110,x67641)),x67642))+~P24(f329(f329(f244(a1),x67641),f329(f106(a1),x67642))) % 178.07/177.93 [6781]E(x67811,f2(a1))+E(f45(a1,x67812,x67811),f2(a1))+E(f329(f329(f22(a1),f329(f80(a1),f329(f329(f39(a1),x67812),x67811))),f79(a1)),f329(f329(f39(a1),x67812),f329(f80(a1),x67811))) % 178.07/177.93 [6796]~P24(f329(f329(f243(a1),f2(a1)),x67961))+~P24(f329(f329(f244(a875),f329(a110,x67961)),x67962))+P24(f329(f329(f244(a1),x67961),f329(f106(a1),x67962))) % 178.07/177.93 [6833]~P24(f329(f329(f243(a875),f329(a110,x68331)),f329(a110,x68332)))+~P24(f329(f329(f244(a1),f2(a1)),x68331))+P24(f329(f329(f243(a1),x68331),x68332)) % 178.07/177.93 [6834]~P24(f329(f329(f243(a875),f329(a110,x68341)),f329(a110,x68342)))+~P24(f329(f329(f243(a1),f2(a1)),x68342))+P24(f329(f329(f243(a1),x68341),x68342)) % 178.07/177.93 [6860]P24(f329(f329(f243(a1),x68601),x68602))+~P24(f329(f329(f243(a875),f329(f109(a875),x68601)),f329(f109(a875),x68602)))+P24(f329(f329(f243(a1),x68601),a84)) % 178.07/177.93 [6887]P24(f329(f329(f243(a1),f2(a1)),f45(a1,x68871,x68872)))+~P24(f329(f329(f243(a1),f2(a1)),x68872))+~P24(f329(f329(f243(a1),f2(a1)),x68871)) % 178.07/177.93 [6987]P24(f329(f329(f244(a1),a84),x69871))+~P24(f329(f329(f244(a1),x69872),x69871))+~P24(f329(f329(f244(a875),f329(f109(a875),x69872)),f329(f109(a875),x69871))) % 178.07/177.93 [7038]E(f329(f329(f264(a1,a1),f329(f329(f39(a1),x70381),x70382)),f45(a1,x70381,x70382)),f50(x70381,x70382))+~P24(f329(f329(f244(a1),x70381),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x70382)) % 178.07/177.93 [7059]E(f329(f329(f264(a1,a1),f329(f329(f39(a1),x70591),x70592)),f45(a1,x70591,x70592)),f47(x70591,x70592))+~P24(f329(f329(f243(a1),f2(a1)),x70592))+~P24(f329(f329(f243(a1),f2(a1)),x70591)) % 178.07/177.93 [7110]~P95(x71102)+E(x71101,f119(x71102))+E(f329(f141(x71102,x71102,f82(x71102),f329(f140(x71102),x71101)),f329(f170(x71102),x71101)),f329(f64(x71102,f82(x71102)),f329(f171(x71102),x71101))) % 178.07/177.93 [7222]~E(x72221,f2(a875))+E(f329(f141(a875,a875,f81(a875),x72221),x72222),f2(a875))+P24(f329(f329(f331(a875),f621(x72222,x72221)),f329(f171(a875),x72222))) % 178.07/177.93 [7269]~P24(f329(f329(f244(a1),x72692),f2(a1)))+P24(f329(f329(f244(a1),f329(f329(f39(a1),x72691),x72692)),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x72691)) % 178.07/177.93 [7271]~P24(f329(f329(f244(a1),x72711),f2(a1)))+P24(f329(f329(f244(a1),f329(f329(f39(a1),x72711),x72712)),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x72712)) % 178.07/177.93 [7272]~P24(f329(f329(f244(a1),x72722),f2(a1)))+P24(f329(f329(f243(a1),f329(f329(f39(a1),x72721),x72722)),f2(a1)))+~P24(f329(f329(f243(a1),f2(a1)),x72721)) % 178.07/177.93 [7273]~P24(f329(f329(f243(a1),x72731),f2(a1)))+P24(f329(f329(f243(a1),f329(f329(f39(a1),x72731),x72732)),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x72732)) % 178.07/177.93 [7279]P24(f329(f329(f331(f883(x72791,a869)),f848(x72792,x72791)),x72792))+~P24(f329(f62(f883(x72791,a869)),x72792))+P24(f329(f62(x72791),f40(f883(x72791,a869),x72792))) % 178.07/177.93 [7377]P21(x73771,x73771,x73772,f252(f883(x73771,a869)))+~E(f329(f308(x73771,x73771,x73772),f252(f883(x73771,a869))),f252(f883(x73771,a869)))+~P24(f329(f62(x73771),f252(f883(x73771,a869)))) % 178.07/177.93 [7505]~P21(x75051,x75051,x75052,f252(f883(x75051,a869)))+E(f329(f308(x75051,x75051,x75052),f252(f883(x75051,a869))),f252(f883(x75051,a869)))+~P24(f329(f62(x75051),f252(f883(x75051,a869)))) % 178.07/177.93 [7641]E(f329(f329(f39(a1),x76411),x76412),f329(f109(a1),a103))+~P24(f329(f329(f243(a1),f329(f329(f81(a1),x76411),x76412)),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x76411)) % 178.07/177.93 [7700]~P24(f329(f329(f244(a1),x77002),f2(a1)))+~P24(f329(f329(f244(a1),f329(f329(f39(a1),x77001),x77002)),f2(a1)))+P24(f329(f329(f244(a1),f2(a1)),x77001)) % 178.07/177.93 [7705]E(f329(f329(f81(a1),x77051),x77052),f45(a1,x77051,x77052))+~P24(f329(f329(f243(a1),f329(f329(f81(a1),x77051),x77052)),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x77051)) % 178.07/177.93 [7708]P24(f329(f329(f244(a1),x77081),f2(a1)))+~P24(f329(f329(f244(a1),f329(f329(f39(a1),x77081),x77082)),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x77082)) % 178.07/177.93 [8099]~P58(x80991)+~P24(f329(f59(f879(x80991)),x80992))+P24(f329(f59(x80991),f329(f329(f8(f879(x80991),a869,x80991),x80992),f236(x80991)))) % 178.07/177.93 [8409]~P105(x84091)+P29(x84091,x84092)+~P24(f329(f329(f243(x84091),f329(f329(f164(x84091),x84092),f646(x84092,x84091))),f329(f329(f164(x84091),x84092),f647(x84092,x84091)))) % 178.07/177.93 [8410]~P105(x84101)+P29(x84101,x84102)+~P24(f329(f329(f243(x84101),f329(f329(f164(x84101),x84102),f652(x84102,x84101))),f329(f329(f164(x84101),x84102),f662(x84102,x84101)))) % 178.07/177.93 [8564]~P58(x85641)+P24(f329(f58(f879(x85641)),x85642))+~P24(f329(f58(x85641),f329(f329(f8(f879(x85641),a869,x85641),x85642),f236(x85641)))) % 178.07/177.93 [9725]~P58(x97251)+~P58(x97252)+E(f329(f329(f153(f876(x97251),f883(x97252,x97251)),f329(f329(f8(f883(x97252,f879(x97251)),f883(x97252,x97251),f876(x97251)),f74(f879(x97251),x97251,x97252,f240(x97251))),f329(f329(f8(f876(f882(x97252,x97251)),f883(x97252,f879(x97251)),f876(x97251)),f177(x97252,x97251)),f329(f181(x97252,x97251),f56(x97252))))),f55(x97251,f329(f194(f876(x97252)),f56(x97252)),f56(x97251))),f56(f883(x97252,x97251))) % 178.07/177.93 [5656]E(x56561,f2(a1))+~E(f45(a1,x56562,x56561),f2(a1))+E(f329(f329(f39(a1),x56562),f329(f80(a1),x56561)),f329(f80(a1),f329(f329(f39(a1),x56562),x56561))) % 178.07/177.93 [5674]~P39(x56742)+~P39(x56741)+P39(f329(f329(f116(f883(a1,a869)),x56741),x56742)) % 178.07/177.93 [5675]~P39(x56752)+~P39(x56751)+P39(f329(f329(f107(f883(a1,a869)),x56751),x56752)) % 178.07/177.93 [5692]~P59(x56921)+~P92(x56921)+E(f329(f80(x56921),f329(f329(f287(x56921),f79(x56921)),x56922)),f329(f329(f287(x56921),f329(f109(x56921),a103)),x56922)) % 178.07/177.93 [5807]E(x58071,f2(a1))+~E(f45(a1,x58072,x58071),f2(a1))+E(f329(f329(f39(a1),f329(f80(a1),x58072)),x58071),f329(f80(a1),f329(f329(f39(a1),x58072),x58071))) % 178.07/177.93 [5944]~P105(x59441)+P29(x59441,x59442)+P24(f329(f329(f244(a875),f647(x59442,x59441)),f329(f194(f876(x59441)),x59442))) % 178.07/177.93 [5945]~P105(x59451)+P29(x59451,x59452)+P24(f329(f329(f244(a875),f662(x59452,x59451)),f329(f194(f876(x59451)),x59452))) % 178.07/177.93 [6099]~P92(x60991)+~E(f329(f109(x60991),x60992),f2(x60991))+P31(x60991,f329(f109(x60991),f329(f329(f81(a1),x60992),f329(f80(a1),a84)))) % 178.07/177.93 [6100]~P92(x61001)+~E(f329(f109(x61001),x61002),f2(x61001))+P31(x61001,f329(f109(x61001),f329(f329(f81(a1),a84),f329(f80(a1),x61002)))) % 178.07/177.93 [6102]E(f329(a51,f47(f329(f80(a1),x61021),f329(f80(a1),x61022))),f46(x61021,x61022))+P24(f329(f329(f244(a1),f2(a1)),x61022))+P24(f329(f329(f243(a1),f2(a1)),x61021)) % 178.07/177.93 [6232]~E(x62322,f2(a875))+~E(x62321,f2(a875))+P24(f329(f329(f243(a1),f329(f106(a1),x62321)),f329(f80(a1),f329(f106(a1),x62322)))) % 178.07/177.93 [6260]E(f329(f329(f81(a875),f329(f109(a875),x62601)),f329(f109(a875),x62602)),f329(f109(a875),f329(f329(f81(a1),x62601),x62602)))+P24(f329(f329(f244(a1),x62601),a84))+P24(f329(f329(f244(a1),x62602),a84)) % 178.07/177.93 [6389]~P75(x63891)+~P24(f329(f329(f244(x63891),f2(x63891)),x63892))+P24(f329(f329(f244(x63891),f329(f80(x63891),x63892)),x63892)) % 178.07/177.93 [6390]~P75(x63901)+~P24(f329(f329(f243(x63901),f2(x63901)),x63902))+P24(f329(f329(f243(x63901),f329(f80(x63901),x63902)),x63902)) % 178.07/177.93 [6563]E(f329(f329(f22(a875),f329(a110,x65631)),f329(a110,x65632)),f329(a110,f329(f329(f22(a1),x65631),x65632)))+~P24(f329(f329(f243(a1),f2(a1)),x65632))+~P24(f329(f329(f243(a1),x65632),x65631)) % 178.07/177.93 [6596]E(f329(a110,f45(a1,f329(f109(a1),x65961),f329(f109(a1),x65962))),f45(a875,f329(f109(a875),x65961),f329(f109(a875),x65962)))+P24(f329(a198,f329(f109(a1),x65961)))+P24(f329(a198,f329(f109(a1),x65962))) % 178.07/177.93 [6614]~P75(x66141)+P24(f329(f329(f244(x66141),f2(x66141)),x66142))+~P24(f329(f329(f244(x66141),f329(f80(x66141),x66142)),x66142)) % 178.07/177.93 [6615]~P75(x66151)+P24(f329(f329(f243(x66151),f2(x66151)),x66152))+~P24(f329(f329(f243(x66151),f329(f80(x66151),x66152)),x66152)) % 178.07/177.93 [6626]~P75(x66261)+~P24(f329(f329(f244(x66261),f2(x66261)),x66262))+P24(f329(f329(f244(x66261),f2(x66261)),f329(f329(f81(x66261),x66262),x66262))) % 178.07/177.93 [6629]~P75(x66291)+~P24(f329(f329(f243(x66291),f2(x66291)),x66292))+P24(f329(f329(f243(x66291),f2(x66291)),f329(f329(f81(x66291),x66292),x66292))) % 178.07/177.93 [6641]E(f329(f329(f81(a875),f329(a110,x66411)),f329(a110,x66412)),f329(a110,f329(f329(f81(a1),x66411),x66412)))+~P24(f329(f329(f243(a1),f2(a1)),x66412))+~P24(f329(f329(f243(a1),f2(a1)),x66411)) % 178.07/177.93 [6652]E(x66521,f2(a875))+P24(f329(f329(f244(a875),f2(a875)),x66522))+~P24(f329(f329(f244(a875),f2(a875)),f329(f329(f254(a875),x66522),x66521))) % 178.07/177.93 [6682]~P92(x66821)+E(f329(f109(x66821),x66822),f2(x66821))+~P31(x66821,f329(f109(x66821),f329(f329(f81(a1),a84),f329(f80(a1),x66822)))) % 178.07/177.93 [6683]~P92(x66831)+E(f329(f109(x66831),x66832),f2(x66831))+~P31(x66831,f329(f109(x66831),f329(f329(f81(a1),x66832),f329(f80(a1),a84)))) % 178.07/177.93 [6742]~P24(f329(f62(x67421),x67422))+~P24(f329(f62(x67421),f252(f883(x67421,a869))))+P24(f329(f62(x67421),f329(f80(f883(x67421,a869)),x67422))) % 178.07/177.93 [6765]~P24(f329(f329(f244(a1),f2(a1)),x67652))+~P24(f329(f329(f243(a1),x67652),x67651))+P24(f329(f329(f244(a1),f2(a1)),f329(f329(f39(a1),x67651),x67652))) % 178.07/177.93 [6766]~P24(f329(f329(f244(a1),x67662),f2(a1)))+~P24(f329(f329(f243(a1),x67661),f2(a1)))+P24(f329(f329(f243(a1),f2(a1)),f329(f329(f39(a1),x67661),x67662))) % 178.07/177.93 [6804]~P24(f329(f329(f244(a875),f2(a875)),x68042))+~P24(f329(f329(f244(a875),f2(a875)),x68041))+P24(f329(f329(f244(a875),f2(a875)),f329(f329(f82(a875),x68041),x68042))) % 178.07/177.93 [6805]~P24(f329(f329(f243(a1),f2(a1)),x68052))+~P24(f329(f329(f243(a1),f2(a1)),x68051))+P24(f329(f329(f243(a1),f2(a1)),f329(f329(f82(a1),x68051),x68052))) % 178.07/177.93 [6806]~P24(f329(f329(f243(a1),f2(a1)),x68062))+~P24(f329(f329(f243(a1),f2(a1)),x68061))+P24(f329(f329(f243(a1),f2(a1)),f329(f329(f81(a1),x68061),x68062))) % 178.07/177.93 [6807]~P24(f329(f329(f244(a1),f2(a1)),x68072))+~P24(f329(f329(f243(a1),f2(a1)),x68071))+P24(f329(f329(f243(a1),f2(a1)),f329(f329(f39(a1),x68071),x68072))) % 178.07/177.93 [6808]~P24(f329(f329(f243(a1),f2(a1)),x68082))+~P24(f329(f329(f243(a1),f2(a1)),x68081))+P24(f329(f329(f243(a1),f2(a1)),f329(f329(f39(a1),x68081),x68082))) % 178.07/177.93 [6873]E(x68731,f2(a1))+E(f45(a1,x68732,x68731),f2(a1))+E(f329(f329(f22(a1),f329(f80(a1),f329(f329(f39(a1),x68732),x68731))),f79(a1)),f329(f329(f39(a1),f329(f80(a1),x68732)),x68731)) % 178.07/177.93 [6928]P24(f329(f329(f244(a875),f2(a875)),x69281))+P24(f329(f329(f244(a875),f2(a875)),x69282))+~P24(f329(f329(f244(a875),f2(a875)),f329(f329(f81(a875),x69282),x69281))) % 178.07/177.93 [6932]~P75(x69321)+P24(f329(f329(f244(x69321),f2(x69321)),x69322))+~P24(f329(f329(f244(x69321),f2(x69321)),f329(f329(f81(x69321),x69322),x69322))) % 178.07/177.93 [6933]~P75(x69331)+P24(f329(f329(f243(x69331),f2(x69331)),x69332))+~P24(f329(f329(f243(x69331),f2(x69331)),f329(f329(f81(x69331),x69332),x69332))) % 178.07/177.93 [6988]~P24(f329(f62(x69881),x69882))+P24(f329(f62(x69881),f252(f883(x69881,a869))))+~P24(f329(f62(x69881),f329(f80(f883(x69881,a869)),x69882))) % 178.07/177.93 [7051]P24(f329(f329(f243(a1),x70511),f2(a1)))+~P24(f329(f329(f244(a1),x70512),f2(a1)))+~P24(f329(f329(f243(a1),f2(a1)),f329(f329(f39(a1),x70511),x70512))) % 178.07/177.93 [7057]~P24(f329(f329(f244(a1),f2(a1)),x70571))+P24(f329(f329(f243(a1),x70571),x70572))+~P24(f329(f329(f244(a1),f2(a1)),f329(f329(f39(a1),x70572),x70571))) % 178.07/177.93 [7058]~P24(f329(f329(f243(a1),f2(a1)),x70582))+P24(f329(f329(f243(a1),x70581),x70582))+~P24(f329(f329(f244(a1),f2(a1)),f329(f329(f39(a1),x70582),x70581))) % 178.07/177.93 [7087]P24(f329(f329(f244(a1),f2(a1)),x70871))+~P24(f329(f329(f243(a1),f2(a1)),x70872))+~P24(f329(f329(f244(a1),f2(a1)),f329(f329(f39(a1),x70872),x70871))) % 178.07/177.93 [7088]P24(f329(f329(f243(a1),f2(a1)),x70881))+~P24(f329(f329(f244(a1),f2(a1)),x70882))+~P24(f329(f329(f243(a1),f2(a1)),f329(f329(f39(a1),x70881),x70882))) % 178.07/177.93 [7535]~P24(f329(f62(x75352),f252(f883(x75352,a869))))+~P24(f329(f62(x75351),f252(f883(x75351,a869))))+P24(f329(f62(f881(x75351,x75352)),f252(f883(f881(x75351,x75352),a869)))) % 178.07/177.93 [7536]~P24(f329(f62(x75362),f252(f883(x75362,a869))))+~P24(f329(f62(x75361),f252(f883(x75361,a869))))+P24(f329(f62(f882(x75361,x75362)),f252(f883(f882(x75361,x75362),a869)))) % 178.07/177.93 [7605]~P24(f329(f329(f244(a875),f329(a118,f2(a875))),x76051))+~P24(f329(f329(f244(a875),f329(a118,f2(a875))),x76052))+P24(f329(f329(f244(a875),x76051),f329(f329(f82(a875),x76052),x76051))) % 178.07/177.93 [7606]~P24(f329(f329(f244(a875),f329(a118,f2(a875))),x76061))+~P24(f329(f329(f244(a875),f329(a118,f2(a875))),x76062))+P24(f329(f329(f244(a875),x76061),f329(f329(f82(a875),x76061),x76062))) % 178.07/177.93 [7640]E(f329(f38(x76401),f252(f883(x76401,a869))),f329(a118,f2(a875)))+P24(f329(f62(x76402),f252(f883(x76402,a869))))+~P24(f329(f62(f883(x76402,x76401)),f252(f883(f883(x76402,x76401),a869)))) % 178.07/177.93 [7767]~P24(f329(f329(f244(a875),f329(a118,f2(a875))),x77672))+~P24(f329(f329(f244(a875),f329(a118,f2(a875))),x77671))+P24(f329(f329(f244(a875),f329(a118,f2(a875))),f329(f329(f82(a875),x77671),x77672))) % 178.07/177.93 [7768]~P24(f329(f329(f243(a875),f329(a118,f2(a875))),x77681))+~P24(f329(f329(f243(a875),f329(a118,f2(a875))),x77682))+P24(f329(f329(f243(a875),f329(a118,f2(a875))),f329(f329(f82(a875),x77681),x77682))) % 178.07/177.93 [8460]E(x84601,f119(x84602))+~P24(f329(f136(x84602),x84601))+E(f176(x84602,f329(f329(f8(a869,a869,x84602),a324),f329(f329(f7(x84602,x84602,a869),a326),f143(x84602,x84601))),x84601),f120(x84602,x84601)) % 178.07/177.93 [8555]~P39(x85552)+~P39(x85551)+E(f329(f308(a875,a1,f106(a1)),f329(f329(f116(f883(a875,a869)),f329(f308(a1,a875,a110),x85551)),f329(f308(a1,a875,a110),x85552))),f329(f329(f116(f883(a1,a869)),x85551),x85552)) % 178.07/177.93 [8556]~P39(x85562)+~P39(x85561)+E(f329(f308(a875,a1,f106(a1)),f329(f329(f107(f883(a875,a869)),f329(f308(a1,a875,a110),x85561)),f329(f308(a1,a875,a110),x85562))),f329(f329(f107(f883(a1,a869)),x85561),x85562)) % 178.07/177.93 [9208]~P92(x92081)+~E(f329(f109(x92081),x92082),f79(x92081))+P31(x92081,f329(f109(x92081),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f80(a1),x92082)))) % 178.07/177.93 [9441]~P92(x94411)+E(f329(f109(x94411),x94412),f79(x94411))+~P31(x94411,f329(f109(x94411),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f80(a1),x94412)))) % 178.07/177.93 [10169]E(x101691,f2(a1))+E(x101692,f2(a1))+E(f329(f269(a1,a1,a1,a1,f35(a1),f329(f82(a1),f83(a1,x101692))),f329(f329(f329(f102(f882(a1,a1)),f329(f329(a326,f83(a1,x101691)),f83(a1,x101692))),f53(x101691,x101692)),f329(f329(f268(a1,a1,f882(a1,a1)),f329(f329(f18(a1,f883(a1,f882(a1,a1)),f883(a1,f882(a1,a1))),f329(f329(f8(f883(a1,f883(f882(a1,a1),f882(a1,a1))),f883(f883(a1,f882(a1,a1)),f883(a1,f882(a1,a1))),a1),f18(a1,f882(a1,a1),f882(a1,a1))),f329(f329(f8(f882(a1,a1),f883(a1,f883(f882(a1,a1),f882(a1,a1))),a1),f329(f7(a1,f882(a1,a1),f883(f882(a1,a1),f882(a1,a1))),f329(f329(f8(a869,f883(f882(a1,a1),f883(f882(a1,a1),f882(a1,a1))),a1),f102(f882(a1,a1))),f329(f329(f7(a1,a1,a869),a326),f2(a1))))),f329(f329(f7(a1,a1,f882(a1,a1)),f329(f329(f8(a1,f883(a1,f882(a1,a1)),a1),f264(a1,a1)),f80(a1))),f2(a1))))),f329(f329(f7(a1,f883(a1,a1),f883(a1,f882(a1,a1))),f329(f329(f8(f883(a1,f882(a1,a1)),f883(f883(a1,a1),f883(a1,f882(a1,a1))),a1),f8(a1,f882(a1,a1),a1)),f329(f329(f8(a1,f883(a1,f882(a1,a1)),a1),f264(a1,a1)),f329(f329(f7(a1,a1,a1),f329(f329(f8(a1,f883(a1,a1),a1),f22(a1)),f80(a1))),f79(a1))))),f329(f22(a1),f329(f76(a1),x101692))))),f53(x101691,x101692)))),f46(x101691,x101692)) % 178.07/177.93 [10170]E(x101701,f2(a1))+E(x101702,f2(a1))+E(f329(f269(a1,a1,a1,a1,f35(a1),f329(f82(a1),f83(a1,x101702))),f329(f329(f329(f102(f882(a1,a1)),f329(f329(a328,f329(f329(a327,f329(f329(f244(a1),f2(a1)),x101702)),f329(f329(f243(a1),f2(a1)),x101701))),f329(f329(a327,f329(f329(f244(a1),x101702),f2(a1))),f329(f329(f244(a1),x101701),f2(a1))))),f53(x101701,x101702)),f329(f329(f268(a1,a1,f882(a1,a1)),f329(f329(f18(a1,f883(a1,f882(a1,a1)),f883(a1,f882(a1,a1))),f329(f329(f8(f883(a1,f883(f882(a1,a1),f882(a1,a1))),f883(f883(a1,f882(a1,a1)),f883(a1,f882(a1,a1))),a1),f18(a1,f882(a1,a1),f882(a1,a1))),f329(f329(f8(f882(a1,a1),f883(a1,f883(f882(a1,a1),f882(a1,a1))),a1),f329(f7(a1,f882(a1,a1),f883(f882(a1,a1),f882(a1,a1))),f329(f329(f8(a869,f883(f882(a1,a1),f883(f882(a1,a1),f882(a1,a1))),a1),f102(f882(a1,a1))),f329(f329(f7(a1,a1,a869),a326),f2(a1))))),f329(f329(f7(a1,a1,f882(a1,a1)),f329(f329(f8(a1,f883(a1,f882(a1,a1)),a1),f264(a1,a1)),f80(a1))),f2(a1))))),f329(f329(f7(a1,f883(a1,a1),f883(a1,f882(a1,a1))),f329(f329(f8(f883(a1,f882(a1,a1)),f883(f883(a1,a1),f883(a1,f882(a1,a1))),a1),f8(a1,f882(a1,a1),a1)),f329(f329(f8(a1,f883(a1,f882(a1,a1)),a1),f264(a1,a1)),f329(f329(f7(a1,a1,a1),f329(f329(f8(a1,f883(a1,a1),a1),f22(a1)),f80(a1))),f79(a1))))),f329(f22(a1),f329(f76(a1),x101702))))),f53(x101701,x101702)))),f46(x101701,x101702)) % 178.07/177.93 [10171]~P4(a5000)+P20(a871,x101711,f329(f329(f307(f874(a871)),f329(a94,x101712)),f193(f883(f874(a871),a869))))+~P20(a871,x101711,f329(f329(f307(f874(a871)),f329(f329(f329(f93(a871),f329(f329(f8(f883(a871,f883(a871,a869)),f883(a871,a869),a871),f329(f8(f883(a871,a869),a869,a871),f89(a871))),f329(f329(f8(f883(a871,a869),f883(a871,f883(a871,a869)),a871),f329(f7(a871,f883(a871,a869),f883(a871,a869)),f329(f329(f8(f883(a871,f883(a869,a869)),f883(f883(a871,a869),f883(a871,a869)),a871),f18(a871,a869,a869)),f329(f329(f8(f883(a871,a869),f883(a871,f883(a869,a869)),a871),f329(f8(a869,f883(a869,a869),a871),a332)),f199(x101712))))),a326))),x101712),a326)),f193(f883(f874(a871),a869)))) % 178.07/177.93 [5682]~P117(x56821)+~P92(x56821)+E(f329(f76(x56821),f329(f329(f254(x56821),f329(f109(x56821),a103)),x56822)),f79(x56821)) % 178.07/177.93 [6172]~P137(x61721)+~P24(f329(f329(f244(a1),x61722),f2(a1)))+E(f329(f80(x61721),f329(f106(x61721),f329(a110,f329(f80(a1),x61722)))),f329(f108(x61721),x61722)) % 178.07/177.93 [6373]P24(f329(f329(f243(a105),x63731),f79(a105)))+E(f329(f329(f81(a105),f79(a105)),f277(x63731,f329(f329(f39(a105),x63732),x63731))),f277(x63731,x63732))+P24(f329(f329(f244(a105),x63732),x63731)) % 178.07/177.93 [6973]~P91(x69731)+~P24(f329(f329(f331(x69731),x69732),f115(x69731)))+~E(f329(f329(f81(x69731),f329(f329(f81(x69731),f79(x69731)),x69732)),x69732),f2(x69731)) % 178.07/177.93 [7089]~P24(f329(f329(f244(a1),x70891),f2(a1)))+~P24(f329(f329(f243(a1),x70892),f2(a1)))+E(f329(f263(a1,a1),f329(a51,f47(f329(f80(a1),x70891),f329(f80(a1),x70892)))),f329(f329(f39(a1),x70891),x70892)) % 178.07/177.93 [7106]~P24(f329(f329(f244(a1),x71061),f2(a1)))+~P24(f329(f329(f243(a1),x71062),f2(a1)))+E(f329(f267(a1,a1),f329(a51,f47(f329(f80(a1),x71061),f329(f80(a1),x71062)))),f45(a1,x71061,x71062)) % 178.07/177.93 [7112]~P24(f329(f329(f244(a1),x71122),f2(a1)))+E(f329(f263(a1,a1),f329(a51,f50(f329(f80(a1),x71121),f329(f80(a1),x71122)))),f329(f329(f39(a1),x71121),x71122))+~P24(f329(f329(f244(a1),f2(a1)),x71121)) % 178.07/177.93 [7130]~P24(f329(f329(f244(a1),x71302),f2(a1)))+E(f329(f267(a1,a1),f329(a51,f50(f329(f80(a1),x71301),f329(f80(a1),x71302)))),f45(a1,x71301,x71302))+~P24(f329(f329(f244(a1),f2(a1)),x71301)) % 178.07/177.93 [7183]E(f329(f329(f39(a1),f329(f329(f254(a1),x71831),x71832)),x71831),f329(f329(f254(a1),x71831),f329(f329(f22(a875),x71832),f329(a118,f2(a875)))))+~P24(f329(f329(f244(a875),f2(a875)),x71832))+~P24(f329(f329(f244(a1),f2(a1)),x71831)) % 178.07/177.93 [7276]~P24(f329(f329(f244(a875),f2(a875)),x72761))+~P24(f329(f329(f244(a875),f2(a875)),x72762))+P24(f329(f329(f244(a875),f329(f329(f22(a875),x72761),x72762)),x72761)) % 178.07/177.93 [7277]~P24(f329(f329(f244(a875),f2(a875)),x72771))+~P24(f329(f329(f244(a875),f79(a875)),x72772))+P24(f329(f329(f244(a875),f329(f329(f39(a875),x72771),x72772)),x72771)) % 178.07/177.93 [7278]~P24(f329(f329(f244(a1),f2(a1)),x72781))+~P24(f329(f329(f244(a1),f79(a1)),x72782))+P24(f329(f329(f244(a1),f329(f329(f39(a1),x72781),x72782)),x72781)) % 178.07/177.93 [7427]E(x74271,f2(a875))+~E(x74272,f2(a1))+~P24(f329(f329(f244(a1),f2(a1)),f329(f329(f254(a1),f329(f76(a1),x74272)),x74271))) % 178.07/177.93 [7845]~E(x78452,f119(f876(x78451)))+E(f329(f194(f876(f876(x78451))),f179(x78451,x78452)),f2(a875))+~P29(a875,f329(f168(a875),f329(f329(f153(f876(x78451),a875),f194(f876(x78451))),x78452))) % 178.07/177.93 [8098]P24(f329(x80981,x80982))+~P24(f329(x80981,f329(a112,f708(x80981,x80982))))+~P24(f329(f329(f331(f883(f882(a875,a875),a869)),x80982),a104)) % 178.07/177.93 [8117]E(x81171,f119(f876(x81172)))+E(f329(f194(f876(x81172)),f329(f329(f164(f876(x81172)),x81171),f2(a875))),f329(f194(f876(f876(x81172))),f179(x81172,x81171)))+~P29(a875,f329(f168(a875),f329(f329(f153(f876(x81172),a875),f194(f876(x81172))),x81171))) % 178.07/177.93 [8817]~P24(f329(f62(x88171),f329(f249(x88171),x88172)))+~P24(f329(f62(x88171),f252(f883(x88171,a869))))+P24(f329(f62(x88171),f329(f249(x88171),f329(f329(f8(a869,a869,x88171),a324),x88172)))) % 178.07/177.93 [8879]E(f329(f329(f264(a875,a875),f329(a118,f329(f329(f39(a875),f329(f329(f22(a875),x88791),x88792)),x88792))),f45(a875,f329(f329(f22(a875),x88791),x88792),x88792)),f86(f882(a875,a875),f48(x88791,x88792)))+~P24(f329(f329(f244(a875),f2(a875)),x88792))+~P24(f329(f329(f243(a875),x88792),x88791)) % 178.07/177.93 [9171]~P24(f329(f62(x91711),f329(f249(x91711),x91712)))+P24(f329(f62(x91711),f252(f883(x91711,a869))))+~P24(f329(f62(x91711),f329(f249(x91711),f329(f329(f8(a869,a869,x91711),a324),x91712)))) % 178.07/177.93 [9892]P22(x98921,x98922)+~P38(x98921,f329(f263(f883(f882(x98921,x98921),a869),f883(f882(x98921,x98921),a869)),x98922))+~P24(f329(f329(f243(f883(f882(x98921,x98921),a869)),f329(f329(f286(x98921,x98921,x98921),f329(f263(f883(f882(x98921,x98921),a869),f883(f882(x98921,x98921),a869)),x98922)),f329(f267(f883(f882(x98921,x98921),a869),f883(f882(x98921,x98921),a869)),x98922))),f329(f263(f883(f882(x98921,x98921),a869),f883(f882(x98921,x98921),a869)),x98922))) % 178.07/177.93 [7209]~P24(f329(f329(f244(a875),f2(a875)),x72092))+P24(f329(f329(f244(a875),x72091),x72092))+E(f329(a118,f329(f329(f39(a875),f329(f329(f22(a875),x72091),x72092)),x72092)),f329(f329(f39(a875),x72091),x72092)) % 178.07/177.93 [7346]~P24(f329(f329(f244(a875),f2(a875)),x73462))+~P24(f329(f329(f243(a875),x73462),x73461))+E(f329(a118,f329(f329(f39(a875),f329(f329(f22(a875),x73461),x73462)),x73462)),f329(f329(f39(a875),x73461),x73462)) % 178.07/177.93 [8326]~P92(x83261)+~P91(x83261)+~P31(x83261,f329(f109(x83261),f329(f329(f22(a1),f329(f329(f81(a1),x83262),x83262)),a103))) % 178.07/177.93 [9078]E(x90781,f2(a875))+E(f329(f329(f268(a875,a875,f882(a875,a875)),f329(f329(f8(a875,f883(a875,f882(a875,a875)),a875),f264(a875,a875)),a118)),f86(f882(a875,a875),f48(f329(f329(f22(a875),x90782),x90781),x90781))),f86(f882(a875,a875),f48(x90782,x90781)))+P24(f329(f329(f244(a875),x90782),x90781)) % 178.07/177.93 [9504]P24(f329(x95042,f793(x95042,x95041)))+P24(f329(x95041,f793(x95042,x95041)))+E(f329(f249(a1),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f243(a1),f2(a1)))),x95041)),f329(f249(a1),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f243(a1),f2(a1)))),x95042))) % 178.07/177.93 [9508]~P24(f329(x95082,f793(x95082,x95081)))+~P24(f329(x95081,f793(x95082,x95081)))+E(f329(f249(a1),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f243(a1),f2(a1)))),x95081)),f329(f249(a1),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f883(a869,a869),a1),a327),f329(f243(a1),f2(a1)))),x95082))) % 178.07/177.93 [7563]~P60(x75631)+~P92(x75631)+E(f329(f329(f287(x75631),x75632),f329(f109(x75631),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))),x75632) % 178.07/177.93 [9207]~P92(x92071)+~E(f329(f109(x92071),x92072),f79(x92071))+P31(x92071,f329(f109(x92071),f329(f329(f81(a1),x92072),f329(f80(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))) % 178.07/177.93 [9384]~P136(x93841)+~E(x93842,f79(x93841))+E(f329(f329(f254(x93841),x93842),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f79(x93841)) % 178.07/177.93 [9385]~P136(x93851)+~E(x93852,f2(x93851))+E(f329(f329(f254(x93851),x93852),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f2(x93851)) % 178.07/177.93 [9398]~P136(x93981)+~E(x93982,f329(f80(x93981),f79(x93981)))+E(f329(f329(f254(x93981),x93982),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f79(x93981)) % 178.07/177.93 [9442]~P92(x94421)+E(f329(f109(x94421),x94422),f79(x94421))+~P31(x94421,f329(f109(x94421),f329(f329(f81(a1),x94422),f329(f80(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))) % 178.07/177.93 [9826]~P117(x98262)+E(x98261,f2(x98262))+P24(f329(f329(f244(x98262),f2(x98262)),f329(f329(f254(x98262),x98261),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))))) % 178.07/177.93 [9891]~P117(x98912)+~E(x98911,f2(x98912))+~P24(f329(f329(f244(x98912),f2(x98912)),f329(f329(f254(x98912),x98911),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))))) % 178.07/177.93 [9917]P24(f329(f329(f243(a1),x99171),f2(a1)))+P24(f329(f329(f244(a1),x99172),x99171))+E(f329(f44(x99171),f47(x99172,f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x99171))),f47(x99172,x99171)) % 178.07/177.93 [9918]~P24(f329(f329(f244(a1),f2(a1)),x99181))+P24(f329(f329(f244(a1),x99182),x99181))+E(f329(f44(x99181),f47(x99182,f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x99181))),f47(x99182,x99181)) % 178.07/177.93 [9919]P24(f329(f329(f243(a1),x99191),f2(a1)))+P24(f329(f329(f243(a1),f2(a1)),f329(f329(f81(a1),x99192),x99191)))+E(f329(f44(x99191),f50(x99192,f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x99191))),f50(x99192,x99191)) % 178.07/177.93 [9920]~P24(f329(f329(f244(a1),f2(a1)),x99201))+P24(f329(f329(f243(a1),f2(a1)),f329(f329(f81(a1),x99202),x99201)))+E(f329(f44(x99201),f50(x99202,f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x99201))),f50(x99202,x99201)) % 178.07/177.93 [9921]~P141(x99211)+~P24(f329(f329(f243(a1),f2(a1)),x99212))+E(f329(f106(x99211),f329(a110,f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x99212))),f329(f329(f81(x99211),f329(f106(x99211),f329(a110,x99212))),f329(f106(x99211),f329(a110,x99212)))) % 178.07/177.93 [5021]~P143(x50211,x50213,x50212)+~E(x50213,f2(a1))+P24(f329(x50211,x50212)) % 178.07/177.93 [5142]~P105(x51421)+~P29(x51421,x51423)+P29(x51421,f169(x51421,x51422,x51423)) % 178.07/177.93 [5143]~P105(x51431)+~P29(x51431,x51433)+P29(x51431,f176(x51431,x51432,x51433)) % 178.07/177.93 [4726]~P67(x47262)+~E(x47263,f329(f80(x47262),x47261))+E(x47261,f329(f80(x47262),x47263)) % 178.07/177.93 [4728]~P67(x47281)+~E(f329(f80(x47281),x47283),x47282)+E(f329(f80(x47281),x47282),x47283) % 178.07/177.93 [4802]~P89(x48023)+E(x48021,x48022)+~E(f329(f80(x48023),x48021),f329(f80(x48023),x48022)) % 178.07/177.93 [4803]~P67(x48033)+E(x48031,x48032)+~E(f329(f80(x48033),x48031),f329(f80(x48033),x48032)) % 178.07/177.93 [4804]~P105(x48043)+E(x48041,x48042)+~E(f329(f250(x48043),x48041),f329(f250(x48043),x48042)) % 178.07/177.93 [4805]~P101(x48053)+E(x48051,x48052)+~E(f329(f106(x48053),x48051),f329(f106(x48053),x48052)) % 178.07/177.93 [4806]~P91(x48063)+E(x48061,x48062)+~E(f329(f108(x48063),x48061),f329(f108(x48063),x48062)) % 178.07/177.93 [4807]~P105(x48073)+E(x48071,x48072)+~E(f329(f301(x48073),x48071),f329(f301(x48073),x48072)) % 178.07/177.93 [4808]~P105(x48083)+E(x48081,x48082)+~E(f329(f251(x48083),x48081),f329(f251(x48083),x48082)) % 178.07/177.93 [4809]~P105(x48093)+E(x48091,x48092)+~E(f329(f298(x48093),x48091),f329(f298(x48093),x48092)) % 178.07/177.93 [4908]~P58(x49081)+~P24(f329(x49082,x49083))+P24(f329(f58(x49081),x49082)) % 178.07/177.93 [4941]~P58(x49413)+P24(f329(x49411,x49412))+~P24(f329(f59(x49413),x49411)) % 178.07/177.93 [5039]~P144(x50391,x50392,x50393)+~E(x50392,f2(a1))+P24(f329(x50391,f2(a1))) % 178.07/177.93 [5076]~E(x50761,f2(a875))+E(f338(x50761,x50762,x50763),f193(f883(x50763,a869)))+~E(f329(f38(x50763),x50762),f329(a118,x50761)) % 178.07/177.93 [5231]~E(x52312,f2(a875))+E(f329(f263(a875,a875),x52311),f2(a875))+~P24(f329(f48(x52313,x52312),x52311)) % 178.07/177.93 [5278]P24(f329(x52781,x52782))+~E(x52783,f329(f106(a1),x52782))+~P24(f329(x52781,f329(a110,x52783))) % 178.07/177.93 [5746]~E(x57463,f2(a875))+~P24(f329(x57461,x57462))+P24(f329(x57461,f45(a875,x57462,x57463))) % 178.07/177.93 [5877]~P24(f329(a25,x58773))+~P24(f329(a25,x58772))+P24(f329(a25,f31(x58771,x58772,x58773))) % 178.07/177.93 [5909]~P58(x59093)+~P7(x59093,x59091,x59092)+P24(f329(x59091,f663(x59092,x59091,x59093))) % 178.07/177.93 [6156]~E(x61563,f2(a875))+P24(f329(x61561,x61562))+~P24(f329(x61561,f45(a875,x61562,x61563))) % 178.07/177.93 [6303]~P58(x63031)+P8(x63031,x63032,x63033)+~P24(f329(x63032,f664(x63033,x63032,x63031))) % 178.07/177.93 [6830]E(x68301,f2(a875))+~P24(f329(x68302,f469(x68301,x68303,x68302)))+P24(f329(x68302,f45(a875,x68303,x68301))) % 178.07/177.93 [6938]~P27(x69381)+~P24(f329(f329(f243(x69381),x69382),f865(x69383,x69382,x69381)))+P24(f329(f329(f243(x69381),x69382),f41(x69381,x69383))) % 178.07/177.93 [6940]~P24(f329(x69401,x69402))+~P24(f329(x69401,f469(x69403,x69402,x69401)))+P24(f329(x69401,f45(a875,x69402,x69403))) % 178.07/177.93 [7044]E(x70441,f119(x70442))+E(f329(f329(f150(x70442),f639(x70443,x70441,x70442)),f643(x70443,x70441,x70442)),x70441)+~P24(f329(f329(f331(f876(x70442)),x70441),f160(x70442,x70443))) % 178.07/177.93 [7075]~P137(x70751)+~P24(f329(f329(f331(x70751),x70752),f115(x70751)))+P24(f329(f329(f331(x70751),f329(f329(f254(x70751),x70752),x70753)),f115(x70751))) % 178.07/177.93 [7396]P38(x73961,x73962)+~P24(f329(f329(f331(x73961),x73963),f780(x73962,x73961)))+P24(f329(f329(f331(x73961),f791(x73962,x73961,x73963)),f780(x73962,x73961))) % 178.07/177.93 [7666]E(x76661,f119(x76662))+~P24(f329(f329(f331(f876(x76662)),x76661),f160(x76662,x76663)))+P24(f329(f329(f331(f876(x76662)),f643(x76663,x76661,x76662)),f160(x76662,x76663))) % 178.07/177.93 [7719]E(x77191,f2(a875))+E(f329(f329(f81(a875),f329(f329(f82(a875),x77191),f470(x77191,x77192,x77193))),f469(x77191,x77192,x77193)),x77192)+P24(f329(x77193,f45(a875,x77192,x77191))) % 178.07/177.93 [7762]~P24(f329(x77623,x77622))+E(f329(f329(f81(a875),f329(f329(f82(a875),x77621),f470(x77621,x77622,x77623))),f469(x77621,x77622,x77623)),x77622)+P24(f329(x77623,f45(a875,x77622,x77621))) % 178.07/177.93 [7901]P24(f329(f329(f244(a1),x79011),f460(x79012,x79013,x79011)))+P24(f329(f329(x79013,f329(f329(f39(a1),x79012),x79011)),f45(a1,x79012,x79011)))+~P24(f329(f329(f244(a1),x79011),f2(a1))) % 178.07/177.93 [8178]P24(f329(f329(x81782,f329(f329(f39(a1),x81781),x81783)),f45(a1,x81781,x81783)))+~P24(f329(f329(f244(a1),x81783),f2(a1)))+P24(f329(f329(f243(a1),f460(x81781,x81782,x81783)),f2(a1))) % 178.07/177.93 [8359]E(f329(f329(f81(a1),f329(f329(f82(a1),x83591),f465(x83592,x83593,x83591))),f460(x83592,x83593,x83591)),x83592)+P24(f329(f329(x83593,f329(f329(f39(a1),x83592),x83591)),f45(a1,x83592,x83591)))+~P24(f329(f329(f244(a1),x83591),f2(a1))) % 178.07/177.93 [8601]~P24(f329(f329(x86011,f465(x86012,x86011,x86013)),f460(x86012,x86011,x86013)))+P24(f329(f329(x86011,f329(f329(f39(a1),x86012),x86013)),f45(a1,x86012,x86013)))+~P24(f329(f329(f244(a1),x86013),f2(a1))) % 178.07/177.93 [8827]~P105(x88271)+~P29(x88271,x88273)+P29(x88271,f148(x88271,x88271,f5(x88271),x88272,x88273)) % 178.07/177.93 [9334]~P121(x93342)+E(x93341,f2(x93342))+~P24(f329(f329(f243(x93342),f329(f329(f81(x93342),f329(f329(f82(x93342),x93343),x93343)),f329(f329(f82(x93342),x93341),x93341))),f2(x93342))) % 178.07/177.93 [9335]~P121(x93352)+E(x93351,f2(x93352))+~P24(f329(f329(f243(x93352),f329(f329(f81(x93352),f329(f329(f82(x93352),x93351),x93351)),f329(f329(f82(x93352),x93353),x93353))),f2(x93352))) % 178.07/177.93 [10107]~P117(x101071)+~P24(f329(f329(f244(x101071),x101072),f2(x101071)))+P24(f329(f329(f244(x101071),f329(f329(f254(x101071),x101072),f329(a118,f329(f329(f82(a875),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x101073)))),f2(x101071))) % 178.07/177.93 [10115]~P117(x101152)+E(x101151,f2(x101152))+~P24(f329(f329(f243(x101152),f329(f329(f81(x101152),f329(f329(f254(x101152),x101153),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f329(f329(f254(x101152),x101151),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))))),f2(x101152))) % 178.07/177.93 [10116]~P117(x101162)+E(x101161,f2(x101162))+~P24(f329(f329(f243(x101162),f329(f329(f81(x101162),f329(f329(f254(x101162),x101161),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f329(f329(f254(x101162),x101163),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))))),f2(x101162))) % 178.07/177.93 [4758]~E(x47582,x47583)+~P66(x47581)+E(f329(f329(f22(x47581),x47582),x47583),f2(x47581)) % 178.07/177.93 [4759]~E(x47592,x47593)+~P67(x47591)+E(f329(f329(f22(x47591),x47592),x47593),f2(x47591)) % 178.07/177.93 [4772]~P139(x47721)+~E(x47723,f2(x47721))+E(f329(f329(f81(x47721),x47722),x47723),x47722) % 178.07/177.93 [4788]~P138(x47881)+~E(x47883,f2(x47881))+E(f329(f329(f82(x47881),x47882),x47883),f2(x47881)) % 178.07/177.93 [4789]~P138(x47891)+~E(x47892,f2(x47891))+E(f329(f329(f82(x47891),x47892),x47893),f2(x47891)) % 178.07/177.93 [4811]~E(x48113,f119(x48111))+~E(x48112,f119(x48111))+E(f329(f329(f127(x48111),x48112),x48113),f119(x48111)) % 178.07/177.93 [4898]~P139(x48982)+E(x48981,f2(x48982))+~E(f329(f329(f81(x48982),x48983),x48981),x48983) % 178.07/177.93 [4899]~P67(x48991)+~E(x48992,f329(f80(x48991),x48993))+E(f329(f329(f81(x48991),x48992),x48993),f2(x48991)) % 178.07/177.93 [4906]E(x49061,f119(x49062))+E(x49063,f2(a875))+~E(f329(f329(f174(x49062),x49063),x49061),f119(x49062)) % 178.07/177.93 [4912]~P66(x49123)+E(x49121,x49122)+~E(f329(f329(f22(x49123),x49121),x49122),f2(x49123)) % 178.07/177.93 [4913]~P67(x49133)+E(x49131,x49132)+~E(f329(f329(f22(x49133),x49131),x49132),f2(x49133)) % 178.07/177.93 [4922]~P136(x49222)+E(x49221,f2(x49222))+~E(f329(f329(f254(x49222),x49221),x49223),f2(x49222)) % 178.07/177.93 [4923]~P64(x49232)+E(x49231,f193(x49232))+~E(f329(f329(f116(x49232),x49233),x49231),f193(x49232)) % 178.07/177.93 [4924]~P64(x49242)+E(x49241,f193(x49242))+~E(f329(f329(f116(x49242),x49241),x49243),f193(x49242)) % 178.07/177.93 [4925]~P98(x49252)+E(x49251,f252(x49252))+~E(f329(f329(f107(x49252),x49253),x49251),f252(x49252)) % 178.07/177.93 [4926]~P98(x49262)+E(x49261,f252(x49262))+~E(f329(f329(f107(x49262),x49261),x49263),f252(x49262)) % 178.07/177.93 [4992]~P67(x49922)+E(x49921,f329(f80(x49922),x49923))+~E(f329(f329(f81(x49922),x49921),x49923),f2(x49922)) % 178.07/177.93 [4993]~P67(x49931)+E(f329(f80(x49931),x49932),x49933)+~E(f329(f329(f81(x49931),x49932),x49933),f2(x49931)) % 178.07/177.93 [4995]~E(x49952,x49953)+~P104(x49951)+P24(f329(f329(f243(x49951),x49952),x49953)) % 178.07/177.93 [4997]~E(x49972,x49973)+~P107(x49971)+P24(f329(f329(f243(x49971),x49972),x49973)) % 178.07/177.93 [4998]~E(x49982,x49983)+~P94(x49981)+P24(f329(f329(f92(x49981),x49982),x49983)) % 178.07/177.93 [5092]~P109(x50921)+~E(x50922,f329(f80(x50921),x50923))+E(f329(f329(f82(x50921),x50922),x50922),f329(f329(f82(x50921),x50923),x50923)) % 178.07/177.93 [5100]~P105(x51001)+~P29(x51001,x51003)+P29(x51001,f329(f329(f174(x51001),x51002),x51003)) % 178.07/177.93 [5101]~P105(x51011)+~P29(x51011,x51013)+P29(x51011,f329(f329(f137(x51011),x51012),x51013)) % 178.07/177.93 [5140]E(x51401,x51402)+E(x51403,f2(a875))+~E(f329(f329(f82(a875),x51403),x51401),f329(f329(f82(a875),x51403),x51402)) % 178.07/177.93 [5141]E(x51411,x51412)+E(x51413,f2(a875))+~E(f329(f329(f82(a875),x51411),x51413),f329(f329(f82(a875),x51412),x51413)) % 178.07/177.93 [5222]~E(x52222,x52223)+~P107(x52221)+E(f300(x52221,x52222,x52223),f329(f329(f307(x52221),x52222),f193(f883(x52221,a869)))) % 178.07/177.93 [5266]E(x52661,x52662)+~P94(x52663)+~P24(f329(f329(f92(x52663),x52661),x52662)) % 178.07/177.93 [5276]~E(x52761,x52762)+~P105(x52763)+~P24(f329(f329(f244(x52763),x52761),x52762)) % 178.07/177.93 [5277]~E(x52771,x52772)+~P107(x52773)+~P24(f329(f329(f244(x52773),x52771),x52772)) % 178.07/177.93 [5287]~P107(x52871)+E(f329(f299(x52871,x52872),x52873),f193(f883(x52871,a869)))+P24(f329(f329(f244(x52871),x52872),x52873)) % 178.07/177.93 [5333]~P107(x53331)+E(f302(x53331,x53332,x53333),f193(f883(x53331,a869)))+P24(f329(f329(f244(x53331),x53332),x53333)) % 178.07/177.93 [5334]~P107(x53341)+E(f300(x53341,x53342,x53343),f193(f883(x53341,a869)))+P24(f329(f329(f243(x53341),x53342),x53343)) % 178.07/177.93 [5335]~P107(x53351)+E(f193(f883(x53351,a869)),f302(x53351,x53352,x53353))+P24(f329(f329(f244(x53351),x53352),x53353)) % 178.07/177.93 [5336]~P107(x53361)+E(f193(f883(x53361,a869)),f300(x53361,x53362,x53363))+P24(f329(f329(f243(x53361),x53362),x53363)) % 178.07/177.93 [5344]~P99(x53441)+~E(f329(f329(f116(x53441),x53442),x53443),x53443)+P24(f329(f329(f243(x53441),x53442),x53443)) % 178.07/177.93 [5345]~P100(x53451)+~E(f329(f329(f107(x53451),x53452),x53453),x53452)+P24(f329(f329(f243(x53451),x53452),x53453)) % 178.07/177.93 [5346]~P105(x53461)+~E(f329(f329(f241(x53461),x53462),x53463),x53462)+P24(f329(f329(f243(x53461),x53462),x53463)) % 178.07/177.93 [5347]~P105(x53471)+~E(f329(f329(f242(x53471),x53472),x53473),x53473)+P24(f329(f329(f243(x53471),x53472),x53473)) % 178.07/177.93 [5367]~P105(x53671)+P29(x53671,x53672)+~P29(x53671,f329(f329(f150(x53671),x53673),x53672)) % 178.07/177.93 [5368]~P105(x53681)+P29(x53681,x53682)+~P29(x53681,f329(f329(f127(x53681),x53683),x53682)) % 178.07/177.93 [5369]~P105(x53691)+P29(x53691,x53692)+~P29(x53691,f329(f329(f127(x53691),x53692),x53693)) % 178.07/177.93 [5437]~P105(x54371)+P24(f329(f329(f243(x54371),x54373),x54372))+P24(f329(f329(f244(x54371),x54372),x54373)) % 178.07/177.93 [5439]~P105(x54391)+P24(f329(f329(f243(x54391),x54393),x54392))+P24(f329(f329(f243(x54391),x54392),x54393)) % 178.07/177.93 [5477]~P99(x54771)+E(f329(f329(f116(x54771),x54772),x54773),x54772)+~P24(f329(f329(f243(x54771),x54773),x54772)) % 178.07/177.93 [5479]~P99(x54791)+E(f329(f329(f116(x54791),x54792),x54793),x54793)+~P24(f329(f329(f243(x54791),x54792),x54793)) % 178.07/177.93 [5480]~P100(x54801)+E(f329(f329(f107(x54801),x54802),x54803),x54803)+~P24(f329(f329(f243(x54801),x54803),x54802)) % 178.07/177.93 [5482]~P100(x54821)+E(f329(f329(f107(x54821),x54822),x54823),x54822)+~P24(f329(f329(f243(x54821),x54822),x54823)) % 178.07/177.93 [5483]~P105(x54831)+E(f329(f329(f241(x54831),x54832),x54833),x54833)+~P24(f329(f329(f243(x54831),x54833),x54832)) % 178.07/177.93 [5485]~P105(x54851)+E(f329(f329(f241(x54851),x54852),x54853),x54852)+~P24(f329(f329(f243(x54851),x54852),x54853)) % 178.07/177.93 [5486]~P105(x54861)+E(f329(f329(f242(x54861),x54862),x54863),x54862)+~P24(f329(f329(f243(x54861),x54863),x54862)) % 178.07/177.93 [5488]~P105(x54881)+E(f329(f329(f242(x54881),x54882),x54883),x54883)+~P24(f329(f329(f243(x54881),x54882),x54883)) % 178.07/177.93 [5495]~P115(x54952)+E(x54951,f2(x54952))+E(f329(f329(f287(x54952),f329(f80(x54952),x54953)),f329(f80(x54952),x54951)),f329(f329(f287(x54952),x54953),x54951)) % 178.07/177.93 [5540]~P107(x55401)+E(f329(f299(x55401,x55402),x55403),f193(f883(x55401,a869)))+~P24(f329(f329(f243(x55401),x55403),x55402)) % 178.07/177.93 [5571]~P107(x55711)+E(f303(x55711,x55712,x55713),f193(f883(x55711,a869)))+~P24(f329(f329(f243(x55711),x55713),x55712)) % 178.07/177.93 [5572]~P107(x55721)+E(f302(x55721,x55722,x55723),f193(f883(x55721,a869)))+~P24(f329(f329(f243(x55721),x55723),x55722)) % 178.07/177.93 [5573]~P107(x55731)+E(f300(x55731,x55732,x55733),f193(f883(x55731,a869)))+~P24(f329(f329(f244(x55731),x55733),x55732)) % 178.07/177.93 [5624]~E(f329(f329(f22(a875),x56241),x56243),x56242)+E(x56241,f329(f329(f81(a875),x56242),x56243))+~P24(f329(f329(f243(a875),x56243),x56241)) % 178.07/177.93 [5625]~E(x56251,f329(f329(f81(a875),x56253),x56252))+E(f329(f329(f22(a875),x56251),x56252),x56253)+~P24(f329(f329(f243(a875),x56252),x56251)) % 178.07/177.93 [5671]~P24(f329(x56711,x56713))+P24(f329(x56711,f385(x56711,x56712)))+~P24(f329(f329(f244(a875),x56713),x56712)) % 178.07/177.93 [5672]~P24(f329(x56721,x56723))+P24(f329(x56721,f411(x56721,x56722)))+~P24(f329(f329(f243(a875),x56723),x56722)) % 178.07/177.93 [5680]~P107(x56801)+~E(f329(f299(x56801,x56802),x56803),f193(f883(x56801,a869)))+~P24(f329(f329(f244(x56801),x56802),x56803)) % 178.07/177.93 [5684]~P104(x56841)+~P24(f329(f329(f244(x56841),x56842),x56843))+P24(f329(f329(f243(x56841),x56842),x56843)) % 178.07/177.93 [5686]~P107(x56861)+~P24(f329(f329(f244(x56861),x56862),x56863))+P24(f329(f329(f243(x56861),x56862),x56863)) % 178.07/177.93 [5794]~P107(x57941)+~E(f302(x57941,x57942,x57943),f193(f883(x57941,a869)))+~P24(f329(f329(f244(x57941),x57942),x57943)) % 178.07/177.93 [5795]~P107(x57951)+~E(f300(x57951,x57952,x57953),f193(f883(x57951,a869)))+~P24(f329(f329(f243(x57951),x57952),x57953)) % 178.07/177.93 [5796]~P107(x57961)+~E(f193(f883(x57961,a869)),f302(x57961,x57962,x57963))+~P24(f329(f329(f244(x57961),x57962),x57963)) % 178.07/177.93 [5797]~P107(x57971)+~E(f193(f883(x57971,a869)),f300(x57971,x57972,x57973))+~P24(f329(f329(f243(x57971),x57972),x57973)) % 178.07/177.93 [5805]P24(f329(x58051,x58052))+~P24(f329(x58051,f387(x58051,x58053)))+~P24(f329(f329(f244(a875),x58052),x58053)) % 178.07/177.93 [5806]P24(f329(x58061,x58062))+~P24(f329(x58061,f413(x58061,x58063)))+~P24(f329(f329(f243(a875),x58062),x58063)) % 178.07/177.93 [5814]~E(x58141,f329(a118,x58143))+P24(f329(f329(f244(a875),x58141),f329(a118,x58142)))+~P24(f329(f329(f244(a875),x58143),x58142)) % 178.07/177.93 [5830]E(x58301,x58302)+~E(f329(f329(f82(a875),x58303),x58301),f329(f329(f82(a875),x58303),x58302))+~P24(f329(f329(f244(a875),f2(a875)),x58303)) % 178.07/177.93 [5888]E(f329(x58881,f360(x58881,x58882,x58883)),f79(a875))+~E(f329(f329(f6(x58883,a875),x58881),x58882),f79(a875))+~P24(f329(f62(x58883),x58882)) % 178.07/177.93 [5900]~P27(x59001)+P24(f329(f329(f243(x59001),x59002),f40(x59001,x59003)))+~P24(f329(f329(f331(x59001),x59002),x59003)) % 178.07/177.93 [5930]~P104(x59301)+~P24(f329(f329(f244(x59301),x59303),x59302))+~P24(f329(f329(f244(x59301),x59302),x59303)) % 178.07/177.93 [5931]~P104(x59311)+~P24(f329(f329(f243(x59311),x59313),x59312))+~P24(f329(f329(f244(x59311),x59312),x59313)) % 178.07/177.93 [5932]~P105(x59321)+~P24(f329(f329(f244(x59321),x59323),x59322))+~P24(f329(f329(f244(x59321),x59322),x59323)) % 178.07/177.93 [5935]~P105(x59351)+~P24(f329(f329(f243(x59351),x59353),x59352))+~P24(f329(f329(f244(x59351),x59352),x59353)) % 178.07/177.93 [5936]~P107(x59361)+~P24(f329(f329(f244(x59361),x59363),x59362))+~P24(f329(f329(f244(x59361),x59362),x59363)) % 178.07/177.93 [5965]~E(f329(x59652,f361(x59652,x59653,x59651)),f2(a875))+E(f329(f329(f6(x59651,a875),x59652),x59653),f2(a875))+~P24(f329(f62(x59651),x59653)) % 178.07/177.93 [5966]~E(f329(x59662,f342(x59662,x59663,x59661)),f79(a875))+E(f329(f329(f9(x59661,a875),x59662),x59663),f79(a875))+~P24(f329(f62(x59661),x59663)) % 178.07/177.93 [5981]~P106(x59811)+~P24(f329(f329(f244(x59811),x59813),x59812))+P24(f329(f329(f331(x59811),x59812),f329(f301(x59811),x59813))) % 178.07/177.93 [5982]~P106(x59821)+~P24(f329(f329(f243(x59821),x59823),x59822))+P24(f329(f329(f331(x59821),x59822),f329(f251(x59821),x59823))) % 178.07/177.93 [5983]~P106(x59831)+~P24(f329(f329(f244(x59831),x59832),x59833))+P24(f329(f329(f331(x59831),x59832),f329(f250(x59831),x59833))) % 178.07/177.93 [5984]~P106(x59841)+~P24(f329(f329(f243(x59841),x59842),x59843))+P24(f329(f329(f331(x59841),x59842),f329(f298(x59841),x59843))) % 178.07/177.93 [5996]E(f329(x59961,f363(x59961,x59962,x59963)),f329(a118,f2(a875)))+~E(f329(f329(f6(x59963,a875),x59961),x59962),f329(a118,f2(a875)))+~P24(f329(f62(x59963),x59962)) % 178.07/177.93 [6079]~P27(x60791)+~P24(f329(f329(f331(x60791),x60793),x60792))+P24(f329(f329(f243(x60791),f41(x60791,x60792)),x60793)) % 178.07/177.93 [6096]~P24(f329(f329(f243(a875),x60961),x60963))+P24(f329(f329(f243(a875),x60961),x60962))+~P24(f329(f329(f243(a875),x60963),x60962)) % 178.07/177.93 [6097]~P24(f329(f329(f243(a1),x60971),x60973))+P24(f329(f329(f243(a1),x60971),x60972))+~P24(f329(f329(f243(a1),x60973),x60972)) % 178.07/177.93 [6114]~P106(x61141)+~P24(f329(f329(f331(x61141),x61143),f329(f301(x61141),x61142)))+P24(f329(f329(f244(x61141),x61142),x61143)) % 178.07/177.93 [6115]~P106(x61151)+~P24(f329(f329(f331(x61151),x61152),f329(f250(x61151),x61153)))+P24(f329(f329(f244(x61151),x61152),x61153)) % 178.07/177.93 [6116]~P106(x61161)+~P24(f329(f329(f331(x61161),x61163),f329(f251(x61161),x61162)))+P24(f329(f329(f243(x61161),x61162),x61163)) % 178.07/177.93 [6117]~P106(x61171)+~P24(f329(f329(f331(x61171),x61172),f329(f298(x61171),x61173)))+P24(f329(f329(f243(x61171),x61172),x61173)) % 178.07/177.93 [6238]P24(f329(x62381,x62382))+~P24(f329(x62381,f591(x62381)))+~P24(f329(f329(f331(x62383),x62382),f252(f883(x62383,a869)))) % 178.07/177.93 [6339]~P61(x63391)+P24(f329(f329(f244(x63391),f2(x63391)),f454(x63393,x63392,x63391)))+P24(f329(f329(f243(x63391),x63392),x63393)) % 178.07/177.93 [6406]~P77(x64061)+~P24(f329(f329(f244(x64061),x64063),f329(f80(x64061),x64062)))+P24(f329(f329(f244(x64061),x64062),f329(f80(x64061),x64063))) % 178.07/177.93 [6408]~P77(x64081)+~P24(f329(f329(f243(x64081),x64083),f329(f80(x64081),x64082)))+P24(f329(f329(f243(x64081),x64082),f329(f80(x64081),x64083))) % 178.07/177.93 [6420]~P24(f329(f329(f244(a875),x64201),x64203))+~P24(f329(f329(f244(a875),x64203),x64202))+P24(f329(f329(f244(a875),f329(a118,x64201)),x64202)) % 178.07/177.93 [6447]~P117(x64471)+P24(f329(f329(f244(x64471),f329(f108(x64471),x64472)),f329(f108(x64471),x64473)))+~P24(f329(f329(f244(a1),x64472),x64473)) % 178.07/177.93 [6448]~P120(x64481)+P24(f329(f329(f244(x64481),f329(f106(x64481),x64482)),f329(f106(x64481),x64483)))+~P24(f329(f329(f244(a875),x64482),x64483)) % 178.07/177.93 [6449]~P120(x64491)+P24(f329(f329(f243(x64491),f329(f106(x64491),x64492)),f329(f106(x64491),x64493)))+~P24(f329(f329(f243(a875),x64492),x64493)) % 178.07/177.93 [6450]~P117(x64501)+P24(f329(f329(f243(x64501),f329(f108(x64501),x64502)),f329(f108(x64501),x64503)))+~P24(f329(f329(f243(a1),x64502),x64503)) % 178.07/177.93 [6456]~P105(x64561)+E(f329(f329(f116(f883(x64561,a869)),f329(f250(x64561),x64562)),f329(f299(x64561,x64562),x64563)),f329(f250(x64561),x64563))+~P24(f329(f329(f243(x64561),x64562),x64563)) % 178.07/177.93 [6485]~P77(x64851)+~P24(f329(f329(f244(x64851),x64853),x64852))+P24(f329(f329(f244(x64851),f329(f80(x64851),x64852)),f329(f80(x64851),x64853))) % 178.07/177.93 [6487]~P77(x64871)+~P24(f329(f329(f243(x64871),x64873),x64872))+P24(f329(f329(f243(x64871),f329(f80(x64871),x64872)),f329(f80(x64871),x64873))) % 178.07/177.93 [6489]~P89(x64891)+~P24(f329(f329(f243(x64891),x64893),x64892))+P24(f329(f329(f243(x64891),f329(f80(x64891),x64892)),f329(f80(x64891),x64893))) % 178.07/177.93 [6521]~P105(x65211)+E(f329(f329(f116(f883(x65211,a869)),f329(f250(x65211),x65212)),f300(x65211,x65212,x65213)),f329(f298(x65211),x65213))+~P24(f329(f329(f243(x65211),x65212),x65213)) % 178.07/177.93 [6522]~P105(x65221)+E(f329(f329(f116(f883(x65221,a869)),f329(f298(x65221),x65222)),f303(x65221,x65222,x65223)),f329(f250(x65221),x65223))+~P24(f329(f329(f244(x65221),x65222),x65223)) % 178.07/177.93 [6523]~P105(x65231)+E(f329(f329(f116(f883(x65231,a869)),f329(f298(x65231),x65232)),f302(x65231,x65232,x65233)),f329(f298(x65231),x65233))+~P24(f329(f329(f243(x65231),x65232),x65233)) % 178.07/177.93 [6558]~P105(x65581)+E(f329(f329(f116(f883(x65581,a869)),f329(f299(x65581,x65582),x65583)),f329(f251(x65581),x65583)),f329(f251(x65581),x65582))+~P24(f329(f329(f243(x65581),x65582),x65583)) % 178.07/177.93 [6713]~P105(x67131)+E(f329(f329(f116(f883(x67131,a869)),f303(x67131,x67132,x67133)),f329(f251(x67131),x67133)),f329(f301(x67131),x67132))+~P24(f329(f329(f244(x67131),x67132),x67133)) % 178.07/177.93 [6714]~P105(x67141)+E(f329(f329(f116(f883(x67141,a869)),f302(x67141,x67142,x67143)),f329(f301(x67141),x67143)),f329(f301(x67141),x67142))+~P24(f329(f329(f243(x67141),x67142),x67143)) % 178.07/177.93 [6715]~P105(x67151)+E(f329(f329(f116(f883(x67151,a869)),f300(x67151,x67152,x67153)),f329(f301(x67151),x67153)),f329(f251(x67151),x67152))+~P24(f329(f329(f243(x67151),x67152),x67153)) % 178.07/177.93 [6733]P24(f329(x67331,x67332))+~P24(f329(f329(f243(a875),x67332),x67333))+P24(f329(f329(f331(a875),f413(x67331,x67333)),f300(a875,f2(a875),x67333))) % 178.07/177.93 [6767]E(x67671,x67672)+~E(f329(f329(f164(x67673),x67671),f569(x67673,x67672,x67671)),f329(f329(f164(x67673),x67672),f569(x67673,x67672,x67671)))+~E(f329(f194(f876(x67673)),x67671),f329(f194(f876(x67673)),x67672)) % 178.07/177.93 [6772]~E(x67723,f329(f329(f39(a875),x67721),x67722))+~P24(f329(f329(f244(a875),f2(a875)),x67722))+P24(f329(f329(f244(a875),x67721),f329(f329(f82(a875),x67722),f329(a118,x67723)))) % 178.07/177.93 [6789]~P24(f329(x67891,x67893))+~P24(f329(f329(f243(a875),x67893),x67892))+P24(f329(f329(f331(a875),f411(x67891,x67892)),f300(a875,f2(a875),x67892))) % 178.07/177.93 [6827]~P24(f329(x68271,x68273))+P24(f329(x68271,f414(x68271,x68272)))+~P24(f329(f329(f331(a875),x68273),f300(a875,f2(a875),x68272))) % 178.07/177.93 [6847]~P120(x68473)+~P24(f329(f329(f244(x68473),f329(f106(x68473),x68471)),f329(f106(x68473),x68472)))+P24(f329(f329(f244(a875),x68471),x68472)) % 178.07/177.93 [6848]~P117(x68483)+~P24(f329(f329(f244(x68483),f329(f108(x68483),x68481)),f329(f108(x68483),x68482)))+P24(f329(f329(f244(a1),x68481),x68482)) % 178.07/177.93 [6849]~P120(x68493)+~P24(f329(f329(f243(x68493),f329(f106(x68493),x68491)),f329(f106(x68493),x68492)))+P24(f329(f329(f243(a875),x68491),x68492)) % 178.07/177.93 [6850]~P117(x68503)+~P24(f329(f329(f243(x68503),f329(f108(x68503),x68501)),f329(f108(x68503),x68502)))+P24(f329(f329(f243(a1),x68501),x68502)) % 178.07/177.93 [6867]~P120(x68671)+~P24(f329(f329(f244(x68671),f79(x68671)),x68672))+P24(f329(f329(f244(x68671),f79(x68671)),f329(f329(f254(x68671),x68672),f329(a118,x68673)))) % 178.07/177.93 [6869]~P77(x68691)+~P24(f329(f329(f244(x68691),f329(f80(x68691),x68693)),f329(f80(x68691),x68692)))+P24(f329(f329(f244(x68691),x68692),x68693)) % 178.07/177.93 [6870]~P77(x68701)+~P24(f329(f329(f243(x68701),f329(f80(x68701),x68703)),f329(f80(x68701),x68702)))+P24(f329(f329(f243(x68701),x68702),x68703)) % 178.07/177.93 [6871]~P89(x68711)+~P24(f329(f329(f243(x68711),f329(f80(x68711),x68713)),f329(f80(x68711),x68712)))+P24(f329(f329(f243(x68711),x68712),x68713)) % 178.07/177.93 [6897]P24(f329(x68971,x68972))+~P24(f329(x68971,f415(x68971,x68973)))+~P24(f329(f329(f331(a875),x68972),f300(a875,f2(a875),x68973))) % 178.07/177.93 [6916]~P61(x69161)+P24(f329(f329(f244(x69161),f454(x69163,x69162,x69161)),f79(x69161)))+P24(f329(f329(f243(x69161),x69162),x69163)) % 178.07/177.93 [6935]~E(f45(a875,x69353,x69352),f45(a875,x69351,x69352))+E(f329(f329(f81(a875),x69351),f329(f329(f82(a875),x69352),f483(x69351,x69352,x69353))),x69353)+~P24(f329(f329(f243(a875),x69351),x69353)) % 178.07/177.93 [6954]E(f329(x69541,f861(x69541,x69542,x69543)),f206(x69542))+~P24(f329(f62(x69543),f183(x69543,x69542,x69541)))+P24(f329(f62(x69543),f252(f883(x69543,a869)))) % 178.07/177.93 [6995]E(f329(f329(f6(x69951,a875),x69952),x69953),f2(a875))+~P24(f329(f62(x69951),x69953))+P24(f329(f329(f331(x69951),f361(x69952,x69953,x69951)),x69953)) % 178.07/177.93 [6996]E(f329(f329(f9(x69961,a875),x69962),x69963),f79(a875))+~P24(f329(f62(x69961),x69963))+P24(f329(f329(f331(x69961),f342(x69962,x69963,x69961)),x69963)) % 178.07/177.93 [7018]~P105(x70181)+~P24(f329(f329(f244(x70181),x70182),x70183))+P24(f329(f329(f244(f883(x70181,a869)),f329(f250(x70181),x70182)),f329(f250(x70181),x70183))) % 178.07/177.93 [7019]~P105(x70191)+~P24(f329(f329(f243(x70191),x70192),x70193))+P24(f329(f329(f243(f883(x70191,a869)),f329(f250(x70191),x70192)),f329(f250(x70191),x70193))) % 178.07/177.93 [7020]~P105(x70201)+~P24(f329(f329(f243(x70201),x70203),x70202))+P24(f329(f329(f243(f883(x70201,a869)),f329(f301(x70201),x70202)),f329(f301(x70201),x70203))) % 178.07/177.93 [7021]~P107(x70211)+~P24(f329(f329(f243(x70211),x70213),x70212))+P24(f329(f329(f243(f883(x70211,a869)),f329(f251(x70211),x70212)),f329(f251(x70211),x70213))) % 178.07/177.93 [7022]~P107(x70221)+~P24(f329(f329(f243(x70221),x70222),x70223))+P24(f329(f329(f243(f883(x70221,a869)),f329(f298(x70221),x70222)),f329(f298(x70221),x70223))) % 178.07/177.93 [7030]~P27(x70301)+P24(f329(f329(f243(x70301),x70302),f41(x70301,x70303)))+P24(f329(f329(f331(x70301),f865(x70303,x70302,x70301)),x70303)) % 178.07/177.93 [7036]~P77(x70361)+P24(f329(f329(f244(x70361),f329(f329(f22(x70361),x70362),x70363)),f2(x70361)))+~P24(f329(f329(f244(x70361),x70362),x70363)) % 178.07/177.93 [7037]~P77(x70371)+P24(f329(f329(f243(x70371),f329(f329(f22(x70371),x70372),x70373)),f2(x70371)))+~P24(f329(f329(f243(x70371),x70372),x70373)) % 178.07/177.93 [7079]P24(f329(x70791,x70792))+P24(f329(f329(f243(a875),f415(x70791,x70793)),x70793))+~P24(f329(f329(f331(a875),x70792),f300(a875,f2(a875),x70793))) % 178.07/177.93 [7119]~E(f329(f329(f6(x71191,a875),x71192),x71193),f79(a875))+~P24(f329(f62(x71191),x71193))+P24(f329(f329(f331(x71191),f360(x71192,x71193,x71191)),x71193)) % 178.07/177.93 [7120]~P24(f329(x71201,x71203))+P24(f329(f329(f243(a875),f414(x71201,x71202)),x71202))+~P24(f329(f329(f331(a875),x71203),f300(a875,f2(a875),x71202))) % 178.07/177.93 [7160]~P27(x71601)+P24(f329(f329(f331(x71601),f866(x71603,x71602,x71601)),x71602))+P24(f329(f329(f243(x71601),f40(x71601,x71602)),x71603)) % 178.07/177.93 [7191]~E(f329(f329(f6(x71911,a875),x71912),x71913),f329(a118,f2(a875)))+~P24(f329(f62(x71911),x71913))+P24(f329(f329(f331(x71911),f363(x71912,x71913,x71911)),x71913)) % 178.07/177.93 [7202]E(x72021,f2(a875))+P24(f329(x72022,f45(a875,x72023,x72021)))+P24(f329(f329(f244(a875),f469(x72021,x72023,x72022)),x72021)) % 178.07/177.93 [7307]~P24(f329(x73071,x73072))+P24(f329(x73071,f45(a875,x73072,x73073)))+P24(f329(f329(f244(a875),f469(x73073,x73072,x73071)),x73073)) % 178.07/177.93 [7431]E(x74311,f119(x74312))+~P24(f329(f329(f331(f876(x74312)),x74311),f160(x74312,x74313)))+P24(f329(f329(f331(x74312),f639(x74313,x74311,x74312)),x74313)) % 178.07/177.93 [7453]~P105(x74531)+E(f329(f329(f116(f883(x74531,a869)),f329(f329(f307(x74531),x74532),f193(f883(x74531,a869)))),f303(x74531,x74532,x74533)),f329(f299(x74531,x74532),x74533))+~P24(f329(f329(f244(x74531),x74532),x74533)) % 178.07/177.93 [7479]~P105(x74791)+E(f329(f329(f116(f883(x74791,a869)),f329(f329(f307(x74791),x74792),f193(f883(x74791,a869)))),f302(x74791,x74792,x74793)),f300(x74791,x74792,x74793))+~P24(f329(f329(f243(x74791),x74792),x74793)) % 178.07/177.93 [7585]~P105(x75851)+P24(f329(f329(f244(x75851),x75852),x75853))+~P24(f329(f329(f244(f883(x75851,a869)),f329(f250(x75851),x75852)),f329(f250(x75851),x75853))) % 178.07/177.93 [7586]~P105(x75861)+P24(f329(f329(f243(x75861),x75862),x75863))+~P24(f329(f329(f243(f883(x75861,a869)),f329(f301(x75861),x75863)),f329(f301(x75861),x75862))) % 178.07/177.93 [7587]~P107(x75871)+P24(f329(f329(f243(x75871),x75872),x75873))+~P24(f329(f329(f243(f883(x75871,a869)),f329(f251(x75871),x75873)),f329(f251(x75871),x75872))) % 178.07/177.93 [7588]~P105(x75881)+P24(f329(f329(f243(x75881),x75882),x75883))+~P24(f329(f329(f243(f883(x75881,a869)),f329(f250(x75881),x75882)),f329(f250(x75881),x75883))) % 178.07/177.93 [7589]~P107(x75891)+P24(f329(f329(f243(x75891),x75892),x75893))+~P24(f329(f329(f243(f883(x75891,a869)),f329(f298(x75891),x75892)),f329(f298(x75891),x75893))) % 178.07/177.93 [7612]~P77(x76121)+~P24(f329(f329(f244(x76121),f329(f329(f22(x76121),x76122),x76123)),f2(x76121)))+P24(f329(f329(f244(x76121),x76122),x76123)) % 178.07/177.93 [7613]~P77(x76131)+~P24(f329(f329(f243(x76131),f329(f329(f22(x76131),x76132),x76133)),f2(x76131)))+P24(f329(f329(f243(x76131),x76132),x76133)) % 178.07/177.93 [7769]E(x77691,f2(a875))+~E(f329(f141(a875,a875,f81(a875),x77692),x77693),f2(a875))+~P24(f329(f329(f331(a875),x77691),f329(f171(a875),x77693))) % 178.07/177.93 [7773]~P27(x77731)+~P24(f329(f329(f243(x77731),f866(x77733,x77732,x77731)),x77733))+P24(f329(f329(f243(x77731),f40(x77731,x77732)),x77733)) % 178.07/177.93 [7927]P24(f329(f329(f243(a1),f2(a1)),f467(x79271,x79272,x79273)))+P24(f329(f329(x79272,f329(f329(f39(a1),x79271),x79273)),f45(a1,x79271,x79273)))+~P24(f329(f329(f244(a1),f2(a1)),x79273)) % 178.07/177.93 [8021]E(x80211,x80212)+~E(f329(f194(f876(x80213)),x80211),f329(f194(f876(x80213)),x80212))+~P24(f329(f329(f268(x80213,x80213,a869),a326),f594(x80213,x80211,x80212))) % 178.07/177.93 [8089]~P38(x80892,x80893)+E(x80891,f193(f883(x80892,a869)))+~P24(f329(f329(f243(f883(x80892,a869)),x80891),f329(f283(x80892,x80892,x80893),x80891))) % 178.07/177.93 [8159]P40(x81591,x81592,x81593)+P24(f329(f329(f331(x81591),f597(x81593,x81592,x81591)),x81592))+P24(f329(f329(f331(f882(x81591,x81591)),f598(x81593,x81592,x81591)),x81593)) % 178.07/177.93 [8182]P24(f329(f329(x81822,f329(f329(f39(a1),x81821),x81823)),f45(a1,x81821,x81823)))+~P24(f329(f329(f244(a1),f2(a1)),x81823))+P24(f329(f329(f244(a1),f467(x81821,x81822,x81823)),x81823)) % 178.07/177.93 [8206]E(f329(f308(a875,a875,f329(f329(f7(a875,a875,a875),f22(a875)),x82061)),f329(f299(a875,x82062),x82063)),f193(f883(a875,a869)))+P24(f329(f329(f244(a875),x82061),x82063))+P24(f329(f329(f244(a875),x82062),x82063)) % 178.07/177.93 [8312]E(f329(f308(a875,a875,f329(f329(f7(a875,a875,a875),f22(a875)),x83121)),f329(f299(a875,x83122),x83123)),f329(f329(f307(a875),f2(a875)),f193(f883(a875,a869))))+P24(f329(f329(f244(a875),x83121),x83123))+~P24(f329(f329(f244(a875),x83122),x83123)) % 178.07/177.93 [8329]~P105(x83291)+E(f148(x83291,x83291,f5(x83291),x83292,x83293),x83293)+~P24(f329(f329(f331(x83291),x83292),f329(f171(x83291),x83293))) % 178.07/177.93 [8343]P21(x83431,x83431,x83432,x83433)+~P24(f329(f62(x83431),x83433))+~P24(f329(f329(f243(f883(x83431,a869)),x83433),f329(f308(x83431,x83431,x83432),x83433))) % 178.07/177.93 [8366]E(f329(f329(f81(a1),f329(f329(f82(a1),x83661),f468(x83662,x83663,x83661))),f467(x83662,x83663,x83661)),x83662)+P24(f329(f329(x83663,f329(f329(f39(a1),x83662),x83661)),f45(a1,x83662,x83661)))+~P24(f329(f329(f244(a1),f2(a1)),x83661)) % 178.07/177.93 [8607]~P24(f329(f329(x86071,f468(x86072,x86071,x86073)),f467(x86072,x86071,x86073)))+P24(f329(f329(x86071,f329(f329(f39(a1),x86072),x86073)),f45(a1,x86072,x86073)))+~P24(f329(f329(f244(a1),f2(a1)),x86073)) % 178.07/177.93 [9471]~P24(f329(f62(x94711),x94712))+~P24(f329(f329(f331(x94711),x94713),x94712))+P24(f329(f329(f244(a875),f329(f38(x94711),f329(f329(f22(f883(x94711,a869)),x94712),f329(f329(f307(x94711),x94713),f193(f883(x94711,a869)))))),f329(f38(x94711),x94712))) % 178.07/177.93 [10068]P40(x100681,x100682,x100683)+~P24(f329(f329(f268(x100681,x100681,a869),f329(f329(f7(x100681,f883(x100681,a869),f883(x100681,a869)),f329(f329(f8(f883(a869,a869),f883(f883(x100681,a869),f883(x100681,a869)),x100681),f8(a869,a869,x100681)),f329(f329(f8(a869,f883(a869,a869),x100681),a327),f329(f329(f7(x100681,f883(x100681,a869),a869),f331(x100681)),x100682)))),f329(f329(f7(x100681,f883(x100681,a869),a869),f331(x100681)),x100682))),f598(x100683,x100682,x100681)))+P24(f329(f329(f331(x100681),f597(x100683,x100682,x100681)),x100682)) % 178.07/177.93 [5456]~P115(x54562)+E(x54561,f2(x54562))+E(f329(f329(f287(x54562),x54563),f329(f80(x54562),x54561)),f329(f80(x54562),f329(f329(f287(x54562),x54563),x54561))) % 178.07/177.93 [5587]~E(x55873,f193(f883(x55871,a869)))+~E(x55872,f193(f883(x55871,a869)))+E(f329(f329(f116(f883(x55871,a869)),x55872),x55873),f193(f883(x55871,a869))) % 178.07/177.93 [5645]~E(x56453,f2(a875))+~P24(f329(x56451,f2(a875)))+P24(f329(x56451,f329(f329(f39(a875),x56452),x56453))) % 178.07/177.93 [5786]~P62(x57862)+E(x57861,f2(x57862))+E(f329(f329(f287(x57862),f329(f76(x57862),x57863)),f329(f76(x57862),x57861)),f329(f76(x57862),f329(f329(f287(x57862),x57863),x57861))) % 178.07/177.93 [5954]~P24(f329(f62(x59541),x59543))+E(f329(f38(x59541),f329(f329(f307(x59541),x59542),x59543)),f329(a118,f329(f38(x59541),x59543)))+P24(f329(f329(f331(x59541),x59542),x59543)) % 178.07/177.93 [6028]~E(x60282,f2(a875))+P24(f329(x60281,f2(a875)))+~P24(f329(x60281,f329(f329(f39(a875),x60283),x60282))) % 178.07/177.93 [6047]~P24(f329(f62(x60471),x60473))+E(f329(f38(x60471),f329(f329(f307(x60471),x60472),x60473)),f329(f38(x60471),x60473))+~P24(f329(f329(f331(x60471),x60472),x60473)) % 178.07/177.93 [6081]~P24(f329(f62(x60811),x60813))+E(f329(f38(x60811),f329(f329(f307(x60811),x60812),x60813)),f329(f329(f81(a875),f79(a875)),f329(f38(x60811),x60813)))+P24(f329(f329(f331(x60811),x60812),x60813)) % 178.07/177.93 [6200]E(f329(f329(f81(a875),x62001),f364(x62001,x62002,x62003)),x62002)+~P24(f329(x62003,f2(a875)))+P24(f329(x62003,f329(f329(f22(a875),x62002),x62001))) % 178.07/177.93 [6201]E(f329(f329(f81(a875),x62011),f365(x62011,x62012,x62013)),x62012)+~P24(f329(x62013,f2(a875)))+P24(f329(x62013,f329(f329(f22(a875),x62012),x62011))) % 178.07/177.93 [6248]~P27(x62481)+~P24(f329(f62(x62481),x62483))+E(f329(f329(f65(x62481,x62481,f116(x62481)),x62482),x62483),f329(f329(f116(x62481),x62482),f40(x62481,x62483))) % 178.07/177.93 [6249]~P27(x62491)+~P24(f329(f62(x62491),x62493))+E(f329(f329(f65(x62491,x62491,f107(x62491)),x62492),x62493),f329(f329(f107(x62491),x62492),f41(x62491,x62493))) % 178.07/177.93 [6255]~P92(x62551)+~E(f329(f109(x62551),x62552),f329(f109(x62551),x62553))+P31(x62551,f329(f109(x62551),f329(f329(f81(a1),x62552),f329(f80(a1),x62553)))) % 178.07/177.93 [6262]~P137(x62621)+E(f329(f329(f22(x62621),f329(f106(x62621),x62622)),f329(f106(x62621),x62623)),f329(f106(x62621),f329(f329(f22(a875),x62622),x62623)))+~P24(f329(f329(f243(a875),x62623),x62622)) % 178.07/177.93 [6349]E(f329(f329(f81(a875),x63491),f364(x63491,x63492,x63493)),x63492)+P24(f329(f329(f244(a875),x63492),x63491))+P24(f329(x63493,f329(f329(f22(a875),x63492),x63491))) % 178.07/177.93 [6350]E(f329(f329(f81(a875),x63501),f365(x63501,x63502,x63503)),x63502)+P24(f329(f329(f244(a875),x63502),x63501))+P24(f329(x63503,f329(f329(f22(a875),x63502),x63501))) % 178.07/177.93 [6365]~P117(x63651)+E(f329(f329(f82(x63651),f329(f76(x63651),x63652)),x63653),f329(f76(x63651),f329(f329(f82(x63651),x63652),x63653)))+~P24(f329(f329(f243(x63651),f2(x63651)),x63653)) % 178.07/177.93 [6366]~P61(x63661)+E(f329(f329(f287(x63661),f329(f76(x63661),x63662)),x63663),f329(f76(x63661),f329(f329(f287(x63661),x63662),x63663)))+~P24(f329(f329(f244(x63661),f2(x63661)),x63663)) % 178.07/177.93 [6374]~P63(x63741)+~P24(f329(f62(x63741),x63743))+E(f329(f329(f65(x63741,x63741,f116(x63741)),x63742),x63743),f13(x63741,f329(f329(f307(x63741),x63742),x63743))) % 178.07/177.93 [6375]~P63(x63751)+~P24(f329(f62(x63751),x63753))+E(f329(f329(f65(x63751,x63751,f107(x63751)),x63752),x63753),f10(x63751,f329(f329(f307(x63751),x63752),x63753))) % 178.07/177.93 [6376]~P105(x63761)+~P24(f329(f62(x63761),x63763))+E(f329(f329(f65(x63761,x63761,f241(x63761)),x63762),x63763),f14(x63761,f329(f329(f307(x63761),x63762),x63763))) % 178.07/177.93 [6377]~P105(x63771)+~P24(f329(f62(x63771),x63773))+E(f329(f329(f65(x63771,x63771,f242(x63771)),x63772),x63773),f15(x63771,f329(f329(f307(x63771),x63772),x63773))) % 178.07/177.93 [6422]E(x64221,f119(x64222))+~E(f179(x64222,x64223),f119(f876(x64222)))+~P24(f329(f329(f331(f876(x64222)),x64221),f329(f171(f876(x64222)),x64223))) % 178.07/177.93 [6464]~P24(f329(f136(x64641),x64643))+P24(f329(f329(f331(x64641),x64642),f329(f171(x64641),x64643)))+P24(f329(f136(x64641),f329(f329(f150(x64641),x64642),x64643))) % 178.07/177.93 [6475]~P95(x64751)+~P24(f329(f62(x64751),x64753))+E(f329(f64(x64751,f82(x64751)),f329(f329(f307(x64751),x64752),x64753)),f329(f329(f65(x64751,x64751,f82(x64751)),x64752),x64753)) % 178.07/177.93 [6497]~P105(x64971)+~P24(f329(f62(x64971),x64973))+E(f11(x64971,f242(x64971),f329(f329(f307(x64971),x64972),x64973)),f329(f329(f65(x64971,x64971,f242(x64971)),x64972),x64973)) % 178.07/177.93 [6498]~P105(x64981)+~P24(f329(f62(x64981),x64983))+E(f12(x64981,f241(x64981),f329(f329(f307(x64981),x64982),x64983)),f329(f329(f65(x64981,x64981,f241(x64981)),x64982),x64983)) % 178.07/177.93 [6500]P24(f329(x65001,f2(a875)))+~P24(f329(f329(f244(a875),x65002),x65003))+~P24(f329(x65001,f329(f329(f22(a875),x65002),x65003))) % 178.07/177.93 [6518]~P117(x65181)+P24(f329(f329(f244(x65181),x65182),x65183))+~P24(f329(f329(f244(x65181),f329(f76(x65181),x65182)),x65183)) % 178.07/177.93 [6520]~P85(x65201)+P24(f329(f329(f243(x65201),x65202),x65203))+~P24(f329(f329(f243(x65201),f329(f76(x65201),x65202)),x65203)) % 178.07/177.93 [6537]E(x65371,f119(x65372))+E(f329(f140(x65372),f329(f329(f137(x65372),x65373),x65371)),f329(f329(f164(x65372),x65371),x65373))+~P24(f329(f329(f244(a875),x65373),f329(f194(f876(x65372)),x65371))) % 178.07/177.93 [6589]~P24(f329(x65891,x65893))+P24(f329(x65891,f390(x65891,x65892)))+~P24(f329(f329(f331(a875),x65893),f329(f299(a875,f2(a875)),x65892))) % 178.07/177.93 [6611]P24(f329(x66111,x66112))+~P24(f329(f329(f244(a875),x66112),x66113))+P24(f329(f329(f331(a875),f387(x66111,x66113)),f329(f299(a875,f2(a875)),x66113))) % 178.07/177.93 [6627]~P120(x66271)+~P24(f329(f329(f244(x66271),f2(x66271)),x66272))+P24(f329(f329(f244(x66271),f2(x66271)),f329(f329(f254(x66271),x66272),x66273))) % 178.07/177.93 [6628]~P120(x66281)+~P24(f329(f329(f243(x66281),f79(x66281)),x66282))+P24(f329(f329(f243(x66281),f79(x66281)),f329(f329(f254(x66281),x66282),x66283))) % 178.07/177.93 [6630]~P120(x66301)+~P24(f329(f329(f243(x66301),f2(x66301)),x66302))+P24(f329(f329(f243(x66301),f2(x66301)),f329(f329(f254(x66301),x66302),x66303))) % 178.07/177.93 [6654]~P24(f329(x66541,x66543))+~P24(f329(f329(f244(a875),x66543),x66542))+P24(f329(f329(f331(a875),f385(x66541,x66542)),f329(f299(a875,f2(a875)),x66542))) % 178.07/177.93 [6661]P24(f329(f62(x66611),x66612))+~P24(f329(f62(x66611),x66613))+~P24(f329(f329(f243(f883(x66611,a869)),x66612),x66613)) % 178.07/177.93 [6669]P24(f329(x66691,x66692))+~P24(f329(x66691,f388(x66691,x66693)))+~P24(f329(f329(f331(a875),x66692),f329(f299(a875,f2(a875)),x66693))) % 178.07/177.93 [6680]E(x66801,f2(a875))+P24(f329(x66802,f391(x66801,x66803,x66802)))+~P24(f329(x66802,f329(f329(f39(a875),x66803),x66801))) % 178.07/177.93 [6688]~P121(x66882)+E(x66881,f2(x66882))+~E(f329(f329(f81(x66882),f329(f329(f82(x66882),x66883),x66883)),f329(f329(f82(x66882),x66881),x66881)),f2(x66882)) % 178.07/177.93 [6689]~P121(x66892)+E(x66891,f2(x66892))+~E(f329(f329(f81(x66892),f329(f329(f82(x66892),x66891),x66891)),f329(f329(f82(x66892),x66893),x66893)),f2(x66892)) % 178.07/177.93 [6734]E(x67341,f2(a875))+~P24(f329(x67342,f392(x67341,x67343,x67342)))+P24(f329(x67342,f329(f329(f39(a875),x67343),x67341))) % 178.07/177.93 [6739]~P105(x67391)+~P29(x67391,x67393)+P29(x67391,f329(f329(f147(x67391,x67391,f5(x67391)),x67392),x67393)) % 178.07/177.93 [6782]P24(f329(x67821,f391(x67822,x67823,x67821)))+P24(f329(x67821,f2(a875)))+~P24(f329(x67821,f329(f329(f39(a875),x67823),x67822))) % 178.07/177.93 [6788]~P92(x67881)+E(f329(f109(x67881),x67882),f329(f109(x67881),x67883))+~P31(x67881,f329(f109(x67881),f329(f329(f81(a1),x67882),f329(f80(a1),x67883)))) % 178.07/177.93 [6853]E(x68531,f2(a1))+E(x68532,f2(a1))+~P24(f329(f49(x68532,x68532),f329(f329(f264(a1,a1),x68533),x68531))) % 178.07/177.93 [6854]E(x68541,f79(a1))+E(x68542,f2(a1))+~P24(f329(f49(x68542,x68542),f329(f329(f264(a1,a1),x68541),x68543))) % 178.07/177.93 [6868]P24(f329(x68681,x68682))+P24(f329(f329(f244(a875),f388(x68681,x68683)),x68683))+~P24(f329(f329(f331(a875),x68682),f329(f299(a875,f2(a875)),x68683))) % 178.07/177.93 [6892]~P24(f329(x68921,f364(x68923,x68922,x68921)))+~P24(f329(x68921,f2(a875)))+P24(f329(x68921,f329(f329(f22(a875),x68922),x68923))) % 178.07/177.93 [6893]~P24(f329(x68931,f365(x68933,x68932,x68931)))+~P24(f329(x68931,f2(a875)))+P24(f329(x68931,f329(f329(f22(a875),x68932),x68933))) % 178.07/177.93 [6894]~P24(f329(x68941,f392(x68943,x68942,x68941)))+~P24(f329(x68941,f2(a875)))+P24(f329(x68941,f329(f329(f39(a875),x68942),x68943))) % 178.07/177.93 [6912]~P24(f329(x69121,x69123))+P24(f329(f329(f244(a875),f390(x69121,x69122)),x69122))+~P24(f329(f329(f331(a875),x69123),f329(f299(a875,f2(a875)),x69122))) % 178.07/177.93 [6913]E(f329(f329(f22(a875),f329(f329(f22(a875),x69131),x69132)),f329(f329(f22(a875),x69133),x69132)),f329(f329(f22(a875),x69131),x69133))+~P24(f329(f329(f243(a875),x69132),x69131))+~P24(f329(f329(f243(a875),x69132),x69133)) % 178.07/177.93 [6948]~P77(x69481)+~P24(f329(f329(f244(x69481),f329(f80(x69481),x69483)),x69482))+P24(f329(f329(f244(x69481),f329(f80(x69481),x69482)),x69483)) % 178.07/177.93 [6949]~P117(x69491)+~P24(f329(f329(f244(x69491),f329(f76(x69491),x69492)),x69493))+P24(f329(f329(f244(x69491),f329(f80(x69491),x69492)),x69493)) % 178.07/177.93 [6951]~P77(x69511)+~P24(f329(f329(f243(x69511),f329(f80(x69511),x69513)),x69512))+P24(f329(f329(f243(x69511),f329(f80(x69511),x69512)),x69513)) % 178.07/177.93 [6953]~P85(x69531)+~P24(f329(f329(f243(x69531),f329(f76(x69531),x69532)),x69533))+P24(f329(f329(f243(x69531),f329(f80(x69531),x69532)),x69533)) % 178.07/177.93 [6989]~P24(f329(x69893,f364(x69892,x69891,x69893)))+P24(f329(f329(f244(a875),x69891),x69892))+P24(f329(x69893,f329(f329(f22(a875),x69891),x69892))) % 178.07/177.93 [6990]~P24(f329(x69903,f365(x69902,x69901,x69903)))+P24(f329(f329(f244(a875),x69901),x69902))+P24(f329(x69903,f329(f329(f22(a875),x69901),x69902))) % 178.07/177.93 [7040]~E(f851(x70403,x70402,x70401),f852(x70403,x70402,x70401))+E(f329(f329(f107(f883(x70401,a869)),x70402),f40(f883(x70401,a869),x70403)),f193(f883(x70401,a869)))+P24(f329(f329(f331(f883(x70401,a869)),x70402),x70403)) % 178.07/177.93 [7049]~P24(f329(f62(x70491),x70493))+P24(f329(f62(x70491),f41(f883(x70491,a869),x70492)))+~P24(f329(f329(f331(f883(x70491,a869)),x70493),x70492)) % 178.07/177.93 [7108]~P105(x71081)+E(f329(f329(f116(f883(x71081,a869)),f329(f299(x71081,x71082),x71083)),f329(f329(f307(x71081),x71083),f193(f883(x71081,a869)))),f300(x71081,x71082,x71083))+~P24(f329(f329(f243(x71081),x71082),x71083)) % 178.07/177.93 [7109]E(x71091,f2(a875))+P24(f329(f329(f244(a875),f398(x71091,x71093,x71092)),x71091))+P24(f329(x71092,f329(f329(f39(a875),x71093),x71091))) % 178.07/177.93 [7144]E(x71441,x71442)+~P24(f329(f329(f243(f883(x71443,a869)),x71441),x71442))+P24(f329(f329(f244(f883(x71443,a869)),x71441),x71442)) % 178.07/177.93 [7157]E(x71571,x71572)+~E(f329(f194(f876(x71573)),x71571),f329(f194(f876(x71573)),x71572))+P24(f329(f329(f244(a875),f569(x71573,x71571,x71572)),f329(f194(f876(x71573)),x71572))) % 178.07/177.93 [7203]P6(x72031,x72032,x72033)+~E(f329(f262(x72031,x72031),x72033),x72032)+~E(f329(f329(f286(x72031,x72031,x72031),f329(f284(x72031,x72031),x72033)),x72033),x72033) % 178.07/177.93 [7275]~P24(f329(x72751,f2(a875)))+P24(f329(f329(f244(a875),f398(x72753,x72752,x72751)),x72753))+P24(f329(x72751,f329(f329(f39(a875),x72752),x72753))) % 178.07/177.93 [7284]~P105(x72841)+E(f329(f329(f116(f883(x72841,a869)),f303(x72841,x72842,x72843)),f329(f329(f307(x72841),x72843),f193(f883(x72841,a869)))),f302(x72841,x72842,x72843))+~P24(f329(f329(f244(x72841),x72842),x72843)) % 178.07/177.93 [7385]~P24(f329(f62(x73851),x73853))+P24(f329(f329(f244(a875),f329(f38(x73851),x73852)),f329(f38(x73851),x73853)))+~P24(f329(f329(f244(f883(x73851,a869)),x73852),x73853)) % 178.07/177.93 [7386]~P24(f329(f62(x73861),x73863))+P24(f329(f329(f243(a875),f329(f38(x73861),x73862)),f329(f38(x73861),x73863)))+~P24(f329(f329(f243(f883(x73861,a869)),x73862),x73863)) % 178.07/177.93 [7424]~P24(f329(x74243,x74242))+P24(f329(f329(f199(x74241),x74242),f622(x74242,x74241,x74243)))+~P24(f329(f329(f199(f33(x74243,x74241)),x74242),x74242)) % 178.07/177.93 [7523]E(x75231,x75232)+~P24(f329(f329(f243(f883(x75233,a869)),x75232),x75231))+~P24(f329(f329(f243(f883(x75233,a869)),x75231),x75232)) % 178.07/177.93 [7526]~P105(x75261)+P29(x75261,x75262)+~P29(x75261,f329(f329(f147(x75261,x75261,f5(x75261)),x75263),x75262)) % 178.07/177.93 [7592]~P24(f329(f329(f244(a875),x75923),x75922))+~P24(f329(f329(f244(a875),x75923),x75921))+P24(f329(f329(f244(a875),f329(f329(f22(a875),x75921),x75922)),f329(f329(f22(a875),x75921),x75923))) % 178.07/177.93 [7593]~P24(f329(f329(f244(a875),x75931),x75933))+~P24(f329(f329(f243(a875),x75932),x75931))+P24(f329(f329(f244(a875),f329(f329(f22(a875),x75931),x75932)),f329(f329(f22(a875),x75933),x75932))) % 178.07/177.93 [7610]~P24(f329(f329(f244(a1),x76102),f2(a1)))+~P24(f329(f329(f243(a1),x76103),x76101))+P24(f329(f329(f243(a1),f329(f329(f39(a1),x76101),x76102)),f329(f329(f39(a1),x76103),x76102))) % 178.07/177.93 [7630]~P24(f329(f329(f244(a875),f2(a875)),x76302))+~P24(f329(f329(f244(a875),x76301),x76303))+P24(f329(f329(f244(a875),f329(f329(f82(a875),x76301),x76302)),f329(f329(f82(a875),x76303),x76302))) % 178.07/177.93 [7631]~P24(f329(f329(f244(a875),f2(a875)),x76311))+~P24(f329(f329(f244(a875),x76312),x76313))+P24(f329(f329(f244(a875),f329(f329(f82(a875),x76311),x76312)),f329(f329(f82(a875),x76311),x76313))) % 178.07/177.93 [7632]~P24(f329(f329(f244(a1),f2(a1)),x76321))+~P24(f329(f329(f244(a1),x76322),x76323))+P24(f329(f329(f244(a1),f329(f329(f82(a1),x76321),x76322)),f329(f329(f82(a1),x76321),x76323))) % 178.07/177.93 [7634]~P24(f329(f329(f244(a875),f2(a875)),x76343))+~P24(f329(f329(f243(a875),x76343),x76342))+P24(f329(f329(f243(a875),f329(f329(f39(a875),x76341),x76342)),f329(f329(f39(a875),x76341),x76343))) % 178.07/177.93 [7635]~P24(f329(f329(f244(a1),f2(a1)),x76352))+~P24(f329(f329(f243(a1),x76351),x76353))+P24(f329(f329(f243(a1),f329(f329(f39(a1),x76351),x76352)),f329(f329(f39(a1),x76353),x76352))) % 178.07/177.93 [7684]E(x76841,f2(a875))+E(f329(f329(f81(a875),f329(f329(f82(a875),x76841),f392(x76841,x76842,x76843))),f398(x76841,x76842,x76843)),x76842)+P24(f329(x76843,f329(f329(f39(a875),x76842),x76841))) % 178.07/177.93 [7743]E(f329(f329(f81(a875),f329(f329(f82(a875),x77431),f392(x77431,x77432,x77433))),f398(x77431,x77432,x77433)),x77432)+~P24(f329(x77433,f2(a875)))+P24(f329(x77433,f329(f329(f39(a875),x77432),x77431))) % 178.07/177.93 [7760]~P24(f329(f62(x77601),x77603))+P24(f329(f329(f331(x77601),f369(x77602,x77603,x77601)),x77603))+P24(f329(f329(f244(a875),f2(a875)),f329(f329(f9(x77601,a875),x77602),x77603))) % 178.07/177.93 [7761]~P24(f329(f62(x77611),x77613))+P24(f329(f329(f331(x77611),f472(x77612,x77613,x77611)),x77613))+P24(f329(f329(f244(a875),f2(a875)),f329(f329(f9(x77611,a875),x77612),x77613))) % 178.07/177.93 [8054]E(x80541,f193(f883(x80542,a869)))+E(x80541,f329(f329(f307(x80542),x80543),f193(f883(x80542,a869))))+~P24(f329(f329(f243(f883(x80542,a869)),x80541),f329(f329(f307(x80542),x80543),f193(f883(x80542,a869))))) % 178.07/177.93 [8072]~P58(x80721)+P8(x80721,x80722,x80723)+P24(f329(f329(f331(f876(x80721)),f664(x80723,x80722,x80721)),f329(f171(f876(x80721)),f55(x80721,x80723,f56(x80721))))) % 178.07/177.93 [8091]~P24(f329(f329(f244(a875),f2(a875)),x80913))+P24(f329(f329(f244(a875),x80911),x80912))+~P24(f329(f329(f244(a875),f329(f329(f254(a875),x80913),x80911)),f329(f329(f254(a875),x80913),x80912))) % 178.07/177.93 [8093]~P24(f329(f329(f244(a875),f2(a875)),x80933))+P24(f329(f329(f243(a875),x80931),x80932))+~P24(f329(f329(f243(a875),f329(f329(f82(a875),x80933),x80931)),f329(f329(f82(a875),x80933),x80932))) % 178.07/177.93 [8094]~P24(f329(f329(f244(a875),f2(a875)),x80943))+P24(f329(f329(f243(a875),x80941),x80942))+~P24(f329(f329(f243(a875),f329(f329(f82(a875),x80941),x80943)),f329(f329(f82(a875),x80942),x80943))) % 178.07/177.93 [8120]~P58(x81201)+~P7(x81201,x81203,x81202)+P24(f329(f329(f331(f876(x81201)),f663(x81202,x81203,x81201)),f329(f171(f876(x81201)),f55(x81201,x81202,f56(x81201))))) % 178.07/177.93 [8128]~P24(f329(x81281,x81283))+P24(f329(f329(f199(f33(x81281,x81282)),f622(x81283,x81282,x81281)),x81283))+~P24(f329(f329(f199(f33(x81281,x81282)),x81283),x81283)) % 178.07/177.93 [8137]~E(f329(f329(f107(f883(x81371,a869)),f852(x81373,x81372,x81371)),f851(x81373,x81372,x81371)),f193(f883(x81371,a869)))+E(f329(f329(f107(f883(x81371,a869)),x81372),f40(f883(x81371,a869),x81373)),f193(f883(x81371,a869)))+P24(f329(f329(f331(f883(x81371,a869)),x81372),x81373)) % 178.07/177.93 [8154]E(x81541,f119(x81542))+~E(f329(f141(f876(x81542),f876(x81542),f127(x81542),f119(x81542)),x81543),f119(x81542))+~P24(f329(f329(f331(f876(x81542)),x81541),f329(f171(f876(x81542)),x81543))) % 178.07/177.93 [8211]E(x82111,f193(f883(f883(x82112,a869),a869)))+P24(f329(f329(f331(f883(x82112,a869)),f475(x82113,x82111,x82112)),x82111))+P24(f329(f329(f243(f883(x82112,a869)),f41(f883(x82112,a869),x82111)),x82113)) % 178.07/177.93 [8218]~P70(x82181)+~P74(x82181)+E(f329(f329(f6(a1,x82181),f329(f329(f8(a875,x82181,a1),x82182),a110)),f329(f308(a875,a1,f106(a1)),x82183)),f329(f329(f6(a875,x82181),x82182),x82183)) % 178.07/177.93 [8219]~P70(x82191)+~P74(x82191)+E(f329(f329(f9(a1,x82191),f329(f329(f8(a875,x82191,a1),x82192),a110)),f329(f308(a875,a1,f106(a1)),x82193)),f329(f329(f9(a875,x82191),x82192),x82193)) % 178.07/177.93 [8258]~P24(f329(f62(x82581),x82583))+~P24(f329(f329(f244(a875),f2(a875)),f329(x82582,f369(x82582,x82583,x82581))))+P24(f329(f329(f244(a875),f2(a875)),f329(f329(f9(x82581,a875),x82582),x82583))) % 178.07/177.93 [8259]~P24(f329(f62(x82591),x82593))+~P24(f329(f329(f244(a875),f2(a875)),f329(x82592,f472(x82592,x82593,x82591))))+P24(f329(f329(f244(a875),f2(a875)),f329(f329(f9(x82591,a875),x82592),x82593))) % 178.07/177.93 [8294]~P60(x82942)+E(x82941,f79(x82942))+E(f329(f329(f287(x82942),f329(f329(f22(x82942),f329(f329(f254(x82942),x82941),x82943)),f79(x82942))),f329(f329(f22(x82942),x82941),f79(x82942))),f329(f329(f6(a875,x82942),f329(f254(x82942),x82941)),f329(f299(a875,f2(a875)),x82943))) % 178.07/177.93 [8352]E(x83521,f2(a875))+~P24(f329(x83523,f329(f329(f39(a875),x83522),x83521)))+P24(f329(f329(f244(a875),x83522),f329(f329(f82(a875),x83521),f329(a118,f391(x83521,x83522,x83523))))) % 178.07/177.93 [8370]P24(f329(x83701,f2(a875)))+~P24(f329(x83701,f329(f329(f39(a875),x83702),x83703)))+P24(f329(f329(f244(a875),x83702),f329(f329(f82(a875),x83703),f329(a118,f391(x83703,x83702,x83701))))) % 178.07/177.93 [8411]E(x84111,f2(a875))+~P24(f329(x84113,f329(f329(f39(a875),x84112),x84111)))+P24(f329(f329(f243(a875),f329(f329(f82(a875),x84111),f391(x84111,x84112,x84113))),x84112)) % 178.07/177.93 [8451]P24(f329(x84511,f2(a875)))+~P24(f329(x84511,f329(f329(f39(a875),x84513),x84512)))+P24(f329(f329(f243(a875),f329(f329(f82(a875),x84512),f391(x84512,x84513,x84511))),x84513)) % 178.07/177.93 [8454]~P105(x84541)+E(f329(f329(f147(x84541,x84541,f5(x84541)),x84542),x84543),f148(x84541,x84541,f5(x84541),x84542,x84543))+P24(f329(f329(f331(x84541),x84542),f329(f171(x84541),x84543))) % 178.07/177.93 [8492]~E(f329(x84923,f716(x84922,x84923,x84921)),f329(x84923,f718(x84922,x84923,x84921)))+~P55(x84921,f329(x84923,f717(x84922,x84923,x84921)))+P55(x84921,f329(f329(f43(x84922,f883(x84921,f883(x84921,a869))),f252(f883(x84922,a869))),x84923)) % 178.07/177.93 [8500]E(x85001,f193(f883(f883(x85002,a869),a869)))+~P24(f329(f329(f243(f883(x85002,a869)),f475(x85003,x85001,x85002)),x85003))+P24(f329(f329(f243(f883(x85002,a869)),f41(f883(x85002,a869),x85001)),x85003)) % 178.07/177.93 [8558]~P62(x85581)+~P24(f329(f329(f244(x85581),x85582),x85583))+P24(f329(f329(f244(x85581),x85582),f329(f329(f287(x85581),f329(f329(f81(x85581),x85582),x85583)),f329(f329(f81(x85581),f79(x85581)),f79(x85581))))) % 178.07/177.93 [8613]~P24(f329(f329(x86131,f550(x86131,x86133,x86132)),f551(x86131,x86133,x86132)))+P24(f329(f329(x86131,x86132),x86133))+~P24(f329(f317(f882(a1,a1),a52),f329(f329(f264(a1,a1),x86132),x86133))) % 178.07/177.93 [8614]~P24(f329(f329(x86141,f552(x86141,x86143,x86142)),f553(x86141,x86143,x86142)))+P24(f329(f329(x86141,x86142),x86143))+~P24(f329(f317(f882(a1,a1),a57),f329(f329(f264(a1,a1),x86142),x86143))) % 178.07/177.93 [8615]~P24(f329(f329(x86151,f558(x86151,x86153,x86152)),f559(x86151,x86153,x86152)))+P24(f329(f329(x86151,x86152),x86153))+~P24(f329(f317(f882(a1,a1),a232),f329(f329(f264(a1,a1),x86152),x86153))) % 178.07/177.93 [8616]~P24(f329(f329(x86161,f560(x86161,x86163,x86162)),f561(x86161,x86163,x86162)))+P24(f329(f329(x86161,x86162),x86163))+~P24(f329(f317(f882(a875,a875),a227),f329(f329(f264(a875,a875),x86162),x86163))) % 178.07/177.93 [8617]~P24(f329(f329(x86171,f611(x86171,x86173,x86172)),f617(x86171,x86173,x86172)))+P24(f329(f329(x86171,x86172),x86173))+~P24(f329(f317(f882(a1,a1),a182),f329(f329(f264(a1,a1),x86172),x86173))) % 178.07/177.93 [8869]P24(f329(f329(x88691,x88692),x88693))+P24(f329(f317(f882(a875,a875),a227),f329(f329(f264(a875,a875),f560(x88691,x88693,x88692)),f561(x88691,x88693,x88692))))+~P24(f329(f317(f882(a875,a875),a227),f329(f329(f264(a875,a875),x88692),x88693))) % 178.07/177.93 [8870]P24(f329(f329(x88701,x88702),x88703))+P24(f329(f317(f882(a1,a1),a52),f329(f329(f264(a1,a1),f550(x88701,x88703,x88702)),f551(x88701,x88703,x88702))))+~P24(f329(f317(f882(a1,a1),a52),f329(f329(f264(a1,a1),x88702),x88703))) % 178.07/177.93 [8871]P24(f329(f329(x88711,x88712),x88713))+P24(f329(f317(f882(a1,a1),a57),f329(f329(f264(a1,a1),f552(x88711,x88713,x88712)),f553(x88711,x88713,x88712))))+~P24(f329(f317(f882(a1,a1),a57),f329(f329(f264(a1,a1),x88712),x88713))) % 178.07/177.93 [8872]P24(f329(f329(x88721,x88722),x88723))+P24(f329(f317(f882(a1,a1),a232),f329(f329(f264(a1,a1),f558(x88721,x88723,x88722)),f559(x88721,x88723,x88722))))+~P24(f329(f317(f882(a1,a1),a232),f329(f329(f264(a1,a1),x88722),x88723))) % 178.07/177.93 [8873]P24(f329(f329(x88731,x88732),x88733))+P24(f329(f317(f882(a1,a1),a182),f329(f329(f264(a1,a1),f611(x88731,x88733,x88732)),f617(x88731,x88733,x88732))))+~P24(f329(f317(f882(a1,a1),a182),f329(f329(f264(a1,a1),x88732),x88733))) % 178.07/177.93 [9218]~P24(f329(f62(x92181),x92183))+P24(f329(f329(f331(f882(f883(x92181,a869),f883(x92181,a869))),f329(f329(f264(f883(x92181,a869),f883(x92181,a869)),x92182),x92183)),f304(x92181)))+~P24(f329(f329(f244(f883(x92181,a869)),x92182),x92183)) % 178.07/177.93 [9226]~P23(a871,f193(f883(f874(a871),a869)),f329(f329(f307(f874(a871)),f329(f329(f329(f93(a871),x92261),x92262),x92263)),f193(f883(f874(a871),a869))))+P20(a871,f193(f883(f874(a871),a869)),f329(f329(f307(f874(a871)),f329(f329(f329(f93(a871),x92261),x92262),x92263)),f193(f883(f874(a871),a869))))+~P20(a871,f193(f883(f874(a871),a869)),f329(f329(f307(f874(a871)),f329(a94,x92262)),f193(f883(f874(a871),a869)))) % 178.07/177.93 [9290]~P55(x92901,f329(x92903,f717(x92902,x92903,x92901)))+P55(x92901,f329(f329(f43(x92902,f883(x92901,f883(x92901,a869))),f252(f883(x92902,a869))),x92903))+~E(f329(f329(f107(f883(x92901,a869)),f258(x92901,x92901,f329(x92903,f716(x92902,x92903,x92901)))),f259(x92901,x92901,f329(x92903,f718(x92902,x92903,x92901)))),f193(f883(x92901,a869))) % 178.07/177.93 [9486]P40(x94861,x94862,x94863)+P24(f329(f329(f331(f882(x94861,x94861)),f598(x94863,x94862,x94861)),x94863))+~P24(f329(f329(f331(f882(x94861,x94861)),f329(f329(f264(x94861,x94861),f597(x94863,x94862,x94861)),f597(x94863,x94862,x94861))),x94863)) % 178.07/177.93 [10069]P40(x100691,x100692,x100693)+~P24(f329(f329(f268(x100691,x100691,a869),f329(f329(f7(x100691,f883(x100691,a869),f883(x100691,a869)),f329(f329(f8(f883(a869,a869),f883(f883(x100691,a869),f883(x100691,a869)),x100691),f8(a869,a869,x100691)),f329(f329(f8(a869,f883(a869,a869),x100691),a327),f329(f329(f7(x100691,f883(x100691,a869),a869),f331(x100691)),x100692)))),f329(f329(f7(x100691,f883(x100691,a869),a869),f331(x100691)),x100692))),f598(x100693,x100692,x100691)))+~P24(f329(f329(f331(f882(x100691,x100691)),f329(f329(f264(x100691,x100691),f597(x100693,x100692,x100691)),f597(x100693,x100692,x100691))),x100693)) % 178.07/177.93 [5626]~P56(x56262)+E(x56261,f2(x56262))+E(f329(f329(f39(x56262),f329(f329(f82(x56262),x56263),x56261)),x56261),x56263) % 178.07/177.93 [5627]~P56(x56272)+E(x56271,f2(x56272))+E(f329(f329(f39(x56272),f329(f329(f82(x56272),x56271),x56273)),x56271),x56273) % 178.07/177.93 [6421]~P70(x64211)+~E(f329(x64212,f2(a875)),f2(x64211))+E(f329(f329(f6(a875,x64211),x64212),f329(f299(a875,f329(a118,f2(a875))),x64213)),f329(f329(f6(a875,x64211),x64212),f329(f299(a875,f2(a875)),x64213))) % 178.07/177.93 [6550]~P56(x65502)+E(x65501,f2(x65502))+E(f329(f329(f39(x65502),f329(f329(f81(x65502),x65503),x65501)),x65501),f329(f329(f81(x65502),f329(f329(f39(x65502),x65503),x65501)),f79(x65502))) % 178.07/177.93 [6551]~P56(x65512)+E(x65511,f2(x65512))+E(f329(f329(f39(x65512),f329(f329(f81(x65512),x65511),x65513)),x65511),f329(f329(f81(x65512),f329(f329(f39(x65512),x65513),x65511)),f79(x65512))) % 178.07/177.93 [6770]~P24(f329(x67703,f2(a1)))+P24(f329(f329(f243(a875),x67701),x67702))+P24(f329(x67703,f329(f106(a1),f329(f329(f22(a875),x67702),x67701)))) % 178.07/177.93 [6874]P24(f329(f329(f243(a875),x68742),x68741))+P24(f329(f329(f244(a875),x68741),x68742))+P24(f329(x68743,f329(f106(a1),f329(f329(f22(a875),x68741),x68742)))) % 178.07/177.93 [6946]E(f329(f329(f81(a875),f329(f109(a875),x69461)),f329(f329(f81(a875),f329(f109(a875),x69462)),x69463)),f329(f329(f81(a875),f329(f109(a875),x69461)),x69463))+P24(f329(a198,f329(f109(a1),x69461)))+~P24(f329(a198,f329(f109(a1),x69462))) % 178.07/177.93 [7027]~E(x70272,f329(f329(f39(a875),x70273),x70271))+~P24(f329(f329(f244(a875),f2(a875)),x70271))+P24(f329(f329(f243(a875),f329(f329(f82(a875),x70271),x70272)),x70273)) % 178.07/177.93 [7141]~P24(f329(f62(x71411),x71413))+~P24(f329(f62(x71411),x71412))+P24(f329(f62(x71411),f329(f329(f116(f883(x71411,a869)),x71412),x71413))) % 178.07/177.93 [7437]~P105(x74371)+~P24(f329(f62(x74371),x74372))+E(f138(x74371,f329(f329(f22(f883(x74371,a869)),x74372),f329(f329(f307(x74371),x74373),f193(f883(x74371,a869))))),f169(x74371,x74373,f138(x74371,x74372))) % 178.07/177.93 [7503]P24(f329(x75031,f2(a1)))+~P24(f329(f329(f244(a875),x75032),x75033))+~P24(f329(x75031,f329(f106(a1),f329(f329(f22(a875),x75032),x75033)))) % 178.07/177.93 [7520]~P24(f329(f62(x75201),x75202))+E(f329(f38(x75201),f329(f329(f22(f883(x75201,a869)),x75202),f329(f329(f307(x75201),x75203),f193(f883(x75201,a869))))),f329(f38(x75201),x75202))+P24(f329(f329(f331(x75201),x75203),x75202)) % 178.07/177.93 [7650]~P120(x76501)+~P24(f329(f329(f244(x76501),f79(x76501)),x76502))+P24(f329(f329(f244(x76501),f79(x76501)),f329(f329(f82(x76501),x76502),f329(f329(f254(x76501),x76502),x76503)))) % 178.07/177.93 [7695]~P24(f329(f62(x76951),x76953))+E(f329(f329(f22(a875),f329(f38(x76951),x76952)),f329(f38(x76951),x76953)),f329(f38(x76951),f329(f329(f22(f883(x76951,a869)),x76952),x76953)))+~P24(f329(f329(f243(f883(x76951,a869)),x76953),x76952)) % 178.07/177.93 [7752]~P24(f329(f329(f243(a875),x77522),x77523))+~P24(f329(f329(f243(a875),x77521),f329(f329(f22(a875),x77523),x77522)))+P24(f329(f329(f243(a875),f329(f329(f81(a875),x77521),x77522)),x77523)) % 178.07/177.93 [7803]P24(f329(f62(x78031),x78032))+~P24(f329(f62(x78031),x78033))+~P24(f329(f62(x78031),f329(f329(f22(f883(x78031,a869)),x78032),x78033))) % 178.07/177.93 [7809]~P24(f329(f62(x78091),x78092))+E(f329(f38(x78091),f329(f329(f22(f883(x78091,a869)),x78092),f329(f329(f307(x78091),x78093),f193(f883(x78091,a869))))),f329(f329(f22(a875),f329(f38(x78091),x78092)),f79(a875)))+~P24(f329(f329(f331(x78091),x78093),x78092)) % 178.07/177.93 [7885]P55(x78851,x78852)+~P55(x78851,x78853)+~P24(f329(f329(f243(f883(x78851,f883(x78851,a869))),x78852),x78853)) % 178.07/177.93 [7926]~P24(f329(f329(f243(a875),x79263),x79262))+P24(f329(f329(f243(a875),x79261),f329(f329(f22(a875),x79262),x79263)))+~P24(f329(f329(f243(a875),f329(f329(f81(a875),x79261),x79263)),x79262)) % 178.07/177.93 [7944]P38(x79441,x79442)+~P38(x79441,x79443)+~P24(f329(f329(f243(f883(f882(x79441,x79441),a869)),x79442),x79443)) % 178.07/177.93 [7945]P53(x79451,x79452)+~P53(x79451,x79453)+~P24(f329(f329(f243(f883(f882(x79451,x79451),a869)),x79452),x79453)) % 178.07/177.93 [8189]~P120(x81891)+~P24(f329(f329(f244(x81891),f79(x81891)),x81892))+P24(f329(f329(f244(x81891),f329(f329(f254(x81891),x81892),x81893)),f329(f329(f82(x81891),x81892),f329(f329(f254(x81891),x81892),x81893)))) % 178.07/177.93 [8278]~P24(f329(x82781,f2(a1)))+~P24(f329(x82781,f329(f329(f22(a1),f329(f106(a1),x82782)),f329(f106(a1),x82783))))+P24(f329(x82781,f329(f106(a1),f329(f329(f22(a875),x82782),x82783)))) % 178.07/177.93 [8291]~P24(f329(f329(f243(a875),x82913),x82912))+P24(f329(x82911,f329(f329(f22(a1),f329(f106(a1),x82912)),f329(f106(a1),x82913))))+~P24(f329(x82911,f329(f106(a1),f329(f329(f22(a875),x82912),x82913)))) % 178.07/177.93 [8309]P24(f329(f329(f244(a875),x83091),x83092))+~P24(f329(x83093,f329(f329(f22(a1),f329(f106(a1),x83091)),f329(f106(a1),x83092))))+P24(f329(x83093,f329(f106(a1),f329(f329(f22(a875),x83091),x83092)))) % 178.07/177.93 [8363]~P121(x83632)+E(x83631,f2(x83632))+P24(f329(f329(f244(x83632),f2(x83632)),f329(f329(f81(x83632),f329(f329(f82(x83632),x83633),x83633)),f329(f329(f82(x83632),x83631),x83631)))) % 178.07/177.93 [8364]~P121(x83642)+E(x83641,f2(x83642))+P24(f329(f329(f244(x83642),f2(x83642)),f329(f329(f81(x83642),f329(f329(f82(x83642),x83641),x83641)),f329(f329(f82(x83642),x83643),x83643)))) % 178.07/177.93 [8472]~P24(f329(f329(f244(a875),f2(a875)),x84721))+~P24(f329(f329(f244(a1),x84722),x84723))+P24(f329(f329(f244(a1),f329(f329(f82(a1),f329(f106(a1),x84721)),x84722)),f329(f329(f82(a1),f329(f106(a1),x84721)),x84723))) % 178.07/177.93 [8528]E(f329(f329(f107(f883(x85281,a869)),x85282),f40(f883(x85281,a869),x85283)),f193(f883(x85281,a869)))+P24(f329(f329(f331(f883(x85281,a869)),x85282),x85283))+P24(f329(f329(f331(f883(x85281,a869)),f852(x85283,x85282,x85281)),f329(f329(f307(f883(x85281,a869)),x85282),x85283))) % 178.07/177.93 [8529]E(f329(f329(f107(f883(x85291,a869)),x85292),f40(f883(x85291,a869),x85293)),f193(f883(x85291,a869)))+P24(f329(f329(f331(f883(x85291,a869)),x85292),x85293))+P24(f329(f329(f331(f883(x85291,a869)),f851(x85293,x85292,x85291)),f329(f329(f307(f883(x85291,a869)),x85292),x85293))) % 178.07/177.93 [8557]E(x85571,x85572)+~E(f329(f194(f876(x85573)),x85571),f329(f194(f876(x85573)),x85572))+P24(f329(f329(f331(f882(x85573,x85573)),f594(x85573,x85571,x85572)),f329(f171(f882(x85573,x85573)),f329(f329(f181(x85573,x85573),x85572),x85571)))) % 178.07/177.93 [8788]E(f305(x87881,x87882),f305(x87881,x87883))+~P24(f329(f329(f243(f883(f882(x87881,x87881),a869)),x87883),f305(x87881,x87882)))+~P24(f329(f329(f243(f883(f882(x87881,x87881),a869)),x87882),x87883)) % 178.07/177.93 [8848]~P40(x88481,f252(f883(x88481,a869)),x88483)+P24(f329(f329(f243(f883(f882(f876(x88481),f876(x88481)),a869)),f156(x88481,x88482)),f157(x88481,x88483)))+~P24(f329(f329(f243(f883(f882(x88481,x88481),a869)),x88482),x88483)) % 178.07/177.93 [9054]P38(x90541,x90542)+~P24(f329(f329(f331(x90541),x90543),f780(x90542,x90541)))+P24(f329(f329(f331(f882(x90541,x90541)),f329(f329(f264(x90541,x90541),f791(x90542,x90541,x90543)),x90543)),x90542)) % 178.07/177.93 [9088]~P24(f329(f62(x90881),x90882))+P24(f329(f62(f883(x90881,a869)),f329(f329(f61(x90881),x90882),x90883)))+~P24(f329(f329(f243(f883(f882(x90881,x90881),a869)),x90883),f329(f329(f266(x90881,x90881),x90882),f329(f16(f883(x90881,a869),x90881),x90882)))) % 178.07/177.93 [9123]P40(x91231,x91232,x91233)+P24(f329(f329(f331(x91231),f612(x91233,x91232,x91231)),x91232))+~P24(f329(f329(f243(f883(f882(x91231,x91231),a869)),x91233),f329(f329(f266(x91231,x91231),x91232),f329(f16(f883(x91231,a869),x91231),x91232)))) % 178.07/177.93 [9124]P40(x91241,x91242,x91243)+P24(f329(f329(f331(x91241),f623(x91242,x91243,x91241)),x91242))+~P24(f329(f329(f243(f883(f882(x91241,x91241),a869)),x91243),f329(f329(f266(x91241,x91241),x91242),f329(f16(f883(x91241,a869),x91241),x91242)))) % 178.07/177.93 [9159]~P62(x91591)+~P24(f329(f329(f244(x91591),x91592),x91593))+P24(f329(f329(f244(x91591),f329(f329(f287(x91591),f329(f329(f81(x91591),x91592),x91593)),f329(f329(f81(x91591),f79(x91591)),f79(x91591)))),x91593)) % 178.07/177.93 [9188]~P61(x91881)+P24(f329(f329(f243(x91881),x91882),x91883))+~P24(f329(f329(f243(x91881),f329(f329(f82(x91881),f454(x91883,x91882,x91881)),x91882)),x91883)) % 178.07/177.93 [9325]E(f329(f194(f876(f876(x93251))),f329(f135(f876(x93251),f329(f329(f8(a875,a869,f876(x93251)),f329(f244(a875),x93252)),f194(f876(x93251)))),f179(x93251,x93253))),f329(f194(f876(x93251)),f329(f329(f164(f876(x93251)),x93253),x93252)))+~P29(a875,f329(f168(a875),f329(f329(f153(f876(x93251),a875),f194(f876(x93251))),x93253)))+~P24(f329(f329(f244(a875),x93252),f329(f194(f876(f876(x93251))),x93253))) % 178.07/177.93 [9432]~P38(x94321,x94322)+P22(x94321,f329(f329(f264(f883(f882(x94321,x94321),a869),f883(f882(x94321,x94321),a869)),x94322),x94323))+~P24(f329(f329(f243(f883(f882(x94321,x94321),a869)),f329(f329(f286(x94321,x94321,x94321),x94322),x94323)),x94322)) % 178.07/177.93 [9439]E(f329(f329(f153(f876(x94391),x94391),f329(f329(f7(f876(x94391),a875,x94391),f164(x94391)),x94392)),f329(f135(f876(x94391),f329(f329(f8(a875,a869,f876(x94391)),f329(f244(a875),x94392)),f194(f876(x94391)))),f179(x94391,x94393))),f329(f329(f164(f876(x94391)),x94393),x94392))+~P29(a875,f329(f168(a875),f329(f329(f153(f876(x94391),a875),f194(f876(x94391))),x94393)))+~P24(f329(f329(f244(a875),x94392),f329(f194(f876(f876(x94391))),x94393))) % 178.07/177.93 [9573]P40(x95731,x95732,x95733)+~P24(f329(f329(f331(f882(x95731,x95731)),f329(f329(f264(x95731,x95731),f612(x95733,x95732,x95731)),f612(x95733,x95732,x95731))),x95733))+~P24(f329(f329(f243(f883(f882(x95731,x95731),a869)),x95733),f329(f329(f266(x95731,x95731),x95732),f329(f16(f883(x95731,a869),x95731),x95732)))) % 178.07/177.93 [9574]P40(x95741,x95742,x95743)+~P24(f329(f329(f331(f882(x95741,x95741)),f329(f329(f264(x95741,x95741),f623(x95742,x95743,x95741)),f623(x95742,x95743,x95741))),x95743))+~P24(f329(f329(f243(f883(f882(x95741,x95741),a869)),x95743),f329(f329(f266(x95741,x95741),x95742),f329(f16(f883(x95741,a869),x95741),x95742)))) % 178.07/177.93 [9748]~P137(x97481)+~P119(x97481)+E(f329(f329(f287(x97481),f329(f108(x97481),f329(f329(f74(f882(a1,a1),a1,x97482,f263(a1,a1)),f220(x97482)),x97483))),f329(f108(x97481),f329(f329(f74(f882(a1,a1),a1,x97482,f267(a1,a1)),f220(x97482)),x97483))),f233(x97482,x97481,x97483)) % 178.07/177.93 [9949]~E(x99493,f2(a875))+~E(f329(f194(f876(x99491)),f329(f329(f164(f876(x99491)),x99492),f656(x99493,x99491,x99492))),x99493)+E(f329(f329(f153(a875,f876(x99491)),f329(f329(f7(a875,f876(a875),f876(x99491)),f329(f329(f8(f883(a875,x99491),f883(f876(a875),f876(x99491)),a875),f153(a875,x99491)),f329(f7(a875,a875,x99491),f329(f329(f8(f876(x99491),f883(a875,x99491),a875),f164(x99491)),f329(f164(f876(x99491)),x99492))))),f138(a875,f329(f299(a875,f2(a875)),f329(f194(f876(f876(x99491))),x99492))))),f138(a875,f329(f299(a875,f2(a875)),x99493))),f179(x99491,x99492)) % 178.07/177.93 [9950]E(x99501,f119(f876(x99502)))+~E(f329(f194(f876(x99502)),f329(f329(f164(f876(x99502)),x99501),f656(x99503,x99502,x99501))),x99503)+E(f329(f329(f153(a875,f876(x99502)),f329(f329(f7(a875,f876(a875),f876(x99502)),f329(f329(f8(f883(a875,x99502),f883(f876(a875),f876(x99502)),a875),f153(a875,x99502)),f329(f7(a875,a875,x99502),f329(f329(f8(f876(x99502),f883(a875,x99502),a875),f164(x99502)),f329(f164(f876(x99502)),x99501))))),f138(a875,f329(f299(a875,f2(a875)),f329(f194(f876(f876(x99502))),x99501))))),f138(a875,f329(f299(a875,f2(a875)),x99503))),f179(x99502,x99501)) % 178.07/177.93 [9951]~E(x99513,f2(a875))+E(f329(f329(f153(a875,f876(x99511)),f329(f329(f7(a875,f876(a875),f876(x99511)),f329(f329(f8(f883(a875,x99511),f883(f876(a875),f876(x99511)),a875),f153(a875,x99511)),f329(f7(a875,a875,x99511),f329(f329(f8(f876(x99511),f883(a875,x99511),a875),f164(x99511)),f329(f164(f876(x99511)),x99512))))),f138(a875,f329(f299(a875,f2(a875)),f329(f194(f876(f876(x99511))),x99512))))),f138(a875,f329(f299(a875,f2(a875)),x99513))),f179(x99511,x99512))+P24(f329(f329(f244(a875),f656(x99513,x99511,x99512)),f329(f194(f876(f876(x99511))),x99512))) % 178.07/177.93 [9952]E(x99521,f119(f876(x99522)))+E(f329(f329(f153(a875,f876(x99522)),f329(f329(f7(a875,f876(a875),f876(x99522)),f329(f329(f8(f883(a875,x99522),f883(f876(a875),f876(x99522)),a875),f153(a875,x99522)),f329(f7(a875,a875,x99522),f329(f329(f8(f876(x99522),f883(a875,x99522),a875),f164(x99522)),f329(f164(f876(x99522)),x99521))))),f138(a875,f329(f299(a875,f2(a875)),f329(f194(f876(f876(x99522))),x99521))))),f138(a875,f329(f299(a875,f2(a875)),x99523))),f179(x99522,x99521))+P24(f329(f329(f244(a875),f656(x99523,x99522,x99521)),f329(f194(f876(f876(x99522))),x99521))) % 178.07/177.93 [7692]E(f329(f329(f81(a875),f329(f109(a875),x76921)),f329(f329(f81(a875),f329(f109(a875),x76922)),x76923)),f329(f329(f81(a875),f329(f109(a875),f329(f329(f81(a1),x76921),x76922))),x76923))+P24(f329(a198,f329(f109(a1),x76921)))+P24(f329(a198,f329(f109(a1),x76922))) % 178.07/177.93 [8463]~P24(f329(f62(x84631),x84632))+~P24(f329(f329(f331(x84631),x84633),x84632))+E(f329(a118,f329(f38(x84631),f329(f329(f22(f883(x84631,a869)),x84632),f329(f329(f307(x84631),x84633),f193(f883(x84631,a869)))))),f329(f38(x84631),x84632)) % 178.07/177.93 [8482]~P24(f329(f62(x84821),x84822))+~P24(f329(f329(f331(x84821),x84823),x84822))+E(f329(f329(f81(a875),f79(a875)),f329(f38(x84821),f329(f329(f22(f883(x84821,a869)),x84822),f329(f329(f307(x84821),x84823),f193(f883(x84821,a869)))))),f329(f38(x84821),x84822)) % 178.07/177.93 [8566]~P105(x85661)+~P24(f329(f62(x85661),x85663))+E(f329(f329(f147(x85661,x85661,f5(x85661)),x85662),f138(x85661,f329(f329(f22(f883(x85661,a869)),x85663),f329(f329(f307(x85661),x85662),f193(f883(x85661,a869)))))),f138(x85661,f329(f329(f307(x85661),x85662),x85663))) % 178.07/177.93 [8718]~P24(f329(f62(x87181),x87183))+~P24(f329(f62(x87181),x87182))+E(f329(f329(f81(a875),f329(f38(x87181),f329(f329(f116(f883(x87181,a869)),x87182),x87183))),f329(f38(x87181),f329(f329(f107(f883(x87181,a869)),x87182),x87183))),f329(f329(f81(a875),f329(f38(x87181),x87182)),f329(f38(x87181),x87183))) % 178.07/177.93 [9897]~P21(x98971,f883(f883(x98971,a869),a869),f329(f329(f7(x98971,f883(f882(x98971,x98971),a869),f883(f883(x98971,a869),a869)),f329(f329(f8(f883(x98971,a869),f883(f883(f882(x98971,x98971),a869),f883(f883(x98971,a869),a869)),x98971),f61(x98971)),f329(f329(f7(x98971,f883(x98971,a869),f883(x98971,a869)),f307(x98971)),f193(f883(x98971,a869))))),x98973),x98972)+~P24(f329(f62(x98971),x98972))+E(f329(f38(f883(x98971,a869)),f329(f329(f61(x98971),x98972),x98973)),f329(f38(x98971),x98972)) % 178.07/177.93 [7960]~P92(x79601)+P24(f329(f329(f243(a1),f2(a1)),f329(f109(a1),x79603)))+E(f329(f329(f254(x79601),x79602),f329(f109(a875),f329(f329(f22(a1),f329(f329(f81(a1),x79603),x79603)),a103))),f79(x79601)) % 178.07/177.93 [9415]~P92(x94151)+~P24(f329(f329(f243(a1),f2(a1)),f329(f109(a1),x94153)))+E(f329(f329(f254(x94151),x94152),f329(f109(a875),f329(f329(f22(a1),f329(f329(f81(a1),x94153),x94153)),a103))),f329(f329(f87(x94151,x94151),f329(f329(f254(x94151),x94152),f329(f109(a875),x94153))),f329(f329(f18(x94151,x94151,x94151),f329(f329(f8(x94151,f883(x94151,x94151),x94151),f82(x94151)),f329(f82(x94151),x94152))),f5(x94151)))) % 178.07/177.93 [9807]~P24(f329(f136(x98071),x98073))+~P24(f329(f329(f331(x98071),x98072),f329(f171(x98071),x98073)))+E(f329(f329(f137(x98071),f329(f194(f876(x98071)),f176(x98071,f329(f329(f8(a869,a869,x98071),a324),f329(f329(f7(x98071,x98071,a869),a326),x98072)),f329(f168(x98071),x98073)))),f329(f168(x98071),x98073)),f329(f329(f150(x98071),x98072),f329(f168(x98071),f176(x98071,f329(f329(f8(a869,a869,x98071),a324),f329(f329(f7(x98071,x98071,a869),a326),x98072)),x98073)))) % 178.07/177.93 [9878]P24(f329(f329(f243(f883(f882(x98781,x98781),a869)),f305(x98781,x98782)),x98783))+~P24(f329(f329(f243(f883(f882(x98781,x98781),a869)),f305(x98781,f193(f883(f882(x98781,x98781),a869)))),x98783))+~P24(f329(f329(f243(f883(f882(x98781,x98781),a869)),f329(f329(f286(x98781,x98781,x98781),f329(f329(f107(f883(f882(x98781,x98781),a869)),f305(x98781,x98782)),x98783)),x98782)),x98783)) % 178.07/177.93 [9719]~P24(f329(f62(x97191),f329(f249(x97191),x97193)))+~P24(f329(f62(x97191),f329(f249(x97191),x97192)))+P24(f329(f62(x97191),f329(f249(x97191),f329(f329(f18(x97191,a869,a869),f329(f329(f8(a869,f883(a869,a869),x97191),a328),x97192)),x97193)))) % 178.07/177.93 [10011]P24(f329(f329(f243(f883(f882(x100111,x100111),a869)),f329(f329(f286(x100111,x100111,x100111),x100112),f305(x100111,x100112))),x100113))+~P24(f329(f329(f243(f883(f882(x100111,x100111),a869)),x100112),x100113))+~P24(f329(f329(f243(f883(f882(x100111,x100111),a869)),f329(f329(f286(x100111,x100111,x100111),f329(f329(f107(f883(f882(x100111,x100111),a869)),f329(f329(f286(x100111,x100111,x100111),x100112),f305(x100111,x100112))),x100113)),x100112)),x100113)) % 178.07/177.93 [9965]~P117(x99652)+E(x99651,f2(x99652))+~E(f329(f329(f81(x99652),f329(f329(f254(x99652),x99653),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f329(f329(f254(x99652),x99651),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f2(x99652)) % 178.07/177.93 [9966]~P117(x99662)+E(x99661,f2(x99662))+~E(f329(f329(f81(x99662),f329(f329(f254(x99662),x99661),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f329(f329(f254(x99662),x99663),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f2(x99662)) % 178.07/177.93 [9971]~P24(f329(f136(x99711),x99713))+~P24(f329(f329(f331(x99711),x99712),f329(f171(x99711),x99713)))+E(f329(f168(x99711),f329(f170(x99711),f329(f329(f137(x99711),f329(f194(f876(x99711)),f176(x99711,f329(f329(f8(a869,a869,x99711),a324),f329(f329(f7(x99711,x99711,a869),a326),x99712)),x99713))),x99713))),f176(x99711,f329(f329(f8(a869,a869,x99711),a324),f329(f329(f7(x99711,x99711,a869),a326),x99712)),f329(f168(x99711),x99713))) % 178.07/177.93 [10056]~P117(x100562)+E(x100561,f2(x100562))+P24(f329(f329(f244(x100562),f2(x100562)),f329(f329(f81(x100562),f329(f329(f254(x100562),x100563),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f329(f329(f254(x100562),x100561),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))))) % 178.07/177.93 [10057]~P117(x100572)+E(x100571,f2(x100572))+P24(f329(f329(f244(x100572),f2(x100572)),f329(f329(f81(x100572),f329(f329(f254(x100572),x100571),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f329(f329(f254(x100572),x100573),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))))) % 178.07/177.93 [10099]~P117(x100991)+P24(f329(f329(f243(x100991),f2(x100991)),x100992))+~P24(f329(f329(f243(x100991),f2(x100991)),f329(f329(f254(x100991),x100992),f329(a118,f329(f329(f82(a875),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),x100993))))) % 178.07/177.93 [5469]~P20(x54691,x54694,x54693)+P20(x54691,x54692,x54693)+~P20(x54691,x54692,x54694) % 178.07/177.93 [4932]~E(x49322,f91(x49323,x49321))+P24(f329(x49321,x49322))+~P24(f329(x49321,x49324)) % 178.07/177.93 [6681]~P38(x66812,x66814)+~P38(x66811,x66813)+P38(f882(x66811,x66812),f321(x66811,x66812,x66813,x66814)) % 178.07/177.93 [5111]~P5(x51114,x51111)+~E(f329(x51111,x51112),f329(x51111,x51113))+P24(f329(f329(x51111,x51112),x51113)) % 178.07/177.93 [5285]~P5(x52854,x52851)+E(f329(x52851,x52852),f329(x52851,x52853))+~P24(f329(f329(x52851,x52852),x52853)) % 178.07/177.93 [5376]~P14(x53763,x53764,x53761)+E(f329(x53761,x53762),f329(f64(x53763,x53764),x53762))+~P24(f329(f62(x53763),x53762)) % 178.07/177.93 [5377]~P2(x53773,x53774,x53771)+E(f329(x53771,x53772),f329(f64(x53773,x53774),x53772))+~P24(f329(f62(x53773),x53772)) % 178.07/177.93 [5502]~P5(x55024,x55021)+~P24(f329(f329(x55021,x55023),x55022))+P24(f329(f329(x55021,x55022),x55023)) % 178.07/177.93 [5569]E(x55691,x55692)+~E(f329(f263(x55693,x55694),x55691),f329(f263(x55693,x55694),x55692))+~E(f329(f267(x55693,x55694),x55691),f329(f267(x55693,x55694),x55692)) % 178.07/177.93 [5594]E(x55941,x55942)+~P24(f329(f48(x55943,x55944),x55942))+~P24(f329(f48(x55943,x55944),x55941)) % 178.07/177.93 [5785]~P70(x57852)+E(f234(x57851,x57852,x57853,x57854),f2(x57852))+P24(f329(f62(x57851),x57854)) % 178.07/177.93 [5922]~P24(f329(f317(x59221,x59222),x59224))+P24(f329(f317(x59221,x59222),x59223))+~P24(f329(f329(x59222,x59223),x59224)) % 178.07/177.93 [7880]~P105(x78802)+~P24(f329(f136(x78801),x78804))+P24(f329(f136(x78801),f149(x78801,x78802,x78803,x78804))) % 178.07/177.93 [8108]~P24(f329(f62(x81082),x81084))+~P24(f329(f62(x81081),x81083))+P24(f329(f62(f881(x81081,x81082)),f316(x81081,x81082,x81083,x81084))) % 178.07/177.93 [8109]~P24(f329(f136(x81092),x81094))+~P24(f329(f136(x81091),x81093))+P24(f329(f136(f882(x81091,x81092)),f60(x81091,x81092,x81093,x81094))) % 178.07/177.93 [8113]P24(f329(f329(f331(f876(x81131)),f329(f329(f127(x81131),x81132),x81133)),f160(x81131,x81134)))+~P24(f329(f329(f331(f876(x81131)),x81133),f160(x81131,x81134)))+~P24(f329(f329(f331(f876(x81131)),x81132),f160(x81131,x81134))) % 178.07/177.93 [8442]~P105(x84423)+~P24(f329(f136(x84421),f149(x84421,x84423,x84424,x84422)))+P24(f329(f136(x84421),x84422)) % 178.07/177.93 [8709]~P24(f329(f329(f331(f882(x87091,x87091)),f329(f329(f264(x87091,x87091),x87092),x87094)),f305(x87091,x87093)))+P24(f329(f329(f331(x87091),x87092),f318(x87091,x87093)))+~P24(f329(f329(f331(x87091),x87094),f318(x87091,x87093))) % 178.07/177.93 [5095]~P70(x50952)+E(f329(f329(f6(x50951,x50952),x50953),x50954),f2(x50952))+P24(f329(f62(x50951),x50954)) % 178.07/177.93 [5098]~P74(x50982)+E(f329(f329(f9(x50981,x50982),x50983),x50984),f79(x50982))+P24(f329(f62(x50981),x50984)) % 178.07/177.93 [5249]~P71(x52493)+E(x52491,x52492)+~E(f329(f329(f81(x52493),x52494),x52491),f329(f329(f81(x52493),x52494),x52492)) % 178.07/177.93 [5250]~P72(x52503)+E(x52501,x52502)+~E(f329(f329(f81(x52503),x52504),x52501),f329(f329(f81(x52503),x52504),x52502)) % 178.07/177.93 [5252]~P71(x52523)+E(x52521,x52522)+~E(f329(f329(f81(x52523),x52521),x52524),f329(f329(f81(x52523),x52522),x52524)) % 178.07/177.93 [5372]~P27(x53723)+E(x53721,f193(f883(x53722,a869)))+E(f329(f329(f42(x53722,x53723),x53721),f329(f16(x53723,x53722),x53724)),x53724) % 178.07/177.93 [5373]~P27(x53733)+E(x53731,f193(f883(x53732,a869)))+E(f329(f329(f43(x53732,x53733),x53731),f329(f16(x53733,x53732),x53734)),x53734) % 178.07/177.93 [5582]~P107(x55823)+E(x55821,x55822)+~E(f300(x55823,x55824,x55821),f329(f329(f307(x55823),x55822),f193(f883(x55823,a869)))) % 178.07/177.93 [5583]~P107(x55833)+E(x55831,x55832)+~E(f300(x55833,x55831,x55832),f329(f329(f307(x55833),x55834),f193(f883(x55833,a869)))) % 178.07/177.93 [5643]~P36(x56433,x56431,x56434)+P36(x56433,x56431,f329(f329(f150(x56433),x56432),x56434))+P24(f329(x56431,x56432)) % 178.07/177.93 [5745]~P32(x57451,x57452,x57454)+~P24(f329(x57452,x57453))+P32(x57451,x57452,f329(f329(f150(x57451),x57453),x57454)) % 178.07/177.93 [5878]P24(f329(x58781,x58782))+~P24(f329(f257(x58783,x58781),x58784))+~P24(f329(f329(f331(x58783),x58782),x58784)) % 178.07/177.93 [5887]~P32(x58871,x58872,x58874)+~P32(x58871,x58872,x58873)+P32(x58871,x58872,f329(f329(f127(x58871),x58873),x58874)) % 178.07/177.93 [5897]P34(x58971,x58972,x58973)+~P34(x58971,x58972,f329(f329(f150(x58971),x58974),x58973))+P24(f329(x58972,x58974)) % 178.07/177.93 [5898]P36(x58981,x58982,x58983)+~P36(x58981,x58982,f329(f329(f150(x58981),x58984),x58983))+P24(f329(x58982,x58984)) % 178.07/177.93 [5911]E(x59111,x59112)+~P24(f329(f329(f199(x59113),x59114),x59112))+~P24(f329(f329(f199(x59113),x59114),x59111)) % 178.07/177.93 [5978]P34(x59781,x59782,x59783)+P34(x59781,x59782,x59784)+~P34(x59781,x59782,f329(f329(f127(x59781),x59784),x59783)) % 178.07/177.93 [5997]~P70(x59971)+E(f329(f329(f6(a875,x59971),x59972),f329(f299(a875,x59973),f329(a118,x59974))),f2(x59971))+~P24(f329(f329(f244(a875),x59974),x59973)) % 178.07/177.93 [6002]~P57(x60021)+~E(f45(x60021,x60022,x60023),f45(x60021,x60024,x60023))+E(f45(x60021,f329(f80(x60021),x60022),x60023),f45(x60021,f329(f80(x60021),x60024),x60023)) % 178.07/177.93 [6070]P24(f329(x60701,x60702))+~E(f329(f135(x60703,x60701),x60704),x60704)+~P24(f329(f329(f331(x60703),x60702),f329(f171(x60703),x60704))) % 178.07/177.93 [6089]~E(f329(f329(f81(a875),x60893),x60892),f329(f329(f81(a875),x60891),x60894))+~P24(f329(f329(f244(a875),x60893),x60894))+P24(f329(f329(f244(a875),x60891),x60892)) % 178.07/177.93 [6093]P34(x60931,x60932,x60933)+~P24(f329(x60932,x60934))+~P24(f329(f329(f331(x60931),x60934),f329(f171(x60931),x60933))) % 178.07/177.93 [6129]~P32(x61293,x61291,x61294)+P24(f329(x61291,x61292))+~P24(f329(f329(f331(x61293),x61292),f329(f171(x61293),x61294))) % 178.07/177.93 [6131]~E(f329(f135(x61311,x61312),x61313),f119(x61311))+~P24(f329(x61312,x61314))+~P24(f329(f329(f331(x61311),x61314),f329(f171(x61311),x61313))) % 178.07/177.93 [6132]~E(f176(x61323,x61321,x61324),x61324)+P24(f329(x61321,x61322))+~P24(f329(f329(f331(x61323),x61322),f329(f171(x61323),x61324))) % 178.07/177.93 [6166]~E(x61664,f193(f883(x61662,a869)))+~E(x61663,f193(f883(x61661,a869)))+E(f316(x61661,x61662,x61663,x61664),f193(f883(f881(x61661,x61662),a869))) % 178.07/177.93 [6310]P24(f329(x63101,x63102))+~P24(f329(f159(x63103,x63101),x63104))+~P24(f329(f329(f331(x63103),x63102),f329(f171(x63103),x63104))) % 178.07/177.93 [6579]~P70(x65791)+E(f329(f329(f6(a875,x65791),x65792),f300(a875,x65793,f329(a118,x65794))),f2(x65791))+~P24(f329(f329(f244(a875),f329(a118,x65794)),x65793)) % 178.07/177.93 [6720]~P105(x67201)+E(f329(f329(f22(f883(x67201,a869)),f329(f299(x67201,x67202),x67203)),f329(f299(x67201,x67202),x67204)),f329(f299(x67201,x67204),x67203))+~P24(f329(f329(f243(x67201),x67202),x67204)) % 178.07/177.93 [7073]~P24(f329(f329(f331(f876(x70731)),x70734),f160(x70731,x70733)))+P24(f329(f329(f331(x70731),x70732),x70733))+~P24(f329(f329(f331(x70731),x70732),f329(f171(x70731),x70734))) % 178.07/177.93 [7080]~P38(x70801,x70802)+P24(f329(f329(f331(x70801),f781(x70802,x70801,x70803)),x70803))+~P24(f329(f329(f331(x70801),x70804),x70803)) % 178.07/177.93 [7136]~P70(x71361)+E(f329(f329(f329(f66(x71361,x71362,f81(x71361)),x71363),f2(x71361)),x71364),f329(f329(f6(x71362,x71361),x71363),x71364))+~P24(f329(f62(x71362),x71364)) % 178.07/177.93 [7138]~P74(x71381)+E(f329(f329(f329(f66(x71381,x71382,f82(x71381)),x71383),f79(x71381)),x71384),f329(f329(f9(x71382,x71381),x71383),x71384))+~P24(f329(f62(x71382),x71384)) % 178.07/177.93 [7166]P21(x71661,x71662,x71663,x71664)+~E(f329(f38(x71662),f329(f308(x71661,x71662,x71663),x71664)),f329(f38(x71661),x71664))+~P24(f329(f62(x71661),x71664)) % 178.07/177.93 [7352]~P70(x73521)+E(f329(f329(f81(x73521),f329(x73522,x73523)),f329(f329(f6(a875,x73521),x73522),f302(a875,x73523,x73524))),f329(f329(f6(a875,x73521),x73522),f300(a875,x73523,x73524)))+~P24(f329(f329(f243(a875),x73523),x73524)) % 178.07/177.93 [7362]~P70(x73621)+~P21(x73622,x73621,x73623,x73624)+E(f329(f329(f6(x73621,x73621),f35(x73621)),f329(f308(x73622,x73621,x73623),x73624)),f329(f329(f6(x73622,x73621),x73623),x73624)) % 178.07/177.93 [7363]~P74(x73631)+~P21(x73632,x73631,x73633,x73634)+E(f329(f329(f9(x73631,x73631),f35(x73631)),f329(f308(x73632,x73631,x73633),x73634)),f329(f329(f9(x73632,x73631),x73633),x73634)) % 178.07/177.93 [7417]E(f329(f38(f881(x74171,x74172)),f316(x74171,x74172,x74173,x74174)),f329(f329(f81(a875),f329(f38(x74171),x74173)),f329(f38(x74172),x74174)))+~P24(f329(f62(x74172),x74174))+~P24(f329(f62(x74171),x74173)) % 178.07/177.93 [7504]E(x75041,x75042)+P24(f329(f329(f331(x75043),x75041),f329(f171(x75043),f169(x75043,x75042,x75044))))+~P24(f329(f329(f331(x75043),x75041),f329(f171(x75043),x75044))) % 178.07/177.93 [7728]~P70(x77281)+E(f329(f329(f81(x77281),f329(f329(f6(a875,x77281),x77282),f329(f299(a875,x77283),x77284))),f329(x77282,x77284)),f329(f329(f6(a875,x77281),x77282),f329(f299(a875,x77283),f329(a118,x77284))))+P24(f329(f329(f244(a875),x77284),x77283)) % 178.07/177.93 [7781]~P21(x77811,x77812,x77813,f252(f883(x77811,a869)))+~P24(f329(f62(x77812),x77814))+P24(f329(f62(x77811),f329(f309(x77811,x77812,x77813),x77814))) % 178.07/177.93 [7893]P24(f329(f329(f331(f876(x78931)),f329(f329(f150(x78931),x78932),x78933)),f160(x78931,x78934)))+~P24(f329(f329(f331(f876(x78931)),x78933),f160(x78931,x78934)))+~P24(f329(f329(f331(x78931),x78932),x78934)) % 178.07/177.93 [7984]~E(f329(f308(x79843,x79841,x79844),f252(f883(x79843,a869))),f252(f883(x79841,a869)))+P24(f329(f62(x79841),x79842))+~P24(f329(f62(x79843),f329(f309(x79843,x79841,x79844),x79842))) % 178.07/177.93 [8080]~P21(x80801,x80803,x80804,x80802)+P24(f329(f62(x80801),x80802))+~P24(f329(f62(x80803),f329(f308(x80801,x80803,x80804),x80802))) % 178.07/177.93 [8101]~E(x81012,x81013)+P24(f329(f329(f331(f882(x81011,x81011)),f329(f329(f264(x81011,x81011),x81012),x81013)),f261(x81011,x81014)))+~P24(f329(f329(f331(x81011),x81012),x81014)) % 178.07/177.93 [8139]~P70(x81391)+E(f329(f329(f81(x81391),f329(f329(f6(a875,x81391),x81392),f300(a875,x81393,x81394))),f329(x81392,f329(a118,x81394))),f329(f329(f6(a875,x81391),x81392),f300(a875,x81393,f329(a118,x81394))))+P24(f329(f329(f244(a875),f329(a118,x81394)),x81393)) % 178.07/177.93 [8203]P24(f329(x82031,x82032))+~P24(f329(x82031,f329(f329(f164(x82033),x82034),f577(x82031,x82034,x82033))))+~P24(f329(f329(f331(x82033),x82032),f329(f171(x82033),x82034))) % 178.07/177.93 [8342]~P24(f329(f329(f331(x83421),x83422),f318(x83421,x83424)))+P24(f329(f329(f331(f876(x83421)),f329(f329(f150(x83421),x83422),x83423)),f318(f876(x83421),f156(x83421,x83424))))+~P24(f329(f329(f331(f876(x83421)),x83423),f318(f876(x83421),f156(x83421,x83424)))) % 178.07/177.93 [8355]~P21(x83552,x83553,x83554,f853(x83554,x83553,x83552,x83551))+P21(x83552,x83553,x83554,f41(f883(x83552,a869),x83551))+E(x83551,f193(f883(f883(x83552,a869),a869))) % 178.07/177.93 [8627]E(x86271,x86272)+~P24(f329(f329(f331(f882(x86273,x86273)),f329(f329(f264(x86273,x86273),x86271),x86272)),f305(x86273,x86274)))+P24(f329(f329(f331(x86273),x86271),f329(f262(x86273,x86273),x86274))) % 178.07/177.93 [8907]P21(x89072,x89073,x89074,f41(f883(x89072,a869),x89071))+E(x89071,f193(f883(f883(x89072,a869),a869)))+P24(f329(f329(f331(f883(x89072,a869)),f853(x89074,x89073,x89072,x89071)),x89071)) % 178.07/177.93 [9045]P24(f329(f62(x90451),x90452))+~P24(f329(f62(x90454),f329(f308(x90451,x90454,x90453),x90452)))+P24(f329(f329(f331(x90451),f500(x90453,x90454,x90452,x90451)),x90452)) % 178.07/177.93 [9137]~P27(x91372)+E(f329(f329(f65(x91371,x91372,f329(f329(f8(x91372,f883(x91372,x91372),x91371),f107(x91372)),x91373)),f252(x91372)),x91374),f329(f329(f42(x91371,x91372),x91374),x91373))+~P24(f329(f62(x91371),x91374)) % 178.07/177.93 [9138]~P27(x91382)+E(f329(f329(f65(x91381,x91382,f329(f329(f8(x91382,f883(x91382,x91382),x91381),f116(x91382)),x91383)),f193(x91382)),x91384),f329(f329(f43(x91381,x91382),x91384),x91383))+~P24(f329(f62(x91381),x91384)) % 178.07/177.93 [9221]P24(f329(x92211,x92212))+~P24(f329(x92211,f329(f329(f164(x92213),x92214),f585(x92212,x92211,x92214,x92213))))+~P24(f329(f329(f331(x92213),x92212),f329(f171(x92213),x92214))) % 178.07/177.93 [9242]E(x92421,x92422)+~P24(f329(f329(f331(f882(x92423,x92423)),f329(f329(f264(x92423,x92423),x92421),x92422)),f305(x92423,x92424)))+P24(f329(f329(f331(f882(x92423,x92423)),f329(f329(f264(x92423,x92423),x92421),x92422)),f329(f329(f286(x92423,x92423,x92423),x92424),f305(x92423,x92424)))) % 178.07/177.93 [9291]~E(f329(f194(f876(x92911)),x92912),f329(f194(f876(x92911)),x92913))+~P24(f329(f329(f331(f882(f876(x92911),f876(x92911))),f329(f329(f264(f876(x92911),f876(x92911)),x92912),x92913)),f146(x92911,x92914)))+P24(f329(f329(f331(f882(f876(x92911),f876(x92911))),f329(f329(f264(f876(x92911),f876(x92911)),x92912),x92913)),f144(x92911,x92914))) % 178.07/177.93 [9520]P32(x95201,f329(f329(f18(x95201,a869,a869),f329(f329(f8(a869,f883(a869,a869),x95201),a328),f329(f329(f8(a869,a869,x95201),a324),x95202))),f329(a326,x95203)),x95204)+~P24(f329(x95202,x95203))+~P36(x95201,x95202,f329(f329(f150(x95201),x95203),x95204)) % 178.07/177.93 [9681]~P32(x96811,f329(f329(f18(x96811,a869,a869),f329(f329(f8(a869,f883(a869,a869),x96811),a328),f329(f329(f8(a869,a869,x96811),a324),x96812))),f329(a326,x96813)),x96814)+~P24(f329(x96812,x96813))+P36(x96811,x96812,f329(f329(f150(x96811),x96813),x96814)) % 178.07/177.93 [9685]~P36(x96851,x96852,x96854)+~P32(x96851,f329(f329(f18(x96851,a869,a869),f329(f329(f8(a869,f883(a869,a869),x96851),a328),f329(f329(f8(a869,a869,x96851),a324),x96852))),f329(a326,x96853)),x96854)+P36(x96851,x96852,f329(f329(f150(x96851),x96853),x96854)) % 178.07/177.93 [9722]~P66(x97221)+E(f329(f329(f6(a875,x97221),f329(f329(f18(a875,x97221,x97221),f329(f329(f8(x97221,f883(x97221,x97221),a875),f22(x97221)),x97222)),f329(f329(f8(a875,x97221,a875),x97222),f329(f329(f7(a875,a875,a875),f81(a875)),f79(a875))))),f300(a875,x97223,x97224)),f2(x97221))+P24(f329(f329(f243(a875),x97223),x97224)) % 178.07/177.93 [9964]~P38(x99642,x99644)+~P21(x99642,x99641,x99643,f252(f883(x99642,a869)))+P38(x99641,f329(f308(f882(x99642,x99642),f882(x99641,x99641),f269(x99642,x99641,x99642,x99641,x99643,x99643)),x99644)) % 178.07/177.93 [10125]~E(f329(f194(f876(x101251)),x101253),f329(f194(f876(x101251)),x101252))+P24(f329(f329(f331(f882(f876(x101251),f876(x101251))),f329(f329(f264(f876(x101251),f876(x101251)),x101252),x101253)),f157(x101251,x101254)))+~P24(f329(f329(f268(x101251,x101251,a869),f329(f329(f7(x101251,f883(f882(x101251,x101251),a869),f883(x101251,a869)),f329(f329(f8(f883(x101251,f883(f883(f882(x101251,x101251),a869),a869)),f883(f883(f882(x101251,x101251),a869),f883(x101251,a869)),x101251),f7(x101251,f883(f882(x101251,x101251),a869),a869)),f329(f329(f8(f883(x101251,f882(x101251,x101251)),f883(x101251,f883(f883(f882(x101251,x101251),a869),a869)),x101251),f329(f8(f882(x101251,x101251),f883(f883(f882(x101251,x101251),a869),a869),x101251),f331(f882(x101251,x101251)))),f264(x101251,x101251)))),x101254)),f589(x101254,x101253,x101252,x101251))) % 178.07/177.93 [5961]~E(x59614,x59612)+P24(f329(x59611,x59612))+P24(f329(f329(f199(f33(x59611,x59613)),x59612),x59614)) % 178.07/177.93 [6054]~P56(x60541)+~E(x60542,f2(x60541))+E(f329(f329(f39(x60541),f329(f329(f82(x60541),x60542),x60543)),f329(f329(f82(x60541),x60542),x60544)),f2(x60541)) % 178.07/177.93 [6092]E(x60921,f119(x60922))+E(x60923,f329(f329(f22(a875),f329(f194(f876(x60922)),x60921)),f79(a875)))+E(f143(x60922,f329(f329(f158(x60922,x60921),x60923),x60924)),f143(x60922,x60921)) % 178.07/177.93 [6120]E(x61201,x61202)+P24(f329(x61203,x61202))+~P24(f329(f329(f329(f307(x61204),x61201),x61203),x61202)) % 178.07/177.93 [6136]~P70(x61361)+~P24(f329(f136(x61362),x61364))+E(f329(f165(x61361),f329(f329(f153(x61362,x61361),x61363),x61364)),f329(f329(f6(x61362,x61361),x61363),f329(f171(x61362),x61364))) % 178.07/177.93 [6159]~P74(x61592)+~P24(f329(f62(x61591),x61594))+E(f329(f329(f9(x61591,x61592),f329(f16(x61592,x61591),x61593)),x61594),f329(f329(f254(x61592),x61593),f329(f38(x61591),x61594))) % 178.07/177.93 [6213]~P56(x62132)+E(x62131,f2(x62132))+E(f329(f329(f39(x62132),f329(f329(f82(x62132),x62133),x62131)),f329(f329(f82(x62132),x62134),x62131)),f329(f329(f39(x62132),x62133),x62134)) % 178.07/177.93 [6215]~P59(x62152)+E(x62151,f2(x62152))+E(f329(f329(f287(x62152),f329(f329(f82(x62152),x62153),x62151)),f329(f329(f82(x62152),x62154),x62151)),f329(f329(f287(x62152),x62153),x62154)) % 178.07/177.93 [6216]~P59(x62162)+E(x62161,f2(x62162))+E(f329(f329(f287(x62162),f329(f329(f82(x62162),x62161),x62163)),f329(f329(f82(x62162),x62161),x62164)),f329(f329(f287(x62162),x62163),x62164)) % 178.07/177.93 [6217]~P56(x62172)+E(x62171,f2(x62172))+E(f329(f329(f39(x62172),f329(f329(f82(x62172),x62171),x62173)),f329(f329(f82(x62172),x62171),x62174)),f329(f329(f39(x62172),x62173),x62174)) % 178.07/177.93 [6280]P24(f329(x62801,x62802))+~E(x62803,f329(f329(f81(a875),x62804),x62802))+~P24(f329(x62801,f329(f329(f22(a875),x62803),x62804))) % 178.07/177.93 [6362]P23(x63621,x63622,x63623)+P30(x63621,f592(x63623,x63622,x63621),x63624)+~P24(f329(f329(f331(f874(x63621)),x63624),x63622)) % 178.07/177.93 [6364]~P24(f329(x63642,x63643))+~P24(f329(f159(x63641,x63642),x63644))+P24(f329(f159(x63641,x63642),f329(f329(f150(x63641),x63643),x63644))) % 178.07/177.93 [6404]E(x64041,f119(x64042))+~E(x64043,f329(f329(f22(a875),f329(f194(f876(x64042)),x64041)),f79(a875)))+E(f143(x64042,f329(f329(f158(x64042,x64041),x64043),x64044)),x64044) % 178.07/177.93 [6427]~P99(x64271)+~P24(f329(f329(f244(x64271),x64272),x64274))+P24(f329(f329(f244(x64271),x64272),f329(f329(f116(x64271),x64273),x64274))) % 178.07/177.93 [6428]~P99(x64281)+~P24(f329(f329(f244(x64281),x64282),x64283))+P24(f329(f329(f244(x64281),x64282),f329(f329(f116(x64281),x64283),x64284))) % 178.07/177.93 [6430]~P105(x64301)+~P24(f329(f329(f244(x64301),x64302),x64304))+P24(f329(f329(f244(x64301),x64302),f329(f329(f242(x64301),x64303),x64304))) % 178.07/177.93 [6432]~P105(x64321)+~P24(f329(f329(f244(x64321),x64322),x64323))+P24(f329(f329(f244(x64321),x64322),f329(f329(f242(x64321),x64323),x64324))) % 178.07/177.93 [6433]~P99(x64331)+~P24(f329(f329(f243(x64331),x64332),x64334))+P24(f329(f329(f243(x64331),x64332),f329(f329(f116(x64331),x64333),x64334))) % 178.07/177.93 [6434]~P99(x64341)+~P24(f329(f329(f243(x64341),x64342),x64343))+P24(f329(f329(f243(x64341),x64342),f329(f329(f116(x64341),x64343),x64344))) % 178.07/177.93 [6436]~P105(x64361)+~P24(f329(f329(f243(x64361),x64362),x64364))+P24(f329(f329(f243(x64361),x64362),f329(f329(f242(x64361),x64363),x64364))) % 178.07/177.93 [6438]~P105(x64381)+~P24(f329(f329(f243(x64381),x64382),x64383))+P24(f329(f329(f243(x64381),x64382),f329(f329(f242(x64381),x64383),x64384))) % 178.07/177.93 [6524]~E(f329(f329(f164(x65241),x65242),x65243),x65244)+E(f329(f329(f158(x65241,x65242),x65243),x65244),x65242)+~P24(f329(f329(f244(a875),x65243),f329(f194(f876(x65241)),x65242))) % 178.07/177.93 [6541]E(x65411,x65412)+P24(f329(x65413,x65411))+~P24(f329(f329(f199(f33(x65413,x65414)),x65411),x65412)) % 178.07/177.93 [6565]P24(f329(x65651,x65652))+~P24(f329(x65653,x65652))+~P24(f329(f329(f243(f883(x65654,a869)),x65653),x65651)) % 178.07/177.93 [6597]~E(f329(f329(f158(x65971,x65972),x65973),x65974),x65972)+E(f329(f329(f164(x65971),x65972),x65973),x65974)+~P24(f329(f329(f244(a875),x65973),f329(f194(f876(x65971)),x65972))) % 178.07/177.93 [6612]~P24(f329(f159(x66121,x66122),x66124))+~P24(f329(f159(x66121,x66122),x66123))+P24(f329(f159(x66121,x66122),f329(f329(f127(x66121),x66123),x66124))) % 178.07/177.93 [6708]P30(x67081,x67082,x67083)+~P30(x67081,f329(a118,x67082),f596(x67082,x67084,x67081))+~P24(f329(f329(f331(f874(x67081)),x67083),x67084)) % 178.07/177.93 [6717]E(x67171,f193(f883(x67172,a869)))+E(x67173,f193(f883(x67174,a869)))+~E(f329(f329(f266(x67174,x67172),x67173),f329(f16(f883(x67172,a869),x67174),x67171)),f193(f883(f882(x67174,x67172),a869))) % 178.07/177.93 [6736]E(x67361,x67362)+P24(f329(f329(f331(x67363),x67361),x67364))+~P24(f329(f329(f331(x67363),x67361),f329(f329(f307(x67363),x67362),x67364))) % 178.07/177.93 [6752]~P105(x67521)+P24(f329(f329(f244(x67521),x67522),x67523))+~P24(f329(f329(f244(x67521),x67522),f329(f329(f241(x67521),x67524),x67523))) % 178.07/177.93 [6753]~P105(x67531)+P24(f329(f329(f244(x67531),x67532),x67533))+~P24(f329(f329(f244(x67531),x67532),f329(f329(f241(x67531),x67533),x67534))) % 178.07/177.93 [6755]~P100(x67551)+P24(f329(f329(f243(x67551),x67552),x67553))+~P24(f329(f329(f243(x67551),x67552),f329(f329(f107(x67551),x67554),x67553))) % 178.07/177.93 [6757]~P100(x67571)+P24(f329(f329(f243(x67571),x67572),x67573))+~P24(f329(f329(f243(x67571),x67572),f329(f329(f107(x67571),x67573),x67574))) % 178.07/177.93 [6759]~P105(x67591)+P24(f329(f329(f243(x67591),x67592),x67593))+~P24(f329(f329(f243(x67591),x67592),f329(f329(f241(x67591),x67594),x67593))) % 178.07/177.93 [6761]~P105(x67611)+P24(f329(f329(f243(x67611),x67612),x67613))+~P24(f329(f329(f243(x67611),x67612),f329(f329(f241(x67611),x67613),x67614))) % 178.07/177.93 [6783]~E(f329(f329(f164(x67831),x67833),x67834),x67832)+P24(f329(f329(f331(x67831),x67832),f329(f171(x67831),x67833)))+~P24(f329(f329(f244(a875),x67834),f329(f194(f876(x67831)),x67833))) % 178.07/177.93 [6794]~P105(x67941)+~P29(x67941,f329(f329(f150(x67941),x67942),f329(f329(f150(x67941),x67943),x67944)))+P24(f329(f329(f243(x67941),x67942),x67943)) % 178.07/177.93 [6936]~P32(x69362,x69361,x69363)+P24(f329(x69361,f329(f329(f164(x69362),x69363),x69364)))+~P24(f329(f329(f244(a875),x69364),f329(f194(f876(x69362)),x69363))) % 178.07/177.93 [6955]E(x69551,f2(a1))+E(f329(f329(f39(a1),x69552),x69551),x69553)+~P24(f329(f49(x69552,x69551),f329(f329(f264(a1,a1),x69553),x69554))) % 178.07/177.93 [6976]E(f45(a1,x69762,x69761),x69763)+E(x69761,f2(a1))+~P24(f329(f49(x69762,x69761),f329(f329(f264(a1,a1),x69764),x69763))) % 178.07/177.93 [7094]P24(f329(f329(f331(x70941),x70942),x70943))+~P24(f329(f329(f331(x70941),x70942),x70944))+~P24(f329(f329(f244(f883(x70941,a869)),x70944),x70943)) % 178.07/177.93 [7098]P24(f329(f329(f331(x70981),x70982),x70983))+~P24(f329(f329(f331(x70981),x70982),x70984))+~P24(f329(f329(f243(f883(x70981,a869)),x70984),x70983)) % 178.07/177.93 [7206]P34(x72061,x72062,x72063)+~P24(f329(x72062,f329(f329(f164(x72061),x72063),x72064)))+~P24(f329(f329(f244(a875),x72064),f329(f194(f876(x72061)),x72063))) % 178.07/177.93 [7317]~P106(x73172)+~P24(f329(f329(f244(f883(x73171,x73172)),x73173),x73174))+P24(f329(f329(f243(f883(x73171,x73172)),x73173),x73174)) % 178.07/177.93 [7405]~P20(x74051,x74052,x74054)+P20(x74051,x74052,f329(f329(f307(f874(x74051)),x74053),x74054))+~P20(x74051,x74052,f329(f329(f307(f874(x74051)),x74053),f193(f883(f874(x74051),a869)))) % 178.07/177.93 [7450]~P24(f329(f329(f331(x74501),x74502),x74504))+P24(f329(f329(f331(x74501),x74502),f40(f883(x74501,a869),x74503)))+~P24(f329(f329(f331(f883(x74501,a869)),x74504),x74503)) % 178.07/177.93 [7462]P30(x74621,x74622,x74623)+P24(f329(f329(f331(f874(x74621)),f596(x74622,x74624,x74621)),x74624))+~P24(f329(f329(f331(f874(x74621)),x74623),x74624)) % 178.07/177.93 [7482]~P82(x74821)+~P24(f329(f329(f244(x74821),x74823),x74824))+P24(f329(f329(f244(x74821),f329(f329(f81(x74821),x74822),x74823)),f329(f329(f81(x74821),x74822),x74824))) % 178.07/177.93 [7483]~P83(x74831)+~P24(f329(f329(f244(x74831),x74833),x74834))+P24(f329(f329(f244(x74831),f329(f329(f81(x74831),x74832),x74833)),f329(f329(f81(x74831),x74832),x74834))) % 178.07/177.93 [7484]~P82(x74841)+~P24(f329(f329(f244(x74841),x74842),x74844))+P24(f329(f329(f244(x74841),f329(f329(f81(x74841),x74842),x74843)),f329(f329(f81(x74841),x74844),x74843))) % 178.07/177.93 [7485]~P83(x74851)+~P24(f329(f329(f244(x74851),x74852),x74854))+P24(f329(f329(f244(x74851),f329(f329(f81(x74851),x74852),x74853)),f329(f329(f81(x74851),x74854),x74853))) % 178.07/177.93 [7486]~P83(x74861)+~P24(f329(f329(f243(x74861),x74863),x74864))+P24(f329(f329(f243(x74861),f329(f329(f81(x74861),x74862),x74863)),f329(f329(f81(x74861),x74862),x74864))) % 178.07/177.93 [7487]~P84(x74871)+~P24(f329(f329(f243(x74871),x74873),x74874))+P24(f329(f329(f243(x74871),f329(f329(f81(x74871),x74872),x74873)),f329(f329(f81(x74871),x74872),x74874))) % 178.07/177.93 [7488]~P83(x74881)+~P24(f329(f329(f243(x74881),x74882),x74884))+P24(f329(f329(f243(x74881),f329(f329(f81(x74881),x74882),x74883)),f329(f329(f81(x74881),x74884),x74883))) % 178.07/177.93 [7489]~P84(x74891)+~P24(f329(f329(f243(x74891),x74892),x74894))+P24(f329(f329(f243(x74891),f329(f329(f81(x74891),x74892),x74893)),f329(f329(f81(x74891),x74894),x74893))) % 178.07/177.93 [7498]~P108(x74981)+~P93(x74981)+E(f329(f329(f22(x74981),f329(f329(f82(x74981),x74982),f329(f109(x74981),x74983))),f329(f329(f82(x74981),x74984),f329(f109(x74981),x74983))),f329(f329(f82(x74981),f329(f329(f22(x74981),x74982),x74984)),f329(f109(x74981),x74983))) % 178.07/177.93 [7499]~P135(x74991)+~P93(x74991)+E(f329(f329(f81(x74991),f329(f329(f82(x74991),x74992),f329(f109(x74991),x74993))),f329(f329(f82(x74991),x74994),f329(f109(x74991),x74993))),f329(f329(f82(x74991),f329(f329(f81(x74991),x74992),x74994)),f329(f109(x74991),x74993))) % 178.07/177.93 [7534]~P70(x75341)+E(f329(f329(f81(x75341),f329(x75342,x75343)),f329(f329(f6(a875,x75341),x75342),f300(a875,f329(a118,x75343),x75344))),f329(f329(f6(a875,x75341),x75342),f300(a875,x75343,x75344)))+~P24(f329(f329(f243(a875),x75343),x75344)) % 178.07/177.93 [7545]~P21(x75452,x75451,x75453,f329(f171(x75452),x75454))+~P24(f329(f136(x75452),x75454))+P24(f329(f136(x75451),f329(f329(f153(x75452,x75451),x75453),x75454))) % 178.07/177.93 [7594]~P24(f329(f329(f244(a875),x75942),x75944))+~P24(f329(f329(f244(a875),x75941),x75943))+P24(f329(f329(f244(a875),f329(f329(f81(a875),x75941),x75942)),f329(f329(f81(a875),x75943),x75944))) % 178.07/177.93 [7595]~P24(f329(f329(f244(a1),x75951),x75953))+~P24(f329(f329(f243(a1),x75952),x75954))+P24(f329(f329(f244(a1),f329(f329(f81(a1),x75951),x75952)),f329(f329(f81(a1),x75953),x75954))) % 178.07/177.93 [7596]~P24(f329(f329(f243(a875),x75962),x75964))+~P24(f329(f329(f243(a875),x75961),x75963))+P24(f329(f329(f243(a875),f329(f329(f82(a875),x75961),x75962)),f329(f329(f82(a875),x75963),x75964))) % 178.07/177.93 [7597]~P24(f329(f329(f243(a875),x75972),x75974))+~P24(f329(f329(f243(a875),x75971),x75973))+P24(f329(f329(f243(a875),f329(f329(f81(a875),x75971),x75972)),f329(f329(f81(a875),x75973),x75974))) % 178.07/177.93 [7645]P24(f329(f329(f331(x76451),x76452),x76453))+~P24(f329(f329(f331(x76451),x76452),f41(f883(x76451,a869),x76454)))+~P24(f329(f329(f331(f883(x76451,a869)),x76453),x76454)) % 178.07/177.93 [7660]~P24(f329(x76601,f576(x76601,x76603,x76602)))+P24(f329(x76601,f329(f329(f164(x76602),x76603),x76604)))+~P24(f329(f329(f244(a875),x76604),f329(f194(f876(x76602)),x76603))) % 178.07/177.93 [7665]P24(f329(x76651,x76652))+~P24(f329(f329(f331(x76654),x76652),f329(f171(x76654),x76653)))+P24(f329(f329(f244(a875),f577(x76651,x76653,x76654)),f329(f194(f876(x76654)),x76653))) % 178.07/177.93 [7685]~P24(f329(f329(f199(x76852),x76853),x76854))+~P24(f329(f329(f199(f33(x76851,x76852)),x76854),x76853))+P24(f329(f329(f199(f33(x76851,x76852)),x76853),x76853)) % 178.07/177.93 [7714]~P106(x77141)+~P24(f329(f329(f243(f883(x77142,x77141)),x77144),x77143))+~P24(f329(f329(f244(f883(x77142,x77141)),x77143),x77144)) % 178.07/177.93 [7758]~P24(f329(x77584,x77582))+~P24(f329(f329(f331(x77581),x77582),x77583))+P24(f329(f329(f331(x77581),x77582),f329(f329(f107(f883(x77581,a869)),x77583),f329(f249(x77581),x77584)))) % 178.07/177.93 [7902]~P24(f329(f329(f331(x79021),x79023),x79024))+~P24(f329(f329(f244(f883(x79021,a869)),x79022),x79024))+P24(f329(f329(f244(f883(x79021,a869)),x79022),f329(f329(f307(x79021),x79023),x79024))) % 178.07/177.93 [7904]E(f329(f329(f107(f883(x79041,a869)),x79042),x79043),f193(f883(x79041,a869)))+~E(f329(f329(f107(f883(x79041,a869)),f40(f883(x79041,a869),x79044)),x79043),f193(f883(x79041,a869)))+~P24(f329(f329(f331(f883(x79041,a869)),x79042),x79044)) % 178.07/177.93 [7980]P24(f329(f329(f331(x79801),x79802),x79803))+~P24(f329(f329(f243(f883(x79801,a869)),x79803),f329(f329(f307(x79801),x79802),x79804)))+P24(f329(f329(f243(f883(x79801,a869)),x79803),x79804)) % 178.07/177.93 [8002]P24(f329(f329(f331(x80022),f576(x80021,x80023,x80022)),f329(f171(x80022),x80023)))+P24(f329(x80021,f329(f329(f164(x80022),x80023),x80024)))+~P24(f329(f329(f244(a875),x80024),f329(f194(f876(x80022)),x80023))) % 178.07/177.93 [8010]~P24(f329(f329(f244(f883(x80101,a869)),x80102),x80104))+P24(f329(f329(f244(f883(x80101,a869)),x80102),x80103))+~P24(f329(f329(f244(f883(x80101,a869)),x80104),x80103)) % 178.07/177.93 [8011]~P24(f329(f329(f243(f883(x80111,a869)),x80112),x80114))+P24(f329(f329(f244(f883(x80111,a869)),x80112),x80113))+~P24(f329(f329(f244(f883(x80111,a869)),x80114),x80113)) % 178.07/177.93 [8012]~P24(f329(f329(f243(f883(x80121,a869)),x80124),x80123))+~P24(f329(f329(f244(f883(x80121,a869)),x80122),x80124))+P24(f329(f329(f244(f883(x80121,a869)),x80122),x80123)) % 178.07/177.93 [8013]~P24(f329(f329(f243(f883(x80131,a869)),x80132),x80134))+P24(f329(f329(f243(f883(x80131,a869)),x80132),x80133))+~P24(f329(f329(f243(f883(x80131,a869)),x80134),x80133)) % 178.07/177.93 [8053]~P24(f329(f329(f331(x80531),x80534),x80533))+~P24(f329(f329(f244(f883(x80531,a869)),x80532),f329(f329(f307(x80531),x80534),x80533)))+P24(f329(f329(f244(f883(x80531,a869)),x80532),x80533)) % 178.07/177.93 [8065]~P83(x80651)+P24(f329(f329(f244(x80651),x80652),x80653))+~P24(f329(f329(f244(x80651),f329(f329(f81(x80651),x80654),x80652)),f329(f329(f81(x80651),x80654),x80653))) % 178.07/177.93 [8067]~P83(x80671)+P24(f329(f329(f244(x80671),x80672),x80673))+~P24(f329(f329(f244(x80671),f329(f329(f81(x80671),x80672),x80674)),f329(f329(f81(x80671),x80673),x80674))) % 178.07/177.93 [8069]~P83(x80691)+P24(f329(f329(f243(x80691),x80692),x80693))+~P24(f329(f329(f243(x80691),f329(f329(f81(x80691),x80694),x80692)),f329(f329(f81(x80691),x80694),x80693))) % 178.07/177.93 [8071]~P83(x80711)+P24(f329(f329(f243(x80711),x80712),x80713))+~P24(f329(f329(f243(x80711),f329(f329(f81(x80711),x80712),x80714)),f329(f329(f81(x80711),x80713),x80714))) % 178.07/177.93 [8119]P24(f329(x81191,x81192))+~E(f329(f329(f137(x81193),f329(f194(f876(x81193)),f176(x81193,x81191,x81194))),x81194),f119(x81193))+~P24(f329(f329(f331(x81193),x81192),f329(f171(x81193),x81194))) % 178.07/177.93 [8245]P24(f329(x82451,x82452))+~P24(f329(f329(f331(x82453),x82452),f329(f171(x82453),x82454)))+P24(f329(f329(f244(a875),f329(f194(f876(x82453)),f329(f135(x82453,x82451),x82454))),f329(f194(f876(x82453)),x82454))) % 178.07/177.93 [8371]E(x83711,x83712)+P24(f329(f329(f199(x83713),x83711),f602(x83712,x83711,x83713,x83714)))+~P24(f329(f329(f199(f33(x83714,x83713)),x83711),x83712)) % 178.07/177.93 [8401]~P24(f329(x84014,x84012))+P24(f329(f329(f199(x84011),x84012),f602(x84013,x84012,x84011,x84014)))+~P24(f329(f329(f199(f33(x84014,x84011)),x84012),x84013)) % 178.07/177.93 [8720]~P24(f329(x87201,f741(x87201,x87203,x87202,x87204)))+P24(f329(x87201,f329(f329(f164(x87202),x87203),x87204)))+~P24(f329(f329(f244(a875),x87204),f329(f194(f876(x87202)),x87203))) % 178.07/177.93 [8743]~P21(x87434,x87433,x87431,f252(f883(x87434,a869)))+E(f329(x87431,f812(x87432,x87431,x87433,x87434)),x87432)+~P24(f329(f329(f331(x87433),x87432),f329(f308(x87434,x87433,x87431),f252(f883(x87434,a869))))) % 178.07/177.93 [8808]E(f176(x88081,x88082,x88083),f329(f329(f174(x88081),x88084),x88083))+P24(f329(f329(f244(a875),f674(x88082,x88083,x88081,x88084)),x88084))+P24(f329(f329(f244(a875),x88084),f329(f194(f876(x88081)),x88083))) % 178.07/177.93 [8811]E(f176(x88111,x88112,x88113),f329(f329(f174(x88111),x88114),x88113))+P24(f329(f329(f244(a875),f674(x88112,x88113,x88111,x88114)),x88114))+P24(f329(x88112,f329(f329(f164(x88111),x88113),x88114))) % 178.07/177.93 [8840]P24(f329(x88401,x88402))+~P24(f329(f329(f331(x88404),x88402),f329(f171(x88404),x88403)))+P24(f329(f329(f244(a875),f585(x88402,x88401,x88403,x88404)),f329(f194(f876(x88404)),x88403))) % 178.07/177.93 [8843]E(f176(x88431,x88432,x88433),f329(f329(f174(x88431),x88434),x88433))+P24(f329(f329(f244(a875),x88434),f329(f194(f876(x88431)),x88433)))+P24(f329(f329(f244(a875),f674(x88432,x88433,x88431,x88434)),f329(f194(f876(x88431)),x88433))) % 178.07/177.93 [8850]E(f176(x88501,x88502,x88503),f329(f329(f174(x88501),x88504),x88503))+P24(f329(x88502,f329(f329(f164(x88501),x88503),x88504)))+P24(f329(f329(f244(a875),f674(x88502,x88503,x88501,x88504)),f329(f194(f876(x88501)),x88503))) % 178.07/177.93 [8876]~P120(x88764)+P24(f329(f329(f331(x88761),f800(x88762,x88763,x88761,x88764)),x88763))+P24(f329(f329(f244(x88764),f2(x88764)),f329(f329(f9(x88761,x88764),x88762),x88763))) % 178.07/177.93 [8877]~P120(x88774)+P24(f329(f329(f331(x88771),f804(x88772,x88773,x88771,x88774)),x88773))+P24(f329(f329(f243(x88774),f2(x88774)),f329(f329(f9(x88771,x88774),x88772),x88773))) % 178.07/177.93 [8909]~P24(f329(f62(x89091),x89094))+P24(f329(f329(f331(x89091),f629(x89092,x89093,x89094,x89091)),x89094))+P24(f329(f62(f882(x89091,x89093)),f329(f329(f266(x89091,x89093),x89094),x89092))) % 178.07/177.93 [8943]P24(f329(f329(f331(x89432),f741(x89431,x89433,x89432,x89434)),f329(f171(x89432),x89433)))+P24(f329(x89431,f329(f329(f164(x89432),x89433),x89434)))+~P24(f329(f329(f244(a875),x89434),f329(f194(f876(x89432)),x89433))) % 178.07/177.93 [8958]E(x89581,x89582)+P24(f329(f329(f199(f33(x89583,x89584)),f602(x89581,x89582,x89584,x89583)),x89581))+~P24(f329(f329(f199(f33(x89583,x89584)),x89582),x89581)) % 178.07/177.93 [8979]~P24(f329(x89791,x89794))+P24(f329(f329(f199(f33(x89791,x89792)),f602(x89793,x89794,x89792,x89791)),x89793))+~P24(f329(f329(f199(f33(x89791,x89792)),x89794),x89793)) % 178.07/177.93 [9074]P24(f329(f329(f243(a875),x90744),f329(f194(f876(x90742)),f176(x90742,x90743,x90741))))+P24(f329(f329(f244(a875),f675(x90741,x90742,x90743,x90744)),x90744))+~P24(f329(f329(f243(a875),x90744),f329(f194(f876(x90742)),x90741))) % 178.07/177.93 [9178]~E(f329(f329(f177(x91781,x91782),x91783),f709(x91784,x91783,x91782,x91781)),f329(f329(f177(x91781,x91782),x91784),f709(x91784,x91783,x91782,x91781)))+E(f329(f177(x91781,x91782),x91783),f329(f177(x91781,x91782),x91784))+~E(f329(f171(x91781),f329(f329(f153(f882(x91781,x91782),x91781),f263(x91781,x91782)),x91783)),f329(f171(x91781),f329(f329(f153(f882(x91781,x91782),x91781),f263(x91781,x91782)),x91784))) % 178.07/177.93 [9224]E(f176(x92241,x92242,x92243),f329(f329(f174(x92241),x92244),x92243))+~P24(f329(x92242,f329(f329(f164(x92241),x92243),f674(x92242,x92243,x92241,x92244))))+P24(f329(f329(f244(a875),x92244),f329(f194(f876(x92241)),x92243))) % 178.07/177.93 [9229]E(f176(x92291,x92292,x92293),f329(f329(f174(x92291),x92294),x92293))+~P24(f329(x92292,f329(f329(f164(x92291),x92293),f674(x92292,x92293,x92291,x92294))))+P24(f329(x92292,f329(f329(f164(x92291),x92293),x92294))) % 178.07/177.93 [9236]~P24(f329(f62(x92361),x92363))+~P24(f329(f62(x92362),f329(x92364,f629(x92364,x92362,x92363,x92361))))+P24(f329(f62(f882(x92361,x92362)),f329(f329(f266(x92361,x92362),x92363),x92364))) % 178.07/177.93 [9244]~P120(x92441)+~P24(f329(f329(f244(x92441),f2(x92441)),f329(x92443,f800(x92443,x92444,x92442,x92441))))+P24(f329(f329(f244(x92441),f2(x92441)),f329(f329(f9(x92442,x92441),x92443),x92444))) % 178.07/177.93 [9245]~P120(x92451)+~P24(f329(f329(f243(x92451),f2(x92451)),f329(x92453,f804(x92453,x92454,x92452,x92451))))+P24(f329(f329(f243(x92451),f2(x92451)),f329(f329(f9(x92452,x92451),x92453),x92454))) % 178.07/177.93 [9251]~E(f329(f194(f876(x92514)),x92512),f329(f194(f876(x92514)),x92513))+P24(f329(f329(f331(f882(f876(x92514),f876(x92514))),f329(f329(f264(f876(x92514),f876(x92514)),x92513),x92512)),f157(x92514,x92511)))+P24(f329(f329(f244(a875),f587(x92511,x92512,x92513,x92514)),f329(f194(f876(x92514)),x92513))) % 178.07/177.93 [9305]~P24(f329(x93053,f329(f329(f164(x93052),x93054),f675(x93054,x93052,x93053,x93051))))+P24(f329(f329(f243(a875),x93051),f329(f194(f876(x93052)),f176(x93052,x93053,x93054))))+~P24(f329(f329(f243(a875),x93051),f329(f194(f876(x93052)),x93054))) % 178.07/177.93 [9381]E(f329(f329(f174(x93811),f588(x93812,x93813,x93814,x93811)),x93813),f329(f329(f174(x93811),f588(x93812,x93813,x93814,x93811)),x93814))+~P24(f329(f329(f331(f882(f876(x93811),f876(x93811))),f329(f329(f264(f876(x93811),f876(x93811)),x93814),x93813)),f146(x93811,x93812)))+P24(f329(f329(f244(a875),f329(f194(f876(x93811)),x93814)),f329(f194(f876(x93811)),x93813))) % 178.07/177.93 [9435]~P24(f329(f329(f244(a875),f2(a875)),x94353))+~P24(f329(f329(f244(a875),x94354),x94351))+P24(f329(f329(f244(a875),f329(f329(f81(a875),f329(f329(f82(a875),x94351),f45(a875,x94352,x94353))),x94354)),f329(f329(f82(a875),x94351),x94353))) % 178.07/177.93 [9626]~P106(x96262)+~P24(f329(f329(f243(x96262),f329(x96263,f863(x96264,x96263,x96261,x96262))),f329(x96264,f863(x96264,x96263,x96261,x96262))))+P24(f329(f329(f243(f883(x96261,x96262)),x96263),x96264)) % 178.07/177.93 [9729]~P66(x97291)+E(f329(f329(f6(a875,x97291),f329(f329(f18(a875,x97291,x97291),f329(f329(f8(x97291,f883(x97291,x97291),a875),f22(x97291)),x97292)),f329(f329(f8(a875,x97291,a875),x97292),f329(f329(f7(a875,a875,a875),f81(a875)),f79(a875))))),f300(a875,x97293,x97294)),f329(f329(f22(x97291),f329(x97292,x97293)),f329(x97292,f329(f329(f81(a875),x97294),f79(a875)))))+~P24(f329(f329(f243(a875),x97293),x97294)) % 178.07/177.93 [6787]E(f329(f329(f127(x67871),x67872),x67873),x67874)+~E(x67873,f329(f329(f137(x67871),f329(f194(f876(x67871)),x67872)),x67874))+~E(f329(f329(f174(x67871),f329(f194(f876(x67871)),x67872)),x67874),x67872) % 178.07/177.93 [6842]~P60(x68422)+E(x68421,f2(x68422))+E(f329(f329(f287(x68422),f329(f329(f254(x68422),x68423),x68424)),f329(f329(f254(x68422),x68421),x68424)),f329(f329(f254(x68422),f329(f329(f287(x68422),x68423),x68421)),x68424)) % 178.07/177.93 [6978]~E(f329(f194(f876(x69781)),x69783),f329(f194(f876(x69782)),x69784))+~P24(f329(f136(x69781),x69783))+E(f183(x69781,x69782,f329(f177(x69781,x69782),f329(f329(f181(x69781,x69782),x69783),x69784))),f329(f171(x69781),x69783)) % 178.07/177.93 [6997]~P100(x69971)+~P24(f329(f329(f244(x69971),x69973),x69974))+P24(f329(f329(f244(x69971),f329(f329(f107(x69971),x69972),x69973)),x69974)) % 178.07/177.93 [6998]~P100(x69981)+~P24(f329(f329(f244(x69981),x69982),x69984))+P24(f329(f329(f244(x69981),f329(f329(f107(x69981),x69982),x69983)),x69984)) % 178.07/177.93 [7000]~P105(x70001)+~P24(f329(f329(f244(x70001),x70003),x70004))+P24(f329(f329(f244(x70001),f329(f329(f241(x70001),x70002),x70003)),x70004)) % 178.07/177.93 [7002]~P105(x70021)+~P24(f329(f329(f244(x70021),x70022),x70024))+P24(f329(f329(f244(x70021),f329(f329(f241(x70021),x70022),x70023)),x70024)) % 178.07/177.93 [7003]~P100(x70031)+~P24(f329(f329(f243(x70031),x70033),x70034))+P24(f329(f329(f243(x70031),f329(f329(f107(x70031),x70032),x70033)),x70034)) % 178.07/177.93 [7004]~P100(x70041)+~P24(f329(f329(f243(x70041),x70042),x70044))+P24(f329(f329(f243(x70041),f329(f329(f107(x70041),x70042),x70043)),x70044)) % 178.07/177.93 [7006]~P105(x70061)+~P24(f329(f329(f243(x70061),x70063),x70064))+P24(f329(f329(f243(x70061),f329(f329(f241(x70061),x70062),x70063)),x70064)) % 178.07/177.93 [7008]~P105(x70081)+~P24(f329(f329(f243(x70081),x70082),x70084))+P24(f329(f329(f243(x70081),f329(f329(f241(x70081),x70082),x70083)),x70084)) % 178.07/177.93 [7028]~P24(f329(x70283,x70284))+~P24(f329(x70282,x70284))+P24(f329(f329(f329(f107(f883(x70281,a869)),x70282),x70283),x70284)) % 178.07/177.93 [7152]P20(x71521,x71522,x71523)+~P20(x71521,x71524,x71523)+~P24(f329(f329(f243(f883(f874(x71521),a869)),x71524),x71522)) % 178.07/177.93 [7153]P20(x71531,x71532,x71533)+~P20(x71531,x71532,x71534)+~P24(f329(f329(f243(f883(f874(x71531),a869)),x71533),x71534)) % 178.07/177.93 [7524]~P70(x75241)+E(f329(f329(f81(x75241),f329(x75242,x75243)),f329(f329(f6(a875,x75241),x75242),f329(f299(a875,f329(a118,x75243)),x75244))),f329(f329(f6(a875,x75241),x75242),f329(f299(a875,x75243),x75244)))+~P24(f329(f329(f244(a875),x75243),x75244)) % 178.07/177.93 [7552]~P105(x75521)+P24(f329(f329(f244(x75521),x75522),x75523))+~P24(f329(f329(f244(x75521),f329(f329(f242(x75521),x75524),x75522)),x75523)) % 178.07/177.93 [7553]~P105(x75531)+P24(f329(f329(f244(x75531),x75532),x75533))+~P24(f329(f329(f244(x75531),f329(f329(f242(x75531),x75532),x75534)),x75533)) % 178.07/177.93 [7555]~P99(x75551)+P24(f329(f329(f243(x75551),x75552),x75553))+~P24(f329(f329(f243(x75551),f329(f329(f116(x75551),x75554),x75552)),x75553)) % 178.07/177.93 [7557]~P99(x75571)+P24(f329(f329(f243(x75571),x75572),x75573))+~P24(f329(f329(f243(x75571),f329(f329(f116(x75571),x75572),x75574)),x75573)) % 178.07/177.93 [7559]~P105(x75591)+P24(f329(f329(f243(x75591),x75592),x75593))+~P24(f329(f329(f243(x75591),f329(f329(f242(x75591),x75594),x75592)),x75593)) % 178.07/177.93 [7561]~P105(x75611)+P24(f329(f329(f243(x75611),x75612),x75613))+~P24(f329(f329(f243(x75611),f329(f329(f242(x75611),x75612),x75614)),x75613)) % 178.07/177.93 [7637]~P24(f329(f329(f331(x76371),x76372),x76374))+P24(f329(f329(f331(x76371),x76372),x76373))+P24(f329(f329(f331(x76371),x76372),f329(f329(f22(f883(x76371,a869)),x76374),x76373))) % 178.07/177.93 [7720]P24(f329(x77201,x77202))+P24(f329(x77203,x77202))+~P24(f329(f329(f329(f116(f883(x77204,a869)),x77203),x77201),x77202)) % 178.07/177.93 [7730]~P24(f329(f329(f331(x77301),x77302),x77304))+~P24(f329(f329(f331(x77301),x77302),x77303))+P24(f329(f329(f331(x77301),x77302),f329(f329(f107(f883(x77301,a869)),x77303),x77304))) % 178.07/177.93 [7782]~P99(x77821)+~P24(f329(f62(x77821),x77824))+E(f329(f329(f65(x77821,x77821,f116(x77821)),x77822),f329(f329(f307(x77821),x77823),x77824)),f329(f329(f116(x77821),x77823),f329(f329(f65(x77821,x77821,f116(x77821)),x77822),x77824))) % 178.07/177.93 [7783]~P100(x77831)+~P24(f329(f62(x77831),x77834))+E(f329(f329(f65(x77831,x77831,f107(x77831)),x77832),f329(f329(f307(x77831),x77833),x77834)),f329(f329(f107(x77831),x77833),f329(f329(f65(x77831,x77831,f107(x77831)),x77832),x77834))) % 178.07/177.93 [7784]~P105(x77841)+~P24(f329(f62(x77841),x77844))+E(f329(f329(f65(x77841,x77841,f241(x77841)),x77842),f329(f329(f307(x77841),x77843),x77844)),f329(f329(f241(x77841),x77843),f329(f329(f65(x77841,x77841,f241(x77841)),x77842),x77844))) % 178.07/177.93 [7785]~P105(x77851)+~P24(f329(f62(x77851),x77854))+E(f329(f329(f65(x77851,x77851,f242(x77851)),x77852),f329(f329(f307(x77851),x77853),x77854)),f329(f329(f242(x77851),x77853),f329(f329(f65(x77851,x77851,f242(x77851)),x77852),x77854))) % 178.07/177.93 [7786]~P108(x77861)+~P93(x77861)+E(f329(f329(f22(x77861),f329(f329(f82(x77861),f329(f109(x77861),x77862)),x77863)),f329(f329(f82(x77861),f329(f109(x77861),x77862)),x77864)),f329(f329(f82(x77861),f329(f109(x77861),x77862)),f329(f329(f22(x77861),x77863),x77864))) % 178.07/177.93 [7787]~P135(x77871)+~P93(x77871)+E(f329(f329(f81(x77871),f329(f329(f82(x77871),f329(f109(x77871),x77872)),x77873)),f329(f329(f82(x77871),f329(f109(x77871),x77872)),x77874)),f329(f329(f82(x77871),f329(f109(x77871),x77872)),f329(f329(f81(x77871),x77873),x77874))) % 178.07/177.93 [7900]E(x79001,x79002)+P24(f329(f329(f331(x79003),x79001),f329(f171(x79003),x79004)))+~P24(f329(f329(f331(x79003),x79001),f329(f171(x79003),f329(f329(f150(x79003),x79002),x79004)))) % 178.07/177.93 [7925]~P58(x79251)+~E(f329(f194(f876(x79252)),x79253),f329(f194(f876(x79251)),f56(x79251)))+E(f329(f329(f177(x79251,x79252),f329(f329(f181(x79251,x79252),f56(x79251)),x79253)),x79254),f329(f236(x79252),f672(x79254,x79253,x79252,x79251))) % 178.07/177.93 [8078]P50(x80781,x80782,x80783)+~P50(x80781,x80782,x80784)+~P24(f329(f329(f243(f883(f882(x80781,x80782),a869)),x80783),x80784)) % 178.07/177.93 [8122]P24(f329(f329(f331(x81221),x81222),x81223))+P24(f329(f329(f331(x81221),x81222),x81224))+~P24(f329(f329(f331(x81221),x81222),f329(f329(f116(f883(x81221,a869)),x81224),x81223))) % 178.07/177.93 [8133]~P40(x81331,x81334,x81333)+~P24(f329(f329(f331(x81331),x81332),x81334))+P24(f329(f329(f331(f882(x81331,x81331)),f329(f329(f264(x81331,x81331),x81332),x81332)),x81333)) % 178.07/177.93 [8148]~P24(f329(f62(x81482),x81484))+~P24(f329(f62(x81481),x81483))+P24(f329(f62(f882(x81481,x81482)),f329(f329(f266(x81481,x81482),x81483),f329(f16(f883(x81482,a869),x81481),x81484)))) % 178.07/177.93 [8149]~P24(f329(f329(f331(x81491),x81492),x81494))+~P24(f329(f329(f243(f883(x81491,a869)),x81493),x81494))+P24(f329(f329(f243(f883(x81491,a869)),f329(f329(f307(x81491),x81492),x81493)),x81494)) % 178.07/177.93 [8157]~P74(x81572)+~P141(x81572)+E(f329(f329(f9(x81571,x81572),f329(f329(f8(a875,x81572,x81571),f106(x81572)),x81573)),x81574),f329(f106(x81572),f329(f329(f9(x81571,a875),x81573),x81574))) % 178.07/177.93 [8158]~P74(x81582)+~P137(x81582)+E(f329(f329(f9(x81581,x81582),f329(f329(f8(a1,x81582,x81581),f108(x81582)),x81583)),x81584),f329(f108(x81582),f329(f329(f9(x81581,a1),x81583),x81584))) % 178.07/177.93 [8184]E(f329(f329(f22(f883(x81841,a869)),x81842),f329(f329(f22(f883(x81841,a869)),x81843),x81844)),x81844)+~P24(f329(f329(f243(f883(x81841,a869)),x81842),x81843))+~P24(f329(f329(f243(f883(x81841,a869)),x81844),x81842)) % 178.07/177.93 [8279]~P24(f329(f62(x82791),x82794))+E(f329(f329(f22(a875),f329(f329(f6(x82791,a875),x82792),x82793)),f329(f329(f6(x82791,a875),x82792),x82794)),f329(f329(f6(x82791,a875),x82792),f329(f329(f22(f883(x82791,a869)),x82793),x82794)))+~P24(f329(f329(f243(f883(x82791,a869)),x82794),x82793)) % 178.07/177.93 [8435]~P6(x84351,x84354,x84353)+~P24(f329(f329(f331(x84351),x84352),x84354))+P24(f329(f329(f331(x84351),x84352),f329(f283(x84351,x84351,x84353),f329(f329(f307(x84351),x84352),f193(f883(x84351,a869)))))) % 178.07/177.93 [8498]~P24(f329(f329(f243(f883(x84981,a869)),x84982),x84983))+~P24(f329(f329(f243(f883(x84981,a869)),x84982),x84984))+P24(f329(f329(f243(f883(x84981,a869)),x84982),f329(f329(f107(f883(x84981,a869)),x84983),x84984))) % 178.07/177.93 [8595]E(x85951,f193(f883(x85952,a869)))+P24(f329(f62(x85953),x85954))+~P24(f329(f62(f882(x85953,x85952)),f329(f329(f266(x85953,x85952),x85954),f329(f16(f883(x85952,a869),x85953),x85951)))) % 178.07/177.93 [8596]E(x85961,f193(f883(x85962,a869)))+P24(f329(f62(x85963),x85964))+~P24(f329(f62(f882(x85962,x85963)),f329(f329(f266(x85962,x85963),x85961),f329(f16(f883(x85963,a869),x85962),x85964)))) % 178.07/177.93 [8663]P24(f329(f329(f331(x86631),x86632),f318(x86631,x86633)))+~P24(f329(f329(f331(x86631),x86634),f318(x86631,x86633)))+~P24(f329(f329(f331(f882(x86631,x86631)),f329(f329(f264(x86631,x86631),x86632),x86634)),x86633)) % 178.07/177.93 [8715]~P38(x87151,x87154)+P24(f329(f329(f331(f882(x87151,x87151)),f329(f329(f264(x87151,x87151),x87153),x87152)),f305(x87151,x87154)))+P38(x87151,f329(f329(f307(f882(x87151,x87151)),f329(f329(f264(x87151,x87151),x87152),x87153)),x87154)) % 178.07/177.93 [8716]~P53(x87161,x87164)+P24(f329(f329(f331(f882(x87161,x87161)),f329(f329(f264(x87161,x87161),x87163),x87162)),f305(x87161,x87164)))+P53(x87161,f329(f329(f307(f882(x87161,x87161)),f329(f329(f264(x87161,x87161),x87162),x87163)),x87164)) % 178.07/177.93 [8793]~E(x87932,x87933)+~P24(f329(f329(f331(x87931),x87932),f329(f171(x87931),x87934)))+P24(f329(f329(f331(f882(x87931,x87931)),f329(f329(f264(x87931,x87931),x87932),x87933)),f329(f171(f882(x87931,x87931)),f329(f329(f181(x87931,x87931),x87934),x87934)))) % 178.07/177.93 [8874]~E(x88743,x88744)+P24(f329(f329(f268(x88741,x88741,a869),a326),x88742))+~P24(f329(f329(f331(f882(x88741,x88741)),x88742),f329(f171(f882(x88741,x88741)),f329(f329(f181(x88741,x88741),x88743),x88744)))) % 178.07/177.93 [8900]~P24(f329(x89004,x89002))+P24(f329(f329(f329(f329(a201,x89001),x89002),x89003),f491(x89003,x89002,x89001,x89004)))+~P24(f329(f329(f329(f329(a201,f33(x89004,x89001)),x89002),x89003),x89002)) % 178.07/177.93 [8927]P24(f329(f329(f331(f882(f876(x89271),f876(x89271))),f329(f329(f264(f876(x89271),f876(x89271)),x89272),x89273)),f146(x89271,x89274)))+~E(f329(f329(f174(x89271),f329(f194(f876(x89271)),x89272)),x89273),x89272)+~P24(f329(f329(f244(a875),f329(f194(f876(x89271)),x89272)),f329(f194(f876(x89271)),x89273))) % 178.07/177.93 [9026]~P24(f329(f62(x90261),x90264))+P24(f329(f329(f331(x90261),f836(x90262,x90263,x90264,x90261)),x90264))+P24(f329(f62(x90263),f329(f329(f43(x90261,f883(x90263,a869)),x90264),x90262))) % 178.07/177.93 [9027]~P24(f329(f62(x90271),x90274))+P24(f329(f329(f331(x90271),f862(x90272,x90273,x90274,x90271)),x90274))+P24(f329(f62(x90273),f329(f329(f43(x90271,f883(x90273,a869)),x90274),x90272))) % 178.07/177.93 [9108]P24(f329(f329(f331(f882(x91081,x91081)),x91082),f329(f329(f286(x91081,x91081,x91081),x91083),f305(x91081,x91083))))+~P24(f329(f329(f244(a875),f2(a875)),x91084))+~P24(f329(f329(f331(f882(x91081,x91081)),x91082),f329(f329(f188(f882(x91081,x91081),a869),x91084),x91083))) % 178.07/177.93 [9116]~P38(x91161,x91162)+~P24(f329(f329(f331(f882(x91161,x91161)),f329(f329(f264(x91161,x91161),x91164),x91163)),x91162))+~P24(f329(f329(f331(f882(x91161,x91161)),f329(f329(f264(x91161,x91161),x91163),x91164)),x91162)) % 178.07/177.93 [9243]~P24(f329(f62(x92431),x92434))+E(f329(f329(f6(x92431,a875),f329(f329(f8(f883(x92432,a869),a875,x92431),f38(x92432)),x92433)),x92434),f329(f38(f882(x92431,x92432)),f329(f329(f266(x92431,x92432),x92434),x92433)))+P24(f329(f329(f331(x92431),f630(x92433,x92432,x92434,x92431)),x92434)) % 178.07/177.93 [9247]~P24(f329(f136(x92471),x92472))+P24(f329(f136(x92471),f329(f329(f158(x92471,x92472),x92473),x92474)))+P24(f329(f329(f331(x92471),x92474),f329(f329(f22(f883(x92471,a869)),f329(f171(x92471),x92472)),f329(f329(f307(x92471),f329(f329(f164(x92471),x92472),x92473)),f193(f883(x92471,a869)))))) % 178.07/177.93 [9263]~P24(f329(f62(x92632),x92633))+~P24(f329(f62(x92631),f329(x92634,f836(x92634,x92631,x92633,x92632))))+P24(f329(f62(x92631),f329(f329(f43(x92632,f883(x92631,a869)),x92633),x92634))) % 178.07/177.93 [9264]~P24(f329(f62(x92642),x92643))+~P24(f329(f62(x92641),f329(x92644,f862(x92644,x92641,x92643,x92642))))+P24(f329(f62(x92641),f329(f329(f43(x92642,f883(x92641,a869)),x92643),x92644))) % 178.07/177.93 [9343]~P24(f329(f329(f331(f882(x93431,x93431)),x93432),f329(f329(f286(x93431,x93431,x93431),x93434),f305(x93431,x93434))))+P24(f329(f329(f331(f882(x93431,x93431)),x93432),f329(f329(f286(x93431,x93431,x93431),x93433),f305(x93431,x93433))))+~P24(f329(f329(f243(f883(f882(x93431,x93431),a869)),x93434),x93433)) % 178.07/177.93 [9350]E(f329(f329(f174(x93501),f588(x93504,x93503,x93502,x93501)),x93503),f329(f329(f174(x93501),f588(x93504,x93503,x93502,x93501)),x93502))+~P24(f329(f329(f331(f882(f876(x93501),f876(x93501))),f329(f329(f264(f876(x93501),f876(x93501)),x93502),x93503)),f146(x93501,x93504)))+E(f329(f329(f174(x93501),f329(f194(f876(x93501)),x93502)),x93503),x93502) % 178.07/177.93 [9366]~P24(f329(f62(x93661),x93664))+E(f329(f329(f6(x93661,a875),f329(f329(f8(f883(x93662,a869),a875,x93661),f38(x93662)),x93663)),x93664),f329(f38(f882(x93661,x93662)),f329(f329(f266(x93661,x93662),x93664),x93663)))+~P24(f329(f62(x93662),f329(x93663,f630(x93663,x93662,x93664,x93661)))) % 178.07/177.93 [9370]~E(f329(f194(f876(x93701)),x93703),f329(f194(f876(x93701)),x93702))+P24(f329(f329(f331(f882(f876(x93701),f876(x93701))),f329(f329(f264(f876(x93701),f876(x93701)),x93702),x93703)),f157(x93701,x93704)))+P24(f329(f329(f331(f882(x93701,x93701)),f589(x93704,x93703,x93702,x93701)),f329(f171(f882(x93701,x93701)),f329(f329(f181(x93701,x93701),x93702),x93703)))) % 178.07/177.93 [9447]~P24(f329(f329(f331(f882(f876(x94471),f876(x94471))),f329(f329(f264(f876(x94471),f876(x94471)),x94472),x94473)),f146(x94471,x94474)))+E(f329(f329(f174(x94471),f329(f194(f876(x94471)),x94472)),x94473),x94472)+P24(f329(f329(f244(a875),f588(x94474,x94473,x94472,x94471)),f329(f329(f241(a875),f329(f194(f876(x94471)),x94472)),f329(f194(f876(x94471)),x94473)))) % 178.07/177.93 [9448]E(f329(f177(x94481,x94482),x94483),f329(f177(x94481,x94482),x94484))+~E(f329(f171(x94481),f329(f329(f153(f882(x94481,x94482),x94481),f263(x94481,x94482)),x94483)),f329(f171(x94481),f329(f329(f153(f882(x94481,x94482),x94481),f263(x94481,x94482)),x94484)))+P24(f329(f329(f331(x94481),f709(x94483,x94484,x94482,x94481)),f329(f171(x94481),f329(f329(f153(f882(x94481,x94482),x94481),f263(x94481,x94482)),x94484)))) % 178.07/177.93 [9464]~P24(f329(x94641,x94644))+P24(f329(f329(f329(f329(a201,f33(x94641,x94642)),f491(x94643,x94644,x94642,x94641)),x94643),x94644))+~P24(f329(f329(f329(f329(a201,f33(x94641,x94642)),x94644),x94643),x94644)) % 178.07/177.93 [9469]~P24(f329(f329(f331(f882(f876(x94691),f876(x94691))),f329(f329(f264(f876(x94691),f876(x94691)),x94692),x94693)),f146(x94691,x94694)))+P24(f329(f329(f244(a875),f329(f194(f876(x94691)),x94692)),f329(f194(f876(x94691)),x94693)))+P24(f329(f329(f244(a875),f588(x94694,x94693,x94692,x94691)),f329(f329(f241(a875),f329(f194(f876(x94691)),x94692)),f329(f194(f876(x94691)),x94693)))) % 178.07/177.93 [9766]~P24(f329(f329(f329(x97661,f554(x97661,x97664,x97663,x97662)),f555(x97661,x97664,x97663,x97662)),f556(x97661,x97664,x97663,x97662)))+P24(f329(f329(f329(x97661,x97662),x97663),x97664))+~P24(f329(f317(f882(f883(a1,f879(f876(a325))),f882(a1,a1)),a315),f329(f329(f264(f883(a1,f879(f876(a325))),f882(a1,a1)),x97662),f329(f329(f264(a1,a1),x97663),x97664)))) % 178.07/177.93 [9845]P24(f329(f329(f329(x98451,x98452),x98453),x98454))+P24(f329(f317(f882(f883(a1,f879(f876(a325))),f882(a1,a1)),a315),f329(f329(f264(f883(a1,f879(f876(a325))),f882(a1,a1)),f554(x98451,x98454,x98453,x98452)),f329(f329(f264(a1,a1),f555(x98451,x98454,x98453,x98452)),f556(x98451,x98454,x98453,x98452)))))+~P24(f329(f317(f882(f883(a1,f879(f876(a325))),f882(a1,a1)),a315),f329(f329(f264(f883(a1,f879(f876(a325))),f882(a1,a1)),x98452),f329(f329(f264(a1,a1),x98453),x98454)))) % 178.07/177.93 [9884]~P24(f329(f329(f331(f882(f876(x98841),f876(x98841))),f329(f329(f264(f876(x98841),f876(x98841)),x98842),x98843)),f146(x98841,x98844)))+E(f329(f329(f174(x98841),f329(f194(f876(x98841)),x98842)),x98843),x98842)+P24(f329(f329(f331(f882(x98841,x98841)),f329(f329(f264(x98841,x98841),f329(f329(f164(x98841),x98842),f588(x98844,x98843,x98842,x98841))),f329(f329(f164(x98841),x98843),f588(x98844,x98843,x98842,x98841)))),x98844)) % 178.07/177.93 [9885]~P24(f329(f329(f331(f882(f876(x98851),f876(x98851))),f329(f329(f264(f876(x98851),f876(x98851)),x98852),x98853)),f146(x98851,x98854)))+P24(f329(f329(f244(a875),f329(f194(f876(x98851)),x98852)),f329(f194(f876(x98851)),x98853)))+P24(f329(f329(f331(f882(x98851,x98851)),f329(f329(f264(x98851,x98851),f329(f329(f164(x98851),x98852),f588(x98854,x98853,x98852,x98851))),f329(f329(f164(x98851),x98853),f588(x98854,x98853,x98852,x98851)))),x98854)) % 178.07/177.93 [9942]~E(f329(f194(f876(x99421)),x99422),f329(f194(f876(x99421)),x99423))+P24(f329(f329(f331(f882(f876(x99421),f876(x99421))),f329(f329(f264(f876(x99421),f876(x99421)),x99422),x99423)),f157(x99421,x99424)))+~P24(f329(f329(f331(f882(x99421,x99421)),f329(f329(f264(x99421,x99421),f329(f329(f164(x99421),x99422),f587(x99424,x99423,x99422,x99421))),f329(f329(f164(x99421),x99423),f587(x99424,x99423,x99422,x99421)))),x99424)) % 178.07/177.93 [10077]~P70(x100771)+~P24(f329(f62(x100772),x100774))+E(f329(f165(x100771),f329(f329(f153(x100772,x100771),x100773),f91(f876(x100772),f329(f329(f18(f876(x100772),a869,a869),f329(f329(f8(a869,f883(a869,a869),f876(x100772)),a327),f329(f329(f7(f876(x100772),f883(x100772,a869),a869),f329(f329(f8(f883(x100772,a869),f883(f883(x100772,a869),a869),f876(x100772)),a326),f171(x100772))),x100774))),f136(x100772))))),f234(x100772,x100771,x100773,x100774)) % 178.07/177.93 [7364]~P59(x73642)+E(x73641,f2(x73642))+E(f329(f329(f287(x73642),f329(f329(f81(x73642),x73643),f329(f329(f82(x73642),x73644),x73641))),x73641),f329(f329(f81(x73642),x73644),f329(f329(f287(x73642),x73643),x73641))) % 178.07/177.93 [7365]~P56(x73652)+E(x73651,f2(x73652))+E(f329(f329(f39(x73652),f329(f329(f81(x73652),x73653),f329(f329(f82(x73652),x73654),x73651))),x73651),f329(f329(f81(x73652),x73654),f329(f329(f39(x73652),x73653),x73651))) % 178.07/177.93 [7366]~P56(x73662)+E(x73661,f2(x73662))+E(f329(f329(f39(x73662),f329(f329(f81(x73662),x73663),f329(f329(f82(x73662),x73661),x73664))),x73661),f329(f329(f81(x73662),x73664),f329(f329(f39(x73662),x73663),x73661))) % 178.07/177.93 [7600]~P60(x76002)+E(x76001,f2(x76002))+E(f329(f329(f287(x76002),f329(f329(f22(x76002),x76003),f329(f329(f82(x76002),x76001),x76004))),x76001),f329(f329(f22(x76002),f329(f329(f287(x76002),x76003),x76001)),x76004)) % 178.07/177.93 [7601]~P59(x76012)+E(x76011,f2(x76012))+E(f329(f329(f287(x76012),f329(f329(f81(x76012),x76013),f329(f329(f82(x76012),x76014),x76011))),x76011),f329(f329(f81(x76012),f329(f329(f287(x76012),x76013),x76011)),x76014)) % 178.07/177.93 [7602]~P60(x76022)+E(x76021,f2(x76022))+E(f329(f329(f287(x76022),f329(f329(f81(x76022),x76023),f329(f329(f82(x76022),x76021),x76024))),x76021),f329(f329(f81(x76022),f329(f329(f287(x76022),x76023),x76021)),x76024)) % 178.07/177.93 [8307]~P24(f329(f159(x83071,x83073),x83074))+~P24(f329(f159(x83071,x83072),x83074))+P24(f329(f159(x83071,f329(f329(f107(f883(x83071,a869)),x83072),x83073)),x83074)) % 178.07/177.93 [8677]~E(f329(f329(f286(x86771,x86771,x86771),x86772),x86774),f193(f883(f882(x86771,x86771),a869)))+~E(f329(f329(f286(x86771,x86771,x86771),x86772),x86773),f193(f883(f882(x86771,x86771),a869)))+E(f329(f329(f286(x86771,x86771,x86771),x86772),f329(f329(f116(f883(f882(x86771,x86771),a869)),x86773),x86774)),f193(f883(f882(x86771,x86771),a869))) % 178.07/177.93 [8794]~P24(f329(f329(f243(f883(x87941,a869)),x87943),x87944))+~P24(f329(f329(f243(f883(x87941,a869)),x87942),x87944))+P24(f329(f329(f243(f883(x87941,a869)),f329(f329(f116(f883(x87941,a869)),x87942),x87943)),x87944)) % 178.07/177.93 [9172]~P24(f329(f62(x91721),x91724))+~P24(f329(f62(x91721),x91723))+E(f329(f329(f22(a875),f329(f329(f81(a875),f329(f329(f6(x91721,a875),x91722),x91723)),f329(f329(f6(x91721,a875),x91722),x91724))),f329(f329(f6(x91721,a875),x91722),f329(f329(f107(f883(x91721,a869)),x91723),x91724))),f329(f329(f6(x91721,a875),x91722),f329(f329(f116(f883(x91721,a869)),x91723),x91724))) % 178.07/177.93 [9260]~P24(f329(f329(f331(x92601),x92603),x92602))+~P24(f329(f329(f243(f883(x92601,a869)),x92602),f329(f329(f307(x92601),x92603),x92604)))+P24(f329(f329(f243(f883(x92601,a869)),f329(f329(f22(f883(x92601,a869)),x92602),f329(f329(f307(x92601),x92603),f193(f883(x92601,a869))))),x92604)) % 178.07/177.93 [9419]~P24(f329(f329(f331(x94191),x94193),x94192))+P24(f329(f329(f243(f883(x94191,a869)),x94192),f329(f329(f307(x94191),x94193),x94194)))+~P24(f329(f329(f243(f883(x94191,a869)),f329(f329(f22(f883(x94191,a869)),x94192),f329(f329(f307(x94191),x94193),f193(f883(x94191,a869))))),x94194)) % 178.07/177.93 [9509]~P24(f329(f329(f244(a875),x95092),x95094))+~P24(f329(f329(f243(a875),x95091),x95093))+P24(f329(f329(f331(f882(f882(a875,a875),f882(a875,a875))),f329(f329(f264(f882(a875,a875),f882(a875,a875)),f329(f329(f264(a875,a875),x95091),x95092)),f329(f329(f264(a875,a875),x95093),x95094))),a36)) % 178.07/177.93 [9510]~P24(f329(f329(f243(a875),x95102),x95104))+~P24(f329(f329(f243(a875),x95101),x95103))+P24(f329(f329(f331(f882(f882(a875,a875),f882(a875,a875))),f329(f329(f264(f882(a875,a875),f882(a875,a875)),f329(f329(f264(a875,a875),x95101),x95102)),f329(f329(f264(a875,a875),x95103),x95104))),a71)) % 178.07/177.93 [9805]~P24(f329(f329(f331(f876(x98051)),x98054),f160(x98051,x98053)))+~P24(f329(f329(f331(f876(x98051)),x98054),f160(x98051,x98052)))+P24(f329(f159(x98051,f329(f329(f107(f883(x98051,a869)),f329(f329(f7(x98051,f883(x98051,a869),a869),f331(x98051)),x98052)),f329(f329(f7(x98051,f883(x98051,a869),a869),f331(x98051)),x98053))),x98054)) % 178.07/177.93 [9907]~P21(x99071,f883(f883(x99071,a869),a869),f329(f329(f7(x99071,f883(f882(x99071,x99071),a869),f883(f883(x99071,a869),a869)),f329(f329(f8(f883(x99071,a869),f883(f883(f882(x99071,x99071),a869),f883(f883(x99071,a869),a869)),x99071),f61(x99071)),f329(f329(f7(x99071,f883(x99071,a869),f883(x99071,a869)),f307(x99071)),f193(f883(x99071,a869))))),x99073),x99072)+~P24(f329(f329(f331(x99071),x99074),x99072))+E(f329(f329(f22(f883(f883(x99071,a869),a869)),f329(f329(f61(x99071),x99072),x99073)),f329(f329(f61(x99071),f329(f329(f307(x99071),x99074),f193(f883(x99071,a869)))),x99073)),f329(f329(f61(x99071),f329(f329(f22(f883(x99071,a869)),x99072),f329(f329(f307(x99071),x99074),f193(f883(x99071,a869))))),x99073)) % 178.07/177.93 [10041]~P40(x100411,x100412,x100414)+~P24(f329(f329(f331(f882(x100411,x100411)),x100413),x100414))+P24(f329(f329(f268(x100411,x100411,a869),f329(f329(f7(x100411,f883(x100411,a869),f883(x100411,a869)),f329(f329(f8(f883(a869,a869),f883(f883(x100411,a869),f883(x100411,a869)),x100411),f8(a869,a869,x100411)),f329(f329(f8(a869,f883(a869,a869),x100411),a327),f329(f329(f7(x100411,f883(x100411,a869),a869),f331(x100411)),x100412)))),f329(f329(f7(x100411,f883(x100411,a869),a869),f331(x100411)),x100412))),x100413)) % 178.07/177.93 [10053]P24(f329(f62(x100531),x100532))+~P24(f329(f62(x100533),f329(f308(x100531,x100533,x100534),x100532)))+~P24(f329(f62(x100531),f329(f249(x100531),f329(f329(f18(x100531,a869,a869),f329(f329(f8(a869,f883(a869,a869),x100531),a327),f329(f329(f7(x100531,f883(x100531,a869),a869),f331(x100531)),x100532))),f329(f329(f7(x100531,x100533,a869),f329(f329(f8(x100533,f883(x100533,a869),x100531),a326),x100534)),f329(x100534,f500(x100534,x100533,x100532,x100531))))))) % 178.07/177.93 [8060]~P60(x80602)+E(x80601,f2(x80602))+E(f329(f329(f287(x80602),f329(f329(f22(x80602),f329(f329(f82(x80602),x80601),x80603)),x80604)),x80601),f329(f329(f22(x80602),x80603),f329(f329(f287(x80602),x80604),x80601))) % 178.07/177.93 [8061]~P60(x80612)+E(x80611,f2(x80612))+E(f329(f329(f287(x80612),f329(f329(f81(x80612),f329(f329(f82(x80612),x80611),x80613)),x80614)),x80611),f329(f329(f81(x80612),x80613),f329(f329(f287(x80612),x80614),x80611))) % 178.07/177.93 [8957]~E(f329(f329(f286(x89571,x89571,x89571),x89573),x89574),f193(f883(f882(x89571,x89571),a869)))+~E(f329(f329(f286(x89571,x89571,x89571),x89572),x89574),f193(f883(f882(x89571,x89571),a869)))+E(f329(f329(f286(x89571,x89571,x89571),f329(f329(f116(f883(f882(x89571,x89571),a869)),x89572),x89573)),x89574),f193(f883(f882(x89571,x89571),a869))) % 178.07/177.93 [9984]~P142(x99841)+~P142(x99842)+E(f329(f329(f314(x99841),f329(f329(f7(x99841,a105,f879(f876(a325))),f329(f329(f8(f883(x99842,f879(f876(a325))),f883(a105,f879(f876(a325))),x99841),f314(x99842)),f329(f329(f8(f883(x99842,f882(x99841,x99842)),f883(x99842,f879(f876(a325))),x99841),f329(f8(f882(x99841,x99842),f879(f876(a325)),x99842),x99843)),f264(x99841,x99842)))),x99844)),x99844),f329(f329(f314(f882(x99841,x99842)),x99843),x99844)) % 178.07/177.93 [9714]~P24(f329(f159(x97141,x97143),x97144))+~P24(f329(f159(x97141,x97142),x97144))+P24(f329(f159(x97141,f329(f329(f18(x97141,a869,a869),f329(f329(f8(a869,f883(a869,a869),x97141),a327),x97142)),x97143)),x97144)) % 178.07/177.93 [9976]P24(f329(x99761,f498(x99762,x99763,x99761,x99764)))+~P24(f329(f62(x99764),f329(f249(x99764),x99761)))+P24(f329(f62(x99763),f329(f249(x99763),f329(f329(f8(f883(x99764,a869),a869,x99763),f88(x99764)),f329(f329(f8(f883(x99764,a869),f883(x99764,a869),x99763),f329(f18(x99764,a869,a869),f329(f329(f8(a869,f883(a869,a869),x99764),a327),x99761))),x99762))))) % 178.07/177.93 [9997]~P24(f329(f62(x99972),f329(f249(x99972),x99973)))+~P24(f329(f62(x99971),f329(f249(x99971),f329(f329(f7(x99971,x99972,a869),x99974),f498(x99974,x99971,x99973,x99972)))))+P24(f329(f62(x99971),f329(f249(x99971),f329(f329(f8(f883(x99972,a869),a869,x99971),f88(x99972)),f329(f329(f8(f883(x99972,a869),f883(x99972,a869),x99971),f329(f18(x99972,a869,a869),f329(f329(f8(a869,f883(a869,a869),x99972),a327),x99973))),x99974))))) % 178.07/177.93 [6505]E(x65051,x65052)+~E(f329(x65053,x65051),f329(x65053,x65052))+~P21(x65054,x65055,x65053,f252(f883(x65054,a869))) % 178.07/177.93 [6665]~E(f329(x66653,x66655),f206(x66652))+~E(f329(x66654,x66655),f206(x66652))+E(f329(f184(x66651,x66652,x66653,x66654),x66655),f206(x66652)) % 178.07/177.93 [7400]E(x74001,x74002)+~P21(x74003,x74004,x74005,f252(f883(x74003,a869)))+~E(f329(f308(x74003,x74004,x74005),x74001),f329(f308(x74003,x74004,x74005),x74002)) % 178.07/177.93 [7654]P21(x76542,x76543,f347(x76544,x76543,x76542,x76541),x76541)+~E(f329(f308(x76543,x76542,x76545),x76544),x76541)+E(x76541,f193(f883(x76542,a869))) % 178.07/177.93 [8195]~P24(f329(f329(x81953,x81952),x81955))+~P24(f329(f329(x81953,x81954),x81952))+P24(f329(f329(f331(x81951),x81952),f296(x81951,x81953,x81954,x81955))) % 178.07/177.93 [8196]~P24(f329(f329(x81963,x81962),x81965))+~P24(f329(f329(x81963,x81964),x81962))+P24(f329(f329(f331(x81961),x81962),f293(x81961,x81963,x81964,x81965))) % 178.07/177.93 [8752]~P21(x87521,x87523,x87525,f252(f883(x87521,a869)))+~P21(x87523,x87522,x87524,f252(f883(x87523,a869)))+P21(x87521,x87522,f329(f74(x87523,x87522,x87521,x87524),x87525),f252(f883(x87521,a869))) % 178.07/177.93 [9319]P24(f329(f329(f331(f882(x93191,x93191)),f329(f329(f264(x93191,x93191),x93192),x93193)),f305(x93191,x93194)))+~P24(f329(f329(f331(f882(x93191,x93191)),f329(f329(f264(x93191,x93191),x93192),x93195)),f305(x93191,x93194)))+~P24(f329(f329(f331(f882(x93191,x93191)),f329(f329(f264(x93191,x93191),x93195),x93193)),f305(x93191,x93194))) % 178.07/177.93 [9357]~P105(x93572)+~P24(f329(f136(x93571),x93575))+P24(f329(f136(x93571),f148(x93571,x93572,x93573,x93574,x93575))) % 178.07/177.93 [5338]~E(x53382,f119(x53381))+E(f329(f329(f127(x53381),x53382),x53383),f329(f329(f150(x53381),x53384),x53385))+~E(x53383,f329(f329(f150(x53381),x53384),x53385)) % 178.07/177.93 [5339]~E(x53392,f119(x53391))+E(f329(f329(f127(x53391),x53392),x53393),f329(f329(f150(x53391),x53394),x53395))+~E(f329(f329(f150(x53391),x53394),x53395),x53393) % 178.07/177.93 [6462]~E(f329(f194(f876(x64621)),x64625),f329(f194(f876(x64622)),x64624))+E(f329(f329(f153(f882(x64621,x64622),x64622),f267(x64621,x64622)),x64623),x64624)+~E(f329(f329(f181(x64621,x64622),x64625),x64624),x64623) % 178.07/177.93 [6463]~E(f329(f194(f876(x64631)),x64634),f329(f194(f876(x64632)),x64635))+E(f329(f329(f153(f882(x64631,x64632),x64631),f263(x64631,x64632)),x64633),x64634)+~E(f329(f329(f181(x64631,x64632),x64634),x64635),x64633) % 178.07/177.93 [6937]~P105(x69371)+~P29(x69371,f329(f329(f153(x69372,x69371),x69373),x69375))+P29(x69371,f329(f329(f153(x69372,x69371),x69373),f329(f135(x69372,x69374),x69375))) % 178.07/177.93 [6984]~P24(f329(x69843,x69845))+~P24(f329(f329(x69842,x69844),x69845))+P24(f329(f329(f98(x69841,x69842,x69843),x69844),x69845)) % 178.07/177.93 [7081]~P105(x70811)+P29(x70811,f329(f329(f153(x70812,x70811),x70813),f169(x70812,x70814,x70815)))+~P29(x70811,f329(f329(f153(x70812,x70811),x70813),x70815)) % 178.07/177.93 [7104]~P50(x71043,x71042,x71045)+~P50(x71041,x71043,x71044)+P50(x71041,x71042,f329(f329(f286(x71041,x71043,x71042),x71044),x71045)) % 178.07/177.93 [7196]E(x71961,x71962)+~P21(x71963,x71964,x71965,f252(f883(x71963,a869)))+~E(f329(f329(f153(x71963,x71964),x71965),x71961),f329(f329(f153(x71963,x71964),x71965),x71962)) % 178.07/177.93 [7350]~P24(f329(f329(f244(a875),x73501),f329(x73503,x73505)))+P24(f329(f329(f244(a875),x73501),f154(x73502,x73503,x73504)))+~P24(f329(f329(f331(x73502),x73505),f329(f171(x73502),x73504))) % 178.07/177.93 [7351]~P24(f329(f329(f243(a875),x73511),f329(x73513,x73515)))+P24(f329(f329(f243(a875),x73511),f154(x73512,x73513,x73514)))+~P24(f329(f329(f331(x73512),x73515),f329(f171(x73512),x73514))) % 178.07/177.93 [7757]~P107(x77571)+P24(f329(f329(f243(f883(x77571,a869)),f300(x77571,x77572,x77573)),f300(x77571,x77574,x77575)))+P24(f329(f329(f243(x77571),x77572),x77573)) % 178.07/177.93 [7780]~P27(x77801)+P24(f329(f329(f243(x77801),f329(f329(f42(x77802,x77801),x77803),x77804)),f329(x77804,x77805)))+~P24(f329(f329(f331(x77802),x77805),x77803)) % 178.07/177.93 [7846]~P21(x78461,x78462,x78464,x78463)+E(f329(f78(x78461,x78462,x78463,x78464),f329(x78464,x78465)),x78465)+~P24(f329(f329(f331(x78461),x78465),x78463)) % 178.07/177.93 [8048]~P24(f329(x80481,x80485))+P24(f329(x80481,f479(x80481,x80482,x80483,x80484)))+~P24(f329(f329(f331(x80484),x80485),x80483)) % 178.07/177.93 [8049]~P24(f329(x80491,x80495))+P24(f329(x80491,f479(x80491,x80492,x80493,x80494)))+~P24(f329(f329(f331(x80494),x80495),x80492)) % 178.07/177.93 [8146]P24(f329(f62(x81461),x81462))+~P24(f329(f62(x81463),x81464))+~P24(f329(f329(f243(f883(x81461,a869)),x81462),f329(f308(x81463,x81461,x81465),x81464))) % 178.07/177.93 [8311]E(x83111,x83112)+~P21(x83113,x83114,x83115,f329(f329(f116(f883(x83113,a869)),f329(f171(x83113),x83111)),f329(f171(x83113),x83112)))+~E(f329(f329(f153(x83113,x83114),x83115),x83111),f329(f329(f153(x83113,x83114),x83115),x83112)) % 178.07/177.93 [8365]~P107(x83651)+~P24(f329(f329(f244(f883(x83651,a869)),f300(x83651,x83654,x83655)),f300(x83651,x83652,x83653)))+P24(f329(f329(f243(x83651),x83652),x83653)) % 178.07/177.93 [8433]~P21(x84331,x84334,x84335,f252(f883(x84331,a869)))+~P24(f329(f329(f331(x84334),f329(x84335,x84332)),f329(f308(x84331,x84334,x84335),x84333)))+P24(f329(f329(f331(x84331),x84332),x84333)) % 178.07/177.93 [8511]P24(f329(x85111,x85112))+~P24(f329(x85111,f496(x85111,x85113,x85114,x85115)))+~P24(f329(f329(f331(x85115),x85112),x85114)) % 178.07/177.93 [8512]P24(f329(x85121,x85122))+~P24(f329(x85121,f496(x85121,x85123,x85124,x85125)))+~P24(f329(f329(f331(x85125),x85122),x85123)) % 178.07/177.93 [8791]~P21(x87912,x87913,x87911,x87914)+E(f329(x87911,f329(f78(x87912,x87913,x87914,x87911),x87915)),x87915)+~P24(f329(f329(f331(x87913),x87915),f329(f308(x87912,x87913,x87911),x87914))) % 178.07/177.93 [8895]E(x88951,f119(x88952))+E(f329(f329(f150(x88952),x88953),f625(x88954,x88953,x88955,x88951,x88952)),x88951)+~E(f329(f329(f127(x88952),x88951),x88955),f329(f329(f150(x88952),x88953),x88954)) % 178.07/177.93 [8896]E(x88961,f119(x88962))+E(f329(f329(f150(x88962),x88963),f628(x88964,x88961,x88965,x88963,x88962)),x88961)+~E(f329(f329(f127(x88962),x88961),x88964),f329(f329(f150(x88962),x88963),x88965)) % 178.07/177.93 [8913]E(f329(f329(f150(x89132),x89133),f625(x89134,x89133,x89131,x89135,x89132)),x89135)+~E(f329(f329(f127(x89132),x89135),x89131),f329(f329(f150(x89132),x89133),x89134))+E(x89131,f329(f329(f150(x89132),x89133),x89134)) % 178.07/177.93 [8914]E(f329(f329(f150(x89141),x89142),f628(x89144,x89145,x89143,x89142,x89141)),x89145)+~E(f329(f329(f127(x89141),x89145),x89144),f329(f329(f150(x89141),x89142),x89143))+E(f329(f329(f150(x89141),x89142),x89143),x89144) % 178.07/177.93 [8996]~E(f329(f308(x89963,x89962,x89964),f252(f883(x89963,a869))),f252(f883(x89962,a869)))+~E(f329(f308(x89961,x89963,x89965),f252(f883(x89961,a869))),f252(f883(x89963,a869)))+E(f329(f308(x89961,x89962,f329(f74(x89963,x89962,x89961,x89964),x89965)),f252(f883(x89961,a869))),f252(f883(x89962,a869))) % 178.07/177.93 [9363]E(x93631,f119(x93632))+~E(f329(f329(f127(x93632),x93631),x93633),f329(f329(f150(x93632),x93635),x93634))+E(f329(f329(f127(x93632),f628(x93633,x93631,x93634,x93635,x93632)),x93633),x93634) % 178.07/177.93 [9364]E(x93641,f119(x93642))+~E(f329(f329(f127(x93642),x93641),x93645),f329(f329(f150(x93642),x93644),x93643))+E(f329(f329(f127(x93642),f625(x93643,x93644,x93645,x93641,x93642)),x93645),x93643) % 178.07/177.93 [9371]E(f329(f329(f127(x93712),f625(x93714,x93713,x93711,x93715,x93712)),x93711),x93714)+~E(f329(f329(f127(x93712),x93715),x93711),f329(f329(f150(x93712),x93713),x93714))+E(x93711,f329(f329(f150(x93712),x93713),x93714)) % 178.07/177.93 [9372]~E(f329(f329(f127(x93721),x93725),x93724),f329(f329(f150(x93721),x93722),x93723))+E(f329(f329(f127(x93721),f628(x93724,x93725,x93723,x93722,x93721)),x93724),x93723)+E(f329(f329(f150(x93721),x93722),x93723),x93724) % 178.07/177.93 [9373]E(f329(f329(f127(x93731),x93735),f632(x93733,x93732,x93734,x93735,x93731)),x93732)+E(f329(f329(f127(x93731),x93732),f631(x93733,x93732,x93734,x93735,x93731)),x93735)+~E(f329(f329(f127(x93731),x93735),x93734),f329(f329(f127(x93731),x93732),x93733)) % 178.07/177.93 [9405]~P105(x94051)+P29(x94051,f329(f329(f153(x94052,x94051),x94053),f148(x94052,x94051,x94053,x94054,x94055)))+~P29(x94051,f329(f329(f153(x94052,x94051),x94053),x94055)) % 178.07/177.93 [9416]~P54(x94165,x94161,x94164,x94163)+P24(f329(f329(x94161,x94162),f692(x94163,x94164,x94161,x94165,x94162)))+~P24(f329(f329(f331(x94165),x94162),x94164)) % 178.07/177.93 [9521]~P24(f329(f329(f331(f882(x95211,x95211)),f329(f329(f264(x95211,x95211),x95215),x95213)),f305(x95211,x95214)))+P24(f329(f329(f331(f882(x95211,x95211)),f329(f329(f264(x95211,x95211),x95212),x95213)),f329(f329(f286(x95211,x95211,x95211),x95214),f305(x95211,x95214))))+~P24(f329(f329(f331(f882(x95211,x95211)),f329(f329(f264(x95211,x95211),x95212),x95215)),f329(f329(f286(x95211,x95211,x95211),x95214),f305(x95211,x95214)))) % 178.07/177.93 [9522]~P24(f329(f329(f331(f882(x95221,x95221)),f329(f329(f264(x95221,x95221),x95222),x95225)),f305(x95221,x95224)))+P24(f329(f329(f331(f882(x95221,x95221)),f329(f329(f264(x95221,x95221),x95222),x95223)),f329(f329(f286(x95221,x95221,x95221),x95224),f305(x95221,x95224))))+~P24(f329(f329(f331(f882(x95221,x95221)),f329(f329(f264(x95221,x95221),x95225),x95223)),f329(f329(f286(x95221,x95221,x95221),x95224),f305(x95221,x95224)))) % 178.07/177.93 [9525]P24(f329(f329(f331(f882(f876(x95251),f876(x95251))),f329(f329(f264(f876(x95251),f876(x95251)),x95252),x95253)),f157(x95251,f305(x95251,x95254))))+~P24(f329(f329(f331(f882(f876(x95251),f876(x95251))),f329(f329(f264(f876(x95251),f876(x95251)),x95252),x95255)),f157(x95251,f305(x95251,x95254))))+~P24(f329(f329(f331(f882(f876(x95251),f876(x95251))),f329(f329(f264(f876(x95251),f876(x95251)),x95255),x95253)),f157(x95251,f305(x95251,x95254)))) % 178.07/177.93 [9529]E(f329(f329(f127(x95291),x95292),f631(x95293,x95292,x95294,x95295,x95291)),x95295)+E(f329(f329(f127(x95291),f632(x95293,x95292,x95294,x95295,x95291)),x95293),x95294)+~E(f329(f329(f127(x95291),x95292),x95293),f329(f329(f127(x95291),x95295),x95294)) % 178.07/177.93 [9530]E(f329(f329(f127(x95301),x95302),f632(x95303,x95304,x95305,x95302,x95301)),x95304)+E(f329(f329(f127(x95301),f631(x95303,x95304,x95305,x95302,x95301)),x95305),x95303)+~E(f329(f329(f127(x95301),x95302),x95305),f329(f329(f127(x95301),x95304),x95303)) % 178.07/177.93 [9584]P24(f329(f329(f331(f882(x95841,x95841)),f329(f329(f264(x95841,x95841),x95842),x95843)),f329(f329(f286(x95841,x95841,x95841),x95844),f305(x95841,x95844))))+~P24(f329(f329(f331(f882(x95841,x95841)),f329(f329(f264(x95841,x95841),x95842),x95845)),f329(f329(f286(x95841,x95841,x95841),x95844),f305(x95841,x95844))))+~P24(f329(f329(f331(f882(x95841,x95841)),f329(f329(f264(x95841,x95841),x95845),x95843)),f329(f329(f286(x95841,x95841,x95841),x95844),f305(x95841,x95844)))) % 178.07/177.93 [9611]P35(x96111,x96112,x96113,x96114,x96115)+~E(f329(f194(f876(x96111)),x96114),f329(f194(f876(x96112)),x96115))+~P24(f329(f329(f268(x96111,x96112,a869),x96113),f677(x96115,x96114,x96113,x96112,x96111))) % 178.07/177.93 [9612]P35(x96121,x96122,x96123,x96124,x96125)+~E(f329(f194(f876(x96121)),x96124),f329(f194(f876(x96122)),x96125))+~P24(f329(f329(f268(x96121,x96122,a869),x96123),f687(x96123,x96125,x96124,x96122,x96121))) % 178.07/177.93 [9617]E(f329(f329(f127(x96171),f631(x96172,x96173,x96174,x96175,x96171)),x96174),x96172)+~E(f329(f329(f127(x96171),x96173),x96172),f329(f329(f127(x96171),x96175),x96174))+E(f329(f329(f127(x96171),f632(x96172,x96173,x96174,x96175,x96171)),x96172),x96174) % 178.07/177.93 [9632]~P105(x96322)+E(f329(f329(f147(x96321,x96322,x96323),x96324),x96325),f329(f329(f150(x96321),x96324),x96325))+P24(f329(f329(f331(x96321),f726(x96324,x96323,x96325,x96321,x96322)),f329(f171(x96321),x96325))) % 178.07/177.93 [9637]~P54(x96371,x96374,x96373,x96372)+~P24(f329(f329(f331(x96371),x96375),x96373))+P24(f329(f329(f331(x96371),f692(x96372,x96373,x96374,x96371,x96375)),x96372)) % 178.07/177.93 [9757]~P24(f329(f329(f331(f882(f883(x97571,a869),f883(x97571,a869))),f329(f329(f264(f883(x97571,a869),f883(x97571,a869)),x97574),x97573)),f320(x97571,x97572)))+~P24(f329(f329(f331(x97571),x97575),x97574))+P24(f329(f329(f331(x97571),f743(x97572,x97573,x97574,x97571,x97575)),x97573)) % 178.07/177.93 [9769]~P105(x97692)+E(f329(f329(f147(x97691,x97692,x97693),x97694),x97695),f329(f329(f150(x97691),x97694),x97695))+~P24(f329(f329(f243(x97692),f329(x97693,x97694)),f329(x97693,f726(x97694,x97693,x97695,x97691,x97692)))) % 178.07/177.93 [9959]P35(x99591,x99592,x99593,x99594,x99595)+~E(f329(f194(f876(x99591)),x99594),f329(f194(f876(x99592)),x99595))+~P24(f329(f329(x99593,f329(f329(f164(x99591),x99594),f688(x99595,x99594,x99593,x99592,x99591))),f329(f329(f164(x99592),x99595),f688(x99595,x99594,x99593,x99592,x99591)))) % 178.07/177.93 [9960]P35(x99601,x99602,x99603,x99604,x99605)+~E(f329(f194(f876(x99601)),x99604),f329(f194(f876(x99602)),x99605))+~P24(f329(f329(x99603,f329(f329(f164(x99601),x99604),f720(x99603,x99605,x99602,x99604,x99601))),f329(f329(f164(x99602),x99605),f720(x99603,x99605,x99602,x99604,x99601)))) % 178.07/177.93 [6533]~P13(x65332,x65335,x65331)+~P24(f329(f62(x65332),x65334))+E(f329(x65331,f329(f329(f307(x65332),x65333),x65334)),f329(f329(f65(x65332,x65332,x65335),x65333),x65334)) % 178.07/177.94 [6534]~E(x65343,x65344)+~E(x65342,x65345)+E(f329(f329(f307(x65341),x65342),f329(f329(f307(x65341),x65343),f193(f883(x65341,a869)))),f329(f329(f307(x65341),x65344),f329(f329(f307(x65341),x65345),f193(f883(x65341,a869))))) % 178.07/177.94 [6545]P24(f329(x65452,x65455))+E(f176(x65451,x65452,f329(f329(f127(x65451),x65453),x65454)),f176(x65451,x65452,x65453))+~P24(f329(f329(f331(x65451),x65455),f329(f171(x65451),x65453))) % 178.07/177.94 [6582]E(f329(x65821,x65822),f193(f883(x65823,a869)))+~E(f329(f329(f43(x65824,f883(x65823,a869)),x65825),x65821),f193(f883(x65823,a869)))+~P24(f329(f329(f331(x65824),x65822),x65825)) % 178.07/177.94 [6583]E(f329(x65831,x65832),f252(f883(x65833,a869)))+~E(f329(f329(f42(x65834,f883(x65833,a869)),x65835),x65831),f252(f883(x65833,a869)))+~P24(f329(f329(f331(x65834),x65832),x65835)) % 178.07/177.94 [6886]~P24(f329(f329(f199(x68861),x68863),x68865))+~P24(f329(f329(f199(x68862),x68865),x68864))+P24(f329(f329(f199(f34(x68861,x68862)),x68863),x68864)) % 178.07/177.94 [7091]~E(x70912,x70914)+~P139(x70911)+E(f329(f329(f81(x70911),f329(f329(f82(x70911),x70912),x70913)),f329(f329(f82(x70911),x70914),x70915)),f329(f329(f81(x70911),f329(f329(f82(x70911),x70912),x70915)),f329(f329(f82(x70911),x70914),x70913))) % 178.07/177.94 [7151]~P27(x71511)+~P24(f329(f329(f331(x71514),x71513),x71515))+P24(f329(f329(f243(x71511),f329(x71512,x71513)),f329(f329(f43(x71514,x71511),x71515),x71512))) % 178.07/177.94 [7201]~P106(x72011)+P24(f329(f329(f243(x72011),f329(x72012,x72013)),f329(x72014,x72013)))+~P24(f329(f329(f243(f883(x72015,x72011)),x72012),x72014)) % 178.07/177.94 [7318]E(x73181,x73182)+E(x73183,x73181)+~E(f329(f329(f307(x73184),x73181),f329(f329(f307(x73184),x73185),f193(f883(x73184,a869)))),f329(f329(f307(x73184),x73182),f329(f329(f307(x73184),x73183),f193(f883(x73184,a869))))) % 178.07/177.94 [7319]E(x73191,x73192)+E(x73193,x73191)+~E(f329(f329(f307(x73194),x73193),f329(f329(f307(x73194),x73192),f193(f883(x73194,a869)))),f329(f329(f307(x73194),x73195),f329(f329(f307(x73194),x73191),f193(f883(x73194,a869))))) % 178.07/177.94 [7320]E(x73201,x73202)+E(x73201,x73203)+~E(f329(f329(f307(x73204),x73203),f329(f329(f307(x73204),x73202),f193(f883(x73204,a869)))),f329(f329(f307(x73204),x73205),f329(f329(f307(x73204),x73201),f193(f883(x73204,a869))))) % 178.07/177.94 [7321]E(x73211,x73212)+E(x73211,x73213)+~E(f329(f329(f307(x73214),x73211),f329(f329(f307(x73214),x73215),f193(f883(x73214,a869)))),f329(f329(f307(x73214),x73212),f329(f329(f307(x73214),x73213),f193(f883(x73214,a869))))) % 178.07/177.94 [7856]P21(x78561,x78562,x78563,x78564)+~P21(x78561,x78562,x78563,x78565)+~P24(f329(f329(f243(f883(x78561,a869)),x78564),x78565)) % 178.07/177.94 [7863]~P24(f329(f329(f243(a875),x78635),x78633))+~P24(f329(f329(f329(f329(a201,x78631),x78632),x78635),x78634))+P24(f329(f329(f329(f329(a201,x78631),x78632),x78633),x78634)) % 178.07/177.94 [7959]P24(f329(x79591,x79592))+~P24(f329(f329(f199(x79594),x79592),x79595))+P24(f329(f329(f199(f31(x79591,x79593,x79594)),x79592),x79595)) % 178.07/177.94 [7987]~P24(f329(x79871,x79874))+~P24(f329(f329(f199(x79872),x79874),x79875))+P24(f329(f329(f199(f31(x79871,x79872,x79873)),x79874),x79875)) % 178.07/177.94 [8038]E(x80381,x80382)+~E(f329(f308(x80383,x80384,x80385),x80381),f329(f308(x80383,x80384,x80385),x80382))+~P21(x80383,x80384,x80385,f329(f329(f116(f883(x80383,a869)),x80381),x80382)) % 178.07/177.94 [8112]P24(f329(x81122,x81124))+E(f329(f329(f137(x81121),f329(f194(f876(x81121)),f176(x81121,x81122,x81123))),x81123),f329(f329(f150(x81121),x81124),x81125))+~E(f329(f329(f127(x81121),f176(x81121,x81122,x81123)),f329(f329(f150(x81121),x81124),x81125)),x81123) % 178.07/177.94 [8143]~P21(x81431,x81432,x81433,x81435)+~P21(x81431,x81432,x81433,x81434)+P21(x81431,x81432,x81433,f329(f329(f107(f883(x81431,a869)),x81434),x81435)) % 178.07/177.94 [8252]~P70(x82521)+E(f329(f329(f81(x82521),f329(x82522,x82523)),f329(f165(x82521),f329(f329(f153(x82524,x82521),x82522),f169(x82524,x82523,x82525)))),f329(f165(x82521),f329(f329(f153(x82524,x82521),x82522),x82525)))+~P24(f329(f329(f331(x82524),x82523),f329(f171(x82524),x82525))) % 178.07/177.94 [8341]~P105(x83411)+~P29(x83411,f329(f329(f153(x83412,x83411),x83413),x83415))+P29(x83411,f329(f329(f153(x83412,x83411),x83413),f329(f329(f147(x83412,x83411,x83413),x83414),x83415))) % 178.07/177.94 [8418]P24(f329(x84181,x84182))+P24(f329(f329(f199(x84183),x84182),x84184))+~P24(f329(f329(f199(f31(x84181,x84185,x84183)),x84182),x84184)) % 178.07/177.94 [8429]~P27(x84291)+P24(f329(f329(f243(x84291),f329(f329(f42(x84292,x84291),x84293),x84294)),f329(f329(f42(x84292,x84291),x84295),x84294)))+~P24(f329(f329(f243(f883(x84292,a869)),x84295),x84293)) % 178.07/177.94 [8430]~P27(x84301)+P24(f329(f329(f243(x84301),f329(f329(f43(x84302,x84301),x84303),x84304)),f329(f329(f43(x84302,x84301),x84305),x84304)))+~P24(f329(f329(f243(f883(x84302,a869)),x84303),x84305)) % 178.07/177.94 [8441]~P24(f329(x84414,x84412))+P24(f329(f329(f199(x84411),x84412),x84413))+~P24(f329(f329(f199(f31(x84414,x84411,x84415)),x84412),x84413)) % 178.07/177.94 [8465]~P105(x84653)+P24(f329(f136(x84651),x84652))+~P24(f329(f136(x84651),f329(f329(f147(x84651,x84653,x84654),x84655),x84652))) % 178.07/177.94 [8475]P24(f329(f329(f199(x84751),x84752),x84753))+P24(f329(f329(f199(x84754),x84752),x84753))+~P24(f329(f329(f199(f31(x84755,x84751,x84754)),x84752),x84753)) % 178.07/177.94 [8606]~P105(x86061)+~P24(f329(f329(f331(x86062),x86063),f329(f171(x86062),x86064)))+~P24(f329(f136(x86062),f329(f329(f147(x86062,x86061,x86065),x86063),x86064))) % 178.07/177.94 [8687]~P105(x86871)+P29(x86871,f329(f329(f153(x86872,x86871),x86873),x86874))+~P29(x86871,f329(f329(f153(x86872,x86871),x86873),f329(f329(f147(x86872,x86871,x86873),x86875),x86874))) % 178.07/177.94 [8779]~P105(x87792)+E(f329(f329(f147(x87791,x87792,x87793),x87794),x87795),f148(x87791,x87792,x87793,x87794,x87795))+P24(f329(f329(f331(x87792),f329(x87793,x87794)),f329(f308(x87791,x87792,x87793),f329(f171(x87791),x87795)))) % 178.07/177.94 [8853]~P105(x88532)+E(f148(x88531,x88532,x88533,x88534,x88535),x88535)+~P24(f329(f329(f331(x88532),f329(x88533,x88534)),f329(f308(x88531,x88532,x88533),f329(f171(x88531),x88535)))) % 178.07/177.94 [8868]~P21(x88682,x88681,x88683,x88685)+P24(f329(f329(f244(f883(x88681,a869)),f329(f308(x88682,x88681,x88683),x88684)),f329(f308(x88682,x88681,x88683),x88685)))+~P24(f329(f329(f244(f883(x88682,a869)),x88684),x88685)) % 178.07/177.94 [9038]~P21(x90381,x90382,x90383,f252(f883(x90381,a869)))+~P24(f329(f329(f243(f883(x90382,a869)),x90384),f329(f308(x90381,x90382,x90383),x90385)))+P24(f329(f329(f243(f883(x90381,a869)),f329(f309(x90381,x90382,x90383),x90384)),x90385)) % 178.07/177.94 [9058]~E(f329(f308(x90583,x90581,x90584),f252(f883(x90583,a869))),f252(f883(x90581,a869)))+P24(f329(f329(f243(f883(x90581,a869)),x90582),f329(f308(x90583,x90581,x90584),x90585)))+~P24(f329(f329(f243(f883(x90583,a869)),f329(f309(x90583,x90581,x90584),x90582)),x90585)) % 178.07/177.94 [9082]~E(f329(f236(x90822),x90824),f329(f329(f177(x90821,x90822),x90825),x90823))+~P24(f329(f136(x90821),f329(f329(f153(f882(x90821,x90822),x90821),f263(x90821,x90822)),x90825)))+P24(f329(f329(f331(f882(x90821,x90822)),f329(f329(f264(x90821,x90822),x90823),x90824)),f329(f171(f882(x90821,x90822)),x90825))) % 178.07/177.94 [9164]~P21(x91641,x91644,x91645,f252(f883(x91641,a869)))+~P24(f329(f329(f243(f883(x91644,a869)),f329(f308(x91641,x91644,x91645),x91642)),f329(f308(x91641,x91644,x91645),x91643)))+P24(f329(f329(f243(f883(x91641,a869)),x91642),x91643)) % 178.07/177.94 [9230]E(f329(f236(x92301),x92302),f329(f329(f177(x92303,x92301),x92304),x92305))+~P24(f329(f136(x92303),f329(f329(f153(f882(x92303,x92301),x92303),f263(x92303,x92301)),x92304)))+~P24(f329(f329(f331(f882(x92303,x92301)),f329(f329(f264(x92303,x92301),x92305),x92302)),f329(f171(f882(x92303,x92301)),x92304))) % 178.07/177.94 [9232]E(f329(f329(f177(x92321,x92322),x92323),x92324),f329(f236(x92322),x92325))+~P24(f329(f136(x92321),f329(f329(f153(f882(x92321,x92322),x92321),f263(x92321,x92322)),x92323)))+~P24(f329(f329(f331(f882(x92321,x92322)),f329(f329(f264(x92321,x92322),x92324),x92325)),f329(f171(f882(x92321,x92322)),x92323))) % 178.07/177.94 [9287]~P80(x92871)+~E(f329(x92873,f661(x92873,x92874,x92875,x92872,x92871)),f2(x92871))+E(f329(f165(x92871),f329(f329(f153(x92872,x92871),x92873),f329(f135(x92872,x92874),x92875))),f329(f165(x92871),f329(f329(f153(x92872,x92871),x92873),x92875))) % 178.07/177.94 [9463]~P12(x94631,x94632,x94633)+~P24(f329(f62(x94631),x94635))+P24(f329(f67(x94631,x94632,x94633,x94634,x94635),f329(f329(f65(x94631,x94632,x94633),x94634),x94635))) % 178.07/177.94 [9542]P24(f329(x95421,f794(x95422,x95421,x95423,x95424,x95425)))+~P24(f329(f329(f243(f883(x95425,a869)),x95424),x95423))+P24(f329(f329(f243(f883(x95425,a869)),f329(f329(f107(f883(x95425,a869)),x95424),f329(f249(x95425),x95421))),f329(f329(f107(f883(x95425,a869)),x95423),f329(f249(x95425),x95422)))) % 178.07/177.94 [9556]~P80(x95561)+~P24(f329(x95564,f661(x95563,x95564,x95565,x95562,x95561)))+E(f329(f165(x95561),f329(f329(f153(x95562,x95561),x95563),f329(f135(x95562,x95564),x95565))),f329(f165(x95561),f329(f329(f153(x95562,x95561),x95563),x95565))) % 178.07/177.94 [9635]~P27(x96355)+P24(f329(f329(f331(x96351),f343(x96352,x96353,x96351,x96354,x96355)),x96353))+P24(f329(f329(f243(x96355),x96354),f329(f329(f42(x96351,x96355),x96353),x96352))) % 178.07/177.94 [9638]~P80(x96381)+E(f329(f165(x96381),f329(f329(f153(x96382,x96381),x96383),f329(f135(x96382,x96384),x96385))),f329(f165(x96381),f329(f329(f153(x96382,x96381),x96383),x96385)))+P24(f329(f329(f331(x96382),f661(x96383,x96384,x96385,x96382,x96381)),f329(f171(x96382),x96385))) % 178.07/177.94 [9648]~P24(f329(x96485,f794(x96485,x96483,x96484,x96482,x96481)))+~P24(f329(f329(f243(f883(x96481,a869)),x96482),x96484))+P24(f329(f329(f243(f883(x96481,a869)),f329(f329(f107(f883(x96481,a869)),x96482),f329(f249(x96481),x96483))),f329(f329(f107(f883(x96481,a869)),x96484),f329(f249(x96481),x96485)))) % 178.07/177.94 [9682]P35(x96821,x96822,x96823,x96824,x96825)+~E(f329(f194(f876(x96822)),x96825),f329(f194(f876(x96821)),x96824))+P24(f329(f329(f244(a875),f688(x96825,x96824,x96823,x96822,x96821)),f329(f194(f876(x96821)),x96824))) % 178.07/177.94 [9683]P35(x96831,x96832,x96833,x96834,x96835)+~E(f329(f194(f876(x96832)),x96835),f329(f194(f876(x96831)),x96834))+P24(f329(f329(f244(a875),f720(x96833,x96835,x96832,x96834,x96831)),f329(f194(f876(x96831)),x96834))) % 178.07/177.94 [9716]P24(f329(f329(f331(x97161),f794(x97162,x97163,x97164,x97165,x97161)),x97165))+~P24(f329(f329(f243(f883(x97161,a869)),x97165),x97164))+P24(f329(f329(f243(f883(x97161,a869)),f329(f329(f107(f883(x97161,a869)),x97165),f329(f249(x97161),x97163))),f329(f329(f107(f883(x97161,a869)),x97164),f329(f249(x97161),x97162)))) % 178.07/177.94 [9770]~P27(x97701)+~P24(f329(f329(f243(x97701),x97702),f329(x97705,f343(x97705,x97704,x97703,x97702,x97701))))+P24(f329(f329(f243(x97701),x97702),f329(f329(f42(x97703,x97701),x97704),x97705))) % 178.07/177.94 [9803]~P74(x98031)+~P24(f329(f62(x98032),x98035))+E(f329(f329(f329(f66(x98031,x98032,f82(x98031)),f329(f329(f18(x98032,x98031,x98031),f329(f329(f8(x98031,f883(x98031,x98031),x98032),f82(x98031)),x98033)),x98034)),f79(x98031)),x98035),f329(f329(f82(x98031),f329(f329(f329(f66(x98031,x98032,f82(x98031)),x98033),f79(x98031)),x98035)),f329(f329(f329(f66(x98031,x98032,f82(x98031)),x98034),f79(x98031)),x98035))) % 178.07/177.94 [9866]~P24(f329(f329(f331(f882(f883(x98661,a869),f883(x98661,a869))),f329(f329(f264(f883(x98661,a869),f883(x98661,a869)),x98665),x98664)),f320(x98661,x98663)))+~P24(f329(f329(f331(x98661),x98662),x98665))+P24(f329(f329(f331(f882(x98661,x98661)),f329(f329(f264(x98661,x98661),x98662),f743(x98663,x98664,x98665,x98661,x98662))),x98663)) % 178.07/177.94 [9994]~P24(f329(f329(f331(f882(f876(x99941),f876(x99941))),f329(f329(f264(f876(x99941),f876(x99941)),f329(f329(f127(x99941),x99945),x99942)),f329(f329(f127(x99941),x99945),x99943))),f146(x99941,x99944)))+P24(f329(f329(f331(f882(f876(x99941),f876(x99941))),f329(f329(f264(f876(x99941),f876(x99941)),x99942),x99943)),f146(x99941,x99944)))+P24(f329(f329(f331(f882(x99941,x99941)),f329(f329(f264(x99941,x99941),f638(x99944,x99943,x99942,x99945,x99941)),f638(x99944,x99943,x99942,x99945,x99941))),x99944)) % 178.07/177.94 [7131]~E(f329(f194(f876(x71311)),x71313),f329(f194(f876(x71312)),x71314))+E(f329(f329(f177(x71311,x71312),f329(f329(f181(x71311,x71312),x71313),x71314)),x71315),f206(x71312))+P24(f329(f329(f331(x71311),x71315),f329(f171(x71311),x71313))) % 178.07/177.94 [7204]~E(x72043,x72045)+E(f329(f329(f164(x72041),f329(f329(f158(x72041,x72042),x72043),x72044)),x72045),x72044)+~P24(f329(f329(f244(a875),x72043),f329(f194(f876(x72041)),x72042))) % 178.07/177.94 [7313]~E(f329(f329(f127(x73131),x73132),x73134),f329(f329(f127(x73131),x73133),x73135))+E(f329(f329(f174(x73131),f329(f194(f876(x73131)),x73132)),x73133),x73132)+P24(f329(f329(f243(a875),f329(f194(f876(x73131)),x73133)),f329(f194(f876(x73131)),x73132))) % 178.07/177.94 [7330]~E(x73305,x73302)+P24(f329(x73301,x73302))+P24(f329(f329(f329(f329(a201,f33(x73301,x73303)),x73302),x73304),x73305)) % 178.07/177.94 [7817]~E(f329(f329(f127(x78171),x78172),x78174),f329(f329(f127(x78171),x78173),x78175))+E(f329(f329(f174(x78171),f329(f194(f876(x78171)),x78172)),x78173),x78172)+~P24(f329(f329(f243(a875),f329(f194(f876(x78171)),x78172)),f329(f194(f876(x78171)),x78173))) % 178.07/177.94 [7841]~P24(f329(f62(x78411),f329(x78414,x78415)))+~P24(f329(f329(f331(x78412),x78415),x78413))+P24(f329(f62(x78411),f329(f329(f42(x78412,f883(x78411,a869)),x78413),x78414))) % 178.07/177.94 [7894]~E(f329(f194(f876(x78941)),x78942),f329(f194(f876(x78943)),x78944))+~E(f329(f329(f177(x78941,x78943),f329(f329(f181(x78941,x78943),x78942),x78944)),x78945),f206(x78943))+~P24(f329(f329(f331(x78941),x78945),f329(f171(x78941),x78942))) % 178.07/177.94 [8023]~P40(x80231,x80233,x80235)+~P40(x80231,x80232,x80234)+P40(x80231,f329(f329(f116(f883(x80231,a869)),x80232),x80233),f329(f329(f116(f883(f882(x80231,x80231),a869)),x80234),x80235)) % 178.07/177.94 [8024]~P40(x80241,x80243,x80245)+~P40(x80241,x80242,x80244)+P40(x80241,f329(f329(f107(f883(x80241,a869)),x80242),x80243),f329(f329(f107(f883(f882(x80241,x80241),a869)),x80244),x80245)) % 178.07/177.94 [8106]E(x81061,x81062)+P24(f329(x81063,x81061))+~P24(f329(f329(f329(f329(a201,f33(x81063,x81064)),x81061),x81065),x81062)) % 178.07/177.94 [8379]E(f329(f329(f264(x83791,x83792),f329(f329(f164(x83791),x83793),x83794)),f329(f329(f164(x83792),x83795),x83794)),f329(f329(f164(f882(x83791,x83792)),f329(f329(f181(x83791,x83792),x83793),x83795)),x83794))+~P24(f329(f329(f244(a875),x83794),f329(f194(f876(x83791)),x83793)))+~P24(f329(f329(f244(a875),x83794),f329(f194(f876(x83792)),x83795))) % 178.07/177.94 [8539]~P40(x85391,x85393,x85394)+P24(f329(f329(f331(x85391),x85392),x85393))+~P24(f329(f329(f331(f882(x85391,x85391)),f329(f329(f264(x85391,x85391),x85395),x85392)),x85394)) % 178.07/177.94 [8540]~P40(x85401,x85403,x85404)+P24(f329(f329(f331(x85401),x85402),x85403))+~P24(f329(f329(f331(f882(x85401,x85401)),f329(f329(f264(x85401,x85401),x85402),x85405)),x85404)) % 178.07/177.94 [8541]~P6(x85411,x85413,x85414)+P24(f329(f329(f331(x85411),x85412),x85413))+~P24(f329(f329(f331(f882(x85411,x85411)),f329(f329(f264(x85411,x85411),x85415),x85412)),x85414)) % 178.07/177.94 [8542]~P6(x85421,x85423,x85424)+P24(f329(f329(f331(x85421),x85422),x85423))+~P24(f329(f329(f331(f882(x85421,x85421)),f329(f329(f264(x85421,x85421),x85422),x85425)),x85424)) % 178.07/177.94 [8801]~P6(x88011,x88015,x88012)+E(f329(f283(x88011,x88011,x88012),f329(f329(f307(x88011),x88013),f193(f883(x88011,a869)))),f329(f283(x88011,x88011,x88012),f329(f329(f307(x88011),x88014),f193(f883(x88011,a869)))))+~P24(f329(f329(f331(f882(x88011,x88011)),f329(f329(f264(x88011,x88011),x88013),x88014)),x88012)) % 178.07/177.94 [8883]~P24(f329(f329(f329(f329(a201,x88832),x88833),x88834),x88835))+~P24(f329(f329(f329(f329(a201,f33(x88831,x88832)),x88835),x88834),x88833))+P24(f329(f329(f329(f329(a201,f33(x88831,x88832)),x88833),x88834),x88833)) % 178.07/177.94 [8993]P24(f329(x89931,x89932))+~P24(f329(f329(f331(x89933),x89932),x89935))+P24(f329(f329(f331(x89933),f496(x89931,x89934,x89935,x89933)),f329(f329(f116(f883(x89933,a869)),x89935),x89934))) % 178.07/177.94 [8994]P24(f329(x89941,x89942))+~P24(f329(f329(f331(x89943),x89942),x89944))+P24(f329(f329(f331(x89943),f496(x89941,x89944,x89945,x89943)),f329(f329(f116(f883(x89943,a869)),x89945),x89944))) % 178.07/177.94 [9002]~P24(f329(x90022,x90025))+~P24(f329(f329(f331(x90021),x90025),x90024))+P24(f329(f329(f331(x90021),f479(x90022,x90023,x90024,x90021)),f329(f329(f116(f883(x90021,a869)),x90024),x90023))) % 178.07/177.94 [9003]~P24(f329(x90032,x90035))+~P24(f329(f329(f331(x90031),x90035),x90033))+P24(f329(f329(f331(x90031),f479(x90032,x90033,x90034,x90031)),f329(f329(f116(f883(x90031,a869)),x90034),x90033))) % 178.07/177.94 [9018]~P24(f329(f329(f243(f883(x90181,a869)),x90183),x90185))+~P24(f329(f329(f243(f883(x90181,a869)),x90182),x90184))+P24(f329(f329(f243(f883(x90181,a869)),f329(f329(f116(f883(x90181,a869)),x90182),x90183)),f329(f329(f116(f883(x90181,a869)),x90184),x90185))) % 178.07/177.94 [9019]~P24(f329(f329(f243(f883(x90191,a869)),x90195),x90193))+~P24(f329(f329(f243(f883(x90191,a869)),x90192),x90194))+P24(f329(f329(f243(f883(x90191,a869)),f329(f329(f22(f883(x90191,a869)),x90192),x90193)),f329(f329(f22(f883(x90191,a869)),x90194),x90195))) % 178.07/177.94 [9020]~P24(f329(f329(f243(f883(x90201,a869)),x90203),x90205))+~P24(f329(f329(f243(f883(x90201,a869)),x90202),x90204))+P24(f329(f329(f243(f883(x90201,a869)),f329(f329(f107(f883(x90201,a869)),x90202),x90203)),f329(f329(f107(f883(x90201,a869)),x90204),x90205))) % 178.07/177.94 [9107]~E(f329(f194(f876(x91071)),x91073),f329(f194(f876(x91072)),x91074))+E(f329(f329(f177(x91071,x91072),f329(f329(f181(x91071,x91072),x91073),x91074)),x91075),f329(f236(x91072),f570(x91075,x91074,x91072,x91073,x91071)))+~P24(f329(f329(f331(x91071),x91075),f329(f171(x91071),x91073))) % 178.07/177.94 [9111]P24(f329(f329(f331(f882(x91111,x91111)),f329(f329(f264(x91111,x91111),x91112),x91113)),f323(x91111,x91114,x91115)))+~P24(f329(f329(f243(a875),f329(x91114,x91112)),f329(x91114,x91113)))+~P24(f329(f329(f331(f882(x91111,x91111)),f329(f329(f264(x91111,x91111),x91112),x91113)),x91115)) % 178.07/177.94 [9297]P24(f329(f329(f331(f882(x92971,x92971)),f329(f329(f264(x92971,x92971),x92972),x92973)),f305(x92971,x92974)))+~P24(f329(f329(f331(f882(x92971,x92971)),f329(f329(f264(x92971,x92971),x92972),x92975)),f305(x92971,x92974)))+~P24(f329(f329(f331(f882(x92971,x92971)),f329(f329(f264(x92971,x92971),x92975),x92973)),x92974)) % 178.07/177.94 [9298]P24(f329(f329(f331(f882(x92981,x92981)),f329(f329(f264(x92981,x92981),x92982),x92983)),f305(x92981,x92984)))+~P24(f329(f329(f331(f882(x92981,x92981)),f329(f329(f264(x92981,x92981),x92985),x92983)),f305(x92981,x92984)))+~P24(f329(f329(f331(f882(x92981,x92981)),f329(f329(f264(x92981,x92981),x92982),x92985)),x92984)) % 178.07/177.94 [9394]E(x93941,x93942)+E(f329(a118,f759(x93943,x93944,x93941,x93942,x93945)),x93944)+~P24(f329(f329(f331(f882(x93945,x93945)),f329(f329(f264(x93945,x93945),x93942),x93941)),f329(f329(f188(f882(x93945,x93945),a869),x93944),x93943))) % 178.07/177.94 [9395]E(x93951,x93952)+E(f329(a118,f761(x93953,x93954,x93951,x93952,x93955)),x93954)+~P24(f329(f329(f331(f882(x93955,x93955)),f329(f329(f264(x93955,x93955),x93952),x93951)),f329(f329(f188(f882(x93955,x93955),a869),x93954),x93953))) % 178.07/177.94 [9396]E(x93961,f2(a875))+E(f329(a118,f759(x93962,x93961,x93963,x93964,x93965)),x93961)+~P24(f329(f329(f331(f882(x93965,x93965)),f329(f329(f264(x93965,x93965),x93964),x93963)),f329(f329(f188(f882(x93965,x93965),a869),x93961),x93962))) % 178.07/177.94 [9397]E(x93971,f2(a875))+E(f329(a118,f761(x93972,x93971,x93973,x93974,x93975)),x93971)+~P24(f329(f329(f331(f882(x93975,x93975)),f329(f329(f264(x93975,x93975),x93974),x93973)),f329(f329(f188(f882(x93975,x93975),a869),x93971),x93972))) % 178.07/177.94 [9413]P24(f329(f329(f331(f882(x94131,x94131)),f329(f329(f264(x94131,x94131),x94132),x94133)),f329(f329(f286(x94131,x94131,x94131),x94134),f305(x94131,x94134))))+~P24(f329(f329(f331(f882(x94131,x94131)),f329(f329(f264(x94131,x94131),x94132),x94135)),x94134))+~P24(f329(f329(f331(f882(x94131,x94131)),f329(f329(f264(x94131,x94131),x94135),x94133)),x94134)) % 178.07/177.94 [9420]~P24(f329(f329(f331(f882(x94201,x94201)),f329(f329(f264(x94201,x94201),x94202),x94205)),f305(x94201,x94204)))+P24(f329(f329(f331(f882(x94201,x94201)),f329(f329(f264(x94201,x94201),x94202),x94203)),f329(f329(f286(x94201,x94201,x94201),x94204),f305(x94201,x94204))))+~P24(f329(f329(f331(f882(x94201,x94201)),f329(f329(f264(x94201,x94201),x94205),x94203)),x94204)) % 178.07/177.94 [9459]~P6(x94591,x94595,x94592)+~P24(f329(f329(f331(f882(x94591,x94591)),f329(f329(f264(x94591,x94591),x94593),x94594)),x94592))+P24(f329(f329(f243(f883(x94591,a869)),f329(f283(x94591,x94591,x94592),f329(f329(f307(x94591),x94593),f193(f883(x94591,a869))))),f329(f283(x94591,x94591,x94592),f329(f329(f307(x94591),x94594),f193(f883(x94591,a869)))))) % 178.07/177.94 [9481]E(x94811,x94812)+P24(f329(f329(f329(f329(a201,x94813),x94811),x94814),f492(x94812,x94814,x94811,x94813,x94815)))+~P24(f329(f329(f329(f329(a201,f33(x94815,x94813)),x94811),x94814),x94812)) % 178.07/177.94 [9485]~P24(f329(x94855,x94852))+P24(f329(f329(f329(f329(a201,x94851),x94852),x94853),f492(x94854,x94853,x94852,x94851,x94855)))+~P24(f329(f329(f329(f329(a201,f33(x94855,x94851)),x94852),x94853),x94854)) % 178.07/177.94 [9514]P24(f329(f329(f331(f882(x95141,x95141)),f329(f329(f264(x95141,x95141),x95142),x95143)),f329(f329(f286(x95141,x95141,x95141),x95144),f305(x95141,x95144))))+~P24(f329(f329(f331(f882(x95141,x95141)),f329(f329(f264(x95141,x95141),x95142),x95145)),f329(f329(f286(x95141,x95141,x95141),x95144),f305(x95141,x95144))))+~P24(f329(f329(f331(f882(x95141,x95141)),f329(f329(f264(x95141,x95141),x95145),x95143)),x95144)) % 178.07/177.94 [9515]P24(f329(f329(f331(f882(x95151,x95151)),f329(f329(f264(x95151,x95151),x95152),x95153)),f329(f329(f286(x95151,x95151,x95151),x95154),f305(x95151,x95154))))+~P24(f329(f329(f331(f882(x95151,x95151)),f329(f329(f264(x95151,x95151),x95155),x95153)),f329(f329(f286(x95151,x95151,x95151),x95154),f305(x95151,x95154))))+~P24(f329(f329(f331(f882(x95151,x95151)),f329(f329(f264(x95151,x95151),x95152),x95155)),x95154)) % 178.07/177.94 [9565]~P24(f329(f67(x95651,x95651,x95654,x95652,x95653),x95655))+P24(f329(f329(f331(x95651),x95652),x95653))+P24(f329(f63(x95651,x95654,f329(f329(f307(x95651),x95652),x95653)),x95655)) % 178.07/177.94 [9604]~E(f329(f308(x96043,x96042,x96045),x96044),x96041)+E(x96041,f193(f883(x96042,a869)))+P24(f329(f329(f243(f883(x96043,a869)),f329(f308(x96042,x96043,f347(x96044,x96043,x96042,x96041)),x96041)),x96044)) % 178.07/177.94 [9651]~P27(x96515)+P24(f329(f329(f331(x96511),f344(x96512,x96513,x96514,x96511,x96515)),x96514))+P24(f329(f329(f243(x96515),f329(f329(f43(x96511,x96515),x96514),x96513)),x96512)) % 178.07/177.94 [9702]P35(x97021,x97022,x97023,x97024,x97025)+~E(f329(f194(f876(x97021)),x97024),f329(f194(f876(x97022)),x97025))+P24(f329(f329(f331(f882(x97021,x97022)),f677(x97025,x97024,x97023,x97022,x97021)),f329(f171(f882(x97021,x97022)),f329(f329(f181(x97021,x97022),x97024),x97025)))) % 178.07/177.94 [9703]P35(x97031,x97032,x97033,x97034,x97035)+~E(f329(f194(f876(x97031)),x97034),f329(f194(f876(x97032)),x97035))+P24(f329(f329(f331(f882(x97031,x97032)),f687(x97033,x97035,x97034,x97032,x97031)),f329(f171(f882(x97031,x97032)),f329(f329(f181(x97031,x97032),x97034),x97035)))) % 178.07/177.94 [9833]E(x98331,x98332)+P24(f329(f329(f329(f329(a201,f33(x98333,x98334)),f492(x98331,x98335,x98332,x98334,x98333)),x98335),x98331))+~P24(f329(f329(f329(f329(a201,f33(x98333,x98334)),x98332),x98335),x98331)) % 178.07/177.94 [9835]~P24(f329(x98351,x98355))+P24(f329(f329(f329(f329(a201,f33(x98351,x98352)),f492(x98353,x98354,x98355,x98352,x98351)),x98354),x98353))+~P24(f329(f329(f329(f329(a201,f33(x98351,x98352)),x98355),x98354),x98353)) % 178.07/177.94 [9843]E(x98431,x98432)+P24(f329(f329(f331(f882(x98433,x98433)),f329(f329(f264(x98433,x98433),x98431),f762(x98434,x98435,x98432,x98431,x98433))),x98434))+~P24(f329(f329(f331(f882(x98433,x98433)),f329(f329(f264(x98433,x98433),x98431),x98432)),f329(f329(f188(f882(x98433,x98433),a869),x98435),x98434))) % 178.07/177.94 [9844]E(x98441,f2(a875))+P24(f329(f329(f331(f882(x98442,x98442)),f329(f329(f264(x98442,x98442),x98443),f762(x98444,x98441,x98445,x98443,x98442))),x98444))+~P24(f329(f329(f331(f882(x98442,x98442)),f329(f329(f264(x98442,x98442),x98443),x98445)),f329(f329(f188(f882(x98442,x98442),a869),x98441),x98444))) % 178.07/177.94 [9887]~P27(x98871)+~P24(f329(f329(f243(x98871),f329(x98874,f344(x98875,x98874,x98873,x98872,x98871))),x98875))+P24(f329(f329(f243(x98871),f329(f329(f43(x98872,x98871),x98873),x98874)),x98875)) % 178.07/177.94 [9929]E(x99291,x99292)+P24(f329(f329(f331(f882(x99293,x99293)),f329(f329(f264(x99293,x99293),f760(x99294,x99295,x99291,x99292,x99293)),x99291)),x99294))+~P24(f329(f329(f331(f882(x99293,x99293)),f329(f329(f264(x99293,x99293),x99292),x99291)),f329(f329(f188(f882(x99293,x99293),a869),x99295),x99294))) % 178.07/177.94 [9930]E(x99301,f2(a875))+P24(f329(f329(f331(f882(x99302,x99302)),f329(f329(f264(x99302,x99302),f760(x99303,x99301,x99304,x99305,x99302)),x99304)),x99303))+~P24(f329(f329(f331(f882(x99302,x99302)),f329(f329(f264(x99302,x99302),x99305),x99304)),f329(f329(f188(f882(x99302,x99302),a869),x99301),x99303))) % 178.07/177.94 [9934]E(x99341,x99342)+P24(f329(f329(f331(f882(x99343,x99343)),f329(f329(f264(x99343,x99343),x99341),f760(x99344,x99345,x99342,x99341,x99343))),f329(f329(f188(f882(x99343,x99343),a869),f759(x99344,x99345,x99342,x99341,x99343)),x99344)))+~P24(f329(f329(f331(f882(x99343,x99343)),f329(f329(f264(x99343,x99343),x99341),x99342)),f329(f329(f188(f882(x99343,x99343),a869),x99345),x99344))) % 178.07/177.94 [9935]E(x99351,f2(a875))+P24(f329(f329(f331(f882(x99352,x99352)),f329(f329(f264(x99352,x99352),x99353),f760(x99354,x99351,x99355,x99353,x99352))),f329(f329(f188(f882(x99352,x99352),a869),f759(x99354,x99351,x99355,x99353,x99352)),x99354)))+~P24(f329(f329(f331(f882(x99352,x99352)),f329(f329(f264(x99352,x99352),x99353),x99355)),f329(f329(f188(f882(x99352,x99352),a869),x99351),x99354))) % 178.07/177.94 [9985]E(x99851,x99852)+P24(f329(f329(f331(f882(x99853,x99853)),f329(f329(f264(x99853,x99853),f762(x99854,x99855,x99851,x99852,x99853)),x99851)),f329(f329(f188(f882(x99853,x99853),a869),f761(x99854,x99855,x99851,x99852,x99853)),x99854)))+~P24(f329(f329(f331(f882(x99853,x99853)),f329(f329(f264(x99853,x99853),x99852),x99851)),f329(f329(f188(f882(x99853,x99853),a869),x99855),x99854))) % 178.07/177.94 [9986]E(x99861,f2(a875))+P24(f329(f329(f331(f882(x99862,x99862)),f329(f329(f264(x99862,x99862),f762(x99863,x99861,x99864,x99865,x99862)),x99864)),f329(f329(f188(f882(x99862,x99862),a869),f761(x99863,x99861,x99864,x99865,x99862)),x99863)))+~P24(f329(f329(f331(f882(x99862,x99862)),f329(f329(f264(x99862,x99862),x99865),x99864)),f329(f329(f188(f882(x99862,x99862),a869),x99861),x99863))) % 178.07/177.94 [10019]~P70(x100192)+~P24(f329(f62(x100191),x100195))+E(f329(f329(f6(x100191,x100192),f329(f329(f7(x100191,x100192,x100192),f329(f329(f18(x100191,x100192,f883(x100192,x100192)),f329(f329(f8(a869,f883(x100192,f883(x100192,x100192)),x100191),f102(x100192)),f329(f329(f7(x100191,f883(x100191,a869),a869),f331(x100191)),x100193))),x100194)),f2(x100192))),x100195),f329(f329(f6(x100191,x100192),x100194),f329(f329(f107(f883(x100191,a869)),x100195),x100193))) % 178.07/177.94 [8603]~P70(x86031)+~P24(f329(f62(x86034),x86035))+E(f329(f329(f81(x86031),f329(x86032,x86033)),f329(f329(f6(x86034,x86031),x86032),f329(f329(f22(f883(x86034,a869)),x86035),f329(f329(f307(x86034),x86033),f193(f883(x86034,a869)))))),f329(f329(f6(x86034,x86031),x86032),f329(f329(f307(x86034),x86033),x86035))) % 178.07/177.94 [8604]~P74(x86041)+~P24(f329(f62(x86044),x86045))+E(f329(f329(f82(x86041),f329(x86042,x86043)),f329(f329(f9(x86044,x86041),x86042),f329(f329(f22(f883(x86044,a869)),x86045),f329(f329(f307(x86044),x86043),f193(f883(x86044,a869)))))),f329(f329(f9(x86044,x86041),x86042),f329(f329(f307(x86044),x86043),x86045))) % 178.07/177.94 [8922]~P105(x89222)+~P29(x89222,f329(f168(x89222),f329(f329(f153(x89221,x89222),x89224),x89225)))+E(f329(f135(x89221,f329(f329(f8(x89222,a869,x89221),f329(f244(x89222),x89223)),x89224)),x89225),f176(x89221,f329(f329(f8(x89222,a869,x89221),f329(f244(x89222),x89223)),x89224),x89225)) % 178.07/177.94 [8947]~P70(x89471)+E(f329(f329(f81(x89471),f329(f329(f6(a875,x89471),x89472),f300(a875,x89473,x89474))),f329(f329(f6(a875,x89471),x89472),f300(a875,f329(f329(f81(a875),x89474),f79(a875)),f329(f329(f81(a875),x89474),x89475)))),f329(f329(f6(a875,x89471),x89472),f300(a875,x89473,f329(f329(f81(a875),x89474),x89475))))+~P24(f329(f329(f243(a875),x89473),f329(f329(f81(a875),x89474),f79(a875)))) % 178.07/177.94 [8948]~P24(f329(f329(f331(x89481),x89484),x89485))+~P24(f329(f329(f243(f883(x89481,a869)),f329(f171(x89481),x89482)),x89485))+P24(f329(f329(f243(f883(x89481,a869)),f329(f171(x89481),f329(f329(f158(x89481,x89482),x89483),x89484))),x89485)) % 178.07/177.94 [9174]~P27(x91742)+~P24(f329(f62(x91741),x91745))+E(f329(f329(f65(x91741,x91742,f329(f329(f8(x91742,f883(x91742,x91742),x91741),f116(x91742)),x91743)),x91744),x91745),f329(f329(f116(x91742),x91744),f329(f329(f43(x91741,x91742),x91745),x91743))) % 178.07/177.94 [9175]~P27(x91752)+~P24(f329(f62(x91751),x91755))+E(f329(f329(f65(x91751,x91752,f329(f329(f8(x91752,f883(x91752,x91752),x91751),f107(x91752)),x91753)),x91754),x91755),f329(f329(f107(x91752),x91754),f329(f329(f42(x91751,x91752),x91755),x91753))) % 178.07/177.94 [9222]E(f329(x92221,x92222),f329(x92221,x92223))+P24(f329(f329(f244(a875),f329(x92221,x92222)),f329(x92221,x92223)))+~P24(f329(f329(f331(f882(x92224,x92224)),f329(f329(f264(x92224,x92224),x92222),x92223)),f152(x92224,f329(f329(f150(f883(x92224,a875)),x92221),x92225)))) % 178.07/177.94 [9254]~E(f329(x92544,x92542),f329(x92544,x92543))+~P24(f329(f329(f331(f882(x92541,x92541)),f329(f329(f264(x92541,x92541),x92542),x92543)),f152(x92541,x92545)))+P24(f329(f329(f331(f882(x92541,x92541)),f329(f329(f264(x92541,x92541),x92542),x92543)),f152(x92541,f329(f329(f150(f883(x92541,a875)),x92544),x92545)))) % 178.07/177.94 [9276]~P21(x92761,x92762,x92763,x92765)+P21(x92761,x92762,x92763,f329(f329(f307(x92761),x92764),x92765))+P24(f329(f329(f331(x92762),f329(x92763,x92764)),f329(f308(x92761,x92762,x92763),f329(f329(f22(f883(x92761,a869)),x92765),f329(f329(f307(x92761),x92764),f193(f883(x92761,a869))))))) % 178.07/177.94 [9280]P24(f329(x92802,x92805))+~P24(f329(f329(f331(x92801),x92805),f329(f171(x92801),x92803)))+E(f329(f329(f137(x92801),f329(f194(f876(x92801)),f176(x92801,x92802,f329(f329(f127(x92801),x92803),x92804)))),f329(f329(f127(x92801),x92803),x92804)),f329(f329(f127(x92801),f329(f329(f137(x92801),f329(f194(f876(x92801)),f176(x92801,x92802,x92803))),x92803)),x92804)) % 178.07/177.94 [9283]~P24(f329(f329(f331(f882(x92831,x92831)),f329(f329(f264(x92831,x92831),x92832),x92833)),f152(x92831,x92835)))+~P24(f329(f329(f243(a875),f329(x92834,x92832)),f329(x92834,x92833)))+P24(f329(f329(f331(f882(x92831,x92831)),f329(f329(f264(x92831,x92831),x92832),x92833)),f152(x92831,f329(f329(f150(f883(x92831,a875)),x92834),x92835)))) % 178.07/177.94 [9348]P24(f329(f329(f331(f882(x93484,x93484)),f329(f329(f264(x93484,x93484),x93482),x93483)),f152(x93484,x93485)))+P24(f329(f329(f244(a875),f329(x93481,x93482)),f329(x93481,x93483)))+~P24(f329(f329(f331(f882(x93484,x93484)),f329(f329(f264(x93484,x93484),x93482),x93483)),f152(x93484,f329(f329(f150(f883(x93484,a875)),x93481),x93485)))) % 178.07/177.94 [9488]~P24(f329(f329(f331(f882(f876(x94881),f876(x94881))),f329(f329(f264(f876(x94881),f876(x94881)),x94882),x94884)),f157(x94881,x94885)))+~P24(f329(f329(f244(a875),x94883),f329(f194(f876(x94881)),x94882)))+P24(f329(f329(f331(f882(x94881,x94881)),f329(f329(f264(x94881,x94881),f329(f329(f164(x94881),x94882),x94883)),f329(f329(f164(x94881),x94884),x94883))),x94885)) % 178.07/177.94 [9730]E(x97301,f2(a1))+~P24(f329(f49(x97303,x97301),f329(f329(f264(a1,a1),x97304),x97305)))+P24(f329(f49(f329(f329(f82(a1),x97302),x97303),x97301),f329(f329(f264(a1,a1),f329(f329(f81(a1),f329(f329(f82(a1),x97302),x97304)),f329(f329(f39(a1),f329(f329(f82(a1),x97302),x97305)),x97301))),f45(a1,f329(f329(f82(a1),x97302),x97305),x97301)))) % 178.07/177.94 [9732]~P24(f329(f329(f244(a875),f2(a875)),x97323))+~P24(f329(f48(x97322,x97323),f329(f329(f264(a875,a875),x97324),x97325)))+P24(f329(f48(f329(f329(f82(a875),x97321),x97322),x97323),f329(f329(f264(a875,a875),f329(f329(f81(a875),f329(f329(f82(a875),x97321),x97324)),f329(f329(f39(a875),f329(f329(f82(a875),x97321),x97325)),x97323))),f45(a875,f329(f329(f82(a875),x97321),x97325),x97323)))) % 178.07/177.94 [10042]~P70(x100422)+~P24(f329(f62(x100421),x100424))+E(f329(f329(f6(x100421,x100422),x100423),f329(f249(x100421),f329(f329(f18(x100421,a869,a869),f329(f329(f8(a869,f883(a869,a869),x100421),a327),f329(f329(f7(x100421,f883(x100421,a869),a869),f331(x100421)),x100424))),f329(f329(f7(x100421,f883(x100421,a869),a869),f331(x100421)),x100425)))),f329(f329(f6(x100421,x100422),f329(f329(f7(x100421,x100422,x100422),f329(f329(f18(x100421,x100422,f883(x100422,x100422)),f329(f329(f8(a869,f883(x100422,f883(x100422,x100422)),x100421),f102(x100422)),f329(f329(f7(x100421,f883(x100421,a869),a869),f331(x100421)),x100425))),x100423)),f2(x100422))),x100424)) % 178.07/177.94 [8234]~E(f329(f329(f127(x82341),x82342),x82345),f329(f329(f127(x82341),x82343),x82344))+E(f329(f329(f127(x82341),f329(f329(f137(x82341),f329(f194(f876(x82341)),x82342)),x82343)),x82344),x82345)+P24(f329(f329(f243(a875),f329(f194(f876(x82341)),x82343)),f329(f194(f876(x82341)),x82342))) % 178.07/177.94 [8432]~E(f329(f329(f127(x84322),x84323),x84321),f329(f329(f127(x84322),x84324),x84325))+E(x84321,f329(f329(f127(x84322),f329(f329(f137(x84322),f329(f194(f876(x84322)),x84323)),x84324)),x84325))+~P24(f329(f329(f243(a875),f329(f194(f876(x84322)),x84323)),f329(f194(f876(x84322)),x84324))) % 178.07/177.94 [8522]~E(f329(f329(f81(a875),f329(f329(f82(a875),x85223),x85224)),x85221),f329(f329(f81(a875),f329(f329(f82(a875),x85222),x85224)),x85225))+~P24(f329(f329(f243(a875),x85223),x85222))+E(x85221,f329(f329(f81(a875),f329(f329(f82(a875),f329(f329(f22(a875),x85222),x85223)),x85224)),x85225)) % 178.07/177.94 [8523]~E(f329(f329(f81(a875),f329(f329(f82(a875),x85231),x85233)),x85234),f329(f329(f81(a875),f329(f329(f82(a875),x85232),x85233)),x85235))+~P24(f329(f329(f243(a875),x85232),x85231))+E(f329(f329(f81(a875),f329(f329(f82(a875),f329(f329(f22(a875),x85231),x85232)),x85233)),x85234),x85235) % 178.07/177.94 [8680]E(f329(f329(f81(a875),f329(f329(f82(a875),x86801),x86802)),x86803),f329(f329(f81(a875),f329(f329(f82(a875),x86804),x86802)),x86805))+~P24(f329(f329(f243(a875),x86804),x86801))+~E(x86805,f329(f329(f81(a875),f329(f329(f82(a875),f329(f329(f22(a875),x86801),x86804)),x86802)),x86803)) % 178.07/177.94 [8681]E(f329(f329(f81(a875),f329(f329(f82(a875),x86811),x86812)),x86813),f329(f329(f81(a875),f329(f329(f82(a875),x86814),x86812)),x86815))+~P24(f329(f329(f243(a875),x86814),x86811))+~E(f329(f329(f81(a875),f329(f329(f82(a875),f329(f329(f22(a875),x86811),x86814)),x86812)),x86813),x86815) % 178.07/177.94 [9541]~P59(x95412)+~P24(f329(f62(x95411),x95415))+E(f329(f329(f9(x95411,x95412),f329(f329(f18(x95411,x95412,x95412),f329(f329(f8(x95412,f883(x95412,x95412),x95411),f287(x95412)),x95413)),x95414)),x95415),f329(f329(f287(x95412),f329(f329(f9(x95411,x95412),x95413),x95415)),f329(f329(f9(x95411,x95412),x95414),x95415))) % 178.07/177.94 [9666]~E(f764(x96665,x96664,x96663,x96662,x96661),f765(x96665,x96664,x96663,x96662,x96661))+P24(f329(f329(f331(f882(x96661,x96661)),f329(f329(f264(x96661,x96661),x96662),x96663)),f305(x96661,x96664)))+~P24(f329(f329(f331(f882(x96661,x96661)),f329(f329(f264(x96661,x96661),x96662),x96663)),f305(x96661,f329(f329(f116(f883(f882(x96661,x96661),a869)),x96664),x96665)))) % 178.07/177.94 [9667]~E(f767(x96675,x96674,x96673,x96672,x96671),f768(x96675,x96674,x96673,x96672,x96671))+P24(f329(f329(f331(f882(x96671,x96671)),f329(f329(f264(x96671,x96671),x96672),x96673)),f305(x96671,x96674)))+~P24(f329(f329(f331(f882(x96671,x96671)),f329(f329(f264(x96671,x96671),x96672),x96673)),f305(x96671,f329(f329(f116(f883(f882(x96671,x96671),a869)),x96674),x96675)))) % 178.07/177.94 [9877]P24(f329(f329(f331(f882(x98771,x98771)),f329(f329(f264(x98771,x98771),x98772),f768(x98775,x98774,x98773,x98772,x98771))),f305(x98771,x98774)))+P24(f329(f329(f331(f882(x98771,x98771)),f329(f329(f264(x98771,x98771),x98772),x98773)),f305(x98771,x98774)))+~P24(f329(f329(f331(f882(x98771,x98771)),f329(f329(f264(x98771,x98771),x98772),x98773)),f305(x98771,f329(f329(f116(f883(f882(x98771,x98771),a869)),x98774),x98775)))) % 178.07/177.94 [9956]P24(f329(f329(f331(f882(x99561,x99561)),f329(f329(f264(x99561,x99561),f765(x99565,x99564,x99563,x99562,x99561)),x99563)),f305(x99561,x99564)))+P24(f329(f329(f331(f882(x99561,x99561)),f329(f329(f264(x99561,x99561),x99562),x99563)),f305(x99561,x99564)))+~P24(f329(f329(f331(f882(x99561,x99561)),f329(f329(f264(x99561,x99561),x99562),x99563)),f305(x99561,f329(f329(f116(f883(f882(x99561,x99561),a869)),x99564),x99565)))) % 178.07/177.94 [9992]P24(f329(f329(f331(f882(x99921,x99921)),f329(f329(f264(x99921,x99921),x99922),x99923)),f305(x99921,x99924)))+P24(f329(f329(f331(f882(x99921,x99921)),f329(f329(f264(x99921,x99921),f764(x99925,x99924,x99923,x99922,x99921)),f765(x99925,x99924,x99923,x99922,x99921))),x99925))+~P24(f329(f329(f331(f882(x99921,x99921)),f329(f329(f264(x99921,x99921),x99922),x99923)),f305(x99921,f329(f329(f116(f883(f882(x99921,x99921),a869)),x99924),x99925)))) % 178.07/177.94 [9993]P24(f329(f329(f331(f882(x99931,x99931)),f329(f329(f264(x99931,x99931),x99932),x99933)),f305(x99931,x99934)))+P24(f329(f329(f331(f882(x99931,x99931)),f329(f329(f264(x99931,x99931),f768(x99935,x99934,x99933,x99932,x99931)),f767(x99935,x99934,x99933,x99932,x99931))),x99935))+~P24(f329(f329(f331(f882(x99931,x99931)),f329(f329(f264(x99931,x99931),x99932),x99933)),f305(x99931,f329(f329(f116(f883(f882(x99931,x99931),a869)),x99934),x99935)))) % 178.07/177.94 [10113]~P24(f329(f329(f331(f882(f876(x101131),f876(x101131))),f329(f329(f264(f876(x101131),f876(x101131)),x101134),x101135)),f157(x101131,x101132)))+~P24(f329(f329(f331(f882(x101131,x101131)),x101133),f329(f171(f882(x101131,x101131)),f329(f329(f181(x101131,x101131),x101134),x101135))))+P24(f329(f329(f268(x101131,x101131,a869),f329(f329(f7(x101131,f883(f882(x101131,x101131),a869),f883(x101131,a869)),f329(f329(f8(f883(x101131,f883(f883(f882(x101131,x101131),a869),a869)),f883(f883(f882(x101131,x101131),a869),f883(x101131,a869)),x101131),f7(x101131,f883(f882(x101131,x101131),a869),a869)),f329(f329(f8(f883(x101131,f882(x101131,x101131)),f883(x101131,f883(f883(f882(x101131,x101131),a869),a869)),x101131),f329(f8(f882(x101131,x101131),f883(f883(f882(x101131,x101131),a869),a869),x101131),f331(f882(x101131,x101131)))),f264(x101131,x101131)))),x101132)),x101133)) % 178.07/177.94 [9569]~P24(f329(f329(f243(a875),x95693),x95692))+~P24(f329(f329(f244(a875),f329(f329(f81(a875),f329(f329(f82(a875),x95693),x95694)),x95691)),f329(f329(f81(a875),f329(f329(f82(a875),x95692),x95694)),x95695)))+P24(f329(f329(f244(a875),x95691),f329(f329(f81(a875),f329(f329(f82(a875),f329(f329(f22(a875),x95692),x95693)),x95694)),x95695))) % 178.07/177.94 [9570]~P24(f329(f329(f243(a875),x95703),x95702))+~P24(f329(f329(f243(a875),f329(f329(f81(a875),f329(f329(f82(a875),x95703),x95704)),x95701)),f329(f329(f81(a875),f329(f329(f82(a875),x95702),x95704)),x95705)))+P24(f329(f329(f243(a875),x95701),f329(f329(f81(a875),f329(f329(f82(a875),f329(f329(f22(a875),x95702),x95703)),x95704)),x95705))) % 178.07/177.94 [9588]~P24(f329(f329(f243(a875),x95881),x95884))+P24(f329(f329(f244(a875),f329(f329(f81(a875),f329(f329(f82(a875),x95881),x95882)),x95883)),f329(f329(f81(a875),f329(f329(f82(a875),x95884),x95882)),x95885)))+~P24(f329(f329(f244(a875),x95883),f329(f329(f81(a875),f329(f329(f82(a875),f329(f329(f22(a875),x95884),x95881)),x95882)),x95885))) % 178.07/177.94 [9589]~P24(f329(f329(f243(a875),x95891),x95894))+P24(f329(f329(f243(a875),f329(f329(f81(a875),f329(f329(f82(a875),x95891),x95892)),x95893)),f329(f329(f81(a875),f329(f329(f82(a875),x95894),x95892)),x95895)))+~P24(f329(f329(f243(a875),x95893),f329(f329(f81(a875),f329(f329(f82(a875),f329(f329(f22(a875),x95894),x95891)),x95892)),x95895))) % 178.07/177.94 [9700]~P24(f329(f329(f243(a875),x97002),x97001))+~P24(f329(f329(f244(a875),f329(f329(f81(a875),f329(f329(f82(a875),x97001),x97003)),x97004)),f329(f329(f81(a875),f329(f329(f82(a875),x97002),x97003)),x97005)))+P24(f329(f329(f244(a875),f329(f329(f81(a875),f329(f329(f82(a875),f329(f329(f22(a875),x97001),x97002)),x97003)),x97004)),x97005)) % 178.07/177.94 [9701]~P24(f329(f329(f243(a875),x97012),x97011))+~P24(f329(f329(f243(a875),f329(f329(f81(a875),f329(f329(f82(a875),x97011),x97013)),x97014)),f329(f329(f81(a875),f329(f329(f82(a875),x97012),x97013)),x97015)))+P24(f329(f329(f243(a875),f329(f329(f81(a875),f329(f329(f82(a875),f329(f329(f22(a875),x97011),x97012)),x97013)),x97014)),x97015)) % 178.07/177.94 [9754]~P24(f329(f329(f243(a875),x97544),x97541))+P24(f329(f329(f244(a875),f329(f329(f81(a875),f329(f329(f82(a875),x97541),x97542)),x97543)),f329(f329(f81(a875),f329(f329(f82(a875),x97544),x97542)),x97545)))+~P24(f329(f329(f244(a875),f329(f329(f81(a875),f329(f329(f82(a875),f329(f329(f22(a875),x97541),x97544)),x97542)),x97543)),x97545)) % 178.07/177.94 [9755]~P24(f329(f329(f243(a875),x97554),x97551))+P24(f329(f329(f243(a875),f329(f329(f81(a875),f329(f329(f82(a875),x97551),x97552)),x97553)),f329(f329(f81(a875),f329(f329(f82(a875),x97554),x97552)),x97555)))+~P24(f329(f329(f243(a875),f329(f329(f81(a875),f329(f329(f82(a875),f329(f329(f22(a875),x97551),x97554)),x97552)),x97553)),x97555)) % 178.07/177.94 [9977]~P9(x99771,x99772,x99775,x99773)+~P24(f329(f329(f331(f882(x99771,x99771)),x99774),x99775))+P24(f329(f329(f268(x99771,x99771,a869),f329(f329(f7(x99771,f883(x99771,x99772),f883(x99771,a869)),f329(f329(f8(f883(x99772,a869),f883(f883(x99771,x99772),f883(x99771,a869)),x99771),f8(x99772,a869,x99771)),f329(f329(f8(x99772,f883(x99772,a869),x99771),a326),x99773))),x99773)),x99774)) % 178.07/177.94 [6775]~E(f329(x67754,x67755),f206(x67752))+E(f329(f184(x67751,x67752,x67753,x67754),x67755),f329(f236(x67752),x67756))+~E(f329(x67753,x67755),f329(f236(x67752),x67756)) % 178.07/177.94 [6875]~E(f329(x68753,x68756),f206(x68751))+E(f329(f238(f879(x68751),x68752,f206(x68751),x68753),f329(x68754,x68755)),f206(x68751))+~E(f329(x68754,x68755),f329(f236(x68752),x68756)) % 178.07/177.94 [7461]E(f329(x74611,x74612),f206(x74613))+~E(f329(f184(x74615,x74613,x74616,x74611),x74612),f329(f236(x74613),x74614))+E(f329(x74611,x74612),f329(f236(x74613),x74614)) % 178.07/177.94 [7497]~E(f329(f184(x74976,x74973,x74975,x74971),x74972),f329(f236(x74973),x74974))+E(f329(x74971,x74972),f329(f236(x74973),x74974))+E(f329(x74975,x74972),f329(f236(x74973),x74974)) % 178.07/177.94 [8392]~P15(x83926,x83921,x83922,x83924)+E(f329(f74(x83921,x83921,x83921,f329(x83922,x83923)),f329(x83924,x83925)),f329(f74(x83921,x83921,x83921,f329(x83924,x83925)),f329(x83922,x83923)))+~P24(f329(f62(x83926),x83925)) % 178.07/177.94 [8813]~P21(x88131,x88133,x88135,x88136)+~P21(x88133,x88132,x88134,f329(f308(x88131,x88133,x88135),x88136))+P21(x88131,x88132,f329(f74(x88133,x88132,x88131,x88134),x88135),x88136) % 178.07/177.94 [9379]~P24(f329(f329(x93793,x93792),x93796))+~P24(f329(f329(x93794,x93795),x93792))+P24(f329(f329(f331(x93791),x93792),f297(x93791,x93793,x93794,x93795,x93796))) % 178.07/177.94 [9380]~P24(f329(f329(x93804,x93802),x93806))+~P24(f329(f329(x93803,x93805),x93802))+P24(f329(f329(f331(x93801),x93802),f294(x93801,x93803,x93804,x93805,x93806))) % 178.07/177.94 [9489]E(x94891,x94892)+E(x94893,x94894)+~P24(f329(f329(f331(f882(f876(x94895),f876(x94895))),f329(f329(f264(f876(x94895),f876(x94895)),f329(f329(f150(x94895),x94893),x94891)),f329(f329(f150(x94895),x94894),x94892))),f156(x94895,x94896))) % 178.07/177.94 [9498]~E(x94982,x94984)+P24(f329(f329(f331(f882(f876(x94981),f876(x94981))),f329(f329(f264(f876(x94981),f876(x94981)),f329(f329(f150(x94981),x94982),x94983)),f329(f329(f150(x94981),x94984),x94985))),f146(x94981,x94986)))+~P24(f329(f329(f331(f882(f876(x94981),f876(x94981))),f329(f329(f264(f876(x94981),f876(x94981)),x94983),x94985)),f146(x94981,x94986))) % 178.07/177.94 [9499]~E(x94992,x94994)+P24(f329(f329(f331(f882(f876(x94991),f876(x94991))),f329(f329(f264(f876(x94991),f876(x94991)),f329(f329(f150(x94991),x94992),x94993)),f329(f329(f150(x94991),x94994),x94995))),f144(x94991,x94996)))+~P24(f329(f329(f331(f882(f876(x94991),f876(x94991))),f329(f329(f264(f876(x94991),f876(x94991)),x94993),x94995)),f144(x94991,x94996))) % 178.07/177.94 [9500]~E(x95002,x95004)+P24(f329(f329(f331(f882(f876(x95001),f876(x95001))),f329(f329(f264(f876(x95001),f876(x95001)),f329(f329(f150(x95001),x95002),x95003)),f329(f329(f150(x95001),x95004),x95005))),f156(x95001,x95006)))+~P24(f329(f329(f331(f882(f876(x95001),f876(x95001))),f329(f329(f264(f876(x95001),f876(x95001)),x95003),x95005)),f156(x95001,x95006))) % 178.07/177.94 [9501]~E(x95012,x95014)+P24(f329(f329(f331(f882(f876(x95011),f876(x95011))),f329(f329(f264(f876(x95011),f876(x95011)),f329(f329(f127(x95011),x95012),x95013)),f329(f329(f127(x95011),x95014),x95015))),f156(x95011,x95016)))+~P24(f329(f329(f331(f882(f876(x95011),f876(x95011))),f329(f329(f264(f876(x95011),f876(x95011)),x95013),x95015)),f156(x95011,x95016))) % 178.07/177.94 [9502]~E(x95023,x95025)+P24(f329(f329(f331(f882(f876(x95021),f876(x95021))),f329(f329(f264(f876(x95021),f876(x95021)),f329(f329(f127(x95021),x95022),x95023)),f329(f329(f127(x95021),x95024),x95025))),f156(x95021,x95026)))+~P24(f329(f329(f331(f882(f876(x95021),f876(x95021))),f329(f329(f264(f876(x95021),f876(x95021)),x95022),x95024)),f156(x95021,x95026))) % 178.07/177.94 [9557]E(x95571,x95572)+P24(f329(f329(f331(f882(f876(x95573),f876(x95573))),f329(f329(f264(f876(x95573),f876(x95573)),x95571),x95572)),f156(x95573,x95574)))+~P24(f329(f329(f331(f882(f876(x95573),f876(x95573))),f329(f329(f264(f876(x95573),f876(x95573)),f329(f329(f150(x95573),x95575),x95571)),f329(f329(f150(x95573),x95576),x95572))),f156(x95573,x95574))) % 178.07/177.94 [9704]~E(x97043,x97045)+P24(f329(f329(f331(f882(f876(x97041),f876(x97041))),f329(f329(f264(f876(x97041),f876(x97041)),f329(f329(f127(x97041),x97042),f329(f329(f150(x97041),x97043),f119(x97041)))),f329(f329(f127(x97041),x97044),f329(f329(f150(x97041),x97045),f119(x97041))))),f156(x97041,x97046)))+~P24(f329(f329(f331(f882(f876(x97041),f876(x97041))),f329(f329(f264(f876(x97041),f876(x97041)),x97042),x97044)),f156(x97041,x97046))) % 178.07/177.94 [9720]E(f329(x97201,x97202),f206(x97203))+~E(f329(f238(f879(x97206),x97203,f206(x97206),x97204),f329(x97201,x97202)),f206(x97206))+E(f329(x97204,f579(x97202,x97201,x97204,x97205,x97206,x97203)),f206(x97206)) % 178.07/177.94 [9721]E(f329(x97211,x97212),f206(x97213))+~E(f329(f238(f879(x97216),x97213,f206(x97216),x97214),f329(x97211,x97212)),f206(x97216))+E(f329(f236(x97213),f579(x97212,x97211,x97214,x97215,x97216,x97213)),f329(x97211,x97212)) % 178.07/177.94 [9758]E(x97581,x97582)+E(x97583,x97584)+~P24(f329(f329(f331(f882(f876(x97585),f876(x97585))),f329(f329(f264(f876(x97585),f876(x97585)),f329(f329(f127(x97585),x97583),f329(f329(f150(x97585),x97581),f119(x97585)))),f329(f329(f127(x97585),x97584),f329(f329(f150(x97585),x97582),f119(x97585))))),f156(x97585,x97586))) % 178.07/177.94 [9783]E(x97831,x97832)+~P24(f329(f329(f331(f882(f876(x97833),f876(x97833))),f329(f329(f264(f876(x97833),f876(x97833)),f329(f329(f127(x97833),x97831),f329(f329(f150(x97833),x97835),f119(x97833)))),f329(f329(f127(x97833),x97832),f329(f329(f150(x97833),x97836),f119(x97833))))),f156(x97833,x97834)))+P24(f329(f329(f331(f882(f876(x97833),f876(x97833))),f329(f329(f264(f876(x97833),f876(x97833)),x97831),x97832)),f156(x97833,x97834))) % 178.07/177.94 [9819]~P24(f329(f329(f331(f882(f883(x98191,a869),f883(x98191,a869))),f329(f329(f264(f883(x98191,a869),f883(x98191,a869)),x98192),x98194)),f320(x98191,x98196)))+~P24(f329(f329(f331(f882(f883(x98191,a869),f883(x98191,a869))),f329(f329(f264(f883(x98191,a869),f883(x98191,a869)),x98193),x98195)),f320(x98191,x98196)))+P24(f329(f329(f331(f882(f883(x98191,a869),f883(x98191,a869))),f329(f329(f264(f883(x98191,a869),f883(x98191,a869)),f329(f329(f116(f883(x98191,a869)),x98192),x98193)),f329(f329(f116(f883(x98191,a869)),x98194),x98195))),f320(x98191,x98196))) % 178.07/177.94 [5223]~E(f329(x52233,x52236),x52235)+~E(x52234,f329(f236(x52231),x52236))+E(f329(f329(f207(x52231,x52232),x52233),x52234),f329(f236(x52232),x52235)) % 178.07/177.94 [5635]~E(f329(f329(f127(x56351),x56356),x56353),x56355)+E(f329(f329(f127(x56351),x56352),x56353),f329(f329(f150(x56351),x56354),x56355))+~E(x56352,f329(f329(f150(x56351),x56354),x56356)) % 178.07/177.94 [5636]~E(f329(f329(f127(x56361),x56366),x56363),x56365)+E(f329(f329(f127(x56361),x56362),x56363),f329(f329(f127(x56361),x56364),x56365))+~E(x56362,f329(f329(f127(x56361),x56364),x56366)) % 178.07/177.94 [5638]E(f329(f329(f127(x56381),x56382),x56383),f329(f329(f150(x56381),x56384),x56385))+~E(f329(f329(f150(x56381),x56384),x56386),x56382)+~E(x56385,f329(f329(f127(x56381),x56386),x56383)) % 178.07/177.94 [5640]~E(f329(f329(f127(x56401),x56402),x56406),x56404)+E(f329(f329(f127(x56401),x56402),x56403),f329(f329(f127(x56401),x56404),x56405))+~E(x56403,f329(f329(f127(x56401),x56406),x56405)) % 178.07/177.94 [6769]E(f329(x67691,x67692),f329(x67693,x67692))+~E(f329(f329(f153(x67694,x67695),x67691),x67696),f329(f329(f153(x67694,x67695),x67693),x67696))+~P24(f329(f329(f331(x67694),x67692),f329(f171(x67694),x67696))) % 178.07/177.94 [7154]~P15(x71544,x71545,x71546,x71541)+E(f329(f329(x71541,x71542),x71543),f329(f329(f65(x71544,x71545,x71546),x71543),x71542))+~P24(f329(f62(x71544),x71542)) % 178.07/177.94 [7220]~E(x72202,f329(x72204,x72206))+~P24(f329(f329(f331(x72203),x72206),x72205))+P24(f329(f329(f331(x72201),x72202),f329(f308(x72203,x72201,x72204),x72205))) % 178.07/177.94 [7221]~E(f329(x72214,x72212),x72216)+~P24(f329(f329(f331(x72213),x72216),x72215))+P24(f329(f329(f331(x72211),x72212),f329(f309(x72211,x72213,x72214),x72215))) % 178.07/177.94 [7675]~P33(x76751,x76752,x76754,x76756)+P33(x76751,x76752,f329(f329(f150(x76751),x76753),x76754),f329(f329(f150(x76751),x76755),x76756))+~P24(f329(f329(x76752,x76753),x76755)) % 178.07/177.94 [8688]~P52(x86884,x86885,x86881,x86882,x86886)+E(f329(x86881,f329(x86882,x86883)),x86883)+~P24(f329(f329(f331(x86885),x86883),x86886)) % 178.07/177.94 [9491]E(x94911,x94912)+E(f329(f194(f876(x94913)),x94914),f329(f194(f876(x94913)),x94915))+~P24(f329(f329(f331(f882(f876(x94913),f876(x94913))),f329(f329(f264(f876(x94913),f876(x94913)),f329(f329(f150(x94913),x94911),x94914)),f329(f329(f150(x94913),x94912),x94915))),f144(x94913,x94916))) % 178.07/177.94 [9553]~P12(x95531,x95532,x95533)+E(f329(f329(f65(x95531,x95532,x95533),x95534),x95535),x95536)+~P24(f329(f67(x95531,x95532,x95533,x95534,x95535),x95536)) % 178.07/177.94 [9560]E(f329(f194(f876(x95601)),x95602),f329(f194(f876(x95601)),x95603))+P24(f329(f329(f331(f882(f876(x95601),f876(x95601))),f329(f329(f264(f876(x95601),f876(x95601)),x95602),x95603)),f144(x95601,x95604)))+~P24(f329(f329(f331(f882(f876(x95601),f876(x95601))),f329(f329(f264(f876(x95601),f876(x95601)),f329(f329(f150(x95601),x95605),x95602)),f329(f329(f150(x95601),x95606),x95603))),f144(x95601,x95604))) % 178.07/177.94 [9582]~P24(f329(f329(f331(f882(x95821,x95821)),f329(f329(f264(x95821,x95821),x95822),x95824)),f305(x95821,x95826)))+P24(f329(f329(f331(f882(f876(x95821),f876(x95821))),f329(f329(f264(f876(x95821),f876(x95821)),f329(f329(f150(x95821),x95822),x95823)),f329(f329(f150(x95821),x95824),x95825))),f305(f876(x95821),f156(x95821,x95826))))+~P24(f329(f329(f331(f882(f876(x95821),f876(x95821))),f329(f329(f264(f876(x95821),f876(x95821)),x95823),x95825)),f305(f876(x95821),f156(x95821,x95826)))) % 178.07/177.94 [9764]~P24(f329(x97642,x97646))+~E(f329(f135(x97641,x97642),x97643),f329(f329(f150(x97641),x97644),x97645))+~P24(f329(f329(f331(x97641),x97646),f329(f171(x97641),f733(x97645,x97644,x97643,x97642,x97641)))) % 178.07/177.94 [9765]~P24(f329(x97654,x97656))+~E(f329(f329(f150(x97651),x97652),x97653),f329(f135(x97651,x97654),x97655))+~P24(f329(f329(f331(x97651),x97656),f329(f171(x97651),f734(x97655,x97654,x97653,x97652,x97651)))) % 178.07/177.94 [10070]~P70(x100702)+E(f329(f329(f6(x100701,x100702),f329(f329(f8(f883(x100703,a869),x100702,x100701),f329(f6(x100703,x100702),x100704)),f329(f329(f8(f883(x100703,a869),f883(x100703,a869),x100701),f249(x100703)),f329(f329(f8(f883(x100703,a869),f883(x100703,a869),x100701),f329(f18(x100703,a869,a869),f329(f329(f8(a869,f883(a869,a869),x100703),a327),f329(f329(f7(x100703,f883(x100703,a869),a869),f331(x100703)),x100705)))),f329(f7(x100703,x100701,a869),f329(f329(f8(x100701,f883(x100701,a869),x100703),a326),x100706)))))),f329(f308(x100703,x100701,x100706),x100705)),f329(f329(f6(x100703,x100702),x100704),x100705))+~P24(f329(f62(x100703),x100705)) % 178.07/177.94 [6826]~P105(x68263)+P24(f329(x68262,x68265))+E(f329(f135(x68261,x68262),f329(f329(f147(x68261,x68263,x68264),x68265),x68266)),f329(f135(x68261,x68262),x68266)) % 178.07/177.94 [6828]P24(f329(x68281,x68282))+~E(f166(x68283,x68281,x68284),f329(f329(f264(f876(x68283),f876(x68283)),x68285),x68286))+~P24(f329(f329(f331(x68283),x68282),f329(f171(x68283),x68285))) % 178.07/177.94 [6872]~P24(f329(x68722,x68726))+~E(f166(x68721,x68722,x68723),f329(f329(f264(f876(x68721),f876(x68721)),x68724),x68725))+~P24(f329(f329(f331(x68721),x68726),f329(f171(x68721),x68725))) % 178.07/177.94 [7541]~P11(x75411,x75412,x75413)+~P24(f329(f62(x75411),x75416))+E(f329(f329(f65(x75411,x75412,x75413),x75414),f329(f329(f307(x75411),x75415),x75416)),f329(f329(f65(x75411,x75412,x75413),f329(f329(x75413,x75415),x75414)),x75416)) % 178.07/177.94 [7591]~P105(x75912)+~P24(f329(f329(f243(x75912),f329(x75913,x75914)),f329(x75913,x75915)))+E(f329(f329(f147(x75911,x75912,x75913),x75914),f329(f329(f150(x75911),x75915),x75916)),f329(f329(f150(x75911),x75914),f329(f329(f150(x75911),x75915),x75916))) % 178.07/177.94 [7706]E(x77061,x77062)+~E(f329(f329(f266(x77063,x77064),x77061),f329(f16(f883(x77064,a869),x77063),x77065)),f329(f329(f266(x77063,x77064),x77062),f329(f16(f883(x77064,a869),x77063),x77065)))+~P24(f329(f329(f331(x77064),x77066),x77065)) % 178.07/177.94 [7770]~P11(x77701,x77702,x77703)+~P24(f329(f62(x77701),x77706))+E(f329(f329(f65(x77701,x77702,x77703),x77704),f329(f329(f307(x77701),x77705),x77706)),f329(f329(x77703,x77705),f329(f329(f65(x77701,x77702,x77703),x77704),x77706))) % 178.07/177.94 [7886]~P12(x78861,x78862,x78863)+~P24(f329(f62(x78861),x78866))+E(f329(f329(f65(x78861,x78862,x78863),f329(f329(x78863,x78864),x78865)),x78866),f329(f329(x78863,x78864),f329(f329(f65(x78861,x78862,x78863),x78865),x78866))) % 178.07/177.94 [7955]~P16(x79552,x79555,x79556,x79551)+~P24(f329(f62(x79552),x79554))+E(f329(x79551,f329(f329(f307(x79552),x79553),x79554)),f329(f74(x79555,x79555,x79555,f329(x79551,x79554)),f329(x79556,x79553))) % 178.07/177.94 [7993]~P105(x79932)+P24(f329(f329(f243(x79932),f329(x79933,x79934)),f329(x79933,x79935)))+E(f329(f329(f147(x79931,x79932,x79933),x79934),f329(f329(f150(x79931),x79935),x79936)),f329(f329(f150(x79931),x79935),f329(f329(f147(x79931,x79932,x79933),x79934),x79936))) % 178.07/177.94 [8135]~E(f329(f194(f876(x81351)),x81355),f329(f194(f876(x81352)),x81356))+~E(f329(f194(f876(x81351)),x81353),f329(f194(f876(x81352)),x81354))+E(f329(f329(f127(f882(x81351,x81352)),f329(f329(f181(x81351,x81352),x81353),x81354)),f329(f329(f181(x81351,x81352),x81355),x81356)),f329(f329(f181(x81351,x81352),f329(f329(f127(x81351),x81353),x81355)),f329(f329(f127(x81352),x81354),x81356))) % 178.07/177.94 [8249]~E(x82492,f329(f308(x82493,x82491,x82494),x82496))+P24(f329(f329(f243(f883(x82491,a869)),x82492),f329(f308(x82493,x82491,x82494),x82495)))+~P24(f329(f329(f243(f883(x82493,a869)),x82496),x82495)) % 178.07/177.94 [8350]~P105(x83505)+E(f329(x83501,x83502),f329(x83501,x83503))+E(f329(f329(f147(x83504,x83505,x83501),x83502),f329(f329(f147(x83504,x83505,x83501),x83503),x83506)),f329(f329(f147(x83504,x83505,x83501),x83503),f329(f329(f147(x83504,x83505,x83501),x83502),x83506))) % 178.07/177.94 [8385]~P21(x83853,x83851,x83854,x83855)+P21(x83853,x83851,f329(f329(f329(f73(x83853,x83851),x83854),x83856),x83852),x83855)+P24(f329(f329(f331(x83851),x83852),f329(f308(x83853,x83851,x83854),x83855))) % 178.07/177.94 [8531]~P24(f329(f329(f331(x85312),x85314),f329(x85316,x85313)))+~P24(f329(f329(f331(x85311),x85313),x85315))+P24(f329(f329(f331(f882(x85311,x85312)),f329(f329(f264(x85311,x85312),x85313),x85314)),f329(f329(f266(x85311,x85312),x85315),x85316))) % 178.07/177.94 [8991]~P70(x89912)+~P21(x89914,x89911,x89915,x89916)+E(f329(f329(f6(x89911,x89912),x89913),f329(f308(x89914,x89911,x89915),x89916)),f329(f329(f6(x89914,x89912),f329(f74(x89911,x89912,x89914,x89913),x89915)),x89916)) % 178.07/177.94 [8992]~P74(x89922)+~P21(x89924,x89921,x89925,x89926)+E(f329(f329(f9(x89921,x89922),x89923),f329(f308(x89924,x89921,x89925),x89926)),f329(f329(f9(x89924,x89922),f329(f74(x89921,x89922,x89924,x89923),x89925)),x89926)) % 178.07/177.94 [9040]~P35(x90402,x90405,x90401,x90403,x90406)+P24(f329(f329(x90401,f329(f329(f164(x90402),x90403),x90404)),f329(f329(f164(x90405),x90406),x90404)))+~P24(f329(f329(f244(a875),x90404),f329(f194(f876(x90405)),x90406))) % 178.07/177.94 [9041]~P35(x90412,x90415,x90411,x90413,x90416)+P24(f329(f329(x90411,f329(f329(f164(x90412),x90413),x90414)),f329(f329(f164(x90415),x90416),x90414)))+~P24(f329(f329(f244(a875),x90414),f329(f194(f876(x90412)),x90413))) % 178.07/177.94 [9250]~P15(x92503,x92501,x92506,x92502)+~P24(f329(f62(x92503),x92504))+E(f329(f74(x92501,x92501,x92501,f329(x92502,f329(f329(f22(f883(x92503,a869)),x92504),f329(f329(f307(x92503),x92505),f193(f883(x92503,a869)))))),f329(x92506,x92505)),f329(x92502,f329(f329(f307(x92503),x92505),x92504))) % 178.07/177.94 [9857]~E(f329(f308(x98572,x98574,x98576),f252(f883(x98572,a869))),f252(f883(x98574,a869)))+~E(f329(f308(x98571,x98573,x98575),f252(f883(x98571,a869))),f252(f883(x98573,a869)))+E(f329(f308(f882(x98571,x98572),f882(x98573,x98574),f269(x98571,x98573,x98572,x98574,x98575,x98576)),f252(f883(f882(x98571,x98572),a869))),f252(f883(f882(x98573,x98574),a869))) % 178.07/177.94 [9905]~P21(x99053,x99054,x99055,f329(x99056,f856(x99056,x99055,x99054,x99053,x99052,x99051)))+P21(x99053,x99054,x99055,f329(f329(f42(x99052,f883(x99053,a869)),x99051),x99056))+E(x99051,f193(f883(x99052,a869))) % 178.07/177.94 [9963]P21(x99636,x99635,x99634,f329(f329(f42(x99632,f883(x99636,a869)),x99631),x99633))+E(x99631,f193(f883(x99632,a869)))+P24(f329(f329(f331(x99632),f856(x99633,x99634,x99635,x99636,x99632,x99631)),x99631)) % 178.07/177.94 [9968]P24(f329(f329(f331(x99681),f738(x99682,x99683,x99684,x99685,x99686,x99681)),x99686))+P24(f329(f329(f243(f883(f882(x99681,x99684),a869)),f329(f329(f266(x99681,x99684),x99686),x99683)),f329(f329(f266(x99681,x99684),x99685),x99682)))+~P24(f329(f329(f243(f883(x99681,a869)),x99686),x99685)) % 178.07/177.94 [10006]P20(x100066,x100065,f329(f329(f307(f874(x100066)),f329(f329(f329(f93(x100066),x100064),x100063),x100062)),f193(f883(f874(x100066),a869))))+~P20(x100066,x100065,f329(f329(f307(f874(x100066)),f329(f329(f329(f93(x100066),x100064),x100063),x100061)),f193(f883(f874(x100066),a869))))+P24(f329(f329(x100061,f396(x100062,x100061,x100063,x100064,x100065,x100066)),f408(x100062,x100061,x100063,x100064,x100065,x100066))) % 178.07/177.94 [10007]P20(x100076,x100075,f329(f329(f307(f874(x100076)),f329(f329(f329(f93(x100076),x100071),x100073),x100072)),f193(f883(f874(x100076),a869))))+~P20(x100076,x100075,f329(f329(f307(f874(x100076)),f329(f329(f329(f93(x100076),x100074),x100073),x100072)),f193(f883(f874(x100076),a869))))+P24(f329(f329(x100071,f416(x100071,x100072,x100073,x100074,x100075,x100076)),f428(x100071,x100072,x100073,x100074,x100075,x100076))) % 178.07/177.94 [10045]~P20(x100451,x100452,f329(f329(f307(f874(x100451)),f329(f329(f329(f93(x100451),x100453),x100454),x100456)),f193(f883(f874(x100451),a869))))+P20(x100451,x100452,f329(f329(f307(f874(x100451)),f329(f329(f329(f93(x100451),x100453),x100454),x100455)),f193(f883(f874(x100451),a869))))+~P24(f329(f329(x100455,f396(x100455,x100456,x100454,x100453,x100452,x100451)),f408(x100455,x100456,x100454,x100453,x100452,x100451))) % 178.07/177.94 [10046]~P20(x100461,x100462,f329(f329(f307(f874(x100461)),f329(f329(f329(f93(x100461),x100466),x100464),x100465)),f193(f883(f874(x100461),a869))))+P20(x100461,x100462,f329(f329(f307(f874(x100461)),f329(f329(f329(f93(x100461),x100463),x100464),x100465)),f193(f883(f874(x100461),a869))))+~P24(f329(f329(x100466,f416(x100463,x100465,x100464,x100466,x100462,x100461)),f428(x100463,x100465,x100464,x100466,x100462,x100461))) % 178.07/177.94 [10081]~P24(f329(f329(f243(f883(x100812,a869)),f329(x100814,f738(x100816,x100814,x100812,x100815,x100813,x100811))),f329(x100816,f738(x100816,x100814,x100812,x100815,x100813,x100811))))+~P24(f329(f329(f243(f883(x100811,a869)),x100813),x100815))+P24(f329(f329(f243(f883(f882(x100811,x100812),a869)),f329(f329(f266(x100811,x100812),x100813),x100814)),f329(f329(f266(x100811,x100812),x100815),x100816))) % 178.07/177.94 [7725]~P24(f329(x77251,x77255))+~P24(f329(x77256,x77254))+P24(f329(x77251,f329(f267(x77252,x77253),f329(f329(f264(x77252,x77253),x77254),x77255)))) % 178.07/177.94 [7726]~P24(f329(x77261,x77264))+~P24(f329(x77266,x77265))+P24(f329(x77261,f329(f263(x77262,x77263),f329(f329(f264(x77262,x77263),x77264),x77265)))) % 178.07/177.94 [7748]~E(f329(f194(f876(x77481)),x77483),f329(f194(f876(x77484)),x77485))+~E(f329(f329(f177(x77481,x77484),f329(f329(f181(x77481,x77484),x77483),x77485)),x77482),f329(f236(x77484),x77486))+P24(f329(f329(f331(x77481),x77482),f329(f171(x77481),x77483))) % 178.07/177.94 [7775]~P24(f329(f329(x77754,x77756),x77755))+~P24(f329(f329(f331(x77751),x77756),x77753))+P24(f329(f329(f329(f43(x77751,f883(x77752,a869)),x77753),x77754),x77755)) % 178.07/177.94 [8084]~P24(f329(f329(f331(x80841),x80842),f329(x80845,x80846)))+~P24(f329(f329(f331(x80843),x80846),x80844))+P24(f329(f329(f331(x80841),x80842),f329(f329(f43(x80843,f883(x80841,a869)),x80844),x80845))) % 178.07/177.94 [8127]P24(f329(f329(x81271,x81272),x81273))+~P24(f329(f329(x81274,x81272),x81273))+~P24(f329(f329(f243(f883(x81275,f883(x81276,a869))),x81274),x81271)) % 178.07/177.94 [8273]P24(f329(f329(x82731,x82732),x82733))+~P24(f329(f329(f331(x82734),x82732),x82735))+~P24(f329(f329(f329(f42(x82734,f883(x82736,a869)),x82735),x82731),x82733)) % 178.07/177.94 [8408]P24(f329(f329(f331(x84081),x84082),f329(x84083,x84084)))+~P24(f329(f329(f331(x84085),x84084),x84086))+~P24(f329(f329(f331(x84081),x84082),f329(f329(f42(x84085,f883(x84081,a869)),x84086),x84083))) % 178.07/177.94 [8600]~P24(f329(f329(f329(f329(a201,x86001),x86003),x86004),x86006))+~P24(f329(f329(f329(f329(a201,x86002),x86006),x86004),x86005))+P24(f329(f329(f329(f329(a201,f34(x86001,x86002)),x86003),x86004),x86005)) % 178.07/177.94 [8670]~P9(x86704,x86705,x86706,x86701)+E(f329(x86701,x86702),f329(x86701,x86703))+~P24(f329(f329(f331(f882(x86704,x86704)),f329(f329(f264(x86704,x86704),x86702),x86703)),x86706)) % 178.07/177.94 [8701]P24(f329(f329(f243(f883(x87011,a869)),x87012),f329(x87013,x87014)))+~P24(f329(f329(f331(x87015),x87014),x87016))+~P24(f329(f329(f243(f883(x87011,a869)),x87012),f329(f329(f42(x87015,f883(x87011,a869)),x87016),x87013))) % 178.07/177.94 [8729]~P50(x87293,x87294,f329(f284(x87294,x87293),x87295))+E(x87291,f193(f883(x87292,a869)))+E(f329(f329(f42(x87292,f883(x87293,a869)),x87291),f329(f329(f8(f883(x87294,a869),f883(x87293,a869),x87292),f283(x87294,x87293,x87295)),x87296)),f329(f283(x87294,x87293,x87295),f329(f329(f42(x87292,f883(x87294,a869)),x87291),x87296))) % 178.07/177.94 [8804]P24(f329(f329(f331(x88041),x88042),f329(f283(x88043,x88041,x88044),x88045)))+~P24(f329(f329(f331(x88043),x88046),x88045))+~P24(f329(f329(f331(f882(x88043,x88041)),f329(f329(f264(x88043,x88041),x88046),x88042)),x88044)) % 178.07/177.94 [8921]P24(f329(x89211,x89212))+~P24(f329(f329(f329(f329(a201,x89214),x89212),x89215),x89216))+P24(f329(f329(f329(f329(a201,f31(x89211,x89213,x89214)),x89212),x89215),x89216)) % 178.07/177.94 [8938]~P24(f329(x89381,x89384))+~P24(f329(f329(f329(f329(a201,x89382),x89384),x89385),x89386))+P24(f329(f329(f329(f329(a201,f31(x89381,x89382,x89383)),x89384),x89385),x89386)) % 178.07/177.94 [9113]P24(f329(f329(f243(f883(x91131,a869)),f329(f283(x91132,x91131,x91133),x91134)),f329(f283(x91132,x91131,x91135),x91136)))+~P24(f329(f329(f243(f883(x91132,a869)),x91134),x91136))+~P24(f329(f329(f243(f883(f882(x91132,x91131),a869)),x91133),x91135)) % 178.07/177.94 [9201]P24(f329(x92011,x92012))+P24(f329(f329(f329(f329(a201,x92013),x92012),x92014),x92015))+~P24(f329(f329(f329(f329(a201,f31(x92011,x92016,x92013)),x92012),x92014),x92015)) % 178.07/177.94 [9206]~P24(f329(x92065,x92062))+P24(f329(f329(f329(f329(a201,x92061),x92062),x92063),x92064))+~P24(f329(f329(f329(f329(a201,f31(x92065,x92061,x92066)),x92062),x92063),x92064)) % 178.07/177.94 [9257]P24(f329(f329(f329(f329(a201,x92571),x92572),x92573),x92574))+P24(f329(f329(f329(f329(a201,x92575),x92572),x92573),x92574))+~P24(f329(f329(f329(f329(a201,f31(x92576,x92571,x92575)),x92572),x92573),x92574)) % 178.07/177.94 [9299]~P24(f329(f329(f331(x92992),x92996),x92994))+~P24(f329(f329(f243(f883(x92991,a869)),x92993),x92995))+P24(f329(f329(f243(f883(f882(x92991,x92992),a869)),f329(f329(f266(x92991,x92992),x92993),f329(f16(f883(x92992,a869),x92991),x92994))),f329(f329(f266(x92991,x92992),x92995),f329(f16(f883(x92992,a869),x92991),x92994)))) % 178.07/177.94 [9312]~P35(x93121,x93122,x93123,x93125,x93126)+P24(f329(f329(f268(x93121,x93122,a869),x93123),x93124))+~P24(f329(f329(f331(f882(x93121,x93122)),x93124),f329(f171(f882(x93121,x93122)),f329(f329(f181(x93121,x93122),x93125),x93126)))) % 178.07/177.94 [9445]~E(x94453,x94455)+P24(f329(f329(f331(f882(f876(x94451),f876(x94451))),f329(f329(f264(f876(x94451),f876(x94451)),f329(f329(f150(x94451),x94452),x94453)),f329(f329(f150(x94451),x94454),x94455))),f156(x94451,x94456)))+~P24(f329(f329(f331(f882(x94451,x94451)),f329(f329(f264(x94451,x94451),x94452),x94454)),x94456)) % 178.07/177.94 [9451]~E(f329(f194(f876(x94511)),x94515),f329(f194(f876(x94512)),x94516))+E(f186(x94511,x94512,f187(x94511,x94512,x94513,f329(f329(f22(f883(x94511,a869)),x94514),f329(f171(x94511),x94515))),x94515,x94516),f187(x94511,x94512,f186(x94511,x94512,x94513,x94515,x94516),x94514))+~P24(f329(f329(f243(f883(x94511,a869)),f329(f171(x94511),x94515)),x94514)) % 178.07/177.94 [9452]~E(f329(f194(f876(x94521)),x94523),f329(f194(f876(x94521)),x94525))+P24(f329(f329(f331(f882(f876(x94521),f876(x94521))),f329(f329(f264(f876(x94521),f876(x94521)),f329(f329(f150(x94521),x94522),x94523)),f329(f329(f150(x94521),x94524),x94525))),f144(x94521,x94526)))+~P24(f329(f329(f331(f882(x94521,x94521)),f329(f329(f264(x94521,x94521),x94522),x94524)),x94526)) % 178.07/177.94 [9482]P24(f329(f329(f331(f882(x94821,x94821)),f329(f329(f264(x94821,x94821),x94822),x94823)),f329(f329(f188(f882(x94821,x94821),a869),f329(a118,x94824)),x94825)))+~P24(f329(f329(f331(f882(x94821,x94821)),f329(f329(f264(x94821,x94821),x94826),x94823)),x94825))+~P24(f329(f329(f331(f882(x94821,x94821)),f329(f329(f264(x94821,x94821),x94822),x94826)),f329(f329(f188(f882(x94821,x94821),a869),x94824),x94825))) % 178.07/177.94 [9483]P24(f329(f329(f331(f882(x94831,x94831)),f329(f329(f264(x94831,x94831),x94832),x94833)),f329(f329(f188(f882(x94831,x94831),a869),f329(a118,x94834)),x94835)))+~P24(f329(f329(f331(f882(x94831,x94831)),f329(f329(f264(x94831,x94831),x94832),x94836)),x94835))+~P24(f329(f329(f331(f882(x94831,x94831)),f329(f329(f264(x94831,x94831),x94836),x94833)),f329(f329(f188(f882(x94831,x94831),a869),x94834),x94835))) % 178.07/177.94 [9487]~P24(f329(f329(f331(x94874),x94875),x94876))+P24(f329(f329(f243(f883(x94871,a869)),x94872),x94873))+~P24(f329(f329(f243(f883(f882(x94871,x94874),a869)),f329(f329(f266(x94871,x94874),x94872),f329(f16(f883(x94874,a869),x94871),x94876))),f329(f329(f266(x94871,x94874),x94873),f329(f16(f883(x94874,a869),x94871),x94876)))) % 178.07/177.94 [9531]E(x95311,x95312)+~P24(f329(f329(f331(f882(f876(x95313),f876(x95313))),f329(f329(f264(f876(x95313),f876(x95313)),f329(f329(f150(x95313),x95311),x95315)),f329(f329(f150(x95313),x95312),x95316))),f146(x95313,x95314)))+P24(f329(f329(f331(f882(x95313,x95313)),f329(f329(f264(x95313,x95313),x95311),x95312)),x95314)) % 178.07/177.94 [9532]E(x95321,x95322)+~P24(f329(f329(f331(f882(f876(x95323),f876(x95323))),f329(f329(f264(f876(x95323),f876(x95323)),f329(f329(f150(x95323),x95321),x95325)),f329(f329(f150(x95323),x95322),x95326))),f144(x95323,x95324)))+P24(f329(f329(f331(f882(x95323,x95323)),f329(f329(f264(x95323,x95323),x95321),x95322)),x95324)) % 178.07/177.94 [9533]E(x95331,x95332)+~P24(f329(f329(f331(f882(f876(x95333),f876(x95333))),f329(f329(f264(f876(x95333),f876(x95333)),f329(f329(f150(x95333),x95331),x95335)),f329(f329(f150(x95333),x95332),x95336))),f156(x95333,x95334)))+P24(f329(f329(f331(f882(x95333,x95333)),f329(f329(f264(x95333,x95333),x95331),x95332)),x95334)) % 178.07/177.94 [9568]P24(f329(f329(f331(f882(f876(x95681),f876(x95681))),f329(f329(f264(f876(x95681),f876(x95681)),f329(f329(f150(x95681),x95682),x95683)),f329(f329(f150(x95681),x95684),x95685))),f157(x95681,x95686)))+~P24(f329(f329(f331(f882(f876(x95681),f876(x95681))),f329(f329(f264(f876(x95681),f876(x95681)),x95683),x95685)),f157(x95681,x95686)))+~P24(f329(f329(f331(f882(x95681,x95681)),f329(f329(f264(x95681,x95681),x95682),x95684)),x95686)) % 178.07/177.94 [9586]P24(f329(x95861,x95862))+~P24(f329(x95861,f846(x95861,x95863,x95864,x95865,x95866)))+~P24(f329(f329(f331(x95866),x95862),f329(f329(f43(x95865,f883(x95866,a869)),x95864),x95863))) % 178.07/177.94 [9591]~P24(f329(f329(f331(f882(f876(x95911),f876(x95911))),f329(f329(f264(f876(x95911),f876(x95911)),f329(f329(f150(x95911),x95912),x95915)),f329(f329(f150(x95911),x95913),x95916))),f146(x95911,x95914)))+P24(f329(f329(f331(f882(f876(x95911),f876(x95911))),f329(f329(f264(f876(x95911),f876(x95911)),x95915),x95916)),f146(x95911,x95914)))+P24(f329(f329(f331(f882(x95911,x95911)),f329(f329(f264(x95911,x95911),x95912),x95913)),x95914)) % 178.07/177.94 [9592]~P24(f329(f329(f331(f882(f876(x95921),f876(x95921))),f329(f329(f264(f876(x95921),f876(x95921)),f329(f329(f150(x95921),x95922),x95925)),f329(f329(f150(x95921),x95923),x95926))),f144(x95921,x95924)))+P24(f329(f329(f331(f882(f876(x95921),f876(x95921))),f329(f329(f264(f876(x95921),f876(x95921)),x95925),x95926)),f144(x95921,x95924)))+P24(f329(f329(f331(f882(x95921,x95921)),f329(f329(f264(x95921,x95921),x95922),x95923)),x95924)) % 178.07/177.94 [9593]~P24(f329(f329(f331(f882(f876(x95931),f876(x95931))),f329(f329(f264(f876(x95931),f876(x95931)),f329(f329(f150(x95931),x95932),x95935)),f329(f329(f150(x95931),x95933),x95936))),f156(x95931,x95934)))+P24(f329(f329(f331(f882(f876(x95931),f876(x95931))),f329(f329(f264(f876(x95931),f876(x95931)),x95935),x95936)),f156(x95931,x95934)))+P24(f329(f329(f331(f882(x95931,x95931)),f329(f329(f264(x95931,x95931),x95932),x95933)),x95934)) % 178.07/177.94 [9676]P24(f329(x96761,x96762))+P24(f329(f329(f331(x96763),f847(x96761,x96764,x96765,x96763,x96766)),x96765))+~P24(f329(f329(f331(x96766),x96762),f329(f329(f43(x96763,f883(x96766,a869)),x96765),x96764))) % 178.07/177.94 [9687]~E(x96872,x96874)+P24(f329(f329(f331(f882(f876(x96871),f876(x96871))),f329(f329(f264(f876(x96871),f876(x96871)),f329(f329(f127(x96871),x96872),f329(f329(f150(x96871),x96873),f119(x96871)))),f329(f329(f127(x96871),x96874),f329(f329(f150(x96871),x96875),f119(x96871))))),f156(x96871,x96876)))+~P24(f329(f329(f331(f882(x96871,x96871)),f329(f329(f264(x96871,x96871),x96873),x96875)),x96876)) % 178.07/177.94 [9774]E(x97741,x97742)+~P24(f329(f329(f331(f882(f876(x97743),f876(x97743))),f329(f329(f264(f876(x97743),f876(x97743)),f329(f329(f127(x97743),x97745),f329(f329(f150(x97743),x97741),f119(x97743)))),f329(f329(f127(x97743),x97746),f329(f329(f150(x97743),x97742),f119(x97743))))),f156(x97743,x97744)))+P24(f329(f329(f331(f882(x97743,x97743)),f329(f329(f264(x97743,x97743),x97741),x97742)),x97744)) % 178.07/177.94 [9802]~P24(f329(f329(f331(f882(f876(x98021),f876(x98021))),f329(f329(f264(f876(x98021),f876(x98021)),f329(f329(f127(x98021),x98025),f329(f329(f150(x98021),x98022),f119(x98021)))),f329(f329(f127(x98021),x98026),f329(f329(f150(x98021),x98023),f119(x98021))))),f156(x98021,x98024)))+P24(f329(f329(f331(f882(f876(x98021),f876(x98021))),f329(f329(f264(f876(x98021),f876(x98021)),x98025),x98026)),f156(x98021,x98024)))+P24(f329(f329(f331(f882(x98021,x98021)),f329(f329(f264(x98021,x98021),x98022),x98023)),x98024)) % 178.07/177.94 [9820]P24(f329(x98201,x98202))+P24(f329(f329(f331(x98203),f846(x98201,x98204,x98205,x98206,x98203)),f329(x98204,f847(x98201,x98204,x98205,x98206,x98203))))+~P24(f329(f329(f331(x98203),x98202),f329(f329(f43(x98206,f883(x98203,a869)),x98205),x98204))) % 178.07/177.94 [8819]~P12(x88193,x88194,x88191)+~P24(f329(f62(x88193),x88196))+E(f329(f329(x88191,x88192),f329(f329(f65(x88193,x88194,x88191),x88195),f329(f329(f22(f883(x88193,a869)),x88196),f329(f329(f307(x88193),x88192),f193(f883(x88193,a869)))))),f329(f329(f65(x88193,x88194,x88191),x88195),f329(f329(f307(x88193),x88192),x88196))) % 178.07/177.94 [8904]~E(f329(f329(f177(x89041,x89042),x89044),x89045),f329(f236(x89042),x89046))+~P24(f329(f329(x89043,x89045),x89046))+E(f329(f329(f177(x89041,x89042),f329(f135(f882(x89041,x89042),f329(f268(x89041,x89042,a869),x89043)),x89044)),x89045),f329(f236(x89042),x89046)) % 178.07/177.94 [9120]~P24(f329(f329(f331(x91205),x91203),x91206))+P24(f329(f329(f243(f883(x91201,a869)),f329(x91202,x91203)),x91204))+~P24(f329(f329(f243(f883(x91201,a869)),f329(f329(f43(x91205,f883(x91201,a869)),x91206),x91202)),x91204)) % 178.07/177.94 [9747]~P6(x97471,x97475,x97474)+P24(f329(f329(f331(f882(x97471,x97471)),f329(f329(f264(x97471,x97471),x97472),x97473)),x97474))+~P24(f329(f329(f331(x97471),x97476),f329(f329(f107(f883(x97471,a869)),f329(f283(x97471,x97471,x97474),f329(f329(f307(x97471),x97472),f193(f883(x97471,a869))))),f329(f283(x97471,x97471,x97474),f329(f329(f307(x97471),x97473),f193(f883(x97471,a869))))))) % 178.07/177.94 [8567]~P108(x85672)+~E(f329(f329(f81(x85672),f329(f329(f82(x85672),x85674),x85675)),x85671),f329(f329(f81(x85672),f329(f329(f82(x85672),x85673),x85675)),x85676))+E(x85671,f329(f329(f81(x85672),f329(f329(f82(x85672),f329(f329(f22(x85672),x85673),x85674)),x85675)),x85676)) % 178.07/177.94 [8568]~P108(x85681)+~E(f329(f329(f81(x85681),f329(f329(f82(x85681),x85682),x85684)),x85685),f329(f329(f81(x85681),f329(f329(f82(x85681),x85683),x85684)),x85686))+E(f329(f329(f81(x85681),f329(f329(f82(x85681),f329(f329(f22(x85681),x85682),x85683)),x85684)),x85685),x85686) % 178.07/177.94 [8732]~P108(x87321)+E(f329(f329(f81(x87321),f329(f329(f82(x87321),x87322),x87323)),x87324),f329(f329(f81(x87321),f329(f329(f82(x87321),x87325),x87323)),x87326))+~E(x87326,f329(f329(f81(x87321),f329(f329(f82(x87321),f329(f329(f22(x87321),x87322),x87325)),x87323)),x87324)) % 178.07/177.94 [8733]~P108(x87331)+E(f329(f329(f81(x87331),f329(f329(f82(x87331),x87332),x87333)),x87334),f329(f329(f81(x87331),f329(f329(f82(x87331),x87335),x87333)),x87336))+~E(f329(f329(f81(x87331),f329(f329(f82(x87331),f329(f329(f22(x87331),x87332),x87335)),x87333)),x87334),x87336) % 178.07/177.94 [9060]~P24(f329(f329(x90604,x90605),x90606))+~P24(f329(f329(x90603,x90605),x90606))+P24(f329(f329(f329(f329(f107(f883(x90601,f883(x90602,a869))),x90603),x90604),x90605),x90606)) % 178.07/177.94 [9320]P24(f329(f329(x93201,x93202),x93203))+P24(f329(f329(x93204,x93202),x93203))+~P24(f329(f329(f329(f329(f116(f883(x93205,f883(x93206,a869))),x93204),x93201),x93202),x93203)) % 178.07/177.94 [9606]~P123(x96061)+~P24(f329(f329(f244(x96061),f329(f329(f81(x96061),f329(f329(f82(x96061),x96064),x96065)),x96062)),f329(f329(f81(x96061),f329(f329(f82(x96061),x96063),x96065)),x96066)))+P24(f329(f329(f244(x96061),x96062),f329(f329(f81(x96061),f329(f329(f82(x96061),f329(f329(f22(x96061),x96063),x96064)),x96065)),x96066))) % 178.07/177.94 [9607]~P123(x96071)+~P24(f329(f329(f243(x96071),f329(f329(f81(x96071),f329(f329(f82(x96071),x96074),x96075)),x96072)),f329(f329(f81(x96071),f329(f329(f82(x96071),x96073),x96075)),x96076)))+P24(f329(f329(f243(x96071),x96072),f329(f329(f81(x96071),f329(f329(f82(x96071),f329(f329(f22(x96071),x96073),x96074)),x96075)),x96076))) % 178.07/177.94 [9630]~P123(x96301)+P24(f329(f329(f244(x96301),f329(f329(f81(x96301),f329(f329(f82(x96301),x96302),x96303)),x96304)),f329(f329(f81(x96301),f329(f329(f82(x96301),x96305),x96303)),x96306)))+~P24(f329(f329(f244(x96301),x96304),f329(f329(f81(x96301),f329(f329(f82(x96301),f329(f329(f22(x96301),x96305),x96302)),x96303)),x96306))) % 178.07/177.94 [9631]~P123(x96311)+P24(f329(f329(f243(x96311),f329(f329(f81(x96311),f329(f329(f82(x96311),x96312),x96313)),x96314)),f329(f329(f81(x96311),f329(f329(f82(x96311),x96315),x96313)),x96316)))+~P24(f329(f329(f243(x96311),x96314),f329(f329(f81(x96311),f329(f329(f82(x96311),f329(f329(f22(x96311),x96315),x96312)),x96313)),x96316))) % 178.07/177.94 [9735]~P123(x97351)+~P24(f329(f329(f244(x97351),f329(f329(f81(x97351),f329(f329(f82(x97351),x97352),x97354)),x97355)),f329(f329(f81(x97351),f329(f329(f82(x97351),x97353),x97354)),x97356)))+P24(f329(f329(f244(x97351),f329(f329(f81(x97351),f329(f329(f82(x97351),f329(f329(f22(x97351),x97352),x97353)),x97354)),x97355)),x97356)) % 178.07/177.94 [9736]~P123(x97361)+~P24(f329(f329(f243(x97361),f329(f329(f81(x97361),f329(f329(f82(x97361),x97362),x97364)),x97365)),f329(f329(f81(x97361),f329(f329(f82(x97361),x97363),x97364)),x97366)))+P24(f329(f329(f243(x97361),f329(f329(f81(x97361),f329(f329(f82(x97361),f329(f329(f22(x97361),x97362),x97363)),x97364)),x97365)),x97366)) % 178.07/177.94 [9785]~P123(x97851)+P24(f329(f329(f244(x97851),f329(f329(f81(x97851),f329(f329(f82(x97851),x97852),x97853)),x97854)),f329(f329(f81(x97851),f329(f329(f82(x97851),x97855),x97853)),x97856)))+~P24(f329(f329(f244(x97851),f329(f329(f81(x97851),f329(f329(f82(x97851),f329(f329(f22(x97851),x97852),x97855)),x97853)),x97854)),x97856)) % 178.07/177.94 [9786]~P123(x97861)+P24(f329(f329(f243(x97861),f329(f329(f81(x97861),f329(f329(f82(x97861),x97862),x97863)),x97864)),f329(f329(f81(x97861),f329(f329(f82(x97861),x97865),x97863)),x97866)))+~P24(f329(f329(f243(x97861),f329(f329(f81(x97861),f329(f329(f82(x97861),f329(f329(f22(x97861),x97862),x97865)),x97863)),x97864)),x97866)) % 178.07/177.94 [9957]~P70(x99572)+~P24(f329(f62(x99571),x99576))+E(f329(f329(f6(x99571,x99572),f329(f329(f18(x99571,x99572,x99572),f329(f329(f18(x99571,x99572,f883(x99572,x99572)),f329(f329(f8(a869,f883(x99572,f883(x99572,x99572)),x99571),f102(x99572)),x99573)),x99574)),x99575)),x99576),f329(f329(f81(x99572),f329(f329(f6(x99571,x99572),x99574),f329(f329(f107(f883(x99571,a869)),x99576),f329(f249(x99571),x99573)))),f329(f329(f6(x99571,x99572),x99575),f329(f329(f107(f883(x99571,a869)),x99576),f329(f80(f883(x99571,a869)),f329(f249(x99571),x99573)))))) % 178.07/177.94 [10015]P24(f329(f329(f331(x100152),x100154),x100156))+P24(f329(f329(f331(x100152),x100155),x100156))+E(f329(f309(x100151,x100152,f329(f329(f7(x100151,x100152,x100152),f329(f329(f7(x100151,x100152,f883(x100152,x100152)),f329(f329(f8(a869,f883(x100152,f883(x100152,x100152)),x100151),f102(x100152)),f329(f329(f7(x100151,f883(x100151,a869),a869),f331(x100151)),x100153))),x100154)),x100155)),x100156),f193(f883(x100151,a869))) % 178.07/177.94 [10016]P24(f329(f329(f331(x100162),x100165),x100166))+~P24(f329(f329(f331(x100162),x100164),x100166))+E(f329(f309(x100161,x100162,f329(f329(f7(x100161,x100162,x100162),f329(f329(f7(x100161,x100162,f883(x100162,x100162)),f329(f329(f8(a869,f883(x100162,f883(x100162,x100162)),x100161),f102(x100162)),f329(f329(f7(x100161,f883(x100161,a869),a869),f331(x100161)),x100163))),x100164)),x100165)),x100166),x100163) % 178.07/177.94 [10017]P24(f329(f329(f331(x100172),x100174),x100176))+~P24(f329(f329(f331(x100172),x100175),x100176))+E(f329(f309(x100171,x100172,f329(f329(f7(x100171,x100172,x100172),f329(f329(f7(x100171,x100172,f883(x100172,x100172)),f329(f329(f8(a869,f883(x100172,f883(x100172,x100172)),x100171),f102(x100172)),f329(f329(f7(x100171,f883(x100171,a869),a869),f331(x100171)),x100173))),x100174)),x100175)),x100176),f329(f80(f883(x100171,a869)),x100173)) % 178.07/177.94 [10018]~P24(f329(f329(f331(x100182),x100184),x100186))+~P24(f329(f329(f331(x100182),x100185),x100186))+E(f329(f309(x100181,x100182,f329(f329(f7(x100181,x100182,x100182),f329(f329(f7(x100181,x100182,f883(x100182,x100182)),f329(f329(f8(a869,f883(x100182,f883(x100182,x100182)),x100181),f102(x100182)),f329(f329(f7(x100181,f883(x100181,a869),a869),f331(x100181)),x100183))),x100184)),x100185)),x100186),f252(f883(x100181,a869))) % 178.07/177.94 [10147]P20(x101471,x101472,f329(f329(f307(f874(x101471)),f329(f329(f329(f93(x101471),f329(x101473,x101474)),f329(a26,x101474)),f329(x101475,x101474))),f193(f883(f874(x101471),a869))))+~P24(f329(f329(f331(a872),x101474),x101476))+~P20(x101471,f329(f329(f116(f883(f874(x101471),a869)),x101472),f329(f308(a872,f874(x101471),f329(f329(f18(a872,f883(x101471,f883(a871,a869)),f874(x101471)),f329(f329(f18(a872,a870,f883(f883(x101471,f883(a871,a869)),f874(x101471))),f329(f329(f8(f883(x101471,f883(a871,a869)),f883(a870,f883(f883(x101471,f883(a871,a869)),f874(x101471))),a872),f93(x101471)),x101473)),a26)),x101475)),x101476)),f329(f308(a872,f874(x101471),f329(f329(f18(a872,f883(x101471,f883(a871,a869)),f874(x101471)),f329(f329(f18(a872,a870,f883(f883(x101471,f883(a871,a869)),f874(x101471))),f329(f329(f8(f883(x101471,f883(a871,a869)),f883(a870,f883(f883(x101471,f883(a871,a869)),f874(x101471))),a872),f93(x101471)),x101473)),f329(f329(f8(f879(a870),a870,a872),f240(a870)),a28))),x101475)),x101476)) % 178.07/177.94 [8597]E(x85971,x85972)+~P52(x85974,x85975,x85973,x85976,x85977)+~E(f329(x85973,x85971),f329(x85973,x85972)) % 178.07/177.94 [6980]E(f329(f238(f879(x69801),x69802,f206(x69801),x69803),f329(x69804,x69805)),f329(f236(x69801),x69806))+~E(f329(x69804,x69805),f329(f236(x69802),x69807))+~E(f329(x69803,x69807),f329(f236(x69801),x69806)) % 178.07/177.94 [8625]~P3(x86256,x86255,x86257,x86254,x86251)+E(f329(f329(x86251,x86252),x86253),x86254)+P24(f329(f62(x86255),x86253)) % 178.07/177.94 [9472]P43(x94721,x94722,x94723,x94724,x94725,f329(f329(x94723,x94726),x94727))+~E(f329(f329(x94723,x94726),x94727),x94724)+~E(x94725,f193(f883(x94721,a869))) % 178.07/177.94 [9652]~P24(f329(x96526,x96523))+~P24(f329(f329(f331(f882(x96522,x96522)),f329(f329(f264(x96522,x96522),x96524),x96525)),f329(x96527,x96523)))+P24(f329(f329(f331(f882(f882(x96521,x96522),f882(x96521,x96522))),f329(f329(f264(f882(x96521,x96522),f882(x96521,x96522)),f329(f329(f264(x96521,x96522),x96523),x96524)),f329(f329(f264(x96521,x96522),x96523),x96525))),f281(x96521,x96522,x96526,x96527))) % 178.07/177.94 [10072]~P43(x100722,x100727,x100723,x100726,x100721,f329(f329(x100723,x100725),x100724))+E(f329(f329(x100723,f690(x100724,x100725,x100721,x100726,x100723,x100727,x100722)),f702(x100724,x100725,x100721,x100726,x100723,x100727,x100722)),f329(f329(x100723,x100725),x100724))+E(x100721,f193(f883(x100722,a869))) % 178.07/177.94 [10073]~P43(x100737,x100736,x100731,x100734,x100735,f329(f329(x100731,x100732),x100733))+E(f329(f329(x100731,f690(x100733,x100732,x100735,x100734,x100731,x100736,x100737)),f702(x100733,x100732,x100735,x100734,x100731,x100736,x100737)),f329(f329(x100731,x100732),x100733))+E(f329(f329(x100731,x100732),x100733),x100734) % 178.07/177.94 [9158]~P35(x91581,x91582,x91583,x91585,x91587)+P35(x91581,x91582,x91583,f329(f329(f150(x91581),x91584),x91585),f329(f329(f150(x91582),x91586),x91587))+~P24(f329(f329(x91583,x91584),x91586)) % 178.07/177.94 [9176]P35(x91761,x91762,x91763,x91764,x91765)+~P35(x91761,x91762,x91763,f329(f329(f127(x91761),x91766),x91764),f329(f329(f127(x91762),x91767),x91765))+~E(f329(f194(f876(x91761)),x91766),f329(f194(f876(x91762)),x91767)) % 178.07/177.94 [9177]P35(x91771,x91772,x91773,x91774,x91775)+~P35(x91771,x91772,x91773,f329(f329(f127(x91771),x91774),x91776),f329(f329(f127(x91772),x91775),x91777))+~E(f329(f194(f876(x91771)),x91774),f329(f194(f876(x91772)),x91775)) % 178.07/177.94 [9382]~P35(x93821,x93822,x93823,x93825,x93827)+~P35(x93821,x93822,x93823,x93824,x93826)+P35(x93821,x93822,x93823,f329(f329(f127(x93821),x93824),x93825),f329(f329(f127(x93822),x93826),x93827)) % 178.07/177.94 [9724]~P24(f329(f67(x97241,x97244,x97245,x97246,x97243),x97247))+P24(f329(f67(x97241,x97244,x97245,x97246,f329(f329(f307(x97241),x97242),x97243)),f329(f329(x97245,x97242),x97247)))+P24(f329(f329(f331(x97241),x97242),x97243)) % 178.07/177.94 [9855]~P21(x98553,x98551,x98554,f252(f883(x98553,a869)))+E(f329(f329(f177(x98551,x98552),f329(f329(f153(f882(x98553,x98552),f882(x98551,x98552)),f329(f268(x98553,x98552,f882(x98551,x98552)),f329(f329(f8(x98551,f883(x98552,f882(x98551,x98552)),x98553),f264(x98551,x98552)),x98554))),x98555)),f329(x98554,x98556)),f329(f236(x98552),x98557))+~E(f329(f329(f177(x98553,x98552),x98555),x98556),f329(f236(x98552),x98557)) % 178.07/177.94 [10093]~P43(x100932,x100937,x100936,x100935,x100931,f329(f329(x100936,x100934),x100933))+E(x100931,f193(f883(x100932,a869)))+P24(f329(f329(f331(x100932),f690(x100933,x100934,x100931,x100935,x100936,x100937,x100932)),x100931)) % 178.07/177.94 [10094]~P43(x100945,x100947,x100941,x100944,x100946,f329(f329(x100941,x100942),x100943))+E(f329(f329(x100941,x100942),x100943),x100944)+P24(f329(f329(f331(x100945),f690(x100943,x100942,x100946,x100944,x100941,x100947,x100945)),x100946)) % 178.07/177.94 [6768]~E(x67685,x67687)+~E(x67686,x67684)+E(f329(f329(f329(f329(f73(x67681,f879(x67682)),x67683),x67684),f329(f236(x67682),x67685)),x67686),f329(f236(x67682),x67687)) % 178.07/177.94 [6896]E(x68961,x68962)+~E(f329(x68965,x68961),f329(f236(x68964),x68967))+E(f329(f329(f329(f329(f73(x68963,f879(x68964)),x68965),x68962),f329(f236(x68964),x68966)),x68961),f329(f236(x68964),x68967)) % 178.07/177.94 [7616]E(x76161,x76162)+~E(x76163,x76164)+~E(f329(f329(f329(f329(f73(x76165,f879(x76166)),x76167),x76164),f329(f236(x76166),x76161)),x76163),f329(f236(x76166),x76162)) % 178.07/177.94 [7681]E(x76811,x76812)+E(f329(x76813,x76814),f329(f236(x76815),x76811))+~E(f329(f329(f329(f329(f73(x76816,f879(x76815)),x76813),x76817),f329(f236(x76815),x76812)),x76814),f329(f236(x76815),x76811)) % 178.07/177.94 [7682]E(x76821,x76822)+E(f329(x76823,x76821),f329(f236(x76824),x76825))+~E(f329(f329(f329(f329(f73(x76826,f879(x76824)),x76823),x76822),f329(f236(x76824),x76827)),x76821),f329(f236(x76824),x76825)) % 178.07/177.94 [8844]~P17(x88444,x88445,x88446,x88447,x88441)+~P24(f329(f62(x88445),x88443))+E(f329(f329(x88441,x88442),x88443),f329(f329(f329(f66(x88444,x88445,x88446),x88442),x88447),x88443)) % 178.07/177.94 [8845]~P3(x88454,x88455,x88456,x88457,x88451)+~P24(f329(f62(x88455),x88453))+E(f329(f329(x88451,x88452),x88453),f329(f329(f329(f66(x88454,x88455,x88456),x88452),x88457),x88453)) % 178.07/177.94 [9438]~P20(x94381,x94382,f329(f329(f307(f874(x94381)),f329(f329(f329(f93(x94381),x94383),x94384),x94387)),f193(f883(f874(x94381),a869))))+P20(x94381,x94382,f329(f329(f307(f874(x94381)),f329(f329(f329(f93(x94381),x94383),f34(x94384,x94385)),x94386)),f193(f883(f874(x94381),a869))))+~P20(x94381,x94382,f329(f329(f307(f874(x94381)),f329(f329(f329(f93(x94381),x94387),x94385),x94386)),f193(f883(f874(x94381),a869)))) % 178.07/177.94 [9625]~P19(x96253,x96254,x96255,x96257,x96256,x96251)+~P24(f329(f62(x96254),x96252))+E(f329(x96251,x96252),f329(f329(f329(f66(x96253,x96254,x96255),x96256),x96257),x96252)) % 178.07/177.94 [9780]P43(x97801,x97802,x97803,x97804,x97805,f329(f329(x97803,x97806),x97807))+~P43(x97801,x97802,x97803,x97804,f329(f329(f22(f883(x97801,a869)),x97805),f329(f329(f307(x97801),x97806),f193(f883(x97801,a869)))),x97807)+~P24(f329(f329(f331(x97801),x97806),x97805)) % 178.07/177.94 [10047]~P20(x100471,x100472,f329(f329(f307(f874(x100471)),f329(f329(f329(f93(x100471),f98(x100471,x100473,x100474)),x100475),x100477)),f193(f883(f874(x100471),a869))))+P20(x100471,x100472,f329(f329(f307(f874(x100471)),f329(f329(f329(f93(x100471),x100473),f31(x100474,x100475,x100476)),x100477)),f193(f883(f874(x100471),a869))))+~P20(x100471,x100472,f329(f329(f307(f874(x100471)),f329(f329(f329(f93(x100471),f98(x100471,x100473,f329(f74(a869,a869,a871,a324),x100474))),x100476),x100477)),f193(f883(f874(x100471),a869)))) % 178.07/177.94 [10118]~P43(x101182,x101183,x101184,x101185,x101181,f329(f329(x101184,x101187),x101186))+P43(x101182,x101183,x101184,x101185,f329(f329(f22(f883(x101182,a869)),x101181),f329(f329(f307(x101182),f690(x101186,x101187,x101181,x101185,x101184,x101183,x101182)),f193(f883(x101182,a869)))),f702(x101186,x101187,x101181,x101185,x101184,x101183,x101182))+E(x101181,f193(f883(x101182,a869))) % 178.07/177.94 [10119]~P43(x101195,x101196,x101191,x101194,x101197,f329(f329(x101191,x101192),x101193))+P43(x101195,x101196,x101191,x101194,f329(f329(f22(f883(x101195,a869)),x101197),f329(f329(f307(x101195),f690(x101193,x101192,x101197,x101194,x101191,x101196,x101195)),f193(f883(x101195,a869)))),f702(x101193,x101192,x101197,x101194,x101191,x101196,x101195))+E(f329(f329(x101191,x101192),x101193),x101194) % 178.07/177.94 [9165]E(f186(x91651,x91652,x91653,x91654,f329(f329(f158(x91652,x91655),x91656),x91657)),f186(x91651,x91652,x91653,x91654,x91655))+~P24(f329(f329(f244(a875),x91656),f329(f194(f876(x91652)),x91655)))+~P24(f329(f329(f243(a875),f329(f194(f876(x91651)),x91654)),x91656)) % 178.07/177.94 [9460]P24(f329(f329(f243(f883(f882(x94601,x94602),a869)),f329(f329(f286(x94601,x94603,x94602),x94604),x94605)),f329(f329(f286(x94601,x94603,x94602),x94606),x94607)))+~P24(f329(f329(f243(f883(f882(x94603,x94602),a869)),x94605),x94607))+~P24(f329(f329(f243(f883(f882(x94601,x94603),a869)),x94604),x94606)) % 178.07/177.94 [9791]~P24(f329(f329(f331(x97911),x97916),x97915))+P24(f329(f67(x97911,x97912,x97913,x97914,x97915),f329(f329(x97913,x97916),x97917)))+~P24(f329(f67(x97911,x97912,x97913,x97914,f329(f329(f22(f883(x97911,a869)),x97915),f329(f329(f307(x97911),x97916),f193(f883(x97911,a869))))),x97917)) % 178.07/177.94 [10178]~P134(x101781)+~P21(f882(x101782,x101783),x101781,f329(f268(x101782,x101783,x101781),f329(f329(f7(x101782,f883(x101783,x101781),f883(x101783,x101781)),f329(f329(f8(f883(x101781,x101781),f883(f883(x101783,x101781),f883(x101783,x101781)),x101782),f8(x101781,x101781,x101783)),f329(f329(f8(x101781,f883(x101781,x101781),x101782),f82(x101781)),x101784))),x101785)),f329(f329(f266(x101782,x101783),x101786),f329(f16(f883(x101783,a869),x101782),x101787)))+E(f329(f329(f6(x101781,x101781),f35(x101781)),f329(f249(x101781),f329(f329(f8(f883(x101782,a869),a869,x101781),f88(x101782)),f329(f329(f8(f883(x101782,f883(x101783,a869)),f883(x101782,a869),x101781),f329(f8(f883(x101783,a869),a869,x101782),f88(x101783))),f329(f329(f7(x101781,f883(x101782,f883(x101783,a869)),f883(x101782,f883(x101783,a869))),f329(f329(f8(f883(x101782,f883(f883(x101783,a869),f883(x101783,a869))),f883(f883(x101782,f883(x101783,a869)),f883(x101782,f883(x101783,a869))),x101781),f18(x101782,f883(x101783,a869),f883(x101783,a869))),f329(f329(f8(f883(x101782,f883(x101783,f883(a869,a869))),f883(x101782,f883(f883(x101783,a869),f883(x101783,a869))),x101781),f329(f8(f883(x101783,f883(a869,a869)),f883(f883(x101783,a869),f883(x101783,a869)),x101782),f18(x101783,a869,a869))),f329(f329(f8(f883(x101782,f883(x101783,a869)),f883(x101782,f883(x101783,f883(a869,a869))),x101781),f329(f8(f883(x101783,a869),f883(x101783,f883(a869,a869)),x101782),f329(f8(a869,f883(a869,a869),x101783),a327))),f329(f329(f7(x101781,f883(x101782,f883(x101783,x101781)),f883(x101782,f883(x101783,a869))),f329(f329(f8(f883(f883(x101783,x101781),f883(x101783,a869)),f883(f883(x101782,f883(x101783,x101781)),f883(x101782,f883(x101783,a869))),x101781),f8(f883(x101783,x101781),f883(x101783,a869),x101782)),f329(f329(f8(f883(x101781,a869),f883(f883(x101783,x101781),f883(x101783,a869)),x101781),f8(x101781,a869,x101783)),a326))),f329(f329(f7(x101782,f883(x101783,x101781),f883(x101783,x101781)),f329(f329(f8(f883(x101781,x101781),f883(f883(x101783,x101781),f883(x101783,x101781)),x101782),f8(x101781,x101781,x101783)),f329(f329(f8(x101781,f883(x101781,x101781),x101782),f82(x101781)),x101784))),x101785)))))),f329(f329(f7(x101782,f883(x101783,a869),f883(x101783,a869)),f329(f329(f8(f883(a869,a869),f883(f883(x101783,a869),f883(x101783,a869)),x101782),f8(a869,a869,x101783)),f329(f329(f8(a869,f883(a869,a869),x101782),a327),f329(f329(f7(x101782,f883(x101782,a869),a869),f331(x101782)),x101786)))),f329(f329(f7(x101783,f883(x101783,a869),a869),f331(x101783)),x101787))))))),f329(f329(f82(x101781),f329(f329(f6(x101782,x101781),x101784),x101786)),f329(f329(f6(x101783,x101781),x101785),x101787))) % 178.07/177.94 [9623]~P24(f329(f329(x96234,x96236),x96238))+~P24(f329(f329(x96235,x96238),x96237))+P24(f329(f329(f265(x96231,x96232,x96233,x96234,x96235),x96236),x96237)) % 178.07/177.94 [9227]~P15(x92278,x92271,x92273,x92275)+~P24(f329(f62(x92278),x92276))+E(f329(f74(x92271,x92271,x92272,f329(x92273,x92274)),f329(f74(x92271,x92271,x92272,f329(x92275,x92276)),x92277)),f329(f74(x92271,x92271,x92272,f329(x92275,x92276)),f329(f74(x92271,x92271,x92272,f329(x92273,x92274)),x92277))) % 178.07/177.94 [9613]~P18(x96137,x96132,x96135,x96138,x96136,x96131)+~P24(f329(f62(x96132),x96134))+E(f329(x96131,f329(f329(f307(x96132),x96133),x96134)),f329(f329(x96135,f329(x96136,x96133)),f329(x96131,x96134))) % 178.07/177.94 [9733]~P21(x97332,x97334,x97336,x97338)+~P21(x97331,x97333,x97335,x97337)+P21(f882(x97331,x97332),f882(x97333,x97334),f269(x97331,x97333,x97332,x97334,x97335,x97336),f329(f329(f266(x97331,x97332),x97337),f329(f16(f883(x97332,a869),x97331),x97338))) % 178.07/177.94 [9406]P24(f329(f329(f331(f882(x94061,x94062)),f329(f329(f264(x94061,x94062),x94063),x94064)),f329(f329(f286(x94061,x94065,x94062),x94066),x94067)))+~P24(f329(f329(f331(f882(x94061,x94065)),f329(f329(f264(x94061,x94065),x94063),x94068)),x94066))+~P24(f329(f329(f331(f882(x94065,x94062)),f329(f329(f264(x94065,x94062),x94068),x94064)),x94067)) % 178.07/177.94 [9594]~P24(f329(f329(f243(f883(f882(x95943,x95942),a869)),x95945),f329(f329(f266(x95943,x95942),x95948),f329(f16(f883(x95942,a869),x95943),x95947))))+~P24(f329(f329(f243(f883(f882(x95941,x95943),a869)),x95944),f329(f329(f266(x95941,x95943),x95946),f329(f16(f883(x95943,a869),x95941),x95948))))+P24(f329(f329(f243(f883(f882(x95941,x95942),a869)),f329(f329(f286(x95941,x95943,x95942),x95944),x95945)),f329(f329(f266(x95941,x95942),x95946),f329(f16(f883(x95942,a869),x95941),x95947)))) % 178.07/177.94 [9647]~E(x96473,x96475)+P24(f329(f329(f331(f882(f882(x96471,x96472),f882(x96471,x96472))),f329(f329(f264(f882(x96471,x96472),f882(x96471,x96472)),f329(f329(f264(x96471,x96472),x96473),x96474)),f329(f329(f264(x96471,x96472),x96475),x96476))),f321(x96471,x96472,x96477,x96478)))+~P24(f329(f329(f331(f882(x96472,x96472)),f329(f329(f264(x96472,x96472),x96474),x96476)),x96478)) % 178.07/177.94 [9756]E(x97561,x97562)+~P24(f329(f329(f331(f882(f882(x97563,x97565),f882(x97563,x97565))),f329(f329(f264(f882(x97563,x97565),f882(x97563,x97565)),f329(f329(f264(x97563,x97565),x97561),x97566)),f329(f329(f264(x97563,x97565),x97562),x97567))),f321(x97563,x97565,x97564,x97568)))+P24(f329(f329(f331(f882(x97563,x97563)),f329(f329(f264(x97563,x97563),x97561),x97562)),x97564)) % 178.07/177.94 [9773]~P24(f329(f329(f331(f882(f882(x97731,x97735),f882(x97731,x97735))),f329(f329(f264(f882(x97731,x97735),f882(x97731,x97735)),f329(f329(f264(x97731,x97735),x97732),x97736)),f329(f329(f264(x97731,x97735),x97733),x97737))),f321(x97731,x97735,x97734,x97738)))+P24(f329(f329(f331(f882(x97731,x97731)),f329(f329(f264(x97731,x97731),x97732),x97733)),x97734))+P24(f329(f329(f331(f882(x97735,x97735)),f329(f329(f264(x97735,x97735),x97736),x97737)),x97738)) % 178.07/177.94 [9677]~P19(x96777,x96775,x96771,x96778,x96772,x96774)+~P24(f329(f62(x96775),x96776))+E(f329(f329(x96771,f329(x96772,x96773)),f329(x96774,f329(f329(f22(f883(x96775,a869)),x96776),f329(f329(f307(x96775),x96773),f193(f883(x96775,a869)))))),f329(x96774,f329(f329(f307(x96775),x96773),x96776))) % 178.07/177.94 [9184]~P24(f329(f329(f329(x91845,x91848),x91846),x91847))+~P24(f329(f329(f331(x91841),x91848),x91844))+P24(f329(f329(f329(f329(f43(x91841,f883(x91842,f883(x91843,a869))),x91844),x91845),x91846),x91847)) % 178.07/177.94 [9393]P24(f329(f329(f329(x93931,x93932),x93933),x93934))+~P24(f329(f329(f331(x93935),x93932),x93936))+~P24(f329(f329(f329(f329(f42(x93935,f883(x93937,f883(x93938,a869))),x93936),x93931),x93933),x93934)) % 178.07/177.94 [9587]~P17(x95873,x95872,x95874,x95878,x95871)+~P24(f329(f62(x95872),x95877))+E(f329(f329(x95871,f329(f329(f18(x95872,x95873,x95873),f329(f329(f8(x95873,f883(x95873,x95873),x95872),x95874),x95875)),x95876)),x95877),f329(f329(x95874,f329(f329(x95871,x95875),x95877)),f329(f329(x95871,x95876),x95877))) % 178.07/177.94 [9863]~E(f329(f308(x98632,x98634,x98636),x98638),x986310)+~E(f329(f308(x98631,x98633,x98635),x98637),x98639)+E(f329(f308(f882(x98631,x98632),f882(x98633,x98634),f269(x98631,x98633,x98632,x98634,x98635,x98636)),f329(f329(f266(x98631,x98632),x98637),f329(f16(f883(x98632,a869),x98631),x98638))),f329(f329(f266(x98633,x98634),x98639),f329(f16(f883(x98634,a869),x98633),x986310))) % 178.07/177.94 [4818]~P105(x48182)+~P29(x48182,x48181)+P29(x48182,f120(x48182,x48181))+E(x48181,f119(x48182)) % 178.07/177.94 [4819]~P105(x48192)+~P29(x48192,x48191)+P29(x48192,f666(x48191,x48192))+E(x48191,f119(x48192)) % 178.07/177.94 [5050]~P27(x50502)+E(f10(x50502,x50501),f41(x50502,x50501))+E(x50501,f193(f883(x50502,a869)))+~P24(f329(f62(x50502),x50501)) % 178.07/177.94 [5051]~P27(x50512)+E(f13(x50512,x50511),f40(x50512,x50511))+E(x50511,f193(f883(x50512,a869)))+~P24(f329(f62(x50512),x50511)) % 178.07/177.94 [5211]~P105(x52112)+~P29(x52112,x52111)+E(x52111,f119(x52112))+E(f329(f329(f150(x52112),f678(x52111,x52112)),f666(x52111,x52112)),x52111) % 178.07/177.94 [6006]~P63(x60062)+E(x60061,f193(f883(x60062,a869)))+P24(f329(f329(f243(x60062),f10(x60062,x60061)),f13(x60062,x60061)))+~P24(f329(f62(x60062),x60061)) % 178.07/177.94 [6018]~P39(x60182)+~P39(x60181)+E(x60181,x60182)+~E(f329(f308(a1,a875,a110),x60181),f329(f308(a1,a875,a110),x60182)) % 178.07/177.94 [9042]~P117(x90421)+~P24(f329(f329(f331(x90421),x90422),f115(x90421)))+P24(f329(f329(f244(x90421),f329(f329(f81(x90421),f329(f329(f81(x90421),f79(x90421)),x90422)),x90422)),f2(x90421)))+~P24(f329(f329(f244(x90421),x90422),f2(x90421))) % 178.07/177.94 [9282]~P117(x92821)+~P24(f329(f329(f331(x92821),x92822),f115(x92821)))+~P24(f329(f329(f244(x92821),f329(f329(f81(x92821),f329(f329(f81(x92821),f79(x92821)),x92822)),x92822)),f2(x92821)))+P24(f329(f329(f244(x92821),x92822),f2(x92821))) % 178.07/177.94 [4874]~P134(x48742)+~P112(x48742)+E(x48741,f2(a875))+E(f329(f329(f254(x48742),f2(x48742)),x48741),f2(x48742)) % 178.07/177.94 [4878]~P134(x48781)+~P112(x48781)+~E(x48782,f2(a875))+E(f329(f329(f254(x48781),f2(x48781)),x48782),f79(x48781)) % 178.07/177.94 [5037]~P136(x50372)+E(x50371,f79(x50372))+E(x50371,f329(f80(x50372),f79(x50372)))+~E(f329(f329(f82(x50372),x50371),x50371),f79(x50372)) % 178.07/177.94 [5294]~P87(x52942)+E(x52941,f2(x52942))+E(f83(x52942,x52941),f329(f80(x52942),f79(x52942)))+P24(f329(f329(f244(x52942),f2(x52942)),x52941)) % 178.07/177.94 [5527]~P87(x55272)+E(f83(x55272,x55271),f79(x55272))+E(x55271,f2(x55272))+~P24(f329(f329(f244(x55272),f2(x55272)),x55271)) % 178.07/177.94 [5536]E(x55361,x55362)+~E(f329(f109(a875),x55361),f329(f109(a875),x55362))+P24(f329(a198,f329(f109(a1),x55362)))+P24(f329(a198,f329(f109(a1),x55361))) % 178.07/177.94 [5585]~P91(x55851)+~E(x55852,f2(x55851))+E(f329(f329(f81(x55851),x55852),x55852),f2(x55851))+~P24(f329(f329(f331(x55851),x55852),f115(x55851))) % 178.07/177.94 [5623]E(x56231,f2(a1))+~E(f329(f329(f39(a1),x56232),x56231),f2(a1))+P24(f329(f329(f244(a1),x56231),x56232))+P24(f329(f329(f244(a1),x56232),x56231)) % 178.07/177.94 [5654]E(x56541,f2(a1))+~E(f329(f329(f39(a1),x56542),x56541),f2(a1))+P24(f329(f329(f243(a1),x56542),f2(a1)))+P24(f329(f329(f244(a1),x56542),x56541)) % 178.07/177.94 [5687]E(x56871,f2(a1))+~E(f329(f329(f39(a1),x56872),x56871),f2(a1))+P24(f329(f329(f243(a1),f2(a1)),x56872))+P24(f329(f329(f244(a1),x56871),x56872)) % 178.07/177.94 [5723]~P91(x57232)+E(x57231,f2(x57232))+~E(f329(f329(f81(x57232),x57231),x57231),f2(x57232))+~P24(f329(f329(f331(x57232),x57231),f115(x57232))) % 178.07/177.94 [5783]E(f329(f109(a875),x57831),f329(f109(a875),x57832))+~E(f329(f109(a1),x57832),f2(a1))+P24(f329(a198,f329(f109(a1),x57832)))+~P24(f329(a198,f329(f109(a1),x57831))) % 178.07/177.94 [5810]~E(f329(f109(a875),x58102),f329(f109(a875),x58101))+E(f329(f109(a1),x58101),f2(a1))+P24(f329(a198,f329(f109(a1),x58101)))+~P24(f329(a198,f329(f109(a1),x58102))) % 178.07/177.94 [5819]~P105(x58192)+E(x58191,f193(f883(x58192,a869)))+~P24(f329(f62(x58192),x58191))+P24(f329(f329(f331(x58192),f14(x58192,x58191)),x58191)) % 178.07/177.94 [5820]~P105(x58202)+E(x58201,f193(f883(x58202,a869)))+~P24(f329(f62(x58202),x58201))+P24(f329(f329(f331(x58202),f15(x58202,x58201)),x58201)) % 178.07/177.94 [5986]~P117(x59861)+~P92(x59861)+P24(f329(f329(f244(x59861),f2(x59861)),f329(f109(x59861),x59862)))+~P24(f329(f329(f244(a1),a84),x59862)) % 178.07/177.94 [5987]~P117(x59871)+~P92(x59871)+P24(f329(f329(f243(x59871),f2(x59871)),f329(f109(x59871),x59872)))+~P24(f329(f329(f243(a1),a84),x59872)) % 178.07/177.94 [6005]~P117(x60051)+~P92(x60051)+E(f329(f76(x60051),f329(f109(x60051),x60052)),f329(f109(x60051),x60052))+P24(f329(f329(f244(x60051),f329(f109(x60051),x60052)),f2(x60051))) % 178.07/177.94 [6045]E(x60451,x60452)+~E(f329(a110,x60451),f329(a110,x60452))+~P24(f329(f329(f243(a1),f2(a1)),x60452))+~P24(f329(f329(f243(a1),f2(a1)),x60451)) % 178.07/177.94 [6240]~P92(x62402)+~P117(x62402)+~P24(f329(f329(f244(x62402),f2(x62402)),f329(f109(x62402),x62401)))+P24(f329(f329(f244(a1),a84),x62401)) % 178.07/177.94 [6241]~P92(x62412)+~P117(x62412)+~P24(f329(f329(f243(x62412),f2(x62412)),f329(f109(x62412),x62411)))+P24(f329(f329(f243(a1),a84),x62411)) % 178.07/177.94 [6246]~P117(x62461)+~P92(x62461)+P24(f329(f329(f244(x62461),f329(f109(x62461),x62462)),f2(x62461)))+~P24(f329(f329(f244(a1),x62462),a84)) % 178.07/177.94 [6247]~P117(x62471)+~P92(x62471)+P24(f329(f329(f243(x62471),f329(f109(x62471),x62472)),f2(x62471)))+~P24(f329(f329(f243(a1),x62472),a84)) % 178.07/177.94 [6556]~P92(x65562)+~P117(x65562)+~P24(f329(f329(f244(x65562),f329(f109(x65562),x65561)),f2(x65562)))+P24(f329(f329(f244(a1),x65561),a84)) % 178.07/177.94 [6557]~P92(x65572)+~P117(x65572)+~P24(f329(f329(f243(x65572),f329(f109(x65572),x65571)),f2(x65572)))+P24(f329(f329(f243(a1),x65571),a84)) % 178.07/177.94 [6648]~P117(x66481)+~P92(x66481)+E(f329(f76(x66481),f329(f109(x66481),x66482)),f329(f80(x66481),f329(f109(x66481),x66482)))+~P24(f329(f329(f244(x66481),f329(f109(x66481),x66482)),f2(x66481))) % 178.07/177.94 [6666]E(f329(f109(a875),x66661),f329(f109(a875),x66662))+~E(f329(f109(a1),x66662),f2(a1))+~P24(f329(f329(f243(a1),f329(f109(a1),x66661)),f2(a1)))+~P24(f329(a198,f329(f109(a1),x66661))) % 178.07/177.94 [7547]~P105(x75472)+E(x75471,f193(f883(x75472,a869)))+~P24(f329(f62(x75472),x75471))+P24(f329(f329(f243(x75472),f12(x75472,f241(x75472),x75471)),f11(x75472,f242(x75472),x75471))) % 178.07/177.94 [7862]~P39(x78622)+~P28(x78621)+P24(f329(f329(f331(a1),x78621),x78622))+~P24(f329(f329(f331(a875),f329(a110,x78621)),f329(f308(a1,a875,a110),x78622))) % 178.07/177.94 [8138]~P58(x81382)+P24(f329(x81381,f206(x81382)))+~P24(f329(f58(f879(x81382)),x81381))+P24(f329(f58(x81382),f329(f329(f8(f879(x81382),a869,x81382),x81381),f236(x81382)))) % 178.07/177.94 [8605]~P58(x86051)+~P24(f329(x86052,f206(x86051)))+P24(f329(f59(f879(x86051)),x86052))+~P24(f329(f59(x86051),f329(f329(f8(f879(x86051),a869,x86051),x86052),f236(x86051)))) % 178.07/177.94 [5816]~P137(x58162)+E(x58161,f2(a1))+E(f329(f80(x58162),f329(f108(x58162),f329(f80(a1),x58161))),f329(f108(x58162),x58161))+~P24(f329(f329(f244(a1),x58161),f2(a1))) % 178.07/177.94 [5889]~P91(x58891)+~P92(x58891)+~P31(x58891,f329(f109(x58891),x58892))+P31(x58891,f329(f109(x58891),f329(f329(f81(a1),x58892),x58892))) % 178.07/177.94 [6228]~P75(x62282)+E(x62281,f193(f883(x62282,a869)))+E(f15(x62282,f329(f308(x62282,x62282,f80(x62282)),x62281)),f329(f80(x62282),f14(x62282,x62281)))+~P24(f329(f62(x62282),x62281)) % 178.07/177.94 [6229]~P75(x62292)+E(x62291,f193(f883(x62292,a869)))+E(f14(x62292,f329(f308(x62292,x62292,f80(x62292)),x62291)),f329(f80(x62292),f15(x62292,x62291)))+~P24(f329(f62(x62292),x62291)) % 178.07/177.94 [6261]~P91(x62611)+~P92(x62611)+P31(x62611,f329(f109(x62611),x62612))+~P31(x62611,f329(f109(x62611),f329(f329(f81(a1),x62612),x62612))) % 178.07/177.94 [6351]E(x63511,f2(a1))+E(f329(a51,f50(f329(f80(a1),x63511),f329(f80(a1),x63512))),f46(x63511,x63512))+P24(f329(f329(f243(a1),f2(a1)),x63512))+~P24(f329(f329(f243(a1),f2(a1)),x63511)) % 178.07/177.94 [7370]~P4(a5000)+~P24(f329(a25,x73701))+P20(a871,x73702,f329(f329(f307(f874(a871)),f329(a94,x73701)),f193(f883(f874(a871),a869))))+P24(f329(f329(f331(a872),f827(x73701,x73702)),f183(a872,a870,a28))) % 178.07/177.94 [8636]~P4(a5000)+~P24(f329(a25,x86362))+P20(a871,x86361,f329(f329(f307(f874(a871)),f329(a94,x86362)),f193(f883(f874(a871),a869))))+~P20(a871,x86361,f329(f329(f307(f874(a871)),f329(a94,f329(a26,f827(x86362,x86361)))),f193(f883(f874(a871),a869)))) % 178.07/177.94 [8649]~P39(x86492)+~P39(x86491)+P24(f329(f329(f244(f883(a875,a869)),f329(f308(a1,a875,a110),x86491)),f329(f308(a1,a875,a110),x86492)))+~P24(f329(f329(f244(f883(a1,a869)),x86491),x86492)) % 178.07/177.94 [8862]~E(f683(x88622,x88621),f684(x88622,x88621))+~P24(f329(f136(x88621),f685(x88622,x88621)))+~P24(f329(f136(f876(x88621)),x88622))+P24(f329(f136(x88621),f329(f141(f876(x88621),f876(x88621),f127(x88621),f119(x88621)),x88622))) % 178.07/177.94 [8959]~P39(x89592)+~P39(x89591)+~P24(f329(f329(f244(f883(a875,a869)),f329(f308(a1,a875,a110),x89591)),f329(f308(a1,a875,a110),x89592)))+P24(f329(f329(f244(f883(a1,a869)),x89591),x89592)) % 178.07/177.94 [8960]~P39(x89602)+~P39(x89601)+~P24(f329(f329(f243(f883(a875,a869)),f329(f308(a1,a875,a110),x89601)),f329(f308(a1,a875,a110),x89602)))+P24(f329(f329(f243(f883(a1,a869)),x89601),x89602)) % 178.07/177.94 [8966]~E(f683(x89662,x89661),f684(x89662,x89661))+~P24(f329(f136(f876(x89661)),x89662))+P24(f329(f136(x89661),f329(f141(f876(x89661),f876(x89661),f127(x89661),f119(x89661)),x89662)))+P24(f329(f329(f331(f876(x89661)),f685(x89662,x89661)),f329(f171(f876(x89661)),x89662))) % 178.07/177.94 [9009]~P24(f329(f136(x90091),f685(x90092,x90091)))+~P24(f329(f136(f876(x90091)),x90092))+P24(f329(f136(x90091),f329(f141(f876(x90091),f876(x90091),f127(x90091),f119(x90091)),x90092)))+P24(f329(f329(f331(f876(x90091)),f684(x90092,x90091)),f329(f171(f876(x90091)),x90092))) % 178.07/177.94 [9010]~P24(f329(f136(x90101),f685(x90102,x90101)))+~P24(f329(f136(f876(x90101)),x90102))+P24(f329(f136(x90101),f329(f141(f876(x90101),f876(x90101),f127(x90101),f119(x90101)),x90102)))+P24(f329(f329(f331(f876(x90101)),f683(x90102,x90101)),f329(f171(f876(x90101)),x90102))) % 178.07/177.94 [9085]~P24(f329(f136(f876(x90851)),x90852))+P24(f329(f136(x90851),f329(f141(f876(x90851),f876(x90851),f127(x90851),f119(x90851)),x90852)))+P24(f329(f329(f331(f876(x90851)),f684(x90852,x90851)),f329(f171(f876(x90851)),x90852)))+P24(f329(f329(f331(f876(x90851)),f685(x90852,x90851)),f329(f171(f876(x90851)),x90852))) % 178.07/177.94 [9086]~P24(f329(f136(f876(x90861)),x90862))+P24(f329(f136(x90861),f329(f141(f876(x90861),f876(x90861),f127(x90861),f119(x90861)),x90862)))+P24(f329(f329(f331(f876(x90861)),f683(x90862,x90861)),f329(f171(f876(x90861)),x90862)))+P24(f329(f329(f331(f876(x90861)),f685(x90862,x90861)),f329(f171(f876(x90861)),x90862))) % 178.07/177.94 [9099]~E(f329(f329(f107(f883(x90991,a869)),f329(f171(x90991),f684(x90992,x90991))),f329(f171(x90991),f683(x90992,x90991))),f193(f883(x90991,a869)))+~P24(f329(f136(x90991),f685(x90992,x90991)))+~P24(f329(f136(f876(x90991)),x90992))+P24(f329(f136(x90991),f329(f141(f876(x90991),f876(x90991),f127(x90991),f119(x90991)),x90992))) % 178.07/177.94 [9161]~E(f329(f329(f107(f883(x91611,a869)),f329(f171(x91611),f684(x91612,x91611))),f329(f171(x91611),f683(x91612,x91611))),f193(f883(x91611,a869)))+~P24(f329(f136(f876(x91611)),x91612))+P24(f329(f136(x91611),f329(f141(f876(x91611),f876(x91611),f127(x91611),f119(x91611)),x91612)))+P24(f329(f329(f331(f876(x91611)),f685(x91612,x91611)),f329(f171(f876(x91611)),x91612))) % 178.07/177.94 [9430]E(x94301,f2(a1))+E(x94302,f2(a1))+E(f329(f329(f87(a1,f882(a1,a1)),f329(f329(a225,x94302),x94301)),f329(f329(f18(a1,a1,f882(a1,a1)),f329(f329(f8(a1,f883(a1,f882(a1,a1)),a1),f264(a1,a1)),f329(f39(a1),x94302))),f329(f39(a1),x94301))),f223(x94302,x94301))+P24(f329(f329(f244(a1),x94301),f2(a1))) % 178.07/177.94 [8199]~P92(x81992)+~P117(x81992)+~P24(f329(f329(f244(x81992),f329(f109(x81992),x81991)),f79(x81992)))+P24(f329(f329(f244(a1),x81991),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))) % 178.07/177.94 [8200]~P92(x82002)+~P117(x82002)+~P24(f329(f329(f243(x82002),f329(f109(x82002),x82001)),f79(x82002)))+P24(f329(f329(f243(a1),x82001),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))) % 178.07/177.94 [8477]~P117(x84771)+~P92(x84771)+P24(f329(f329(f244(x84771),f329(f109(x84771),x84772)),f79(x84771)))+~P24(f329(f329(f244(a1),x84772),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))) % 178.07/177.94 [8478]~P117(x84781)+~P92(x84781)+P24(f329(f329(f243(x84781),f329(f109(x84781),x84782)),f79(x84781)))+~P24(f329(f329(f243(a1),x84782),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))) % 178.07/177.94 [8675]~P92(x86752)+~P117(x86752)+~P24(f329(f329(f244(x86752),f79(x86752)),f329(f109(x86752),x86751)))+P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),x86751)) % 178.07/177.94 [8676]~P92(x86762)+~P117(x86762)+~P24(f329(f329(f243(x86762),f79(x86762)),f329(f109(x86762),x86761)))+P24(f329(f329(f243(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),x86761)) % 178.07/177.94 [9048]~P117(x90481)+~P92(x90481)+P24(f329(f329(f244(x90481),f79(x90481)),f329(f109(x90481),x90482)))+~P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),x90482)) % 178.07/177.94 [9049]~P117(x90491)+~P92(x90491)+P24(f329(f329(f243(x90491),f79(x90491)),f329(f109(x90491),x90492)))+~P24(f329(f329(f243(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),x90492)) % 178.07/177.94 [9559]~P136(x95592)+E(x95591,f79(x95592))+E(x95591,f329(f80(x95592),f79(x95592)))+~E(f329(f329(f254(x95592),x95591),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f79(x95592)) % 178.07/177.94 [9831]~P61(x98311)+~P92(x98311)+~P24(f329(f329(f244(x98311),f2(x98311)),x98312))+P24(f329(f329(f244(x98311),f2(x98311)),f329(f329(f287(x98311),x98312),f329(f109(x98311),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))))) % 178.07/177.94 [9893]~P61(x98931)+~P92(x98931)+P24(f329(f329(f244(x98931),f2(x98931)),x98932))+~P24(f329(f329(f244(x98931),f2(x98931)),f329(f329(f287(x98931),x98932),f329(f109(x98931),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))))) % 178.07/177.94 [10146]~P137(x101462)+E(x101461,f2(a1))+P24(f329(f329(f244(a1),x101461),f2(a1)))+E(f329(f329(f268(a1,a1,x101462),f329(f329(f7(a1,f883(a1,f883(x101462,x101462)),f883(a1,x101462)),f329(f329(f8(f883(f883(x101462,x101462),x101462),f883(f883(a1,f883(x101462,x101462)),f883(a1,x101462)),a1),f8(f883(x101462,x101462),x101462,a1)),f329(f329(f8(x101462,f883(f883(x101462,x101462),x101462),a1),f87(x101462,x101462)),f108(x101462)))),f329(f329(f7(a1,f883(x101462,x101462),f883(x101462,x101462)),f329(f329(f8(f883(x101462,f883(x101462,x101462)),f883(f883(x101462,x101462),f883(x101462,x101462)),a1),f18(x101462,x101462,x101462)),f329(f329(f7(a1,f883(x101462,x101462),f883(x101462,f883(x101462,x101462))),f329(f329(f8(f883(x101462,f883(x101462,x101462)),f883(f883(x101462,x101462),f883(x101462,f883(x101462,x101462))),a1),f8(x101462,f883(x101462,x101462),x101462)),f329(f329(f8(a869,f883(x101462,f883(x101462,x101462)),a1),f102(x101462)),f329(f329(f7(a1,a1,a869),a326),f2(a1))))),f329(f329(f18(x101462,x101462,x101462),f81(x101462)),f5(x101462))))),f329(f329(f7(x101462,x101462,x101462),f329(f329(f8(x101462,f883(x101462,x101462),x101462),f81(x101462)),f329(f329(f18(x101462,x101462,x101462),f81(x101462)),f5(x101462)))),f79(x101462))))),f46(x101461,f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f329(f108(x101462),x101461)) % 178.07/177.94 [5206]~P58(x52063)+~P36(x52063,x52062,f56(x52063))+E(x52061,f777(x52062,x52063))+~P24(f329(x52062,x52061)) % 178.07/177.94 [5364]~P58(x53641)+P36(x53641,x53642,f56(x53641))+~E(f778(x53642,x53641,x53643),x53643)+~P24(f329(x53642,x53643)) % 178.07/177.94 [4845]~P91(x48453)+~P92(x48453)+E(x48451,x48452)+~E(f329(f109(x48453),x48451),f329(f109(x48453),x48452)) % 178.07/177.94 [5985]~P58(x59851)+P36(x59851,x59852,f56(x59851))+~P24(f329(x59852,x59853))+P24(f329(x59852,f778(x59852,x59851,x59853))) % 178.07/177.94 [5995]~P24(f329(x59951,x59952))+~P24(f329(x59951,x59953))+~P24(f329(f329(f243(a875),x59953),f412(x59952,x59951)))+P24(f329(x59951,f2(a875))) % 178.07/177.94 [6414]P144(x64142,x64141,x64143)+E(x64141,f2(a1))+P24(f329(f329(f243(a1),f2(a1)),f807(x64143,x64141,x64142)))+P24(f329(f329(f244(a1),x64141),f2(a1))) % 178.07/177.94 [6415]P143(x64152,x64151,x64153)+E(x64151,f2(a1))+P24(f329(f329(f243(a1),f2(a1)),f815(x64153,x64151,x64152)))+P24(f329(f329(f244(a1),x64151),f2(a1))) % 178.07/177.94 [6535]P143(x65351,x65352,x65353)+~P24(f329(x65351,x65353))+P24(f329(f329(f243(a1),f2(a1)),f815(x65353,x65352,x65351)))+P24(f329(f329(f244(a1),x65352),f2(a1))) % 178.07/177.94 [6562]P144(x65621,x65622,x65623)+P24(f329(f329(f243(a1),f2(a1)),f807(x65623,x65622,x65621)))+~P24(f329(x65621,f2(a1)))+P24(f329(f329(f244(a1),x65622),f2(a1))) % 178.07/177.94 [6590]P144(x65902,x65901,x65903)+E(x65901,f2(a1))+~P24(f329(x65902,f808(x65903,x65901,x65902)))+P24(f329(f329(f244(a1),x65901),f2(a1))) % 178.07/177.94 [6591]P143(x65912,x65911,x65913)+E(x65911,f2(a1))+~P24(f329(x65912,f815(x65913,x65911,x65912)))+P24(f329(f329(f244(a1),x65911),f2(a1))) % 178.07/177.94 [6691]~P27(x66911)+~P105(x66911)+~P24(f329(f329(f244(x66911),x66912),f40(x66911,x66913)))+P24(f329(f329(f244(x66911),x66912),f864(x66913,x66912,x66911))) % 178.07/177.94 [6700]P143(x67001,x67002,x67003)+~P24(f329(x67001,x67003))+~P24(f329(x67001,f815(x67003,x67002,x67001)))+P24(f329(f329(f244(a1),x67002),f2(a1))) % 178.07/177.94 [6732]P144(x67321,x67322,x67323)+~P24(f329(x67321,f808(x67323,x67322,x67321)))+~P24(f329(x67321,f2(a1)))+P24(f329(f329(f244(a1),x67322),f2(a1))) % 178.07/177.94 [6985]P144(x69852,x69851,x69853)+E(x69851,f2(a1))+P24(f329(f329(f243(a1),f2(a1)),f807(x69853,x69851,x69852)))+P24(f329(f329(f244(a1),x69851),f806(x69853,x69851,x69852))) % 178.07/177.94 [6986]P143(x69862,x69861,x69863)+E(x69861,f2(a1))+P24(f329(f329(f243(a1),f2(a1)),f815(x69863,x69861,x69862)))+P24(f329(f329(f244(a1),x69861),f814(x69863,x69861,x69862))) % 178.07/177.94 [7103]P143(x71031,x71032,x71033)+~P24(f329(x71031,x71033))+P24(f329(f329(f243(a1),f2(a1)),f815(x71033,x71032,x71031)))+P24(f329(f329(f244(a1),x71032),f814(x71033,x71032,x71031))) % 178.07/177.94 [7122]P144(x71221,x71222,x71223)+P24(f329(f329(f243(a1),f2(a1)),f807(x71223,x71222,x71221)))+P24(f329(f329(f244(a1),x71222),f806(x71223,x71222,x71221)))+~P24(f329(x71221,f2(a1))) % 178.07/177.94 [7155]P144(x71552,x71551,x71553)+E(x71551,f2(a1))+~P24(f329(x71552,f808(x71553,x71551,x71552)))+P24(f329(f329(f244(a1),x71551),f806(x71553,x71551,x71552))) % 178.07/177.94 [7156]P143(x71562,x71561,x71563)+E(x71561,f2(a1))+~P24(f329(x71562,f815(x71563,x71561,x71562)))+P24(f329(f329(f244(a1),x71561),f814(x71563,x71561,x71562))) % 178.07/177.94 [7197]P144(x71972,x71971,x71973)+E(x71971,f2(a1))+P24(f329(f329(f243(a1),f2(a1)),f807(x71973,x71971,x71972)))+~P24(f329(x71972,f813(x71973,x71971,x71972))) % 178.07/177.94 [7198]P143(x71982,x71981,x71983)+E(x71981,f2(a1))+P24(f329(f329(f243(a1),f2(a1)),f815(x71983,x71981,x71982)))+~P24(f329(x71982,f814(x71983,x71981,x71982))) % 178.07/177.94 [7286]P143(x72861,x72862,x72863)+~P24(f329(x72861,x72863))+~P24(f329(x72861,f815(x72863,x72862,x72861)))+P24(f329(f329(f244(a1),x72862),f814(x72863,x72862,x72861))) % 178.07/177.94 [7302]P144(x73021,x73022,x73023)+~P24(f329(x73021,f808(x73023,x73022,x73021)))+P24(f329(f329(f244(a1),x73022),f806(x73023,x73022,x73021)))+~P24(f329(x73021,f2(a1))) % 178.07/177.94 [7306]P143(x73061,x73062,x73063)+~P24(f329(x73061,x73063))+P24(f329(f329(f243(a1),f2(a1)),f815(x73063,x73062,x73061)))+~P24(f329(x73061,f814(x73063,x73062,x73061))) % 178.07/177.94 [7324]P144(x73241,x73242,x73243)+P24(f329(f329(f243(a1),f2(a1)),f807(x73243,x73242,x73241)))+~P24(f329(x73241,f813(x73243,x73242,x73241)))+~P24(f329(x73241,f2(a1))) % 178.07/177.94 [7348]P144(x73482,x73481,x73483)+E(x73481,f2(a1))+~P24(f329(x73482,f808(x73483,x73481,x73482)))+~P24(f329(x73482,f813(x73483,x73481,x73482))) % 178.07/177.94 [7349]P143(x73492,x73491,x73493)+E(x73491,f2(a1))+~P24(f329(x73492,f815(x73493,x73491,x73492)))+~P24(f329(x73492,f814(x73493,x73491,x73492))) % 178.07/177.94 [7442]P143(x74421,x74422,x74423)+~P24(f329(x74421,x74423))+~P24(f329(x74421,f815(x74423,x74422,x74421)))+~P24(f329(x74421,f814(x74423,x74422,x74421))) % 178.07/177.94 [7459]P144(x74591,x74592,x74593)+~P24(f329(x74591,f808(x74593,x74592,x74591)))+~P24(f329(x74591,f813(x74593,x74592,x74591)))+~P24(f329(x74591,f2(a1))) % 178.07/177.94 [7507]P144(x75072,x75071,x75073)+E(x75071,f2(a1))+P24(f329(f329(f243(a1),f2(a1)),f807(x75073,x75071,x75072)))+P24(f329(f329(f243(a1),f806(x75073,x75071,x75072)),f2(a1))) % 178.07/177.94 [7508]P143(x75082,x75081,x75083)+E(x75081,f2(a1))+P24(f329(f329(f243(a1),f2(a1)),f815(x75083,x75081,x75082)))+P24(f329(f329(f243(a1),f814(x75083,x75081,x75082)),f2(a1))) % 178.07/177.94 [7509]~P137(x75091)+~P24(f329(f329(f331(x75091),x75093),f115(x75091)))+~P24(f329(f329(f331(x75091),x75092),f115(x75091)))+P24(f329(f329(f331(x75091),f329(f329(f22(x75091),x75092),x75093)),f115(x75091))) % 178.07/177.94 [7510]~P137(x75101)+~P24(f329(f329(f331(x75101),x75103),f115(x75101)))+~P24(f329(f329(f331(x75101),x75102),f115(x75101)))+P24(f329(f329(f331(x75101),f329(f329(f82(x75101),x75102),x75103)),f115(x75101))) % 178.07/177.94 [7511]~P141(x75111)+~P24(f329(f329(f331(x75111),x75113),f191(x75111)))+~P24(f329(f329(f331(x75111),x75112),f191(x75111)))+P24(f329(f329(f331(x75111),f329(f329(f82(x75111),x75112),x75113)),f191(x75111))) % 178.07/177.94 [7512]~P137(x75121)+~P24(f329(f329(f331(x75121),x75123),f115(x75121)))+~P24(f329(f329(f331(x75121),x75122),f115(x75121)))+P24(f329(f329(f331(x75121),f329(f329(f81(x75121),x75122),x75123)),f115(x75121))) % 178.07/177.94 [7513]~P141(x75131)+~P24(f329(f329(f331(x75131),x75133),f191(x75131)))+~P24(f329(f329(f331(x75131),x75132),f191(x75131)))+P24(f329(f329(f331(x75131),f329(f329(f81(x75131),x75132),x75133)),f191(x75131))) % 178.07/177.94 [7514]~P86(x75141)+~P24(f329(f329(f244(x75141),x75143),f2(x75141)))+~P24(f329(f329(f244(x75141),x75142),f2(x75141)))+P24(f329(f329(f244(x75141),f329(f329(f81(x75141),x75142),x75143)),f2(x75141))) % 178.07/177.94 [7515]~P86(x75151)+~P24(f329(f329(f243(x75151),x75152),f2(x75151)))+~P24(f329(f329(f244(x75151),x75153),f2(x75151)))+P24(f329(f329(f244(x75151),f329(f329(f81(x75151),x75152),x75153)),f2(x75151))) % 178.07/177.94 [7516]~P86(x75161)+~P24(f329(f329(f243(x75161),x75163),f2(x75161)))+~P24(f329(f329(f244(x75161),x75162),f2(x75161)))+P24(f329(f329(f244(x75161),f329(f329(f81(x75161),x75162),x75163)),f2(x75161))) % 178.07/177.94 [7517]~P86(x75171)+~P24(f329(f329(f243(x75171),x75173),f2(x75171)))+~P24(f329(f329(f243(x75171),x75172),f2(x75171)))+P24(f329(f329(f243(x75171),f329(f329(f81(x75171),x75172),x75173)),f2(x75171))) % 178.07/177.94 [7543]P144(x75433,x75431,x75432)+E(x75431,f2(a1))+E(f329(f329(f81(a1),f329(f329(f82(a1),x75431),f808(x75432,x75431,x75433))),f807(x75432,x75431,x75433)),x75432)+P24(f329(f329(f244(a1),x75431),f2(a1))) % 178.07/177.94 [7544]P143(x75443,x75441,x75442)+E(x75441,f2(a1))+E(f329(f329(f81(a1),f329(f329(f82(a1),x75441),f816(x75442,x75441,x75443))),f815(x75442,x75441,x75443)),x75442)+P24(f329(f329(f244(a1),x75441),f2(a1))) % 178.07/177.94 [7626]P143(x76261,x76262,x76263)+~P24(f329(x76261,x76263))+P24(f329(f329(f243(a1),f2(a1)),f815(x76263,x76262,x76261)))+P24(f329(f329(f243(a1),f814(x76263,x76262,x76261)),f2(a1))) % 178.07/177.94 [7655]P144(x76551,x76552,x76553)+P24(f329(f329(f243(a1),f2(a1)),f807(x76553,x76552,x76551)))+~P24(f329(x76551,f2(a1)))+P24(f329(f329(f243(a1),f806(x76553,x76552,x76551)),f2(a1))) % 178.07/177.94 [7664]P143(x76643,x76641,x76642)+~P24(f329(x76643,x76642))+E(f329(f329(f81(a1),f329(f329(f82(a1),x76641),f816(x76642,x76641,x76643))),f815(x76642,x76641,x76643)),x76642)+P24(f329(f329(f244(a1),x76641),f2(a1))) % 178.07/177.94 [7670]P144(x76702,x76701,x76703)+E(x76701,f2(a1))+~P24(f329(x76702,f808(x76703,x76701,x76702)))+P24(f329(f329(f243(a1),f806(x76703,x76701,x76702)),f2(a1))) % 178.07/177.94 [7671]P143(x76712,x76711,x76713)+E(x76711,f2(a1))+~P24(f329(x76712,f815(x76713,x76711,x76712)))+P24(f329(f329(f243(a1),f814(x76713,x76711,x76712)),f2(a1))) % 178.07/177.94 [7676]P144(x76763,x76761,x76762)+E(f329(f329(f81(a1),f329(f329(f82(a1),x76761),f808(x76762,x76761,x76763))),f807(x76762,x76761,x76763)),x76762)+~P24(f329(x76763,f2(a1)))+P24(f329(f329(f244(a1),x76761),f2(a1))) % 178.07/177.94 [7731]P143(x77311,x77312,x77313)+~P24(f329(x77311,x77313))+~P24(f329(x77311,f815(x77313,x77312,x77311)))+P24(f329(f329(f243(a1),f814(x77313,x77312,x77311)),f2(a1))) % 178.07/177.94 [7735]P144(x77351,x77352,x77353)+~P24(f329(x77351,f808(x77353,x77352,x77351)))+~P24(f329(x77351,f2(a1)))+P24(f329(f329(f243(a1),f806(x77353,x77352,x77351)),f2(a1))) % 178.07/177.94 [7804]~P61(x78041)+~P24(f329(f329(f244(x78041),f329(f329(f287(x78041),x78043),x78042)),f2(x78041)))+P24(f329(f329(f244(x78041),x78042),f2(x78041)))+P24(f329(f329(f244(x78041),x78043),f2(x78041))) % 178.07/177.94 [7805]~P121(x78051)+~P24(f329(f329(f243(x78051),f329(f329(f82(x78051),x78053),x78052)),f2(x78051)))+P24(f329(f329(f243(x78051),x78052),f2(x78051)))+P24(f329(f329(f243(x78051),x78053),f2(x78051))) % 178.07/177.94 [7806]~P61(x78061)+~P24(f329(f329(f243(x78061),f329(f329(f287(x78061),x78063),x78062)),f2(x78061)))+P24(f329(f329(f243(x78061),x78062),f2(x78061)))+P24(f329(f329(f243(x78061),x78063),f2(x78061))) % 178.07/177.94 [7920]P144(x79203,x79201,x79202)+E(x79201,f2(a1))+E(f329(f329(f81(a1),f329(f329(f82(a1),x79201),f808(x79202,x79201,x79203))),f807(x79202,x79201,x79203)),x79202)+P24(f329(f329(f244(a1),x79201),f806(x79202,x79201,x79203))) % 178.07/177.94 [7921]P143(x79213,x79211,x79212)+E(x79211,f2(a1))+E(f329(f329(f81(a1),f329(f329(f82(a1),x79211),f816(x79212,x79211,x79213))),f815(x79212,x79211,x79213)),x79212)+P24(f329(f329(f244(a1),x79211),f814(x79212,x79211,x79213))) % 178.07/177.94 [7933]P144(x79333,x79331,x79332)+E(x79331,f2(a1))+E(f329(f329(f81(a1),f329(f329(f82(a1),x79331),f813(x79332,x79331,x79333))),f806(x79332,x79331,x79333)),x79332)+P24(f329(f329(f243(a1),f2(a1)),f807(x79332,x79331,x79333))) % 178.07/177.94 [7934]P143(x79343,x79341,x79342)+E(x79341,f2(a1))+E(f329(f329(f81(a1),f329(f329(f82(a1),x79341),f817(x79342,x79341,x79343))),f814(x79342,x79341,x79343)),x79342)+P24(f329(f329(f243(a1),f2(a1)),f815(x79342,x79341,x79343))) % 178.07/177.94 [7978]P143(x79783,x79781,x79782)+~P24(f329(x79783,x79782))+E(f329(f329(f81(a1),f329(f329(f82(a1),x79781),f816(x79782,x79781,x79783))),f815(x79782,x79781,x79783)),x79782)+P24(f329(f329(f244(a1),x79781),f814(x79782,x79781,x79783))) % 178.07/177.94 [7990]P144(x79903,x79901,x79902)+E(f329(f329(f81(a1),f329(f329(f82(a1),x79901),f808(x79902,x79901,x79903))),f807(x79902,x79901,x79903)),x79902)+P24(f329(f329(f244(a1),x79901),f806(x79902,x79901,x79903)))+~P24(f329(x79903,f2(a1))) % 178.07/177.94 [7996]P143(x79963,x79961,x79962)+~P24(f329(x79963,x79962))+E(f329(f329(f81(a1),f329(f329(f82(a1),x79961),f817(x79962,x79961,x79963))),f814(x79962,x79961,x79963)),x79962)+P24(f329(f329(f243(a1),f2(a1)),f815(x79962,x79961,x79963))) % 178.07/177.94 [8004]P144(x80043,x80041,x80042)+E(f329(f329(f81(a1),f329(f329(f82(a1),x80041),f813(x80042,x80041,x80043))),f806(x80042,x80041,x80043)),x80042)+P24(f329(f329(f243(a1),f2(a1)),f807(x80042,x80041,x80043)))+~P24(f329(x80043,f2(a1))) % 178.07/177.94 [8015]P144(x80153,x80151,x80152)+E(x80151,f2(a1))+E(f329(f329(f81(a1),f329(f329(f82(a1),x80151),f808(x80152,x80151,x80153))),f807(x80152,x80151,x80153)),x80152)+~P24(f329(x80153,f813(x80152,x80151,x80153))) % 178.07/177.94 [8016]P143(x80163,x80161,x80162)+E(x80161,f2(a1))+E(f329(f329(f81(a1),f329(f329(f82(a1),x80161),f816(x80162,x80161,x80163))),f815(x80162,x80161,x80163)),x80162)+~P24(f329(x80163,f814(x80162,x80161,x80163))) % 178.07/177.94 [8017]P144(x80173,x80171,x80172)+E(x80171,f2(a1))+E(f329(f329(f81(a1),f329(f329(f82(a1),x80171),f813(x80172,x80171,x80173))),f806(x80172,x80171,x80173)),x80172)+~P24(f329(x80173,f808(x80172,x80171,x80173))) % 178.07/177.94 [8018]P143(x80183,x80181,x80182)+E(x80181,f2(a1))+E(f329(f329(f81(a1),f329(f329(f82(a1),x80181),f817(x80182,x80181,x80183))),f814(x80182,x80181,x80183)),x80182)+~P24(f329(x80183,f815(x80182,x80181,x80183))) % 178.07/177.94 [8076]P143(x80763,x80761,x80762)+~P24(f329(x80763,x80762))+E(f329(f329(f81(a1),f329(f329(f82(a1),x80761),f816(x80762,x80761,x80763))),f815(x80762,x80761,x80763)),x80762)+~P24(f329(x80763,f814(x80762,x80761,x80763))) % 178.07/177.94 [8077]P143(x80773,x80771,x80772)+~P24(f329(x80773,x80772))+E(f329(f329(f81(a1),f329(f329(f82(a1),x80771),f817(x80772,x80771,x80773))),f814(x80772,x80771,x80773)),x80772)+~P24(f329(x80773,f815(x80772,x80771,x80773))) % 178.07/177.94 [8087]P144(x80873,x80871,x80872)+E(f329(f329(f81(a1),f329(f329(f82(a1),x80871),f808(x80872,x80871,x80873))),f807(x80872,x80871,x80873)),x80872)+~P24(f329(x80873,f813(x80872,x80871,x80873)))+~P24(f329(x80873,f2(a1))) % 178.07/177.94 [8088]P144(x80883,x80881,x80882)+E(f329(f329(f81(a1),f329(f329(f82(a1),x80881),f813(x80882,x80881,x80883))),f806(x80882,x80881,x80883)),x80882)+~P24(f329(x80883,f808(x80882,x80881,x80883)))+~P24(f329(x80883,f2(a1))) % 178.07/177.94 [8192]P144(x81923,x81921,x81922)+E(x81921,f2(a1))+E(f329(f329(f81(a1),f329(f329(f82(a1),x81921),f808(x81922,x81921,x81923))),f807(x81922,x81921,x81923)),x81922)+P24(f329(f329(f243(a1),f806(x81922,x81921,x81923)),f2(a1))) % 178.07/177.94 [8193]P143(x81933,x81931,x81932)+E(x81931,f2(a1))+E(f329(f329(f81(a1),f329(f329(f82(a1),x81931),f816(x81932,x81931,x81933))),f815(x81932,x81931,x81933)),x81932)+P24(f329(f329(f243(a1),f814(x81932,x81931,x81933)),f2(a1))) % 178.07/177.94 [8233]P143(x82333,x82331,x82332)+~P24(f329(x82333,x82332))+E(f329(f329(f81(a1),f329(f329(f82(a1),x82331),f816(x82332,x82331,x82333))),f815(x82332,x82331,x82333)),x82332)+P24(f329(f329(f243(a1),f814(x82332,x82331,x82333)),f2(a1))) % 178.07/177.94 [8238]P144(x82383,x82381,x82382)+E(f329(f329(f81(a1),f329(f329(f82(a1),x82381),f808(x82382,x82381,x82383))),f807(x82382,x82381,x82383)),x82382)+~P24(f329(x82383,f2(a1)))+P24(f329(f329(f243(a1),f806(x82382,x82381,x82383)),f2(a1))) % 178.07/177.94 [8367]P144(x83673,x83671,x83672)+E(x83671,f2(a1))+E(f329(f329(f81(a1),f329(f329(f82(a1),x83671),f813(x83672,x83671,x83673))),f806(x83672,x83671,x83673)),x83672)+E(f329(f329(f81(a1),f329(f329(f82(a1),x83671),f808(x83672,x83671,x83673))),f807(x83672,x83671,x83673)),x83672) % 178.07/177.94 [8368]P143(x83683,x83681,x83682)+E(x83681,f2(a1))+E(f329(f329(f81(a1),f329(f329(f82(a1),x83681),f817(x83682,x83681,x83683))),f814(x83682,x83681,x83683)),x83682)+E(f329(f329(f81(a1),f329(f329(f82(a1),x83681),f816(x83682,x83681,x83683))),f815(x83682,x83681,x83683)),x83682) % 178.07/177.94 [8391]P143(x83913,x83911,x83912)+~P24(f329(x83913,x83912))+E(f329(f329(f81(a1),f329(f329(f82(a1),x83911),f817(x83912,x83911,x83913))),f814(x83912,x83911,x83913)),x83912)+E(f329(f329(f81(a1),f329(f329(f82(a1),x83911),f816(x83912,x83911,x83913))),f815(x83912,x83911,x83913)),x83912) % 178.07/177.94 [8403]P144(x84033,x84031,x84032)+E(f329(f329(f81(a1),f329(f329(f82(a1),x84031),f813(x84032,x84031,x84033))),f806(x84032,x84031,x84033)),x84032)+E(f329(f329(f81(a1),f329(f329(f82(a1),x84031),f808(x84032,x84031,x84033))),f807(x84032,x84031,x84033)),x84032)+~P24(f329(x84033,f2(a1))) % 178.07/177.94 [9053]~P121(x90531)+~E(x90533,f2(x90531))+~E(x90532,f2(x90531))+P24(f329(f329(f243(x90531),f329(f329(f81(x90531),f329(f329(f82(x90531),x90532),x90532)),f329(f329(f82(x90531),x90533),x90533))),f2(x90531))) % 178.07/177.94 [10096]~P117(x100961)+~E(x100963,f2(x100961))+~E(x100962,f2(x100961))+P24(f329(f329(f243(x100961),f329(f329(f81(x100961),f329(f329(f254(x100961),x100962),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f329(f329(f254(x100961),x100963),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))))),f2(x100961))) % 178.07/177.94 [4793]~E(x47933,x47931)+~P115(x47932)+E(x47931,f2(x47932))+E(f329(f329(f287(x47932),x47933),x47931),f79(x47932)) % 178.07/177.94 [4846]~P64(x48461)+~E(x48463,f193(x48461))+~E(x48462,f193(x48461))+E(f329(f329(f116(x48461),x48462),x48463),f193(x48461)) % 178.07/177.94 [4847]~P98(x48471)+~E(x48473,f252(x48471))+~E(x48472,f252(x48471))+E(f329(f329(f107(x48471),x48472),x48473),f252(x48471)) % 178.07/177.94 [4933]~P115(x49333)+E(x49331,x49332)+E(x49332,f2(x49333))+~E(f329(f329(f287(x49333),x49331),x49332),f79(x49333)) % 178.07/177.94 [4952]~P129(x49522)+E(x49521,f2(x49522))+E(x49523,f2(x49522))+~E(f329(f329(f82(x49522),x49523),x49521),f2(x49522)) % 178.07/177.94 [4953]~P138(x49532)+E(x49531,f2(x49532))+E(x49533,f2(x49532))+~E(f329(f329(f82(x49532),x49533),x49531),f2(x49532)) % 178.07/177.94 [5331]~P109(x53313)+E(x53311,x53312)+E(x53311,f329(f80(x53313),x53312))+~E(f329(f329(f82(x53313),x53311),x53311),f329(f329(f82(x53313),x53312),x53312)) % 178.07/177.94 [5371]~P89(x53711)+E(f329(f80(x53711),x53712),x53713)+~E(f329(f329(f116(x53711),x53712),x53713),f252(x53711))+~E(f329(f329(f107(x53711),x53712),x53713),f193(x53711)) % 178.07/177.94 [5450]~P117(x54503)+E(x54501,x54502)+P24(f329(f329(f244(x54503),x54502),x54501))+P24(f329(f329(f244(x54503),x54501),x54502)) % 178.07/177.94 [5451]~P105(x54513)+E(x54511,x54512)+P24(f329(f329(f244(x54513),x54512),x54511))+P24(f329(f329(f244(x54513),x54511),x54512)) % 178.07/177.94 [5452]~E(x54522,x54523)+~P105(x54521)+P24(f329(f329(f243(x54521),x54522),x54523))+P24(f329(f329(f244(x54521),x54522),x54523)) % 178.07/177.94 [5703]~P107(x57033)+E(x57031,x57032)+~P24(f329(f329(f243(x57033),x57032),x57031))+P24(f329(f329(f244(x57033),x57032),x57031)) % 178.07/177.94 [5705]~P105(x57053)+E(x57051,x57052)+~P24(f329(f329(f243(x57053),x57051),x57052))+P24(f329(f329(f244(x57053),x57051),x57052)) % 178.07/177.94 [5711]~P107(x57113)+E(x57111,x57112)+~P24(f329(f329(f243(x57113),x57111),x57112))+P24(f329(f329(f244(x57113),x57111),x57112)) % 178.07/177.94 [5813]P143(x58131,x58132,x58133)+~P24(f329(x58131,x58133))+P24(f329(f329(f244(a1),x58132),f2(a1)))+P24(f329(f329(f244(a1),f2(a1)),x58132)) % 178.07/177.94 [5860]P144(x58601,x58602,x58603)+~P24(f329(x58601,f2(a1)))+P24(f329(f329(f244(a1),x58602),f2(a1)))+P24(f329(f329(f244(a1),f2(a1)),x58602)) % 178.07/177.94 [5864]~P63(x58641)+E(f329(f329(f116(x58641),x58642),f10(x58641,x58643)),x58642)+~P24(f329(f62(x58641),x58643))+~P24(f329(f329(f331(x58641),x58642),x58643)) % 178.07/177.94 [5865]~P63(x58651)+E(f329(f329(f107(x58651),x58652),f13(x58651,x58653)),x58652)+~P24(f329(f62(x58651),x58653))+~P24(f329(f329(f331(x58651),x58652),x58653)) % 178.07/177.94 [5901]~P63(x59011)+E(f329(f329(f116(x59011),x59012),f13(x59011,x59013)),f13(x59011,x59013))+~P24(f329(f62(x59011),x59013))+~P24(f329(f329(f331(x59011),x59012),x59013)) % 178.07/177.94 [5902]~P63(x59021)+E(f329(f329(f107(x59021),x59022),f10(x59021,x59023)),f10(x59021,x59023))+~P24(f329(f62(x59021),x59023))+~P24(f329(f329(f331(x59021),x59022),x59023)) % 178.07/177.94 [5903]~P105(x59031)+E(f329(f329(f241(x59031),x59032),f14(x59031,x59033)),f14(x59031,x59033))+~P24(f329(f62(x59031),x59033))+~P24(f329(f329(f331(x59031),x59032),x59033)) % 178.07/177.94 [5904]~P105(x59041)+E(f329(f329(f242(x59041),x59042),f15(x59041,x59043)),f15(x59041,x59043))+~P24(f329(f62(x59041),x59043))+~P24(f329(f329(f331(x59041),x59042),x59043)) % 178.07/177.94 [5949]E(x59491,x59492)+~P107(x59493)+~P24(f329(f329(f243(x59493),x59492),x59491))+~P24(f329(f329(f243(x59493),x59491),x59492)) % 178.07/177.94 [6090]~P104(x60901)+P24(f329(f329(f243(x60901),x60903),x60902))+~P24(f329(f329(f243(x60901),x60902),x60903))+P24(f329(f329(f244(x60901),x60902),x60903)) % 178.07/177.94 [6111]~P105(x61111)+~P24(f329(f62(x61111),x61113))+P24(f329(f329(f243(x61111),x61112),f15(x61111,x61113)))+~P24(f329(f329(f331(x61111),x61112),x61113)) % 178.07/177.94 [6164]~P105(x61641)+E(f329(f329(f241(x61641),x61642),f11(x61641,f242(x61641),x61643)),x61642)+~P24(f329(f62(x61641),x61643))+~P24(f329(f329(f331(x61641),x61642),x61643)) % 178.07/177.94 [6165]~P105(x61651)+E(f329(f329(f242(x61651),x61652),f12(x61651,f241(x61651),x61653)),x61652)+~P24(f329(f62(x61651),x61653))+~P24(f329(f329(f331(x61651),x61652),x61653)) % 178.07/177.94 [6302]E(x63021,x63022)+~E(f329(f329(f22(a875),x63021),x63023),f329(f329(f22(a875),x63022),x63023))+~P24(f329(f329(f243(a875),x63023),x63021))+~P24(f329(f329(f243(a875),x63023),x63022)) % 178.07/177.94 [6331]~P105(x63311)+~P24(f329(f62(x63311),x63312))+~P24(f329(f329(f331(x63311),x63313),x63312))+P24(f329(f329(f243(x63311),f14(x63311,x63312)),x63313)) % 178.07/177.94 [6393]P144(x63932,x63931,x63933)+E(x63931,f2(a1))+P24(f329(f329(f244(a1),x63931),f806(x63933,x63931,x63932)))+P24(f329(f329(f244(a1),f2(a1)),x63931)) % 178.07/177.94 [6394]P143(x63942,x63941,x63943)+E(x63941,f2(a1))+P24(f329(f329(f244(a1),x63941),f814(x63943,x63941,x63942)))+P24(f329(f329(f244(a1),f2(a1)),x63941)) % 178.07/177.94 [6395]~P105(x63951)+E(f329(f329(f241(x63951),x63952),f12(x63951,f241(x63951),x63953)),f12(x63951,f241(x63951),x63953))+~P24(f329(f62(x63951),x63953))+~P24(f329(f329(f331(x63951),x63952),x63953)) % 178.07/177.94 [6396]~P105(x63961)+E(f329(f329(f242(x63961),x63962),f11(x63961,f242(x63961),x63963)),f11(x63961,f242(x63961),x63963))+~P24(f329(f62(x63961),x63963))+~P24(f329(f329(f331(x63961),x63962),x63963)) % 178.07/177.94 [6402]~P24(f329(x64021,x64022))+P24(f329(x64021,f526(x64022,x64021,x64023)))+P24(f329(x64021,f2(a875)))+~P24(f329(f329(f244(a875),x64022),x64023)) % 178.07/177.94 [6457]~P24(f329(x64571,x64572))+~P24(f329(f62(x64573),x64572))+P24(f329(x64571,f665(x64571,x64572,x64573)))+P24(f329(x64571,f193(f883(x64573,a869)))) % 178.07/177.94 [6470]~P117(x64701)+~P92(x64701)+P24(f329(f329(f244(x64701),f329(f109(x64701),x64702)),f329(f109(x64701),x64703)))+~P24(f329(f329(f244(a1),x64702),x64703)) % 178.07/177.94 [6471]~P117(x64711)+~P92(x64711)+P24(f329(f329(f243(x64711),f329(f109(x64711),x64712)),f329(f109(x64711),x64713)))+~P24(f329(f329(f243(a1),x64712),x64713)) % 178.07/177.94 [6474]~P24(f329(x64741,x64743))+~P24(f329(f62(x64742),x64743))+P24(f329(f62(x64742),f665(x64741,x64743,x64742)))+P24(f329(x64741,f193(f883(x64742,a869)))) % 178.07/177.94 [6507]P143(x65071,x65072,x65073)+~P24(f329(x65071,x65073))+P24(f329(f329(f244(a1),x65072),f814(x65073,x65072,x65071)))+P24(f329(f329(f244(a1),f2(a1)),x65072)) % 178.07/177.94 [6542]P144(x65421,x65422,x65423)+P24(f329(f329(f244(a1),x65422),f806(x65423,x65422,x65421)))+~P24(f329(x65421,f2(a1)))+P24(f329(f329(f244(a1),f2(a1)),x65422)) % 178.07/177.94 [6573]~P106(x65731)+~P93(x65731)+E(f329(f329(f241(x65731),f329(f109(x65731),x65732)),f329(f109(x65731),x65733)),f329(f109(x65731),x65733))+P24(f329(f329(f243(x65731),f329(f109(x65731),x65732)),f329(f109(x65731),x65733))) % 178.07/177.94 [6574]~P106(x65741)+~P93(x65741)+E(f329(f329(f242(x65741),f329(f109(x65741),x65742)),f329(f109(x65741),x65743)),f329(f109(x65741),x65742))+P24(f329(f329(f243(x65741),f329(f109(x65741),x65742)),f329(f109(x65741),x65743))) % 178.07/177.94 [6632]P144(x66322,x66321,x66323)+E(x66321,f2(a1))+~P24(f329(x66322,f813(x66323,x66321,x66322)))+P24(f329(f329(f244(a1),f2(a1)),x66321)) % 178.07/177.94 [6633]P143(x66332,x66331,x66333)+E(x66331,f2(a1))+~P24(f329(x66332,f814(x66333,x66331,x66332)))+P24(f329(f329(f244(a1),f2(a1)),x66331)) % 178.07/177.94 [6637]P24(f329(x66371,x66372))+~P24(f329(f62(x66373),x66372))+P24(f329(x66371,f568(x66371,x66372,x66373)))+~P24(f329(x66371,f193(f883(x66373,a869)))) % 178.07/177.94 [6656]P24(f329(x66561,x66562))+P24(f329(f62(x66563),f568(x66561,x66562,x66563)))+~P24(f329(f62(x66563),x66562))+~P24(f329(x66561,f193(f883(x66563,a869)))) % 178.07/177.94 [6721]P143(x67211,x67212,x67213)+~P24(f329(x67211,x67213))+~P24(f329(x67211,f814(x67213,x67212,x67211)))+P24(f329(f329(f244(a1),f2(a1)),x67212)) % 178.07/177.94 [6751]P144(x67511,x67512,x67513)+~P24(f329(x67511,f813(x67513,x67512,x67511)))+~P24(f329(x67511,f2(a1)))+P24(f329(f329(f244(a1),f2(a1)),x67512)) % 178.07/177.94 [6858]~P92(x68583)+~P117(x68583)+~P24(f329(f329(f244(x68583),f329(f109(x68583),x68581)),f329(f109(x68583),x68582)))+P24(f329(f329(f244(a1),x68581),x68582)) % 178.07/177.94 [6859]~P92(x68593)+~P117(x68593)+~P24(f329(f329(f243(x68593),f329(f109(x68593),x68591)),f329(f109(x68593),x68592)))+P24(f329(f329(f243(a1),x68591),x68592)) % 178.07/177.94 [6888]~P105(x68881)+~P29(x68881,x68883)+P29(x68881,f329(f329(f150(x68881),x68882),x68883))+~P24(f329(f329(f243(x68881),x68882),f648(x68883,x68882,x68881))) % 178.07/177.94 [6889]~P105(x68891)+~P29(x68891,x68893)+P29(x68891,f329(f329(f150(x68891),x68892),x68893))+~P24(f329(f329(f243(x68891),x68892),f649(x68893,x68892,x68891))) % 178.07/177.94 [6890]~P105(x68901)+~P29(x68901,x68903)+P29(x68901,f329(f329(f150(x68901),x68902),x68903))+~P24(f329(f329(f243(x68901),x68902),f730(x68902,x68903,x68901))) % 178.07/177.94 [6974]P144(x69742,x69741,x69743)+E(x69741,f2(a1))+P24(f329(f329(f244(a1),x69741),f2(a1)))+P24(f329(f329(f244(a1),f807(x69743,x69741,x69742)),x69741)) % 178.07/177.94 [6975]P143(x69752,x69751,x69753)+E(x69751,f2(a1))+P24(f329(f329(f244(a1),x69751),f2(a1)))+P24(f329(f329(f244(a1),f815(x69753,x69751,x69752)),x69751)) % 178.07/177.94 [7016]P144(x70162,x70161,x70163)+E(x70161,f2(a1))+P24(f329(f329(f243(a1),f806(x70163,x70161,x70162)),f2(a1)))+P24(f329(f329(f244(a1),f2(a1)),x70161)) % 178.07/177.94 [7017]P143(x70172,x70171,x70173)+E(x70171,f2(a1))+P24(f329(f329(f243(a1),f814(x70173,x70171,x70172)),f2(a1)))+P24(f329(f329(f244(a1),f2(a1)),x70171)) % 178.07/177.94 [7039]~P105(x70391)+~P29(x70391,x70393)+E(f329(f329(f147(x70391,x70391,f5(x70391)),x70392),f169(x70391,x70392,x70393)),x70393)+~P24(f329(f329(f331(x70391),x70392),f329(f171(x70391),x70393))) % 178.07/177.94 [7086]P143(x70861,x70862,x70863)+~P24(f329(x70861,x70863))+P24(f329(f329(f244(a1),x70862),f2(a1)))+P24(f329(f329(f244(a1),f815(x70863,x70862,x70861)),x70862)) % 178.07/177.94 [7092]~P106(x70921)+~P93(x70921)+E(f329(f329(f241(x70921),f329(f109(x70921),x70922)),f329(f109(x70921),x70923)),f329(f109(x70921),x70922))+~P24(f329(f329(f243(x70921),f329(f109(x70921),x70922)),f329(f109(x70921),x70923))) % 178.07/177.94 [7093]~P106(x70931)+~P93(x70931)+E(f329(f329(f242(x70931),f329(f109(x70931),x70932)),f329(f109(x70931),x70933)),f329(f109(x70931),x70933))+~P24(f329(f329(f243(x70931),f329(f109(x70931),x70932)),f329(f109(x70931),x70933))) % 178.07/177.94 [7107]P144(x71071,x71072,x71073)+~P24(f329(x71071,f2(a1)))+P24(f329(f329(f244(a1),x71072),f2(a1)))+P24(f329(f329(f244(a1),f807(x71073,x71072,x71071)),x71072)) % 178.07/177.94 [7115]P143(x71151,x71152,x71153)+~P24(f329(x71151,x71153))+P24(f329(f329(f243(a1),f814(x71153,x71152,x71151)),f2(a1)))+P24(f329(f329(f244(a1),f2(a1)),x71152)) % 178.07/177.94 [7139]P144(x71391,x71392,x71393)+~P24(f329(x71391,f2(a1)))+P24(f329(f329(f243(a1),f806(x71393,x71392,x71391)),f2(a1)))+P24(f329(f329(f244(a1),f2(a1)),x71392)) % 178.07/177.94 [7167]~P24(f329(x71671,x71672))+P24(f329(x71671,f2(a875)))+~P24(f329(f329(f244(a875),x71672),x71673))+P24(f329(f329(f244(a875),f526(x71672,x71671,x71673)),x71673)) % 178.07/177.94 [7184]~P105(x71841)+~P29(x71841,x71843)+P29(x71841,f329(f329(f150(x71841),x71842),x71843))+P24(f329(f329(f331(x71841),f648(x71843,x71842,x71841)),f329(f171(x71841),x71843))) % 178.07/177.94 [7185]~P105(x71851)+~P29(x71851,x71853)+P29(x71851,f329(f329(f150(x71851),x71852),x71853))+P24(f329(f329(f331(x71851),f649(x71853,x71852,x71851)),f329(f171(x71851),x71853))) % 178.07/177.94 [7186]~P105(x71861)+~P29(x71861,x71863)+P29(x71861,f329(f329(f150(x71861),x71862),x71863))+P24(f329(f329(f331(x71861),f730(x71862,x71863,x71861)),f329(f171(x71861),x71863))) % 178.07/177.94 [7290]~P27(x72901)+~P105(x72901)+~P24(f329(f329(f244(x72901),x72903),f40(x72901,x72902)))+P24(f329(f329(f331(x72901),f864(x72902,x72903,x72901)),x72902)) % 178.07/177.94 [7457]~P27(x74571)+~P105(x74571)+~P24(f329(f329(f244(x74571),f41(x74571,x74573)),x74572))+P24(f329(f329(f331(x74571),f867(x74572,x74573,x74571)),x74573)) % 178.07/177.94 [7458]~P27(x74581)+~P105(x74581)+~P24(f329(f329(f244(x74581),f41(x74581,x74583)),x74582))+P24(f329(f329(f244(x74581),f867(x74582,x74583,x74581)),x74582)) % 178.07/177.94 [7473]P144(x74732,x74731,x74733)+E(x74731,f2(a1))+P24(f329(f329(f244(a1),x74731),f806(x74733,x74731,x74732)))+P24(f329(f329(f244(a1),f807(x74733,x74731,x74732)),x74731)) % 178.07/177.94 [7474]P143(x74742,x74741,x74743)+E(x74741,f2(a1))+P24(f329(f329(f244(a1),x74741),f814(x74743,x74741,x74742)))+P24(f329(f329(f244(a1),f815(x74743,x74741,x74742)),x74741)) % 178.07/177.94 [7564]P144(x75643,x75641,x75642)+E(x75641,f2(a1))+E(f329(f329(f81(a1),f329(f329(f82(a1),x75641),f813(x75642,x75641,x75643))),f806(x75642,x75641,x75643)),x75642)+P24(f329(f329(f244(a1),f2(a1)),x75641)) % 178.07/177.94 [7565]P143(x75653,x75651,x75652)+E(x75651,f2(a1))+E(f329(f329(f81(a1),f329(f329(f82(a1),x75651),f817(x75652,x75651,x75653))),f814(x75652,x75651,x75653)),x75652)+P24(f329(f329(f244(a1),f2(a1)),x75651)) % 178.07/177.94 [7567]~P125(x75671)+~P24(f329(f329(f244(x75671),x75673),f2(x75671)))+P24(f329(f329(f244(x75671),f329(f329(f82(x75671),x75672),x75673)),f2(x75671)))+~P24(f329(f329(f244(x75671),f2(x75671)),x75672)) % 178.07/177.94 [7568]~P125(x75681)+~P24(f329(f329(f244(x75681),x75682),f2(x75681)))+P24(f329(f329(f244(x75681),f329(f329(f82(x75681),x75682),x75683)),f2(x75681)))+~P24(f329(f329(f244(x75681),f2(x75681)),x75683)) % 178.07/177.94 [7569]~P61(x75691)+~P24(f329(f329(f244(x75691),x75693),f2(x75691)))+P24(f329(f329(f244(x75691),f329(f329(f287(x75691),x75692),x75693)),f2(x75691)))+~P24(f329(f329(f244(x75691),f2(x75691)),x75692)) % 178.07/177.94 [7570]~P61(x75701)+~P24(f329(f329(f244(x75701),x75702),f2(x75701)))+P24(f329(f329(f244(x75701),f329(f329(f287(x75701),x75702),x75703)),f2(x75701)))+~P24(f329(f329(f244(x75701),f2(x75701)),x75703)) % 178.07/177.94 [7571]~P62(x75711)+~P24(f329(f329(f244(x75711),x75713),f2(x75711)))+P24(f329(f329(f244(x75711),f329(f329(f287(x75711),x75712),x75713)),f2(x75711)))+~P24(f329(f329(f244(x75711),f2(x75711)),x75712)) % 178.07/177.94 [7572]~P62(x75721)+~P24(f329(f329(f244(x75721),x75722),f2(x75721)))+P24(f329(f329(f244(x75721),f329(f329(f287(x75721),x75722),x75723)),f2(x75721)))+~P24(f329(f329(f244(x75721),f2(x75721)),x75723)) % 178.07/177.94 [7575]~P130(x75751)+~P24(f329(f329(f243(x75751),x75753),f2(x75751)))+P24(f329(f329(f243(x75751),f329(f329(f82(x75751),x75752),x75753)),f2(x75751)))+~P24(f329(f329(f243(x75751),f2(x75751)),x75752)) % 178.07/177.94 [7577]~P130(x75771)+~P24(f329(f329(f243(x75771),x75772),f2(x75771)))+P24(f329(f329(f243(x75771),f329(f329(f82(x75771),x75772),x75773)),f2(x75771)))+~P24(f329(f329(f243(x75771),f2(x75771)),x75773)) % 178.07/177.94 [7578]~P121(x75781)+~P24(f329(f329(f243(x75781),x75783),f2(x75781)))+P24(f329(f329(f243(x75781),f329(f329(f82(x75781),x75782),x75783)),f2(x75781)))+~P24(f329(f329(f243(x75781),f2(x75781)),x75782)) % 178.07/177.94 [7579]~P121(x75791)+~P24(f329(f329(f243(x75791),x75792),f2(x75791)))+P24(f329(f329(f243(x75791),f329(f329(f82(x75791),x75792),x75793)),f2(x75791)))+~P24(f329(f329(f243(x75791),f2(x75791)),x75793)) % 178.07/177.94 [7580]~P61(x75801)+~P24(f329(f329(f243(x75801),x75803),f2(x75801)))+P24(f329(f329(f243(x75801),f329(f329(f287(x75801),x75802),x75803)),f2(x75801)))+~P24(f329(f329(f243(x75801),f2(x75801)),x75802)) % 178.07/177.94 [7581]~P61(x75811)+~P24(f329(f329(f243(x75811),x75812),f2(x75811)))+P24(f329(f329(f243(x75811),f329(f329(f287(x75811),x75812),x75813)),f2(x75811)))+~P24(f329(f329(f243(x75811),f2(x75811)),x75813)) % 178.07/177.94 [7582]~P62(x75821)+~P24(f329(f329(f244(x75821),x75823),f2(x75821)))+P24(f329(f329(f243(x75821),f329(f329(f287(x75821),x75822),x75823)),f2(x75821)))+~P24(f329(f329(f243(x75821),f2(x75821)),x75822)) % 178.07/177.94 [7583]~P62(x75831)+~P24(f329(f329(f243(x75831),x75832),f2(x75831)))+P24(f329(f329(f243(x75831),f329(f329(f287(x75831),x75832),x75833)),f2(x75831)))+~P24(f329(f329(f244(x75831),f2(x75831)),x75833)) % 178.07/177.94 [7598]P143(x75981,x75982,x75983)+~P24(f329(x75981,x75983))+P24(f329(f329(f244(a1),x75982),f814(x75983,x75982,x75981)))+P24(f329(f329(f244(a1),f815(x75983,x75982,x75981)),x75982)) % 178.07/177.94 [7611]P144(x76111,x76112,x76113)+P24(f329(f329(f244(a1),x76112),f806(x76113,x76112,x76111)))+~P24(f329(x76111,f2(a1)))+P24(f329(f329(f244(a1),f807(x76113,x76112,x76111)),x76112)) % 178.07/177.94 [7661]P144(x76612,x76611,x76613)+E(x76611,f2(a1))+~P24(f329(x76612,f813(x76613,x76611,x76612)))+P24(f329(f329(f244(a1),f807(x76613,x76611,x76612)),x76611)) % 178.07/177.94 [7662]P143(x76622,x76621,x76623)+E(x76621,f2(a1))+~P24(f329(x76622,f814(x76623,x76621,x76622)))+P24(f329(f329(f244(a1),f815(x76623,x76621,x76622)),x76621)) % 178.07/177.94 [7673]P143(x76733,x76731,x76732)+~P24(f329(x76733,x76732))+E(f329(f329(f81(a1),f329(f329(f82(a1),x76731),f817(x76732,x76731,x76733))),f814(x76732,x76731,x76733)),x76732)+P24(f329(f329(f244(a1),f2(a1)),x76731)) % 178.07/177.94 [7691]P144(x76913,x76911,x76912)+E(f329(f329(f81(a1),f329(f329(f82(a1),x76911),f813(x76912,x76911,x76913))),f806(x76912,x76911,x76913)),x76912)+~P24(f329(x76913,f2(a1)))+P24(f329(f329(f244(a1),f2(a1)),x76911)) % 178.07/177.94 [7716]~P24(f329(x77161,x77163))+~P24(f329(f62(x77162),x77163))+P24(f329(f329(f331(x77162),f657(x77161,x77163,x77162)),f665(x77161,x77163,x77162)))+P24(f329(x77161,f193(f883(x77162,a869)))) % 178.07/177.94 [7727]P143(x77271,x77272,x77273)+~P24(f329(x77271,x77273))+~P24(f329(x77271,f814(x77273,x77272,x77271)))+P24(f329(f329(f244(a1),f815(x77273,x77272,x77271)),x77272)) % 178.07/177.94 [7732]P144(x77321,x77322,x77323)+~P24(f329(x77321,f813(x77323,x77322,x77321)))+~P24(f329(x77321,f2(a1)))+P24(f329(f329(f244(a1),f807(x77323,x77322,x77321)),x77322)) % 178.07/177.94 [7835]~P61(x78351)+~P24(f329(f329(f244(x78351),f329(f329(f287(x78351),x78353),x78352)),f2(x78351)))+P24(f329(f329(f244(x78351),x78352),f2(x78351)))+P24(f329(f329(f244(x78351),f2(x78351)),x78352)) % 178.07/177.94 [7836]~P61(x78361)+~P24(f329(f329(f244(x78361),f329(f329(f287(x78361),x78362),x78363)),f2(x78361)))+P24(f329(f329(f244(x78361),x78362),f2(x78361)))+P24(f329(f329(f244(x78361),f2(x78361)),x78362)) % 178.07/177.94 [7837]~P121(x78371)+~P24(f329(f329(f243(x78371),f329(f329(f82(x78371),x78373),x78372)),f2(x78371)))+P24(f329(f329(f243(x78371),x78372),f2(x78371)))+P24(f329(f329(f243(x78371),f2(x78371)),x78372)) % 178.07/177.94 [7838]~P121(x78381)+~P24(f329(f329(f243(x78381),f329(f329(f82(x78381),x78382),x78383)),f2(x78381)))+P24(f329(f329(f243(x78381),x78382),f2(x78381)))+P24(f329(f329(f243(x78381),f2(x78381)),x78382)) % 178.07/177.94 [7839]~P61(x78391)+~P24(f329(f329(f243(x78391),f329(f329(f287(x78391),x78393),x78392)),f2(x78391)))+P24(f329(f329(f243(x78391),x78392),f2(x78391)))+P24(f329(f329(f243(x78391),f2(x78391)),x78392)) % 178.07/177.94 [7840]~P61(x78401)+~P24(f329(f329(f243(x78401),f329(f329(f287(x78401),x78402),x78403)),f2(x78401)))+P24(f329(f329(f243(x78401),x78402),f2(x78401)))+P24(f329(f329(f243(x78401),f2(x78401)),x78402)) % 178.07/177.94 [7864]~P61(x78641)+~P24(f329(f329(f244(x78641),f329(f329(f287(x78641),x78642),x78643)),f2(x78641)))+P24(f329(f329(f244(x78641),f2(x78641)),x78642))+P24(f329(f329(f244(x78641),f2(x78641)),x78643)) % 178.07/177.94 [7865]~P121(x78651)+~P24(f329(f329(f243(x78651),f329(f329(f82(x78651),x78652),x78653)),f2(x78651)))+P24(f329(f329(f243(x78651),f2(x78651)),x78652))+P24(f329(f329(f243(x78651),f2(x78651)),x78653)) % 178.07/177.94 [7866]~P61(x78661)+~P24(f329(f329(f243(x78661),f329(f329(f287(x78661),x78662),x78663)),f2(x78661)))+P24(f329(f329(f243(x78661),f2(x78661)),x78662))+P24(f329(f329(f243(x78661),f2(x78661)),x78663)) % 178.07/177.94 [7887]P144(x78872,x78871,x78873)+E(x78871,f2(a1))+P24(f329(f329(f243(a1),f806(x78873,x78871,x78872)),f2(a1)))+P24(f329(f329(f244(a1),f807(x78873,x78871,x78872)),x78871)) % 178.07/177.94 [7888]P143(x78882,x78881,x78883)+E(x78881,f2(a1))+P24(f329(f329(f243(a1),f814(x78883,x78881,x78882)),f2(a1)))+P24(f329(f329(f244(a1),f815(x78883,x78881,x78882)),x78881)) % 178.07/177.94 [7895]~P120(x78951)+~P24(f329(f329(f244(x78951),x78952),f79(x78951)))+P24(f329(f329(f244(x78951),f329(f329(f254(x78951),x78952),f329(a118,x78953))),f79(x78951)))+~P24(f329(f329(f244(x78951),f2(x78951)),x78952)) % 178.07/177.94 [7950]~P105(x79501)+~E(x79503,f119(x79501))+~P29(x79501,f329(f168(x79501),x79503))+E(f329(f141(x79501,x79501,f329(f7(x79501,x79501,x79501),f242(x79501)),x79502),f329(f168(x79501),x79503)),x79502) % 178.07/177.94 [7952]P143(x79521,x79522,x79523)+~P24(f329(x79521,x79523))+P24(f329(f329(f243(a1),f814(x79523,x79522,x79521)),f2(a1)))+P24(f329(f329(f244(a1),f815(x79523,x79522,x79521)),x79522)) % 178.07/177.94 [7962]P144(x79621,x79622,x79623)+~P24(f329(x79621,f2(a1)))+P24(f329(f329(f243(a1),f806(x79623,x79622,x79621)),f2(a1)))+P24(f329(f329(f244(a1),f807(x79623,x79622,x79621)),x79622)) % 178.07/177.94 [8187]P144(x81873,x81871,x81872)+E(x81871,f2(a1))+E(f329(f329(f81(a1),f329(f329(f82(a1),x81871),f813(x81872,x81871,x81873))),f806(x81872,x81871,x81873)),x81872)+P24(f329(f329(f244(a1),f807(x81872,x81871,x81873)),x81871)) % 178.07/177.94 [8188]P143(x81883,x81881,x81882)+E(x81881,f2(a1))+E(f329(f329(f81(a1),f329(f329(f82(a1),x81881),f817(x81882,x81881,x81883))),f814(x81882,x81881,x81883)),x81882)+P24(f329(f329(f244(a1),f815(x81882,x81881,x81883)),x81881)) % 178.07/177.94 [8224]P143(x82243,x82241,x82242)+~P24(f329(x82243,x82242))+E(f329(f329(f81(a1),f329(f329(f82(a1),x82241),f817(x82242,x82241,x82243))),f814(x82242,x82241,x82243)),x82242)+P24(f329(f329(f244(a1),f815(x82242,x82241,x82243)),x82241)) % 178.07/177.94 [8225]~P70(x82251)+~P74(x82251)+~P39(x82253)+E(f329(f329(f6(a875,x82251),f329(f329(f8(a1,x82251,a875),x82252),f106(a1))),f329(f308(a1,a875,a110),x82253)),f329(f329(f6(a1,x82251),x82252),x82253)) % 178.07/177.94 [8226]~P70(x82261)+~P74(x82261)+~P39(x82263)+E(f329(f329(f9(a875,x82261),f329(f329(f8(a1,x82261,a875),x82262),f106(a1))),f329(f308(a1,a875,a110),x82263)),f329(f329(f9(a1,x82261),x82262),x82263)) % 178.07/177.94 [8235]P144(x82353,x82351,x82352)+E(f329(f329(f81(a1),f329(f329(f82(a1),x82351),f813(x82352,x82351,x82353))),f806(x82352,x82351,x82353)),x82352)+~P24(f329(x82353,f2(a1)))+P24(f329(f329(f244(a1),f807(x82352,x82351,x82353)),x82351)) % 178.07/177.94 [8254]~E(x82542,f2(a875))+~E(f329(f263(a875,a875),x82543),f2(a875))+~E(x82541,f329(f329(f81(a875),f329(f329(f82(a875),f329(f263(a875,a875),x82543)),x82542)),f329(f267(a875,a875),x82543)))+P24(f329(f48(x82541,x82542),x82543)) % 178.07/177.94 [8308]P24(f329(x83081,x83082))+~P24(f329(f329(f331(x83083),f548(x83081,x83082,x83083)),f568(x83081,x83082,x83083)))+~P24(f329(f62(x83083),x83082))+~P24(f329(x83081,f193(f883(x83083,a869)))) % 178.07/177.94 [8923]P24(f329(x89231,x89232))+~P24(f329(f62(x89233),x89232))+~P24(f329(x89231,f329(f329(f307(x89233),f548(x89231,x89232,x89233)),f568(x89231,x89232,x89233))))+~P24(f329(x89231,f193(f883(x89233,a869)))) % 178.07/177.94 [9157]P24(f329(f329(f243(a1),x91571),f2(a1)))+~P24(f329(f329(f244(a1),f329(f329(f81(a1),f329(f329(f82(a1),x91572),x91571)),x91573)),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x91572))+~P24(f329(f329(f243(a1),f2(a1)),x91573)) % 178.07/177.94 [5774]~P63(x57742)+E(x57741,f193(f883(x57742,a869)))+~P24(f329(f62(x57742),x57741))+E(f13(x57742,f329(f329(f307(x57742),x57743),x57741)),f329(f329(f116(x57742),x57743),f13(x57742,x57741))) % 178.07/177.94 [5775]~P63(x57752)+E(x57751,f193(f883(x57752,a869)))+~P24(f329(f62(x57752),x57751))+E(f10(x57752,f329(f329(f307(x57752),x57753),x57751)),f329(f329(f107(x57752),x57753),f10(x57752,x57751))) % 178.07/177.94 [5776]~P105(x57762)+E(x57761,f193(f883(x57762,a869)))+~P24(f329(f62(x57762),x57761))+E(f14(x57762,f329(f329(f307(x57762),x57763),x57761)),f329(f329(f241(x57762),x57763),f14(x57762,x57761))) % 178.07/177.94 [5777]~P105(x57772)+E(x57771,f193(f883(x57772,a869)))+~P24(f329(f62(x57772),x57771))+E(f15(x57772,f329(f329(f307(x57772),x57773),x57771)),f329(f329(f242(x57772),x57773),f15(x57772,x57771))) % 178.07/177.94 [6087]~P121(x60871)+~E(x60873,f2(x60871))+~E(x60872,f2(x60871))+E(f329(f329(f81(x60871),f329(f329(f82(x60871),x60872),x60872)),f329(f329(f82(x60871),x60873),x60873)),f2(x60871)) % 178.07/177.94 [6158]~P95(x61582)+E(x61581,f193(f883(x61582,a869)))+~P24(f329(f62(x61582),x61581))+E(f329(f64(x61582,f82(x61582)),f329(f329(f307(x61582),x61583),x61581)),f329(f329(f82(x61582),x61583),f329(f64(x61582,f82(x61582)),x61581))) % 178.07/177.94 [6281]~P105(x62812)+E(x62811,f193(f883(x62812,a869)))+~P24(f329(f62(x62812),x62811))+E(f11(x62812,f242(x62812),f329(f329(f307(x62812),x62813),x62811)),f329(f329(f242(x62812),x62813),f11(x62812,f242(x62812),x62811))) % 178.07/177.94 [6282]~P105(x62822)+E(x62821,f193(f883(x62822,a869)))+~P24(f329(f62(x62822),x62821))+E(f12(x62822,f241(x62822),f329(f329(f307(x62822),x62823),x62821)),f329(f329(f241(x62822),x62823),f12(x62822,f241(x62822),x62821))) % 178.07/177.94 [6786]~P68(x67861)+~P24(f329(f62(x67861),x67863))+E(f329(f64(x67861,f82(x67861)),f329(f329(f307(x67861),x67862),x67863)),f329(f329(f65(x67861,x67861,f82(x67861)),x67862),x67863))+P24(f329(f329(f331(x67861),x67862),x67863)) % 178.07/177.94 [6866]~E(f329(f329(f81(a1),x68662),f329(f329(f82(a1),x68663),x68661)),x68663)+~P24(f329(f329(f244(a1),f2(a1)),x68663))+P24(f329(f329(f243(a1),f79(a1)),x68661))+~P24(f329(f329(f244(a1),x68662),x68663)) % 178.07/177.94 [6895]~E(f329(f329(f81(a1),x68952),f329(f329(f82(a1),x68953),x68951)),x68953)+P24(f329(f329(f243(a1),x68951),f79(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x68953))+~P24(f329(f329(f243(a1),f2(a1)),x68952)) % 178.07/177.94 [6911]E(x69111,f2(a875))+~P24(f329(f48(x69113,x69111),x69112))+~P24(f329(f329(f244(a875),f2(a875)),x69111))+P24(f329(f329(f244(a875),f329(f267(a875,a875),x69112)),x69111)) % 178.07/177.94 [6941]~P133(x69411)+~P24(f329(f329(f243(x69411),x69412),f2(x69411)))+~P24(f329(f329(f243(x69411),x69413),f2(x69411)))+E(f329(f329(f82(x69411),f329(f76(x69411),x69412)),f329(f76(x69411),x69413)),f329(f76(x69411),f329(f329(f82(x69411),x69412),x69413))) % 178.07/177.94 [6993]~P133(x69931)+~P24(f329(f329(f243(x69931),x69932),f2(x69931)))+E(f329(f329(f82(x69931),f329(f76(x69931),x69932)),f329(f76(x69931),x69933)),f329(f76(x69931),f329(f329(f82(x69931),x69932),x69933)))+~P24(f329(f329(f243(x69931),f2(x69931)),x69933)) % 178.07/177.94 [6994]~P133(x69941)+~P24(f329(f329(f243(x69941),x69943),f2(x69941)))+E(f329(f329(f82(x69941),f329(f76(x69941),x69942)),f329(f76(x69941),x69943)),f329(f76(x69941),f329(f329(f82(x69941),x69942),x69943)))+~P24(f329(f329(f243(x69941),f2(x69941)),x69942)) % 178.07/177.94 [7048]~P133(x70481)+E(f329(f329(f82(x70481),f329(f76(x70481),x70482)),f329(f76(x70481),x70483)),f329(f76(x70481),f329(f329(f82(x70481),x70482),x70483)))+~P24(f329(f329(f243(x70481),f2(x70481)),x70482))+~P24(f329(f329(f243(x70481),f2(x70481)),x70483)) % 178.07/177.94 [7064]~P121(x70641)+~P24(f329(f329(f244(x70641),x70643),f2(x70641)))+~P24(f329(f329(f244(x70641),x70642),f2(x70641)))+P24(f329(f329(f244(x70641),f2(x70641)),f329(f329(f82(x70641),x70642),x70643))) % 178.07/177.94 [7065]~P61(x70651)+~P24(f329(f329(f244(x70651),x70653),f2(x70651)))+~P24(f329(f329(f244(x70651),x70652),f2(x70651)))+P24(f329(f329(f244(x70651),f2(x70651)),f329(f329(f287(x70651),x70652),x70653))) % 178.07/177.94 [7066]~P62(x70661)+~P24(f329(f329(f244(x70661),x70663),f2(x70661)))+~P24(f329(f329(f244(x70661),x70662),f2(x70661)))+P24(f329(f329(f244(x70661),f2(x70661)),f329(f329(f287(x70661),x70662),x70663))) % 178.07/177.94 [7068]~P123(x70681)+~P24(f329(f329(f243(x70681),x70683),f2(x70681)))+~P24(f329(f329(f243(x70681),x70682),f2(x70681)))+P24(f329(f329(f243(x70681),f2(x70681)),f329(f329(f82(x70681),x70682),x70683))) % 178.07/177.94 [7069]~P121(x70691)+~P24(f329(f329(f243(x70691),x70693),f2(x70691)))+~P24(f329(f329(f243(x70691),x70692),f2(x70691)))+P24(f329(f329(f243(x70691),f2(x70691)),f329(f329(f82(x70691),x70692),x70693))) % 178.07/177.94 [7070]~P61(x70701)+~P24(f329(f329(f243(x70701),x70703),f2(x70701)))+~P24(f329(f329(f243(x70701),x70702),f2(x70701)))+P24(f329(f329(f243(x70701),f2(x70701)),f329(f329(f287(x70701),x70702),x70703))) % 178.07/177.94 [7071]~P62(x70711)+~P24(f329(f329(f244(x70711),x70713),f2(x70711)))+~P24(f329(f329(f243(x70711),x70712),f2(x70711)))+P24(f329(f329(f243(x70711),f2(x70711)),f329(f329(f287(x70711),x70712),x70713))) % 178.07/177.94 [7072]~P120(x70721)+~P24(f329(f329(f244(a875),f2(a875)),x70723))+~P24(f329(f329(f244(x70721),f79(x70721)),x70722))+P24(f329(f329(f244(x70721),f79(x70721)),f329(f329(f254(x70721),x70722),x70723))) % 178.07/177.94 [7168]~P120(x71681)+~P24(f329(f329(f244(x71681),f79(x71681)),x71683))+~P24(f329(f329(f244(x71681),f79(x71681)),x71682))+P24(f329(f329(f244(x71681),f79(x71681)),f329(f329(f82(x71681),x71682),x71683))) % 178.07/177.94 [7169]~P125(x71691)+~P24(f329(f329(f244(x71691),f2(x71691)),x71693))+~P24(f329(f329(f244(x71691),f2(x71691)),x71692))+P24(f329(f329(f244(x71691),f2(x71691)),f329(f329(f82(x71691),x71692),x71693))) % 178.07/177.94 [7170]~P86(x71701)+~P24(f329(f329(f244(x71701),f2(x71701)),x71703))+~P24(f329(f329(f244(x71701),f2(x71701)),x71702))+P24(f329(f329(f244(x71701),f2(x71701)),f329(f329(f81(x71701),x71702),x71703))) % 178.07/177.94 [7173]~P61(x71731)+~P24(f329(f329(f244(x71731),f2(x71731)),x71733))+~P24(f329(f329(f244(x71731),f2(x71731)),x71732))+P24(f329(f329(f244(x71731),f2(x71731)),f329(f329(f287(x71731),x71732),x71733))) % 178.07/177.94 [7174]~P62(x71741)+~P24(f329(f329(f244(x71741),f2(x71741)),x71743))+~P24(f329(f329(f244(x71741),f2(x71741)),x71742))+P24(f329(f329(f244(x71741),f2(x71741)),f329(f329(f287(x71741),x71742),x71743))) % 178.07/177.94 [7175]~P123(x71751)+~P24(f329(f329(f243(x71751),f2(x71751)),x71753))+~P24(f329(f329(f243(x71751),f2(x71751)),x71752))+P24(f329(f329(f243(x71751),f2(x71751)),f329(f329(f82(x71751),x71752),x71753))) % 178.07/177.94 [7176]~P130(x71761)+~P24(f329(f329(f243(x71761),f2(x71761)),x71763))+~P24(f329(f329(f243(x71761),f2(x71761)),x71762))+P24(f329(f329(f243(x71761),f2(x71761)),f329(f329(f82(x71761),x71762),x71763))) % 178.07/177.94 [7177]~P121(x71771)+~P24(f329(f329(f243(x71771),f2(x71771)),x71773))+~P24(f329(f329(f243(x71771),f2(x71771)),x71772))+P24(f329(f329(f243(x71771),f2(x71771)),f329(f329(f82(x71771),x71772),x71773))) % 178.07/177.94 [7179]~P61(x71791)+~P24(f329(f329(f243(x71791),f2(x71791)),x71793))+~P24(f329(f329(f243(x71791),f2(x71791)),x71792))+P24(f329(f329(f243(x71791),f2(x71791)),f329(f329(f287(x71791),x71792),x71793))) % 178.07/177.94 [7180]~P62(x71801)+~P24(f329(f329(f244(x71801),f2(x71801)),x71803))+~P24(f329(f329(f243(x71801),f2(x71801)),x71802))+P24(f329(f329(f243(x71801),f2(x71801)),f329(f329(f287(x71801),x71802),x71803))) % 178.07/177.94 [7251]~P63(x72511)+~P24(f329(f62(x72511),x72513))+E(f13(x72511,f329(f329(f307(x72511),x72512),x72513)),x72512)+~E(f329(f329(f22(f883(x72511,a869)),x72513),f329(f329(f307(x72511),x72512),f193(f883(x72511,a869)))),f193(f883(x72511,a869))) % 178.07/177.94 [7252]~P63(x72521)+~P24(f329(f62(x72521),x72523))+E(f10(x72521,f329(f329(f307(x72521),x72522),x72523)),x72522)+~E(f329(f329(f22(f883(x72521,a869)),x72523),f329(f329(f307(x72521),x72522),f193(f883(x72521,a869)))),f193(f883(x72521,a869))) % 178.07/177.94 [7253]~P105(x72531)+~P24(f329(f62(x72531),x72533))+E(f14(x72531,f329(f329(f307(x72531),x72532),x72533)),x72532)+~E(f329(f329(f22(f883(x72531,a869)),x72533),f329(f329(f307(x72531),x72532),f193(f883(x72531,a869)))),f193(f883(x72531,a869))) % 178.07/177.94 [7254]~P105(x72541)+~P24(f329(f62(x72541),x72543))+E(f15(x72541,f329(f329(f307(x72541),x72542),x72543)),x72542)+~E(f329(f329(f22(f883(x72541,a869)),x72543),f329(f329(f307(x72541),x72542),f193(f883(x72541,a869)))),f193(f883(x72541,a869))) % 178.07/177.94 [7255]~P61(x72551)+P24(f329(f329(f244(x72551),x72552),f2(x72551)))+P24(f329(f329(f244(x72551),f2(x72551)),x72553))+~P24(f329(f329(f244(x72551),f2(x72551)),f329(f329(f287(x72551),x72553),x72552))) % 178.07/177.94 [7256]~P61(x72561)+P24(f329(f329(f244(x72561),x72562),f2(x72561)))+P24(f329(f329(f244(x72561),f2(x72561)),x72563))+~P24(f329(f329(f244(x72561),f2(x72561)),f329(f329(f287(x72561),x72562),x72563))) % 178.07/177.94 [7257]~P61(x72571)+P24(f329(f329(f244(x72571),x72572),f2(x72571)))+P24(f329(f329(f244(x72571),f2(x72571)),x72572))+~P24(f329(f329(f244(x72571),f2(x72571)),f329(f329(f287(x72571),x72573),x72572))) % 178.07/177.94 [7258]~P61(x72581)+P24(f329(f329(f244(x72581),x72582),f2(x72581)))+P24(f329(f329(f244(x72581),f2(x72581)),x72582))+~P24(f329(f329(f244(x72581),f2(x72581)),f329(f329(f287(x72581),x72582),x72583))) % 178.07/177.94 [7259]~P121(x72591)+P24(f329(f329(f243(x72591),x72592),f2(x72591)))+P24(f329(f329(f243(x72591),f2(x72591)),x72593))+~P24(f329(f329(f243(x72591),f2(x72591)),f329(f329(f82(x72591),x72593),x72592))) % 178.07/177.94 [7260]~P121(x72601)+P24(f329(f329(f243(x72601),x72602),f2(x72601)))+P24(f329(f329(f243(x72601),f2(x72601)),x72603))+~P24(f329(f329(f243(x72601),f2(x72601)),f329(f329(f82(x72601),x72602),x72603))) % 178.07/177.94 [7261]~P61(x72611)+P24(f329(f329(f243(x72611),x72612),f2(x72611)))+P24(f329(f329(f243(x72611),f2(x72611)),x72613))+~P24(f329(f329(f243(x72611),f2(x72611)),f329(f329(f287(x72611),x72613),x72612))) % 178.07/177.94 [7262]~P61(x72621)+P24(f329(f329(f243(x72621),x72622),f2(x72621)))+P24(f329(f329(f243(x72621),f2(x72621)),x72623))+~P24(f329(f329(f243(x72621),f2(x72621)),f329(f329(f287(x72621),x72622),x72623))) % 178.07/177.94 [7263]~P121(x72631)+P24(f329(f329(f243(x72631),x72632),f2(x72631)))+P24(f329(f329(f243(x72631),f2(x72631)),x72632))+~P24(f329(f329(f243(x72631),f2(x72631)),f329(f329(f82(x72631),x72633),x72632))) % 178.07/177.94 [7264]~P121(x72641)+P24(f329(f329(f243(x72641),x72642),f2(x72641)))+P24(f329(f329(f243(x72641),f2(x72641)),x72642))+~P24(f329(f329(f243(x72641),f2(x72641)),f329(f329(f82(x72641),x72642),x72643))) % 178.07/177.94 [7265]~P61(x72651)+P24(f329(f329(f243(x72651),x72652),f2(x72651)))+P24(f329(f329(f243(x72651),f2(x72651)),x72652))+~P24(f329(f329(f243(x72651),f2(x72651)),f329(f329(f287(x72651),x72653),x72652))) % 178.07/177.94 [7266]~P61(x72661)+P24(f329(f329(f243(x72661),x72662),f2(x72661)))+P24(f329(f329(f243(x72661),f2(x72661)),x72662))+~P24(f329(f329(f243(x72661),f2(x72661)),f329(f329(f287(x72661),x72662),x72663))) % 178.07/177.94 [7356]~E(f329(f329(f107(f883(x73561,a869)),f329(f171(x73561),x73562)),f329(f171(x73561),x73563)),f193(f883(x73561,a869)))+~P24(f329(f136(x73561),x73563))+~P24(f329(f136(x73561),x73562))+P24(f329(f136(x73561),f329(f329(f127(x73561),x73562),x73563))) % 178.07/177.94 [7357]~P105(x73571)+~P24(f329(f62(x73571),x73573))+E(f11(x73571,f242(x73571),f329(f329(f307(x73571),x73572),x73573)),x73572)+~E(f329(f329(f22(f883(x73571,a869)),x73573),f329(f329(f307(x73571),x73572),f193(f883(x73571,a869)))),f193(f883(x73571,a869))) % 178.07/177.94 [7358]~P105(x73581)+~P24(f329(f62(x73581),x73583))+E(f12(x73581,f241(x73581),f329(f329(f307(x73581),x73582),x73583)),x73582)+~E(f329(f329(f22(f883(x73581,a869)),x73583),f329(f329(f307(x73581),x73582),f193(f883(x73581,a869)))),f193(f883(x73581,a869))) % 178.07/177.94 [7374]~P117(x73741)+~P24(f329(f329(f244(x73741),x73742),x73743))+~P24(f329(f329(f244(x73741),f329(f80(x73741),x73742)),x73743))+P24(f329(f329(f244(x73741),f329(f76(x73741),x73742)),x73743)) % 178.07/177.94 [7376]~P85(x73761)+~P24(f329(f329(f243(x73761),x73762),x73763))+~P24(f329(f329(f243(x73761),f329(f80(x73761),x73762)),x73763))+P24(f329(f329(f243(x73761),f329(f76(x73761),x73762)),x73763)) % 178.07/177.94 [7447]~P125(x74471)+P24(f329(f329(f244(x74471),f2(x74471)),x74472))+~P24(f329(f329(f244(x74471),f2(x74471)),x74473))+~P24(f329(f329(f244(x74471),f2(x74471)),f329(f329(f82(x74471),x74473),x74472))) % 178.07/177.94 [7448]~P125(x74481)+P24(f329(f329(f244(x74481),f2(x74481)),x74482))+~P24(f329(f329(f244(x74481),f2(x74481)),x74483))+~P24(f329(f329(f244(x74481),f2(x74481)),f329(f329(f82(x74481),x74482),x74483))) % 178.07/177.94 [7750]E(x77501,x77502)+~P24(f329(f62(x77503),x77501))+~P24(f329(f329(f243(a875),f329(f38(x77503),x77501)),f329(f38(x77503),x77502)))+~P24(f329(f329(f243(f883(x77503,a869)),x77502),x77501)) % 178.07/177.94 [7891]~P24(f329(f329(f244(a1),x78911),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x78912))+~P24(f329(f329(f243(a1),x78912),x78913))+P24(f329(f329(f243(a1),f329(f329(f39(a1),x78911),x78912)),f329(f329(f39(a1),x78911),x78913))) % 178.07/177.94 [7903]~P24(f329(f329(f244(a1),f2(a1)),x79033))+~P24(f329(f329(f243(a1),f2(a1)),x79031))+~P24(f329(f329(f243(a1),x79033),x79032))+P24(f329(f329(f243(a1),f329(f329(f39(a1),x79031),x79032)),f329(f329(f39(a1),x79031),x79033))) % 178.07/177.94 [8043]E(f329(x80431,f473(x80432,x80431,x80433)),x80432)+~P24(f329(f329(f243(a1),x80432),f329(x80431,x80433)))+P24(f329(f329(f244(a875),f474(x80432,x80431,x80433)),x80433))+~P24(f329(f329(f243(a1),f329(x80431,f2(a875))),x80432)) % 178.07/177.94 [8044]E(f329(x80441,f477(x80442,x80441,x80443)),x80442)+~P24(f329(f329(f243(a1),x80442),f329(x80441,x80443)))+P24(f329(f329(f244(a875),f478(x80442,x80441,x80443)),x80443))+~P24(f329(f329(f243(a1),f329(x80441,f2(a875))),x80442)) % 178.07/177.94 [8147]~P24(f329(f62(x81471),x81473))+~P24(f329(f329(f244(a875),f329(f38(x81471),x81472)),f329(f38(x81471),x81473)))+~P24(f329(f329(f243(f883(x81471,a869)),x81472),x81473))+P24(f329(f329(f244(f883(x81471,a869)),x81472),x81473)) % 178.07/177.94 [8176]E(f329(f329(f81(a1),f418(x81763,x81761,x81762)),f419(x81763,x81761,x81762)),x81761)+E(f329(f329(f22(a1),x81761),x81762),x81761)+~P24(f329(f329(f244(a1),f2(a1)),x81762))+~P24(f329(f329(f331(a1),f329(f329(f22(a1),x81761),f79(a1))),x81763)) % 178.07/177.94 [8177]E(f329(f329(f22(a1),f431(x81773,x81771,x81772)),f432(x81773,x81771,x81772)),x81771)+E(f329(f329(f81(a1),x81771),x81772),x81771)+~P24(f329(f329(f244(a1),f2(a1)),x81772))+~P24(f329(f329(f331(a1),f329(f329(f81(a1),x81771),f79(a1))),x81773)) % 178.07/177.94 [8230]~P24(f329(f329(f243(a875),x82303),x82301))+P24(f329(f329(f244(a875),x82301),x82302))+~P24(f329(f329(f243(a875),x82303),x82302))+~P24(f329(f329(f244(a875),f329(f329(f22(a875),x82301),x82303)),f329(f329(f22(a875),x82302),x82303))) % 178.07/177.94 [8231]~P24(f329(f329(f243(a875),x82313),x82311))+P24(f329(f329(f243(a875),x82311),x82312))+~P24(f329(f329(f243(a875),x82313),x82312))+~P24(f329(f329(f243(a875),f329(f329(f22(a875),x82311),x82313)),f329(f329(f22(a875),x82312),x82313))) % 178.07/177.94 [8247]~P105(x82472)+E(x82471,f119(x82472))+~P29(x82472,f329(f168(x82472),x82471))+E(f329(f141(x82472,x82472,f329(f7(x82472,x82472,x82472),f242(x82472)),x82473),f329(f168(x82472),x82471)),f329(f329(f242(x82472),f329(f329(f164(x82472),x82471),f2(a875))),x82473)) % 178.07/177.94 [8313]E(f329(f329(f22(a1),x83131),x83132),x83131)+~P24(f329(f329(f244(a1),f2(a1)),x83132))+P24(f329(f329(f331(a1),f418(x83133,x83131,x83132)),x83133))+~P24(f329(f329(f331(a1),f329(f329(f22(a1),x83131),f79(a1))),x83133)) % 178.07/177.94 [8314]E(f329(f329(f81(a1),x83141),x83142),x83141)+~P24(f329(f329(f244(a1),f2(a1)),x83142))+P24(f329(f329(f331(a1),f431(x83143,x83141,x83142)),x83143))+~P24(f329(f329(f331(a1),f329(f329(f81(a1),x83141),f79(a1))),x83143)) % 178.07/177.94 [8389]~P24(f329(f329(f243(a1),x83891),f329(x83892,x83893)))+P24(f329(f329(f243(a875),f473(x83891,x83892,x83893)),x83893))+P24(f329(f329(f244(a875),f474(x83891,x83892,x83893)),x83893))+~P24(f329(f329(f243(a1),f329(x83892,f2(a875))),x83891)) % 178.07/177.94 [8390]~P24(f329(f329(f243(a1),x83901),f329(x83902,x83903)))+P24(f329(f329(f243(a875),f477(x83901,x83902,x83903)),x83903))+P24(f329(f329(f244(a875),f478(x83901,x83902,x83903)),x83903))+~P24(f329(f329(f243(a1),f329(x83902,f2(a875))),x83901)) % 178.07/177.94 [8468]E(f329(f329(f22(a1),x84681),x84682),x84681)+~P24(f329(f329(f244(a1),f2(a1)),x84682))+P24(f329(f329(f331(a1),f419(x84683,x84681,x84682)),f300(a1,f79(a1),x84682)))+~P24(f329(f329(f331(a1),f329(f329(f22(a1),x84681),f79(a1))),x84683)) % 178.07/177.94 [8469]E(f329(f329(f81(a1),x84691),x84692),x84691)+~P24(f329(f329(f244(a1),f2(a1)),x84692))+P24(f329(f329(f331(a1),f432(x84693,x84691,x84692)),f300(a1,f79(a1),x84692)))+~P24(f329(f329(f331(a1),f329(f329(f81(a1),x84691),f79(a1))),x84693)) % 178.07/177.94 [8598]~P120(x85981)+~P24(f329(f329(f244(x85981),x85982),f79(x85981)))+~P24(f329(f329(f244(x85981),f2(x85981)),x85982))+P24(f329(f329(f244(x85981),f329(f329(f82(x85981),x85982),f329(f329(f254(x85981),x85982),x85983))),f329(f329(f254(x85981),x85982),x85983))) % 178.07/177.94 [8682]~P24(f329(x86821,x86822))+P24(f329(x86821,f2(a875)))+~P24(f329(f329(f244(a875),x86822),x86823))+~P24(f329(x86821,f45(a875,f329(a118,f526(x86822,x86821,x86823)),x86823))) % 178.07/177.94 [8820]E(f561(x88201,x88202,x88203),f2(a875))+P24(f329(f329(x88201,x88203),x88202))+P24(f329(f329(x88201,f561(x88201,x88202,x88203)),f45(a875,f560(x88201,x88202,x88203),f561(x88201,x88202,x88203))))+~P24(f329(f317(f882(a875,a875),a227),f329(f329(f264(a875,a875),x88203),x88202))) % 178.07/177.94 [8858]~P21(x88581,x88581,x88582,x88583)+E(f329(f308(x88581,x88581,x88582),x88583),x88583)+~P24(f329(f62(x88581),x88583))+~P24(f329(f329(f243(f883(x88581,a869)),f329(f308(x88581,x88581,x88582),x88583)),x88583)) % 178.07/177.94 [9098]P24(f329(f329(x90981,x90982),x90983))+~P24(f329(f329(f244(a1),f559(x90981,x90983,x90982)),f2(a1)))+P24(f329(f329(x90981,f329(f80(a1),f558(x90981,x90983,x90982))),f329(f80(a1),f559(x90981,x90983,x90982))))+~P24(f329(f317(f882(a1,a1),a232),f329(f329(f264(a1,a1),x90982),x90983))) % 178.07/177.94 [9286]P24(f329(f329(x92861,x92862),x92863))+P24(f329(f329(x92861,f329(f329(f81(a1),f611(x92861,x92863,x92862)),f79(a1))),f617(x92861,x92863,x92862)))+~P24(f329(f329(f243(a1),f611(x92861,x92863,x92862)),f617(x92861,x92863,x92862)))+~P24(f329(f317(f882(a1,a1),a182),f329(f329(f264(a1,a1),x92862),x92863))) % 178.07/177.94 [9709]~P58(x97092)+~P58(x97091)+~P24(f329(f59(f882(x97091,x97092)),x97093))+P24(f329(f59(x97091),f329(f329(f8(f883(x97092,a869),a869,x97091),f59(x97092)),f329(f329(f8(f883(x97092,f882(x97091,x97092)),f883(x97092,a869),x97091),f329(f8(f882(x97091,x97092),a869,x97092),x97093)),f264(x97091,x97092))))) % 178.07/177.94 [9710]~P58(x97102)+~P58(x97101)+~P24(f329(f58(f882(x97101,x97102)),x97103))+P24(f329(f58(x97101),f329(f329(f8(f883(x97102,a869),a869,x97101),f58(x97102)),f329(f329(f8(f883(x97102,f882(x97101,x97102)),f883(x97102,a869),x97101),f329(f8(f882(x97101,x97102),a869,x97102),x97103)),f264(x97101,x97102))))) % 178.07/177.94 [9812]~P58(x98122)+~P58(x98121)+P24(f329(f59(f882(x98121,x98122)),x98123))+~P24(f329(f59(x98121),f329(f329(f8(f883(x98122,a869),a869,x98121),f59(x98122)),f329(f329(f8(f883(x98122,f882(x98121,x98122)),f883(x98122,a869),x98121),f329(f8(f882(x98121,x98122),a869,x98122),x98123)),f264(x98121,x98122))))) % 178.07/177.94 [9813]~P58(x98132)+~P58(x98131)+P24(f329(f58(f882(x98131,x98132)),x98133))+~P24(f329(f58(x98131),f329(f329(f8(f883(x98132,a869),a869,x98131),f58(x98132)),f329(f329(f8(f883(x98132,f882(x98131,x98132)),f883(x98132,a869),x98131),f329(f8(f882(x98131,x98132),a869,x98132),x98133)),f264(x98131,x98132))))) % 178.07/177.94 [9982]E(f329(x99821,f473(x99822,x99821,x99823)),x99822)+~P24(f329(f329(f243(a1),x99822),f329(x99821,x99823)))+~P24(f329(f329(f243(a1),f329(f76(a1),f329(f329(f22(a1),f329(x99821,f329(f329(f81(a875),f474(x99822,x99821,x99823)),f79(a875)))),f329(x99821,f474(x99822,x99821,x99823))))),f79(a1)))+~P24(f329(f329(f243(a1),f329(x99821,f2(a875))),x99822)) % 178.07/177.94 [9983]E(f329(x99831,f477(x99832,x99831,x99833)),x99832)+~P24(f329(f329(f243(a1),x99832),f329(x99831,x99833)))+~P24(f329(f329(f243(a1),f329(f76(a1),f329(f329(f22(a1),f329(x99831,f329(f329(f81(a875),f478(x99832,x99831,x99833)),f79(a875)))),f329(x99831,f478(x99832,x99831,x99833))))),f79(a1)))+~P24(f329(f329(f243(a1),f329(x99831,f2(a875))),x99832)) % 178.07/177.94 [9987]~P24(f329(f329(f243(a1),x99871),f329(x99872,x99873)))+~P24(f329(f329(f243(a1),f329(f76(a1),f329(f329(f22(a1),f329(x99872,f329(f329(f81(a875),f474(x99871,x99872,x99873)),f79(a875)))),f329(x99872,f474(x99871,x99872,x99873))))),f79(a1)))+P24(f329(f329(f243(a875),f473(x99871,x99872,x99873)),x99873))+~P24(f329(f329(f243(a1),f329(x99872,f2(a875))),x99871)) % 178.07/177.94 [9988]~P24(f329(f329(f243(a1),x99881),f329(x99882,x99883)))+~P24(f329(f329(f243(a1),f329(f76(a1),f329(f329(f22(a1),f329(x99882,f329(f329(f81(a875),f478(x99881,x99882,x99883)),f79(a875)))),f329(x99882,f478(x99881,x99882,x99883))))),f79(a1)))+P24(f329(f329(f243(a875),f477(x99881,x99882,x99883)),x99883))+~P24(f329(f329(f243(a1),f329(x99882,f2(a875))),x99881)) % 178.07/177.94 [10043]E(x100431,x100432)+~E(f329(f141(f876(x100433),f876(x100433),f127(x100433),f119(x100433)),x100431),f329(f141(f876(x100433),f876(x100433),f127(x100433),f119(x100433)),x100432))+~E(f329(f194(f876(f876(x100433))),x100431),f329(f194(f876(f876(x100433))),x100432))+~P24(f329(f329(f268(f876(x100433),f876(x100433),a869),f329(f329(f7(f876(x100433),f883(f876(x100433),a875),f883(f876(x100433),a869)),f329(f329(f8(f883(a875,a869),f883(f883(f876(x100433),a875),f883(f876(x100433),a869)),f876(x100433)),f8(a875,a869,f876(x100433))),f329(f329(f8(a875,f883(a875,a869),f876(x100433)),a326),f194(f876(x100433))))),f194(f876(x100433)))),f658(x100431,x100432,x100433))) % 178.07/177.94 [10044]E(x100441,x100442)+~E(f329(f141(f876(x100443),f876(x100443),f127(x100443),f119(x100443)),x100441),f329(f141(f876(x100443),f876(x100443),f127(x100443),f119(x100443)),x100442))+~E(f329(f194(f876(f876(x100443))),x100441),f329(f194(f876(f876(x100443))),x100442))+~P24(f329(f329(f268(f876(x100443),f876(x100443),a869),f329(f329(f7(f876(x100443),f883(f876(x100443),a875),f883(f876(x100443),a869)),f329(f329(f8(f883(a875,a869),f883(f883(f876(x100443),a875),f883(f876(x100443),a869)),f876(x100443)),f8(a875,a869,f876(x100443))),f329(f329(f8(a875,f883(a875,a869),f876(x100443)),a326),f194(f876(x100443))))),f194(f876(x100443)))),f659(x100442,x100441,x100443))) % 178.07/177.94 [6773]~E(f79(a875),f2(a875))+~P24(f329(f62(x67731),x67733))+~P24(f329(f62(x67731),x67732))+E(f329(f329(f81(a875),f329(f38(x67731),x67732)),f329(f38(x67731),x67733)),f329(f38(x67731),f329(f329(f116(f883(x67731,a869)),x67732),x67733))) % 178.07/177.94 [7187]~P100(x71871)+~P24(f329(f62(x71871),x71872))+~P24(f329(f329(f331(x71871),x71873),x71872))+P24(f329(f329(f243(x71871),f329(f64(x71871,f107(x71871)),x71872)),x71873)) % 178.07/177.94 [7188]~P105(x71881)+~P24(f329(f62(x71881),x71882))+~P24(f329(f329(f331(x71881),x71883),x71882))+P24(f329(f329(f243(x71881),f329(f64(x71881,f241(x71881)),x71882)),x71883)) % 178.07/177.94 [7441]~P24(f329(f62(x74411),x74413))+~P24(f329(f62(x74411),x74412))+~E(f329(f329(f107(f883(x74411,a869)),x74412),x74413),f193(f883(x74411,a869)))+E(f329(f329(f81(a875),f329(f38(x74411),x74412)),f329(f38(x74411),x74413)),f329(f38(x74411),f329(f329(f116(f883(x74411,a869)),x74412),x74413))) % 178.07/177.94 [8236]~P38(x82361,x82363)+~P38(x82361,x82362)+~E(f329(f329(f107(f883(x82361,a869)),f329(f262(x82361,x82361),x82362)),f329(f260(x82361,x82361),x82363)),f193(f883(x82361,a869)))+P38(x82361,f329(f329(f116(f883(f882(x82361,x82361),a869)),x82362),x82363)) % 178.07/177.94 [8328]E(x83281,f329(f329(f39(a875),x83282),x83283))+~P24(f329(f329(f244(a875),f2(a875)),x83283))+~P24(f329(f329(f244(a875),x83282),f329(f329(f82(a875),x83283),f329(a118,x83281))))+~P24(f329(f329(f243(a875),f329(f329(f82(a875),x83283),x83281)),x83282)) % 178.07/177.94 [8466]~P24(f329(f62(x84661),x84662))+~P24(f329(f62(x84661),x84663))+E(f329(f329(f81(a875),f329(f38(x84661),x84662)),f329(f38(x84661),x84663)),f329(f38(x84661),f329(f329(f116(f883(x84661,a869)),x84662),x84663)))+P24(f329(f329(f331(x84661),f370(x84663,x84662,x84661)),f329(f329(f107(f883(x84661,a869)),x84662),x84663))) % 178.07/177.94 [8832]~P121(x88322)+~E(x88321,f2(x88322))+~E(x88323,f2(x88322))+~P24(f329(f329(f244(x88322),f2(x88322)),f329(f329(f81(x88322),f329(f329(f82(x88322),x88323),x88323)),f329(f329(f82(x88322),x88321),x88321)))) % 178.07/177.94 [9365]~P38(x93651,x93653)+~P38(x93651,x93652)+P38(x93651,f329(f329(f116(f883(f882(x93651,x93651),a869)),x93652),x93653))+~P24(f329(f329(f243(f883(f882(x93651,x93651),a869)),f329(f329(f286(x93651,x93651,x93651),x93652),x93653)),x93652)) % 178.07/177.94 [9490]~P24(f329(x94901,x94903))+~P24(f329(f62(x94902),x94903))+P24(f329(x94901,f193(f883(x94902,a869))))+~P24(f329(x94901,f329(f329(f22(f883(x94902,a869)),f665(x94901,x94903,x94902)),f329(f329(f307(x94902),f657(x94901,x94903,x94902)),f193(f883(x94902,a869)))))) % 178.07/177.94 [9739]~P58(x97391)+~P58(x97392)+P8(x97391,f329(f329(f8(f883(x97392,x97391),a869,f876(x97391)),x97393),f329(f329(f8(f883(x97392,f879(x97391)),f883(x97392,x97391),f876(x97391)),f74(f879(x97391),x97391,x97392,f240(x97391))),f329(f329(f8(f876(f882(x97392,x97391)),f883(x97392,f879(x97391)),f876(x97391)),f177(x97392,x97391)),f329(f181(x97392,x97391),f56(x97392))))),f329(f194(f876(x97392)),f56(x97392)))+~P24(f329(f59(f883(x97392,x97391)),x97393)) % 178.07/177.94 [9740]~P58(x97401)+~P58(x97402)+P7(x97401,f329(f329(f8(f883(x97402,x97401),a869,f876(x97401)),x97403),f329(f329(f8(f883(x97402,f879(x97401)),f883(x97402,x97401),f876(x97401)),f74(f879(x97401),x97401,x97402,f240(x97401))),f329(f329(f8(f876(f882(x97402,x97401)),f883(x97402,f879(x97401)),f876(x97401)),f177(x97402,x97401)),f329(f181(x97402,x97401),f56(x97402))))),f329(f194(f876(x97402)),f56(x97402)))+~P24(f329(f58(f883(x97402,x97401)),x97403)) % 178.07/177.94 [9836]~P58(x98361)+~P58(x98362)+~P8(x98362,f329(f329(f8(f883(x98361,x98362),a869,f876(x98362)),x98363),f329(f329(f8(f883(x98361,f879(x98362)),f883(x98361,x98362),f876(x98362)),f74(f879(x98362),x98362,x98361,f240(x98362))),f329(f329(f8(f876(f882(x98361,x98362)),f883(x98361,f879(x98362)),f876(x98362)),f177(x98361,x98362)),f329(f181(x98361,x98362),f56(x98361))))),f329(f194(f876(x98361)),f56(x98361)))+P24(f329(f59(f883(x98361,x98362)),x98363)) % 178.07/177.94 [9837]~P58(x98371)+~P58(x98372)+~P7(x98372,f329(f329(f8(f883(x98371,x98372),a869,f876(x98372)),x98373),f329(f329(f8(f883(x98371,f879(x98372)),f883(x98371,x98372),f876(x98372)),f74(f879(x98372),x98372,x98371,f240(x98372))),f329(f329(f8(f876(f882(x98371,x98372)),f883(x98371,f879(x98372)),f876(x98372)),f177(x98371,x98372)),f329(f181(x98371,x98372),f56(x98371))))),f329(f194(f876(x98371)),f56(x98371)))+P24(f329(f58(f883(x98371,x98372)),x98373)) % 178.07/177.94 [8633]~P24(f329(f329(f244(a1),f2(a1)),x86333))+P24(f329(f329(f243(a1),f2(a1)),x86331))+~P24(f329(f329(f244(a1),x86332),x86333))+~P24(f329(f329(f243(a1),f2(a1)),f329(f329(f81(a1),f329(f329(f82(a1),x86333),x86331)),x86332))) % 178.07/177.94 [8656]~P63(x86561)+~P24(f329(f62(x86561),x86562))+E(f329(f329(f22(f883(x86561,a869)),x86562),f329(f329(f307(x86561),x86563),f193(f883(x86561,a869)))),f193(f883(x86561,a869)))+E(f329(f329(f116(x86561),x86563),f13(x86561,f329(f329(f22(f883(x86561,a869)),x86562),f329(f329(f307(x86561),x86563),f193(f883(x86561,a869)))))),f13(x86561,f329(f329(f307(x86561),x86563),x86562))) % 178.07/177.94 [8657]~P63(x86571)+~P24(f329(f62(x86571),x86572))+E(f329(f329(f22(f883(x86571,a869)),x86572),f329(f329(f307(x86571),x86573),f193(f883(x86571,a869)))),f193(f883(x86571,a869)))+E(f329(f329(f107(x86571),x86573),f10(x86571,f329(f329(f22(f883(x86571,a869)),x86572),f329(f329(f307(x86571),x86573),f193(f883(x86571,a869)))))),f10(x86571,f329(f329(f307(x86571),x86573),x86572))) % 178.07/177.94 [8658]~P105(x86581)+~P24(f329(f62(x86581),x86582))+E(f329(f329(f22(f883(x86581,a869)),x86582),f329(f329(f307(x86581),x86583),f193(f883(x86581,a869)))),f193(f883(x86581,a869)))+E(f329(f329(f241(x86581),x86583),f14(x86581,f329(f329(f22(f883(x86581,a869)),x86582),f329(f329(f307(x86581),x86583),f193(f883(x86581,a869)))))),f14(x86581,f329(f329(f307(x86581),x86583),x86582))) % 178.07/177.94 [8659]~P105(x86591)+~P24(f329(f62(x86591),x86592))+E(f329(f329(f22(f883(x86591,a869)),x86592),f329(f329(f307(x86591),x86593),f193(f883(x86591,a869)))),f193(f883(x86591,a869)))+E(f329(f329(f242(x86591),x86593),f15(x86591,f329(f329(f22(f883(x86591,a869)),x86592),f329(f329(f307(x86591),x86593),f193(f883(x86591,a869)))))),f15(x86591,f329(f329(f307(x86591),x86593),x86592))) % 178.07/177.94 [8723]~P105(x87231)+~P24(f329(f62(x87231),x87232))+E(f329(f329(f22(f883(x87231,a869)),x87232),f329(f329(f307(x87231),x87233),f193(f883(x87231,a869)))),f193(f883(x87231,a869)))+E(f329(f329(f242(x87231),x87233),f11(x87231,f242(x87231),f329(f329(f22(f883(x87231,a869)),x87232),f329(f329(f307(x87231),x87233),f193(f883(x87231,a869)))))),f11(x87231,f242(x87231),f329(f329(f307(x87231),x87233),x87232))) % 178.07/177.94 [8724]~P105(x87241)+~P24(f329(f62(x87241),x87242))+E(f329(f329(f22(f883(x87241,a869)),x87242),f329(f329(f307(x87241),x87243),f193(f883(x87241,a869)))),f193(f883(x87241,a869)))+E(f329(f329(f241(x87241),x87243),f12(x87241,f241(x87241),f329(f329(f22(f883(x87241,a869)),x87242),f329(f329(f307(x87241),x87243),f193(f883(x87241,a869)))))),f12(x87241,f241(x87241),f329(f329(f307(x87241),x87243),x87242))) % 178.07/177.94 [9306]E(x93061,x93062)+~E(f329(f141(f876(x93063),f876(x93063),f127(x93063),f119(x93063)),x93061),f329(f141(f876(x93063),f876(x93063),f127(x93063),f119(x93063)),x93062))+~E(f329(f194(f876(f876(x93063))),x93061),f329(f194(f876(f876(x93063))),x93062))+P24(f329(f329(f331(f882(f876(x93063),f876(x93063))),f658(x93061,x93062,x93063)),f329(f171(f882(f876(x93063),f876(x93063))),f329(f329(f181(f876(x93063),f876(x93063)),x93062),x93061)))) % 178.07/177.94 [9307]E(x93071,x93072)+~E(f329(f141(f876(x93073),f876(x93073),f127(x93073),f119(x93073)),x93071),f329(f141(f876(x93073),f876(x93073),f127(x93073),f119(x93073)),x93072))+~E(f329(f194(f876(f876(x93073))),x93071),f329(f194(f876(f876(x93073))),x93072))+P24(f329(f329(f331(f882(f876(x93073),f876(x93073))),f659(x93072,x93071,x93073)),f329(f171(f882(f876(x93073),f876(x93073))),f329(f329(f181(f876(x93073),f876(x93073)),x93071),x93072)))) % 178.07/177.94 [10128]~P97(x101282)+E(x101281,f193(f883(x101282,a869)))+~P24(f329(f62(x101282),x101281))+E(f10(x101282,f329(f249(x101282),f329(f329(f8(f883(x101282,a869),a869,x101282),f88(x101282)),f329(f329(f7(x101282,f883(x101282,a869),f883(x101282,a869)),f329(f329(f8(f883(x101282,f883(a869,a869)),f883(f883(x101282,a869),f883(x101282,a869)),x101282),f18(x101282,a869,a869)),f329(f329(f8(f883(x101282,a869),f883(x101282,f883(a869,a869)),x101282),f329(f8(a869,f883(a869,a869),x101282),a327)),f329(f329(f7(x101282,f883(x101282,x101282),f883(x101282,a869)),f329(f329(f8(f883(x101282,a869),f883(f883(x101282,x101282),f883(x101282,a869)),x101282),f8(x101282,a869,x101282)),a326)),f329(f116(x101282),x101283))))),f329(f329(f7(x101282,f883(x101282,a869),a869),f331(x101282)),x101281))))),f329(f329(f116(x101282),x101283),f10(x101282,x101281))) % 178.07/177.94 [10129]~P97(x101292)+E(x101291,f193(f883(x101292,a869)))+~P24(f329(f62(x101292),x101291))+E(f13(x101292,f329(f249(x101292),f329(f329(f8(f883(x101292,a869),a869,x101292),f88(x101292)),f329(f329(f7(x101292,f883(x101292,a869),f883(x101292,a869)),f329(f329(f8(f883(x101292,f883(a869,a869)),f883(f883(x101292,a869),f883(x101292,a869)),x101292),f18(x101292,a869,a869)),f329(f329(f8(f883(x101292,a869),f883(x101292,f883(a869,a869)),x101292),f329(f8(a869,f883(a869,a869),x101292),a327)),f329(f329(f7(x101292,f883(x101292,x101292),f883(x101292,a869)),f329(f329(f8(f883(x101292,a869),f883(f883(x101292,x101292),f883(x101292,a869)),x101292),f8(x101292,a869,x101292)),a326)),f329(f107(x101292),x101293))))),f329(f329(f7(x101292,f883(x101292,a869),a869),f331(x101292)),x101291))))),f329(f329(f107(x101292),x101293),f13(x101292,x101291))) % 178.07/177.94 [10130]~P76(x101302)+E(x101301,f193(f883(x101302,a869)))+~P24(f329(f62(x101302),x101301))+E(f14(x101302,f329(f249(x101302),f329(f329(f8(f883(x101302,a869),a869,x101302),f88(x101302)),f329(f329(f7(x101302,f883(x101302,a869),f883(x101302,a869)),f329(f329(f8(f883(x101302,f883(a869,a869)),f883(f883(x101302,a869),f883(x101302,a869)),x101302),f18(x101302,a869,a869)),f329(f329(f8(f883(x101302,a869),f883(x101302,f883(a869,a869)),x101302),f329(f8(a869,f883(a869,a869),x101302),a327)),f329(f329(f7(x101302,f883(x101302,x101302),f883(x101302,a869)),f329(f329(f8(f883(x101302,a869),f883(f883(x101302,x101302),f883(x101302,a869)),x101302),f8(x101302,a869,x101302)),a326)),f329(f81(x101302),x101303))))),f329(f329(f7(x101302,f883(x101302,a869),a869),f331(x101302)),x101301))))),f329(f329(f81(x101302),x101303),f14(x101302,x101301))) % 178.07/177.94 [10131]~P76(x101312)+E(x101311,f193(f883(x101312,a869)))+~P24(f329(f62(x101312),x101311))+E(f15(x101312,f329(f249(x101312),f329(f329(f8(f883(x101312,a869),a869,x101312),f88(x101312)),f329(f329(f7(x101312,f883(x101312,a869),f883(x101312,a869)),f329(f329(f8(f883(x101312,f883(a869,a869)),f883(f883(x101312,a869),f883(x101312,a869)),x101312),f18(x101312,a869,a869)),f329(f329(f8(f883(x101312,a869),f883(x101312,f883(a869,a869)),x101312),f329(f8(a869,f883(a869,a869),x101312),a327)),f329(f329(f7(x101312,f883(x101312,x101312),f883(x101312,a869)),f329(f329(f8(f883(x101312,a869),f883(f883(x101312,x101312),f883(x101312,a869)),x101312),f8(x101312,a869,x101312)),a326)),f329(f81(x101312),x101313))))),f329(f329(f7(x101312,f883(x101312,a869),a869),f331(x101312)),x101311))))),f329(f329(f81(x101312),x101313),f15(x101312,x101311))) % 178.07/177.94 [10132]~P105(x101322)+E(x101321,f193(f883(x101322,a869)))+~P24(f329(f62(x101322),x101321))+E(f11(x101322,f242(x101322),f329(f249(x101322),f329(f329(f8(f883(x101322,a869),a869,x101322),f88(x101322)),f329(f329(f7(x101322,f883(x101322,a869),f883(x101322,a869)),f329(f329(f8(f883(x101322,f883(a869,a869)),f883(f883(x101322,a869),f883(x101322,a869)),x101322),f18(x101322,a869,a869)),f329(f329(f8(f883(x101322,a869),f883(x101322,f883(a869,a869)),x101322),f329(f8(a869,f883(a869,a869),x101322),a327)),f329(f329(f7(x101322,f883(x101322,x101322),f883(x101322,a869)),f329(f329(f8(f883(x101322,a869),f883(f883(x101322,x101322),f883(x101322,a869)),x101322),f8(x101322,a869,x101322)),a326)),f329(f241(x101322),x101323))))),f329(f329(f7(x101322,f883(x101322,a869),a869),f331(x101322)),x101321))))),f329(f329(f241(x101322),x101323),f11(x101322,f242(x101322),x101321))) % 178.07/177.94 [10133]~P105(x101332)+E(x101331,f193(f883(x101332,a869)))+~P24(f329(f62(x101332),x101331))+E(f12(x101332,f241(x101332),f329(f249(x101332),f329(f329(f8(f883(x101332,a869),a869,x101332),f88(x101332)),f329(f329(f7(x101332,f883(x101332,a869),f883(x101332,a869)),f329(f329(f8(f883(x101332,f883(a869,a869)),f883(f883(x101332,a869),f883(x101332,a869)),x101332),f18(x101332,a869,a869)),f329(f329(f8(f883(x101332,a869),f883(x101332,f883(a869,a869)),x101332),f329(f8(a869,f883(a869,a869),x101332),a327)),f329(f329(f7(x101332,f883(x101332,x101332),f883(x101332,a869)),f329(f329(f8(f883(x101332,a869),f883(f883(x101332,x101332),f883(x101332,a869)),x101332),f8(x101332,a869,x101332)),a326)),f329(f242(x101332),x101333))))),f329(f329(f7(x101332,f883(x101332,a869),a869),f331(x101332)),x101331))))),f329(f329(f242(x101332),x101333),f12(x101332,f241(x101332),x101331))) % 178.07/177.94 [9886]~P117(x98861)+~E(x98863,f2(x98861))+~E(x98862,f2(x98861))+E(f329(f329(f81(x98861),f329(f329(f254(x98861),x98862),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f329(f329(f254(x98861),x98863),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f2(x98861)) % 178.07/177.94 [10028]~P120(x100281)+~P24(f329(f329(f243(x100281),f2(x100281)),x100283))+P24(f329(f329(f243(x100281),x100282),x100283))+~P24(f329(f329(f243(x100281),f329(f329(f254(x100281),x100282),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f329(f329(f254(x100281),x100283),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))))) % 178.07/177.94 [10074]~P117(x100742)+~E(x100741,f2(x100742))+~E(x100743,f2(x100742))+~P24(f329(f329(f244(x100742),f2(x100742)),f329(f329(f81(x100742),f329(f329(f254(x100742),x100743),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))),f329(f329(f254(x100742),x100741),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))))) % 178.07/177.94 [9268]E(x92681,x92682)+~E(f604(x92681,x92682,x92684,x92683),f607(x92681,x92682,x92684,x92683))+P24(f329(f329(f331(f882(f876(x92683),f876(x92683))),f329(f329(f264(f876(x92683),f876(x92683)),x92682),x92681)),f146(x92683,x92684)))+P24(f329(f329(f331(f882(f876(x92683),f876(x92683))),f329(f329(f264(f876(x92683),f876(x92683)),x92681),x92682)),f146(x92683,x92684))) % 178.07/177.94 [4832]~P59(x48322)+~E(x48324,f2(x48322))+~E(x48321,f2(x48322))+E(x48321,f329(f329(f287(x48322),x48323),x48324)) % 178.07/177.94 [4833]~P59(x48331)+~E(x48333,f2(x48331))+~E(x48334,f2(x48331))+E(f329(f329(f287(x48331),x48332),x48333),x48334) % 178.07/177.94 [4942]~P59(x49422)+E(x49421,f2(x49422))+~E(x49423,f2(x49422))+~E(x49421,f329(f329(f287(x49422),x49424),x49423)) % 178.07/177.94 [4943]~P59(x49432)+E(x49431,f2(x49432))+~E(x49433,f2(x49432))+~E(f329(f329(f287(x49432),x49434),x49433),x49431) % 178.07/177.94 [5118]~P115(x51182)+E(x51181,f2(x51182))+~E(f329(f329(f287(x51182),x51183),x51181),x51184)+E(x51183,f329(f329(f82(x51182),x51184),x51181)) % 178.07/177.94 [5120]~P115(x51202)+E(x51201,f2(x51202))+~E(f329(f329(f82(x51202),x51203),x51201),x51204)+E(x51203,f329(f329(f287(x51202),x51204),x51201)) % 178.07/177.94 [5121]~P59(x51212)+E(x51211,f2(x51212))+~E(f329(f329(f287(x51212),x51213),x51211),x51214)+E(x51213,f329(f329(f82(x51212),x51214),x51211)) % 178.07/177.94 [5122]~P59(x51222)+E(x51221,f2(x51222))+~E(f329(f329(f82(x51222),x51223),x51221),x51224)+E(x51223,f329(f329(f287(x51222),x51224),x51221)) % 178.07/177.94 [5123]~P115(x51232)+E(x51231,f2(x51232))+~E(x51233,f329(f329(f287(x51232),x51234),x51231))+E(f329(f329(f82(x51232),x51233),x51231),x51234) % 178.07/177.94 [5125]~P115(x51252)+E(x51251,f2(x51252))+~E(x51253,f329(f329(f82(x51252),x51254),x51251))+E(f329(f329(f287(x51252),x51253),x51251),x51254) % 178.07/177.94 [5126]~P59(x51262)+E(x51261,f2(x51262))+~E(x51263,f329(f329(f287(x51262),x51264),x51261))+E(f329(f329(f82(x51262),x51263),x51261),x51264) % 178.07/177.94 [5127]~P59(x51272)+E(x51271,f2(x51272))+~E(x51273,f329(f329(f82(x51272),x51274),x51271))+E(f329(f329(f287(x51272),x51273),x51271),x51274) % 178.07/177.94 [5160]~P59(x51602)+~E(x51601,f2(x51602))+~E(f329(f329(f82(x51602),x51601),x51604),x51603)+E(x51601,f329(f329(f287(x51602),x51603),x51604)) % 178.07/177.94 [5161]~P59(x51611)+~E(x51614,f2(x51611))+~E(x51612,f329(f329(f82(x51611),x51614),x51613))+E(f329(f329(f287(x51611),x51612),x51613),x51614) % 178.07/177.94 [5234]~E(x52343,x52344)+~E(x52342,x52343)+~P107(x52341)+E(f300(x52341,x52342,x52343),f329(f329(f307(x52341),x52344),f193(f883(x52341,a869)))) % 178.07/177.94 [5440]~E(f120(x54402,x54401),x54403)+~E(f143(x54402,x54401),x54404)+E(x54401,f119(x54402))+E(f329(f329(f127(x54402),x54403),f329(f329(f150(x54402),x54404),f119(x54402))),x54401) % 178.07/177.94 [6055]~P120(x60553)+E(x60551,x60552)+~E(f329(f329(f254(x60553),x60554),x60551),f329(f329(f254(x60553),x60554),x60552))+~P24(f329(f329(f244(x60553),f79(x60553)),x60554)) % 178.07/177.94 [6056]E(x60561,x60562)+~E(f329(f329(f307(x60563),x60564),x60561),f329(f329(f307(x60563),x60564),x60562))+P24(f329(f329(f331(x60563),x60564),x60562))+P24(f329(f329(f331(x60563),x60564),x60561)) % 178.07/177.94 [6094]E(f329(x60941,x60942),f79(a875))+~E(f329(f329(f9(x60943,a875),x60941),x60944),f79(a875))+~P24(f329(f62(x60943),x60944))+~P24(f329(f329(f331(x60943),x60942),x60944)) % 178.07/177.94 [6095]E(f329(x60951,x60952),f2(a875))+~E(f329(f329(f6(x60953,a875),x60951),x60954),f2(a875))+~P24(f329(f62(x60953),x60954))+~P24(f329(f329(f331(x60953),x60952),x60954)) % 178.07/177.94 [6314]~P107(x63141)+~P24(f329(f329(f244(x63141),x63144),x63143))+P24(f329(f329(f244(x63141),x63142),x63143))+~P24(f329(f329(f244(x63141),x63142),x63144)) % 178.07/177.94 [6315]~P107(x63151)+~P24(f329(f329(f243(x63151),x63154),x63153))+P24(f329(f329(f244(x63151),x63152),x63153))+~P24(f329(f329(f244(x63151),x63152),x63154)) % 178.07/177.94 [6316]~P107(x63161)+~P24(f329(f329(f243(x63161),x63162),x63164))+P24(f329(f329(f244(x63161),x63162),x63163))+~P24(f329(f329(f244(x63161),x63164),x63163)) % 178.07/177.94 [6317]~P104(x63171)+~P24(f329(f329(f244(x63171),x63172),x63174))+P24(f329(f329(f244(x63171),x63172),x63173))+~P24(f329(f329(f244(x63171),x63174),x63173)) % 178.07/177.94 [6318]~P104(x63181)+~P24(f329(f329(f243(x63181),x63182),x63184))+P24(f329(f329(f244(x63181),x63182),x63183))+~P24(f329(f329(f244(x63181),x63184),x63183)) % 178.07/177.94 [6319]~P104(x63191)+~P24(f329(f329(f243(x63191),x63194),x63193))+P24(f329(f329(f244(x63191),x63192),x63193))+~P24(f329(f329(f244(x63191),x63192),x63194)) % 178.07/177.94 [6320]~P107(x63201)+~P24(f329(f329(f243(x63201),x63204),x63203))+P24(f329(f329(f243(x63201),x63202),x63203))+~P24(f329(f329(f243(x63201),x63202),x63204)) % 178.07/177.94 [6321]~P104(x63211)+~P24(f329(f329(f243(x63211),x63212),x63214))+P24(f329(f329(f243(x63211),x63212),x63213))+~P24(f329(f329(f243(x63211),x63214),x63213)) % 178.07/177.94 [6403]~P36(x64034,x64033,x64032)+E(x64031,f805(x64032,x64033,x64034))+~P24(f329(x64033,x64031))+~P24(f329(f329(f331(x64034),x64031),f329(f171(x64034),x64032))) % 178.07/177.94 [6548]~P27(x65481)+~P24(f329(f329(f243(x65481),x65482),f41(x65481,x65484)))+P24(f329(f329(f243(x65481),x65482),x65483))+~P24(f329(f329(f331(x65481),x65483),x65484)) % 178.07/177.94 [6694]~P105(x66941)+~P29(x66941,f329(f329(f150(x66941),x66942),x66944))+~P24(f329(f329(f331(x66941),x66943),f329(f171(x66941),x66944)))+P24(f329(f329(f243(x66941),x66942),x66943)) % 178.07/177.94 [6784]~P27(x67841)+~P24(f329(f329(f243(x67841),f40(x67841,x67844)),x67843))+P24(f329(f329(f243(x67841),x67842),x67843))+~P24(f329(f329(f331(x67841),x67842),x67844)) % 178.07/177.94 [7190]~P105(x71901)+E(f329(f329(f116(f883(x71901,a869)),f329(f299(x71901,x71902),x71903)),f329(f299(x71901,x71903),x71904)),f329(f299(x71901,x71902),x71904))+~P24(f329(f329(f243(x71901),x71903),x71904))+~P24(f329(f329(f243(x71901),x71902),x71903)) % 178.07/177.94 [7227]P36(x72271,x72272,x72273)+~E(f809(x72273,x72272,x72271,x72274),x72274)+~P24(f329(x72272,x72274))+~P24(f329(f329(f331(x72271),x72274),f329(f171(x72271),x72273))) % 178.07/177.94 [7301]~P105(x73011)+E(f329(f329(f116(f883(x73011,a869)),f329(f299(x73011,x73012),x73013)),f300(x73011,x73013,x73014)),f300(x73011,x73012,x73014))+~P24(f329(f329(f243(x73011),x73013),x73014))+~P24(f329(f329(f243(x73011),x73012),x73013)) % 178.07/177.94 [7367]~P105(x73671)+E(f329(f329(f116(f883(x73671,a869)),f303(x73671,x73672,x73673)),f329(f299(x73671,x73673),x73674)),f303(x73671,x73672,x73674))+~P24(f329(f329(f244(x73671),x73672),x73673))+~P24(f329(f329(f243(x73671),x73673),x73674)) % 178.07/177.94 [7388]~P105(x73881)+E(f329(f329(f116(f883(x73881,a869)),f300(x73881,x73882,x73883)),f303(x73881,x73883,x73884)),f329(f299(x73881,x73882),x73884))+~P24(f329(f329(f244(x73881),x73883),x73884))+~P24(f329(f329(f243(x73881),x73882),x73883)) % 178.07/177.94 [7420]~P105(x74201)+E(f329(f329(f116(f883(x74201,a869)),f303(x74201,x74202,x74203)),f300(x74201,x74203,x74204)),f302(x74201,x74202,x74204))+~P24(f329(f329(f244(x74201),x74202),x74203))+~P24(f329(f329(f243(x74201),x74203),x74204)) % 178.07/177.94 [7421]~P105(x74211)+E(f329(f329(f116(f883(x74211,a869)),f302(x74211,x74212,x74213)),f303(x74211,x74213,x74214)),f303(x74211,x74212,x74214))+~P24(f329(f329(f244(x74211),x74213),x74214))+~P24(f329(f329(f243(x74211),x74212),x74213)) % 178.07/177.94 [7422]~P105(x74221)+E(f329(f329(f116(f883(x74221,a869)),f302(x74221,x74222,x74223)),f302(x74221,x74223,x74224)),f302(x74221,x74222,x74224))+~P24(f329(f329(f243(x74221),x74223),x74224))+~P24(f329(f329(f243(x74221),x74222),x74223)) % 178.07/177.94 [7423]~P105(x74231)+E(f329(f329(f116(f883(x74231,a869)),f300(x74231,x74232,x74233)),f302(x74231,x74233,x74234)),f300(x74231,x74232,x74234))+~P24(f329(f329(f243(x74231),x74233),x74234))+~P24(f329(f329(f243(x74231),x74232),x74233)) % 178.07/177.94 [8220]P21(x82201,x82202,f348(x82203,x82202,x82204,x82201),x82204)+~P24(f329(f62(x82202),x82203))+~P24(f329(f62(x82201),x82204))+~P24(f329(f329(f243(a875),f329(f38(x82201),x82204)),f329(f38(x82202),x82203))) % 178.07/177.94 [8241]P36(x82411,x82412,x82413)+~P24(f329(x82412,x82414))+P24(f329(x82412,f809(x82413,x82412,x82411,x82414)))+~P24(f329(f329(f331(x82411),x82414),f329(f171(x82411),x82413))) % 178.07/177.94 [8292]~P74(x82921)+~E(f329(x82923,f523(x82923,x82924,x82922,x82921)),f79(x82921))+E(f329(f329(f329(f66(x82921,x82922,f82(x82921)),x82923),f79(x82921)),x82924),f79(x82921))+~P24(f329(f62(x82922),x82924)) % 178.07/177.94 [8565]~P120(x85651)+~P24(f329(f329(f243(x85651),f2(x85651)),x85653))+P24(f329(f329(f243(x85651),x85652),x85653))+~P24(f329(f329(f243(x85651),f329(f329(f254(x85651),x85652),f329(a118,x85654))),f329(f329(f254(x85651),x85653),f329(a118,x85654)))) % 178.07/177.94 [8859]P36(x88591,x88592,x88593)+~P24(f329(x88592,x88594))+~P24(f329(f329(f331(x88591),x88594),f329(f171(x88591),x88593)))+P24(f329(f329(f331(x88591),f809(x88593,x88592,x88591,x88594)),f329(f171(x88591),x88593))) % 178.07/177.94 [8944]~P74(x89441)+E(f329(f329(f329(f66(x89441,x89442,f82(x89441)),x89443),f79(x89441)),x89444),f79(x89441))+~P24(f329(f62(x89442),x89444))+P24(f329(f329(f331(x89442),f523(x89443,x89444,x89442,x89441)),x89444)) % 178.07/177.94 [9431]~P24(f329(f329(f243(a1),x94314),f2(a1)))+P24(f329(f329(f243(a1),f329(f329(f81(a1),f329(f329(f82(a1),x94311),f45(a1,x94312,x94313))),x94314)),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x94313))+~P24(f329(f329(f244(a1),x94311),x94314)) % 178.07/177.94 [9879]~P24(f329(f62(x98791),x98792))+~P24(f329(f329(f331(x98791),x98794),x98792))+~P24(f329(f329(f331(x98791),x98793),x98792))+P24(f329(f329(f244(a875),f329(f38(x98791),f329(f329(f22(f883(x98791,a869)),f329(f329(f22(f883(x98791,a869)),x98792),f329(f329(f307(x98791),x98793),f193(f883(x98791,a869))))),f329(f329(f307(x98791),x98794),f193(f883(x98791,a869)))))),f329(f38(x98791),x98792))) % 178.07/177.94 [6898]~P105(x68981)+~P24(f329(f329(f244(x68981),x68982),x68984))+~P24(f329(f329(f244(x68981),x68982),x68983))+P24(f329(f329(f244(x68981),x68982),f329(f329(f241(x68981),x68983),x68984))) % 178.07/177.94 [6901]~P100(x69011)+~P24(f329(f329(f243(x69011),x69012),x69014))+~P24(f329(f329(f243(x69011),x69012),x69013))+P24(f329(f329(f243(x69011),x69012),f329(f329(f107(x69011),x69013),x69014))) % 178.07/177.94 [6904]~P105(x69041)+~P24(f329(f329(f243(x69041),x69042),x69044))+~P24(f329(f329(f243(x69041),x69042),x69043))+P24(f329(f329(f243(x69041),x69042),f329(f329(f241(x69041),x69043),x69044))) % 178.07/177.94 [6923]~P60(x69232)+E(x69231,f2(x69232))+E(f329(f329(f287(x69232),f329(f329(f254(x69232),x69231),x69233)),f329(f329(f254(x69232),x69231),x69234)),f329(f329(f254(x69232),x69231),f329(f329(f22(a875),x69233),x69234)))+~P24(f329(f329(f243(a875),x69234),x69233)) % 178.07/177.94 [6968]~P105(x69681)+~P29(x69681,f329(f329(f150(x69681),x69683),x69684))+P29(x69681,f329(f329(f150(x69681),x69682),f329(f329(f150(x69681),x69683),x69684)))+~P24(f329(f329(f243(x69681),x69682),x69683)) % 178.07/177.94 [7009]~P120(x70091)+~P24(f329(f329(f244(x70091),f2(x70091)),x70093))+~P24(f329(f329(f244(x70091),x70092),x70094))+P24(f329(f329(f244(x70091),x70092),f329(f329(f81(x70091),x70093),x70094))) % 178.07/177.94 [7010]~P86(x70101)+~P24(f329(f329(f243(x70101),f2(x70101)),x70103))+~P24(f329(f329(f244(x70101),x70102),x70104))+P24(f329(f329(f244(x70101),x70102),f329(f329(f81(x70101),x70103),x70104))) % 178.07/177.94 [7011]~P86(x70111)+~P24(f329(f329(f243(x70111),x70112),x70114))+~P24(f329(f329(f244(x70111),f2(x70111)),x70113))+P24(f329(f329(f244(x70111),x70112),f329(f329(f81(x70111),x70113),x70114))) % 178.07/177.94 [7012]~P86(x70121)+~P24(f329(f329(f243(x70121),f2(x70121)),x70124))+~P24(f329(f329(f243(x70121),x70122),x70123))+P24(f329(f329(f243(x70121),x70122),f329(f329(f81(x70121),x70123),x70124))) % 178.07/177.94 [7013]~P86(x70131)+~P24(f329(f329(f243(x70131),f2(x70131)),x70133))+~P24(f329(f329(f243(x70131),x70132),x70134))+P24(f329(f329(f243(x70131),x70132),f329(f329(f81(x70131),x70133),x70134))) % 178.07/177.94 [7052]~P105(x70521)+P24(f329(f329(f244(x70521),x70522),x70523))+P24(f329(f329(f244(x70521),x70522),x70524))+~P24(f329(f329(f244(x70521),x70522),f329(f329(f242(x70521),x70524),x70523))) % 178.07/177.94 [7053]~P105(x70531)+P24(f329(f329(f243(x70531),x70532),x70533))+P24(f329(f329(f243(x70531),x70532),x70534))+~P24(f329(f329(f243(x70531),x70532),f329(f329(f242(x70531),x70534),x70533))) % 178.07/177.94 [7340]~P107(x73402)+~P58(x73401)+~P24(f329(f329(f244(f883(x73401,x73402)),x73403),x73404))+P24(f329(f329(f243(f883(x73401,x73402)),x73403),x73404)) % 178.07/177.94 [7710]~P62(x77101)+~P24(f329(f329(f244(x77101),x77104),f2(x77101)))+~P24(f329(f329(f244(x77101),x77103),f329(f329(f287(x77101),x77102),x77104)))+P24(f329(f329(f244(x77101),x77102),f329(f329(f82(x77101),x77103),x77104))) % 178.07/177.94 [7711]~P62(x77111)+~P24(f329(f329(f244(x77111),x77114),f2(x77111)))+~P24(f329(f329(f244(x77111),x77113),f329(f329(f82(x77111),x77112),x77114)))+P24(f329(f329(f244(x77111),x77112),f329(f329(f287(x77111),x77113),x77114))) % 178.07/177.94 [7712]~P62(x77121)+~P24(f329(f329(f244(x77121),x77124),f2(x77121)))+~P24(f329(f329(f243(x77121),x77123),f329(f329(f287(x77121),x77122),x77124)))+P24(f329(f329(f243(x77121),x77122),f329(f329(f82(x77121),x77123),x77124))) % 178.07/177.94 [7713]~P62(x77131)+~P24(f329(f329(f244(x77131),x77134),f2(x77131)))+~P24(f329(f329(f243(x77131),x77133),f329(f329(f82(x77131),x77132),x77134)))+P24(f329(f329(f243(x77131),x77132),f329(f329(f287(x77131),x77133),x77134))) % 178.07/177.94 [7821]~P121(x78211)+~P24(f329(f329(f244(x78211),x78213),f2(x78211)))+~P24(f329(f329(f244(x78211),x78214),x78212))+P24(f329(f329(f244(x78211),f329(f329(f82(x78211),x78212),x78213)),f329(f329(f82(x78211),x78214),x78213))) % 178.07/177.94 [7822]~P121(x78221)+~P24(f329(f329(f244(x78221),x78222),f2(x78221)))+~P24(f329(f329(f244(x78221),x78224),x78223))+P24(f329(f329(f244(x78221),f329(f329(f82(x78221),x78222),x78223)),f329(f329(f82(x78221),x78222),x78224))) % 178.07/177.94 [7823]~P62(x78231)+~P24(f329(f329(f244(x78231),x78233),f2(x78231)))+~P24(f329(f329(f244(x78231),x78234),x78232))+P24(f329(f329(f244(x78231),f329(f329(f287(x78231),x78232),x78233)),f329(f329(f287(x78231),x78234),x78233))) % 178.07/177.94 [7824]~P123(x78241)+~P24(f329(f329(f243(x78241),x78242),f2(x78241)))+~P24(f329(f329(f243(x78241),x78244),x78243))+P24(f329(f329(f243(x78241),f329(f329(f82(x78241),x78242),x78243)),f329(f329(f82(x78241),x78242),x78244))) % 178.07/177.94 [7825]~P121(x78251)+~P24(f329(f329(f244(x78251),x78252),f2(x78251)))+~P24(f329(f329(f243(x78251),x78254),x78253))+P24(f329(f329(f243(x78251),f329(f329(f82(x78251),x78252),x78253)),f329(f329(f82(x78251),x78252),x78254))) % 178.07/177.94 [7826]~P123(x78261)+~P24(f329(f329(f243(x78261),x78263),f2(x78261)))+~P24(f329(f329(f243(x78261),x78264),x78262))+P24(f329(f329(f243(x78261),f329(f329(f82(x78261),x78262),x78263)),f329(f329(f82(x78261),x78264),x78263))) % 178.07/177.94 [7827]~P61(x78271)+~P24(f329(f329(f243(x78271),x78273),f2(x78271)))+~P24(f329(f329(f243(x78271),x78274),x78272))+P24(f329(f329(f243(x78271),f329(f329(f287(x78271),x78272),x78273)),f329(f329(f287(x78271),x78274),x78273))) % 178.07/177.94 [7829]~P120(x78291)+~P24(f329(f329(f244(x78291),f79(x78291)),x78292))+~P24(f329(f329(f244(a875),x78293),x78294))+P24(f329(f329(f244(x78291),f329(f329(f254(x78291),x78292),x78293)),f329(f329(f254(x78291),x78292),x78294))) % 178.07/177.94 [7830]~P120(x78301)+~P24(f329(f329(f244(x78301),f79(x78301)),x78302))+~P24(f329(f329(f243(a875),x78303),x78304))+P24(f329(f329(f243(x78301),f329(f329(f254(x78301),x78302),x78303)),f329(f329(f254(x78301),x78302),x78304))) % 178.07/177.94 [7831]~P120(x78311)+~P24(f329(f329(f243(x78311),f79(x78311)),x78312))+~P24(f329(f329(f243(a875),x78313),x78314))+P24(f329(f329(f243(x78311),f329(f329(f254(x78311),x78312),x78313)),f329(f329(f254(x78311),x78312),x78314))) % 178.07/177.94 [7858]P24(f329(f329(f244(a875),f2(a875)),f329(x78581,x78582)))+~P24(f329(f62(x78583),x78584))+~P24(f329(f329(f331(x78583),x78582),x78584))+~P24(f329(f329(f244(a875),f2(a875)),f329(f329(f9(x78583,a875),x78581),x78584))) % 178.07/177.94 [7868]~P118(x78681)+~P24(f329(f329(f244(x78681),x78683),x78684))+~P24(f329(f329(f244(x78681),f2(x78681)),x78682))+P24(f329(f329(f244(x78681),f329(f329(f82(x78681),x78682),x78683)),f329(f329(f82(x78681),x78682),x78684))) % 178.07/177.94 [7869]~P125(x78691)+~P24(f329(f329(f244(x78691),x78693),x78694))+~P24(f329(f329(f244(x78691),f2(x78691)),x78692))+P24(f329(f329(f244(x78691),f329(f329(f82(x78691),x78692),x78693)),f329(f329(f82(x78691),x78692),x78694))) % 178.07/177.94 [7870]~P121(x78701)+~P24(f329(f329(f244(x78701),x78702),x78704))+~P24(f329(f329(f244(x78701),f2(x78701)),x78703))+P24(f329(f329(f244(x78701),f329(f329(f82(x78701),x78702),x78703)),f329(f329(f82(x78701),x78704),x78703))) % 178.07/177.94 [7871]~P125(x78711)+~P24(f329(f329(f244(x78711),x78712),x78714))+~P24(f329(f329(f244(x78711),f2(x78711)),x78713))+P24(f329(f329(f244(x78711),f329(f329(f82(x78711),x78712),x78713)),f329(f329(f82(x78711),x78714),x78713))) % 178.07/177.94 [7872]~P121(x78721)+~P24(f329(f329(f244(x78721),x78723),x78724))+~P24(f329(f329(f244(x78721),f2(x78721)),x78722))+P24(f329(f329(f244(x78721),f329(f329(f82(x78721),x78722),x78723)),f329(f329(f82(x78721),x78722),x78724))) % 178.07/177.94 [7873]~P62(x78731)+~P24(f329(f329(f244(x78731),x78732),x78734))+~P24(f329(f329(f244(x78731),f2(x78731)),x78733))+P24(f329(f329(f244(x78731),f329(f329(f287(x78731),x78732),x78733)),f329(f329(f287(x78731),x78734),x78733))) % 178.07/177.94 [7874]~P132(x78741)+~P24(f329(f329(f243(x78741),x78743),x78744))+~P24(f329(f329(f243(x78741),f2(x78741)),x78742))+P24(f329(f329(f243(x78741),f329(f329(f82(x78741),x78742),x78743)),f329(f329(f82(x78741),x78742),x78744))) % 178.07/177.94 [7875]~P131(x78751)+~P24(f329(f329(f243(x78751),x78753),x78754))+~P24(f329(f329(f243(x78751),f2(x78751)),x78752))+P24(f329(f329(f243(x78751),f329(f329(f82(x78751),x78752),x78753)),f329(f329(f82(x78751),x78752),x78754))) % 178.07/177.94 [7876]~P121(x78761)+~P24(f329(f329(f244(x78761),f2(x78761)),x78762))+~P24(f329(f329(f243(x78761),x78763),x78764))+P24(f329(f329(f243(x78761),f329(f329(f82(x78761),x78762),x78763)),f329(f329(f82(x78761),x78762),x78764))) % 178.07/177.94 [7877]~P132(x78771)+~P24(f329(f329(f243(x78771),x78772),x78774))+~P24(f329(f329(f243(x78771),f2(x78771)),x78773))+P24(f329(f329(f243(x78771),f329(f329(f82(x78771),x78772),x78773)),f329(f329(f82(x78771),x78774),x78773))) % 178.07/177.94 [7878]~P120(x78781)+~P24(f329(f329(f243(x78781),x78782),x78784))+~P24(f329(f329(f243(x78781),f2(x78781)),x78782))+P24(f329(f329(f243(x78781),f329(f329(f254(x78781),x78782),x78783)),f329(f329(f254(x78781),x78784),x78783))) % 178.07/177.94 [7879]~P61(x78791)+~P24(f329(f329(f243(x78791),x78792),x78794))+~P24(f329(f329(f243(x78791),f2(x78791)),x78793))+P24(f329(f329(f243(x78791),f329(f329(f287(x78791),x78792),x78793)),f329(f329(f287(x78791),x78794),x78793))) % 178.07/177.94 [7922]~P106(x79222)+P24(f329(f329(f243(f883(x79221,x79222)),x79224),x79223))+~P24(f329(f329(f243(f883(x79221,x79222)),x79223),x79224))+P24(f329(f329(f244(f883(x79221,x79222)),x79223),x79224)) % 178.07/177.94 [7964]P24(f329(f329(f331(x79641),x79642),x79643))+P24(f329(f329(f331(x79641),x79642),x79644))+~P24(f329(f329(f243(f883(x79641,a869)),x79644),x79643))+P24(f329(f329(f244(f883(x79641,a869)),x79644),f329(f329(f307(x79641),x79642),x79643))) % 178.07/177.94 [8125]P24(f329(f329(f331(x81251),x81252),x81253))+P24(f329(f329(f331(x81251),x81252),x81254))+~P24(f329(f329(f244(f883(x81251,a869)),x81254),f329(f329(f307(x81251),x81252),x81253)))+P24(f329(f329(f243(f883(x81251,a869)),x81254),x81253)) % 178.07/177.94 [8134]~P58(x81341)+P7(x81341,x81342,x81343)+~P24(f329(x81342,x81344))+~P24(f329(f329(f331(f876(x81341)),x81344),f329(f171(f876(x81341)),f55(x81341,x81343,f56(x81341))))) % 178.07/177.94 [8144]~P8(x81443,x81441,x81444)+~P58(x81443)+P24(f329(x81441,x81442))+~P24(f329(f329(f331(f876(x81443)),x81442),f329(f171(f876(x81443)),f55(x81443,x81444,f56(x81443))))) % 178.07/177.94 [8197]~P121(x81971)+P24(f329(f329(f244(x81971),x81973),x81972))+P24(f329(f329(f244(x81971),x81972),x81973))+~P24(f329(f329(f244(x81971),f329(f329(f82(x81971),x81974),x81972)),f329(f329(f82(x81971),x81974),x81973))) % 178.07/177.94 [8198]~P121(x81981)+P24(f329(f329(f244(x81981),x81983),x81982))+P24(f329(f329(f244(x81981),x81982),x81983))+~P24(f329(f329(f244(x81981),f329(f329(f82(x81981),x81982),x81984)),f329(f329(f82(x81981),x81983),x81984))) % 178.07/177.94 [8209]~P121(x82091)+P24(f329(f329(f244(x82091),x82094),f2(x82091)))+P24(f329(f329(f244(x82091),x82092),x82093))+~P24(f329(f329(f244(x82091),f329(f329(f82(x82091),x82092),x82094)),f329(f329(f82(x82091),x82093),x82094))) % 178.07/177.94 [8210]~P121(x82101)+P24(f329(f329(f244(x82101),x82104),f2(x82101)))+P24(f329(f329(f244(x82101),x82102),x82103))+~P24(f329(f329(f244(x82101),f329(f329(f82(x82101),x82104),x82102)),f329(f329(f82(x82101),x82104),x82103))) % 178.07/177.94 [8214]~P121(x82141)+P24(f329(f329(f244(x82141),x82142),x82143))+P24(f329(f329(f244(x82141),f2(x82141)),x82144))+~P24(f329(f329(f244(x82141),f329(f329(f82(x82141),x82144),x82143)),f329(f329(f82(x82141),x82144),x82142))) % 178.07/177.94 [8215]~P121(x82151)+P24(f329(f329(f244(x82151),x82152),x82153))+P24(f329(f329(f244(x82151),f2(x82151)),x82154))+~P24(f329(f329(f244(x82151),f329(f329(f82(x82151),x82153),x82154)),f329(f329(f82(x82151),x82152),x82154))) % 178.07/177.94 [8228]~P121(x82281)+P24(f329(f329(f244(x82281),x82282),f2(x82281)))+P24(f329(f329(f244(x82281),f2(x82281)),x82282))+~P24(f329(f329(f244(x82281),f329(f329(f82(x82281),x82283),x82282)),f329(f329(f82(x82281),x82284),x82282))) % 178.07/177.94 [8229]~P121(x82291)+P24(f329(f329(f244(x82291),x82292),f2(x82291)))+P24(f329(f329(f244(x82291),f2(x82291)),x82292))+~P24(f329(f329(f244(x82291),f329(f329(f82(x82291),x82292),x82293)),f329(f329(f82(x82291),x82292),x82294))) % 178.07/177.94 [8255]~P121(x82551)+~P24(f329(f329(f244(x82551),x82554),f2(x82551)))+P24(f329(f329(f244(x82551),x82552),x82553))+~P24(f329(f329(f244(x82551),f329(f329(f82(x82551),x82554),x82553)),f329(f329(f82(x82551),x82554),x82552))) % 178.07/177.94 [8256]~P121(x82561)+~P24(f329(f329(f244(x82561),x82564),f2(x82561)))+P24(f329(f329(f243(x82561),x82562),x82563))+~P24(f329(f329(f243(x82561),f329(f329(f82(x82561),x82564),x82563)),f329(f329(f82(x82561),x82564),x82562))) % 178.07/177.94 [8268]~P120(x82683)+~P24(f329(f329(f244(x82683),f79(x82683)),x82684))+P24(f329(f329(f244(a875),x82681),x82682))+~P24(f329(f329(f244(x82683),f329(f329(f254(x82683),x82684),x82681)),f329(f329(f254(x82683),x82684),x82682))) % 178.07/177.94 [8270]~P120(x82703)+~P24(f329(f329(f244(x82703),f79(x82703)),x82704))+P24(f329(f329(f243(a875),x82701),x82702))+~P24(f329(f329(f243(x82703),f329(f329(f254(x82703),x82704),x82701)),f329(f329(f254(x82703),x82704),x82702))) % 178.07/177.94 [8280]~P121(x82801)+P24(f329(f329(f244(x82801),x82802),x82803))+~P24(f329(f329(f244(x82801),f2(x82801)),x82804))+~P24(f329(f329(f244(x82801),f329(f329(f82(x82801),x82804),x82802)),f329(f329(f82(x82801),x82804),x82803))) % 178.07/177.94 [8281]~P125(x82811)+P24(f329(f329(f244(x82811),x82812),x82813))+~P24(f329(f329(f243(x82811),f2(x82811)),x82814))+~P24(f329(f329(f244(x82811),f329(f329(f82(x82811),x82814),x82812)),f329(f329(f82(x82811),x82814),x82813))) % 178.07/177.94 [8282]~P126(x82821)+P24(f329(f329(f244(x82821),x82822),x82823))+~P24(f329(f329(f243(x82821),f2(x82821)),x82824))+~P24(f329(f329(f244(x82821),f329(f329(f82(x82821),x82824),x82822)),f329(f329(f82(x82821),x82824),x82823))) % 178.07/177.94 [8283]~P120(x82831)+~P24(f329(f329(f243(x82831),f2(x82831)),x82833))+P24(f329(f329(f244(x82831),x82832),x82833))+~P24(f329(f329(f244(x82831),f329(f329(f254(x82831),x82832),x82834)),f329(f329(f254(x82831),x82833),x82834))) % 178.07/177.94 [8284]~P125(x82841)+P24(f329(f329(f244(x82841),x82842),x82843))+~P24(f329(f329(f243(x82841),f2(x82841)),x82844))+~P24(f329(f329(f244(x82841),f329(f329(f82(x82841),x82842),x82844)),f329(f329(f82(x82841),x82843),x82844))) % 178.07/177.94 [8285]~P126(x82851)+P24(f329(f329(f244(x82851),x82852),x82853))+~P24(f329(f329(f243(x82851),f2(x82851)),x82854))+~P24(f329(f329(f244(x82851),f329(f329(f82(x82851),x82852),x82854)),f329(f329(f82(x82851),x82853),x82854))) % 178.07/177.94 [8286]~P121(x82861)+P24(f329(f329(f243(x82861),x82862),x82863))+~P24(f329(f329(f244(x82861),f2(x82861)),x82864))+~P24(f329(f329(f243(x82861),f329(f329(f82(x82861),x82864),x82862)),f329(f329(f82(x82861),x82864),x82863))) % 178.07/177.94 [8287]~P125(x82871)+P24(f329(f329(f243(x82871),x82872),x82873))+~P24(f329(f329(f244(x82871),f2(x82871)),x82874))+~P24(f329(f329(f243(x82871),f329(f329(f82(x82871),x82874),x82872)),f329(f329(f82(x82871),x82874),x82873))) % 178.07/177.94 [8288]~P125(x82881)+P24(f329(f329(f243(x82881),x82882),x82883))+~P24(f329(f329(f244(x82881),f2(x82881)),x82884))+~P24(f329(f329(f243(x82881),f329(f329(f82(x82881),x82882),x82884)),f329(f329(f82(x82881),x82883),x82884))) % 178.07/177.94 [8331]P24(f329(f329(f331(x83311),x83312),x83313))+~P24(f329(f329(f243(f883(x83311,a869)),x83313),x83314))+~P24(f329(f329(f244(f883(x83311,a869)),x83313),x83314))+P24(f329(f329(f244(f883(x83311,a869)),x83313),f329(f329(f307(x83311),x83312),x83314))) % 178.07/177.94 [8588]~P58(x85881)+~P94(x85882)+~E(f329(x85883,f810(x85884,x85883,x85881,x85882)),f329(x85884,f810(x85884,x85883,x85881,x85882)))+P24(f329(f329(f92(f883(x85881,x85882)),x85883),x85884)) % 178.07/177.94 [8703]E(f329(f329(f22(a1),f434(x87031,x87032,x87033,x87034)),f435(x87031,x87032,x87033,x87034)),x87034)+~P24(f329(f329(f244(a1),f2(a1)),x87033))+~P24(f329(f329(f243(a1),x87031),x87034))+P24(f329(f329(f243(a1),x87031),f329(f329(f81(a1),x87034),x87033))) % 178.07/177.94 [8704]E(f329(f329(f22(a1),f451(x87041,x87042,x87043,x87044)),f452(x87041,x87042,x87043,x87044)),x87044)+~P24(f329(f329(f244(a1),f2(a1)),x87043))+~P24(f329(f329(f244(a1),x87041),x87044))+P24(f329(f329(f244(a1),x87041),f329(f329(f81(a1),x87044),x87043))) % 178.07/177.94 [8839]~E(f329(f329(f164(x88391),x88393),f603(x88394,x88393,x88391,x88392)),f329(f329(f164(x88391),x88394),f603(x88394,x88393,x88391,x88392)))+E(f329(f329(f174(x88391),x88392),x88393),f329(f329(f174(x88391),x88392),x88394))+~P24(f329(f329(f243(a875),x88392),f329(f194(f876(x88391)),x88393)))+~P24(f329(f329(f243(a875),x88392),f329(f194(f876(x88391)),x88394))) % 178.07/177.94 [8910]~P24(f329(f329(f244(a1),f2(a1)),x89103))+~P24(f329(f329(f243(a1),x89101),x89104))+P24(f329(f329(f331(a1),f434(x89101,x89102,x89103,x89104)),x89102))+P24(f329(f329(f243(a1),x89101),f329(f329(f81(a1),x89104),x89103))) % 178.07/177.94 [8911]~P24(f329(f329(f244(a1),f2(a1)),x89113))+~P24(f329(f329(f244(a1),x89111),x89114))+P24(f329(f329(f331(a1),f451(x89111,x89112,x89113,x89114)),x89112))+P24(f329(f329(f244(a1),x89111),f329(f329(f81(a1),x89114),x89113))) % 178.07/177.94 [8953]~P100(x89531)+~P24(f329(f62(x89531),x89533))+~P24(f329(f329(f331(x89531),x89534),x89533))+P24(f329(f329(f243(x89531),f329(f329(f65(x89531,x89531,f107(x89531)),x89532),x89533)),f329(f329(f107(x89531),x89534),x89532))) % 178.07/177.94 [8954]~P105(x89541)+~P24(f329(f62(x89541),x89543))+~P24(f329(f329(f331(x89541),x89544),x89543))+P24(f329(f329(f243(x89541),f329(f329(f65(x89541,x89541,f241(x89541)),x89542),x89543)),f329(f329(f241(x89541),x89544),x89542))) % 178.07/177.94 [9001]E(f329(f329(f174(x90011),x90012),x90013),f329(f329(f174(x90011),x90012),x90014))+P24(f329(f329(f244(a875),f603(x90013,x90014,x90011,x90012)),x90012))+~P24(f329(f329(f243(a875),x90012),f329(f194(f876(x90011)),x90013)))+~P24(f329(f329(f243(a875),x90012),f329(f194(f876(x90011)),x90014))) % 178.07/177.94 [9006]~P24(f329(f329(f244(a1),f2(a1)),x90063))+~P24(f329(f329(f244(a1),x90061),x90062))+P24(f329(f329(f331(a1),f452(x90061,x90064,x90063,x90062)),f300(a1,f79(a1),x90063)))+P24(f329(f329(f244(a1),x90061),f329(f329(f81(a1),x90062),x90063))) % 178.07/177.94 [9007]~P24(f329(f329(f244(a1),f2(a1)),x90073))+~P24(f329(f329(f243(a1),x90071),x90072))+P24(f329(f329(f331(a1),f435(x90071,x90074,x90073,x90072)),f300(a1,f79(a1),x90073)))+P24(f329(f329(f243(a1),x90071),f329(f329(f81(a1),x90072),x90073))) % 178.07/177.94 [9170]~E(f329(f177(x91701,x91702),x91703),f329(f177(x91701,x91702),x91704))+E(f329(f171(f882(x91701,x91702)),x91703),f329(f171(f882(x91701,x91702)),x91704))+~P24(f329(f136(x91701),f329(f329(f153(f882(x91701,x91702),x91701),f263(x91701,x91702)),x91704)))+~P24(f329(f136(x91701),f329(f329(f153(f882(x91701,x91702),x91701),f263(x91701,x91702)),x91703))) % 178.07/177.94 [9182]E(f329(f177(x91821,x91822),x91823),f329(f177(x91821,x91822),x91824))+~E(f329(f171(f882(x91821,x91822)),x91823),f329(f171(f882(x91821,x91822)),x91824))+~P24(f329(f136(x91821),f329(f329(f153(f882(x91821,x91822),x91821),f263(x91821,x91822)),x91824)))+~P24(f329(f136(x91821),f329(f329(f153(f882(x91821,x91822),x91821),f263(x91821,x91822)),x91823))) % 178.07/177.94 [9326]~P105(x93261)+~P24(f329(f62(x93261),x93264))+P24(f329(f329(f331(x93261),f528(x93262,x93263,x93264,x93261)),x93264))+P24(f329(f329(f243(x93261),f329(f329(f65(x93261,x93261,f242(x93261)),x93262),x93264)),f329(f329(f242(x93261),x93263),x93262))) % 178.07/177.94 [9327]~P99(x93271)+~P24(f329(f62(x93271),x93274))+P24(f329(f329(f331(x93271),f534(x93272,x93273,x93274,x93271)),x93274))+P24(f329(f329(f243(x93271),f329(f329(f65(x93271,x93271,f116(x93271)),x93272),x93274)),f329(f329(f116(x93271),x93273),x93272))) % 178.07/177.94 [9449]~P99(x94491)+~P24(f329(f62(x94491),x94493))+~P24(f329(f329(f243(x94491),f534(x94492,x94494,x94493,x94491)),x94494))+P24(f329(f329(f243(x94491),f329(f329(f65(x94491,x94491,f116(x94491)),x94492),x94493)),f329(f329(f116(x94491),x94494),x94492))) % 178.07/177.94 [9450]~P105(x94501)+~P24(f329(f62(x94501),x94503))+~P24(f329(f329(f243(x94501),f528(x94502,x94504,x94503,x94501)),x94504))+P24(f329(f329(f243(x94501),f329(f329(f65(x94501,x94501,f242(x94501)),x94502),x94503)),f329(f329(f242(x94501),x94504),x94502))) % 178.07/177.94 [9453]~P24(f329(f329(f244(a1),f2(a1)),x94533))+~P24(f329(f329(f243(a1),f2(a1)),x94534))+~P24(f329(f329(f244(a1),x94534),x94531))+P24(f329(f329(f244(a1),f329(f329(f81(a1),f329(f329(f82(a1),x94531),f45(a1,x94532,x94533))),x94534)),f329(f329(f82(a1),x94531),x94533))) % 178.07/177.94 [9848]E(x98481,x98482)+P24(f329(f329(f331(f882(f876(x98483),f876(x98483))),f329(f329(f264(f876(x98483),f876(x98483)),x98482),x98481)),f146(x98483,x98484)))+P24(f329(f329(f331(f882(f876(x98483),f876(x98483))),f329(f329(f264(f876(x98483),f876(x98483)),x98481),x98482)),f146(x98483,x98484)))+~P24(f329(f329(f331(f882(x98483,x98483)),f329(f329(f264(x98483,x98483),f604(x98481,x98482,x98484,x98483)),f607(x98481,x98482,x98484,x98483))),x98484)) % 178.07/177.94 [9849]E(x98491,x98492)+P24(f329(f329(f331(f882(f876(x98493),f876(x98493))),f329(f329(f264(f876(x98493),f876(x98493)),x98492),x98491)),f146(x98493,x98494)))+P24(f329(f329(f331(f882(f876(x98493),f876(x98493))),f329(f329(f264(f876(x98493),f876(x98493)),x98491),x98492)),f146(x98493,x98494)))+~P24(f329(f329(f331(f882(x98493,x98493)),f329(f329(f264(x98493,x98493),f607(x98491,x98492,x98494,x98493)),f604(x98491,x98492,x98494,x98493))),x98494)) % 178.07/177.94 [7408]~P105(x74081)+~P24(f329(f329(f244(x74081),x74083),x74084))+~P24(f329(f329(f244(x74081),x74082),x74084))+P24(f329(f329(f244(x74081),f329(f329(f242(x74081),x74082),x74083)),x74084)) % 178.07/177.94 [7411]~P99(x74111)+~P24(f329(f329(f243(x74111),x74113),x74114))+~P24(f329(f329(f243(x74111),x74112),x74114))+P24(f329(f329(f243(x74111),f329(f329(f116(x74111),x74112),x74113)),x74114)) % 178.07/177.94 [7414]~P105(x74141)+~P24(f329(f329(f243(x74141),x74143),x74144))+~P24(f329(f329(f243(x74141),x74142),x74144))+P24(f329(f329(f243(x74141),f329(f329(f242(x74141),x74142),x74143)),x74144)) % 178.07/177.94 [7733]~E(x77331,x77333)+E(f138(a875,f329(f299(a875,x77331),x77332)),f329(f329(f150(a875),x77333),x77334))+~E(f138(a875,f329(f299(a875,f329(f329(f81(a875),x77331),f79(a875))),x77332)),x77334)+~P24(f329(f329(f244(a875),x77331),x77332)) % 178.07/177.94 [7744]~P105(x77441)+P24(f329(f329(f244(x77441),x77442),x77443))+P24(f329(f329(f244(x77441),x77444),x77443))+~P24(f329(f329(f244(x77441),f329(f329(f241(x77441),x77444),x77442)),x77443)) % 178.07/177.94 [7745]~P105(x77451)+P24(f329(f329(f243(x77451),x77452),x77453))+P24(f329(f329(f243(x77451),x77454),x77453))+~P24(f329(f329(f243(x77451),f329(f329(f241(x77451),x77454),x77452)),x77453)) % 178.07/177.94 [8025]~P61(x80251)+~P24(f329(f329(f244(x80251),f2(x80251)),x80253))+~P24(f329(f329(f244(x80251),x80252),f329(f329(f287(x80251),x80254),x80253)))+P24(f329(f329(f244(x80251),f329(f329(f82(x80251),x80252),x80253)),x80254)) % 178.07/177.94 [8026]~P62(x80261)+~P24(f329(f329(f244(x80261),f2(x80261)),x80263))+~P24(f329(f329(f244(x80261),x80262),f329(f329(f287(x80261),x80264),x80263)))+P24(f329(f329(f244(x80261),f329(f329(f82(x80261),x80262),x80263)),x80264)) % 178.07/177.94 [8027]~P61(x80271)+~P24(f329(f329(f244(x80271),f2(x80271)),x80273))+~P24(f329(f329(f244(x80271),x80272),f329(f329(f82(x80271),x80274),x80273)))+P24(f329(f329(f244(x80271),f329(f329(f287(x80271),x80272),x80273)),x80274)) % 178.07/177.94 [8029]~P62(x80291)+~P24(f329(f329(f244(x80291),f2(x80291)),x80293))+~P24(f329(f329(f244(x80291),x80292),f329(f329(f82(x80291),x80294),x80293)))+P24(f329(f329(f244(x80291),f329(f329(f287(x80291),x80292),x80293)),x80294)) % 178.07/177.94 [8030]~P61(x80301)+~P24(f329(f329(f244(x80301),f2(x80301)),x80303))+~P24(f329(f329(f243(x80301),x80302),f329(f329(f287(x80301),x80304),x80303)))+P24(f329(f329(f243(x80301),f329(f329(f82(x80301),x80302),x80303)),x80304)) % 178.07/177.94 [8031]~P62(x80311)+~P24(f329(f329(f244(x80311),f2(x80311)),x80313))+~P24(f329(f329(f243(x80311),x80312),f329(f329(f287(x80311),x80314),x80313)))+P24(f329(f329(f243(x80311),f329(f329(f82(x80311),x80312),x80313)),x80314)) % 178.07/177.94 [8032]~P61(x80321)+~P24(f329(f329(f244(x80321),f2(x80321)),x80323))+~P24(f329(f329(f243(x80321),x80322),f329(f329(f82(x80321),x80324),x80323)))+P24(f329(f329(f243(x80321),f329(f329(f287(x80321),x80322),x80323)),x80324)) % 178.07/177.94 [8034]~P62(x80341)+~P24(f329(f329(f244(x80341),f2(x80341)),x80343))+~P24(f329(f329(f243(x80341),x80342),f329(f329(f82(x80341),x80344),x80343)))+P24(f329(f329(f243(x80341),f329(f329(f287(x80341),x80342),x80343)),x80344)) % 178.07/177.94 [8166]~P61(x81661)+~P24(f329(f329(f244(x81661),f2(x81661)),x81664))+P24(f329(f329(f244(x81661),x81662),f329(f329(f82(x81661),x81663),x81664)))+~P24(f329(f329(f244(x81661),f329(f329(f287(x81661),x81662),x81664)),x81663)) % 178.07/177.94 [8167]~P61(x81671)+~P24(f329(f329(f244(x81671),f2(x81671)),x81674))+P24(f329(f329(f244(x81671),x81672),f329(f329(f287(x81671),x81673),x81674)))+~P24(f329(f329(f244(x81671),f329(f329(f82(x81671),x81672),x81674)),x81673)) % 178.07/177.94 [8169]~P62(x81691)+~P24(f329(f329(f244(x81691),f2(x81691)),x81694))+P24(f329(f329(f244(x81691),x81692),f329(f329(f82(x81691),x81693),x81694)))+~P24(f329(f329(f244(x81691),f329(f329(f287(x81691),x81692),x81694)),x81693)) % 178.07/177.94 [8170]~P62(x81701)+~P24(f329(f329(f244(x81701),f2(x81701)),x81704))+P24(f329(f329(f244(x81701),x81702),f329(f329(f287(x81701),x81703),x81704)))+~P24(f329(f329(f244(x81701),f329(f329(f82(x81701),x81702),x81704)),x81703)) % 178.07/177.94 [8171]~P61(x81711)+~P24(f329(f329(f244(x81711),f2(x81711)),x81714))+P24(f329(f329(f243(x81711),x81712),f329(f329(f82(x81711),x81713),x81714)))+~P24(f329(f329(f243(x81711),f329(f329(f287(x81711),x81712),x81714)),x81713)) % 178.07/177.94 [8172]~P61(x81721)+~P24(f329(f329(f244(x81721),f2(x81721)),x81724))+P24(f329(f329(f243(x81721),x81722),f329(f329(f287(x81721),x81723),x81724)))+~P24(f329(f329(f243(x81721),f329(f329(f82(x81721),x81722),x81724)),x81723)) % 178.07/177.94 [8174]~P62(x81741)+~P24(f329(f329(f244(x81741),f2(x81741)),x81744))+P24(f329(f329(f243(x81741),x81742),f329(f329(f82(x81741),x81743),x81744)))+~P24(f329(f329(f243(x81741),f329(f329(f287(x81741),x81742),x81744)),x81743)) % 178.07/177.94 [8175]~P62(x81751)+~P24(f329(f329(f244(x81751),f2(x81751)),x81754))+P24(f329(f329(f243(x81751),x81752),f329(f329(f287(x81751),x81753),x81754)))+~P24(f329(f329(f243(x81751),f329(f329(f82(x81751),x81752),x81754)),x81753)) % 178.07/177.94 [8335]~P62(x83351)+~P24(f329(f329(f244(x83351),x83353),f2(x83351)))+~P24(f329(f329(f244(x83351),f329(f329(f287(x83351),x83354),x83353)),x83352))+P24(f329(f329(f244(x83351),f329(f329(f82(x83351),x83352),x83353)),x83354)) % 178.07/177.94 [8336]~P62(x83361)+~P24(f329(f329(f244(x83361),x83363),f2(x83361)))+~P24(f329(f329(f244(x83361),f329(f329(f82(x83361),x83364),x83363)),x83362))+P24(f329(f329(f244(x83361),f329(f329(f287(x83361),x83362),x83363)),x83364)) % 178.07/177.94 [8337]~P62(x83371)+~P24(f329(f329(f244(x83371),x83373),f2(x83371)))+~P24(f329(f329(f243(x83371),f329(f329(f287(x83371),x83374),x83373)),x83372))+P24(f329(f329(f243(x83371),f329(f329(f82(x83371),x83372),x83373)),x83374)) % 178.07/177.94 [8338]~P62(x83381)+~P24(f329(f329(f244(x83381),x83383),f2(x83381)))+~P24(f329(f329(f243(x83381),f329(f329(f82(x83381),x83384),x83383)),x83382))+P24(f329(f329(f243(x83381),f329(f329(f287(x83381),x83382),x83383)),x83384)) % 178.07/177.94 [8348]~P24(f329(x83481,x83484))+~P24(f329(f329(f244(a875),x83482),f329(f329(f82(a875),x83483),f329(a118,x83484))))+P24(f329(x83481,f329(f329(f39(a875),x83482),x83483)))+~P24(f329(f329(f243(a875),f329(f329(f82(a875),x83483),x83484)),x83482)) % 178.07/177.94 [8562]~P99(x85621)+~P24(f329(f62(x85621),x85624))+~P24(f329(f329(f331(x85621),x85622),x85624))+P24(f329(f329(f243(x85621),f329(f329(f116(x85621),x85622),x85623)),f329(f329(f65(x85621,x85621,f116(x85621)),x85623),x85624))) % 178.07/177.94 [8563]~P105(x85631)+~P24(f329(f62(x85631),x85634))+~P24(f329(f329(f331(x85631),x85632),x85634))+P24(f329(f329(f243(x85631),f329(f329(f242(x85631),x85632),x85633)),f329(f329(f65(x85631,x85631,f242(x85631)),x85633),x85634))) % 178.07/177.94 [8705]~P24(f329(f62(x87051),x87052))+E(f329(f38(x87051),f329(f329(f22(f883(x87051,a869)),x87052),f329(f329(f307(x87051),x87053),x87054))),f329(f329(f22(a875),f329(f38(x87051),f329(f329(f22(f883(x87051,a869)),x87052),x87054))),f79(a875)))+P24(f329(f329(f331(x87051),x87053),x87054))+~P24(f329(f329(f331(x87051),x87053),x87052)) % 178.07/177.94 [8775]E(f329(f329(f81(a1),f441(x87751,x87752,x87753,x87754)),f442(x87751,x87752,x87753,x87754)),x87754)+~P24(f329(f329(f244(a1),f2(a1)),x87753))+~P24(f329(f329(f243(a1),x87754),x87751))+P24(f329(f329(f243(a1),f329(f329(f22(a1),x87754),x87753)),x87751)) % 178.07/177.94 [8776]E(f329(f329(f81(a1),f453(x87761,x87762,x87763,x87764)),f446(x87761,x87762,x87763,x87764)),x87764)+~P24(f329(f329(f244(a1),f2(a1)),x87763))+~P24(f329(f329(f244(a1),x87764),x87761))+P24(f329(f329(f244(a1),f329(f329(f22(a1),x87764),x87763)),x87761)) % 178.07/177.94 [8986]~P24(f329(f329(f244(a1),f2(a1)),x89863))+~P24(f329(f329(f243(a1),x89864),x89861))+P24(f329(f329(f331(a1),f441(x89861,x89862,x89863,x89864)),x89862))+P24(f329(f329(f243(a1),f329(f329(f22(a1),x89864),x89863)),x89861)) % 178.07/177.94 [8987]~P24(f329(f329(f244(a1),f2(a1)),x89873))+~P24(f329(f329(f244(a1),x89874),x89871))+P24(f329(f329(f331(a1),f453(x89871,x89872,x89873,x89874)),x89872))+P24(f329(f329(f244(a1),f329(f329(f22(a1),x89874),x89873)),x89871)) % 178.07/177.94 [9072]~P24(f329(f329(f244(a1),f2(a1)),x90722))+~P24(f329(f329(f244(a1),x90721),x90723))+P24(f329(f329(f331(a1),f446(x90723,x90724,x90722,x90721)),f300(a1,f79(a1),x90722)))+P24(f329(f329(f244(a1),f329(f329(f22(a1),x90721),x90722)),x90723)) % 178.07/177.94 [9073]~P24(f329(f329(f244(a1),f2(a1)),x90732))+~P24(f329(f329(f243(a1),x90731),x90733))+P24(f329(f329(f331(a1),f442(x90733,x90734,x90732,x90731)),f300(a1,f79(a1),x90732)))+P24(f329(f329(f243(a1),f329(f329(f22(a1),x90731),x90732)),x90733)) % 178.07/177.94 [9089]~P24(f329(f329(f244(a1),f2(a1)),x90893))+~P24(f329(f329(f243(a1),f2(a1)),x90894))+~P24(f329(f329(f244(a1),x90894),x90891))+P24(f329(f329(f243(a1),f2(a1)),f329(f329(f81(a1),f329(f329(f82(a1),x90891),f45(a1,x90892,x90893))),x90894))) % 178.07/177.94 [9153]~P100(x91531)+~P24(f329(f62(x91531),x91534))+~P24(f329(f329(f243(x91531),x91532),f533(x91533,x91532,x91534,x91531)))+P24(f329(f329(f243(x91531),f329(f329(f107(x91531),x91532),x91533)),f329(f329(f65(x91531,x91531,f107(x91531)),x91533),x91534))) % 178.07/177.94 [9154]~P105(x91541)+~P24(f329(f62(x91541),x91544))+~P24(f329(f329(f243(x91541),x91542),f527(x91543,x91542,x91544,x91541)))+P24(f329(f329(f243(x91541),f329(f329(f241(x91541),x91542),x91543)),f329(f329(f65(x91541,x91541,f241(x91541)),x91543),x91544))) % 178.07/177.94 [9169]~P24(f329(f329(f243(a1),x91694),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x91692))+~P24(f329(f329(f244(a1),x91691),x91694))+P24(f329(f329(f244(a1),f329(f329(f82(a1),x91691),x91692)),f329(f329(f81(a1),f329(f329(f82(a1),x91691),f45(a1,x91693,x91692))),x91694))) % 178.07/177.94 [9191]P24(f329(f62(x91911),x91912))+~P24(f329(f62(x91911),x91913))+~P24(f329(f329(f331(f883(x91911,a869)),x91912),f329(f329(f61(x91911),x91913),x91914)))+~P24(f329(f329(f243(f883(f882(x91911,x91911),a869)),x91914),f329(f329(f266(x91911,x91911),x91913),f329(f16(f883(x91911,a869),x91911),x91913)))) % 178.07/177.94 [9219]~P105(x92191)+~P24(f329(f62(x92191),x92194))+P24(f329(f329(f331(x92191),f527(x92192,x92193,x92194,x92191)),x92194))+P24(f329(f329(f243(x92191),f329(f329(f241(x92191),x92193),x92192)),f329(f329(f65(x92191,x92191,f241(x92191)),x92192),x92194))) % 178.07/177.94 [9220]~P100(x92201)+~P24(f329(f62(x92201),x92204))+P24(f329(f329(f331(x92201),f533(x92202,x92203,x92204,x92201)),x92204))+P24(f329(f329(f243(x92201),f329(f329(f107(x92201),x92203),x92202)),f329(f329(f65(x92201,x92201,f107(x92201)),x92202),x92204))) % 178.07/177.94 [9615]~P24(f329(f62(x96152),x96154))+~P24(f329(f62(x96151),x96153))+~P24(f329(f329(f243(a875),f329(f38(x96152),x96154)),f329(f38(x96151),x96153)))+P24(f329(f329(f243(f883(x96151,a869)),f329(f308(x96152,x96151,f348(x96153,x96151,x96154,x96152)),x96154)),x96153)) % 178.07/177.94 [9267]~P24(f329(f329(f331(x92671),x92672),x92674))+P24(f329(f329(f331(x92671),x92672),x92673))+~P24(f329(f329(f244(f883(x92671,a869)),x92674),f329(f329(f307(x92671),x92672),x92673)))+P24(f329(f329(f244(f883(x92671,a869)),f329(f329(f22(f883(x92671,a869)),x92674),f329(f329(f307(x92671),x92672),f193(f883(x92671,a869))))),x92673)) % 178.07/177.94 [9427]~P24(f329(f329(f331(x94271),x94272),x94274))+P24(f329(f329(f331(x94271),x94272),x94273))+P24(f329(f329(f244(f883(x94271,a869)),x94274),f329(f329(f307(x94271),x94272),x94273)))+~P24(f329(f329(f244(f883(x94271,a869)),f329(f329(f22(f883(x94271,a869)),x94274),f329(f329(f307(x94271),x94272),f193(f883(x94271,a869))))),x94273)) % 178.07/177.94 [9456]P24(f329(f329(f331(x94561),x94562),x94563))+~P24(f329(f329(f243(f883(x94561,a869)),x94564),x94563))+P24(f329(f329(f244(f883(x94561,a869)),x94564),f329(f329(f307(x94561),x94562),x94563)))+~P24(f329(f329(f244(f883(x94561,a869)),f329(f329(f22(f883(x94561,a869)),x94564),f329(f329(f307(x94561),x94562),f193(f883(x94561,a869))))),x94563)) % 178.07/177.94 [9461]~P24(f329(f329(f331(x94611),x94613),x94612))+~P24(f329(f329(f244(f883(x94611,a869)),x94612),x94614))+P24(f329(f329(f244(f883(x94611,a869)),x94612),f329(f329(f307(x94611),x94613),x94614)))+~P24(f329(f329(f244(f883(x94611,a869)),f329(f329(f22(f883(x94611,a869)),x94612),f329(f329(f307(x94611),x94613),f193(f883(x94611,a869))))),x94614)) % 178.07/177.94 [9474]~P24(f329(f329(f243(f883(x94741,a869)),x94742),x94744))+~P24(f329(f329(f244(f883(x94741,a869)),x94742),x94744))+P24(f329(f329(f244(f883(x94741,a869)),x94742),f329(f329(f307(x94741),x94743),x94744)))+~P24(f329(f329(f244(f883(x94741,a869)),f329(f329(f22(f883(x94741,a869)),x94742),f329(f329(f307(x94741),x94743),f193(f883(x94741,a869))))),x94744)) % 178.07/177.94 [9518]~P107(x95182)+~P58(x95181)+~P24(f329(f329(f243(f883(x95181,x95182)),x95183),x95184))+P24(f329(f59(x95181),f329(f329(f18(x95181,x95182,a869),f329(f329(f8(x95182,f883(x95182,a869),x95181),f243(x95182)),x95183)),x95184))) % 178.07/177.94 [9662]~P107(x96622)+~P58(x96621)+P24(f329(f329(f243(f883(x96621,x96622)),x96623),x96624))+~P24(f329(f59(x96621),f329(f329(f18(x96621,x96622,a869),f329(f329(f8(x96622,f883(x96622,a869),x96621),f243(x96622)),x96623)),x96624))) % 178.07/177.94 [9832]E(f329(f329(f164(x98321),f329(f329(f164(f876(x98321)),f179(x98321,x98322)),x98323)),x98324),f329(f329(f164(x98321),f329(f329(f164(f876(x98321)),x98322),x98324)),x98323))+~P24(f329(f329(f244(a875),x98323),f329(f194(f876(f876(x98321))),f179(x98321,x98322))))+~P29(a875,f329(f168(a875),f329(f329(f153(f876(x98321),a875),f194(f876(x98321))),x98322)))+~P24(f329(f329(f244(a875),x98324),f329(f194(f876(f876(x98321))),f329(f135(f876(x98321),f329(f329(f8(a875,a869,f876(x98321)),f329(f244(a875),x98323)),f194(f876(x98321)))),x98322)))) % 178.07/177.94 [9861]~P24(f329(f329(f331(f882(a875,a875)),x98614),x98611))+~P24(f329(f329(f331(f882(f882(a875,a875),f882(a875,a875))),f329(f329(f264(f882(a875,a875),f882(a875,a875)),x98614),x98612)),a36))+~P24(f329(f329(f331(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869))),f329(f329(f264(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),x98611),x98613)),a69))+P24(f329(f329(f331(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869))),f329(f329(f264(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),x98611),f329(f329(f307(f882(a875,a875)),x98612),x98613))),a69)) % 178.07/177.94 [9862]~P24(f329(f329(f331(f882(a875,a875)),x98624),x98621))+~P24(f329(f329(f331(f882(f882(a875,a875),f882(a875,a875))),f329(f329(f264(f882(a875,a875),f882(a875,a875)),x98624),x98622)),a71))+~P24(f329(f329(f331(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869))),f329(f329(f264(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),x98621),x98623)),a72))+P24(f329(f329(f331(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869))),f329(f329(f264(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),x98621),f329(f329(f307(f882(a875,a875)),x98622),x98623))),a72)) % 178.07/177.94 [9746]~P107(x97462)+~P58(x97461)+~P24(f329(f329(f244(f883(x97461,x97462)),x97463),x97464))+P24(f329(f58(x97461),f329(f329(f8(a869,a869,x97461),a324),f329(f329(f18(x97461,x97462,a869),f329(f329(f8(x97462,f883(x97462,a869),x97461),a326),x97463)),x97464)))) % 178.07/177.94 [9875]~P24(f329(f329(f331(f882(a875,a875)),x98754),x98753))+~P24(f329(f329(f331(f882(f882(a875,a875),f882(a875,a875))),f329(f329(f264(f882(a875,a875),f882(a875,a875)),x98751),x98754)),a36))+~P24(f329(f329(f331(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869))),f329(f329(f264(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),x98752),x98753)),a37))+P24(f329(f329(f331(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869))),f329(f329(f264(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),f329(f329(f307(f882(a875,a875)),x98751),x98752)),x98753)),a37)) % 178.07/177.94 [9876]~P24(f329(f329(f331(f882(a875,a875)),x98764),x98763))+~P24(f329(f329(f331(f882(f882(a875,a875),f882(a875,a875))),f329(f329(f264(f882(a875,a875),f882(a875,a875)),x98761),x98764)),a71))+~P24(f329(f329(f331(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869))),f329(f329(f264(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),x98762),x98763)),a70))+P24(f329(f329(f331(f882(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869))),f329(f329(f264(f883(f882(a875,a875),a869),f883(f882(a875,a875),a869)),f329(f329(f307(f882(a875,a875)),x98761),x98762)),x98763)),a70)) % 178.07/177.94 [6004]~P5(x60044,x60041)+~P24(f329(f329(x60041,x60042),x60045))+P24(f329(f329(x60041,x60042),x60043))+~P24(f329(f329(x60041,x60045),x60043)) % 178.07/177.94 [5268]~P66(x52685)+E(x52681,x52682)+~E(x52683,x52684)+~E(f329(f329(f22(x52685),x52683),x52684),f329(f329(f22(x52685),x52681),x52682)) % 178.07/177.94 [6112]~P13(x61125,x61121,x61123)+E(f329(f329(x61121,x61122),f329(x61123,x61124)),f329(x61123,x61124))+~P24(f329(f62(x61125),x61124))+~P24(f329(f329(f331(x61125),x61122),x61124)) % 178.07/177.94 [6305]~P77(x63051)+~E(f329(f329(f22(x63051),x63054),x63055),f329(f329(f22(x63051),x63052),x63053))+~P24(f329(f329(f244(x63051),x63054),x63055))+P24(f329(f329(f244(x63051),x63052),x63053)) % 178.07/177.94 [6307]~P77(x63071)+~E(f329(f329(f22(x63071),x63074),x63075),f329(f329(f22(x63071),x63072),x63073))+~P24(f329(f329(f243(x63071),x63074),x63075))+P24(f329(f329(f243(x63071),x63072),x63073)) % 178.07/177.94 [7268]~E(x72682,f329(f329(f150(x72681),x72684),x72685))+P24(f329(f329(f331(f876(x72681)),x72682),f160(x72681,x72683)))+~P24(f329(f329(f331(f876(x72681)),x72685),f160(x72681,x72683)))+~P24(f329(f329(f331(x72681),x72684),x72683)) % 178.07/177.94 [7686]~E(f329(f194(f876(x76861)),x76863),f329(f194(f876(x76862)),x76864))+~E(f329(f329(f153(f882(x76861,x76862),x76862),f267(x76861,x76862)),x76865),x76864)+~E(f329(f329(f153(f882(x76861,x76862),x76861),f263(x76861,x76862)),x76865),x76863)+E(f329(f329(f181(x76861,x76862),x76863),x76864),x76865) % 178.07/177.94 [8022]~P107(x80221)+P24(f329(f329(f244(f883(x80221,a869)),f300(x80221,x80222,x80223)),f300(x80221,x80224,x80225)))+~P24(f329(f329(f243(x80221),x80224),x80225))+P24(f329(f329(f243(x80221),x80222),x80223)) % 178.07/177.94 [8118]~P107(x81181)+P24(f329(f329(f243(f883(x81181,a869)),f300(x81181,x81182,x81183)),f300(x81181,x81184,x81185)))+~P24(f329(f329(f243(x81181),x81183),x81185))+~P24(f329(f329(f243(x81181),x81184),x81182)) % 178.07/177.94 [8243]~P105(x82431)+P24(f329(f329(f243(x82431),x82432),x82433))+P24(f329(f329(f243(x82431),x82434),x82433))+~P24(f329(f329(f243(f883(x82431,a869)),f329(f299(x82431,x82433),x82432)),f329(f299(x82431,x82434),x82435))) % 178.07/177.94 [8244]~P105(x82441)+P24(f329(f329(f243(x82441),x82442),x82443))+P24(f329(f329(f243(x82441),x82442),x82444))+~P24(f329(f329(f243(f883(x82441,a869)),f329(f299(x82441,x82443),x82442)),f329(f299(x82441,x82445),x82444))) % 178.07/177.94 [8483]~P107(x84831)+~P24(f329(f329(f244(f883(x84831,a869)),f300(x84831,x84834,x84832)),f300(x84831,x84835,x84833)))+P24(f329(f329(f243(x84831),x84832),x84833))+~P24(f329(f329(f243(x84831),x84834),x84832)) % 178.07/177.94 [8484]~P107(x84841)+~P24(f329(f329(f243(f883(x84841,a869)),f300(x84841,x84844,x84842)),f300(x84841,x84845,x84843)))+P24(f329(f329(f243(x84841),x84842),x84843))+~P24(f329(f329(f243(x84841),x84844),x84842)) % 178.07/177.94 [8485]~P107(x84851)+~P24(f329(f329(f244(f883(x84851,a869)),f300(x84851,x84853,x84854)),f300(x84851,x84852,x84855)))+P24(f329(f329(f243(x84851),x84852),x84853))+~P24(f329(f329(f243(x84851),x84853),x84854)) % 178.07/177.94 [8486]~P107(x84861)+~P24(f329(f329(f243(f883(x84861,a869)),f300(x84861,x84863,x84864)),f300(x84861,x84862,x84865)))+P24(f329(f329(f243(x84861),x84862),x84863))+~P24(f329(f329(f243(x84861),x84863),x84864)) % 178.07/177.94 [6003]~P13(x60032,x60035,x60033)+E(x60031,f193(f883(x60032,a869)))+~P24(f329(f62(x60032),x60031))+E(f329(x60033,f329(f329(f307(x60032),x60034),x60031)),f329(f329(x60035,x60034),f329(x60033,x60031))) % 178.07/177.94 [6771]~E(x67711,x67712)+~E(f329(f329(f107(f883(x67713,a869)),x67714),x67715),f193(f883(x67713,a869)))+~P24(f329(f329(f331(x67713),x67712),x67715))+~P24(f329(f329(f331(x67713),x67711),x67714)) % 178.07/177.94 [6852]~P14(x68522,x68525,x68521)+~P24(f329(f62(x68522),x68524))+E(f329(x68521,f329(f329(f307(x68522),x68523),x68524)),f329(f329(f65(x68522,x68522,x68525),x68523),x68524))+P24(f329(f329(f331(x68522),x68523),x68524)) % 178.07/177.94 [6919]~P70(x69192)+~P24(f329(f62(x69191),x69195))+E(f329(f329(f6(x69191,x69192),x69193),f329(f329(f307(x69191),x69194),x69195)),f329(f329(f81(x69192),f329(x69193,x69194)),f329(f329(f6(x69191,x69192),x69193),x69195)))+P24(f329(f329(f331(x69191),x69194),x69195)) % 178.07/177.94 [6921]~P74(x69212)+~P24(f329(f62(x69211),x69215))+E(f329(f329(f9(x69211,x69212),x69213),f329(f329(f307(x69211),x69214),x69215)),f329(f329(f82(x69212),f329(x69213,x69214)),f329(f329(f9(x69211,x69212),x69213),x69215)))+P24(f329(f329(f331(x69211),x69214),x69215)) % 178.07/177.94 [7426]~P14(x74262,x74265,x74261)+~P24(f329(f62(x74262),x74264))+E(f329(x74261,f329(f329(f307(x74262),x74263),x74264)),x74263)+~E(f329(f329(f22(f883(x74262,a869)),x74264),f329(f329(f307(x74262),x74263),f193(f883(x74262,a869)))),f193(f883(x74262,a869))) % 178.07/177.94 [7737]~P24(f329(x77371,x77373))+~P24(f329(f329(f199(x77372),x77373),x77375))+~P24(f329(f329(f199(f33(x77371,x77372)),x77375),x77374))+P24(f329(f329(f199(f33(x77371,x77372)),x77373),x77374)) % 178.07/177.94 [7789]~P82(x77891)+~P24(f329(f329(f244(x77891),x77893),x77895))+~P24(f329(f329(f244(x77891),x77892),x77894))+P24(f329(f329(f244(x77891),f329(f329(f81(x77891),x77892),x77893)),f329(f329(f81(x77891),x77894),x77895))) % 178.07/177.94 [7790]~P82(x77901)+~P24(f329(f329(f243(x77901),x77902),x77904))+~P24(f329(f329(f244(x77901),x77903),x77905))+P24(f329(f329(f244(x77901),f329(f329(f81(x77901),x77902),x77903)),f329(f329(f81(x77901),x77904),x77905))) % 178.07/177.94 [7791]~P82(x77911)+~P24(f329(f329(f243(x77911),x77913),x77915))+~P24(f329(f329(f244(x77911),x77912),x77914))+P24(f329(f329(f244(x77911),f329(f329(f81(x77911),x77912),x77913)),f329(f329(f81(x77911),x77914),x77915))) % 178.07/177.94 [7792]~P99(x77921)+~P24(f329(f329(f243(x77921),x77923),x77925))+~P24(f329(f329(f243(x77921),x77922),x77924))+P24(f329(f329(f243(x77921),f329(f329(f116(x77921),x77922),x77923)),f329(f329(f116(x77921),x77924),x77925))) % 178.07/177.94 [7793]~P100(x77931)+~P24(f329(f329(f243(x77931),x77933),x77935))+~P24(f329(f329(f243(x77931),x77932),x77934))+P24(f329(f329(f243(x77931),f329(f329(f107(x77931),x77932),x77933)),f329(f329(f107(x77931),x77934),x77935))) % 178.07/177.94 [7794]~P84(x77941)+~P24(f329(f329(f243(x77941),x77943),x77945))+~P24(f329(f329(f243(x77941),x77942),x77944))+P24(f329(f329(f243(x77941),f329(f329(f81(x77941),x77942),x77943)),f329(f329(f81(x77941),x77944),x77945))) % 178.07/177.94 [7795]~P105(x77951)+~P24(f329(f329(f243(x77951),x77953),x77955))+~P24(f329(f329(f243(x77951),x77952),x77954))+P24(f329(f329(f243(x77951),f329(f329(f241(x77951),x77952),x77953)),f329(f329(f241(x77951),x77954),x77955))) % 178.07/177.94 [7796]~P105(x77961)+~P24(f329(f329(f243(x77961),x77963),x77965))+~P24(f329(f329(f243(x77961),x77962),x77964))+P24(f329(f329(f243(x77961),f329(f329(f242(x77961),x77962),x77963)),f329(f329(f242(x77961),x77964),x77965))) % 178.07/177.94 [7932]~P139(x79325)+E(x79321,x79322)+E(x79323,x79324)+~E(f329(f329(f81(x79325),f329(f329(f82(x79325),x79323),x79321)),f329(f329(f82(x79325),x79324),x79322)),f329(f329(f81(x79325),f329(f329(f82(x79325),x79323),x79322)),f329(f329(f82(x79325),x79324),x79321))) % 178.07/177.94 [8073]P30(x80731,x80732,x80733)+~P23(x80731,x80734,x80735)+~P30(x80731,x80732,f599(x80735,x80734,x80731,x80732))+~P24(f329(f329(f331(f874(x80731)),x80733),x80735)) % 178.07/177.94 [8141]~P105(x81414)+~P24(f329(f136(x81411),x81413))+P24(f329(f329(f331(x81411),x81412),f329(f171(x81411),x81413)))+P24(f329(f136(x81411),f329(f329(f147(x81411,x81414,x81415),x81412),x81413))) % 178.07/177.94 [8289]~P66(x82891)+E(f329(f329(f22(x82891),f329(f329(f6(a875,x82891),x82892),f329(f299(a875,x82893),x82894))),f329(f329(f6(a875,x82891),x82892),f329(f299(a875,x82893),x82895))),f329(f329(f6(a875,x82891),x82892),f329(f299(a875,x82895),x82894)))+~P24(f329(f329(f243(a875),x82895),x82894))+~P24(f329(f329(f243(a875),x82893),x82895)) % 178.07/177.94 [8290]~P70(x82901)+E(f329(f329(f81(x82901),f329(f329(f6(a875,x82901),x82902),f329(f299(a875,x82903),x82904))),f329(f329(f6(a875,x82901),x82902),f329(f299(a875,x82904),x82905))),f329(f329(f6(a875,x82901),x82902),f329(f299(a875,x82903),x82905)))+~P24(f329(f329(f243(a875),x82904),x82905))+~P24(f329(f329(f243(a875),x82903),x82904)) % 178.07/177.94 [8619]~P60(x86192)+E(x86191,f2(x86192))+E(x86193,f2(x86192))+E(f329(f329(f287(x86192),f329(f329(f22(x86192),f329(f329(f82(x86192),x86194),x86191)),f329(f329(f82(x86192),x86195),x86193))),f329(f329(f82(x86192),x86193),x86191)),f329(f329(f22(x86192),f329(f329(f287(x86192),x86194),x86193)),f329(f329(f287(x86192),x86195),x86191))) % 178.07/177.94 [8620]~P60(x86202)+E(x86201,f2(x86202))+E(x86203,f2(x86202))+E(f329(f329(f287(x86202),f329(f329(f81(x86202),f329(f329(f82(x86202),x86204),x86201)),f329(f329(f82(x86202),x86205),x86203))),f329(f329(f82(x86202),x86203),x86201)),f329(f329(f81(x86202),f329(f329(f287(x86202),x86204),x86203)),f329(f329(f287(x86202),x86205),x86201))) % 178.07/177.94 [8629]~E(x86292,f329(x86293,x86291))+E(x86291,f812(x86292,x86293,x86294,x86295))+~P21(x86295,x86294,x86293,f252(f883(x86295,a869)))+~P24(f329(f329(f331(x86294),x86292),f329(f308(x86295,x86294,x86293),f252(f883(x86295,a869))))) % 178.07/177.94 [8824]~P117(x88241)+~P24(f329(f329(f244(x88241),f329(f76(x88241),x88242)),x88244))+P24(f329(f329(f244(x88241),f329(f329(f82(x88241),f329(f76(x88241),x88242)),f329(f76(x88241),x88243))),f329(f329(f82(x88241),x88244),x88245)))+~P24(f329(f329(f244(x88241),f329(f76(x88241),x88243)),x88245)) % 178.07/177.94 [8841]~P23(x88411,x88415,x88414)+P30(x88411,x88412,x88413)+P24(f329(f329(f331(f874(x88411)),f599(x88414,x88415,x88411,x88412)),x88415))+~P24(f329(f329(f331(f874(x88411)),x88413),x88414)) % 178.07/177.94 [8945]~P21(x89451,x89453,x89455,x89452)+~P24(f329(f62(x89453),x89454))+P24(f329(f329(f243(a875),f329(f38(x89451),x89452)),f329(f38(x89453),x89454)))+~P24(f329(f329(f243(f883(x89453,a869)),f329(f308(x89451,x89453,x89455),x89452)),x89454)) % 178.07/177.94 [9015]~P70(x90152)+~P21(x90151,x90151,x90154,x90155)+~P24(f329(f62(x90151),x90155))+E(f329(f329(f6(x90151,x90152),f329(f74(x90151,x90152,x90151,x90153),x90154)),x90155),f329(f329(f6(x90151,x90152),x90153),f329(f308(x90151,x90151,x90154),x90155))) % 178.07/177.94 [9016]~P74(x90162)+~P21(x90161,x90161,x90164,x90165)+~P24(f329(f62(x90161),x90165))+E(f329(f329(f9(x90161,x90162),f329(f74(x90161,x90162,x90161,x90163),x90164)),x90165),f329(f329(f9(x90161,x90162),x90163),f329(f308(x90161,x90161,x90164),x90165))) % 178.07/177.94 [9130]~P38(x91301,x91302)+~P24(f329(f329(f331(x91301),x91303),x91304))+~P24(f329(f329(f331(x91301),x91305),x91304))+~P24(f329(f329(f331(f882(x91301,x91301)),f329(f329(f264(x91301,x91301),x91305),f781(x91302,x91301,x91304))),x91302)) % 178.07/177.94 [9168]~P21(x91682,x91683,x91685,x91681)+E(x91681,f193(f883(x91682,a869)))+E(f329(f308(x91683,x91682,f355(x91684,x91683,x91682,x91681)),x91684),x91681)+~P24(f329(f329(f243(f883(x91683,a869)),f329(f308(x91682,x91683,x91685),x91681)),x91684)) % 178.07/177.94 [9644]~P27(x96445)+~P105(x96445)+P24(f329(f329(f331(x96441),f868(x96442,x96443,x96441,x96444,x96445)),x96443))+~P24(f329(f329(f244(x96445),x96444),f329(f329(f43(x96441,x96445),x96443),x96442))) % 178.07/177.94 [9649]~P27(x96491)+~P105(x96491)+P24(f329(f329(f244(x96491),x96492),f329(x96493,f868(x96493,x96494,x96495,x96492,x96491))))+~P24(f329(f329(f244(x96491),x96492),f329(f329(f43(x96495,x96491),x96494),x96493))) % 178.07/177.94 [9726]~P68(x97261)+~P24(f329(f67(x97261,x97261,f82(x97261),x97262,x97263),x97265))+P24(f329(f329(f331(x97261),x97262),x97263))+P24(f329(f67(x97261,x97261,f82(x97261),x97264,f329(f329(f307(x97261),x97262),x97263)),f329(f329(f82(x97261),x97264),x97265))) % 178.07/177.94 [9943]~P70(x99432)+~P24(f329(f62(x99431),x99435))+E(f329(f329(f6(x99431,x99432),f329(f329(f7(x99431,x99432,x99432),f329(f329(f18(x99431,x99432,f883(x99432,x99432)),f329(f329(f8(a869,f883(x99432,f883(x99432,x99432)),x99431),f102(x99432)),f329(a326,x99433))),x99434)),f2(x99432))),x99435),f2(x99432))+P24(f329(f329(f331(x99431),x99433),x99435)) % 178.07/177.94 [9944]~P74(x99442)+~P24(f329(f62(x99441),x99445))+E(f329(f329(f9(x99441,x99442),f329(f329(f7(x99441,x99442,x99442),f329(f329(f18(x99441,x99442,f883(x99442,x99442)),f329(f329(f8(a869,f883(x99442,f883(x99442,x99442)),x99441),f102(x99442)),f329(a326,x99443))),x99444)),f79(x99442))),x99445),f79(x99442))+P24(f329(f329(f331(x99441),x99443),x99445)) % 178.07/177.94 [9945]~P70(x99452)+~P24(f329(f62(x99451),x99455))+E(f329(f329(f6(x99451,x99452),f329(f329(f7(x99451,x99452,x99452),f329(f329(f18(x99451,x99452,f883(x99452,x99452)),f329(f329(f8(a869,f883(x99452,f883(x99452,x99452)),x99451),f102(x99452)),f329(a326,x99453))),x99454)),f2(x99452))),x99455),f329(x99454,x99453))+~P24(f329(f329(f331(x99451),x99453),x99455)) % 178.07/177.94 [9946]~P74(x99462)+~P24(f329(f62(x99461),x99465))+E(f329(f329(f9(x99461,x99462),f329(f329(f7(x99461,x99462,x99462),f329(f329(f18(x99461,x99462,f883(x99462,x99462)),f329(f329(f8(a869,f883(x99462,f883(x99462,x99462)),x99461),f102(x99462)),f329(a326,x99463))),x99464)),f79(x99462))),x99465),f329(x99464,x99463))+~P24(f329(f329(f331(x99461),x99463),x99465)) % 178.07/177.94 [10001]~P70(x100012)+~P24(f329(f62(x100011),x100015))+E(f329(f329(f6(x100011,x100012),f329(f329(f7(x100011,x100012,x100012),f329(f329(f18(x100011,x100012,f883(x100012,x100012)),f329(f329(f8(a869,f883(x100012,f883(x100012,x100012)),x100011),f102(x100012)),f329(f329(f7(x100011,x100011,a869),a326),x100013))),x100014)),f2(x100012))),x100015),f2(x100012))+P24(f329(f329(f331(x100011),x100013),x100015)) % 178.07/177.94 [10002]~P74(x100022)+~P24(f329(f62(x100021),x100025))+E(f329(f329(f9(x100021,x100022),f329(f329(f7(x100021,x100022,x100022),f329(f329(f18(x100021,x100022,f883(x100022,x100022)),f329(f329(f8(a869,f883(x100022,f883(x100022,x100022)),x100021),f102(x100022)),f329(f329(f7(x100021,x100021,a869),a326),x100023))),x100024)),f79(x100022))),x100025),f79(x100022))+P24(f329(f329(f331(x100021),x100023),x100025)) % 178.07/177.94 [10004]~P70(x100042)+~P24(f329(f62(x100041),x100045))+E(f329(f329(f6(x100041,x100042),f329(f329(f7(x100041,x100042,x100042),f329(f329(f18(x100041,x100042,f883(x100042,x100042)),f329(f329(f8(a869,f883(x100042,f883(x100042,x100042)),x100041),f102(x100042)),f329(f329(f7(x100041,x100041,a869),a326),x100043))),x100044)),f2(x100042))),x100045),f329(x100044,x100043))+~P24(f329(f329(f331(x100041),x100043),x100045)) % 178.07/177.94 [10005]~P74(x100052)+~P24(f329(f62(x100051),x100055))+E(f329(f329(f9(x100051,x100052),f329(f329(f7(x100051,x100052,x100052),f329(f329(f18(x100051,x100052,f883(x100052,x100052)),f329(f329(f8(a869,f883(x100052,f883(x100052,x100052)),x100051),f102(x100052)),f329(f329(f7(x100051,x100051,a869),a326),x100053))),x100054)),f79(x100052))),x100055),f329(x100054,x100053))+~P24(f329(f329(f331(x100051),x100053),x100055)) % 178.07/177.94 [7788]~P66(x77882)+~P24(f329(f62(x77881),x77884))+E(f329(f329(f6(x77881,x77882),x77883),f329(f329(f22(f883(x77881,a869)),x77884),f329(f329(f307(x77881),x77885),f193(f883(x77881,a869))))),f329(f329(f6(x77881,x77882),x77883),x77884))+P24(f329(f329(f331(x77881),x77885),x77884)) % 178.07/177.94 [8295]~P108(x82952)+~P24(f329(f62(x82951),x82954))+E(f329(f329(f6(x82951,x82952),x82953),f329(f329(f22(f883(x82951,a869)),x82954),f329(f329(f307(x82951),x82955),f193(f883(x82951,a869))))),f329(f329(f22(x82952),f329(f329(f6(x82951,x82952),x82953),x82954)),f329(x82953,x82955)))+~P24(f329(f329(f331(x82951),x82955),x82954)) % 178.07/177.94 [8296]~P66(x82962)+~P24(f329(f62(x82961),x82964))+E(f329(f329(f6(x82961,x82962),x82963),f329(f329(f22(f883(x82961,a869)),x82964),f329(f329(f307(x82961),x82965),f193(f883(x82961,a869))))),f329(f329(f22(x82962),f329(f329(f6(x82961,x82962),x82963),x82964)),f329(x82963,x82965)))+~P24(f329(f329(f331(x82961),x82965),x82964)) % 178.07/177.94 [8327]~P66(x83271)+~P24(f329(f62(x83272),x83274))+E(f329(f329(f22(x83271),f329(f329(f6(x83272,x83271),x83273),x83274)),f329(f329(f6(x83272,x83271),x83273),x83275)),f329(f329(f6(x83272,x83271),x83273),f329(f329(f22(f883(x83272,a869)),x83274),x83275)))+~P24(f329(f329(f243(f883(x83272,a869)),x83275),x83274)) % 178.07/177.94 [8347]P24(f329(f62(x83471),f329(x83472,x83473)))+~P24(f329(f62(x83474),x83475))+~P24(f329(f329(f331(x83474),x83473),x83475))+~P24(f329(f62(x83471),f329(f329(f43(x83474,f883(x83471,a869)),x83475),x83472))) % 178.07/177.94 [8787]~P6(x87871,x87875,x87874)+~E(f329(f283(x87871,x87871,x87874),f329(f329(f307(x87871),x87872),f193(f883(x87871,a869)))),f329(f283(x87871,x87871,x87874),f329(f329(f307(x87871),x87873),f193(f883(x87871,a869)))))+~P24(f329(f329(f331(x87871),x87873),x87875))+P24(f329(f329(f331(f882(x87871,x87871)),f329(f329(f264(x87871,x87871),x87872),x87873)),x87874)) % 178.07/177.94 [9087]~P24(f329(x90871,x90875))+P24(f329(x90871,f471(x90871,x90872,x90873,x90874)))+P24(f329(x90871,f464(x90871,x90872,x90873,x90874)))+~P24(f329(f329(f331(x90874),x90875),f329(f329(f116(f883(x90874,a869)),x90873),x90872))) % 178.07/177.94 [9272]~P24(f329(x92721,x92725))+P24(f329(x92721,f464(x92721,x92722,x92723,x92724)))+P24(f329(f329(f331(x92724),f471(x92721,x92722,x92723,x92724)),x92722))+~P24(f329(f329(f331(x92724),x92725),f329(f329(f116(f883(x92724,a869)),x92723),x92722))) % 178.07/177.94 [9273]~P24(f329(x92731,x92735))+P24(f329(x92731,f471(x92731,x92732,x92733,x92734)))+P24(f329(f329(f331(x92734),f464(x92731,x92732,x92733,x92734)),x92733))+~P24(f329(f329(f331(x92734),x92735),f329(f329(f116(f883(x92734,a869)),x92733),x92732))) % 178.07/177.94 [9279]P24(f329(x92791,x92792))+~P24(f329(x92791,f518(x92791,x92793,x92794,x92795)))+~P24(f329(x92791,f507(x92791,x92793,x92794,x92795)))+~P24(f329(f329(f331(x92795),x92792),f329(f329(f116(f883(x92795,a869)),x92794),x92793))) % 178.07/177.94 [9321]E(x93211,x93212)+~P24(f329(f329(f331(f882(x93213,x93213)),f329(f329(f264(x93213,x93213),x93211),x93212)),f305(x93213,x93215)))+P24(f329(f329(f331(x93213),x93211),x93214))+~P24(f329(f329(f243(f883(f882(x93213,x93213),a869)),x93215),f329(f329(f266(x93213,x93213),x93214),f329(f16(f883(x93213,a869),x93213),x93214)))) % 178.07/177.94 [9340]P24(f329(x93401,x93402))+~P24(f329(x93401,f507(x93401,x93404,x93405,x93403)))+P24(f329(f329(f331(x93403),f518(x93401,x93404,x93405,x93403)),x93404))+~P24(f329(f329(f331(x93403),x93402),f329(f329(f116(f883(x93403,a869)),x93405),x93404))) % 178.07/177.94 [9341]P24(f329(x93411,x93412))+~P24(f329(x93411,f518(x93411,x93414,x93415,x93413)))+P24(f329(f329(f331(x93413),f507(x93411,x93414,x93415,x93413)),x93415))+~P24(f329(f329(f331(x93413),x93412),f329(f329(f116(f883(x93413,a869)),x93415),x93414))) % 178.07/177.94 [9401]P24(f329(x94011,x94012))+P24(f329(f329(f331(x94013),f518(x94011,x94014,x94015,x94013)),x94014))+P24(f329(f329(f331(x94013),f507(x94011,x94014,x94015,x94013)),x94015))+~P24(f329(f329(f331(x94013),x94012),f329(f329(f116(f883(x94013,a869)),x94015),x94014))) % 178.07/177.94 [9403]~P24(f329(x94032,x94035))+P24(f329(f329(f331(x94031),f471(x94032,x94033,x94034,x94031)),x94033))+P24(f329(f329(f331(x94031),f464(x94032,x94033,x94034,x94031)),x94034))+~P24(f329(f329(f331(x94031),x94035),f329(f329(f116(f883(x94031,a869)),x94034),x94033))) % 178.07/177.94 [9551]~P6(x95511,x95515,x95514)+~P24(f329(f329(f331(x95511),x95513),x95515))+P24(f329(f329(f331(f882(x95511,x95511)),f329(f329(f264(x95511,x95511),x95512),x95513)),x95514))+~P24(f329(f329(f243(f883(x95511,a869)),f329(f283(x95511,x95511,x95514),f329(f329(f307(x95511),x95513),f193(f883(x95511,a869))))),f329(f283(x95511,x95511,x95514),f329(f329(f307(x95511),x95512),f193(f883(x95511,a869)))))) % 178.07/177.94 [9674]~P27(x96745)+~P105(x96745)+P24(f329(f329(f331(x96741),f345(x96742,x96743,x96744,x96741,x96745)),x96744))+~P24(f329(f329(f244(x96745),f329(f329(f42(x96741,x96745),x96744),x96743)),x96742)) % 178.07/177.94 [9706]~P84(x97065)+~P80(x97065)+P24(f329(f329(f331(x97061),f583(x97062,x97063,x97064,x97061,x97065)),f329(f171(x97061),x97064)))+P24(f329(f329(f243(x97065),f329(f165(x97065),f329(f329(f153(x97061,x97065),x97063),x97064))),f329(f165(x97065),f329(f329(f153(x97061,x97065),x97062),x97064)))) % 178.07/177.94 [9821]~P27(x98211)+~P105(x98211)+P24(f329(f329(f244(x98211),f329(x98212,f345(x98213,x98212,x98214,x98215,x98211))),x98213))+~P24(f329(f329(f244(x98211),f329(f329(f42(x98215,x98211),x98214),x98212)),x98213)) % 178.07/177.94 [9961]~P84(x99611)+~P80(x99611)+~P24(f329(f329(f243(x99611),f329(x99613,f583(x99615,x99613,x99614,x99612,x99611))),f329(x99615,f583(x99615,x99613,x99614,x99612,x99611))))+P24(f329(f329(f243(x99611),f329(f165(x99611),f329(f329(f153(x99612,x99611),x99613),x99614))),f329(f165(x99611),f329(f329(f153(x99612,x99611),x99615),x99614)))) % 178.07/177.94 [8638]~P70(x86381)+~P24(f329(f62(x86384),x86385))+~P24(f329(f329(f331(x86384),x86383),x86385))+E(f329(f329(f81(x86381),f329(x86382,x86383)),f329(f329(f6(x86384,x86381),x86382),f329(f329(f22(f883(x86384,a869)),x86385),f329(f329(f307(x86384),x86383),f193(f883(x86384,a869)))))),f329(f329(f6(x86384,x86381),x86382),x86385)) % 178.07/177.94 [8639]~P74(x86391)+~P24(f329(f62(x86394),x86395))+~P24(f329(f329(f331(x86394),x86393),x86395))+E(f329(f329(f82(x86391),f329(x86392,x86393)),f329(f329(f9(x86394,x86391),x86392),f329(f329(f22(f883(x86394,a869)),x86395),f329(f329(f307(x86394),x86393),f193(f883(x86394,a869)))))),f329(f329(f9(x86394,x86391),x86392),x86395)) % 178.07/177.94 [8694]~P14(x86941,x86944,x86945)+~P24(f329(f62(x86941),x86942))+E(f329(f329(f22(f883(x86941,a869)),x86942),f329(f329(f307(x86941),x86943),f193(f883(x86941,a869)))),f193(f883(x86941,a869)))+E(f329(f329(x86944,x86943),f329(x86945,f329(f329(f22(f883(x86941,a869)),x86942),f329(f329(f307(x86941),x86943),f193(f883(x86941,a869)))))),f329(x86945,f329(f329(f307(x86941),x86943),x86942))) % 178.07/177.94 [9068]~P74(x90681)+~P24(f329(f62(x90682),x90685))+~P24(f329(f62(x90682),x90684))+E(f329(f329(f82(x90681),f329(f329(f9(x90682,x90681),x90683),f329(f329(f116(f883(x90682,a869)),x90684),x90685))),f329(f329(f9(x90682,x90681),x90683),f329(f329(f107(f883(x90682,a869)),x90684),x90685))),f329(f329(f82(x90681),f329(f329(f9(x90682,x90681),x90683),x90684)),f329(f329(f9(x90682,x90681),x90683),x90685))) % 178.07/177.94 [9069]~P70(x90691)+~P24(f329(f62(x90692),x90695))+~P24(f329(f62(x90692),x90694))+E(f329(f329(f81(x90691),f329(f329(f6(x90692,x90691),x90693),f329(f329(f116(f883(x90692,a869)),x90694),x90695))),f329(f329(f6(x90692,x90691),x90693),f329(f329(f107(f883(x90692,a869)),x90694),x90695))),f329(f329(f81(x90691),f329(f329(f6(x90692,x90691),x90693),x90694)),f329(f329(f6(x90692,x90691),x90693),x90695))) % 178.07/177.94 [9210]~P66(x92101)+~P24(f329(f62(x92102),x92105))+~P24(f329(f62(x92102),x92104))+E(f329(f329(f22(x92101),f329(f329(f81(x92101),f329(f329(f6(x92102,x92101),x92103),x92104)),f329(f329(f6(x92102,x92101),x92103),x92105))),f329(f329(f6(x92102,x92101),x92103),f329(f329(f107(f883(x92102,a869)),x92104),x92105))),f329(f329(f6(x92102,x92101),x92103),f329(f329(f116(f883(x92102,a869)),x92104),x92105))) % 178.07/177.94 [9412]~P21(x94121,x94122,x94123,x94125)+~P21(x94121,x94122,x94123,x94124)+P21(x94121,x94122,x94123,f329(f329(f116(f883(x94121,a869)),x94124),x94125))+~E(f329(f329(f107(f883(x94122,a869)),f329(f308(x94121,x94122,x94123),f329(f329(f22(f883(x94121,a869)),x94124),x94125))),f329(f308(x94121,x94122,x94123),f329(f329(f22(f883(x94121,a869)),x94125),x94124))),f193(f883(x94122,a869))) % 178.07/177.94 [9526]E(x95261,f2(a1))+~P24(f329(f329(f244(a1),f2(a1)),x95263))+~P24(f329(f49(x95262,x95261),f329(f329(f264(a1,a1),x95264),x95265)))+P24(f329(f49(x95262,f329(f329(f82(a1),x95261),x95263)),f329(f329(f264(a1,a1),f329(f329(f39(a1),x95264),x95263)),f329(f329(f81(a1),f329(f329(f82(a1),x95261),f45(a1,x95264,x95263))),x95265)))) % 178.07/177.94 [9534]~P24(f329(f329(f244(a875),f2(a875)),x95343))+~P24(f329(f329(f244(a875),f2(a875)),x95342))+~P24(f329(f48(x95341,x95342),f329(f329(f264(a875,a875),x95344),x95345)))+P24(f329(f48(x95341,f329(f329(f82(a875),x95342),x95343)),f329(f329(f264(a875,a875),f329(f329(f39(a875),x95344),x95343)),f329(f329(f81(a875),f329(f329(f82(a875),x95342),f45(a875,x95344,x95343))),x95345)))) % 178.07/177.94 [9583]~P74(x95831)+~P24(f329(f62(x95832),x95835))+~P24(f329(f62(x95832),x95834))+E(f329(f329(f82(x95831),f329(f329(f329(f66(x95831,x95832,f82(x95831)),x95833),f79(x95831)),f329(f329(f116(f883(x95832,a869)),x95834),x95835))),f329(f329(f329(f66(x95831,x95832,f82(x95831)),x95833),f79(x95831)),f329(f329(f107(f883(x95832,a869)),x95834),x95835))),f329(f329(f82(x95831),f329(f329(f329(f66(x95831,x95832,f82(x95831)),x95833),f79(x95831)),x95834)),f329(f329(f329(f66(x95831,x95832,f82(x95831)),x95833),f79(x95831)),x95835))) % 178.07/177.94 [9585]~E(f329(f329(f174(x95851),x95855),x95852),f329(f329(f174(x95851),x95855),x95853))+P24(f329(f329(f331(f882(f876(x95851),f876(x95851))),f329(f329(f264(f876(x95851),f876(x95851)),x95852),x95853)),f146(x95851,x95854)))+~P24(f329(f329(f244(a875),x95855),f329(f329(f241(a875),f329(f194(f876(x95851)),x95852)),f329(f194(f876(x95851)),x95853))))+~P24(f329(f329(f331(f882(x95851,x95851)),f329(f329(f264(x95851,x95851),f329(f329(f164(x95851),x95852),x95855)),f329(f329(f164(x95851),x95853),x95855))),x95854)) % 178.07/177.94 [9694]~P84(x96945)+~P141(x96945)+P24(f329(f329(f331(x96941),f380(x96942,x96943,x96944,x96941,x96945)),x96944))+P24(f329(f329(f243(x96945),f329(f329(f6(x96941,x96945),x96943),x96944)),f329(f329(f82(x96945),f329(f106(x96945),f329(f38(x96941),x96944))),x96942))) % 178.07/177.94 [9889]~P84(x98891)+~P141(x98891)+~P24(f329(f329(f243(x98891),f329(x98893,f380(x98895,x98893,x98894,x98892,x98891))),x98895))+P24(f329(f329(f243(x98891),f329(f329(f6(x98892,x98891),x98893),x98894)),f329(f329(f82(x98891),f329(f106(x98891),f329(f38(x98892),x98894))),x98895))) % 178.07/177.94 [8666]E(f329(f329(f127(x86661),x86662),x86663),f329(f329(f127(x86661),x86664),x86665))+~E(f329(f329(f174(x86661),f329(f194(f876(x86661)),x86662)),x86664),x86662)+~E(f329(f329(f127(x86661),f329(f329(f137(x86661),f329(f194(f876(x86661)),x86662)),x86664)),x86665),x86663)+P24(f329(f329(f243(a875),f329(f194(f876(x86661)),x86664)),f329(f194(f876(x86661)),x86662))) % 178.07/177.94 [8786]E(f329(f329(f127(x87861),x87862),x87863),f329(f329(f127(x87861),x87864),x87865))+~E(f329(f329(f174(x87861),f329(f194(f876(x87861)),x87862)),x87864),x87862)+~E(x87863,f329(f329(f127(x87861),f329(f329(f137(x87861),f329(f194(f876(x87861)),x87862)),x87864)),x87865))+~P24(f329(f329(f243(a875),f329(f194(f876(x87861)),x87862)),f329(f194(f876(x87861)),x87864))) % 178.07/177.94 [10023]~P24(f329(x100235,x100234))+~P24(f329(f62(x100232),f329(f249(x100232),x100235)))+P24(f329(f62(x100231),f329(f249(x100231),f329(f329(f7(x100231,x100232,a869),x100233),x100234))))+~P24(f329(f62(x100231),f329(f249(x100231),f329(f329(f8(f883(x100232,a869),a869,x100231),f88(x100232)),f329(f329(f8(f883(x100232,a869),f883(x100232,a869),x100231),f329(f18(x100232,a869,a869),f329(f329(f8(a869,f883(a869,a869),x100232),a327),x100235))),x100233))))) % 178.07/177.94 [8461]~P15(x84615,x84611,x84616,x84612)+E(f329(f74(x84611,x84611,x84611,f329(x84612,x84613)),f329(x84612,x84614)),f329(f74(x84611,x84611,x84611,f329(x84612,x84614)),f329(x84612,x84613)))+~P24(f329(f62(x84615),x84614))+~P24(f329(f62(x84615),x84613)) % 178.07/177.94 [7843]~P21(x78431,x78432,x78434,x78433)+~E(f329(x78434,x78436),x78435)+E(f329(f78(x78431,x78432,x78433,x78434),x78435),x78436)+~P24(f329(f329(f331(x78431),x78436),x78433)) % 178.07/177.94 [8042]~P16(x80426,x80421,x80424,x80422)+E(f329(f74(x80421,x80421,x80421,f329(x80422,x80423)),f329(x80424,x80425)),f329(x80422,x80423))+~P24(f329(f62(x80426),x80423))+~P24(f329(f329(f331(x80426),x80425),x80423)) % 178.07/177.94 [9258]~P15(x92583,x92581,x92586,x92582)+E(f329(f74(x92581,x92581,x92581,f329(x92582,f329(f329(f22(f883(x92583,a869)),x92584),f329(f329(f307(x92583),x92585),f193(f883(x92583,a869)))))),f329(x92586,x92585)),f329(x92582,x92584))+~P24(f329(f62(x92583),x92584))+~P24(f329(f329(f331(x92583),x92585),x92584)) % 178.07/177.94 [6924]~P57(x69241)+~E(f45(x69241,x69243,x69244),f45(x69241,x69246,x69244))+~E(f45(x69241,x69242,x69244),f45(x69241,x69245,x69244))+E(f45(x69241,f329(f329(f22(x69241),x69242),x69243),x69244),f45(x69241,f329(f329(f22(x69241),x69245),x69246),x69244)) % 178.07/177.94 [6925]~P56(x69251)+~E(f45(x69251,x69253,x69254),f45(x69251,x69256,x69254))+~E(f45(x69251,x69252,x69254),f45(x69251,x69255,x69254))+E(f45(x69251,f329(f329(f82(x69251),x69252),x69253),x69254),f45(x69251,f329(f329(f82(x69251),x69255),x69256),x69254)) % 178.07/177.94 [6926]~P56(x69261)+~E(f45(x69261,x69263,x69264),f45(x69261,x69266,x69264))+~E(f45(x69261,x69262,x69264),f45(x69261,x69265,x69264))+E(f45(x69261,f329(f329(f81(x69261),x69262),x69263),x69264),f45(x69261,f329(f329(f81(x69261),x69265),x69266),x69264)) % 178.07/177.94 [7739]~P12(x77391,x77392,x77393)+~P24(f329(f62(x77391),x77396))+E(f329(f329(f65(x77391,x77392,x77393),x77394),f329(f329(f307(x77391),x77395),x77396)),f329(f329(f65(x77391,x77392,x77393),f329(f329(x77393,x77395),x77394)),x77396))+P24(f329(f329(f331(x77391),x77395),x77396)) % 178.07/177.94 [7801]~P27(x78011)+P24(f329(f329(f243(x78011),x78012),f329(x78013,x78014)))+~P24(f329(f329(f331(x78015),x78014),x78016))+~P24(f329(f329(f243(x78011),x78012),f329(f329(f42(x78015,x78011),x78016),x78013))) % 178.07/177.94 [7961]~P12(x79611,x79612,x79613)+~P24(f329(f62(x79611),x79616))+E(f329(f329(f65(x79611,x79612,x79613),x79614),f329(f329(f307(x79611),x79615),x79616)),f329(f329(x79613,x79615),f329(f329(f65(x79611,x79612,x79613),x79614),x79616)))+P24(f329(f329(f331(x79611),x79615),x79616)) % 178.07/177.94 [8058]~P105(x80583)+~P24(f329(x80582,x80585))+~P29(x80583,f329(f329(f153(x80581,x80583),x80584),x80586))+E(f329(f135(x80581,x80582),f329(f329(f147(x80581,x80583,x80584),x80585),x80586)),f329(f329(f147(x80581,x80583,x80584),x80585),f329(f135(x80581,x80582),x80586))) % 178.07/177.94 [8081]E(x80811,x80812)+E(x80813,f2(a1))+~P24(f329(f49(x80814,x80813),f329(f329(f264(a1,a1),x80815),x80812)))+~P24(f329(f49(x80814,x80813),f329(f329(f264(a1,a1),x80816),x80811))) % 178.07/177.94 [8082]E(x80821,x80822)+E(x80823,f2(a1))+~P24(f329(f49(x80824,x80823),f329(f329(f264(a1,a1),x80822),x80825)))+~P24(f329(f49(x80824,x80823),f329(f329(f264(a1,a1),x80821),x80826))) % 178.07/177.94 [8102]~P15(x81022,x81025,x81026,x81021)+~P24(f329(f62(x81022),x81024))+E(f329(x81021,f329(f329(f307(x81022),x81023),x81024)),f329(f74(x81025,x81025,x81025,f329(x81021,x81024)),f329(x81026,x81023)))+P24(f329(f329(f331(x81022),x81023),x81024)) % 178.07/177.94 [8330]~P16(x83305,x83301,x83306,x83302)+E(f329(f74(x83301,x83301,x83301,f329(x83302,x83303)),f329(x83302,x83304)),f329(x83302,x83303))+~P24(f329(f62(x83305),x83303))+~P24(f329(f329(f243(f883(x83305,a869)),x83304),x83303)) % 178.07/177.94 [9458]~P21(x94581,x94582,x94584,x94583)+~P24(f329(f329(f331(x94582),x94585),f329(f308(x94581,x94582,x94584),x94583)))+P24(f329(f329(f331(x94581),f329(f78(x94581,x94582,x94583,x94584),x94585)),x94586))+~P24(f329(f329(f243(f883(x94581,a869)),x94583),x94586)) % 178.07/177.94 [9834]~P70(x98342)+~E(f573(x98341,x98343,x98345,x98346,x98344,x98342),f574(x98341,x98343,x98345,x98346,x98344,x98342))+~P24(f329(f62(x98344),x98346))+E(f329(f329(f6(x98341,x98342),x98343),f329(f308(x98344,x98341,x98345),x98346)),f329(f329(f6(x98344,x98342),f329(f74(x98341,x98342,x98344,x98343),x98345)),x98346)) % 178.07/177.94 [9871]~P70(x98716)+E(f329(x98711,f573(x98712,x98713,x98711,x98714,x98715,x98716)),f329(x98711,f574(x98712,x98713,x98711,x98714,x98715,x98716)))+E(f329(f329(f6(x98712,x98716),x98713),f329(f308(x98715,x98712,x98711),x98714)),f329(f329(f6(x98715,x98716),f329(f74(x98712,x98716,x98715,x98713),x98711)),x98714))+~P24(f329(f62(x98715),x98714)) % 178.07/177.94 [9911]~P70(x99112)+~E(f329(x99113,f329(x99115,f574(x99111,x99113,x99115,x99116,x99114,x99112))),f2(x99112))+~P24(f329(f62(x99114),x99116))+E(f329(f329(f6(x99111,x99112),x99113),f329(f308(x99114,x99111,x99115),x99116)),f329(f329(f6(x99114,x99112),f329(f74(x99111,x99112,x99114,x99113),x99115)),x99116)) % 178.07/177.94 [9969]~P70(x99692)+~P24(f329(f62(x99694),x99696))+E(f329(f329(f6(x99691,x99692),x99693),f329(f308(x99694,x99691,x99695),x99696)),f329(f329(f6(x99694,x99692),f329(f74(x99691,x99692,x99694,x99693),x99695)),x99696))+P24(f329(f329(f331(x99694),f574(x99691,x99693,x99695,x99696,x99694,x99692)),x99696)) % 178.07/177.94 [9970]~P70(x99702)+~P24(f329(f62(x99704),x99706))+E(f329(f329(f6(x99701,x99702),x99703),f329(f308(x99704,x99701,x99705),x99706)),f329(f329(f6(x99704,x99702),f329(f74(x99701,x99702,x99704,x99703),x99705)),x99706))+P24(f329(f329(f331(x99704),f573(x99701,x99703,x99705,x99706,x99704,x99702)),x99706)) % 178.07/177.94 [10082]~P74(x100821)+~P24(f329(f62(x100822),x100826))+E(f329(f329(f329(f66(x100821,x100822,f82(x100821)),f329(f329(f18(x100822,f883(x100823,a869),x100821),f329(f329(f7(x100822,x100821,f883(f883(x100823,a869),x100821)),f329(f329(f8(f883(x100823,x100821),f883(x100821,f883(f883(x100823,a869),x100821)),x100822),f66(x100821,x100823,f82(x100821))),x100824)),f79(x100821))),x100825)),f79(x100821)),x100826),f329(f329(f329(f66(x100821,f882(x100822,x100823),f82(x100821)),f329(f268(x100822,x100823,x100821),x100824)),f79(x100821)),f329(f329(f266(x100822,x100823),x100826),x100825)))+P24(f329(f329(f331(x100822),f627(x100824,x100825,x100823,x100826,x100822,x100821)),x100826)) % 178.07/177.94 [10100]~P74(x101001)+~P24(f329(f62(x101002),x101006))+E(f329(f329(f329(f66(x101001,x101002,f82(x101001)),f329(f329(f18(x101002,f883(x101003,a869),x101001),f329(f329(f7(x101002,x101001,f883(f883(x101003,a869),x101001)),f329(f329(f8(f883(x101003,x101001),f883(x101001,f883(f883(x101003,a869),x101001)),x101002),f66(x101001,x101003,f82(x101001))),x101004)),f79(x101001))),x101005)),f79(x101001)),x101006),f329(f329(f329(f66(x101001,f882(x101002,x101003),f82(x101001)),f329(f268(x101002,x101003,x101001),x101004)),f79(x101001)),f329(f329(f266(x101002,x101003),x101006),x101005)))+~P24(f329(f62(x101003),f329(x101005,f627(x101004,x101005,x101003,x101006,x101002,x101001)))) % 178.07/177.94 [8242]~P16(x82422,x82425,x82426,x82421)+~P24(f329(f62(x82422),x82424))+~P24(f329(f62(x82422),x82423))+E(f329(x82421,f329(f329(f116(f883(x82422,a869)),x82423),x82424)),f329(f74(x82425,x82425,x82425,f329(x82421,x82423)),f329(x82421,x82424))) % 178.07/177.94 [8462]~P27(x84621)+P24(f329(f329(f243(x84621),f329(x84622,x84623)),x84624))+~P24(f329(f329(f331(x84625),x84623),x84626))+~P24(f329(f329(f243(x84621),f329(f329(f43(x84625,x84621),x84626),x84622)),x84624)) % 178.07/177.94 [8865]~P21(x88652,x88651,x88653,x88656)+E(f329(f329(f22(f883(x88651,a869)),f329(f308(x88652,x88651,x88653),x88654)),f329(f308(x88652,x88651,x88653),x88655)),f329(f308(x88652,x88651,x88653),f329(f329(f22(f883(x88652,a869)),x88654),x88655)))+~P24(f329(f329(f243(f883(x88652,a869)),x88655),x88656))+~P24(f329(f329(f243(f883(x88652,a869)),x88654),x88656)) % 178.07/177.94 [8866]~P21(x88662,x88661,x88663,x88666)+E(f329(f329(f107(f883(x88661,a869)),f329(f308(x88662,x88661,x88663),x88664)),f329(f308(x88662,x88661,x88663),x88665)),f329(f308(x88662,x88661,x88663),f329(f329(f107(f883(x88662,a869)),x88664),x88665)))+~P24(f329(f329(f243(f883(x88662,a869)),x88665),x88666))+~P24(f329(f329(f243(f883(x88662,a869)),x88664),x88666)) % 178.07/177.94 [8903]~P24(f329(x89031,x89033))+~P24(f329(f329(f329(f329(a201,x89032),x89033),x89034),x89036))+~P24(f329(f329(f329(f329(a201,f33(x89031,x89032)),x89036),x89034),x89035))+P24(f329(f329(f329(f329(a201,f33(x89031,x89032)),x89033),x89034),x89035)) % 178.07/177.94 [9132]E(x91321,x91322)+~P50(x91323,x91324,x91325)+~P24(f329(f329(f331(f882(x91323,x91324)),f329(f329(f264(x91323,x91324),x91326),x91322)),x91325))+~P24(f329(f329(f331(f882(x91323,x91324)),f329(f329(f264(x91323,x91324),x91326),x91321)),x91325)) % 178.07/177.94 [9906]~P68(x99061)+~E(f329(x99063,f532(x99064,x99066,x99063,x99065,x99062,x99061)),f329(x99066,f532(x99064,x99066,x99063,x99065,x99062,x99061)))+~P24(f329(f62(x99062),x99065))+E(f329(f329(f329(f66(x99061,x99062,f82(x99061)),x99063),x99064),x99065),f329(f329(f329(f66(x99061,x99062,f82(x99061)),x99066),x99064),x99065)) % 178.07/177.94 [9967]~P68(x99671)+~P24(f329(f62(x99672),x99675))+E(f329(f329(f329(f66(x99671,x99672,f82(x99671)),x99673),x99674),x99675),f329(f329(f329(f66(x99671,x99672,f82(x99671)),x99676),x99674),x99675))+P24(f329(f329(f331(x99672),f532(x99674,x99673,x99676,x99675,x99672,x99671)),x99675)) % 178.07/177.94 [8679]~P68(x86791)+~P24(f329(f62(x86792),x86796))+P24(f329(f329(f331(x86792),x86795),x86796))+E(f329(f329(f329(f66(x86791,x86792,f82(x86791)),x86793),x86794),f329(f329(f307(x86792),x86795),x86796)),f329(f329(f82(x86791),f329(x86793,x86795)),f329(f329(f329(f66(x86791,x86792,f82(x86791)),x86793),x86794),x86796))) % 178.07/177.94 [8725]~P6(x87251,x87256,x87253)+~P9(x87251,f883(x87252,a869),x87253,x87255)+~P24(f329(f329(f331(x87251),x87254),x87256))+E(f329(f329(f43(x87251,f883(x87252,a869)),f329(f283(x87251,x87251,x87253),f329(f329(f307(x87251),x87254),f193(f883(x87251,a869))))),x87255),f329(x87255,x87254)) % 178.07/177.94 [8842]~P12(x88423,x88424,x88421)+~P24(f329(f62(x88423),x88426))+~P24(f329(f329(f331(x88423),x88422),x88426))+E(f329(f329(x88421,x88422),f329(f329(f65(x88423,x88424,x88421),x88425),f329(f329(f22(f883(x88423,a869)),x88426),f329(f329(f307(x88423),x88422),f193(f883(x88423,a869)))))),f329(f329(f65(x88423,x88424,x88421),x88425),x88426)) % 178.07/177.94 [9145]~P15(x91453,x91451,x91456,x91452)+~P24(f329(f62(x91453),x91455))+~P24(f329(f62(x91453),x91454))+E(f329(f74(x91451,x91451,x91451,f329(x91452,f329(f329(f116(f883(x91453,a869)),x91454),x91455))),f329(x91452,f329(f329(f107(f883(x91453,a869)),x91454),x91455))),f329(f74(x91451,x91451,x91451,f329(x91452,x91454)),f329(x91452,x91455))) % 178.07/177.94 [9478]~E(x94783,f329(f329(f158(x94781,x94782),x94785),x94786))+P24(f329(f329(f331(f882(f876(x94781),f876(x94781))),f329(f329(f264(f876(x94781),f876(x94781)),x94782),x94783)),f156(x94781,x94784)))+~P24(f329(f329(f244(a875),x94785),f329(f194(f876(x94781)),x94782)))+~P24(f329(f329(f331(f882(x94781,x94781)),f329(f329(f264(x94781,x94781),f329(f329(f164(x94781),x94782),x94785)),x94786)),x94784)) % 178.07/177.94 [9980]~P70(x99802)+~P24(f329(f62(x99801),x99806))+P24(f329(f329(f331(x99801),f626(x99804,x99805,x99803,x99806,x99801,x99802)),x99806))+E(f329(f329(f6(x99801,x99802),f329(f329(f18(x99801,f883(x99803,a869),x99802),f329(f329(f8(f883(x99803,x99802),f883(f883(x99803,a869),x99802),x99801),f6(x99803,x99802)),x99804)),x99805)),x99806),f329(f329(f6(f882(x99801,x99803),x99802),f329(f268(x99801,x99803,x99802),x99804)),f329(f329(f266(x99801,x99803),x99806),x99805))) % 178.07/177.94 [9981]~P74(x99812)+~P24(f329(f62(x99811),x99816))+P24(f329(f329(f331(x99811),f624(x99814,x99815,x99813,x99816,x99811,x99812)),x99816))+E(f329(f329(f9(x99811,x99812),f329(f329(f18(x99811,f883(x99813,a869),x99812),f329(f329(f8(f883(x99813,x99812),f883(f883(x99813,a869),x99812),x99811),f9(x99813,x99812)),x99814)),x99815)),x99816),f329(f329(f9(f882(x99811,x99813),x99812),f329(f268(x99811,x99813,x99812),x99814)),f329(f329(f266(x99811,x99813),x99816),x99815))) % 178.07/177.94 [10020]~P70(x100202)+~P24(f329(f62(x100201),x100206))+~P24(f329(f62(x100203),f329(x100205,f626(x100204,x100205,x100203,x100206,x100201,x100202))))+E(f329(f329(f6(x100201,x100202),f329(f329(f18(x100201,f883(x100203,a869),x100202),f329(f329(f8(f883(x100203,x100202),f883(f883(x100203,a869),x100202),x100201),f6(x100203,x100202)),x100204)),x100205)),x100206),f329(f329(f6(f882(x100201,x100203),x100202),f329(f268(x100201,x100203,x100202),x100204)),f329(f329(f266(x100201,x100203),x100206),x100205))) % 178.07/177.94 [10021]~P74(x100212)+~P24(f329(f62(x100211),x100216))+~P24(f329(f62(x100213),f329(x100215,f624(x100214,x100215,x100213,x100216,x100211,x100212))))+E(f329(f329(f9(x100211,x100212),f329(f329(f18(x100211,f883(x100213,a869),x100212),f329(f329(f8(f883(x100213,x100212),f883(f883(x100213,a869),x100212),x100211),f9(x100213,x100212)),x100214)),x100215)),x100216),f329(f329(f9(f882(x100211,x100213),x100212),f329(f268(x100211,x100213,x100212),x100214)),f329(f329(f266(x100211,x100213),x100216),x100215))) % 178.07/177.94 [10003]~P74(x100032)+~P24(f329(f62(x100031),x100036))+P24(f329(f329(f331(x100031),x100033),x100036))+E(f329(f329(f9(x100031,x100032),f329(f329(f7(x100031,x100032,x100032),f329(f329(f18(x100031,x100032,f883(x100032,x100032)),f329(f329(f8(a869,f883(x100032,f883(x100032,x100032)),x100031),f102(x100032)),f329(f329(f7(x100031,x100031,a869),a326),x100033))),x100034)),x100035)),x100036),f329(f329(f254(x100032),x100035),f329(f38(x100031),x100036))) % 178.07/177.94 [10008]~P74(x100082)+~P24(f329(f62(x100081),x100086))+~P24(f329(f329(f331(x100081),x100083),x100086))+E(f329(f329(f9(x100081,x100082),f329(f329(f7(x100081,x100082,x100082),f329(f329(f18(x100081,x100082,f883(x100082,x100082)),f329(f329(f8(a869,f883(x100082,f883(x100082,x100082)),x100081),f102(x100082)),f329(f329(f7(x100081,x100081,a869),a326),x100083))),x100084)),x100085)),x100086),f329(f329(f82(x100082),f329(x100084,x100083)),f329(f329(f254(x100082),x100085),f329(f329(f22(a875),f329(f38(x100081),x100086)),f79(a875))))) % 178.07/177.94 [10075]~P24(f329(f62(x100751),x100755))+~P24(f329(f62(x100752),x100753))+P24(f329(f329(f331(x100752),f497(x100756,x100754,x100753,x100752,x100755,x100751)),x100753))+E(f329(f329(f6(x100751,a875),f329(f329(f8(f883(x100752,a869),a875,x100751),f38(x100752)),f329(f329(f8(f883(x100752,a869),f883(x100752,a869),x100751),f249(x100752)),f329(f329(f8(f883(x100752,a869),f883(x100752,a869),x100751),f329(f18(x100752,a869,a869),f329(f329(f8(a869,f883(a869,a869),x100752),a327),f329(f329(f7(x100752,f883(x100752,a869),a869),f331(x100752)),x100753)))),x100754)))),x100755),f329(f329(f82(a875),x100756),f329(f38(x100752),x100753))) % 178.07/177.94 [10076]~P24(f329(f62(x100761),x100765))+~P24(f329(f62(x100762),x100763))+P24(f329(f329(f331(x100762),f499(x100766,x100764,x100763,x100762,x100765,x100761)),x100763))+E(f329(f329(f6(x100761,a875),f329(f329(f8(f883(x100762,a869),a875,x100761),f38(x100762)),f329(f329(f8(f883(x100762,a869),f883(x100762,a869),x100761),f249(x100762)),f329(f329(f8(f883(x100762,a869),f883(x100762,a869),x100761),f329(f18(x100762,a869,a869),f329(f329(f8(a869,f883(a869,a869),x100762),a327),f329(f329(f7(x100762,f883(x100762,a869),a869),f331(x100762)),x100763)))),x100764)))),x100765),f329(f329(f6(x100762,a875),x100766),x100763)) % 178.07/177.94 [10106]~P24(f329(f62(x101062),x101063))+~P24(f329(f62(x101061),x101065))+~E(f329(f38(x101061),f329(f249(x101061),f329(f329(f18(x101061,a869,a869),f329(f329(f8(a869,f883(a869,a869),x101061),a327),f329(f329(f7(x101061,f883(x101061,a869),a869),f331(x101061)),x101065))),f329(f329(f7(x101061,x101062,a869),x101064),f497(x101066,x101064,x101063,x101062,x101065,x101061))))),x101066)+E(f329(f329(f6(x101061,a875),f329(f329(f8(f883(x101062,a869),a875,x101061),f38(x101062)),f329(f329(f8(f883(x101062,a869),f883(x101062,a869),x101061),f249(x101062)),f329(f329(f8(f883(x101062,a869),f883(x101062,a869),x101061),f329(f18(x101062,a869,a869),f329(f329(f8(a869,f883(a869,a869),x101062),a327),f329(f329(f7(x101062,f883(x101062,a869),a869),f331(x101062)),x101063)))),x101064)))),x101065),f329(f329(f82(a875),x101066),f329(f38(x101062),x101063))) % 178.07/177.94 [10108]~P24(f329(f62(x101082),x101083))+~P24(f329(f62(x101081),x101085))+~E(f329(f38(x101081),f329(f249(x101081),f329(f329(f18(x101081,a869,a869),f329(f329(f8(a869,f883(a869,a869),x101081),a327),f329(f329(f7(x101081,f883(x101081,a869),a869),f331(x101081)),x101085))),f329(f329(f7(x101081,x101082,a869),x101084),f499(x101086,x101084,x101083,x101082,x101085,x101081))))),f329(x101086,f499(x101086,x101084,x101083,x101082,x101085,x101081)))+E(f329(f329(f6(x101081,a875),f329(f329(f8(f883(x101082,a869),a875,x101081),f38(x101082)),f329(f329(f8(f883(x101082,a869),f883(x101082,a869),x101081),f249(x101082)),f329(f329(f8(f883(x101082,a869),f883(x101082,a869),x101081),f329(f18(x101082,a869,a869),f329(f329(f8(a869,f883(a869,a869),x101082),a327),f329(f329(f7(x101082,f883(x101082,a869),a869),f331(x101082)),x101083)))),x101084)))),x101085),f329(f329(f6(x101082,a875),x101086),x101083)) % 178.07/177.94 [9761]E(x97611,x97612)+~P12(x97613,x97614,x97615)+~P24(f329(f67(x97613,x97614,x97615,x97616,x97617),x97612))+~P24(f329(f67(x97613,x97614,x97615,x97616,x97617),x97611)) % 178.07/177.94 [9554]P24(f329(x95541,x95542))+~P24(f329(f329(f331(x95547),x95542),f329(x95546,x95544)))+~P24(f329(x95541,f845(x95541,x95546,x95545,x95543,x95547)))+~P24(f329(f329(f331(x95543),x95544),x95545)) % 178.07/177.94 [9995]~P12(x99957,x99956,x99951)+E(f329(f329(x99951,x99952),f837(x99952,x99953,x99954,x99955,x99951,x99956,x99957)),x99953)+~P24(f329(f67(x99957,x99956,x99951,x99955,x99954),x99953))+~P24(f329(f329(f331(x99957),x99952),x99954)) % 178.07/177.94 [10060]~P12(x100601,x100602,x100603)+~P24(f329(f67(x100601,x100602,x100603,x100604,x100605),x100607))+P24(f329(f67(x100601,x100602,x100603,x100604,f329(f329(f22(f883(x100601,a869)),x100605),f329(f329(f307(x100601),x100606),f193(f883(x100601,a869))))),f837(x100606,x100607,x100605,x100604,x100603,x100602,x100601)))+~P24(f329(f329(f331(x100601),x100606),x100605)) % 178.07/177.94 [9454]~P68(x94541)+~P21(x94545,x94542,x94546,x94547)+~P24(f329(f62(x94545),x94547))+E(f329(f329(f329(f66(x94541,x94542,f82(x94541)),x94543),x94544),f329(f308(x94545,x94542,x94546),x94547)),f329(f329(f329(f66(x94541,x94545,f82(x94541)),f329(f74(x94542,x94541,x94545,x94543),x94546)),x94544),x94547)) % 178.07/177.94 [9578]~E(f329(f329(f307(x95781),x95785),x95786),f329(f329(f307(x95781),x95782),x95783))+~P24(f329(f67(x95781,x95781,x95784,x95782,x95783),x95787))+P24(f329(f329(f331(x95781),x95782),x95783))+P24(f329(f63(x95781,x95784,f329(f329(f307(x95781),x95785),x95786)),x95787)) % 178.07/177.94 [9661]P24(f329(x96611,x96612))+~P24(f329(f329(f331(x96613),x96612),f329(x96614,x96617)))+~P24(f329(f329(f331(x96616),x96617),x96615))+P24(f329(f329(f331(x96613),f845(x96611,x96614,x96615,x96616,x96613)),f329(f329(f43(x96616,f883(x96613,a869)),x96615),x96614))) % 178.07/177.94 [9675]~P21(x96752,x96751,x96755,x96754)+~P21(x96751,x96753,x96756,f329(f308(x96752,x96751,x96755),x96754))+E(f329(f329(f74(x96751,x96752,x96753,f78(x96752,x96751,x96754,x96755)),f78(x96751,x96753,f329(f308(x96752,x96751,x96755),x96754),x96756)),x96757),f329(f78(x96752,x96753,x96754,f329(f74(x96751,x96753,x96752,x96756),x96755)),x96757))+~P24(f329(f329(f331(x96753),x96757),f329(f308(x96751,x96753,x96756),f329(f308(x96752,x96751,x96755),x96754)))) % 178.07/177.94 [9996]~P12(x99967,x99966,x99961)+E(f329(f329(x99961,x99962),f857(x99963,x99964,x99962,x99965,x99961,x99966,x99967)),x99963)+P24(f329(f329(f331(x99967),x99962),x99964))+~P24(f329(f67(x99967,x99966,x99961,x99965,f329(f329(f307(x99967),x99962),x99964)),x99963)) % 178.07/177.94 [10059]~P12(x100591,x100594,x100595)+P24(f329(f67(x100591,x100594,x100595,x100596,x100593),f857(x100597,x100593,x100592,x100596,x100595,x100594,x100591)))+P24(f329(f329(f331(x100591),x100592),x100593))+~P24(f329(f67(x100591,x100594,x100595,x100596,f329(f329(f307(x100591),x100592),x100593)),x100597)) % 178.07/177.94 [9743]E(x97431,f2(a1))+~P24(f329(f49(x97433,x97431),f329(f329(f264(a1,a1),x97435),x97437)))+~P24(f329(f49(x97432,x97431),f329(f329(f264(a1,a1),x97434),x97436)))+P24(f329(f49(f329(f329(f81(a1),x97432),x97433),x97431),f329(f329(f264(a1,a1),f329(f329(f81(a1),f329(f329(f81(a1),x97434),x97435)),f329(f329(f39(a1),f329(f329(f81(a1),x97436),x97437)),x97431))),f45(a1,f329(f329(f81(a1),x97436),x97437),x97431)))) % 178.07/177.94 [9745]~P24(f329(f329(f244(a875),f2(a875)),x97453))+~P24(f329(f48(x97452,x97453),f329(f329(f264(a875,a875),x97455),x97457)))+~P24(f329(f48(x97451,x97453),f329(f329(f264(a875,a875),x97454),x97456)))+P24(f329(f48(f329(f329(f81(a875),x97451),x97452),x97453),f329(f329(f264(a875,a875),f329(f329(f81(a875),f329(f329(f81(a875),x97454),x97455)),f329(f329(f39(a875),f329(f329(f81(a875),x97456),x97457)),x97453))),f45(a875,f329(f329(f81(a875),x97456),x97457),x97453)))) % 178.07/177.94 [10105]~P70(x101052)+~P24(f329(f62(x101053),x101055))+~P24(f329(f62(x101051),x101057))+E(f329(f329(f6(x101051,x101052),f329(f329(f18(x101051,f883(x101053,a869),x101052),f329(f329(f8(f883(x101053,x101052),f883(f883(x101053,a869),x101052),x101051),f6(x101053,x101052)),x101054)),f329(f329(f8(f883(x101053,a869),f883(x101053,a869),x101051),f249(x101053)),f329(f329(f8(f883(x101053,a869),f883(x101053,a869),x101051),f329(f18(x101053,a869,a869),f329(f329(f8(a869,f883(a869,a869),x101053),a327),f329(f329(f7(x101053,f883(x101053,a869),a869),f331(x101053)),x101055)))),x101056)))),x101057),f329(f329(f6(x101053,x101052),f329(f329(f18(x101053,f883(x101051,a869),x101052),f329(f329(f8(f883(x101051,x101052),f883(f883(x101051,a869),x101052),x101053),f6(x101051,x101052)),f329(f7(x101051,x101053,x101052),x101054))),f329(f329(f8(f883(x101051,a869),f883(x101051,a869),x101053),f249(x101051)),f329(f329(f8(f883(x101051,a869),f883(x101051,a869),x101053),f329(f18(x101051,a869,a869),f329(f329(f8(a869,f883(a869,a869),x101051),a327),f329(f329(f7(x101051,f883(x101051,a869),a869),f331(x101051)),x101057)))),f329(f7(x101051,x101053,a869),x101056))))),x101055)) % 178.07/177.94 [9614]~P18(x96147,x96146,x96141,x96148,x96142,x96144)+E(f329(f329(x96141,f329(x96142,x96143)),f329(x96144,x96145)),f329(x96144,x96145))+~P24(f329(f62(x96146),x96145))+~P24(f329(f329(f331(x96146),x96143),x96145)) % 178.07/177.94 [9618]~P10(x96186,x96181,x96182,x96188,x96183,x96184)+~P6(x96186,x96187,x96188)+P9(x96181,x96182,x96183,f329(x96184,x96185))+~P24(f329(f329(f331(x96186),x96185),x96187)) % 178.07/177.94 [8059]~P30(x80598,x80597,f329(f329(f329(f93(x80598),x80594),x80596),x80591))+P24(f329(f329(x80591,x80592),x80593))+~P24(f329(f329(x80594,x80592),x80595))+~P24(f329(f329(f329(f329(a201,x80596),x80595),x80597),x80593)) % 178.07/177.94 [9240]~P15(x92407,x92401,x92408,x92403)+~P24(f329(f62(x92407),x92405))+~P24(f329(f62(x92407),x92404))+E(f329(f74(x92401,x92401,x92402,f329(x92403,x92404)),f329(f74(x92401,x92401,x92402,f329(x92403,x92405)),x92406)),f329(f74(x92401,x92401,x92402,f329(x92403,x92405)),f329(f74(x92401,x92401,x92402,f329(x92403,x92404)),x92406))) % 178.07/177.94 [9248]~P35(x92481,x92482,x92483,x92484,x92487)+P35(x92481,x92482,x92483,f329(f329(f158(x92481,x92484),x92485),x92486),f329(f329(f158(x92482,x92487),x92485),x92488))+~P24(f329(f329(x92483,x92486),x92488))+~P24(f329(f329(f244(a875),x92485),f329(f194(f876(x92481)),x92484))) % 178.07/177.94 [9249]~P35(x92491,x92492,x92493,x92494,x92497)+P35(x92491,x92492,x92493,f329(f329(f158(x92491,x92494),x92495),x92496),f329(f329(f158(x92492,x92497),x92495),x92498))+~P24(f329(f329(x92493,x92496),x92498))+~P24(f329(f329(f244(a875),x92495),f329(f194(f876(x92492)),x92497))) % 178.07/177.94 [9328]~P21(x93282,x93282,x93285,x93286)+~P17(x93283,x93282,x93287,x93288,x93281)+~P24(f329(f62(x93282),x93286))+E(f329(f329(x93281,f329(f74(x93282,x93283,x93282,x93284),x93285)),x93286),f329(f329(x93281,x93284),f329(f308(x93282,x93282,x93285),x93286))) % 178.07/177.94 [9616]~P19(x96167,x96162,x96165,x96168,x96166,x96161)+~P24(f329(f62(x96162),x96164))+E(f329(x96161,f329(f329(f307(x96162),x96163),x96164)),f329(f329(x96165,f329(x96166,x96163)),f329(x96161,x96164)))+P24(f329(f329(f331(x96162),x96163),x96164)) % 178.07/177.94 [9627]~P18(x96276,x96275,x96271,x96277,x96278,x96272)+E(f329(f329(x96271,f329(x96272,x96273)),f329(x96272,x96274)),f329(x96272,x96274))+~P24(f329(f62(x96275),x96274))+~P24(f329(f329(f243(f883(x96275,a869)),x96273),x96274)) % 178.07/177.94 [9225]P24(f329(f329(f331(f882(f876(x92251),f876(x92251))),f329(f329(f264(f876(x92251),f876(x92251)),x92252),x92253)),f156(x92251,x92254)))+~E(x92253,f329(f329(f127(x92251),x92255),f329(f329(f150(x92251),x92256),x92257)))+~E(x92252,f329(f329(f127(x92251),x92255),f329(f329(f150(x92251),x92258),x92257)))+~P24(f329(f329(f331(f882(x92251,x92251)),f329(f329(f264(x92251,x92251),x92258),x92256)),x92254)) % 178.07/177.94 [9621]~P18(x96216,x96212,x96215,x96217,x96218,x96211)+~P24(f329(f62(x96212),x96214))+~P24(f329(f62(x96212),x96213))+E(f329(x96211,f329(f329(f116(f883(x96212,a869)),x96213),x96214)),f329(f329(x96215,f329(x96211,x96213)),f329(x96211,x96214))) % 178.07/177.94 [10143]~P21(x101434,x101432,x101435,x101438)+E(f329(f329(f42(x101431,f883(x101432,a869)),x101433),f329(f329(f8(f883(x101434,a869),f883(x101432,a869),x101431),f308(x101434,x101432,x101435)),x101436)),f329(f308(x101434,x101432,x101435),f329(f329(f42(x101431,f883(x101434,a869)),x101433),x101436)))+~P24(f329(f329(f331(x101431),x101437),x101433))+P24(f329(f329(f331(x101431),f397(x101437,x101436,x101433,x101431,x101438,x101435,x101432,x101434)),x101433)) % 178.07/177.94 [10167]~P21(x101674,x101672,x101675,x101677)+E(f329(f329(f42(x101671,f883(x101672,a869)),x101673),f329(f329(f8(f883(x101674,a869),f883(x101672,a869),x101671),f308(x101674,x101672,x101675)),x101676)),f329(f308(x101674,x101672,x101675),f329(f329(f42(x101671,f883(x101674,a869)),x101673),x101676)))+~P24(f329(f329(f331(x101671),x101678),x101673))+~P24(f329(f329(f243(f883(x101674,a869)),f329(x101676,f397(x101678,x101676,x101673,x101671,x101677,x101675,x101672,x101674))),x101677)) % 178.07/177.94 [9684]~P19(x96847,x96845,x96841,x96848,x96842,x96844)+~P24(f329(f62(x96845),x96846))+~P24(f329(f329(f331(x96845),x96843),x96846))+E(f329(f329(x96841,f329(x96842,x96843)),f329(x96844,f329(f329(f22(f883(x96845,a869)),x96846),f329(f329(f307(x96845),x96843),f193(f883(x96845,a869)))))),f329(x96844,x96846)) % 178.07/177.94 [9692]~P19(x96926,x96923,x96921,x96927,x96928,x96922)+~P24(f329(f62(x96923),x96925))+~P24(f329(f62(x96923),x96924))+E(f329(f329(x96921,f329(x96922,f329(f329(f116(f883(x96923,a869)),x96924),x96925))),f329(x96922,f329(f329(f107(f883(x96923,a869)),x96924),x96925))),f329(f329(x96921,f329(x96922,x96924)),f329(x96922,x96925))) % 178.07/177.94 [9784]P43(x97841,x97842,x97843,x97844,x97845,f329(f329(x97843,x97846),x97847))+~P43(x97841,x97842,x97843,x97844,f329(f329(f22(f883(x97841,a869)),x97845),f329(f329(f307(x97841),x97848),f193(f883(x97841,a869)))),x97849)+~E(f329(f329(x97843,x97846),x97847),f329(f329(x97843,x97848),x97849))+~P24(f329(f329(f331(x97841),x97848),x97845)) % 178.07/177.94 [10182]P20(x101821,x101822,f329(f329(f307(f874(x101821)),f329(f329(f329(f93(x101821),f329(x101823,f362(x101824,x101825,x101826,x101827,x101823,x101822,x101821,x101828,x101829))),f329(x101827,f362(x101824,x101825,x101826,x101827,x101823,x101822,x101821,x101828,x101829))),f329(x101826,f362(x101824,x101825,x101826,x101827,x101823,x101822,x101821,x101828,x101829)))),f193(f883(f874(x101821),a869))))+~P24(f329(f62(x101829),x101828))+~P20(x101821,x101822,f329(f308(x101829,f874(x101821),f329(f329(f18(x101829,f883(x101821,f883(a871,a869)),f874(x101821)),f329(f329(f18(x101829,a870,f883(f883(x101821,f883(a871,a869)),f874(x101821))),f329(f329(f8(f883(x101821,f883(a871,a869)),f883(a870,f883(f883(x101821,f883(a871,a869)),f874(x101821))),x101829),f93(x101821)),x101823)),x101827)),x101826)),x101828))+P20(x101821,x101822,f329(f308(x101829,f874(x101821),f329(f329(f18(x101829,f883(x101821,f883(a871,a869)),f874(x101821)),f329(f329(f18(x101829,a870,f883(f883(x101821,f883(a871,a869)),f874(x101821))),f329(f329(f8(f883(x101821,f883(a871,a869)),f883(a870,f883(f883(x101821,f883(a871,a869)),f874(x101821))),x101829),f93(x101821)),x101825)),x101827)),x101824)),x101828)) % 178.07/177.94 [10183]~P20(x101831,x101832,f329(f329(f307(f874(x101831)),f329(f329(f329(f93(x101831),f329(x101834,f362(x101836,x101834,x101838,x101835,x101839,x101832,x101831,x101837,x101833))),f329(x101835,f362(x101836,x101834,x101838,x101835,x101839,x101832,x101831,x101837,x101833))),f329(x101836,f362(x101836,x101834,x101838,x101835,x101839,x101832,x101831,x101837,x101833)))),f193(f883(f874(x101831),a869))))+~P24(f329(f62(x101833),x101837))+~P20(x101831,x101832,f329(f308(x101833,f874(x101831),f329(f329(f18(x101833,f883(x101831,f883(a871,a869)),f874(x101831)),f329(f329(f18(x101833,a870,f883(f883(x101831,f883(a871,a869)),f874(x101831))),f329(f329(f8(f883(x101831,f883(a871,a869)),f883(a870,f883(f883(x101831,f883(a871,a869)),f874(x101831))),x101833),f93(x101831)),x101839)),x101835)),x101838)),x101837))+P20(x101831,x101832,f329(f308(x101833,f874(x101831),f329(f329(f18(x101833,f883(x101831,f883(a871,a869)),f874(x101831)),f329(f329(f18(x101833,a870,f883(f883(x101831,f883(a871,a869)),f874(x101831))),f329(f329(f8(f883(x101831,f883(a871,a869)),f883(a870,f883(f883(x101831,f883(a871,a869)),f874(x101831))),x101833),f93(x101831)),x101834)),x101835)),x101836)),x101837)) % 178.07/177.94 [9718]~P10(x97186,x97187,x97188,x97189,x971810,x97181)+E(f329(f329(x97181,x97182),x97183),f329(f329(x97181,x97184),x97185))+~P24(f329(f329(f331(f882(x97187,x97187)),f329(f329(f264(x97187,x97187),x97183),x97185)),x971810))+~P24(f329(f329(f331(f882(x97186,x97186)),f329(f329(f264(x97186,x97186),x97182),x97184)),x97189)) % 178.07/177.94 [9330]~P63(x93302)+E(x93301,f193(f883(x93302,a869)))+~P24(f329(f62(x93302),x93301))+P24(f329(f329(f331(x93302),f13(x93302,x93301)),x93301))+~P24(f329(f329(f331(x93302),f329(f329(f116(x93302),f763(x93301,x93302)),f775(x93301,x93302))),f329(f329(f307(x93302),f763(x93301,x93302)),f329(f329(f307(x93302),f775(x93301,x93302)),f193(f883(x93302,a869)))))) % 178.07/177.94 [9331]~P63(x93312)+E(x93311,f193(f883(x93312,a869)))+~P24(f329(f62(x93312),x93311))+P24(f329(f329(f331(x93312),f10(x93312,x93311)),x93311))+~P24(f329(f329(f331(x93312),f329(f329(f107(x93312),f820(x93311,x93312)),f821(x93311,x93312))),f329(f329(f307(x93312),f820(x93311,x93312)),f329(f329(f307(x93312),f821(x93311,x93312)),f193(f883(x93312,a869)))))) % 178.07/177.94 [9362]~P68(x93622)+E(x93621,f193(f883(x93622,a869)))+~P24(f329(f62(x93622),x93621))+P24(f329(f329(f331(x93622),f329(f64(x93622,f82(x93622)),x93621)),x93621))+~P24(f329(f329(f331(x93622),f329(f329(f82(x93622),f842(x93621,x93622)),f844(x93621,x93622))),f329(f329(f307(x93622),f842(x93621,x93622)),f329(f329(f307(x93622),f844(x93621,x93622)),f193(f883(x93622,a869)))))) % 178.07/177.94 [9368]~P105(x93682)+E(x93681,f193(f883(x93682,a869)))+~P24(f329(f62(x93682),x93681))+P24(f329(f329(f331(x93682),f11(x93682,f242(x93682),x93681)),x93681))+~P24(f329(f329(f331(x93682),f329(f329(f242(x93682),f509(x93681,x93682)),f510(x93681,x93682))),f329(f329(f307(x93682),f509(x93681,x93682)),f329(f329(f307(x93682),f510(x93681,x93682)),f193(f883(x93682,a869)))))) % 178.07/177.94 [9369]~P105(x93692)+E(x93691,f193(f883(x93692,a869)))+~P24(f329(f62(x93692),x93691))+P24(f329(f329(f331(x93692),f12(x93692,f241(x93692),x93691)),x93691))+~P24(f329(f329(f331(x93692),f329(f329(f241(x93692),f511(x93691,x93692)),f512(x93691,x93692))),f329(f329(f307(x93692),f511(x93691,x93692)),f329(f329(f307(x93692),f512(x93691,x93692)),f193(f883(x93692,a869)))))) % 178.07/177.94 [6493]~P86(x64932)+E(x64931,f2(x64932))+~E(f329(f329(f81(x64932),x64933),x64931),f2(x64932))+~P24(f329(f329(f243(x64932),f2(x64932)),x64933))+~P24(f329(f329(f243(x64932),f2(x64932)),x64931)) % 178.07/177.94 [6494]~P86(x64942)+E(x64941,f2(x64942))+~E(f329(f329(f81(x64942),x64941),x64943),f2(x64942))+~P24(f329(f329(f243(x64942),f2(x64942)),x64943))+~P24(f329(f329(f243(x64942),f2(x64942)),x64941)) % 178.07/177.94 [7026]~P105(x70262)+~P29(x70262,x70261)+E(x70261,f119(x70262))+~P24(f329(f329(f331(x70262),x70263),f329(f171(x70262),f666(x70261,x70262))))+P24(f329(f329(f243(x70262),f678(x70261,x70262)),x70263)) % 178.07/177.94 [7192]~P105(x71921)+E(f14(x71921,x71922),x71923)+~P24(f329(f62(x71921),x71922))+~P24(f329(f329(f243(x71921),x71923),f530(x71923,x71922,x71921)))+~P24(f329(f329(f331(x71921),x71923),x71922)) % 178.07/177.94 [7223]~P105(x72231)+~P29(x72231,x72232)+~P29(x72231,x72233)+P29(x72231,f329(f329(f127(x72231),x72232),x72233))+P24(f329(f329(f331(x72231),f650(x72233,x72232,x72231)),f329(f171(x72231),x72232))) % 178.07/177.94 [7224]~P105(x72241)+~P29(x72241,x72242)+~P29(x72241,x72243)+P29(x72241,f329(f329(f127(x72241),x72242),x72243))+P24(f329(f329(f331(x72241),f651(x72243,x72242,x72241)),f329(f171(x72241),x72243))) % 178.07/177.94 [7280]~P105(x72801)+E(f14(x72801,x72802),x72803)+~P24(f329(f62(x72801),x72802))+P24(f329(f329(f331(x72801),f530(x72803,x72802,x72801)),x72802))+~P24(f329(f329(f331(x72801),x72803),x72802)) % 178.07/177.94 [7281]~P105(x72811)+E(f15(x72811,x72812),x72813)+~P24(f329(f62(x72811),x72812))+P24(f329(f329(f331(x72811),f531(x72813,x72812,x72811)),x72812))+~P24(f329(f329(f331(x72811),x72813),x72812)) % 178.07/177.94 [7861]~P105(x78611)+E(f15(x78611,x78612),x78613)+~P24(f329(f62(x78611),x78612))+~P24(f329(f329(f331(x78611),x78613),x78612))+~P24(f329(f329(f243(x78611),f531(x78613,x78612,x78611)),x78613)) % 178.07/177.94 [8190]~P105(x81901)+~P29(x81901,x81902)+~P29(x81901,x81903)+P29(x81901,f329(f329(f127(x81901),x81902),x81903))+~P24(f329(f329(f243(x81901),f650(x81903,x81902,x81901)),f651(x81903,x81902,x81901))) % 178.07/177.94 [8969]~P63(x89692)+E(x89691,f193(f883(x89692,a869)))+~E(f329(f329(f116(x89692),f329(x89693,f792(x89691,x89693,x89692))),f329(x89693,f801(x89691,x89693,x89692))),f329(x89693,f329(f329(f116(x89692),f792(x89691,x89693,x89692)),f801(x89691,x89693,x89692))))+E(f13(x89692,f329(f308(x89692,x89692,x89693),x89691)),f329(x89693,f13(x89692,x89691)))+~P24(f329(f62(x89692),x89691)) % 178.07/177.94 [8970]~P63(x89702)+E(x89701,f193(f883(x89702,a869)))+~E(f329(f329(f107(x89702),f329(x89703,f818(x89701,x89703,x89702))),f329(x89703,f822(x89701,x89703,x89702))),f329(x89703,f329(f329(f107(x89702),f818(x89701,x89703,x89702)),f822(x89701,x89703,x89702))))+E(f10(x89702,f329(f308(x89702,x89702,x89703),x89701)),f329(x89703,f10(x89702,x89701)))+~P24(f329(f62(x89702),x89701)) % 178.07/177.94 [8971]~P105(x89712)+E(x89711,f193(f883(x89712,a869)))+~E(f329(f329(f241(x89712),f329(x89713,f504(x89711,x89713,x89712))),f329(x89713,f522(x89711,x89713,x89712))),f329(x89713,f329(f329(f241(x89712),f504(x89711,x89713,x89712)),f522(x89711,x89713,x89712))))+E(f14(x89712,f329(f308(x89712,x89712,x89713),x89711)),f329(x89713,f14(x89712,x89711)))+~P24(f329(f62(x89712),x89711)) % 178.07/177.94 [8972]~P105(x89722)+E(x89721,f193(f883(x89722,a869)))+~E(f329(f329(f242(x89722),f329(x89723,f505(x89721,x89723,x89722))),f329(x89723,f521(x89721,x89723,x89722))),f329(x89723,f329(f329(f242(x89722),f505(x89721,x89723,x89722)),f521(x89721,x89723,x89722))))+E(f15(x89722,f329(f308(x89722,x89722,x89723),x89721)),f329(x89723,f15(x89722,x89721)))+~P24(f329(f62(x89722),x89721)) % 178.07/177.94 [9043]~P105(x90432)+E(x90431,f193(f883(x90432,a869)))+~E(f329(f329(f242(x90432),f329(x90433,f514(x90431,x90433,x90432))),f329(x90433,f517(x90431,x90433,x90432))),f329(x90433,f329(f329(f242(x90432),f514(x90431,x90433,x90432)),f517(x90431,x90433,x90432))))+E(f11(x90432,f242(x90432),f329(f308(x90432,x90432,x90433),x90431)),f329(x90433,f11(x90432,f242(x90432),x90431)))+~P24(f329(f62(x90432),x90431)) % 178.07/177.94 [9044]~P105(x90442)+E(x90441,f193(f883(x90442,a869)))+~E(f329(f329(f241(x90442),f329(x90443,f519(x90441,x90443,x90442))),f329(x90443,f520(x90441,x90443,x90442))),f329(x90443,f329(f329(f241(x90442),f519(x90441,x90443,x90442)),f520(x90441,x90443,x90442))))+E(f12(x90442,f241(x90442),f329(f308(x90442,x90442,x90443),x90441)),f329(x90443,f12(x90442,f241(x90442),x90441)))+~P24(f329(f62(x90442),x90441)) % 178.07/177.94 [6509]~P68(x65092)+E(x65091,f193(f883(x65092,a869)))+~P24(f329(f62(x65092),x65091))+E(f329(f64(x65092,f82(x65092)),f329(f329(f307(x65092),x65093),x65091)),f329(f329(f82(x65092),x65093),f329(f64(x65092,f82(x65092)),x65091)))+P24(f329(f329(f331(x65092),x65093),x65091)) % 178.07/177.94 [7032]~P63(x70322)+E(f329(f329(f116(x70322),f13(x70322,x70321)),f13(x70322,x70323)),f13(x70322,x70323))+E(x70321,f193(f883(x70322,a869)))+~P24(f329(f62(x70322),x70323))+~P24(f329(f329(f243(f883(x70322,a869)),x70321),x70323)) % 178.07/177.94 [7033]~P63(x70332)+E(f329(f329(f107(x70332),f10(x70332,x70331)),f10(x70332,x70333)),f10(x70332,x70333))+E(x70331,f193(f883(x70332,a869)))+~P24(f329(f62(x70332),x70333))+~P24(f329(f329(f243(f883(x70332,a869)),x70331),x70333)) % 178.07/177.94 [7034]~P105(x70342)+E(f329(f329(f241(x70342),f14(x70342,x70341)),f14(x70342,x70343)),f14(x70342,x70343))+E(x70341,f193(f883(x70342,a869)))+~P24(f329(f62(x70342),x70343))+~P24(f329(f329(f243(f883(x70342,a869)),x70341),x70343)) % 178.07/177.94 [7035]~P105(x70352)+E(f329(f329(f242(x70352),f15(x70352,x70351)),f15(x70352,x70353)),f15(x70352,x70353))+E(x70351,f193(f883(x70352,a869)))+~P24(f329(f62(x70352),x70353))+~P24(f329(f329(f243(f883(x70352,a869)),x70351),x70353)) % 178.07/177.94 [7332]~P105(x73322)+E(x73321,f193(f883(x73322,a869)))+~P24(f329(f62(x73322),x73323))+P24(f329(f329(f243(x73322),f14(x73322,x73323)),f14(x73322,x73321)))+~P24(f329(f329(f243(f883(x73322,a869)),x73321),x73323)) % 178.07/177.94 [7333]~P105(x73332)+E(x73331,f193(f883(x73332,a869)))+~P24(f329(f62(x73332),x73333))+P24(f329(f329(f243(x73332),f15(x73332,x73331)),f15(x73332,x73333)))+~P24(f329(f329(f243(f883(x73332,a869)),x73331),x73333)) % 178.07/177.94 [7392]~P63(x73921)+E(f13(x73921,x73922),x73923)+~P24(f329(f62(x73921),x73922))+~E(f329(f329(f22(f883(x73921,a869)),x73922),f329(f329(f307(x73921),x73923),f193(f883(x73921,a869)))),f193(f883(x73921,a869)))+~P24(f329(f329(f331(x73921),x73923),x73922)) % 178.07/177.94 [7393]~P63(x73931)+E(f10(x73931,x73932),x73933)+~P24(f329(f62(x73931),x73932))+~E(f329(f329(f22(f883(x73931,a869)),x73932),f329(f329(f307(x73931),x73933),f193(f883(x73931,a869)))),f193(f883(x73931,a869)))+~P24(f329(f329(f331(x73931),x73933),x73932)) % 178.07/177.94 [7394]~P105(x73941)+E(f14(x73941,x73942),x73943)+~P24(f329(f62(x73941),x73942))+~E(f329(f329(f22(f883(x73941,a869)),x73942),f329(f329(f307(x73941),x73943),f193(f883(x73941,a869)))),f193(f883(x73941,a869)))+~P24(f329(f329(f331(x73941),x73943),x73942)) % 178.07/177.94 [7395]~P105(x73951)+E(f15(x73951,x73952),x73953)+~P24(f329(f62(x73951),x73952))+~E(f329(f329(f22(f883(x73951,a869)),x73952),f329(f329(f307(x73951),x73953),f193(f883(x73951,a869)))),f193(f883(x73951,a869)))+~P24(f329(f329(f331(x73951),x73953),x73952)) % 178.07/177.94 [7494]~P105(x74941)+E(f11(x74941,f242(x74941),x74942),x74943)+~P24(f329(f62(x74941),x74942))+~E(f329(f329(f22(f883(x74941,a869)),x74942),f329(f329(f307(x74941),x74943),f193(f883(x74941,a869)))),f193(f883(x74941,a869)))+~P24(f329(f329(f331(x74941),x74943),x74942)) % 178.07/177.94 [7495]~P105(x74951)+E(f12(x74951,f241(x74951),x74952),x74953)+~P24(f329(f62(x74951),x74952))+~E(f329(f329(f22(f883(x74951,a869)),x74952),f329(f329(f307(x74951),x74953),f193(f883(x74951,a869)))),f193(f883(x74951,a869)))+~P24(f329(f329(f331(x74951),x74953),x74952)) % 178.07/177.94 [7531]~P105(x75312)+E(x75311,f193(f883(x75312,a869)))+~P24(f329(f62(x75312),x75311))+~P24(f329(f329(f244(x75312),x75313),f484(x75313,x75311,x75312)))+P24(f329(f329(f244(x75312),x75313),f329(f64(x75312,f241(x75312)),x75311))) % 178.07/177.94 [7532]~P100(x75322)+E(x75321,f193(f883(x75322,a869)))+~P24(f329(f62(x75322),x75321))+~P24(f329(f329(f243(x75322),x75323),f346(x75323,x75321,x75322)))+P24(f329(f329(f243(x75322),x75323),f329(f64(x75322,f107(x75322)),x75321))) % 178.07/177.94 [7533]~P105(x75332)+E(x75331,f193(f883(x75332,a869)))+~P24(f329(f62(x75332),x75331))+~P24(f329(f329(f243(x75332),x75333),f485(x75333,x75331,x75332)))+P24(f329(f329(f243(x75332),x75333),f329(f64(x75332,f241(x75332)),x75331))) % 178.07/177.94 [7618]~P100(x76182)+E(x76181,f193(f883(x76182,a869)))+~P24(f329(f62(x76182),x76181))+P24(f329(f329(f331(x76182),f346(x76183,x76181,x76182)),x76181))+P24(f329(f329(f243(x76182),x76183),f329(f64(x76182,f107(x76182)),x76181))) % 178.07/177.94 [7619]~P105(x76192)+E(x76191,f193(f883(x76192,a869)))+~P24(f329(f62(x76192),x76191))+P24(f329(f329(f331(x76192),f485(x76193,x76191,x76192)),x76191))+P24(f329(f329(f243(x76192),x76193),f329(f64(x76192,f241(x76192)),x76191))) % 178.07/177.94 [7620]~P105(x76202)+E(x76201,f193(f883(x76202,a869)))+~P24(f329(f62(x76202),x76201))+P24(f329(f329(f331(x76202),f484(x76203,x76201,x76202)),x76201))+P24(f329(f329(f244(x76202),x76203),f329(f64(x76202,f241(x76202)),x76201))) % 178.07/177.94 [7741]~P105(x77412)+E(x77411,f193(f883(x77412,a869)))+E(f329(f329(f241(x77412),f12(x77412,f241(x77412),x77411)),f12(x77412,f241(x77412),x77413)),f12(x77412,f241(x77412),x77413))+~P24(f329(f62(x77412),x77413))+~P24(f329(f329(f243(f883(x77412,a869)),x77411),x77413)) % 178.07/177.94 [7742]~P105(x77422)+E(x77421,f193(f883(x77422,a869)))+E(f329(f329(f242(x77422),f11(x77422,f242(x77422),x77421)),f11(x77422,f242(x77422),x77423)),f11(x77422,f242(x77422),x77423))+~P24(f329(f62(x77422),x77423))+~P24(f329(f329(f243(f883(x77422,a869)),x77421),x77423)) % 178.07/177.94 [7940]~E(f461(x79401,x79403,x79402),f462(x79401,x79403,x79402))+~E(f329(f38(x79402),f463(x79401,x79403,x79402)),x79401)+E(f329(f329(f82(a875),x79401),f329(f38(f883(x79402,a869)),x79403)),f329(f38(x79402),f40(f883(x79402,a869),x79403)))+~P24(f329(f62(x79402),f40(f883(x79402,a869),x79403)))+~P24(f329(f62(f883(x79402,a869)),x79403)) % 178.07/177.94 [8123]~P105(x81232)+E(x81231,f193(f883(x81232,a869)))+~P24(f329(f62(x81232),x81233))+P24(f329(f329(f243(x81232),f329(f64(x81232,f241(x81232)),x81233)),f329(f64(x81232,f241(x81232)),x81231)))+~P24(f329(f329(f243(f883(x81232,a869)),x81231),x81233)) % 178.07/177.94 [8431]~E(f461(x84311,x84313,x84312),f462(x84311,x84313,x84312))+E(f329(f329(f82(a875),x84311),f329(f38(f883(x84312,a869)),x84313)),f329(f38(x84312),f40(f883(x84312,a869),x84313)))+P24(f329(f329(f331(f883(x84312,a869)),f463(x84311,x84313,x84312)),x84313))+~P24(f329(f62(x84312),f40(f883(x84312,a869),x84313)))+~P24(f329(f62(f883(x84312,a869)),x84313)) % 178.07/177.94 [8458]~E(f329(f38(x84582),f463(x84581,x84583,x84582)),x84581)+E(f329(f329(f82(a875),x84581),f329(f38(f883(x84582,a869)),x84583)),f329(f38(x84582),f40(f883(x84582,a869),x84583)))+P24(f329(f329(f331(f883(x84582,a869)),f462(x84581,x84583,x84582)),x84583))+~P24(f329(f62(x84582),f40(f883(x84582,a869),x84583)))+~P24(f329(f62(f883(x84582,a869)),x84583)) % 178.07/177.94 [8459]~E(f329(f38(x84592),f463(x84591,x84593,x84592)),x84591)+E(f329(f329(f82(a875),x84591),f329(f38(f883(x84592,a869)),x84593)),f329(f38(x84592),f40(f883(x84592,a869),x84593)))+P24(f329(f329(f331(f883(x84592,a869)),f461(x84591,x84593,x84592)),x84593))+~P24(f329(f62(x84592),f40(f883(x84592,a869),x84593)))+~P24(f329(f62(f883(x84592,a869)),x84593)) % 178.07/177.94 [8487]~E(f329(f38(x84872),f463(x84871,x84873,x84872)),x84871)+~E(f329(f329(f107(f883(x84872,a869)),f462(x84871,x84873,x84872)),f461(x84871,x84873,x84872)),f193(f883(x84872,a869)))+E(f329(f329(f82(a875),x84871),f329(f38(f883(x84872,a869)),x84873)),f329(f38(x84872),f40(f883(x84872,a869),x84873)))+~P24(f329(f62(f883(x84872,a869)),x84873))+~P24(f329(f62(x84872),f40(f883(x84872,a869),x84873))) % 178.07/177.94 [8730]E(f329(f329(f82(a875),x87301),f329(f38(f883(x87302,a869)),x87303)),f329(f38(x87302),f40(f883(x87302,a869),x87303)))+P24(f329(f329(f331(f883(x87302,a869)),f463(x87301,x87303,x87302)),x87303))+P24(f329(f329(f331(f883(x87302,a869)),f462(x87301,x87303,x87302)),x87303))+~P24(f329(f62(f883(x87302,a869)),x87303))+~P24(f329(f62(x87302),f40(f883(x87302,a869),x87303))) % 178.07/177.94 [8731]E(f329(f329(f82(a875),x87311),f329(f38(f883(x87312,a869)),x87313)),f329(f38(x87312),f40(f883(x87312,a869),x87313)))+P24(f329(f329(f331(f883(x87312,a869)),f463(x87311,x87313,x87312)),x87313))+P24(f329(f329(f331(f883(x87312,a869)),f461(x87311,x87313,x87312)),x87313))+~P24(f329(f62(f883(x87312,a869)),x87313))+~P24(f329(f62(x87312),f40(f883(x87312,a869),x87313))) % 178.07/177.94 [8756]~E(f329(f329(f107(f883(x87562,a869)),f462(x87561,x87563,x87562)),f461(x87561,x87563,x87562)),f193(f883(x87562,a869)))+E(f329(f329(f82(a875),x87561),f329(f38(f883(x87562,a869)),x87563)),f329(f38(x87562),f40(f883(x87562,a869),x87563)))+~P24(f329(f62(f883(x87562,a869)),x87563))+P24(f329(f329(f331(f883(x87562,a869)),f463(x87561,x87563,x87562)),x87563))+~P24(f329(f62(x87562),f40(f883(x87562,a869),x87563))) % 178.07/177.94 [9017]~P95(x90172)+E(x90171,f193(f883(x90172,a869)))+~E(f329(f329(f82(x90172),f329(x90173,f854(x90171,x90173,x90172))),f329(x90173,f855(x90171,x90173,x90172))),f329(x90173,f329(f329(f82(x90172),f854(x90171,x90173,x90172)),f855(x90171,x90173,x90172))))+~P24(f329(f62(x90172),x90171))+E(f329(f64(x90172,f82(x90172)),f329(f308(x90172,x90172,x90173),x90171)),f329(x90173,f329(f64(x90172,f82(x90172)),x90171))) % 178.07/177.94 [9941]P24(f329(f329(x99411,x99412),x99413))+P24(f329(f329(f244(a1),f552(x99411,x99413,x99412)),f553(x99411,x99413,x99412)))+P24(f329(f329(f243(a1),f553(x99411,x99413,x99412)),f2(a1)))+P24(f329(f329(x99411,f552(x99411,x99413,x99412)),f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f553(x99411,x99413,x99412))))+~P24(f329(f317(f882(a1,a1),a57),f329(f329(f264(a1,a1),x99412),x99413))) % 178.07/177.94 [9947]P24(f329(f329(x99471,x99472),x99473))+P24(f329(f329(f243(a1),f551(x99471,x99473,x99472)),f2(a1)))+P24(f329(f329(x99471,f550(x99471,x99473,x99472)),f329(f329(f82(a1),f329(f109(a1),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f551(x99471,x99473,x99472))))+P24(f329(f329(f243(a1),f2(a1)),f329(f329(f81(a1),f550(x99471,x99473,x99472)),f551(x99471,x99473,x99472))))+~P24(f329(f317(f882(a1,a1),a52),f329(f329(f264(a1,a1),x99472),x99473))) % 178.07/177.94 [7911]~P117(x79111)+~P24(f329(f329(f243(x79111),x79112),f79(x79111)))+~P24(f329(f329(f243(x79111),f2(x79111)),x79112))+~P24(f329(f329(f243(x79111),f2(x79111)),x79113))+P24(f329(f329(f243(x79111),f329(f329(f82(x79111),x79112),x79113)),x79113)) % 178.07/177.94 [7912]~P117(x79121)+~P24(f329(f329(f243(x79121),x79123),f79(x79121)))+~P24(f329(f329(f243(x79121),f2(x79121)),x79123))+~P24(f329(f329(f243(x79121),f2(x79121)),x79122))+P24(f329(f329(f243(x79121),f329(f329(f82(x79121),x79122),x79123)),x79122)) % 178.07/177.94 [8274]~P105(x82742)+E(x82741,f193(f883(x82742,a869)))+~P24(f329(f62(x82742),x82741))+P24(f329(f329(f331(x82742),f501(x82743,x82741,x82742)),x82741))+~P24(f329(f329(f243(x82742),f329(f64(x82742,f241(x82742)),x82741)),x82743)) % 178.07/177.94 [8275]~P105(x82752)+E(x82751,f193(f883(x82752,a869)))+~P24(f329(f62(x82752),x82751))+P24(f329(f329(f331(x82752),f502(x82753,x82751,x82752)),x82751))+~P24(f329(f329(f244(x82752),f329(f64(x82752,f241(x82752)),x82751)),x82753)) % 178.07/177.94 [8276]~P105(x82762)+E(x82761,f193(f883(x82762,a869)))+~P24(f329(f62(x82762),x82761))+P24(f329(f329(f244(x82762),f502(x82763,x82761,x82762)),x82763))+~P24(f329(f329(f244(x82762),f329(f64(x82762,f241(x82762)),x82761)),x82763)) % 178.07/177.94 [8277]~P105(x82772)+E(x82771,f193(f883(x82772,a869)))+~P24(f329(f62(x82772),x82771))+P24(f329(f329(f243(x82772),f501(x82773,x82771,x82772)),x82773))+~P24(f329(f329(f243(x82772),f329(f64(x82772,f241(x82772)),x82771)),x82773)) % 178.07/177.94 [8361]~P24(f329(x83611,x83613))+P24(f329(x83611,f443(x83611,x83612)))+P24(f329(x83611,f433(x83611,x83612)))+~P24(f329(f329(f244(a1),f2(a1)),x83612))+P24(f329(x83611,f329(f329(f22(a1),f433(x83611,x83612)),f329(f329(f82(a1),f444(x83611,x83612)),x83612)))) % 178.07/177.94 [8582]~P24(f329(x85821,x85823))+P24(f329(x85821,f433(x85821,x85822)))+~P24(f329(f329(f244(a1),f2(a1)),x85822))+P24(f329(f329(f331(a1),f443(x85821,x85822)),f300(a1,f79(a1),x85822)))+P24(f329(x85821,f329(f329(f22(a1),f433(x85821,x85822)),f329(f329(f82(a1),f444(x85821,x85822)),x85822)))) % 178.07/177.94 [8778]~P24(f329(x87781,x87783))+~P24(f329(x87781,f433(x87781,x87782)))+P24(f329(x87781,f443(x87781,x87782)))+~P24(f329(f329(f244(a1),f2(a1)),x87782))+~P24(f329(x87781,f329(f329(f22(a1),f433(x87781,x87782)),f329(f329(f82(a1),f444(x87781,x87782)),x87782)))) % 178.07/177.94 [8901]~P24(f329(x89011,x89013))+~P24(f329(x89011,f433(x89011,x89012)))+~P24(f329(f329(f244(a1),f2(a1)),x89012))+P24(f329(f329(f331(a1),f443(x89011,x89012)),f300(a1,f79(a1),x89012)))+~P24(f329(x89011,f329(f329(f22(a1),f433(x89011,x89012)),f329(f329(f82(a1),f444(x89011,x89012)),x89012)))) % 178.07/177.94 [8690]~P63(x86901)+~P24(f329(f62(x86901),x86902))+E(f329(f329(f22(f883(x86901,a869)),x86902),f329(f329(f307(x86901),x86903),f193(f883(x86901,a869)))),f193(f883(x86901,a869)))+~P24(f329(f329(f331(x86901),x86903),x86902))+E(f329(f329(f116(x86901),x86903),f13(x86901,f329(f329(f22(f883(x86901,a869)),x86902),f329(f329(f307(x86901),x86903),f193(f883(x86901,a869)))))),f13(x86901,x86902)) % 178.07/177.94 [8691]~P63(x86911)+~P24(f329(f62(x86911),x86912))+E(f329(f329(f22(f883(x86911,a869)),x86912),f329(f329(f307(x86911),x86913),f193(f883(x86911,a869)))),f193(f883(x86911,a869)))+~P24(f329(f329(f331(x86911),x86913),x86912))+E(f329(f329(f107(x86911),x86913),f10(x86911,f329(f329(f22(f883(x86911,a869)),x86912),f329(f329(f307(x86911),x86913),f193(f883(x86911,a869)))))),f10(x86911,x86912)) % 178.07/177.94 [8692]~P105(x86921)+~P24(f329(f62(x86921),x86922))+E(f329(f329(f22(f883(x86921,a869)),x86922),f329(f329(f307(x86921),x86923),f193(f883(x86921,a869)))),f193(f883(x86921,a869)))+~P24(f329(f329(f331(x86921),x86923),x86922))+E(f329(f329(f241(x86921),x86923),f14(x86921,f329(f329(f22(f883(x86921,a869)),x86922),f329(f329(f307(x86921),x86923),f193(f883(x86921,a869)))))),f14(x86921,x86922)) % 178.07/177.94 [8693]~P105(x86931)+~P24(f329(f62(x86931),x86932))+E(f329(f329(f22(f883(x86931,a869)),x86932),f329(f329(f307(x86931),x86933),f193(f883(x86931,a869)))),f193(f883(x86931,a869)))+~P24(f329(f329(f331(x86931),x86933),x86932))+E(f329(f329(f242(x86931),x86933),f15(x86931,f329(f329(f22(f883(x86931,a869)),x86932),f329(f329(f307(x86931),x86933),f193(f883(x86931,a869)))))),f15(x86931,x86932)) % 178.07/177.94 [8750]~P105(x87501)+~P24(f329(f62(x87501),x87502))+E(f329(f329(f22(f883(x87501,a869)),x87502),f329(f329(f307(x87501),x87503),f193(f883(x87501,a869)))),f193(f883(x87501,a869)))+~P24(f329(f329(f331(x87501),x87503),x87502))+E(f329(f329(f242(x87501),x87503),f11(x87501,f242(x87501),f329(f329(f22(f883(x87501,a869)),x87502),f329(f329(f307(x87501),x87503),f193(f883(x87501,a869)))))),f11(x87501,f242(x87501),x87502)) % 178.07/177.94 [8751]~P105(x87511)+~P24(f329(f62(x87511),x87512))+E(f329(f329(f22(f883(x87511,a869)),x87512),f329(f329(f307(x87511),x87513),f193(f883(x87511,a869)))),f193(f883(x87511,a869)))+~P24(f329(f329(f331(x87511),x87513),x87512))+E(f329(f329(f241(x87511),x87513),f12(x87511,f241(x87511),f329(f329(f22(f883(x87511,a869)),x87512),f329(f329(f307(x87511),x87513),f193(f883(x87511,a869)))))),f12(x87511,f241(x87511),x87512)) % 178.07/177.94 [8765]~P63(x87651)+~P24(f329(f62(x87651),x87653))+~P24(f329(f62(x87651),x87652))+E(f329(f329(f107(f883(x87651,a869)),x87652),x87653),f193(f883(x87651,a869)))+E(f329(f329(f116(x87651),f13(x87651,f329(f329(f116(f883(x87651,a869)),x87652),x87653))),f13(x87651,f329(f329(f107(f883(x87651,a869)),x87652),x87653))),f329(f329(f116(x87651),f13(x87651,x87652)),f13(x87651,x87653))) % 178.07/177.94 [8766]~P63(x87661)+~P24(f329(f62(x87661),x87663))+~P24(f329(f62(x87661),x87662))+E(f329(f329(f107(f883(x87661,a869)),x87662),x87663),f193(f883(x87661,a869)))+E(f329(f329(f107(x87661),f10(x87661,f329(f329(f116(f883(x87661,a869)),x87662),x87663))),f10(x87661,f329(f329(f107(f883(x87661,a869)),x87662),x87663))),f329(f329(f107(x87661),f10(x87661,x87662)),f10(x87661,x87663))) % 178.07/177.94 [8767]~P105(x87671)+~P24(f329(f62(x87671),x87673))+~P24(f329(f62(x87671),x87672))+E(f329(f329(f107(f883(x87671,a869)),x87672),x87673),f193(f883(x87671,a869)))+E(f329(f329(f241(x87671),f14(x87671,f329(f329(f116(f883(x87671,a869)),x87672),x87673))),f14(x87671,f329(f329(f107(f883(x87671,a869)),x87672),x87673))),f329(f329(f241(x87671),f14(x87671,x87672)),f14(x87671,x87673))) % 178.07/177.94 [8768]~P105(x87681)+~P24(f329(f62(x87681),x87683))+~P24(f329(f62(x87681),x87682))+E(f329(f329(f107(f883(x87681,a869)),x87682),x87683),f193(f883(x87681,a869)))+E(f329(f329(f242(x87681),f15(x87681,f329(f329(f116(f883(x87681,a869)),x87682),x87683))),f15(x87681,f329(f329(f107(f883(x87681,a869)),x87682),x87683))),f329(f329(f242(x87681),f15(x87681,x87682)),f15(x87681,x87683))) % 178.07/177.94 [8989]~P105(x89891)+~P24(f329(f62(x89891),x89893))+~P24(f329(f62(x89891),x89892))+E(f329(f329(f107(f883(x89891,a869)),x89892),x89893),f193(f883(x89891,a869)))+E(f329(f329(f241(x89891),f12(x89891,f241(x89891),f329(f329(f116(f883(x89891,a869)),x89892),x89893))),f12(x89891,f241(x89891),f329(f329(f107(f883(x89891,a869)),x89892),x89893))),f329(f329(f241(x89891),f12(x89891,f241(x89891),x89892)),f12(x89891,f241(x89891),x89893))) % 178.07/177.94 [8990]~P105(x89901)+~P24(f329(f62(x89901),x89903))+~P24(f329(f62(x89901),x89902))+E(f329(f329(f107(f883(x89901,a869)),x89902),x89903),f193(f883(x89901,a869)))+E(f329(f329(f242(x89901),f11(x89901,f242(x89901),f329(f329(f116(f883(x89901,a869)),x89902),x89903))),f11(x89901,f242(x89901),f329(f329(f107(f883(x89901,a869)),x89902),x89903))),f329(f329(f242(x89901),f11(x89901,f242(x89901),x89902)),f11(x89901,f242(x89901),x89903))) % 178.07/177.94 [9781]~P120(x97813)+E(x97811,x97812)+~P24(f329(f329(f243(x97813),f2(x97813)),x97812))+~P24(f329(f329(f243(x97813),f2(x97813)),x97811))+~E(f329(f329(f254(x97813),x97811),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)))),f329(f329(f254(x97813),x97812),f329(f109(a875),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103)),f329(f329(f22(a1),f329(f329(f81(a1),a84),a84)),a103))))) % 178.07/177.94 [6309]E(f360(x63091,x63092,x63093),x63094)+E(f329(x63091,x63094),f2(a875))+~E(f329(f329(f6(x63093,a875),x63091),x63092),f79(a875))+~P24(f329(f62(x63093),x63092))+~P24(f329(f329(f331(x63093),x63094),x63092)) % 178.07/177.94 [6372]E(f363(x63721,x63722,x63723),x63724)+E(f329(x63721,x63724),f2(a875))+~E(f329(f329(f6(x63723,a875),x63721),x63722),f329(a118,f2(a875)))+~P24(f329(f62(x63723),x63722))+~P24(f329(f329(f331(x63723),x63724),x63722)) % 178.07/177.94 [6478]~P27(x64781)+~P105(x64781)+P24(f329(f329(f244(x64781),x64782),f40(x64781,x64783)))+~P24(f329(f329(f244(x64781),x64782),x64784))+~P24(f329(f329(f331(x64781),x64784),x64783)) % 178.07/177.94 [6651]~P27(x66511)+~P105(x66511)+~P24(f329(f329(f244(x66511),x66514),x66513))+P24(f329(f329(f244(x66511),f41(x66511,x66512)),x66513))+~P24(f329(f329(f331(x66511),x66514),x66512)) % 178.07/177.94 [6910]~P120(x69103)+E(x69101,x69102)+~E(f329(f329(f254(x69103),x69101),f329(a118,x69104)),f329(f329(f254(x69103),x69102),f329(a118,x69104)))+~P24(f329(f329(f243(x69103),f2(x69103)),x69102))+~P24(f329(f329(f243(x69103),f2(x69103)),x69101)) % 178.07/177.94 [7121]~E(f368(x71212,x71213,x71211,x71214),x71214)+~E(f329(x71212,x71214),f79(a875))+E(f329(f329(f6(x71211,a875),x71212),x71213),f79(a875))+~P24(f329(f62(x71211),x71213))+~P24(f329(f329(f331(x71211),x71214),x71213)) % 178.07/177.94 [7128]~P114(x71284)+~P129(x71284)+E(f329(x71281,f359(x71281,x71282,x71283,x71284)),f2(x71284))+~E(f329(f329(f9(x71283,x71284),x71281),x71282),f2(x71284))+~P24(f329(f62(x71283),x71282)) % 178.07/177.94 [7214]~E(f366(x72142,x72143,x72141,x72144),x72144)+~E(f329(x72142,x72144),f329(a118,f2(a875)))+E(f329(f329(f6(x72141,a875),x72142),x72143),f329(a118,f2(a875)))+~P24(f329(f62(x72141),x72143))+~P24(f329(f329(f331(x72141),x72144),x72143)) % 178.07/177.94 [7951]~E(f329(x79512,x79514),f79(a875))+~E(f329(x79512,f368(x79512,x79513,x79511,x79514)),f2(a875))+E(f329(f329(f6(x79511,a875),x79512),x79513),f79(a875))+~P24(f329(f62(x79511),x79513))+~P24(f329(f329(f331(x79511),x79514),x79513)) % 178.07/177.94 [7995]~E(f329(x79952,x79954),f329(a118,f2(a875)))+~E(f329(x79952,f366(x79952,x79953,x79951,x79954)),f2(a875))+E(f329(f329(f6(x79951,a875),x79952),x79953),f329(a118,f2(a875)))+~P24(f329(f62(x79951),x79953))+~P24(f329(f329(f331(x79951),x79954),x79953)) % 178.07/177.94 [8552]~P105(x85521)+~P29(x85521,x85524)+P29(x85521,x85522)+~E(x85522,f329(f329(f150(x85521),x85523),x85524))+~P24(f329(f329(f243(x85521),x85523),f682(x85522,x85521,x85524,x85523))) % 178.07/177.94 [8586]E(x85861,x85862)+E(f329(f329(f22(a1),f420(x85863,x85862,x85864,x85861)),f421(x85863,x85862,x85864,x85861)),x85861)+~E(f329(f329(f81(a1),x85861),x85864),x85862)+~P24(f329(f329(f244(a1),f2(a1)),x85864))+~P24(f329(f329(f331(a1),x85862),x85863)) % 178.07/177.94 [8587]E(x85871,x85872)+E(f329(f329(f81(a1),f429(x85873,x85872,x85874,x85871)),f430(x85873,x85872,x85874,x85871)),x85871)+~E(f329(f329(f22(a1),x85871),x85874),x85872)+~P24(f329(f329(f244(a1),f2(a1)),x85874))+~P24(f329(f329(f331(a1),x85872),x85873)) % 178.07/177.94 [8763]E(f329(x87631,f773(x87632,x87631,x87633,x87634)),x87632)+P24(f329(f329(f243(a875),x87634),f774(x87632,x87631,x87633,x87634)))+~P24(f329(f329(f243(a1),x87632),f329(x87631,x87633)))+~P24(f329(f329(f244(a875),x87634),x87633))+~P24(f329(f329(f243(a1),f329(x87631,x87634)),x87632)) % 178.07/177.94 [8764]~P105(x87641)+~P29(x87641,x87643)+P29(x87641,x87642)+~E(x87642,f329(f329(f150(x87641),x87644),x87643))+P24(f329(f329(f331(x87641),f682(x87642,x87641,x87643,x87644)),f329(f171(x87641),x87643))) % 178.07/177.94 [8782]~P114(x87824)+~P129(x87824)+~E(f329(f329(f9(x87821,x87824),x87822),x87823),f2(x87824))+~P24(f329(f62(x87821),x87823))+P24(f329(f329(f331(x87821),f359(x87822,x87823,x87821,x87824)),x87823)) % 178.07/177.94 [8816]~E(f329(x88162,x88164),f79(a875))+E(f329(f329(f6(x88161,a875),x88162),x88163),f79(a875))+~P24(f329(f62(x88161),x88163))+~P24(f329(f329(f331(x88161),x88164),x88163))+P24(f329(f329(f331(x88161),f368(x88162,x88163,x88161,x88164)),x88163)) % 178.07/177.94 [8825]E(x88251,x88252)+~E(f329(f329(f81(a1),x88252),x88254),x88251)+~P24(f329(f329(f244(a1),f2(a1)),x88254))+~P24(f329(f329(f331(a1),x88251),x88253))+P24(f329(f329(f331(a1),f420(x88253,x88251,x88254,x88252)),x88253)) % 178.07/177.94 [8826]E(x88261,x88262)+~E(f329(f329(f22(a1),x88262),x88264),x88261)+~P24(f329(f329(f244(a1),f2(a1)),x88264))+~P24(f329(f329(f331(a1),x88261),x88263))+P24(f329(f329(f331(a1),f429(x88263,x88261,x88264,x88262)),x88263)) % 178.07/177.94 [8828]~E(f329(x88282,x88284),f329(a118,f2(a875)))+E(f329(f329(f6(x88281,a875),x88282),x88283),f329(a118,f2(a875)))+~P24(f329(f62(x88281),x88283))+~P24(f329(f329(f331(x88281),x88284),x88283))+P24(f329(f329(f331(x88281),f366(x88282,x88283,x88281,x88284)),x88283)) % 178.07/177.94 [8833]P54(x88332,x88333,x88334,x88331)+E(x88331,f193(f883(x88332,a869)))+~P24(f329(f62(x88332),x88334))+~P24(f329(f62(x88332),x88331))+P24(f329(f329(f331(x88332),f691(x88331,x88334,x88333,x88332)),x88334)) % 178.07/177.94 [8915]E(x89151,x89152)+~E(f329(f329(f81(a1),x89152),x89154),x89151)+~P24(f329(f329(f244(a1),f2(a1)),x89154))+~P24(f329(f329(f331(a1),x89151),x89153))+P24(f329(f329(f331(a1),f421(x89153,x89151,x89154,x89152)),f300(a1,f79(a1),x89154))) % 178.07/177.94 [8916]E(x89161,x89162)+~E(f329(f329(f22(a1),x89162),x89164),x89161)+~P24(f329(f329(f244(a1),f2(a1)),x89164))+~P24(f329(f329(f331(a1),x89161),x89163))+P24(f329(f329(f331(a1),f430(x89163,x89161,x89164,x89162)),f300(a1,f79(a1),x89164))) % 178.07/177.94 [8995]P24(f329(f329(f243(a875),x89951),f773(x89952,x89953,x89954,x89951)))+~P24(f329(f329(f243(a1),x89952),f329(x89953,x89954)))+P24(f329(f329(f243(a875),x89951),f774(x89952,x89953,x89954,x89951)))+~P24(f329(f329(f244(a875),x89951),x89954))+~P24(f329(f329(f243(a1),f329(x89953,x89951)),x89952)) % 178.07/177.94 [9105]E(f329(x91051,f773(x91052,x91051,x91053,x91054)),x91052)+~P24(f329(f329(f243(a1),x91052),f329(x91051,x91053)))+P24(f329(f329(f244(a875),f774(x91052,x91051,x91053,x91054)),x91053))+~P24(f329(f329(f244(a875),x91054),x91053))+~P24(f329(f329(f243(a1),f329(x91051,x91054)),x91052)) % 178.07/177.94 [9237]~P24(f329(f329(f243(a1),x92372),f329(x92373,x92374)))+P24(f329(f329(f243(a875),x92371),f774(x92372,x92373,x92374,x92371)))+P24(f329(f329(f243(a875),f773(x92372,x92373,x92374,x92371)),x92374))+~P24(f329(f329(f244(a875),x92371),x92374))+~P24(f329(f329(f243(a1),f329(x92373,x92371)),x92372)) % 178.07/177.94 [9238]~P24(f329(f329(f243(a1),x92382),f329(x92383,x92384)))+P24(f329(f329(f243(a875),x92381),f773(x92382,x92383,x92384,x92381)))+P24(f329(f329(f244(a875),f774(x92382,x92383,x92384,x92381)),x92384))+~P24(f329(f329(f244(a875),x92381),x92384))+~P24(f329(f329(f243(a1),f329(x92383,x92381)),x92382)) % 178.07/177.94 [9345]~P24(f329(f329(f243(a1),x93451),f329(x93452,x93453)))+P24(f329(f329(f243(a875),f773(x93451,x93452,x93453,x93454)),x93453))+~P24(f329(f329(f244(a875),x93454),x93453))+~P24(f329(f329(f243(a1),f329(x93452,x93454)),x93451))+P24(f329(f329(f244(a875),f774(x93451,x93452,x93453,x93454)),x93453)) % 178.07/177.94 [9422]E(x94221,f193(f883(x94222,a869)))+~P24(f329(f62(x94222),x94224))+~P24(f329(f62(x94222),x94221))+P24(f329(f329(f331(f882(f883(x94222,a869),f883(x94222,a869))),f329(f329(f264(f883(x94222,a869),f883(x94222,a869)),x94224),x94221)),f320(x94222,x94223)))+P24(f329(f329(f331(x94222),f699(x94223,x94221,x94224,x94222)),x94224)) % 178.07/177.94 [9423]E(x94231,f193(f883(x94232,a869)))+~P24(f329(f62(x94232),x94234))+~P24(f329(f62(x94232),x94231))+P24(f329(f329(f331(f882(f883(x94232,a869),f883(x94232,a869))),f329(f329(f264(f883(x94232,a869),f883(x94232,a869)),x94234),x94231)),f320(x94232,x94233)))+P24(f329(f329(f331(x94232),f742(x94233,x94231,x94234,x94232)),x94234)) % 178.07/177.94 [10083]E(f329(x100831,f773(x100832,x100831,x100833,x100834)),x100832)+~P24(f329(f329(f243(a1),x100832),f329(x100831,x100833)))+~P24(f329(f329(f243(a1),f329(f76(a1),f329(f329(f22(a1),f329(x100831,f329(f329(f81(a875),f774(x100832,x100831,x100833,x100834)),f79(a875)))),f329(x100831,f774(x100832,x100831,x100833,x100834))))),f79(a1)))+~P24(f329(f329(f244(a875),x100834),x100833))+~P24(f329(f329(f243(a1),f329(x100831,x100834)),x100832)) % 178.07/177.94 [10084]~P24(f329(f329(f243(a1),x100842),f329(x100843,x100844)))+P24(f329(f329(f243(a875),x100841),f773(x100842,x100843,x100844,x100841)))+~P24(f329(f329(f243(a1),f329(f76(a1),f329(f329(f22(a1),f329(x100843,f329(f329(f81(a875),f774(x100842,x100843,x100844,x100841)),f79(a875)))),f329(x100843,f774(x100842,x100843,x100844,x100841))))),f79(a1)))+~P24(f329(f329(f244(a875),x100841),x100844))+~P24(f329(f329(f243(a1),f329(x100843,x100841)),x100842)) % 178.07/177.94 [10085]~P24(f329(f329(f243(a1),x100851),f329(x100852,x100853)))+~P24(f329(f329(f243(a1),f329(f76(a1),f329(f329(f22(a1),f329(x100852,f329(f329(f81(a875),f774(x100851,x100852,x100853,x100854)),f79(a875)))),f329(x100852,f774(x100851,x100852,x100853,x100854))))),f79(a1)))+~P24(f329(f329(f244(a875),x100854),x100853))+~P24(f329(f329(f243(a1),f329(x100852,x100854)),x100851))+P24(f329(f329(f243(a875),f773(x100851,x100852,x100853,x100854)),x100853)) % 178.07/177.94 [7181]~P61(x71811)+P24(f329(f329(f244(x71811),x71812),f2(x71811)))+~P24(f329(f329(f244(x71811),x71813),f2(x71811)))+P24(f329(f329(f244(x71811),f2(x71811)),x71812))+P24(f329(f329(f244(x71811),x71813),f329(f329(f287(x71811),x71814),x71812))) % 178.07/177.94 [7182]~P61(x71821)+P24(f329(f329(f244(x71821),x71822),f2(x71821)))+~P24(f329(f329(f243(x71821),x71823),f2(x71821)))+P24(f329(f329(f244(x71821),f2(x71821)),x71822))+P24(f329(f329(f243(x71821),x71823),f329(f329(f287(x71821),x71824),x71822))) % 178.07/177.94 [7432]~P61(x74321)+P24(f329(f329(f244(x74321),x74322),f2(x74321)))+P24(f329(f329(f244(x74321),x74323),f2(x74321)))+P24(f329(f329(f244(x74321),f2(x74321)),x74323))+~P24(f329(f329(f244(x74321),x74322),f329(f329(f287(x74321),x74324),x74323))) % 178.07/177.94 [7433]~P61(x74331)+P24(f329(f329(f244(x74331),x74332),f2(x74331)))+P24(f329(f329(f243(x74331),x74333),f2(x74331)))+P24(f329(f329(f244(x74331),f2(x74331)),x74332))+~P24(f329(f329(f243(x74331),x74333),f329(f329(f287(x74331),x74334),x74332))) % 178.07/177.94 [7551]E(x75511,x75512)+~E(f329(f329(f164(x75513),x75514),x75511),f329(f329(f164(x75513),x75514),x75512))+~P24(f329(f136(x75513),x75514))+~P24(f329(f329(f244(a875),x75512),f329(f194(f876(x75513)),x75514)))+~P24(f329(f329(f244(a875),x75511),f329(f194(f876(x75513)),x75514))) % 178.07/177.94 [7913]~P61(x79131)+~P24(f329(f329(f244(x79131),x79133),f2(x79131)))+P24(f329(f329(f244(x79131),f2(x79131)),x79132))+~P24(f329(f329(f244(x79131),x79134),f329(f329(f82(x79131),x79133),x79132)))+P24(f329(f329(f244(x79131),x79133),f329(f329(f287(x79131),x79134),x79132))) % 178.07/177.94 [7914]~P61(x79141)+~P24(f329(f329(f243(x79141),x79143),f2(x79141)))+P24(f329(f329(f244(x79141),f2(x79141)),x79142))+~P24(f329(f329(f243(x79141),x79144),f329(f329(f82(x79141),x79143),x79142)))+P24(f329(f329(f243(x79141),x79143),f329(f329(f287(x79141),x79144),x79142))) % 178.07/177.94 [7915]~P61(x79151)+~P24(f329(f329(f244(x79151),x79152),f2(x79151)))+P24(f329(f329(f244(x79151),f2(x79151)),x79152))+~P24(f329(f329(f244(x79151),x79154),f329(f329(f82(x79151),x79153),x79152)))+P24(f329(f329(f244(x79151),x79153),f329(f329(f287(x79151),x79154),x79152))) % 178.07/177.94 [7916]~P61(x79161)+~P24(f329(f329(f244(x79161),x79162),f2(x79161)))+P24(f329(f329(f244(x79161),f2(x79161)),x79162))+~P24(f329(f329(f244(x79161),x79164),f329(f329(f287(x79161),x79163),x79162)))+P24(f329(f329(f244(x79161),x79163),f329(f329(f82(x79161),x79164),x79162))) % 178.07/177.94 [7917]~P61(x79171)+~P24(f329(f329(f244(x79171),x79172),f2(x79171)))+P24(f329(f329(f244(x79171),f2(x79171)),x79172))+~P24(f329(f329(f243(x79171),x79174),f329(f329(f82(x79171),x79173),x79172)))+P24(f329(f329(f243(x79171),x79173),f329(f329(f287(x79171),x79174),x79172))) % 178.07/177.94 [7918]~P61(x79181)+~P24(f329(f329(f244(x79181),x79182),f2(x79181)))+P24(f329(f329(f244(x79181),f2(x79181)),x79182))+~P24(f329(f329(f243(x79181),x79184),f329(f329(f287(x79181),x79183),x79182)))+P24(f329(f329(f243(x79181),x79183),f329(f329(f82(x79181),x79184),x79182))) % 178.07/177.94 [8063]~P105(x80631)+~P29(x80631,x80632)+~P24(f329(f329(f243(a875),x80633),x80634))+P24(f329(f329(f243(x80631),f329(f329(f164(x80631),x80632),x80633)),f329(f329(f164(x80631),x80632),x80634)))+~P24(f329(f329(f244(a875),x80634),f329(f194(f876(x80631)),x80632))) % 178.07/177.94 [8114]~P120(x81141)+~P24(f329(f329(f244(x81141),x81142),f79(x81141)))+~P24(f329(f329(f244(x81141),f2(x81141)),x81142))+~P24(f329(f329(f244(a875),x81144),x81143))+P24(f329(f329(f244(x81141),f329(f329(f254(x81141),x81142),x81143)),f329(f329(f254(x81141),x81142),x81144))) % 178.07/177.94 [8115]~P120(x81151)+~P24(f329(f329(f243(x81151),x81152),f79(x81151)))+~P24(f329(f329(f243(x81151),f2(x81151)),x81152))+~P24(f329(f329(f243(a875),x81154),x81153))+P24(f329(f329(f243(x81151),f329(f329(f254(x81151),x81152),x81153)),f329(f329(f254(x81151),x81152),x81154))) % 178.07/177.94 [8116]~P120(x81161)+~P24(f329(f329(f243(x81161),f2(x81161)),x81162))+~P24(f329(f329(f244(a875),f2(a875)),x81163))+~P24(f329(f329(f244(x81161),x81162),x81164))+P24(f329(f329(f244(x81161),f329(f329(f254(x81161),x81162),x81163)),f329(f329(f254(x81161),x81164),x81163))) % 178.07/177.94 [8136]~P105(x81361)+~P29(x81361,f329(f168(x81361),x81362))+~P24(f329(f329(f243(a875),x81364),x81363))+P24(f329(f329(f243(x81361),f329(f329(f164(x81361),x81362),x81363)),f329(f329(f164(x81361),x81362),x81364)))+~P24(f329(f329(f244(a875),x81363),f329(f194(f876(x81361)),x81362))) % 178.07/177.94 [8383]~P62(x83831)+~P24(f329(f329(f244(x83831),x83832),f2(x83831)))+~P24(f329(f329(f244(x83831),x83833),x83834))+~P24(f329(f329(f244(x83831),f2(x83831)),f329(f329(f82(x83831),x83833),x83834)))+P24(f329(f329(f244(x83831),f329(f329(f287(x83831),x83832),x83833)),f329(f329(f287(x83831),x83832),x83834))) % 178.07/177.94 [8384]~P61(x83841)+~P24(f329(f329(f243(x83841),x83842),f2(x83841)))+~P24(f329(f329(f243(x83841),x83843),x83844))+~P24(f329(f329(f244(x83841),f2(x83841)),f329(f329(f82(x83841),x83843),x83844)))+P24(f329(f329(f243(x83841),f329(f329(f287(x83841),x83842),x83843)),f329(f329(f287(x83841),x83842),x83844))) % 178.07/177.94 [8394]~P62(x83941)+~P24(f329(f329(f244(x83941),x83944),x83943))+~P24(f329(f329(f244(x83941),f2(x83941)),x83942))+~P24(f329(f329(f244(x83941),f2(x83941)),f329(f329(f82(x83941),x83943),x83944)))+P24(f329(f329(f244(x83941),f329(f329(f287(x83941),x83942),x83943)),f329(f329(f287(x83941),x83942),x83944))) % 178.07/177.94 [8395]~P62(x83951)+~P24(f329(f329(f243(x83951),x83954),x83953))+~P24(f329(f329(f243(x83951),f2(x83951)),x83952))+~P24(f329(f329(f244(x83951),f2(x83951)),f329(f329(f82(x83951),x83953),x83954)))+P24(f329(f329(f243(x83951),f329(f329(f287(x83951),x83952),x83953)),f329(f329(f287(x83951),x83952),x83954))) % 178.07/177.94 [8502]P24(f329(x85021,x85022))+~P24(f329(f62(x85024),x85022))+P24(f329(x85021,f455(x85021,x85023,x85022,x85024)))+~P24(f329(x85021,f193(f883(x85024,a869))))+~P24(f329(f329(f243(f883(x85024,a869)),x85022),x85023)) % 178.07/177.94 [8510]P24(f329(x85101,x85102))+P24(f329(f62(x85103),f455(x85101,x85104,x85102,x85103)))+~P24(f329(f62(x85103),x85102))+~P24(f329(x85101,f193(f883(x85103,a869))))+~P24(f329(f329(f243(f883(x85103,a869)),x85102),x85104)) % 178.07/177.94 [8758]E(f329(f329(f81(a1),f436(x87581,x87582,x87583,x87584)),f437(x87581,x87582,x87583,x87584)),x87584)+~P24(f329(f329(f244(a1),f2(a1)),x87583))+~P24(f329(f329(f244(a1),x87582),x87584))+~P24(f329(f329(f331(a1),x87582),x87581))+P24(f329(f329(f244(a1),x87582),f329(f329(f22(a1),x87584),x87583))) % 178.07/177.94 [8975]~P24(f329(f329(f244(a1),f2(a1)),x89753))+~P24(f329(f329(f244(a1),x89752),x89754))+~P24(f329(f329(f331(a1),x89752),x89751))+P24(f329(f329(f331(a1),f436(x89751,x89752,x89753,x89754)),x89751))+P24(f329(f329(f244(a1),x89752),f329(f329(f22(a1),x89754),x89753))) % 178.07/177.94 [8988]P24(f329(x89881,x89882))+~P24(f329(f62(x89883),x89882))+P24(f329(f329(f331(x89883),f456(x89881,x89884,x89882,x89883)),x89884))+~P24(f329(x89881,f193(f883(x89883,a869))))+~P24(f329(f329(f243(f883(x89883,a869)),x89882),x89884)) % 178.07/177.94 [9005]E(f329(f329(f81(a1),f422(x90051,x90052,x90053,x90054)),f423(x90051,x90052,x90053,x90054)),x90054)+~P24(f329(f329(f244(a1),f2(a1)),x90053))+~P24(f329(f329(f243(a1),x90052),x90054))+P24(f329(f329(f243(a1),x90052),f329(f329(f22(a1),x90054),x90053)))+~P24(f329(f329(f331(a1),f329(f329(f22(a1),x90052),f79(a1))),x90051)) % 178.07/177.94 [9057]~P24(f329(f329(f244(a1),f2(a1)),x90573))+~P24(f329(f329(f244(a1),x90571),x90572))+~P24(f329(f329(f331(a1),x90571),x90574))+P24(f329(f329(f331(a1),f437(x90574,x90571,x90573,x90572)),f300(a1,f79(a1),x90573)))+P24(f329(f329(f244(a1),x90571),f329(f329(f22(a1),x90572),x90573))) % 178.07/177.94 [9152]~P24(f329(f329(f244(a1),f2(a1)),x91523))+~P24(f329(f329(f243(a1),x91522),x91524))+P24(f329(f329(f331(a1),f422(x91521,x91522,x91523,x91524)),x91521))+P24(f329(f329(f243(a1),x91522),f329(f329(f22(a1),x91524),x91523)))+~P24(f329(f329(f331(a1),f329(f329(f22(a1),x91522),f79(a1))),x91521)) % 178.07/177.94 [9192]~P24(f329(f329(f244(a1),f2(a1)),x91923))+~P24(f329(f329(f243(a1),x91921),x91922))+P24(f329(f329(f331(a1),f423(x91924,x91921,x91923,x91922)),f300(a1,f79(a1),x91923)))+P24(f329(f329(f243(a1),x91921),f329(f329(f22(a1),x91922),x91923)))+~P24(f329(f329(f331(a1),f329(f329(f22(a1),x91921),f79(a1))),x91924)) % 178.07/177.94 [9425]P24(f329(x94251,x94252))+~P24(f329(f329(f331(x94253),f456(x94251,x94254,x94252,x94253)),f455(x94251,x94254,x94252,x94253)))+~P24(f329(f62(x94253),x94252))+~P24(f329(x94251,f193(f883(x94253,a869))))+~P24(f329(f329(f243(f883(x94253,a869)),x94252),x94254)) % 178.07/177.94 [9641]P24(f329(x96411,x96412))+~P24(f329(f62(x96413),x96412))+~P24(f329(x96411,f329(f329(f307(x96413),f456(x96411,x96414,x96412,x96413)),f455(x96411,x96414,x96412,x96413))))+~P24(f329(x96411,f193(f883(x96413,a869))))+~P24(f329(f329(f243(f883(x96413,a869)),x96412),x96414)) % 178.07/177.94 [7687]~P61(x76871)+P24(f329(f329(f244(x76871),x76872),f2(x76871)))+P24(f329(f329(f244(x76871),f2(x76871)),x76872))+~P24(f329(f329(f244(x76871),f2(x76871)),x76874))+P24(f329(f329(f244(x76871),f329(f329(f287(x76871),x76873),x76872)),x76874)) % 178.07/177.94 [7688]~P61(x76881)+P24(f329(f329(f244(x76881),x76882),f2(x76881)))+~P24(f329(f329(f243(x76881),f2(x76881)),x76884))+P24(f329(f329(f244(x76881),f2(x76881)),x76882))+P24(f329(f329(f243(x76881),f329(f329(f287(x76881),x76883),x76882)),x76884)) % 178.07/177.94 [7967]~P24(f329(f329(f243(a1),x79674),f2(a1)))+~E(x79672,f329(f329(f81(a1),f329(f329(f82(a1),x79671),x79673)),x79674))+P24(f329(f329(f244(a1),f2(a1)),x79671))+~P24(f329(f329(f244(a1),x79671),x79674))+P24(f329(f49(x79672,x79671),f329(f329(f264(a1,a1),x79673),x79674))) % 178.07/177.94 [8006]~P24(f329(x80061,x80064))+P24(f329(x80061,f403(x80062,x80061,x80063)))+~P24(f329(f329(f244(a1),f2(a1)),x80063))+~P24(f329(f329(f243(a1),f2(a1)),x80062))+P24(f329(x80061,f329(f329(f22(a1),x80064),f329(f329(f82(a1),x80062),x80063)))) % 178.07/177.94 [8007]~P24(f329(x80071,x80074))+P24(f329(x80071,f417(x80072,x80071,x80073)))+~P24(f329(f329(f244(a1),f2(a1)),x80073))+~P24(f329(f329(f243(a1),f2(a1)),x80072))+P24(f329(x80071,f329(f329(f81(a1),x80074),f329(f329(f82(a1),x80072),x80073)))) % 178.07/177.94 [8008]~P61(x80081)+P24(f329(f329(f244(x80081),x80082),f2(x80081)))+P24(f329(f329(f244(x80081),f2(x80081)),x80082))+P24(f329(f329(f244(x80081),f2(x80081)),x80083))+~P24(f329(f329(f244(x80081),f329(f329(f287(x80081),x80084),x80082)),x80083)) % 178.07/177.94 [8009]~P61(x80091)+P24(f329(f329(f244(x80091),x80092),f2(x80091)))+P24(f329(f329(f244(x80091),f2(x80091)),x80092))+P24(f329(f329(f243(x80091),f2(x80091)),x80093))+~P24(f329(f329(f243(x80091),f329(f329(f287(x80091),x80094),x80092)),x80093)) % 178.07/177.94 [8057]~E(x80571,f329(f329(f81(a1),f329(f329(f82(a1),x80572),x80573)),x80574))+~P24(f329(f329(f244(a1),f2(a1)),x80572))+~P24(f329(f329(f243(a1),f2(a1)),x80574))+~P24(f329(f329(f244(a1),x80574),x80572))+P24(f329(f49(x80571,x80572),f329(f329(f264(a1,a1),x80573),x80574))) % 178.07/177.94 [8180]~P61(x81801)+P24(f329(f329(f244(x81801),x81802),f2(x81801)))+~P24(f329(f329(f244(x81801),f2(x81801)),x81804))+~P24(f329(f329(f244(x81801),x81803),f329(f329(f82(x81801),x81804),x81802)))+P24(f329(f329(f244(x81801),f329(f329(f287(x81801),x81803),x81802)),x81804)) % 178.07/177.94 [8181]~P61(x81811)+P24(f329(f329(f244(x81811),x81812),f2(x81811)))+~P24(f329(f329(f243(x81811),f2(x81811)),x81814))+~P24(f329(f329(f243(x81811),x81813),f329(f329(f82(x81811),x81814),x81812)))+P24(f329(f329(f243(x81811),f329(f329(f287(x81811),x81813),x81812)),x81814)) % 178.07/177.94 [8262]~P61(x82621)+P24(f329(f329(f244(x82621),x82622),f2(x82621)))+~P24(f329(f329(f244(x82621),x82623),f2(x82621)))+P24(f329(f329(f244(x82621),x82623),f329(f329(f287(x82621),x82624),x82622)))+~P24(f329(f329(f244(x82621),f329(f329(f82(x82621),x82623),x82622)),x82624)) % 178.07/177.94 [8263]~P61(x82631)+P24(f329(f329(f244(x82631),x82632),f2(x82631)))+~P24(f329(f329(f243(x82631),x82633),f2(x82631)))+P24(f329(f329(f243(x82631),x82633),f329(f329(f287(x82631),x82634),x82632)))+~P24(f329(f329(f243(x82631),f329(f329(f82(x82631),x82633),x82632)),x82634)) % 178.07/177.94 [8420]~P61(x84201)+~P24(f329(f329(f244(x84201),x84202),f2(x84201)))+P24(f329(f329(f244(x84201),f2(x84201)),x84202))+~P24(f329(f329(f244(x84201),f329(f329(f287(x84201),x84204),x84202)),x84203))+P24(f329(f329(f244(x84201),f329(f329(f82(x84201),x84203),x84202)),x84204)) % 178.07/177.94 [8421]~P61(x84211)+~P24(f329(f329(f244(x84211),x84212),f2(x84211)))+P24(f329(f329(f244(x84211),f2(x84211)),x84212))+~P24(f329(f329(f244(x84211),f329(f329(f82(x84211),x84214),x84212)),x84213))+P24(f329(f329(f244(x84211),f329(f329(f287(x84211),x84213),x84212)),x84214)) % 178.07/177.94 [8422]~P61(x84221)+~P24(f329(f329(f244(x84221),x84222),f2(x84221)))+P24(f329(f329(f244(x84221),f2(x84221)),x84222))+~P24(f329(f329(f243(x84221),f329(f329(f287(x84221),x84224),x84222)),x84223))+P24(f329(f329(f243(x84221),f329(f329(f82(x84221),x84223),x84222)),x84224)) % 178.07/177.94 [8423]~P61(x84231)+~P24(f329(f329(f244(x84231),x84232),f2(x84231)))+P24(f329(f329(f244(x84231),f2(x84231)),x84232))+~P24(f329(f329(f243(x84231),f329(f329(f82(x84231),x84234),x84232)),x84233))+P24(f329(f329(f243(x84231),f329(f329(f287(x84231),x84233),x84232)),x84234)) % 178.07/177.94 [8445]~P61(x84451)+~P24(f329(f329(f244(x84451),f2(x84451)),x84454))+P24(f329(f329(f244(x84451),f2(x84451)),x84452))+~P24(f329(f329(f244(x84451),f329(f329(f82(x84451),x84454),x84452)),x84453))+P24(f329(f329(f244(x84451),f329(f329(f287(x84451),x84453),x84452)),x84454)) % 178.07/177.94 [8446]~P61(x84461)+~P24(f329(f329(f243(x84461),f2(x84461)),x84464))+P24(f329(f329(f244(x84461),f2(x84461)),x84462))+~P24(f329(f329(f243(x84461),f329(f329(f82(x84461),x84464),x84462)),x84463))+P24(f329(f329(f243(x84461),f329(f329(f287(x84461),x84463),x84462)),x84464)) % 178.07/177.94 [8518]~P61(x85181)+~P24(f329(f329(f244(x85181),x85184),f2(x85181)))+~P24(f329(f329(f244(x85181),x85183),f329(f329(f82(x85181),x85182),x85184)))+P24(f329(f329(f244(x85181),x85182),f329(f329(f287(x85181),x85183),x85184)))+~P24(f329(f329(f244(x85181),f329(f329(f82(x85181),x85182),x85184)),x85183)) % 178.07/177.94 [8519]~P61(x85191)+~P24(f329(f329(f244(x85191),x85192),f2(x85191)))+~P24(f329(f329(f244(x85191),x85193),f329(f329(f82(x85191),x85192),x85194)))+P24(f329(f329(f244(x85191),x85192),f329(f329(f287(x85191),x85193),x85194)))+~P24(f329(f329(f244(x85191),f329(f329(f82(x85191),x85192),x85194)),x85193)) % 178.07/177.94 [8520]~P61(x85201)+~P24(f329(f329(f244(x85201),x85204),f2(x85201)))+~P24(f329(f329(f243(x85201),x85203),f329(f329(f82(x85201),x85202),x85204)))+P24(f329(f329(f243(x85201),x85202),f329(f329(f287(x85201),x85203),x85204)))+~P24(f329(f329(f243(x85201),f329(f329(f82(x85201),x85202),x85204)),x85203)) % 178.07/177.94 [8521]~P61(x85211)+~P24(f329(f329(f243(x85211),x85212),f2(x85211)))+~P24(f329(f329(f243(x85211),x85213),f329(f329(f82(x85211),x85212),x85214)))+P24(f329(f329(f243(x85211),x85212),f329(f329(f287(x85211),x85213),x85214)))+~P24(f329(f329(f243(x85211),f329(f329(f82(x85211),x85212),x85214)),x85213)) % 178.07/177.94 [8634]~P61(x86341)+~P24(f329(f329(f244(x86341),x86343),f2(x86341)))+~P24(f329(f329(f244(x86341),x86342),f329(f329(f82(x86341),x86344),x86343)))+~P24(f329(f329(f244(x86341),f329(f329(f82(x86341),x86344),x86343)),x86342))+P24(f329(f329(f244(x86341),f329(f329(f287(x86341),x86342),x86343)),x86344)) % 178.07/177.94 [8635]~P61(x86351)+~P24(f329(f329(f244(x86351),x86353),f2(x86351)))+~P24(f329(f329(f243(x86351),x86352),f329(f329(f82(x86351),x86354),x86353)))+~P24(f329(f329(f243(x86351),f329(f329(f82(x86351),x86354),x86353)),x86352))+P24(f329(f329(f243(x86351),f329(f329(f287(x86351),x86352),x86353)),x86354)) % 178.07/177.94 [8651]~P61(x86511)+~P24(f329(f329(f244(x86511),f2(x86511)),x86514))+~P24(f329(f329(f244(x86511),x86512),f329(f329(f82(x86511),x86514),x86513)))+~P24(f329(f329(f244(x86511),f329(f329(f82(x86511),x86514),x86513)),x86512))+P24(f329(f329(f244(x86511),f329(f329(f287(x86511),x86512),x86513)),x86514)) % 178.07/177.94 [8652]~P61(x86521)+~P24(f329(f329(f243(x86521),f2(x86521)),x86524))+~P24(f329(f329(f243(x86521),x86522),f329(f329(f82(x86521),x86524),x86523)))+~P24(f329(f329(f243(x86521),f329(f329(f82(x86521),x86524),x86523)),x86522))+P24(f329(f329(f243(x86521),f329(f329(f287(x86521),x86522),x86523)),x86524)) % 178.07/177.94 [8818]E(f329(f329(f22(a1),f438(x88181,x88182,x88183,x88184)),f439(x88181,x88182,x88183,x88184)),x88184)+~P24(f329(f329(f244(a1),f2(a1)),x88183))+~P24(f329(f329(f331(a1),x88182),x88181))+~P24(f329(f329(f244(a1),x88184),x88182))+P24(f329(f329(f244(a1),f329(f329(f81(a1),x88184),x88183)),x88182)) % 178.07/177.94 [8897]~P24(f329(x88971,x88972))+~P24(f329(f329(f244(a1),f2(a1)),x88974))+~P24(f329(f329(f243(a1),f2(a1)),x88973))+~P24(f329(x88971,f329(f329(f22(a1),f403(x88973,x88971,x88974)),x88974)))+P24(f329(x88971,f329(f329(f22(a1),x88972),f329(f329(f82(a1),x88973),x88974)))) % 178.07/177.94 [8898]~P24(f329(x88981,x88982))+~P24(f329(f329(f244(a1),f2(a1)),x88984))+~P24(f329(f329(f243(a1),f2(a1)),x88983))+~P24(f329(x88981,f329(f329(f81(a1),f417(x88983,x88981,x88984)),x88984)))+P24(f329(x88981,f329(f329(f81(a1),x88982),f329(f329(f82(a1),x88983),x88984)))) % 178.07/177.94 [9051]~P24(f329(f329(f244(a1),f2(a1)),x90513))+~P24(f329(f329(f331(a1),x90512),x90511))+~P24(f329(f329(f244(a1),x90514),x90512))+P24(f329(f329(f331(a1),f438(x90511,x90512,x90513,x90514)),x90511))+P24(f329(f329(f244(a1),f329(f329(f81(a1),x90514),x90513)),x90512)) % 178.07/177.94 [9071]E(f329(f329(f22(a1),f426(x90711,x90712,x90713,x90714)),f427(x90711,x90712,x90713,x90714)),x90714)+~P24(f329(f329(f244(a1),f2(a1)),x90713))+~P24(f329(f329(f243(a1),x90714),x90712))+~P24(f329(f329(f331(a1),f329(f329(f81(a1),x90712),f79(a1))),x90711))+P24(f329(f329(f243(a1),f329(f329(f81(a1),x90714),x90713)),x90712)) % 178.07/177.94 [9097]~P24(f329(f329(f244(a1),f2(a1)),x90972))+~P24(f329(f329(f331(a1),x90973),x90974))+~P24(f329(f329(f244(a1),x90971),x90973))+P24(f329(f329(f331(a1),f439(x90974,x90973,x90972,x90971)),f300(a1,f79(a1),x90972)))+P24(f329(f329(f244(a1),f329(f329(f81(a1),x90971),x90972)),x90973)) % 178.07/177.94 [9187]~P24(f329(f329(f244(a1),f2(a1)),x91873))+~P24(f329(f329(f243(a1),x91874),x91872))+P24(f329(f329(f331(a1),f426(x91871,x91872,x91873,x91874)),x91871))+~P24(f329(f329(f331(a1),f329(f329(f81(a1),x91872),f79(a1))),x91871))+P24(f329(f329(f243(a1),f329(f329(f81(a1),x91874),x91873)),x91872)) % 178.07/177.94 [9233]~P24(f329(f329(f244(a1),f2(a1)),x92332))+~P24(f329(f329(f243(a1),x92331),x92333))+P24(f329(f329(f331(a1),f427(x92334,x92333,x92332,x92331)),f300(a1,f79(a1),x92332)))+~P24(f329(f329(f331(a1),f329(f329(f81(a1),x92333),f79(a1))),x92334))+P24(f329(f329(f243(a1),f329(f329(f81(a1),x92331),x92332)),x92333)) % 178.07/177.94 [9517]~P38(x95171,x95173)+~P22(x95171,x95174)+P38(x95171,f329(f329(f116(f883(f882(x95171,x95171),a869)),x95172),x95173))+~P24(f329(f329(f243(f883(f882(x95171,x95171),a869)),x95172),f329(f263(f883(f882(x95171,x95171),a869),f883(f882(x95171,x95171),a869)),x95174)))+~P24(f329(f329(f243(f883(f882(x95171,x95171),a869)),x95173),f329(f267(f883(f882(x95171,x95171),a869),f883(f882(x95171,x95171),a869)),x95174))) % 178.07/177.94 [9809]~E(f329(f554(x98091,x98094,x98093,x98092),f556(x98091,x98094,x98093,x98092)),f206(f876(a325)))+P24(f329(f329(f244(a1),f555(x98091,x98094,x98093,x98092)),f556(x98091,x98094,x98093,x98092)))+P24(f329(f329(f329(x98091,x98092),x98093),x98094))+P24(f329(f329(f329(x98091,f554(x98091,x98094,x98093,x98092)),f555(x98091,x98094,x98093,x98092)),f329(f329(f81(a1),f556(x98091,x98094,x98093,x98092)),f79(a1))))+~P24(f329(f317(f882(f883(a1,f879(f876(a325))),f882(a1,a1)),a315),f329(f329(f264(f883(a1,f879(f876(a325))),f882(a1,a1)),x98092),f329(f329(f264(a1,a1),x98093),x98094)))) % 178.07/177.94 [9910]~P14(x99102,x99104,x99103)+E(x99101,f193(f883(x99102,a869)))+~P24(f329(f62(x99102),x99101))+P24(f329(f329(f331(x99102),f329(x99103,x99101)),x99101))+~P24(f329(f329(f331(x99102),f329(f329(x99104,f637(x99101,x99103,x99104,x99102)),f645(x99101,x99103,x99104,x99102))),f329(f329(f307(x99102),f637(x99101,x99103,x99104,x99102)),f329(f329(f307(x99102),f645(x99101,x99103,x99104,x99102)),f193(f883(x99102,a869)))))) % 178.07/177.94 [9841]~P107(x98412)+~P58(x98411)+~P24(f329(f329(f243(f883(x98411,x98412)),x98413),x98414))+P24(f329(f329(f244(f883(x98411,x98412)),x98413),x98414))+~P24(f329(f58(x98411),f329(f329(f8(a869,a869,x98411),a324),f329(f329(f18(x98411,x98412,a869),f329(f329(f8(x98412,f883(x98412,a869),x98411),a326),x98413)),x98414)))) % 178.07/177.94 [9433]~P50(x94331,x94331,x94334)+P24(f329(f329(f331(f882(x94331,x94331)),f329(f329(f264(x94331,x94331),x94332),x94333)),f305(x94331,x94334)))+P24(f329(f329(f331(f882(x94331,x94331)),f329(f329(f264(x94331,x94331),x94333),x94332)),f305(x94331,x94334)))+~P24(f329(f329(f331(f882(x94331,x94331)),f329(f329(f264(x94331,x94331),x94335),x94332)),f305(x94331,x94334)))+~P24(f329(f329(f331(f882(x94331,x94331)),f329(f329(f264(x94331,x94331),x94335),x94333)),f305(x94331,x94334))) % 178.07/177.94 [5592]E(x55921,f2(a875))+~E(f329(f38(x55922),x55925),x55921)+E(f329(f38(x55922),x55923),f329(a118,x55921))+~E(x55923,f329(f329(f307(x55922),x55924),x55925))+P24(f329(f329(f331(x55922),x55924),x55925)) % 178.07/177.94 [5717]~P60(x57172)+E(x57171,f2(x57172))+E(x57173,f2(x57172))+~E(f329(f329(f287(x57172),x57174),x57173),f329(f329(f287(x57172),x57175),x57171))+E(f329(f329(f82(x57172),x57174),x57171),f329(f329(f82(x57172),x57175),x57173)) % 178.07/177.94 [5718]~P60(x57182)+E(x57181,f2(x57182))+E(x57183,f2(x57182))+~E(f329(f329(f82(x57182),x57184),x57183),f329(f329(f82(x57182),x57185),x57181))+E(f329(f329(f287(x57182),x57184),x57181),f329(f329(f287(x57182),x57185),x57183)) % 178.07/177.94 [5784]~E(f329(f38(x57841),x57845),x57843)+~E(x57845,f193(f883(x57841,a869)))+E(f329(f38(x57841),x57842),f329(a118,x57843))+~E(x57842,f329(f329(f307(x57841),x57844),x57845))+P24(f329(f329(f331(x57841),x57844),x57845)) % 178.07/177.94 [6013]~P114(x60132)+~E(f329(x60133,x60135),f2(x60132))+E(f329(f329(f9(x60131,x60132),x60133),x60134),f2(x60132))+~P24(f329(f62(x60131),x60134))+~P24(f329(f329(f331(x60131),x60135),x60134)) % 178.07/177.94 [6385]~P105(x63853)+E(x63851,x63852)+~E(f329(f299(x63853,x63854),x63851),f329(f299(x63853,x63855),x63852))+~P24(f329(f329(f244(x63853),x63855),x63852))+~P24(f329(f329(f244(x63853),x63854),x63851)) % 178.07/177.94 [6386]~P105(x63863)+E(x63861,x63862)+~E(f329(f299(x63863,x63861),x63864),f329(f299(x63863,x63862),x63865))+~P24(f329(f329(f244(x63863),x63862),x63865))+~P24(f329(f329(f244(x63863),x63861),x63864)) % 178.07/177.94 [7449]~P105(x74491)+~P29(x74491,f329(f329(f127(x74491),x74494),x74495))+~P24(f329(f329(f331(x74491),x74493),f329(f171(x74491),x74495)))+~P24(f329(f329(f331(x74491),x74492),f329(f171(x74491),x74494)))+P24(f329(f329(f243(x74491),x74492),x74493)) % 178.07/177.94 [8554]~P107(x85541)+~P24(f329(f329(f244(f883(x85541,a869)),f300(x85541,x85545,x85542)),f300(x85541,x85544,x85543)))+~P24(f329(f329(f243(x85541),x85545),x85542))+P24(f329(f329(f244(x85541),x85542),x85543))+P24(f329(f329(f244(x85541),x85544),x85545)) % 178.07/177.94 [9953]~P13(x99532,x99535,x99533)+E(x99531,f193(f883(x99532,a869)))+~E(f329(f329(x99535,f329(x99534,f440(x99531,x99534,x99533,x99535,x99532))),f329(x99534,f447(x99531,x99534,x99533,x99535,x99532))),f329(x99534,f329(f329(x99535,f440(x99531,x99534,x99533,x99535,x99532)),f447(x99531,x99534,x99533,x99535,x99532))))+E(f329(x99533,f329(f308(x99532,x99532,x99534),x99531)),f329(x99534,f329(x99533,x99531)))+~P24(f329(f62(x99532),x99531)) % 178.07/177.94 [6382]~P14(x63822,x63825,x63823)+E(x63821,f193(f883(x63822,a869)))+~P24(f329(f62(x63822),x63821))+E(f329(x63823,f329(f329(f307(x63822),x63824),x63821)),f329(f329(x63825,x63824),f329(x63823,x63821)))+P24(f329(f329(f331(x63822),x63824),x63821)) % 178.07/177.94 [7205]~P13(x72052,x72053,x72054)+E(f329(f329(x72053,f329(x72054,x72051)),f329(x72054,x72055)),f329(x72054,x72055))+E(x72051,f193(f883(x72052,a869)))+~P24(f329(f62(x72052),x72055))+~P24(f329(f329(f243(f883(x72052,a869)),x72051),x72055)) % 178.07/177.94 [7425]~P58(x74254)+~P94(x74255)+E(f329(x74251,x74252),f329(x74253,x74252))+~P24(f329(f329(f331(x74254),x74252),f329(f171(x74254),f56(x74254))))+~P24(f329(f329(f92(f883(x74254,x74255)),x74251),x74253)) % 178.07/177.94 [7584]~P14(x75844,x75845,x75841)+E(f329(x75841,x75842),x75843)+~P24(f329(f62(x75844),x75842))+~E(f329(f329(f22(f883(x75844,a869)),x75842),f329(f329(f307(x75844),x75843),f193(f883(x75844,a869)))),f193(f883(x75844,a869)))+~P24(f329(f329(f331(x75844),x75843),x75842)) % 178.07/177.94 [7669]E(x76691,x76692)+~E(f329(f194(f876(x76693)),x76692),f329(f194(f876(x76694)),x76695))+~E(f329(f194(f876(x76693)),x76691),f329(f194(f876(x76694)),x76695))+~E(f329(f177(x76694,x76693),f329(f329(f181(x76694,x76693),x76695),x76691)),f329(f177(x76694,x76693),f329(f329(f181(x76694,x76693),x76695),x76692)))+~P24(f329(f136(x76694),x76695)) % 178.07/177.94 [8525]E(x85251,x85252)+~P6(x85253,x85254,x85255)+E(f329(f329(f107(f883(x85253,a869)),x85251),x85252),f193(f883(x85253,a869)))+~P24(f329(f329(f331(f883(x85253,a869)),x85252),f329(f329(f61(x85253),x85254),x85255)))+~P24(f329(f329(f331(f883(x85253,a869)),x85251),f329(f329(f61(x85253),x85254),x85255))) % 178.07/177.94 [9315]~P70(x93152)+~E(f329(x93153,f457(x93153,x93154,x93155,x93151,x93152)),f2(x93152))+E(f329(f329(f6(x93151,x93152),x93153),x93154),f329(f329(f6(x93151,x93152),x93153),x93155))+~P24(f329(f62(x93151),x93155))+~P24(f329(f329(f243(f883(x93151,a869)),x93154),x93155)) % 178.07/177.94 [9316]~P70(x93162)+~E(f329(x93163,f458(x93163,x93164,x93165,x93161,x93162)),f2(x93162))+E(f329(f329(f6(x93161,x93162),x93163),x93164),f329(f329(f6(x93161,x93162),x93163),x93165))+~P24(f329(f62(x93161),x93165))+~P24(f329(f329(f243(f883(x93161,a869)),x93164),x93165)) % 178.07/177.94 [9317]~P74(x93172)+~E(f329(x93173,f424(x93173,x93174,x93175,x93171,x93172)),f79(x93172))+E(f329(f329(f9(x93171,x93172),x93173),x93174),f329(f329(f9(x93171,x93172),x93173),x93175))+~P24(f329(f62(x93171),x93175))+~P24(f329(f329(f243(f883(x93171,a869)),x93174),x93175)) % 178.07/177.94 [9318]~P74(x93182)+~E(f329(x93183,f425(x93183,x93184,x93185,x93181,x93182)),f79(x93182))+E(f329(f329(f9(x93181,x93182),x93183),x93184),f329(f329(f9(x93181,x93182),x93183),x93185))+~P24(f329(f62(x93181),x93185))+~P24(f329(f329(f243(f883(x93181,a869)),x93184),x93185)) % 178.07/177.94 [9789]~P86(x97891)+~P24(f329(f62(x97892),x97895))+~P24(f329(f329(f243(x97891),f2(x97891)),f329(x97893,f372(x97893,x97894,x97895,x97892,x97891))))+P24(f329(f329(f243(x97891),f329(f329(f6(x97892,x97891),x97893),x97894)),f329(f329(f6(x97892,x97891),x97893),x97895)))+~P24(f329(f329(f243(f883(x97892,a869)),x97894),x97895)) % 178.07/177.94 [7446]E(x74461,f2(a875))+P24(f329(x74462,x74463))+~E(x74464,f329(f329(f81(a875),f329(f329(f82(a875),x74461),x74463)),x74465))+~P24(f329(f329(f244(a875),x74465),x74461))+~P24(f329(x74462,f329(f329(f39(a875),x74464),x74461))) % 178.07/177.94 [7525]E(x75251,f2(a875))+P24(f329(x75252,x75253))+~P24(f329(x75252,f45(a875,x75254,x75251)))+~E(x75254,f329(f329(f81(a875),f329(f329(f82(a875),x75251),x75255)),x75253))+~P24(f329(f329(f244(a875),x75253),x75251)) % 178.07/177.94 [7814]~P60(x78143)+E(f329(x78141,x78142),f2(x78143))+~P24(f329(f62(x78144),x78145))+E(f329(f329(f9(x78144,x78143),x78141),f329(f329(f22(f883(x78144,a869)),x78145),f329(f329(f307(x78144),x78142),f193(f883(x78144,a869))))),f329(f329(f9(x78144,x78143),x78141),x78145))+P24(f329(f329(f331(x78144),x78142),x78145)) % 178.07/177.94 [8221]~P70(x82211)+~P24(f329(f62(x82212),x82215))+~P24(f329(f62(x82212),x82214))+~E(f329(f329(f107(f883(x82212,a869)),x82214),x82215),f193(f883(x82212,a869)))+E(f329(f329(f81(x82211),f329(f329(f6(x82212,x82211),x82213),x82214)),f329(f329(f6(x82212,x82211),x82213),x82215)),f329(f329(f6(x82212,x82211),x82213),f329(f329(f116(f883(x82212,a869)),x82214),x82215))) % 178.07/177.94 [8223]~P74(x82231)+~P24(f329(f62(x82232),x82235))+~P24(f329(f62(x82232),x82234))+~E(f329(f329(f107(f883(x82232,a869)),x82234),x82235),f193(f883(x82232,a869)))+E(f329(f329(f82(x82231),f329(f329(f9(x82232,x82231),x82233),x82234)),f329(f329(f9(x82232,x82231),x82233),x82235)),f329(f329(f9(x82232,x82231),x82233),f329(f329(f116(f883(x82232,a869)),x82234),x82235))) % 178.07/177.94 [8316]~P60(x83163)+E(f329(x83161,x83162),f2(x83163))+~P24(f329(f62(x83164),x83165))+E(f329(f329(f9(x83164,x83163),x83161),f329(f329(f22(f883(x83164,a869)),x83165),f329(f329(f307(x83164),x83162),f193(f883(x83164,a869))))),f329(f329(f287(x83163),f329(f329(f9(x83164,x83163),x83161),x83165)),f329(x83161,x83162)))+~P24(f329(f329(f331(x83164),x83162),x83165)) % 178.07/177.94 [9030]~P6(x90301,x90305,x90304)+~E(f329(f329(f61(x90301),f329(f329(f307(x90301),x90302),f193(f883(x90301,a869)))),x90304),f329(f329(f61(x90301),f329(f329(f307(x90301),x90303),f193(f883(x90301,a869)))),x90304))+~P24(f329(f329(f331(x90301),x90303),x90305))+~P24(f329(f329(f331(x90301),x90302),x90305))+P24(f329(f329(f331(f882(x90301,x90301)),f329(f329(f264(x90301,x90301),x90302),x90303)),x90304)) % 178.07/177.94 [9050]~P6(x90501,x90505,x90503)+E(f329(f329(f61(x90501),f329(f329(f307(x90501),x90502),f193(f883(x90501,a869)))),x90503),f329(f329(f61(x90501),f329(f329(f307(x90501),x90504),f193(f883(x90501,a869)))),x90503))+~P24(f329(f329(f331(x90501),x90504),x90505))+~P24(f329(f329(f331(x90501),x90502),x90505))+~P24(f329(f329(f331(f882(x90501,x90501)),f329(f329(f264(x90501,x90501),x90502),x90504)),x90503)) % 178.07/177.94 [9344]~P74(x93441)+~P24(f329(f62(x93442),x93445))+~P24(f329(f62(x93442),x93444))+~E(f329(f329(f107(f883(x93442,a869)),x93444),x93445),f193(f883(x93442,a869)))+E(f329(f329(f82(x93441),f329(f329(f329(f66(x93441,x93442,f82(x93441)),x93443),f79(x93441)),x93444)),f329(f329(f329(f66(x93441,x93442,f82(x93441)),x93443),f79(x93441)),x93445)),f329(f329(f329(f66(x93441,x93442,f82(x93441)),x93443),f79(x93441)),f329(f329(f116(f883(x93442,a869)),x93444),x93445))) % 178.07/177.94 [9353]~P70(x93531)+~E(f329(x93533,f371(x93533,x93535,x93534,x93532,x93531)),f2(x93531))+~P24(f329(f62(x93532),x93534))+~P24(f329(f62(x93532),x93535))+E(f329(f329(f81(x93531),f329(f329(f6(x93532,x93531),x93533),x93534)),f329(f329(f6(x93532,x93531),x93533),x93535)),f329(f329(f6(x93532,x93531),x93533),f329(f329(f116(f883(x93532,a869)),x93534),x93535))) % 178.07/177.94 [9354]~P70(x93541)+~E(f329(x93543,f374(x93543,x93545,x93544,x93542,x93541)),f2(x93541))+~P24(f329(f62(x93542),x93544))+~P24(f329(f62(x93542),x93545))+E(f329(f329(f81(x93541),f329(f329(f6(x93542,x93541),x93543),x93544)),f329(f329(f6(x93542,x93541),x93543),x93545)),f329(f329(f6(x93542,x93541),x93543),f329(f329(f116(f883(x93542,a869)),x93544),x93545))) % 178.07/177.94 [9355]~P74(x93551)+~E(f329(x93553,f351(x93553,x93555,x93554,x93552,x93551)),f79(x93551))+~P24(f329(f62(x93552),x93554))+~P24(f329(f62(x93552),x93555))+E(f329(f329(f82(x93551),f329(f329(f9(x93552,x93551),x93553),x93554)),f329(f329(f9(x93552,x93551),x93553),x93555)),f329(f329(f9(x93552,x93551),x93553),f329(f329(f116(f883(x93552,a869)),x93554),x93555))) % 178.07/177.94 [9356]~P74(x93561)+~E(f329(x93563,f352(x93563,x93565,x93564,x93562,x93561)),f79(x93561))+~P24(f329(f62(x93562),x93564))+~P24(f329(f62(x93562),x93565))+E(f329(f329(f82(x93561),f329(f329(f9(x93562,x93561),x93563),x93564)),f329(f329(f9(x93562,x93561),x93563),x93565)),f329(f329(f9(x93562,x93561),x93563),f329(f329(f116(f883(x93562,a869)),x93564),x93565))) % 178.07/177.94 [9561]~P74(x95611)+~E(f329(x95613,f843(x95613,x95615,x95614,x95612,x95611)),f79(x95611))+~P24(f329(f62(x95612),x95614))+~P24(f329(f62(x95612),x95615))+E(f329(f329(f82(x95611),f329(f329(f329(f66(x95611,x95612,f82(x95611)),x95613),f79(x95611)),x95614)),f329(f329(f329(f66(x95611,x95612,f82(x95611)),x95613),f79(x95611)),x95615)),f329(f329(f329(f66(x95611,x95612,f82(x95611)),x95613),f79(x95611)),f329(f329(f116(f883(x95612,a869)),x95614),x95615))) % 178.07/177.94 [9668]~P70(x96682)+E(f329(f329(f6(x96681,x96682),x96683),x96684),f329(f329(f6(x96681,x96682),x96683),x96685))+~P24(f329(f62(x96681),x96685))+~P24(f329(f329(f243(f883(x96681,a869)),x96684),x96685))+P24(f329(f329(f331(x96681),f457(x96683,x96684,x96685,x96681,x96682)),f329(f329(f22(f883(x96681,a869)),x96685),x96684))) % 178.07/177.94 [9669]~P70(x96692)+E(f329(f329(f6(x96691,x96692),x96693),x96694),f329(f329(f6(x96691,x96692),x96693),x96695))+~P24(f329(f62(x96691),x96695))+~P24(f329(f329(f243(f883(x96691,a869)),x96694),x96695))+P24(f329(f329(f331(x96691),f458(x96693,x96694,x96695,x96691,x96692)),f329(f329(f22(f883(x96691,a869)),x96695),x96694))) % 178.07/177.94 [9670]~P74(x96702)+E(f329(f329(f9(x96701,x96702),x96703),x96704),f329(f329(f9(x96701,x96702),x96703),x96705))+~P24(f329(f62(x96701),x96705))+~P24(f329(f329(f243(f883(x96701,a869)),x96704),x96705))+P24(f329(f329(f331(x96701),f424(x96703,x96704,x96705,x96701,x96702)),f329(f329(f22(f883(x96701,a869)),x96705),x96704))) % 178.07/177.94 [9671]~P74(x96712)+E(f329(f329(f9(x96711,x96712),x96713),x96714),f329(f329(f9(x96711,x96712),x96713),x96715))+~P24(f329(f62(x96711),x96715))+~P24(f329(f329(f243(f883(x96711,a869)),x96714),x96715))+P24(f329(f329(f331(x96711),f425(x96713,x96714,x96715,x96711,x96712)),f329(f329(f22(f883(x96711,a869)),x96715),x96714))) % 178.07/177.94 [9688]~P70(x96881)+~P24(f329(f62(x96882),x96884))+~P24(f329(f62(x96882),x96885))+E(f329(f329(f81(x96881),f329(f329(f6(x96882,x96881),x96883),x96884)),f329(f329(f6(x96882,x96881),x96883),x96885)),f329(f329(f6(x96882,x96881),x96883),f329(f329(f116(f883(x96882,a869)),x96884),x96885)))+P24(f329(f329(f331(x96882),f371(x96883,x96885,x96884,x96882,x96881)),f329(f329(f107(f883(x96882,a869)),x96884),x96885))) % 178.07/177.94 [9689]~P70(x96891)+~P24(f329(f62(x96892),x96894))+~P24(f329(f62(x96892),x96895))+E(f329(f329(f81(x96891),f329(f329(f6(x96892,x96891),x96893),x96894)),f329(f329(f6(x96892,x96891),x96893),x96895)),f329(f329(f6(x96892,x96891),x96893),f329(f329(f116(f883(x96892,a869)),x96894),x96895)))+P24(f329(f329(f331(x96892),f374(x96893,x96895,x96894,x96892,x96891)),f329(f329(f107(f883(x96892,a869)),x96894),x96895))) % 178.07/177.94 [9690]~P74(x96901)+~P24(f329(f62(x96902),x96904))+~P24(f329(f62(x96902),x96905))+E(f329(f329(f82(x96901),f329(f329(f9(x96902,x96901),x96903),x96904)),f329(f329(f9(x96902,x96901),x96903),x96905)),f329(f329(f9(x96902,x96901),x96903),f329(f329(f116(f883(x96902,a869)),x96904),x96905)))+P24(f329(f329(f331(x96902),f351(x96903,x96905,x96904,x96902,x96901)),f329(f329(f107(f883(x96902,a869)),x96904),x96905))) % 178.07/177.94 [9691]~P74(x96911)+~P24(f329(f62(x96912),x96914))+~P24(f329(f62(x96912),x96915))+E(f329(f329(f82(x96911),f329(f329(f9(x96912,x96911),x96913),x96914)),f329(f329(f9(x96912,x96911),x96913),x96915)),f329(f329(f9(x96912,x96911),x96913),f329(f329(f116(f883(x96912,a869)),x96914),x96915)))+P24(f329(f329(f331(x96912),f352(x96913,x96915,x96914,x96912,x96911)),f329(f329(f107(f883(x96912,a869)),x96914),x96915))) % 178.07/177.94 [9698]~P86(x96985)+~P24(f329(f62(x96981),x96984))+P24(f329(f329(f243(x96985),f329(f329(f6(x96981,x96985),x96982),x96983)),f329(f329(f6(x96981,x96985),x96982),x96984)))+~P24(f329(f329(f243(f883(x96981,a869)),x96983),x96984))+P24(f329(f329(f331(x96981),f372(x96982,x96983,x96984,x96981,x96985)),f329(f329(f22(f883(x96981,a869)),x96984),x96983))) % 178.07/177.94 [9752]~P74(x97521)+~P24(f329(f62(x97522),x97524))+~P24(f329(f62(x97522),x97525))+E(f329(f329(f82(x97521),f329(f329(f329(f66(x97521,x97522,f82(x97521)),x97523),f79(x97521)),x97524)),f329(f329(f329(f66(x97521,x97522,f82(x97521)),x97523),f79(x97521)),x97525)),f329(f329(f329(f66(x97521,x97522,f82(x97521)),x97523),f79(x97521)),f329(f329(f116(f883(x97522,a869)),x97524),x97525)))+P24(f329(f329(f331(x97522),f843(x97523,x97525,x97524,x97522,x97521)),f329(f329(f107(f883(x97522,a869)),x97524),x97525))) % 178.07/177.94 [8719]~P14(x87191,x87194,x87195)+~P24(f329(f62(x87191),x87192))+E(f329(f329(f22(f883(x87191,a869)),x87192),f329(f329(f307(x87191),x87193),f193(f883(x87191,a869)))),f193(f883(x87191,a869)))+~P24(f329(f329(f331(x87191),x87193),x87192))+E(f329(f329(x87194,x87193),f329(x87195,f329(f329(f22(f883(x87191,a869)),x87192),f329(f329(f307(x87191),x87193),f193(f883(x87191,a869)))))),f329(x87195,x87192)) % 178.07/177.94 [8792]~P14(x87921,x87924,x87925)+~P24(f329(f62(x87921),x87923))+~P24(f329(f62(x87921),x87922))+E(f329(f329(f107(f883(x87921,a869)),x87922),x87923),f193(f883(x87921,a869)))+E(f329(f329(x87924,f329(x87925,f329(f329(f116(f883(x87921,a869)),x87922),x87923))),f329(x87925,f329(f329(f107(f883(x87921,a869)),x87922),x87923))),f329(f329(x87924,f329(x87925,x87922)),f329(x87925,x87923))) % 178.07/177.94 [9358]~P24(f329(f329(f243(a1),x93584),f2(a1)))+~P24(f329(f329(f244(a1),x93583),x93585))+P24(f329(f329(f243(a1),x93581),x93582))+~P24(f329(f329(f244(a1),x93583),x93584))+~P24(f329(f329(f243(a1),f329(f329(f81(a1),f329(f329(f82(a1),x93583),x93582)),x93585)),f329(f329(f81(a1),f329(f329(f82(a1),x93583),x93581)),x93584))) % 178.07/177.94 [9360]~P24(f329(f329(f243(a1),f2(a1)),x93605))+P24(f329(f329(f243(a1),x93601),x93602))+~P24(f329(f329(f244(a1),x93603),x93604))+~P24(f329(f329(f244(a1),x93605),x93604))+~P24(f329(f329(f243(a1),f329(f329(f81(a1),f329(f329(f82(a1),x93604),x93601)),x93605)),f329(f329(f81(a1),f329(f329(f82(a1),x93604),x93602)),x93603))) % 178.07/177.94 [9470]~P60(x94705)+E(f329(x94701,f406(x94701,x94702,x94703,x94704,x94705)),f2(x94705))+~P24(f329(f62(x94704),x94703))+~P24(f329(f62(x94704),x94702))+E(f329(f329(f287(x94705),f329(f329(f82(x94705),f329(f329(f9(x94704,x94705),x94701),x94703)),f329(f329(f9(x94704,x94705),x94701),x94702))),f329(f329(f9(x94704,x94705),x94701),f329(f329(f107(f883(x94704,a869)),x94703),x94702))),f329(f329(f9(x94704,x94705),x94701),f329(f329(f116(f883(x94704,a869)),x94703),x94702))) % 178.07/177.94 [9744]~P60(x97441)+~P24(f329(f62(x97442),x97444))+~P24(f329(f62(x97442),x97445))+E(f329(f329(f287(x97441),f329(f329(f82(x97441),f329(f329(f9(x97442,x97441),x97443),x97444)),f329(f329(f9(x97442,x97441),x97443),x97445))),f329(f329(f9(x97442,x97441),x97443),f329(f329(f107(f883(x97442,a869)),x97444),x97445))),f329(f329(f9(x97442,x97441),x97443),f329(f329(f116(f883(x97442,a869)),x97444),x97445)))+P24(f329(f329(f331(x97442),f406(x97443,x97445,x97444,x97442,x97441)),f329(f329(f107(f883(x97442,a869)),x97444),x97445))) % 178.07/177.94 [9070]E(f329(f329(f127(x90701),x90702),x90703),f329(f329(f127(x90701),x90704),x90705))+~E(f329(f329(f174(x90701),f329(f194(f876(x90701)),x90704)),x90702),x90704)+~E(f329(f329(f174(x90701),f329(f194(f876(x90701)),x90702)),x90704),x90702)+~E(x90705,f329(f329(f127(x90701),f329(f329(f137(x90701),f329(f194(f876(x90701)),x90704)),x90702)),x90703))+~E(f329(f329(f127(x90701),f329(f329(f137(x90701),f329(f194(f876(x90701)),x90702)),x90704)),x90705),x90703) % 178.07/177.94 [9468]~P105(x94682)+E(f329(f329(f147(x94681,x94682,x94683),x94684),f169(x94681,x94684,x94685)),x94685)+~P29(x94682,f329(f329(f153(x94681,x94682),x94683),x94685))+~P24(f329(f329(f331(x94681),x94684),f329(f171(x94681),x94685)))+~E(f329(f140(x94681),f329(f135(x94681,f329(f329(f8(x94682,a869,x94681),f329(a326,f329(x94683,x94684))),x94683)),x94685)),x94684) % 178.07/177.94 [9806]~P68(x98061)+~P24(f329(f67(x98061,x98061,f82(x98061),x98062,x98063),x98065))+~P24(f329(f329(f331(x98061),x98064),x98063))+P24(f329(f329(f331(x98061),x98062),x98063))+P24(f329(f67(x98061,x98061,f82(x98061),x98064,f329(f329(f307(x98061),x98062),f329(f329(f22(f883(x98061,a869)),x98063),f329(f329(f307(x98061),x98064),f193(f883(x98061,a869)))))),x98065)) % 178.07/177.94 [7213]E(x72131,x72132)+~P21(x72134,x72135,x72133,x72136)+~E(f329(x72133,x72131),f329(x72133,x72132))+~P24(f329(f329(f331(x72134),x72132),x72136))+~P24(f329(f329(f331(x72134),x72131),x72136)) % 178.07/177.94 [6473]~P139(x64734)+E(x64731,x64732)+~E(x64735,x64736)+E(x64733,f2(x64734))+~E(f329(f329(f81(x64734),x64735),f329(f329(f82(x64734),x64733),x64731)),f329(f329(f81(x64734),x64736),f329(f329(f82(x64734),x64733),x64732))) % 178.07/177.94 [7506]~P27(x75061)+~P105(x75061)+~P24(f329(f329(f244(x75061),x75062),f329(x75065,x75066)))+~P24(f329(f329(f331(x75063),x75066),x75064))+P24(f329(f329(f244(x75061),x75062),f329(f329(f43(x75063,x75061),x75064),x75065))) % 178.07/177.94 [8191]~P27(x81911)+~P105(x81911)+~P24(f329(f329(f244(x81911),f329(x81914,x81916)),x81915))+~P24(f329(f329(f331(x81912),x81916),x81913))+P24(f329(f329(f244(x81911),f329(f329(f42(x81912,x81911),x81913),x81914)),x81915)) % 178.07/177.94 [8452]~P15(x84522,x84525,x84526,x84521)+~P24(f329(f62(x84522),x84524))+~P24(f329(f62(x84522),x84523))+~E(f329(f329(f107(f883(x84522,a869)),x84523),x84524),f193(f883(x84522,a869)))+E(f329(x84521,f329(f329(f116(f883(x84522,a869)),x84523),x84524)),f329(f74(x84525,x84525,x84525,f329(x84521,x84523)),f329(x84521,x84524))) % 178.07/177.94 [8762]E(x87621,x87622)+~P52(x87624,x87625,x87626,x87623,x87627)+~E(f329(x87623,x87621),f329(x87623,x87622))+~P24(f329(f329(f331(x87625),x87622),x87627))+~P24(f329(f329(f331(x87625),x87621),x87627)) % 178.07/177.94 [10051]~P24(f329(x100512,x100514))+~E(x100515,f329(f135(x100511,x100512),x100517))+E(f329(f135(x100511,x100512),x100513),f329(f329(f150(x100511),x100514),x100515))+~E(x100513,f329(f329(f127(x100511),x100516),f329(f329(f150(x100511),x100514),x100517)))+P24(f329(x100512,f735(x100515,x100514,x100513,x100512,x100511,x100516,x100517))) % 178.07/177.94 [10052]~P24(f329(x100524,x100522))+~E(x100523,f329(f135(x100521,x100524),x100527))+E(f329(f329(f150(x100521),x100522),x100523),f329(f135(x100521,x100524),x100525))+~E(x100525,f329(f329(f127(x100521),x100526),f329(f329(f150(x100521),x100522),x100527)))+P24(f329(x100524,f739(x100525,x100524,x100523,x100522,x100521,x100526,x100527))) % 178.07/177.94 [10086]~P24(f329(x100862,x100864))+~E(x100865,f329(f135(x100861,x100862),x100867))+E(f329(f135(x100861,x100862),x100863),f329(f329(f150(x100861),x100864),x100865))+~E(x100863,f329(f329(f127(x100861),x100866),f329(f329(f150(x100861),x100864),x100867)))+P24(f329(f329(f331(x100861),f735(x100865,x100864,x100863,x100862,x100861,x100866,x100867)),f329(f171(x100861),x100866))) % 178.07/177.94 [10087]~P24(f329(x100874,x100872))+~E(x100873,f329(f135(x100871,x100874),x100877))+E(f329(f329(f150(x100871),x100872),x100873),f329(f135(x100871,x100874),x100875))+~E(x100875,f329(f329(f127(x100871),x100876),f329(f329(f150(x100871),x100872),x100877)))+P24(f329(f329(f331(x100871),f739(x100875,x100874,x100873,x100872,x100871,x100876,x100877)),f329(f171(x100871),x100876))) % 178.07/177.94 [10090]~P6(x100901,x100907,x100906)+~P9(x100901,f883(x100905,a869),x100906,x100904)+P24(f329(f329(f331(x100901),f538(x100902,x100903,x100904,x100905,x100906,x100907,x100901)),x100907))+~P24(f329(f329(f331(f883(x100901,a869)),x100903),f329(f329(f61(x100901),x100907),x100906)))+P24(f329(f329(f331(f883(x100905,a869)),f329(f329(f43(x100901,f883(x100905,a869)),x100903),x100904)),x100902)) % 178.07/177.94 [10135]~P6(x101352,x101356,x101357)+~P9(x101352,f883(x101351,a869),x101357,x101354)+~P24(f329(f329(f331(f883(x101352,a869)),x101353),f329(f329(f61(x101352),x101356),x101357)))+~P24(f329(f329(f331(f883(x101351,a869)),f329(x101354,f538(x101355,x101353,x101354,x101351,x101357,x101356,x101352))),x101355))+P24(f329(f329(f331(f883(x101351,a869)),f329(f329(f43(x101352,f883(x101351,a869)),x101353),x101354)),x101355)) % 178.07/177.94 [8360]~P74(x83602)+~P21(x83601,x83605,x83608,x83604)+~E(x83603,f329(f74(x83605,x83602,x83601,x83606),x83608))+~E(x83607,f329(f308(x83601,x83605,x83608),x83604))+E(f329(f329(f9(x83601,x83602),x83603),x83604),f329(f329(f9(x83605,x83602),x83606),x83607)) % 178.07/177.94 [10139]~P74(x101392)+~P21(x101395,x101391,x101398,x101397)+~E(f329(x101396,f575(x101393,x101396,x101394,x101397,x101398,x101391,x101395,x101392)),f329(f329(f74(x101391,x101392,x101395,x101393),x101398),f575(x101393,x101396,x101394,x101397,x101398,x101391,x101395,x101392)))+~E(x101394,f329(f308(x101395,x101391,x101398),x101397))+E(f329(f329(f9(x101391,x101392),x101393),x101394),f329(f329(f9(x101395,x101392),x101396),x101397)) % 178.07/177.94 [10141]~P70(x101412)+~P21(x101411,x101415,x101418,x101414)+~E(x101417,f329(f308(x101411,x101415,x101418),x101414))+E(f329(f329(f6(x101411,x101412),x101413),x101414),f329(f329(f6(x101415,x101412),x101416),x101417))+P24(f329(f329(f331(x101411),f747(x101416,x101413,x101417,x101414,x101418,x101415,x101411,x101412)),x101414)) % 178.07/177.94 [10142]~P74(x101422)+~P21(x101421,x101425,x101428,x101424)+~E(x101427,f329(f308(x101421,x101425,x101428),x101424))+E(f329(f329(f9(x101421,x101422),x101423),x101424),f329(f329(f9(x101425,x101422),x101426),x101427))+P24(f329(f329(f331(x101421),f575(x101426,x101423,x101427,x101424,x101428,x101425,x101421,x101422)),x101424)) % 178.07/177.94 [10148]~P70(x101482)+~P21(x101485,x101481,x101488,x101487)+~E(x101484,f329(f308(x101485,x101481,x101488),x101487))+~E(f329(x101486,f747(x101483,x101486,x101484,x101487,x101488,x101481,x101485,x101482)),f329(x101483,f329(x101488,f747(x101483,x101486,x101484,x101487,x101488,x101481,x101485,x101482))))+E(f329(f329(f6(x101481,x101482),x101483),x101484),f329(f329(f6(x101485,x101482),x101486),x101487)) % 178.07/177.94 [9523]~E(f329(f194(f876(x95232)),x95235),f329(f194(f876(x95231)),x95233))+~E(f329(f194(f876(x95232)),x95234),f329(f194(f876(x95231)),x95233))+~E(f329(f329(f329(f73(x95231,f879(x95232)),f329(f177(x95231,x95232),f329(f329(f181(x95231,x95232),x95233),x95234))),x95236),f329(f236(x95232),x95237)),f329(f329(f329(f73(x95231,f879(x95232)),f329(f177(x95231,x95232),f329(f329(f181(x95231,x95232),x95233),x95235))),x95236),f329(f236(x95232),x95238)))+E(f329(f177(x95231,x95232),f329(f329(f181(x95231,x95232),x95233),x95234)),f329(f177(x95231,x95232),f329(f329(f181(x95231,x95232),x95233),x95235)))+P24(f329(f329(f331(x95231),x95236),f329(f171(x95231),x95233))) % 178.07/177.94 [9636]~P19(x96366,x96362,x96365,x96367,x96368,x96361)+~P24(f329(f62(x96362),x96364))+~P24(f329(f62(x96362),x96363))+~E(f329(f329(f107(f883(x96362,a869)),x96363),x96364),f193(f883(x96362,a869)))+E(f329(x96361,f329(f329(f116(f883(x96362,a869)),x96363),x96364)),f329(f329(x96365,f329(x96361,x96363)),f329(x96361,x96364))) % 178.07/177.94 [10038]~P19(x100388,x100382,x100385,x100387,x100386,x100381)+~E(f329(x100386,f832(x100384,x100383,x100381,x100386,x100387,x100385,x100382)),x100387)+~P24(f329(f62(x100382),x100383))+~P24(f329(f62(x100382),x100384))+E(f329(x100381,f329(f329(f116(f883(x100382,a869)),x100383),x100384)),f329(f329(x100385,f329(x100381,x100383)),f329(x100381,x100384))) % 178.07/177.94 [10095]~P19(x100958,x100952,x100955,x100957,x100956,x100951)+~P24(f329(f62(x100952),x100953))+~P24(f329(f62(x100952),x100954))+E(f329(x100951,f329(f329(f116(f883(x100952,a869)),x100953),x100954)),f329(f329(x100955,f329(x100951,x100953)),f329(x100951,x100954)))+P24(f329(f329(f331(x100952),f832(x100954,x100953,x100951,x100956,x100957,x100955,x100952)),f329(f329(f107(f883(x100952,a869)),x100953),x100954))) % 178.07/177.94 [9794]~P6(x97944,x97948,x97945)+~P6(x97941,x97949,x97943)+~P10(x97941,x97944,f883(x97942,a869),x97943,x97945,x97947)+P9(x97941,f883(x97942,a869),x97943,f329(f329(f8(f883(x97944,f883(x97942,a869)),f883(x97942,a869),x97941),f329(f43(x97944,f883(x97942,a869)),f329(f283(x97944,x97944,x97945),f329(f329(f307(x97944),x97946),f193(f883(x97944,a869)))))),x97947))+~P24(f329(f329(f331(x97944),x97946),x97948)) % 178.07/177.94 [5400]~P105(x54003)+~P29(x54003,x54001)+E(x54001,f713(x54002,x54003))+~E(f329(f171(x54003),x54001),x54002)+~P24(f329(f62(x54003),x54002))+~P24(f329(f136(x54003),x54001)) % 178.07/177.94 [5022]~P112(x50222)+~P124(x50222)+~P129(x50222)+~P140(x50222)+E(x50221,f2(x50222))+~E(f329(f329(f254(x50222),x50221),x50223),f2(x50222)) % 178.07/177.94 [5023]~P112(x50232)+~P124(x50232)+~P129(x50232)+~P140(x50232)+~E(x50231,f2(a875))+~E(f329(f329(f254(x50232),x50233),x50231),f2(x50232)) % 178.07/177.94 [6455]~P86(x64551)+~E(x64553,f2(x64551))+~E(x64552,f2(x64551))+E(f329(f329(f81(x64551),x64552),x64553),f2(x64551))+~P24(f329(f329(f243(x64551),f2(x64551)),x64553))+~P24(f329(f329(f243(x64551),f2(x64551)),x64552)) % 178.07/177.94 [8823]~E(f329(f263(a875,a875),x88233),f2(a875))+~E(x88231,f329(f329(f81(a875),f329(f329(f82(a875),f329(f263(a875,a875),x88233)),x88232)),f329(f267(a875,a875),x88233)))+P24(f329(f48(x88231,x88232),x88233))+~P24(f329(f329(f243(a875),f329(f267(a875,a875),x88233)),f2(a875)))+P24(f329(f329(f244(a875),f2(a875)),x88232))+~P24(f329(f329(f244(a875),x88232),f329(f267(a875,a875),x88233))) % 178.07/177.94 [8831]E(x88311,f2(a875))+~E(x88312,f329(f329(f81(a875),f329(f329(f82(a875),f329(f263(a875,a875),x88313)),x88311)),f329(f267(a875,a875),x88313)))+P24(f329(f48(x88312,x88311),x88313))+~P24(f329(f329(f244(a875),f2(a875)),x88311))+~P24(f329(f329(f243(a875),f2(a875)),f329(f267(a875,a875),x88313)))+~P24(f329(f329(f244(a875),f329(f267(a875,a875),x88313)),x88311)) % 178.07/177.94 [8849]~E(f329(f263(a875,a875),x88493),f2(a875))+~E(x88491,f329(f329(f81(a875),f329(f329(f82(a875),f329(f263(a875,a875),x88493)),x88492)),f329(f267(a875,a875),x88493)))+P24(f329(f48(x88491,x88492),x88493))+~P24(f329(f329(f244(a875),f2(a875)),x88492))+~P24(f329(f329(f243(a875),f2(a875)),f329(f267(a875,a875),x88493)))+~P24(f329(f329(f244(a875),f329(f267(a875,a875),x88493)),x88492)) % 178.07/177.94 [6836]~P63(x68362)+E(x68361,f193(f883(x68362,a869)))+E(x68363,f193(f883(x68362,a869)))+~P24(f329(f62(x68362),x68361))+~P24(f329(f62(x68362),x68363))+E(f13(x68362,f329(f329(f116(f883(x68362,a869)),x68363),x68361)),f329(f329(f116(x68362),f13(x68362,x68363)),f13(x68362,x68361))) % 178.07/177.94 [6837]~P63(x68372)+E(x68371,f193(f883(x68372,a869)))+E(x68373,f193(f883(x68372,a869)))+~P24(f329(f62(x68372),x68371))+~P24(f329(f62(x68372),x68373))+E(f10(x68372,f329(f329(f116(f883(x68372,a869)),x68373),x68371)),f329(f329(f107(x68372),f10(x68372,x68373)),f10(x68372,x68371))) % 178.07/177.94 [6838]~P105(x68382)+E(x68381,f193(f883(x68382,a869)))+E(x68383,f193(f883(x68382,a869)))+~P24(f329(f62(x68382),x68381))+~P24(f329(f62(x68382),x68383))+E(f14(x68382,f329(f329(f116(f883(x68382,a869)),x68383),x68381)),f329(f329(f241(x68382),f14(x68382,x68383)),f14(x68382,x68381))) % 178.07/177.94 [6839]~P105(x68392)+E(x68391,f193(f883(x68392,a869)))+E(x68393,f193(f883(x68392,a869)))+~P24(f329(f62(x68392),x68391))+~P24(f329(f62(x68392),x68393))+E(f15(x68392,f329(f329(f116(f883(x68392,a869)),x68393),x68391)),f329(f329(f242(x68392),f15(x68392,x68393)),f15(x68392,x68391))) % 178.07/177.94 [7481]~P95(x74812)+E(x74811,f193(f883(x74812,a869)))+E(x74813,f193(f883(x74812,a869)))+~P24(f329(f62(x74812),x74811))+~P24(f329(f62(x74812),x74813))+E(f329(f329(f82(x74812),f329(f64(x74812,f82(x74812)),x74813)),f329(f64(x74812,f82(x74812)),x74811)),f329(f64(x74812,f82(x74812)),f329(f329(f116(f883(x74812,a869)),x74813),x74811))) % 178.07/177.94 [7638]~P105(x76382)+E(x76381,f193(f883(x76382,a869)))+E(x76383,f193(f883(x76382,a869)))+~P24(f329(f62(x76382),x76381))+~P24(f329(f62(x76382),x76383))+E(f329(f329(f242(x76382),f11(x76382,f242(x76382),x76383)),f11(x76382,f242(x76382),x76381)),f11(x76382,f242(x76382),f329(f329(f116(f883(x76382,a869)),x76383),x76381))) % 178.07/177.94 [7639]~P105(x76392)+E(x76391,f193(f883(x76392,a869)))+E(x76393,f193(f883(x76392,a869)))+~P24(f329(f62(x76392),x76391))+~P24(f329(f62(x76392),x76393))+E(f329(f329(f241(x76392),f12(x76392,f241(x76392),x76393)),f12(x76392,f241(x76392),x76391)),f12(x76392,f241(x76392),f329(f329(f116(f883(x76392,a869)),x76393),x76391))) % 178.07/177.94 [8672]~P24(f329(x86721,x86723))+P24(f329(x86721,f445(x86721,x86722)))+P24(f329(x86721,f433(x86721,x86722)))+~P24(f329(f329(f244(a1),f2(a1)),x86722))+~P24(f329(f329(f331(a1),x86723),f300(a1,f79(a1),x86722)))+P24(f329(x86721,f329(f329(f22(a1),f433(x86721,x86722)),f329(f329(f82(a1),f444(x86721,x86722)),x86722)))) % 178.07/177.94 [8968]~P24(f329(x89681,x89683))+~P24(f329(x89681,f433(x89681,x89682)))+P24(f329(x89681,f445(x89681,x89682)))+~P24(f329(f329(f244(a1),f2(a1)),x89682))+~P24(f329(f329(f331(a1),x89683),f300(a1,f79(a1),x89682)))+~P24(f329(x89681,f329(f329(f22(a1),f433(x89681,x89682)),f329(f329(f82(a1),f444(x89681,x89682)),x89682)))) % 178.07/177.94 [10173]~P97(x101732)+E(x101731,f193(f883(x101732,a869)))+E(x101733,f193(f883(x101732,a869)))+~P24(f329(f62(x101732),x101731))+~P24(f329(f62(x101732),x101733))+E(f10(x101732,f329(f249(x101732),f329(f329(f8(f883(x101732,a869),a869,x101732),f88(x101732)),f329(f329(f8(f883(x101732,f883(x101732,a869)),f883(x101732,a869),x101732),f329(f8(f883(x101732,a869),a869,x101732),f88(x101732))),f329(f329(f7(x101732,f883(x101732,f883(x101732,a869)),f883(x101732,f883(x101732,a869))),f329(f329(f8(f883(x101732,f883(f883(x101732,a869),f883(x101732,a869))),f883(f883(x101732,f883(x101732,a869)),f883(x101732,f883(x101732,a869))),x101732),f18(x101732,f883(x101732,a869),f883(x101732,a869))),f329(f329(f8(f883(x101732,f883(x101732,f883(a869,a869))),f883(x101732,f883(f883(x101732,a869),f883(x101732,a869))),x101732),f329(f8(f883(x101732,f883(a869,a869)),f883(f883(x101732,a869),f883(x101732,a869)),x101732),f18(x101732,a869,a869))),f329(f329(f8(f883(x101732,f883(x101732,a869)),f883(x101732,f883(x101732,f883(a869,a869))),x101732),f329(f8(f883(x101732,a869),f883(x101732,f883(a869,a869)),x101732),f329(f8(a869,f883(a869,a869),x101732),a327))),f329(f329(f7(x101732,f883(x101732,f883(x101732,x101732)),f883(x101732,f883(x101732,a869))),f329(f329(f8(f883(f883(x101732,x101732),f883(x101732,a869)),f883(f883(x101732,f883(x101732,x101732)),f883(x101732,f883(x101732,a869))),x101732),f8(f883(x101732,x101732),f883(x101732,a869),x101732)),f329(f329(f8(f883(x101732,a869),f883(f883(x101732,x101732),f883(x101732,a869)),x101732),f8(x101732,a869,x101732)),a326))),f116(x101732)))))),f329(f329(f7(x101732,f883(x101732,a869),f883(x101732,a869)),f329(f329(f8(f883(a869,a869),f883(f883(x101732,a869),f883(x101732,a869)),x101732),f8(a869,a869,x101732)),f329(f329(f8(a869,f883(a869,a869),x101732),a327),f329(f329(f7(x101732,f883(x101732,a869),a869),f331(x101732)),x101733)))),f329(f329(f7(x101732,f883(x101732,a869),a869),f331(x101732)),x101731))))))),f329(f329(f116(x101732),f10(x101732,x101733)),f10(x101732,x101731))) % 178.07/177.94 [10174]~P97(x101742)+E(x101741,f193(f883(x101742,a869)))+E(x101743,f193(f883(x101742,a869)))+~P24(f329(f62(x101742),x101741))+~P24(f329(f62(x101742),x101743))+E(f13(x101742,f329(f249(x101742),f329(f329(f8(f883(x101742,a869),a869,x101742),f88(x101742)),f329(f329(f8(f883(x101742,f883(x101742,a869)),f883(x101742,a869),x101742),f329(f8(f883(x101742,a869),a869,x101742),f88(x101742))),f329(f329(f7(x101742,f883(x101742,f883(x101742,a869)),f883(x101742,f883(x101742,a869))),f329(f329(f8(f883(x101742,f883(f883(x101742,a869),f883(x101742,a869))),f883(f883(x101742,f883(x101742,a869)),f883(x101742,f883(x101742,a869))),x101742),f18(x101742,f883(x101742,a869),f883(x101742,a869))),f329(f329(f8(f883(x101742,f883(x101742,f883(a869,a869))),f883(x101742,f883(f883(x101742,a869),f883(x101742,a869))),x101742),f329(f8(f883(x101742,f883(a869,a869)),f883(f883(x101742,a869),f883(x101742,a869)),x101742),f18(x101742,a869,a869))),f329(f329(f8(f883(x101742,f883(x101742,a869)),f883(x101742,f883(x101742,f883(a869,a869))),x101742),f329(f8(f883(x101742,a869),f883(x101742,f883(a869,a869)),x101742),f329(f8(a869,f883(a869,a869),x101742),a327))),f329(f329(f7(x101742,f883(x101742,f883(x101742,x101742)),f883(x101742,f883(x101742,a869))),f329(f329(f8(f883(f883(x101742,x101742),f883(x101742,a869)),f883(f883(x101742,f883(x101742,x101742)),f883(x101742,f883(x101742,a869))),x101742),f8(f883(x101742,x101742),f883(x101742,a869),x101742)),f329(f329(f8(f883(x101742,a869),f883(f883(x101742,x101742),f883(x101742,a869)),x101742),f8(x101742,a869,x101742)),a326))),f107(x101742)))))),f329(f329(f7(x101742,f883(x101742,a869),f883(x101742,a869)),f329(f329(f8(f883(a869,a869),f883(f883(x101742,a869),f883(x101742,a869)),x101742),f8(a869,a869,x101742)),f329(f329(f8(a869,f883(a869,a869),x101742),a327),f329(f329(f7(x101742,f883(x101742,a869),a869),f331(x101742)),x101743)))),f329(f329(f7(x101742,f883(x101742,a869),a869),f331(x101742)),x101741))))))),f329(f329(f107(x101742),f13(x101742,x101743)),f13(x101742,x101741))) % 178.07/177.94 [10175]~P105(x101752)+E(x101751,f193(f883(x101752,a869)))+E(x101753,f193(f883(x101752,a869)))+~P24(f329(f62(x101752),x101751))+~P24(f329(f62(x101752),x101753))+E(f11(x101752,f242(x101752),f329(f249(x101752),f329(f329(f8(f883(x101752,a869),a869,x101752),f88(x101752)),f329(f329(f8(f883(x101752,f883(x101752,a869)),f883(x101752,a869),x101752),f329(f8(f883(x101752,a869),a869,x101752),f88(x101752))),f329(f329(f7(x101752,f883(x101752,f883(x101752,a869)),f883(x101752,f883(x101752,a869))),f329(f329(f8(f883(x101752,f883(f883(x101752,a869),f883(x101752,a869))),f883(f883(x101752,f883(x101752,a869)),f883(x101752,f883(x101752,a869))),x101752),f18(x101752,f883(x101752,a869),f883(x101752,a869))),f329(f329(f8(f883(x101752,f883(x101752,f883(a869,a869))),f883(x101752,f883(f883(x101752,a869),f883(x101752,a869))),x101752),f329(f8(f883(x101752,f883(a869,a869)),f883(f883(x101752,a869),f883(x101752,a869)),x101752),f18(x101752,a869,a869))),f329(f329(f8(f883(x101752,f883(x101752,a869)),f883(x101752,f883(x101752,f883(a869,a869))),x101752),f329(f8(f883(x101752,a869),f883(x101752,f883(a869,a869)),x101752),f329(f8(a869,f883(a869,a869),x101752),a327))),f329(f329(f7(x101752,f883(x101752,f883(x101752,x101752)),f883(x101752,f883(x101752,a869))),f329(f329(f8(f883(f883(x101752,x101752),f883(x101752,a869)),f883(f883(x101752,f883(x101752,x101752)),f883(x101752,f883(x101752,a869))),x101752),f8(f883(x101752,x101752),f883(x101752,a869),x101752)),f329(f329(f8(f883(x101752,a869),f883(f883(x101752,x101752),f883(x101752,a869)),x101752),f8(x101752,a869,x101752)),a326))),f241(x101752)))))),f329(f329(f7(x101752,f883(x101752,a869),f883(x101752,a869)),f329(f329(f8(f883(a869,a869),f883(f883(x101752,a869),f883(x101752,a869)),x101752),f8(a869,a869,x101752)),f329(f329(f8(a869,f883(a869,a869),x101752),a327),f329(f329(f7(x101752,f883(x101752,a869),a869),f331(x101752)),x101753)))),f329(f329(f7(x101752,f883(x101752,a869),a869),f331(x101752)),x101751))))))),f329(f329(f241(x101752),f11(x101752,f242(x101752),x101753)),f11(x101752,f242(x101752),x101751))) % 178.07/177.94 [10176]~P105(x101762)+E(x101761,f193(f883(x101762,a869)))+E(x101763,f193(f883(x101762,a869)))+~P24(f329(f62(x101762),x101761))+~P24(f329(f62(x101762),x101763))+E(f12(x101762,f241(x101762),f329(f249(x101762),f329(f329(f8(f883(x101762,a869),a869,x101762),f88(x101762)),f329(f329(f8(f883(x101762,f883(x101762,a869)),f883(x101762,a869),x101762),f329(f8(f883(x101762,a869),a869,x101762),f88(x101762))),f329(f329(f7(x101762,f883(x101762,f883(x101762,a869)),f883(x101762,f883(x101762,a869))),f329(f329(f8(f883(x101762,f883(f883(x101762,a869),f883(x101762,a869))),f883(f883(x101762,f883(x101762,a869)),f883(x101762,f883(x101762,a869))),x101762),f18(x101762,f883(x101762,a869),f883(x101762,a869))),f329(f329(f8(f883(x101762,f883(x101762,f883(a869,a869))),f883(x101762,f883(f883(x101762,a869),f883(x101762,a869))),x101762),f329(f8(f883(x101762,f883(a869,a869)),f883(f883(x101762,a869),f883(x101762,a869)),x101762),f18(x101762,a869,a869))),f329(f329(f8(f883(x101762,f883(x101762,a869)),f883(x101762,f883(x101762,f883(a869,a869))),x101762),f329(f8(f883(x101762,a869),f883(x101762,f883(a869,a869)),x101762),f329(f8(a869,f883(a869,a869),x101762),a327))),f329(f329(f7(x101762,f883(x101762,f883(x101762,x101762)),f883(x101762,f883(x101762,a869))),f329(f329(f8(f883(f883(x101762,x101762),f883(x101762,a869)),f883(f883(x101762,f883(x101762,x101762)),f883(x101762,f883(x101762,a869))),x101762),f8(f883(x101762,x101762),f883(x101762,a869),x101762)),f329(f329(f8(f883(x101762,a869),f883(f883(x101762,x101762),f883(x101762,a869)),x101762),f8(x101762,a869,x101762)),a326))),f242(x101762)))))),f329(f329(f7(x101762,f883(x101762,a869),f883(x101762,a869)),f329(f329(f8(f883(a869,a869),f883(f883(x101762,a869),f883(x101762,a869)),x101762),f8(a869,a869,x101762)),f329(f329(f8(a869,f883(a869,a869),x101762),a327),f329(f329(f7(x101762,f883(x101762,a869),a869),f331(x101762)),x101763)))),f329(f329(f7(x101762,f883(x101762,a869),a869),f331(x101762)),x101761))))))),f329(f329(f242(x101762),f12(x101762,f241(x101762),x101763)),f12(x101762,f241(x101762),x101761))) % 178.07/177.94 [7164]~P120(x71643)+E(x71641,x71642)+~E(f329(f329(f254(x71643),x71641),x71644),f329(f329(f254(x71643),x71642),x71644))+~P24(f329(f329(f243(x71643),f2(x71643)),x71642))+~P24(f329(f329(f243(x71643),f2(x71643)),x71641))+~P24(f329(f329(f244(a875),f2(a875)),x71644)) % 178.07/177.94 [7438]~P105(x74382)+E(x74381,f193(f883(x74382,a869)))+~P24(f329(f62(x74382),x74381))+~P24(f329(f329(f331(x74382),x74384),x74381))+P24(f329(f329(f244(x74382),x74383),x74384))+~P24(f329(f329(f244(x74382),x74383),f329(f64(x74382,f241(x74382)),x74381))) % 178.07/177.94 [7439]~P100(x74392)+E(x74391,f193(f883(x74392,a869)))+~P24(f329(f62(x74392),x74391))+~P24(f329(f329(f331(x74392),x74394),x74391))+P24(f329(f329(f243(x74392),x74393),x74394))+~P24(f329(f329(f243(x74392),x74393),f329(f64(x74392,f107(x74392)),x74391))) % 178.07/177.94 [7440]~P105(x74402)+E(x74401,f193(f883(x74402,a869)))+~P24(f329(f62(x74402),x74401))+~P24(f329(f329(f331(x74402),x74404),x74401))+P24(f329(f329(f243(x74402),x74403),x74404))+~P24(f329(f329(f243(x74402),x74403),f329(f64(x74402,f241(x74402)),x74401))) % 178.07/177.94 [7338]E(x73381,f2(a1))+E(f329(f329(f39(a1),x73382),x73381),x73383)+~P24(f329(f329(f243(a1),x73384),f2(a1)))+~E(x73382,f329(f329(f81(a1),f329(f329(f82(a1),x73381),x73383)),x73384))+P24(f329(f329(f244(a1),f2(a1)),x73381))+~P24(f329(f329(f244(a1),x73381),x73384)) % 178.07/177.94 [7353]E(f45(a1,x73532,x73531),x73533)+E(x73531,f2(a1))+~P24(f329(f329(f243(a1),x73533),f2(a1)))+~E(x73532,f329(f329(f81(a1),f329(f329(f82(a1),x73531),x73534)),x73533))+P24(f329(f329(f244(a1),f2(a1)),x73531))+~P24(f329(f329(f244(a1),x73531),x73533)) % 178.07/177.94 [7480]E(x74801,f2(a1))+E(f329(f329(f39(a1),x74802),x74801),x74803)+~E(x74802,f329(f329(f81(a1),f329(f329(f82(a1),x74801),x74803)),x74804))+~P24(f329(f329(f244(a1),f2(a1)),x74801))+~P24(f329(f329(f243(a1),f2(a1)),x74804))+~P24(f329(f329(f244(a1),x74804),x74801)) % 178.07/177.94 [7502]E(f45(a1,x75022,x75021),x75023)+E(x75021,f2(a1))+~E(x75022,f329(f329(f81(a1),f329(f329(f82(a1),x75021),x75024)),x75023))+~P24(f329(f329(f244(a1),f2(a1)),x75021))+~P24(f329(f329(f243(a1),f2(a1)),x75023))+~P24(f329(f329(f244(a1),x75023),x75021)) % 178.07/177.94 [7642]~P105(x76422)+E(x76421,f193(f883(x76422,a869)))+~P24(f329(f62(x76422),x76421))+~P24(f329(f329(f244(x76422),x76424),x76423))+~P24(f329(f329(f331(x76422),x76424),x76421))+P24(f329(f329(f244(x76422),f329(f64(x76422,f241(x76422)),x76421)),x76423)) % 178.07/177.94 [7643]~P105(x76432)+E(x76431,f193(f883(x76432,a869)))+~P24(f329(f62(x76432),x76431))+~P24(f329(f329(f243(x76432),x76434),x76433))+~P24(f329(f329(f331(x76432),x76434),x76431))+P24(f329(f329(f243(x76432),f329(f64(x76432,f241(x76432)),x76431)),x76433)) % 178.07/177.94 [8216]~P24(f329(f329(f243(a1),x82164),f2(a1)))+~E(x82161,f329(f329(f81(a1),f329(f329(f82(a1),x82162),x82163)),x82164))+~P24(f329(f329(f243(a1),f2(a1)),x82164))+~P24(f329(f329(f244(a1),x82164),x82162))+~P24(f329(f329(f244(a1),x82162),x82164))+P24(f329(f49(x82161,x82162),f329(f329(f264(a1,a1),x82163),x82164))) % 178.07/177.94 [9162]~P58(x91623)+~P58(x91624)+E(x91621,x91622)+~E(f329(f194(f876(x91623)),x91622),f329(f194(f876(x91624)),f56(x91624)))+~E(f329(f194(f876(x91623)),x91621),f329(f194(f876(x91624)),f56(x91624)))+~E(f329(f74(f879(x91623),x91623,x91624,f240(x91623)),f329(f177(x91624,x91623),f329(f329(f181(x91624,x91623),f56(x91624)),x91621))),f329(f74(f879(x91623),x91623,x91624,f240(x91623)),f329(f177(x91624,x91623),f329(f329(f181(x91624,x91623),f56(x91624)),x91622)))) % 178.07/177.94 [8380]~P107(x83801)+P24(f329(f329(f244(f883(x83801,a869)),f300(x83801,x83802,x83803)),f300(x83801,x83804,x83805)))+~P24(f329(f329(f244(x83801),x83803),x83805))+~P24(f329(f329(f243(x83801),x83804),x83802))+~P24(f329(f329(f243(x83801),x83804),x83805))+~P24(f329(f329(f243(x83801),x83803),x83805)) % 178.07/177.94 [8381]~P107(x83811)+P24(f329(f329(f244(f883(x83811,a869)),f300(x83811,x83812,x83813)),f300(x83811,x83814,x83815)))+~P24(f329(f329(f244(x83811),x83814),x83812))+~P24(f329(f329(f243(x83811),x83813),x83815))+~P24(f329(f329(f243(x83811),x83814),x83815))+~P24(f329(f329(f243(x83811),x83814),x83812)) % 178.07/177.94 [9228]P54(x92282,x92283,x92284,x92281)+E(x92281,f193(f883(x92282,a869)))+~P24(f329(f62(x92282),x92284))+~P24(f329(f62(x92282),x92281))+~P24(f329(f329(x92283,f691(x92281,x92284,x92283,x92282)),x92285))+~P24(f329(f329(f331(x92282),x92285),x92281)) % 178.07/177.94 [9376]~E(x93763,x93765)+~P70(x93761)+~P74(x93761)+~P39(x93763)+E(f329(f329(f6(a1,x93761),x93762),x93763),f329(f329(f6(a1,x93761),x93764),x93765))+P24(f329(f329(f243(a1),f2(a1)),f476(x93762,x93764,x93763,x93765,x93761))) % 178.07/177.94 [9377]~E(x93773,x93775)+~P70(x93771)+~P74(x93771)+~P39(x93773)+E(f329(f329(f9(a1,x93771),x93772),x93773),f329(f329(f9(a1,x93771),x93774),x93775))+P24(f329(f329(f243(a1),f2(a1)),f466(x93772,x93774,x93773,x93775,x93771))) % 178.07/177.94 [9544]~E(x95445,x95443)+~P70(x95441)+~P74(x95441)+~P39(x95445)+~E(f329(x95442,f476(x95444,x95442,x95445,x95443,x95441)),f329(x95444,f476(x95444,x95442,x95445,x95443,x95441)))+E(f329(f329(f6(a1,x95441),x95442),x95443),f329(f329(f6(a1,x95441),x95444),x95445)) % 178.07/177.94 [9545]~E(x95455,x95453)+~P70(x95451)+~P74(x95451)+~P39(x95455)+~E(f329(x95452,f466(x95454,x95452,x95455,x95453,x95451)),f329(x95454,f466(x95454,x95452,x95455,x95453,x95451)))+E(f329(f329(f9(a1,x95451),x95452),x95453),f329(f329(f9(a1,x95451),x95454),x95455)) % 178.07/177.94 [9633]~P77(x96333)+E(f329(x96331,x96332),f2(x96333))+~E(f329(f329(f6(x96334,x96333),x96331),x96335),f2(x96333))+~P24(f329(f62(x96334),x96335))+P24(f329(f329(f331(x96334),f407(x96332,x96331,x96335,x96334,x96333)),x96335))+~P24(f329(f329(f331(x96334),x96332),x96335)) % 178.07/177.94 [9768]~P77(x97683)+E(f329(x97681,x97682),f2(x97683))+~E(f329(f329(f6(x97684,x97683),x97681),x97685),f2(x97683))+~P24(f329(f62(x97684),x97685))+~P24(f329(f329(f331(x97684),x97682),x97685))+~P24(f329(f329(f243(x97683),f2(x97683)),f329(x97681,f407(x97682,x97681,x97685,x97684,x97683)))) % 178.07/177.94 [8297]~P125(x82971)+~P24(f329(f329(f243(x82971),f2(x82971)),x82973))+~P24(f329(f329(f244(x82971),x82973),x82975))+~P24(f329(f329(f244(x82971),x82972),x82974))+~P24(f329(f329(f244(x82971),f2(x82971)),x82974))+P24(f329(f329(f244(x82971),f329(f329(f82(x82971),x82972),x82973)),f329(f329(f82(x82971),x82974),x82975))) % 178.07/177.94 [8298]~P125(x82981)+~P24(f329(f329(f243(x82981),f2(x82981)),x82983))+~P24(f329(f329(f243(x82981),f2(x82981)),x82982))+~P24(f329(f329(f244(x82981),x82983),x82985))+~P24(f329(f329(f244(x82981),x82982),x82984))+P24(f329(f329(f244(x82981),f329(f329(f82(x82981),x82982),x82983)),f329(f329(f82(x82981),x82984),x82985))) % 178.07/177.94 [8299]~P125(x82991)+~P24(f329(f329(f243(x82991),x82992),x82994))+~P24(f329(f329(f243(x82991),f2(x82991)),x82993))+~P24(f329(f329(f244(x82991),x82993),x82995))+~P24(f329(f329(f244(x82991),f2(x82991)),x82992))+P24(f329(f329(f244(x82991),f329(f329(f82(x82991),x82992),x82993)),f329(f329(f82(x82991),x82994),x82995))) % 178.07/177.94 [8300]~P125(x83001)+~P24(f329(f329(f243(x83001),x83003),x83005))+~P24(f329(f329(f243(x83001),f2(x83001)),x83002))+~P24(f329(f329(f244(x83001),x83002),x83004))+~P24(f329(f329(f244(x83001),f2(x83001)),x83003))+P24(f329(f329(f244(x83001),f329(f329(f82(x83001),x83002),x83003)),f329(f329(f82(x83001),x83004),x83005))) % 178.07/177.94 [8301]~P62(x83011)+~P24(f329(f329(f243(x83011),x83012),x83014))+~P24(f329(f329(f244(x83011),x83015),x83013))+~P24(f329(f329(f244(x83011),f2(x83011)),x83015))+~P24(f329(f329(f244(x83011),f2(x83011)),x83012))+P24(f329(f329(f244(x83011),f329(f329(f287(x83011),x83012),x83013)),f329(f329(f287(x83011),x83014),x83015))) % 178.07/177.94 [8302]~P62(x83021)+~P24(f329(f329(f243(x83021),x83025),x83023))+~P24(f329(f329(f243(x83021),f2(x83021)),x83022))+~P24(f329(f329(f244(x83021),x83022),x83024))+~P24(f329(f329(f244(x83021),f2(x83021)),x83025))+P24(f329(f329(f244(x83021),f329(f329(f287(x83021),x83022),x83023)),f329(f329(f287(x83021),x83024),x83025))) % 178.07/177.94 [8303]~P132(x83031)+~P24(f329(f329(f243(x83031),x83033),x83035))+~P24(f329(f329(f243(x83031),x83032),x83034))+~P24(f329(f329(f243(x83031),f2(x83031)),x83033))+~P24(f329(f329(f243(x83031),f2(x83031)),x83034))+P24(f329(f329(f243(x83031),f329(f329(f82(x83031),x83032),x83033)),f329(f329(f82(x83031),x83034),x83035))) % 178.07/177.94 [8304]~P132(x83041)+~P24(f329(f329(f243(x83041),x83043),x83045))+~P24(f329(f329(f243(x83041),x83042),x83044))+~P24(f329(f329(f243(x83041),f2(x83041)),x83043))+~P24(f329(f329(f243(x83041),f2(x83041)),x83042))+P24(f329(f329(f243(x83041),f329(f329(f82(x83041),x83042),x83043)),f329(f329(f82(x83041),x83044),x83045))) % 178.07/177.94 [8305]~P62(x83051)+~P24(f329(f329(f244(x83051),f2(x83051)),x83055))+~P24(f329(f329(f243(x83051),x83055),x83053))+~P24(f329(f329(f243(x83051),x83052),x83054))+~P24(f329(f329(f243(x83051),f2(x83051)),x83052))+P24(f329(f329(f243(x83051),f329(f329(f287(x83051),x83052),x83053)),f329(f329(f287(x83051),x83054),x83055))) % 178.07/177.94 [9672]~P70(x96725)+~P82(x96725)+E(x96721,f193(f883(x96722,a869)))+~P24(f329(f62(x96722),x96721))+P24(f329(f329(f331(x96722),f459(x96723,x96724,x96721,x96722,x96725)),x96721))+P24(f329(f329(f244(x96725),f329(f329(f6(x96722,x96725),x96724),x96721)),f329(f329(f6(x96722,x96725),x96723),x96721))) % 178.07/177.94 [9790]~P70(x97901)+~P84(x97901)+~P24(f329(f62(x97902),x97905))+~P24(f329(f329(f243(x97901),f2(x97901)),f329(x97903,f379(x97903,x97904,x97905,x97902,x97901))))+P24(f329(f329(f243(x97901),f329(f329(f6(x97902,x97901),x97903),x97904)),f329(f329(f6(x97902,x97901),x97903),x97905)))+~P24(f329(f329(f243(f883(x97902,a869)),x97904),x97905)) % 178.07/177.94 [9958]~P70(x99583)+~P82(x99583)+E(x99581,f193(f883(x99582,a869)))+~P24(f329(f62(x99582),x99581))+~P24(f329(f329(f244(x99583),f329(x99584,f459(x99585,x99584,x99581,x99582,x99583))),f329(x99585,f459(x99585,x99584,x99581,x99582,x99583))))+P24(f329(f329(f244(x99583),f329(f329(f6(x99582,x99583),x99584),x99581)),f329(f329(f6(x99582,x99583),x99585),x99581))) % 178.07/177.94 [7023]~P13(x70232,x70235,x70234)+E(x70231,f193(f883(x70232,a869)))+E(x70233,f193(f883(x70232,a869)))+~P24(f329(f62(x70232),x70231))+~P24(f329(f62(x70232),x70233))+E(f329(x70234,f329(f329(f116(f883(x70232,a869)),x70233),x70231)),f329(f329(x70235,f329(x70234,x70233)),f329(x70234,x70231))) % 178.07/177.94 [7608]~P144(x76081,x76084,x76083)+P24(f329(x76081,x76082))+~P24(f329(f329(f244(a1),x76084),f2(a1)))+~P24(f329(f329(f243(a1),x76085),f2(a1)))+~E(x76083,f329(f329(f81(a1),f329(f329(f82(a1),x76084),x76082)),x76085))+~P24(f329(f329(f244(a1),x76084),x76085)) % 178.07/177.94 [7609]~P143(x76091,x76094,x76093)+P24(f329(x76091,x76092))+~P24(f329(f329(f244(a1),x76094),f2(a1)))+~P24(f329(f329(f243(a1),x76092),f2(a1)))+~E(x76093,f329(f329(f81(a1),f329(f329(f82(a1),x76094),x76095)),x76092))+~P24(f329(f329(f244(a1),x76094),x76092)) % 178.07/177.94 [7651]~P144(x76511,x76514,x76513)+P24(f329(x76511,x76512))+~E(x76513,f329(f329(f81(a1),f329(f329(f82(a1),x76514),x76512)),x76515))+~P24(f329(f329(f244(a1),f2(a1)),x76514))+~P24(f329(f329(f243(a1),f2(a1)),x76515))+~P24(f329(f329(f244(a1),x76515),x76514)) % 178.07/177.94 [7652]~P143(x76521,x76524,x76523)+P24(f329(x76521,x76522))+~E(x76523,f329(f329(f81(a1),f329(f329(f82(a1),x76524),x76525)),x76522))+~P24(f329(f329(f244(a1),f2(a1)),x76524))+~P24(f329(f329(f243(a1),f2(a1)),x76522))+~P24(f329(f329(f244(a1),x76522),x76524)) % 178.07/177.94 [8593]P24(f329(f329(x85931,x85932),x85933))+~P24(f329(f329(x85931,f329(f329(f39(a1),x85934),x85935)),f45(a1,x85934,x85935)))+~P24(f329(f329(f244(a1),x85935),f2(a1)))+~P24(f329(f329(f243(a1),x85933),f2(a1)))+~E(x85934,f329(f329(f81(a1),f329(f329(f82(a1),x85935),x85932)),x85933))+~P24(f329(f329(f244(a1),x85935),x85933)) % 178.07/177.94 [8602]P24(f329(f329(x86021,x86022),x86023))+~P24(f329(f329(x86021,f329(f329(f39(a1),x86024),x86025)),f45(a1,x86024,x86025)))+~E(x86024,f329(f329(f81(a1),f329(f329(f82(a1),x86025),x86022)),x86023))+~P24(f329(f329(f244(a1),f2(a1)),x86025))+~P24(f329(f329(f243(a1),f2(a1)),x86023))+~P24(f329(f329(f244(a1),x86023),x86025)) % 178.07/177.94 [8837]E(x88371,x88372)+~P51(x88373,x88375,x88374)+~P24(f329(f329(f331(x88373),x88372),x88375))+~P24(f329(f329(f331(x88373),x88371),x88375))+P24(f329(f329(f331(f882(x88373,x88373)),f329(f329(f264(x88373,x88373),x88371),x88372)),x88374))+P24(f329(f329(f331(f882(x88373,x88373)),f329(f329(f264(x88373,x88373),x88372),x88371)),x88374)) % 178.07/177.94 [9699]~P70(x96995)+~P84(x96995)+~P24(f329(f62(x96991),x96994))+P24(f329(f329(f243(x96995),f329(f329(f6(x96991,x96995),x96992),x96993)),f329(f329(f6(x96991,x96995),x96992),x96994)))+~P24(f329(f329(f243(f883(x96991,a869)),x96993),x96994))+P24(f329(f329(f331(x96991),f379(x96992,x96993,x96994,x96991,x96995)),f329(f329(f22(f883(x96991,a869)),x96994),x96993))) % 178.07/177.94 [9798]E(x97981,f193(f883(x97982,a869)))+~P24(f329(f62(x97982),x97983))+~P24(f329(f62(x97982),x97981))+P24(f329(f329(f331(f882(f883(x97982,a869),f883(x97982,a869))),f329(f329(f264(f883(x97982,a869),f883(x97982,a869)),x97983),x97981)),f320(x97982,x97984)))+~P24(f329(f329(f331(x97982),x97985),x97981))+~P24(f329(f329(f331(f882(x97982,x97982)),f329(f329(f264(x97982,x97982),f699(x97984,x97981,x97983,x97982)),x97985)),x97984)) % 178.07/177.94 [9799]E(x97991,f193(f883(x97992,a869)))+~P24(f329(f62(x97992),x97993))+~P24(f329(f62(x97992),x97991))+P24(f329(f329(f331(f882(f883(x97992,a869),f883(x97992,a869))),f329(f329(f264(f883(x97992,a869),f883(x97992,a869)),x97993),x97991)),f320(x97992,x97994)))+~P24(f329(f329(f331(x97992),x97995),x97991))+~P24(f329(f329(f331(f882(x97992,x97992)),f329(f329(f264(x97992,x97992),f742(x97994,x97991,x97993,x97992)),x97995)),x97994)) % 178.07/177.94 [9962]~P77(x99621)+~E(f329(f329(f6(x99625,x99621),x99622),x99626),x99624)+~P24(f329(f62(x99625),x99626))+P24(f329(f329(f331(x99625),f409(x99623,x99624,x99622,x99626,x99625,x99621)),x99626))+P24(f329(f329(f243(x99621),f329(x99622,x99623)),x99624))+~P24(f329(f329(f331(x99625),x99623),x99626)) % 178.07/177.94 [10009]~P77(x100091)+~E(f329(f329(f6(x100095,x100091),x100092),x100096),x100094)+~P24(f329(f62(x100095),x100096))+~P24(f329(f329(f331(x100095),x100093),x100096))+~P24(f329(f329(f243(x100091),f2(x100091)),f329(x100092,f409(x100093,x100094,x100092,x100096,x100095,x100091))))+P24(f329(f329(f243(x100091),f329(x100092,x100093)),x100094)) % 178.07/177.94 [10121]~E(x101215,x101218)+~E(x101214,x101217)+~P70(x101212)+~P106(x101211)+E(f329(f329(f6(x101211,x101212),x101213),f329(f299(x101211,x101214),x101215)),f329(f329(f6(x101211,x101212),x101216),f329(f299(x101211,x101217),x101218)))+P24(f329(f329(f243(x101211),x101214),f749(x101213,x101216,x101215,x101218,x101214,x101217,x101211,x101212))) % 178.07/177.94 [10138]~E(x101387,x101384)+~E(x101388,x101385)+~P70(x101382)+~P106(x101381)+~E(f329(x101383,f749(x101386,x101383,x101388,x101385,x101387,x101384,x101381,x101382)),f329(x101386,f749(x101386,x101383,x101388,x101385,x101387,x101384,x101381,x101382)))+E(f329(f329(f6(x101381,x101382),x101383),f329(f299(x101381,x101384),x101385)),f329(f329(f6(x101381,x101382),x101386),f329(f299(x101381,x101387),x101388))) % 178.07/177.94 [10140]~E(x101404,x101407)+~E(x101405,x101408)+~P70(x101402)+~P106(x101401)+E(f329(f329(f6(x101401,x101402),x101403),f329(f299(x101401,x101404),x101405)),f329(f329(f6(x101401,x101402),x101406),f329(f299(x101401,x101407),x101408)))+P24(f329(f329(f244(x101401),f749(x101403,x101406,x101405,x101408,x101404,x101407,x101401,x101402)),x101405)) % 178.07/177.94 [9804]~P6(x98045,x98049,x98046)+~P6(x98041,x980410,x98043)+~P10(x98041,x98045,f883(x98042,a869),x98043,x98046,x98048)+~P24(f329(f329(f331(x98045),x98047),x98049))+~P24(f329(f329(f331(x98041),x98044),x980410))+E(f329(f329(f43(x98041,f883(x98042,a869)),f329(f283(x98041,x98041,x98043),f329(f329(f307(x98041),x98044),f193(f883(x98041,a869))))),f329(f329(f8(f883(x98045,f883(x98042,a869)),f883(x98042,a869),x98041),f329(f43(x98045,f883(x98042,a869)),f329(f283(x98045,x98045,x98046),f329(f329(f307(x98045),x98047),f193(f883(x98045,a869)))))),x98048)),f329(f329(x98048,x98044),x98047)) % 178.07/177.94 [5565]~P105(x55653)+~P29(x55653,x55652)+~P29(x55653,x55651)+E(x55651,x55652)+~E(f329(f171(x55653),x55651),f329(f171(x55653),x55652))+~P24(f329(f136(x55653),x55652))+~P24(f329(f136(x55653),x55651)) % 178.07/177.94 [4905]~P112(x49052)+~P124(x49052)+~P129(x49052)+~P140(x49052)+~E(x49053,f2(x49052))+E(x49051,f2(a875))+E(f329(f329(f254(x49052),x49053),x49051),f2(x49052)) % 178.07/177.94 [9103]E(x91031,f2(a875))+~E(x91032,f329(f329(f81(a875),f329(f329(f82(a875),f329(f263(a875,a875),x91033)),x91031)),f329(f267(a875,a875),x91033)))+P24(f329(f48(x91032,x91031),x91033))+~P24(f329(f329(f243(a875),f329(f267(a875,a875),x91033)),f2(a875)))+~P24(f329(f329(f243(a875),f2(a875)),f329(f267(a875,a875),x91033)))+~P24(f329(f329(f244(a875),x91031),f329(f267(a875,a875),x91033)))+~P24(f329(f329(f244(a875),f329(f267(a875,a875),x91033)),x91031)) % 178.07/177.94 [9112]~E(f329(f263(a875,a875),x91123),f2(a875))+~E(x91121,f329(f329(f81(a875),f329(f329(f82(a875),f329(f263(a875,a875),x91123)),x91122)),f329(f267(a875,a875),x91123)))+P24(f329(f48(x91121,x91122),x91123))+~P24(f329(f329(f243(a875),f329(f267(a875,a875),x91123)),f2(a875)))+~P24(f329(f329(f243(a875),f2(a875)),f329(f267(a875,a875),x91123)))+~P24(f329(f329(f244(a875),x91122),f329(f267(a875,a875),x91123)))+~P24(f329(f329(f244(a875),f329(f267(a875,a875),x91123)),x91122)) % 178.07/177.94 [7963]~P68(x79632)+E(x79631,f193(f883(x79632,a869)))+E(x79633,f193(f883(x79632,a869)))+~P24(f329(f62(x79632),x79631))+~P24(f329(f62(x79632),x79633))+~E(f329(f329(f107(f883(x79632,a869)),x79633),x79631),f193(f883(x79632,a869)))+E(f329(f329(f82(x79632),f329(f64(x79632,f82(x79632)),x79633)),f329(f64(x79632,f82(x79632)),x79631)),f329(f64(x79632,f82(x79632)),f329(f329(f116(f883(x79632,a869)),x79633),x79631))) % 178.07/177.94 [7747]E(x77471,f2(a1))+E(f329(f329(f39(a1),x77472),x77471),x77473)+~P24(f329(f329(f243(a1),x77474),f2(a1)))+~E(x77472,f329(f329(f81(a1),f329(f329(f82(a1),x77471),x77473)),x77474))+~P24(f329(f329(f243(a1),f2(a1)),x77474))+~P24(f329(f329(f244(a1),x77474),x77471))+~P24(f329(f329(f244(a1),x77471),x77474)) % 178.07/177.94 [7754]E(f45(a1,x77542,x77541),x77543)+E(x77541,f2(a1))+~P24(f329(f329(f243(a1),x77543),f2(a1)))+~E(x77542,f329(f329(f81(a1),f329(f329(f82(a1),x77541),x77544)),x77543))+~P24(f329(f329(f243(a1),f2(a1)),x77543))+~P24(f329(f329(f244(a1),x77543),x77541))+~P24(f329(f329(f244(a1),x77541),x77543)) % 178.07/177.94 [7659]~P14(x76592,x76595,x76594)+E(x76591,f193(f883(x76592,a869)))+E(x76593,f193(f883(x76592,a869)))+~P24(f329(f62(x76592),x76591))+~P24(f329(f62(x76592),x76593))+~E(f329(f329(f107(f883(x76592,a869)),x76593),x76591),f193(f883(x76592,a869)))+E(f329(x76594,f329(f329(f116(f883(x76592,a869)),x76593),x76591)),f329(f329(x76595,f329(x76594,x76593)),f329(x76594,x76591))) % 178.07/177.94 [9349]~P21(x93493,x93491,x93495,x93494)+~P21(x93491,x93493,x93496,x93492)+E(f329(f38(x93491),x93492),f329(f38(x93493),x93494))+~P24(f329(f62(x93493),x93494))+~P24(f329(f62(x93491),x93492))+~P24(f329(f329(f243(f883(x93493,a869)),f329(f308(x93491,x93493,x93496),x93492)),x93494))+~P24(f329(f329(f243(f883(x93491,a869)),f329(f308(x93493,x93491,x93495),x93494)),x93492)) % 178.07/177.94 [9293]~P24(f329(f329(f244(a1),f329(f329(f81(a1),f329(f329(f82(a1),x92935),x92931)),x92936)),f2(a1)))+~E(f329(f329(f81(a1),f329(f329(f82(a1),x92933),x92932)),x92934),f329(f329(f81(a1),f329(f329(f82(a1),x92935),x92931)),x92936))+~P24(f329(f329(f244(a1),f2(a1)),x92935))+~P24(f329(f329(f243(a1),f2(a1)),x92936))+~P24(f329(f329(f244(a1),x92934),x92933))+~P24(f329(f329(f243(a1),x92935),x92933))+P24(f329(f329(f243(a1),x92931),x92932)) % 178.07/177.94 [9056]~E(f329(f329(f81(a1),f329(f329(f82(a1),x90563),x90561)),x90564),f329(f329(f81(a1),f329(f329(f82(a1),x90565),x90562)),x90566))+~P24(f329(f329(f244(a1),f2(a1)),x90565))+~P24(f329(f329(f243(a1),f2(a1)),x90564))+~P24(f329(f329(f244(a1),x90566),x90565))+~P24(f329(f329(f243(a1),x90565),x90563))+P24(f329(f329(f243(a1),x90561),x90562))+~P24(f329(f329(f243(a1),f2(a1)),f329(f329(f81(a1),f329(f329(f82(a1),x90565),x90562)),x90566))) % 178.07/177.94 [9234]~P128(x92341)+~E(f329(f329(f81(x92341),x92342),x92344),f79(x92341))+~P24(f329(f329(f243(x92341),f2(x92341)),x92344))+~P24(f329(f329(f243(x92341),f2(x92341)),x92342))+~P24(f329(f329(f244(x92341),x92345),x92346))+~P24(f329(f329(f244(x92341),x92343),x92346))+P24(f329(f329(f244(x92341),f329(f329(f81(x92341),f329(f329(f82(x92341),x92342),x92343)),f329(f329(f82(x92341),x92344),x92345))),x92346)) % 178.07/177.94 [9235]~P127(x92351)+~E(f329(f329(f81(x92351),x92352),x92354),f79(x92351))+~P24(f329(f329(f243(x92351),x92355),x92356))+~P24(f329(f329(f243(x92351),x92353),x92356))+~P24(f329(f329(f243(x92351),f2(x92351)),x92354))+~P24(f329(f329(f243(x92351),f2(x92351)),x92352))+P24(f329(f329(f243(x92351),f329(f329(f81(x92351),f329(f329(f82(x92351),x92352),x92353)),f329(f329(f82(x92351),x92354),x92355))),x92356)) % 178.07/177.94 [10054]~P6(x100547,x100546,x100545)+E(x100541,x100542)+~P9(x100547,f883(x100544,a869),x100545,x100543)+E(f329(x100543,f545(x100541,x100542,x100543,x100544,x100545,x100546,x100547)),f329(x100543,f546(x100541,x100542,x100543,x100544,x100545,x100546,x100547)))+~E(f329(f329(f43(x100547,f883(x100544,a869)),x100541),x100543),f329(f329(f43(x100547,f883(x100544,a869)),x100542),x100543))+~P24(f329(f329(f331(f883(x100547,a869)),x100542),f329(f329(f61(x100547),x100546),x100545)))+~P24(f329(f329(f331(f883(x100547,a869)),x100541),f329(f329(f61(x100547),x100546),x100545))) % 178.07/177.94 [10088]~P6(x100883,x100887,x100886)+E(x100881,x100882)+~P9(x100883,f883(x100885,a869),x100886,x100884)+~E(f329(f329(f43(x100883,f883(x100885,a869)),x100881),x100884),f329(f329(f43(x100883,f883(x100885,a869)),x100882),x100884))+P24(f329(f329(f331(x100883),f546(x100881,x100882,x100884,x100885,x100886,x100887,x100883)),x100887))+~P24(f329(f329(f331(f883(x100883,a869)),x100882),f329(f329(f61(x100883),x100887),x100886)))+~P24(f329(f329(f331(f883(x100883,a869)),x100881),f329(f329(f61(x100883),x100887),x100886))) % 178.07/177.94 [10089]~P6(x100893,x100897,x100896)+E(x100891,x100892)+~P9(x100893,f883(x100895,a869),x100896,x100894)+~E(f329(f329(f43(x100893,f883(x100895,a869)),x100891),x100894),f329(f329(f43(x100893,f883(x100895,a869)),x100892),x100894))+P24(f329(f329(f331(x100893),f545(x100891,x100892,x100894,x100895,x100896,x100897,x100893)),x100897))+~P24(f329(f329(f331(f883(x100893,a869)),x100892),f329(f329(f61(x100893),x100897),x100896)))+~P24(f329(f329(f331(f883(x100893,a869)),x100891),f329(f329(f61(x100893),x100897),x100896))) % 178.07/177.94 [10157]E(x101571,x101572)+~P6(x101573,x101576,x101577)+~P9(x101573,f883(x101574,a869),x101577,x101575)+~E(f329(f329(f43(x101573,f883(x101574,a869)),x101571),x101575),f329(f329(f43(x101573,f883(x101574,a869)),x101572),x101575))+~P24(f329(f329(f331(f882(x101573,x101573)),f329(f329(f264(x101573,x101573),f546(x101571,x101572,x101575,x101574,x101577,x101576,x101573)),f545(x101571,x101572,x101575,x101574,x101577,x101576,x101573))),x101577))+~P24(f329(f329(f331(f883(x101573,a869)),x101572),f329(f329(f61(x101573),x101576),x101577)))+~P24(f329(f329(f331(f883(x101573,a869)),x101571),f329(f329(f61(x101573),x101576),x101577))) % 178.07/177.94 [9055]~P6(x90551,x90557,x90554)+~E(x90555,x90556)+~P24(f329(f329(f331(x90551),x90553),x90556))+~P24(f329(f329(f331(x90551),x90552),x90555))+~P24(f329(f329(f331(f883(x90551,a869)),x90556),f329(f329(f61(x90551),x90557),x90554)))+~P24(f329(f329(f331(f883(x90551,a869)),x90555),f329(f329(f61(x90551),x90557),x90554)))+P24(f329(f329(f331(f882(x90551,x90551)),f329(f329(f264(x90551,x90551),x90552),x90553)),x90554)) % 178.07/177.94 [9190]E(x91901,x91902)+~P6(x91903,x91904,x91905)+~P24(f329(f329(f331(x91903),x91906),x91902))+~P24(f329(f329(f331(x91903),x91907),x91901))+~P24(f329(f329(f331(f883(x91903,a869)),x91902),f329(f329(f61(x91903),x91904),x91905)))+~P24(f329(f329(f331(f883(x91903,a869)),x91901),f329(f329(f61(x91903),x91904),x91905)))+~P24(f329(f329(f331(f882(x91903,x91903)),f329(f329(f264(x91903,x91903),x91907),x91906)),x91905)) % 178.07/177.94 [10180]~P6(x101809,x101808,x101807)+~P6(x101801,x1018011,x1018010)+~P10(x101801,x101809,f883(x101806,a869),x1018010,x101807,x101805)+P24(f329(f329(f331(x101801),f539(x101802,x101803,x101804,x101805,x101806,x101807,x101808,x101809,x1018010,x1018011,x101801)),x1018011))+~P24(f329(f329(f331(f883(x101809,a869)),x101803),f329(f329(f61(x101809),x101808),x101807)))+~P24(f329(f329(f331(f883(x101801,a869)),x101804),f329(f329(f61(x101801),x1018011),x1018010)))+P24(f329(f329(f331(f883(x101806,a869)),f329(f329(f43(x101801,f883(x101806,a869)),x101804),f329(f329(f8(f883(x101809,f883(x101806,a869)),f883(x101806,a869),x101801),f329(f43(x101809,f883(x101806,a869)),x101803)),x101805))),x101802)) % 178.07/177.94 [10181]~P6(x1018111,x1018110,x101819)+~P6(x101811,x101818,x101817)+~P10(x1018111,x101811,f883(x101816,a869),x101819,x101817,x101815)+P24(f329(f329(f331(x101811),f540(x101812,x101813,x101814,x101815,x101816,x101817,x101818,x101811,x101819,x1018110,x1018111)),x101818))+~P24(f329(f329(f331(f883(x1018111,a869)),x101814),f329(f329(f61(x1018111),x1018110),x101819)))+~P24(f329(f329(f331(f883(x101811,a869)),x101813),f329(f329(f61(x101811),x101818),x101817)))+P24(f329(f329(f331(f883(x101816,a869)),f329(f329(f43(x1018111,f883(x101816,a869)),x101814),f329(f329(f8(f883(x101811,f883(x101816,a869)),f883(x101816,a869),x1018111),f329(f43(x101811,f883(x101816,a869)),x101813)),x101815))),x101812)) % 178.07/177.94 [10184]~P6(x101842,x101848,x101849)+~P6(x101844,x1018410,x1018411)+~P10(x101842,x101844,f883(x101841,a869),x101849,x1018411,x101846)+~P24(f329(f329(f331(f883(x101842,a869)),x101843),f329(f329(f61(x101842),x101848),x101849)))+~P24(f329(f329(f331(f883(x101844,a869)),x101845),f329(f329(f61(x101844),x1018410),x1018411)))+~P24(f329(f329(f331(f883(x101841,a869)),f329(f329(x101846,f539(x101847,x101845,x101843,x101846,x101841,x1018411,x1018410,x101844,x101849,x101848,x101842)),f540(x101847,x101845,x101843,x101846,x101841,x1018411,x1018410,x101844,x101849,x101848,x101842))),x101847))+P24(f329(f329(f331(f883(x101841,a869)),f329(f329(f43(x101842,f883(x101841,a869)),x101843),f329(f329(f8(f883(x101844,f883(x101841,a869)),f883(x101841,a869),x101842),f329(f43(x101844,f883(x101841,a869)),x101845)),x101846))),x101847)) % 178.07/177.94 [9090]E(x90901,x90902)+~P105(x90904)+~P21(x90903,x90904,x90905,f329(f329(f116(f883(x90903,a869)),f329(f171(x90903),x90901)),f329(f171(x90903),x90902)))+~E(f329(f171(x90903),x90901),f329(f171(x90903),x90902))+~P29(x90904,f329(f329(f153(x90903,x90904),x90905),x90902))+~P29(x90904,f329(f329(f153(x90903,x90904),x90905),x90901))+~P24(f329(f136(x90904),f329(f329(f153(x90903,x90904),x90905),x90902)))+~P24(f329(f136(x90904),f329(f329(f153(x90903,x90904),x90905),x90901))) % 178.07/177.94 %EqnAxiom % 178.07/177.94 [1]E(x11,x11) % 178.07/177.94 [2]E(x22,x21)+~E(x21,x22) % 178.07/177.94 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 178.07/177.94 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 178.07/177.94 [5]~E(x51,x52)+E(f106(x51),f106(x52)) % 178.07/177.94 [6]~E(x61,x62)+E(f22(x61),f22(x62)) % 178.07/177.94 [7]~E(x71,x72)+E(f193(x71),f193(x72)) % 178.07/177.94 [8]~E(x81,x82)+E(f329(x81,x83),f329(x82,x83)) % 178.07/177.94 [9]~E(x91,x92)+E(f329(x93,x91),f329(x93,x92)) % 178.07/177.94 [10]~E(x101,x102)+E(f32(x101),f32(x102)) % 178.07/177.94 [11]~E(x111,x112)+E(f150(x111),f150(x112)) % 178.07/177.94 [12]~E(x121,x122)+E(f107(x121),f107(x122)) % 178.07/177.94 [13]~E(x131,x132)+E(f241(x131),f241(x132)) % 178.07/177.94 [14]~E(x141,x142)+E(f116(x141),f116(x142)) % 178.07/177.94 [15]~E(x151,x152)+E(f242(x151),f242(x152)) % 178.07/177.94 [16]~E(x161,x162)+E(f108(x161),f108(x162)) % 178.07/177.94 [17]~E(x171,x172)+E(f35(x171),f35(x172)) % 178.07/177.94 [18]~E(x181,x182)+E(f85(x181),f85(x182)) % 178.07/177.94 [19]~E(x191,x192)+E(f10(x191,x193),f10(x192,x193)) % 178.07/177.94 [20]~E(x201,x202)+E(f10(x203,x201),f10(x203,x202)) % 178.07/177.94 [21]~E(x211,x212)+E(f883(x211,x213),f883(x212,x213)) % 178.07/177.94 [22]~E(x221,x222)+E(f883(x223,x221),f883(x223,x222)) % 178.07/177.94 [23]~E(x231,x232)+E(f540(x231,x233,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312),f540(x232,x233,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312)) % 178.07/177.94 [24]~E(x241,x242)+E(f540(x243,x241,x244,x245,x246,x247,x248,x249,x2410,x2411,x2412),f540(x243,x242,x244,x245,x246,x247,x248,x249,x2410,x2411,x2412)) % 178.07/177.94 [25]~E(x251,x252)+E(f540(x253,x254,x251,x255,x256,x257,x258,x259,x2510,x2511,x2512),f540(x253,x254,x252,x255,x256,x257,x258,x259,x2510,x2511,x2512)) % 178.07/177.94 [26]~E(x261,x262)+E(f540(x263,x264,x265,x261,x266,x267,x268,x269,x2610,x2611,x2612),f540(x263,x264,x265,x262,x266,x267,x268,x269,x2610,x2611,x2612)) % 178.07/177.94 [27]~E(x271,x272)+E(f540(x273,x274,x275,x276,x271,x277,x278,x279,x2710,x2711,x2712),f540(x273,x274,x275,x276,x272,x277,x278,x279,x2710,x2711,x2712)) % 178.07/177.94 [28]~E(x281,x282)+E(f540(x283,x284,x285,x286,x287,x281,x288,x289,x2810,x2811,x2812),f540(x283,x284,x285,x286,x287,x282,x288,x289,x2810,x2811,x2812)) % 178.07/177.94 [29]~E(x291,x292)+E(f540(x293,x294,x295,x296,x297,x298,x291,x299,x2910,x2911,x2912),f540(x293,x294,x295,x296,x297,x298,x292,x299,x2910,x2911,x2912)) % 178.07/177.94 [30]~E(x301,x302)+E(f540(x303,x304,x305,x306,x307,x308,x309,x301,x3010,x3011,x3012),f540(x303,x304,x305,x306,x307,x308,x309,x302,x3010,x3011,x3012)) % 178.07/177.94 [31]~E(x311,x312)+E(f540(x313,x314,x315,x316,x317,x318,x319,x3110,x311,x3111,x3112),f540(x313,x314,x315,x316,x317,x318,x319,x3110,x312,x3111,x3112)) % 178.07/177.94 [32]~E(x321,x322)+E(f540(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x321,x3212),f540(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x322,x3212)) % 178.07/177.94 [33]~E(x331,x332)+E(f540(x333,x334,x335,x336,x337,x338,x339,x3310,x3311,x3312,x331),f540(x333,x334,x335,x336,x337,x338,x339,x3310,x3311,x3312,x332)) % 178.07/177.94 [34]~E(x341,x342)+E(f79(x341),f79(x342)) % 178.07/177.94 [35]~E(x351,x352)+E(f876(x351),f876(x352)) % 178.07/177.94 [36]~E(x361,x362)+E(f539(x361,x363,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612),f539(x362,x363,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612)) % 178.07/177.94 [37]~E(x371,x372)+E(f539(x373,x371,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712),f539(x373,x372,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712)) % 178.07/177.94 [38]~E(x381,x382)+E(f539(x383,x384,x381,x385,x386,x387,x388,x389,x3810,x3811,x3812),f539(x383,x384,x382,x385,x386,x387,x388,x389,x3810,x3811,x3812)) % 178.07/177.94 [39]~E(x391,x392)+E(f539(x393,x394,x395,x391,x396,x397,x398,x399,x3910,x3911,x3912),f539(x393,x394,x395,x392,x396,x397,x398,x399,x3910,x3911,x3912)) % 178.07/177.94 [40]~E(x401,x402)+E(f539(x403,x404,x405,x406,x401,x407,x408,x409,x4010,x4011,x4012),f539(x403,x404,x405,x406,x402,x407,x408,x409,x4010,x4011,x4012)) % 178.07/177.94 [41]~E(x411,x412)+E(f539(x413,x414,x415,x416,x417,x411,x418,x419,x4110,x4111,x4112),f539(x413,x414,x415,x416,x417,x412,x418,x419,x4110,x4111,x4112)) % 178.07/177.94 [42]~E(x421,x422)+E(f539(x423,x424,x425,x426,x427,x428,x421,x429,x4210,x4211,x4212),f539(x423,x424,x425,x426,x427,x428,x422,x429,x4210,x4211,x4212)) % 178.07/177.94 [43]~E(x431,x432)+E(f539(x433,x434,x435,x436,x437,x438,x439,x431,x4310,x4311,x4312),f539(x433,x434,x435,x436,x437,x438,x439,x432,x4310,x4311,x4312)) % 178.07/177.94 [44]~E(x441,x442)+E(f539(x443,x444,x445,x446,x447,x448,x449,x4410,x441,x4411,x4412),f539(x443,x444,x445,x446,x447,x448,x449,x4410,x442,x4411,x4412)) % 178.07/177.94 [45]~E(x451,x452)+E(f539(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x451,x4512),f539(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x452,x4512)) % 178.07/177.94 [46]~E(x461,x462)+E(f539(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x4612,x461),f539(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x4612,x462)) % 178.07/177.94 [47]~E(x471,x472)+E(f117(x471),f117(x472)) % 178.07/177.94 [48]~E(x481,x482)+E(f331(x481),f331(x482)) % 178.07/177.94 [49]~E(x491,x492)+E(f81(x491),f81(x492)) % 178.07/177.94 [50]~E(x501,x502)+E(f4(x501),f4(x502)) % 178.07/177.94 [51]~E(x511,x512)+E(f179(x511,x513),f179(x512,x513)) % 178.07/177.94 [52]~E(x521,x522)+E(f179(x523,x521),f179(x523,x522)) % 178.07/177.94 [53]~E(x531,x532)+E(f874(x531),f874(x532)) % 178.07/177.94 [54]~E(x541,x542)+E(f879(x541),f879(x542)) % 178.07/177.94 [55]~E(x551,x552)+E(f5(x551),f5(x552)) % 178.07/177.94 [56]~E(x561,x562)+E(f877(x561),f877(x562)) % 178.07/177.94 [57]~E(x571,x572)+E(f83(x571,x573),f83(x572,x573)) % 178.07/177.94 [58]~E(x581,x582)+E(f83(x583,x581),f83(x583,x582)) % 178.07/177.94 [59]~E(x591,x592)+E(f308(x591,x593,x594),f308(x592,x593,x594)) % 178.07/177.94 [60]~E(x601,x602)+E(f308(x603,x601,x604),f308(x603,x602,x604)) % 178.07/177.94 [61]~E(x611,x612)+E(f308(x613,x614,x611),f308(x613,x614,x612)) % 178.07/177.94 [62]~E(x621,x622)+E(f109(x621),f109(x622)) % 178.07/177.94 [63]~E(x631,x632)+E(f12(x631,x633,x634),f12(x632,x633,x634)) % 178.07/177.94 [64]~E(x641,x642)+E(f12(x643,x641,x644),f12(x643,x642,x644)) % 178.07/177.94 [65]~E(x651,x652)+E(f12(x653,x654,x651),f12(x653,x654,x652)) % 178.07/177.94 [66]~E(x661,x662)+E(f80(x661),f80(x662)) % 178.07/177.94 [67]~E(x671,x672)+E(f155(x671,x673,x674,x675),f155(x672,x673,x674,x675)) % 178.07/177.94 [68]~E(x681,x682)+E(f155(x683,x681,x684,x685),f155(x683,x682,x684,x685)) % 178.07/177.94 [69]~E(x691,x692)+E(f155(x693,x694,x691,x695),f155(x693,x694,x692,x695)) % 178.07/177.94 [70]~E(x701,x702)+E(f155(x703,x704,x705,x701),f155(x703,x704,x705,x702)) % 178.07/177.94 [71]~E(x711,x712)+E(f194(x711),f194(x712)) % 178.07/177.94 [72]~E(x721,x722)+E(f119(x721),f119(x722)) % 178.07/177.94 [73]~E(x731,x732)+E(f243(x731),f243(x732)) % 178.07/177.94 [74]~E(x741,x742)+E(f147(x741,x743,x744),f147(x742,x743,x744)) % 178.07/177.94 [75]~E(x751,x752)+E(f147(x753,x751,x754),f147(x753,x752,x754)) % 178.07/177.94 [76]~E(x761,x762)+E(f147(x763,x764,x761),f147(x763,x764,x762)) % 178.07/177.94 [77]~E(x771,x772)+E(f82(x771),f82(x772)) % 178.07/177.94 [78]~E(x781,x782)+E(f317(x781,x783),f317(x782,x783)) % 178.07/177.94 [79]~E(x791,x792)+E(f317(x793,x791),f317(x793,x792)) % 178.07/177.94 [80]~E(x801,x802)+E(f8(x801,x803,x804),f8(x802,x803,x804)) % 178.07/177.94 [81]~E(x811,x812)+E(f8(x813,x811,x814),f8(x813,x812,x814)) % 178.07/177.94 [82]~E(x821,x822)+E(f8(x823,x824,x821),f8(x823,x824,x822)) % 178.07/177.94 [83]~E(x831,x832)+E(f9(x831,x833),f9(x832,x833)) % 178.07/177.94 [84]~E(x841,x842)+E(f9(x843,x841),f9(x843,x842)) % 178.07/177.94 [85]~E(x851,x852)+E(f7(x851,x853,x854),f7(x852,x853,x854)) % 178.07/177.94 [86]~E(x861,x862)+E(f7(x863,x861,x864),f7(x863,x862,x864)) % 178.07/177.94 [87]~E(x871,x872)+E(f7(x873,x874,x871),f7(x873,x874,x872)) % 178.07/177.94 [88]~E(x881,x882)+E(f62(x881),f62(x882)) % 178.07/177.94 [89]~E(x891,x892)+E(f244(x891),f244(x892)) % 178.07/177.94 [90]~E(x901,x902)+E(f236(x901),f236(x902)) % 178.07/177.94 [91]~E(x911,x912)+E(f134(x911),f134(x912)) % 178.07/177.94 [92]~E(x921,x922)+E(f45(x921,x923,x924),f45(x922,x923,x924)) % 178.07/177.94 [93]~E(x931,x932)+E(f45(x933,x931,x934),f45(x933,x932,x934)) % 178.07/177.94 [94]~E(x941,x942)+E(f45(x943,x944,x941),f45(x943,x944,x942)) % 178.07/177.94 [95]~E(x951,x952)+E(f148(x951,x953,x954,x955,x956),f148(x952,x953,x954,x955,x956)) % 178.07/177.94 [96]~E(x961,x962)+E(f148(x963,x961,x964,x965,x966),f148(x963,x962,x964,x965,x966)) % 178.07/177.94 [97]~E(x971,x972)+E(f148(x973,x974,x971,x975,x976),f148(x973,x974,x972,x975,x976)) % 178.07/177.94 [98]~E(x981,x982)+E(f148(x983,x984,x985,x981,x986),f148(x983,x984,x985,x982,x986)) % 178.07/177.94 [99]~E(x991,x992)+E(f148(x993,x994,x995,x996,x991),f148(x993,x994,x995,x996,x992)) % 178.07/177.94 [100]~E(x1001,x1002)+E(f61(x1001),f61(x1002)) % 178.07/177.94 [101]~E(x1011,x1012)+E(f153(x1011,x1013),f153(x1012,x1013)) % 178.07/177.94 [102]~E(x1021,x1022)+E(f153(x1023,x1021),f153(x1023,x1022)) % 178.07/177.94 [103]~E(x1031,x1032)+E(f238(x1031,x1033,x1034,x1035),f238(x1032,x1033,x1034,x1035)) % 178.07/177.94 [104]~E(x1041,x1042)+E(f238(x1043,x1041,x1044,x1045),f238(x1043,x1042,x1044,x1045)) % 178.07/177.94 [105]~E(x1051,x1052)+E(f238(x1053,x1054,x1051,x1055),f238(x1053,x1054,x1052,x1055)) % 178.07/177.94 [106]~E(x1061,x1062)+E(f238(x1063,x1064,x1065,x1061),f238(x1063,x1064,x1065,x1062)) % 178.07/177.94 [107]~E(x1071,x1072)+E(f635(x1071,x1073,x1074,x1075),f635(x1072,x1073,x1074,x1075)) % 178.07/177.94 [108]~E(x1081,x1082)+E(f635(x1083,x1081,x1084,x1085),f635(x1083,x1082,x1084,x1085)) % 178.07/177.94 [109]~E(x1091,x1092)+E(f635(x1093,x1094,x1091,x1095),f635(x1093,x1094,x1092,x1095)) % 178.07/177.94 [110]~E(x1101,x1102)+E(f635(x1103,x1104,x1105,x1101),f635(x1103,x1104,x1105,x1102)) % 178.07/177.94 [111]~E(x1111,x1112)+E(f174(x1111),f174(x1112)) % 178.07/177.94 [112]~E(x1121,x1122)+E(f16(x1121,x1123),f16(x1122,x1123)) % 178.07/177.94 [113]~E(x1131,x1132)+E(f16(x1133,x1131),f16(x1133,x1132)) % 178.07/177.94 [114]~E(x1141,x1142)+E(f882(x1141,x1143),f882(x1142,x1143)) % 178.07/177.94 [115]~E(x1151,x1152)+E(f882(x1153,x1151),f882(x1153,x1152)) % 178.07/177.94 [116]~E(x1161,x1162)+E(f461(x1161,x1163,x1164),f461(x1162,x1163,x1164)) % 178.07/177.94 [117]~E(x1171,x1172)+E(f461(x1173,x1171,x1174),f461(x1173,x1172,x1174)) % 178.07/177.94 [118]~E(x1181,x1182)+E(f461(x1183,x1184,x1181),f461(x1183,x1184,x1182)) % 178.07/177.94 [119]~E(x1191,x1192)+E(f816(x1191,x1193,x1194),f816(x1192,x1193,x1194)) % 178.07/177.94 [120]~E(x1201,x1202)+E(f816(x1203,x1201,x1204),f816(x1203,x1202,x1204)) % 178.07/177.94 [121]~E(x1211,x1212)+E(f816(x1213,x1214,x1211),f816(x1213,x1214,x1212)) % 178.07/177.94 [122]~E(x1221,x1222)+E(f136(x1221),f136(x1222)) % 178.07/177.94 [123]~E(x1231,x1232)+E(f64(x1231,x1233),f64(x1232,x1233)) % 178.07/177.94 [124]~E(x1241,x1242)+E(f64(x1243,x1241),f64(x1243,x1242)) % 178.07/177.94 [125]~E(x1251,x1252)+E(f171(x1251),f171(x1252)) % 178.07/177.94 [126]~E(x1261,x1262)+E(f18(x1261,x1263,x1264),f18(x1262,x1263,x1264)) % 178.07/177.94 [127]~E(x1271,x1272)+E(f18(x1273,x1271,x1274),f18(x1273,x1272,x1274)) % 178.07/177.94 [128]~E(x1281,x1282)+E(f18(x1283,x1284,x1281),f18(x1283,x1284,x1282)) % 178.07/177.94 [129]~E(x1291,x1292)+E(f625(x1291,x1293,x1294,x1295,x1296),f625(x1292,x1293,x1294,x1295,x1296)) % 178.07/177.94 [130]~E(x1301,x1302)+E(f625(x1303,x1301,x1304,x1305,x1306),f625(x1303,x1302,x1304,x1305,x1306)) % 178.07/177.94 [131]~E(x1311,x1312)+E(f625(x1313,x1314,x1311,x1315,x1316),f625(x1313,x1314,x1312,x1315,x1316)) % 178.07/177.94 [132]~E(x1321,x1322)+E(f625(x1323,x1324,x1325,x1321,x1326),f625(x1323,x1324,x1325,x1322,x1326)) % 178.07/177.94 [133]~E(x1331,x1332)+E(f625(x1333,x1334,x1335,x1336,x1331),f625(x1333,x1334,x1335,x1336,x1332)) % 178.07/177.94 [134]~E(x1341,x1342)+E(f636(x1341,x1343,x1344,x1345),f636(x1342,x1343,x1344,x1345)) % 178.07/177.94 [135]~E(x1351,x1352)+E(f636(x1353,x1351,x1354,x1355),f636(x1353,x1352,x1354,x1355)) % 178.07/177.94 [136]~E(x1361,x1362)+E(f636(x1363,x1364,x1361,x1365),f636(x1363,x1364,x1362,x1365)) % 178.07/177.94 [137]~E(x1371,x1372)+E(f636(x1373,x1374,x1375,x1371),f636(x1373,x1374,x1375,x1372)) % 178.07/177.94 [138]~E(x1381,x1382)+E(f252(x1381),f252(x1382)) % 178.07/177.94 [139]~E(x1391,x1392)+E(f175(x1391,x1393,x1394),f175(x1392,x1393,x1394)) % 178.07/177.94 [140]~E(x1401,x1402)+E(f175(x1403,x1401,x1404),f175(x1403,x1402,x1404)) % 178.07/177.94 [141]~E(x1411,x1412)+E(f175(x1413,x1414,x1411),f175(x1413,x1414,x1412)) % 178.07/177.94 [142]~E(x1421,x1422)+E(f157(x1421,x1423),f157(x1422,x1423)) % 178.07/177.94 [143]~E(x1431,x1432)+E(f157(x1433,x1431),f157(x1433,x1432)) % 178.07/177.94 [144]~E(x1441,x1442)+E(f206(x1441),f206(x1442)) % 178.07/177.94 [145]~E(x1451,x1452)+E(f141(x1451,x1453,x1454,x1455),f141(x1452,x1453,x1454,x1455)) % 178.07/177.94 [146]~E(x1461,x1462)+E(f141(x1463,x1461,x1464,x1465),f141(x1463,x1462,x1464,x1465)) % 178.07/177.94 [147]~E(x1471,x1472)+E(f141(x1473,x1474,x1471,x1475),f141(x1473,x1474,x1472,x1475)) % 178.07/177.94 [148]~E(x1481,x1482)+E(f141(x1483,x1484,x1485,x1481),f141(x1483,x1484,x1485,x1482)) % 178.07/177.94 [149]~E(x1491,x1492)+E(f264(x1491,x1493),f264(x1492,x1493)) % 178.07/177.94 [150]~E(x1501,x1502)+E(f264(x1503,x1501),f264(x1503,x1502)) % 178.07/177.94 [151]~E(x1511,x1512)+E(f298(x1511),f298(x1512)) % 178.07/177.94 [152]~E(x1521,x1522)+E(f184(x1521,x1523,x1524,x1525),f184(x1522,x1523,x1524,x1525)) % 178.07/177.94 [153]~E(x1531,x1532)+E(f184(x1533,x1531,x1534,x1535),f184(x1533,x1532,x1534,x1535)) % 178.07/177.94 [154]~E(x1541,x1542)+E(f184(x1543,x1544,x1541,x1545),f184(x1543,x1544,x1542,x1545)) % 178.07/177.94 [155]~E(x1551,x1552)+E(f184(x1553,x1554,x1555,x1551),f184(x1553,x1554,x1555,x1552)) % 178.07/177.94 [156]~E(x1561,x1562)+E(f249(x1561),f249(x1562)) % 178.07/177.94 [157]~E(x1571,x1572)+E(f240(x1571),f240(x1572)) % 178.07/177.94 [158]~E(x1581,x1582)+E(f74(x1581,x1583,x1584,x1585),f74(x1582,x1583,x1584,x1585)) % 178.07/177.94 [159]~E(x1591,x1592)+E(f74(x1593,x1591,x1594,x1595),f74(x1593,x1592,x1594,x1595)) % 178.07/177.94 [160]~E(x1601,x1602)+E(f74(x1603,x1604,x1601,x1605),f74(x1603,x1604,x1602,x1605)) % 178.07/177.94 [161]~E(x1611,x1612)+E(f74(x1613,x1614,x1615,x1611),f74(x1613,x1614,x1615,x1612)) % 178.07/177.94 [162]~E(x1621,x1622)+E(f425(x1621,x1623,x1624,x1625,x1626),f425(x1622,x1623,x1624,x1625,x1626)) % 178.07/177.94 [163]~E(x1631,x1632)+E(f425(x1633,x1631,x1634,x1635,x1636),f425(x1633,x1632,x1634,x1635,x1636)) % 178.07/177.94 [164]~E(x1641,x1642)+E(f425(x1643,x1644,x1641,x1645,x1646),f425(x1643,x1644,x1642,x1645,x1646)) % 178.07/177.94 [165]~E(x1651,x1652)+E(f425(x1653,x1654,x1655,x1651,x1656),f425(x1653,x1654,x1655,x1652,x1656)) % 178.07/177.94 [166]~E(x1661,x1662)+E(f425(x1663,x1664,x1665,x1666,x1661),f425(x1663,x1664,x1665,x1666,x1662)) % 178.07/177.94 [167]~E(x1671,x1672)+E(f550(x1671,x1673,x1674),f550(x1672,x1673,x1674)) % 178.07/177.94 [168]~E(x1681,x1682)+E(f550(x1683,x1681,x1684),f550(x1683,x1682,x1684)) % 178.07/177.94 [169]~E(x1691,x1692)+E(f550(x1693,x1694,x1691),f550(x1693,x1694,x1692)) % 178.07/177.94 [170]~E(x1701,x1702)+E(f111(x1701),f111(x1702)) % 178.07/177.94 [171]~E(x1711,x1712)+E(f113(x1711),f113(x1712)) % 178.07/177.94 [172]~E(x1721,x1722)+E(f330(x1721),f330(x1722)) % 178.07/177.94 [173]~E(x1731,x1732)+E(f307(x1731),f307(x1732)) % 178.07/177.94 [174]~E(x1741,x1742)+E(f446(x1741,x1743,x1744,x1745),f446(x1742,x1743,x1744,x1745)) % 178.07/177.94 [175]~E(x1751,x1752)+E(f446(x1753,x1751,x1754,x1755),f446(x1753,x1752,x1754,x1755)) % 178.07/177.94 [176]~E(x1761,x1762)+E(f446(x1763,x1764,x1761,x1765),f446(x1763,x1764,x1762,x1765)) % 178.07/177.94 [177]~E(x1771,x1772)+E(f446(x1773,x1774,x1775,x1771),f446(x1773,x1774,x1775,x1772)) % 178.07/177.94 [178]~E(x1781,x1782)+E(f266(x1781,x1783),f266(x1782,x1783)) % 178.07/177.94 [179]~E(x1791,x1792)+E(f266(x1793,x1791),f266(x1793,x1792)) % 178.07/177.94 [180]~E(x1801,x1802)+E(f815(x1801,x1803,x1804),f815(x1802,x1803,x1804)) % 178.07/177.94 [181]~E(x1811,x1812)+E(f815(x1813,x1811,x1814),f815(x1813,x1812,x1814)) % 178.07/177.94 [182]~E(x1821,x1822)+E(f815(x1823,x1824,x1821),f815(x1823,x1824,x1822)) % 178.07/177.94 [183]~E(x1831,x1832)+E(f47(x1831,x1833),f47(x1832,x1833)) % 178.07/177.94 [184]~E(x1841,x1842)+E(f47(x1843,x1841),f47(x1843,x1842)) % 178.07/177.94 [185]~E(x1851,x1852)+E(f149(x1851,x1853,x1854,x1855),f149(x1852,x1853,x1854,x1855)) % 178.07/177.94 [186]~E(x1861,x1862)+E(f149(x1863,x1861,x1864,x1865),f149(x1863,x1862,x1864,x1865)) % 178.07/177.94 [187]~E(x1871,x1872)+E(f149(x1873,x1874,x1871,x1875),f149(x1873,x1874,x1872,x1875)) % 178.07/177.94 [188]~E(x1881,x1882)+E(f149(x1883,x1884,x1885,x1881),f149(x1883,x1884,x1885,x1882)) % 178.07/177.94 [189]~E(x1891,x1892)+E(f39(x1891),f39(x1892)) % 178.07/177.94 [190]~E(x1901,x1902)+E(f250(x1901),f250(x1902)) % 178.07/177.94 [191]~E(x1911,x1912)+E(f131(x1911,x1913),f131(x1912,x1913)) % 178.07/177.94 [192]~E(x1921,x1922)+E(f131(x1923,x1921),f131(x1923,x1922)) % 178.07/177.94 [193]~E(x1931,x1932)+E(f127(x1931),f127(x1932)) % 178.07/177.94 [194]~E(x1941,x1942)+E(f168(x1941),f168(x1942)) % 178.07/177.94 [195]~E(x1951,x1952)+E(f302(x1951,x1953,x1954),f302(x1952,x1953,x1954)) % 178.07/177.94 [196]~E(x1961,x1962)+E(f302(x1963,x1961,x1964),f302(x1963,x1962,x1964)) % 178.07/177.94 [197]~E(x1971,x1972)+E(f302(x1973,x1974,x1971),f302(x1973,x1974,x1972)) % 178.07/177.94 [198]~E(x1981,x1982)+E(f49(x1981,x1983),f49(x1982,x1983)) % 178.07/177.94 [199]~E(x1991,x1992)+E(f49(x1993,x1991),f49(x1993,x1992)) % 178.07/177.94 [200]~E(x2001,x2002)+E(f355(x2001,x2003,x2004,x2005),f355(x2002,x2003,x2004,x2005)) % 178.07/177.94 [201]~E(x2011,x2012)+E(f355(x2013,x2011,x2014,x2015),f355(x2013,x2012,x2014,x2015)) % 178.07/177.94 [202]~E(x2021,x2022)+E(f355(x2023,x2024,x2021,x2025),f355(x2023,x2024,x2022,x2025)) % 178.07/177.94 [203]~E(x2031,x2032)+E(f355(x2033,x2034,x2035,x2031),f355(x2033,x2034,x2035,x2032)) % 178.07/177.94 [204]~E(x2041,x2042)+E(f43(x2041,x2043),f43(x2042,x2043)) % 178.07/177.94 [205]~E(x2051,x2052)+E(f43(x2053,x2051),f43(x2053,x2052)) % 178.07/177.94 [206]~E(x2061,x2062)+E(f42(x2061,x2063),f42(x2062,x2063)) % 178.07/177.94 [207]~E(x2071,x2072)+E(f42(x2073,x2071),f42(x2073,x2072)) % 178.07/177.94 [208]~E(x2081,x2082)+E(f287(x2081),f287(x2082)) % 178.07/177.94 [209]~E(x2091,x2092)+E(f73(x2091,x2093),f73(x2092,x2093)) % 178.07/177.94 [210]~E(x2101,x2102)+E(f73(x2103,x2101),f73(x2103,x2102)) % 178.07/177.94 [211]~E(x2111,x2112)+E(f65(x2111,x2113,x2114),f65(x2112,x2113,x2114)) % 178.07/177.94 [212]~E(x2121,x2122)+E(f65(x2123,x2121,x2124),f65(x2123,x2122,x2124)) % 178.07/177.94 [213]~E(x2131,x2132)+E(f65(x2133,x2134,x2131),f65(x2133,x2134,x2132)) % 178.07/177.94 [214]~E(x2141,x2142)+E(f156(x2141,x2143),f156(x2142,x2143)) % 178.07/177.94 [215]~E(x2151,x2152)+E(f156(x2153,x2151),f156(x2153,x2152)) % 178.07/177.94 [216]~E(x2161,x2162)+E(f87(x2161,x2163),f87(x2162,x2163)) % 178.07/177.94 [217]~E(x2171,x2172)+E(f87(x2173,x2171),f87(x2173,x2172)) % 178.07/177.94 [218]~E(x2181,x2182)+E(f437(x2181,x2183,x2184,x2185),f437(x2182,x2183,x2184,x2185)) % 178.07/177.94 [219]~E(x2191,x2192)+E(f437(x2193,x2191,x2194,x2195),f437(x2193,x2192,x2194,x2195)) % 178.07/177.94 [220]~E(x2201,x2202)+E(f437(x2203,x2204,x2201,x2205),f437(x2203,x2204,x2202,x2205)) % 178.07/177.94 [221]~E(x2211,x2212)+E(f437(x2213,x2214,x2215,x2211),f437(x2213,x2214,x2215,x2212)) % 178.07/177.94 [222]~E(x2221,x2222)+E(f160(x2221,x2223),f160(x2222,x2223)) % 178.07/177.94 [223]~E(x2231,x2232)+E(f160(x2233,x2231),f160(x2233,x2232)) % 178.07/177.94 [224]~E(x2241,x2242)+E(f135(x2241,x2243),f135(x2242,x2243)) % 178.07/177.94 [225]~E(x2251,x2252)+E(f135(x2253,x2251),f135(x2253,x2252)) % 178.07/177.94 [226]~E(x2261,x2262)+E(f67(x2261,x2263,x2264,x2265,x2266),f67(x2262,x2263,x2264,x2265,x2266)) % 178.07/177.94 [227]~E(x2271,x2272)+E(f67(x2273,x2271,x2274,x2275,x2276),f67(x2273,x2272,x2274,x2275,x2276)) % 178.07/177.94 [228]~E(x2281,x2282)+E(f67(x2283,x2284,x2281,x2285,x2286),f67(x2283,x2284,x2282,x2285,x2286)) % 178.07/177.94 [229]~E(x2291,x2292)+E(f67(x2293,x2294,x2295,x2291,x2296),f67(x2293,x2294,x2295,x2292,x2296)) % 178.07/177.94 [230]~E(x2301,x2302)+E(f67(x2303,x2304,x2305,x2306,x2301),f67(x2303,x2304,x2305,x2306,x2302)) % 178.07/177.94 [231]~E(x2311,x2312)+E(f366(x2311,x2313,x2314,x2315),f366(x2312,x2313,x2314,x2315)) % 178.07/177.94 [232]~E(x2321,x2322)+E(f366(x2323,x2321,x2324,x2325),f366(x2323,x2322,x2324,x2325)) % 178.07/177.94 [233]~E(x2331,x2332)+E(f366(x2333,x2334,x2331,x2335),f366(x2333,x2334,x2332,x2335)) % 178.07/177.94 [234]~E(x2341,x2342)+E(f366(x2343,x2344,x2345,x2341),f366(x2343,x2344,x2345,x2342)) % 178.07/177.94 [235]~E(x2351,x2352)+E(f120(x2351,x2353),f120(x2352,x2353)) % 178.07/177.94 [236]~E(x2361,x2362)+E(f120(x2363,x2361),f120(x2363,x2362)) % 178.07/177.94 [237]~E(x2371,x2372)+E(f814(x2371,x2373,x2374),f814(x2372,x2373,x2374)) % 178.07/177.94 [238]~E(x2381,x2382)+E(f814(x2383,x2381,x2384),f814(x2383,x2382,x2384)) % 178.07/177.94 [239]~E(x2391,x2392)+E(f814(x2393,x2394,x2391),f814(x2393,x2394,x2392)) % 178.07/177.94 [240]~E(x2401,x2402)+E(f299(x2401,x2403),f299(x2402,x2403)) % 178.07/177.94 [241]~E(x2411,x2412)+E(f299(x2413,x2411),f299(x2413,x2412)) % 178.07/177.94 [242]~E(x2421,x2422)+E(f158(x2421,x2423),f158(x2422,x2423)) % 178.07/177.94 [243]~E(x2431,x2432)+E(f158(x2433,x2431),f158(x2433,x2432)) % 178.07/177.94 [244]~E(x2441,x2442)+E(f40(x2441,x2443),f40(x2442,x2443)) % 178.07/177.94 [245]~E(x2451,x2452)+E(f40(x2453,x2451),f40(x2453,x2452)) % 178.07/177.94 [246]~E(x2461,x2462)+E(f813(x2461,x2463,x2464),f813(x2462,x2463,x2464)) % 178.07/177.94 [247]~E(x2471,x2472)+E(f813(x2473,x2471,x2474),f813(x2473,x2472,x2474)) % 178.07/177.94 [248]~E(x2481,x2482)+E(f813(x2483,x2484,x2481),f813(x2483,x2484,x2482)) % 178.07/177.94 [249]~E(x2491,x2492)+E(f176(x2491,x2493,x2494),f176(x2492,x2493,x2494)) % 178.07/177.94 [250]~E(x2501,x2502)+E(f176(x2503,x2501,x2504),f176(x2503,x2502,x2504)) % 178.07/177.94 [251]~E(x2511,x2512)+E(f176(x2513,x2514,x2511),f176(x2513,x2514,x2512)) % 178.07/177.94 [252]~E(x2521,x2522)+E(f303(x2521,x2523,x2524),f303(x2522,x2523,x2524)) % 178.07/177.94 [253]~E(x2531,x2532)+E(f303(x2533,x2531,x2534),f303(x2533,x2532,x2534)) % 178.07/177.94 [254]~E(x2541,x2542)+E(f303(x2543,x2544,x2541),f303(x2543,x2544,x2542)) % 178.07/177.94 [255]~E(x2551,x2552)+E(f188(x2551,x2553),f188(x2552,x2553)) % 178.07/177.94 [256]~E(x2561,x2562)+E(f188(x2563,x2561),f188(x2563,x2562)) % 178.07/177.94 [257]~E(x2571,x2572)+E(f858(x2571,x2573),f858(x2572,x2573)) % 178.07/177.94 [258]~E(x2581,x2582)+E(f858(x2583,x2581),f858(x2583,x2582)) % 178.07/177.94 [259]~E(x2591,x2592)+E(f263(x2591,x2593),f263(x2592,x2593)) % 178.07/177.94 [260]~E(x2601,x2602)+E(f263(x2603,x2601),f263(x2603,x2602)) % 178.07/177.94 [261]~E(x2611,x2612)+E(f164(x2611),f164(x2612)) % 178.07/177.94 [262]~E(x2621,x2622)+E(f455(x2621,x2623,x2624,x2625),f455(x2622,x2623,x2624,x2625)) % 178.07/177.94 [263]~E(x2631,x2632)+E(f455(x2633,x2631,x2634,x2635),f455(x2633,x2632,x2634,x2635)) % 178.07/177.94 [264]~E(x2641,x2642)+E(f455(x2643,x2644,x2641,x2645),f455(x2643,x2644,x2642,x2645)) % 178.07/177.94 [265]~E(x2651,x2652)+E(f455(x2653,x2654,x2655,x2651),f455(x2653,x2654,x2655,x2652)) % 178.07/177.94 [266]~E(x2661,x2662)+E(f628(x2661,x2663,x2664,x2665,x2666),f628(x2662,x2663,x2664,x2665,x2666)) % 178.07/177.94 [267]~E(x2671,x2672)+E(f628(x2673,x2671,x2674,x2675,x2676),f628(x2673,x2672,x2674,x2675,x2676)) % 178.07/177.94 [268]~E(x2681,x2682)+E(f628(x2683,x2684,x2681,x2685,x2686),f628(x2683,x2684,x2682,x2685,x2686)) % 178.07/177.94 [269]~E(x2691,x2692)+E(f628(x2693,x2694,x2695,x2691,x2696),f628(x2693,x2694,x2695,x2692,x2696)) % 178.07/177.94 [270]~E(x2701,x2702)+E(f628(x2703,x2704,x2705,x2706,x2701),f628(x2703,x2704,x2705,x2706,x2702)) % 178.07/177.94 [271]~E(x2711,x2712)+E(f76(x2711),f76(x2712)) % 178.07/177.94 [272]~E(x2721,x2722)+E(f186(x2721,x2723,x2724,x2725,x2726),f186(x2722,x2723,x2724,x2725,x2726)) % 178.07/177.94 [273]~E(x2731,x2732)+E(f186(x2733,x2731,x2734,x2735,x2736),f186(x2733,x2732,x2734,x2735,x2736)) % 178.07/177.94 [274]~E(x2741,x2742)+E(f186(x2743,x2744,x2741,x2745,x2746),f186(x2743,x2744,x2742,x2745,x2746)) % 178.07/177.94 [275]~E(x2751,x2752)+E(f186(x2753,x2754,x2755,x2751,x2756),f186(x2753,x2754,x2755,x2752,x2756)) % 178.07/177.94 [276]~E(x2761,x2762)+E(f186(x2763,x2764,x2765,x2766,x2761),f186(x2763,x2764,x2765,x2766,x2762)) % 178.07/177.94 [277]~E(x2771,x2772)+E(f183(x2771,x2773,x2774),f183(x2772,x2773,x2774)) % 178.07/177.94 [278]~E(x2781,x2782)+E(f183(x2783,x2781,x2784),f183(x2783,x2782,x2784)) % 178.07/177.94 [279]~E(x2791,x2792)+E(f183(x2793,x2794,x2791),f183(x2793,x2794,x2792)) % 178.07/177.94 [280]~E(x2801,x2802)+E(f254(x2801),f254(x2802)) % 178.07/177.94 [281]~E(x2811,x2812)+E(f151(x2811,x2813),f151(x2812,x2813)) % 178.07/177.94 [282]~E(x2821,x2822)+E(f151(x2823,x2821),f151(x2823,x2822)) % 178.07/177.94 [283]~E(x2831,x2832)+E(f6(x2831,x2833),f6(x2832,x2833)) % 178.07/177.94 [284]~E(x2841,x2842)+E(f6(x2843,x2841),f6(x2843,x2842)) % 178.07/177.94 [285]~E(x2851,x2852)+E(f196(x2851),f196(x2852)) % 178.07/177.94 [286]~E(x2861,x2862)+E(f705(x2861,x2863,x2864,x2865),f705(x2862,x2863,x2864,x2865)) % 178.07/177.94 [287]~E(x2871,x2872)+E(f705(x2873,x2871,x2874,x2875),f705(x2873,x2872,x2874,x2875)) % 178.07/177.94 [288]~E(x2881,x2882)+E(f705(x2883,x2884,x2881,x2885),f705(x2883,x2884,x2882,x2885)) % 178.07/177.94 [289]~E(x2891,x2892)+E(f705(x2893,x2894,x2895,x2891),f705(x2893,x2894,x2895,x2892)) % 178.07/177.94 [290]~E(x2901,x2902)+E(f121(x2901),f121(x2902)) % 178.07/177.94 [291]~E(x2911,x2912)+E(f300(x2911,x2913,x2914),f300(x2912,x2913,x2914)) % 178.07/177.94 [292]~E(x2921,x2922)+E(f300(x2923,x2921,x2924),f300(x2923,x2922,x2924)) % 178.07/177.94 [293]~E(x2931,x2932)+E(f300(x2933,x2934,x2931),f300(x2933,x2934,x2932)) % 178.07/177.94 [294]~E(x2941,x2942)+E(f577(x2941,x2943,x2944),f577(x2942,x2943,x2944)) % 178.07/177.94 [295]~E(x2951,x2952)+E(f577(x2953,x2951,x2954),f577(x2953,x2952,x2954)) % 178.07/177.94 [296]~E(x2961,x2962)+E(f577(x2963,x2964,x2961),f577(x2963,x2964,x2962)) % 178.07/177.94 [297]~E(x2971,x2972)+E(f38(x2971),f38(x2972)) % 178.07/177.94 [298]~E(x2981,x2982)+E(f181(x2981,x2983),f181(x2982,x2983)) % 178.07/177.94 [299]~E(x2991,x2992)+E(f181(x2993,x2991),f181(x2993,x2992)) % 178.07/177.94 [300]~E(x3001,x3002)+E(f807(x3001,x3003,x3004),f807(x3002,x3003,x3004)) % 178.07/177.94 [301]~E(x3011,x3012)+E(f807(x3013,x3011,x3014),f807(x3013,x3012,x3014)) % 178.07/177.94 [302]~E(x3021,x3022)+E(f807(x3023,x3024,x3021),f807(x3023,x3024,x3022)) % 178.07/177.94 [303]~E(x3031,x3032)+E(f306(x3031),f306(x3032)) % 178.07/177.94 [304]~E(x3041,x3042)+E(f881(x3041,x3043),f881(x3042,x3043)) % 178.07/177.94 [305]~E(x3051,x3052)+E(f881(x3053,x3051),f881(x3053,x3052)) % 178.07/177.94 [306]~E(x3061,x3062)+E(f267(x3061,x3063),f267(x3062,x3063)) % 178.07/177.94 [307]~E(x3071,x3072)+E(f267(x3073,x3071),f267(x3073,x3072)) % 178.07/177.94 [308]~E(x3081,x3082)+E(f30(x3081,x3083,x3084),f30(x3082,x3083,x3084)) % 178.07/177.94 [309]~E(x3091,x3092)+E(f30(x3093,x3091,x3094),f30(x3093,x3092,x3094)) % 178.07/177.94 [310]~E(x3101,x3102)+E(f30(x3103,x3104,x3101),f30(x3103,x3104,x3102)) % 178.07/177.94 [311]~E(x3111,x3112)+E(f44(x3111),f44(x3112)) % 178.07/177.94 [312]~E(x3121,x3122)+E(f167(x3121),f167(x3122)) % 178.07/177.94 [313]~E(x3131,x3132)+E(f358(x3131,x3133),f358(x3132,x3133)) % 178.07/177.94 [314]~E(x3141,x3142)+E(f358(x3143,x3141),f358(x3143,x3142)) % 178.07/177.94 [315]~E(x3151,x3152)+E(f860(x3151,x3153),f860(x3152,x3153)) % 178.07/177.94 [316]~E(x3161,x3162)+E(f860(x3163,x3161),f860(x3163,x3162)) % 178.07/177.94 [317]~E(x3171,x3172)+E(f199(x3171),f199(x3172)) % 178.07/177.94 [318]~E(x3181,x3182)+E(f170(x3181),f170(x3182)) % 178.07/177.94 [319]~E(x3191,x3192)+E(f663(x3191,x3193,x3194),f663(x3192,x3193,x3194)) % 178.07/177.94 [320]~E(x3201,x3202)+E(f663(x3203,x3201,x3204),f663(x3203,x3202,x3204)) % 178.07/177.94 [321]~E(x3211,x3212)+E(f663(x3213,x3214,x3211),f663(x3213,x3214,x3212)) % 178.07/177.94 [322]~E(x3221,x3222)+E(f318(x3221,x3223),f318(x3222,x3223)) % 178.07/177.94 [323]~E(x3231,x3232)+E(f318(x3233,x3231),f318(x3233,x3232)) % 178.07/177.94 [324]~E(x3241,x3242)+E(f50(x3241,x3243),f50(x3242,x3243)) % 178.07/177.94 [325]~E(x3251,x3252)+E(f50(x3253,x3251),f50(x3253,x3252)) % 178.07/177.94 [326]~E(x3261,x3262)+E(f48(x3261,x3263),f48(x3262,x3263)) % 178.07/177.94 [327]~E(x3271,x3272)+E(f48(x3273,x3271),f48(x3273,x3272)) % 178.07/177.94 [328]~E(x3281,x3282)+E(f92(x3281),f92(x3282)) % 178.07/177.94 [329]~E(x3291,x3292)+E(f231(x3291,x3293,x3294),f231(x3292,x3293,x3294)) % 178.07/177.94 [330]~E(x3301,x3302)+E(f231(x3303,x3301,x3304),f231(x3303,x3302,x3304)) % 178.07/177.94 [331]~E(x3311,x3312)+E(f231(x3313,x3314,x3311),f231(x3313,x3314,x3312)) % 178.07/177.94 [332]~E(x3321,x3322)+E(f137(x3321),f137(x3322)) % 178.07/177.94 [333]~E(x3331,x3332)+E(f283(x3331,x3333,x3334),f283(x3332,x3333,x3334)) % 178.07/177.94 [334]~E(x3341,x3342)+E(f283(x3343,x3341,x3344),f283(x3343,x3342,x3344)) % 178.07/177.94 [335]~E(x3351,x3352)+E(f283(x3353,x3354,x3351),f283(x3353,x3354,x3352)) % 178.07/177.94 [336]~E(x3361,x3362)+E(f381(x3361),f381(x3362)) % 178.07/177.94 [337]~E(x3371,x3372)+E(f685(x3371,x3373),f685(x3372,x3373)) % 178.07/177.94 [338]~E(x3381,x3382)+E(f685(x3383,x3381),f685(x3383,x3382)) % 178.07/177.94 [339]~E(x3391,x3392)+E(f684(x3391,x3393),f684(x3392,x3393)) % 178.07/177.94 [340]~E(x3401,x3402)+E(f684(x3403,x3401),f684(x3403,x3402)) % 178.07/177.94 [341]~E(x3411,x3412)+E(f177(x3411,x3413),f177(x3412,x3413)) % 178.07/177.94 [342]~E(x3421,x3422)+E(f177(x3423,x3421),f177(x3423,x3422)) % 178.07/177.94 [343]~E(x3431,x3432)+E(f138(x3431,x3433),f138(x3432,x3433)) % 178.07/177.94 [344]~E(x3441,x3442)+E(f138(x3443,x3441),f138(x3443,x3442)) % 178.07/177.94 [345]~E(x3451,x3452)+E(f102(x3451),f102(x3452)) % 178.07/177.94 [346]~E(x3461,x3462)+E(f320(x3461,x3463),f320(x3462,x3463)) % 178.07/177.94 [347]~E(x3471,x3472)+E(f320(x3473,x3471),f320(x3473,x3472)) % 178.07/177.94 [348]~E(x3481,x3482)+E(f269(x3481,x3483,x3484,x3485,x3486,x3487),f269(x3482,x3483,x3484,x3485,x3486,x3487)) % 178.07/177.94 [349]~E(x3491,x3492)+E(f269(x3493,x3491,x3494,x3495,x3496,x3497),f269(x3493,x3492,x3494,x3495,x3496,x3497)) % 178.07/177.94 [350]~E(x3501,x3502)+E(f269(x3503,x3504,x3501,x3505,x3506,x3507),f269(x3503,x3504,x3502,x3505,x3506,x3507)) % 178.07/177.94 [351]~E(x3511,x3512)+E(f269(x3513,x3514,x3515,x3511,x3516,x3517),f269(x3513,x3514,x3515,x3512,x3516,x3517)) % 178.07/177.94 [352]~E(x3521,x3522)+E(f269(x3523,x3524,x3525,x3526,x3521,x3527),f269(x3523,x3524,x3525,x3526,x3522,x3527)) % 178.07/177.94 [353]~E(x3531,x3532)+E(f269(x3533,x3534,x3535,x3536,x3537,x3531),f269(x3533,x3534,x3535,x3536,x3537,x3532)) % 178.07/177.94 [354]~E(x3541,x3542)+E(f322(x3541,x3543),f322(x3542,x3543)) % 178.07/177.94 [355]~E(x3551,x3552)+E(f322(x3553,x3551),f322(x3553,x3552)) % 178.07/177.94 [356]~E(x3561,x3562)+E(f190(x3561,x3563,x3564,x3565),f190(x3562,x3563,x3564,x3565)) % 178.07/177.94 [357]~E(x3571,x3572)+E(f190(x3573,x3571,x3574,x3575),f190(x3573,x3572,x3574,x3575)) % 178.07/177.94 [358]~E(x3581,x3582)+E(f190(x3583,x3584,x3581,x3585),f190(x3583,x3584,x3582,x3585)) % 178.07/177.94 [359]~E(x3591,x3592)+E(f190(x3593,x3594,x3595,x3591),f190(x3593,x3594,x3595,x3592)) % 178.07/177.94 [360]~E(x3601,x3602)+E(f31(x3601,x3603,x3604),f31(x3602,x3603,x3604)) % 178.07/177.94 [361]~E(x3611,x3612)+E(f31(x3613,x3611,x3614),f31(x3613,x3612,x3614)) % 178.07/177.94 [362]~E(x3621,x3622)+E(f31(x3623,x3624,x3621),f31(x3623,x3624,x3622)) % 178.07/177.94 [363]~E(x3631,x3632)+E(f648(x3631,x3633,x3634),f648(x3632,x3633,x3634)) % 178.07/177.94 [364]~E(x3641,x3642)+E(f648(x3643,x3641,x3644),f648(x3643,x3642,x3644)) % 178.07/177.94 [365]~E(x3651,x3652)+E(f648(x3653,x3654,x3651),f648(x3653,x3654,x3652)) % 178.07/177.94 [366]~E(x3661,x3662)+E(f178(x3661,x3663),f178(x3662,x3663)) % 178.07/177.94 [367]~E(x3671,x3672)+E(f178(x3673,x3671),f178(x3673,x3672)) % 178.07/177.94 [368]~E(x3681,x3682)+E(f463(x3681,x3683,x3684),f463(x3682,x3683,x3684)) % 178.07/177.94 [369]~E(x3691,x3692)+E(f463(x3693,x3691,x3694),f463(x3693,x3692,x3694)) % 178.07/177.94 [370]~E(x3701,x3702)+E(f463(x3703,x3704,x3701),f463(x3703,x3704,x3702)) % 178.07/177.94 [371]~E(x3711,x3712)+E(f716(x3711,x3713,x3714),f716(x3712,x3713,x3714)) % 178.07/177.94 [372]~E(x3721,x3722)+E(f716(x3723,x3721,x3724),f716(x3723,x3722,x3724)) % 178.07/177.94 [373]~E(x3731,x3732)+E(f716(x3733,x3734,x3731),f716(x3733,x3734,x3732)) % 178.07/177.94 [374]~E(x3741,x3742)+E(f796(x3741,x3743,x3744,x3745),f796(x3742,x3743,x3744,x3745)) % 178.07/177.94 [375]~E(x3751,x3752)+E(f796(x3753,x3751,x3754,x3755),f796(x3753,x3752,x3754,x3755)) % 178.07/177.94 [376]~E(x3761,x3762)+E(f796(x3763,x3764,x3761,x3765),f796(x3763,x3764,x3762,x3765)) % 178.07/177.94 [377]~E(x3771,x3772)+E(f796(x3773,x3774,x3775,x3771),f796(x3773,x3774,x3775,x3772)) % 178.07/177.94 [378]~E(x3781,x3782)+E(f93(x3781),f93(x3782)) % 178.07/177.94 [379]~E(x3791,x3792)+E(f13(x3791,x3793),f13(x3792,x3793)) % 178.07/177.94 [380]~E(x3801,x3802)+E(f13(x3803,x3801),f13(x3803,x3802)) % 178.07/177.94 [381]~E(x3811,x3812)+E(f338(x3811,x3813,x3814),f338(x3812,x3813,x3814)) % 178.07/177.94 [382]~E(x3821,x3822)+E(f338(x3823,x3821,x3824),f338(x3823,x3822,x3824)) % 178.07/177.94 [383]~E(x3831,x3832)+E(f338(x3833,x3834,x3831),f338(x3833,x3834,x3832)) % 178.07/177.94 [384]~E(x3841,x3842)+E(f659(x3841,x3843,x3844),f659(x3842,x3843,x3844)) % 178.07/177.94 [385]~E(x3851,x3852)+E(f659(x3853,x3851,x3854),f659(x3853,x3852,x3854)) % 178.07/177.94 [386]~E(x3861,x3862)+E(f659(x3863,x3864,x3861),f659(x3863,x3864,x3862)) % 178.07/177.94 [387]~E(x3871,x3872)+E(f675(x3871,x3873,x3874,x3875),f675(x3872,x3873,x3874,x3875)) % 178.07/177.94 [388]~E(x3881,x3882)+E(f675(x3883,x3881,x3884,x3885),f675(x3883,x3882,x3884,x3885)) % 178.07/177.94 [389]~E(x3891,x3892)+E(f675(x3893,x3894,x3891,x3895),f675(x3893,x3894,x3892,x3895)) % 178.07/177.94 [390]~E(x3901,x3902)+E(f675(x3903,x3904,x3905,x3901),f675(x3903,x3904,x3905,x3902)) % 178.07/177.94 [391]~E(x3911,x3912)+E(f284(x3911,x3913),f284(x3912,x3913)) % 178.07/177.94 [392]~E(x3921,x3922)+E(f284(x3923,x3921),f284(x3923,x3922)) % 178.07/177.94 [393]~E(x3931,x3932)+E(f499(x3931,x3933,x3934,x3935,x3936,x3937),f499(x3932,x3933,x3934,x3935,x3936,x3937)) % 178.07/177.94 [394]~E(x3941,x3942)+E(f499(x3943,x3941,x3944,x3945,x3946,x3947),f499(x3943,x3942,x3944,x3945,x3946,x3947)) % 178.07/177.94 [395]~E(x3951,x3952)+E(f499(x3953,x3954,x3951,x3955,x3956,x3957),f499(x3953,x3954,x3952,x3955,x3956,x3957)) % 178.07/177.94 [396]~E(x3961,x3962)+E(f499(x3963,x3964,x3965,x3961,x3966,x3967),f499(x3963,x3964,x3965,x3962,x3966,x3967)) % 178.07/177.94 [397]~E(x3971,x3972)+E(f499(x3973,x3974,x3975,x3976,x3971,x3977),f499(x3973,x3974,x3975,x3976,x3972,x3977)) % 178.07/177.94 [398]~E(x3981,x3982)+E(f499(x3983,x3984,x3985,x3986,x3987,x3981),f499(x3983,x3984,x3985,x3986,x3987,x3982)) % 178.07/177.94 [399]~E(x3991,x3992)+E(f305(x3991,x3993),f305(x3992,x3993)) % 178.07/177.94 [400]~E(x4001,x4002)+E(f305(x4003,x4001),f305(x4003,x4002)) % 178.07/177.94 [401]~E(x4011,x4012)+E(f268(x4011,x4013,x4014),f268(x4012,x4013,x4014)) % 178.07/177.94 [402]~E(x4021,x4022)+E(f268(x4023,x4021,x4024),f268(x4023,x4022,x4024)) % 178.07/177.94 [403]~E(x4031,x4032)+E(f268(x4033,x4034,x4031),f268(x4033,x4034,x4032)) % 178.07/177.94 [404]~E(x4041,x4042)+E(f86(x4041,x4043),f86(x4042,x4043)) % 178.07/177.94 [405]~E(x4051,x4052)+E(f86(x4053,x4051),f86(x4053,x4052)) % 178.07/177.94 [406]~E(x4061,x4062)+E(f286(x4061,x4063,x4064),f286(x4062,x4063,x4064)) % 178.07/177.94 [407]~E(x4071,x4072)+E(f286(x4073,x4071,x4074),f286(x4073,x4072,x4074)) % 178.07/177.94 [408]~E(x4081,x4082)+E(f286(x4083,x4084,x4081),f286(x4083,x4084,x4082)) % 178.07/177.94 [409]~E(x4091,x4092)+E(f91(x4091,x4093),f91(x4092,x4093)) % 178.07/177.94 [410]~E(x4101,x4102)+E(f91(x4103,x4101),f91(x4103,x4102)) % 178.07/177.94 [411]~E(x4111,x4112)+E(f418(x4111,x4113,x4114),f418(x4112,x4113,x4114)) % 178.07/177.94 [412]~E(x4121,x4122)+E(f418(x4123,x4121,x4124),f418(x4123,x4122,x4124)) % 178.07/177.94 [413]~E(x4131,x4132)+E(f418(x4133,x4134,x4131),f418(x4133,x4134,x4132)) % 178.07/177.94 [414]~E(x4141,x4142)+E(f152(x4141,x4143),f152(x4142,x4143)) % 178.07/177.94 [415]~E(x4151,x4152)+E(f152(x4153,x4151),f152(x4153,x4152)) % 178.07/177.94 [416]~E(x4161,x4162)+E(f604(x4161,x4163,x4164,x4165),f604(x4162,x4163,x4164,x4165)) % 178.07/177.94 [417]~E(x4171,x4172)+E(f604(x4173,x4171,x4174,x4175),f604(x4173,x4172,x4174,x4175)) % 178.07/177.94 [418]~E(x4181,x4182)+E(f604(x4183,x4184,x4181,x4185),f604(x4183,x4184,x4182,x4185)) % 178.07/177.94 [419]~E(x4191,x4192)+E(f604(x4193,x4194,x4195,x4191),f604(x4193,x4194,x4195,x4192)) % 178.07/177.94 [420]~E(x4201,x4202)+E(f34(x4201,x4203),f34(x4202,x4203)) % 178.07/177.94 [421]~E(x4211,x4212)+E(f34(x4213,x4211),f34(x4213,x4212)) % 178.07/177.94 [422]~E(x4221,x4222)+E(f220(x4221),f220(x4222)) % 178.07/177.94 [423]~E(x4231,x4232)+E(f753(x4231,x4233,x4234),f753(x4232,x4233,x4234)) % 178.07/177.94 [424]~E(x4241,x4242)+E(f753(x4243,x4241,x4244),f753(x4243,x4242,x4244)) % 178.07/177.94 [425]~E(x4251,x4252)+E(f753(x4253,x4254,x4251),f753(x4253,x4254,x4252)) % 178.07/177.94 [426]~E(x4261,x4262)+E(f143(x4261,x4263),f143(x4262,x4263)) % 178.07/177.94 [427]~E(x4271,x4272)+E(f143(x4273,x4271),f143(x4273,x4272)) % 178.07/177.94 [428]~E(x4281,x4282)+E(f140(x4281),f140(x4282)) % 178.07/177.94 [429]~E(x4291,x4292)+E(f169(x4291,x4293,x4294),f169(x4292,x4293,x4294)) % 178.07/177.94 [430]~E(x4301,x4302)+E(f169(x4303,x4301,x4304),f169(x4303,x4302,x4304)) % 178.07/177.94 [431]~E(x4311,x4312)+E(f169(x4313,x4314,x4311),f169(x4313,x4314,x4312)) % 178.07/177.94 [432]~E(x4321,x4322)+E(f234(x4321,x4323,x4324,x4325),f234(x4322,x4323,x4324,x4325)) % 178.07/177.94 [433]~E(x4331,x4332)+E(f234(x4333,x4331,x4334,x4335),f234(x4333,x4332,x4334,x4335)) % 178.07/177.94 [434]~E(x4341,x4342)+E(f234(x4343,x4344,x4341,x4345),f234(x4343,x4344,x4342,x4345)) % 178.07/177.94 [435]~E(x4351,x4352)+E(f234(x4353,x4354,x4355,x4351),f234(x4353,x4354,x4355,x4352)) % 178.07/177.94 [436]~E(x4361,x4362)+E(f251(x4361),f251(x4362)) % 178.07/177.94 [437]~E(x4371,x4372)+E(f59(x4371),f59(x4372)) % 178.07/177.94 [438]~E(x4381,x4382)+E(f665(x4381,x4383,x4384),f665(x4382,x4383,x4384)) % 178.07/177.94 [439]~E(x4391,x4392)+E(f665(x4393,x4391,x4394),f665(x4393,x4392,x4394)) % 178.07/177.94 [440]~E(x4401,x4402)+E(f665(x4403,x4404,x4401),f665(x4403,x4404,x4402)) % 178.07/177.94 [441]~E(x4411,x4412)+E(f810(x4411,x4413,x4414,x4415),f810(x4412,x4413,x4414,x4415)) % 178.07/177.94 [442]~E(x4421,x4422)+E(f810(x4423,x4421,x4424,x4425),f810(x4423,x4422,x4424,x4425)) % 178.07/177.94 [443]~E(x4431,x4432)+E(f810(x4433,x4434,x4431,x4435),f810(x4433,x4434,x4432,x4435)) % 178.07/177.94 [444]~E(x4441,x4442)+E(f810(x4443,x4444,x4445,x4441),f810(x4443,x4444,x4445,x4442)) % 178.07/177.94 [445]~E(x4451,x4452)+E(f839(x4451,x4453,x4454,x4455),f839(x4452,x4453,x4454,x4455)) % 178.07/177.94 [446]~E(x4461,x4462)+E(f839(x4463,x4461,x4464,x4465),f839(x4463,x4462,x4464,x4465)) % 178.07/177.94 [447]~E(x4471,x4472)+E(f839(x4473,x4474,x4471,x4475),f839(x4473,x4474,x4472,x4475)) % 178.07/177.94 [448]~E(x4481,x4482)+E(f839(x4483,x4484,x4485,x4481),f839(x4483,x4484,x4485,x4482)) % 178.07/177.94 [449]~E(x4491,x4492)+E(f503(x4491,x4493,x4494,x4495),f503(x4492,x4493,x4494,x4495)) % 178.07/177.94 [450]~E(x4501,x4502)+E(f503(x4503,x4501,x4504,x4505),f503(x4503,x4502,x4504,x4505)) % 178.07/177.94 [451]~E(x4511,x4512)+E(f503(x4513,x4514,x4511,x4515),f503(x4513,x4514,x4512,x4515)) % 178.07/177.94 [452]~E(x4521,x4522)+E(f503(x4523,x4524,x4525,x4521),f503(x4523,x4524,x4525,x4522)) % 178.07/177.94 [453]~E(x4531,x4532)+E(f41(x4531,x4533),f41(x4532,x4533)) % 178.07/177.94 [454]~E(x4541,x4542)+E(f41(x4543,x4541),f41(x4543,x4542)) % 178.07/177.94 [455]~E(x4551,x4552)+E(f33(x4551,x4553),f33(x4552,x4553)) % 178.07/177.94 [456]~E(x4561,x4562)+E(f33(x4563,x4561),f33(x4563,x4562)) % 178.07/177.94 [457]~E(x4571,x4572)+E(f11(x4571,x4573,x4574),f11(x4572,x4573,x4574)) % 178.07/177.94 [458]~E(x4581,x4582)+E(f11(x4583,x4581,x4584),f11(x4583,x4582,x4584)) % 178.07/177.94 [459]~E(x4591,x4592)+E(f11(x4593,x4594,x4591),f11(x4593,x4594,x4592)) % 178.07/177.94 [460]~E(x4601,x4602)+E(f652(x4601,x4603),f652(x4602,x4603)) % 178.07/177.94 [461]~E(x4611,x4612)+E(f652(x4613,x4611),f652(x4613,x4612)) % 178.07/177.94 [462]~E(x4621,x4622)+E(f56(x4621),f56(x4622)) % 178.07/177.94 [463]~E(x4631,x4632)+E(f760(x4631,x4633,x4634,x4635,x4636),f760(x4632,x4633,x4634,x4635,x4636)) % 178.07/177.94 [464]~E(x4641,x4642)+E(f760(x4643,x4641,x4644,x4645,x4646),f760(x4643,x4642,x4644,x4645,x4646)) % 178.07/177.94 [465]~E(x4651,x4652)+E(f760(x4653,x4654,x4651,x4655,x4656),f760(x4653,x4654,x4652,x4655,x4656)) % 178.07/177.94 [466]~E(x4661,x4662)+E(f760(x4663,x4664,x4665,x4661,x4666),f760(x4663,x4664,x4665,x4662,x4666)) % 178.07/177.94 [467]~E(x4671,x4672)+E(f760(x4673,x4674,x4675,x4676,x4671),f760(x4673,x4674,x4675,x4676,x4672)) % 178.07/177.94 [468]~E(x4681,x4682)+E(f553(x4681,x4683,x4684),f553(x4682,x4683,x4684)) % 178.07/177.94 [469]~E(x4691,x4692)+E(f553(x4693,x4691,x4694),f553(x4693,x4692,x4694)) % 178.07/177.94 [470]~E(x4701,x4702)+E(f553(x4703,x4704,x4701),f553(x4703,x4704,x4702)) % 178.07/177.94 [471]~E(x4711,x4712)+E(f146(x4711,x4713),f146(x4712,x4713)) % 178.07/177.94 [472]~E(x4721,x4722)+E(f146(x4723,x4721),f146(x4723,x4722)) % 178.07/177.94 [473]~E(x4731,x4732)+E(f846(x4731,x4733,x4734,x4735,x4736),f846(x4732,x4733,x4734,x4735,x4736)) % 178.07/177.94 [474]~E(x4741,x4742)+E(f846(x4743,x4741,x4744,x4745,x4746),f846(x4743,x4742,x4744,x4745,x4746)) % 178.07/177.94 [475]~E(x4751,x4752)+E(f846(x4753,x4754,x4751,x4755,x4756),f846(x4753,x4754,x4752,x4755,x4756)) % 178.07/177.94 [476]~E(x4761,x4762)+E(f846(x4763,x4764,x4765,x4761,x4766),f846(x4763,x4764,x4765,x4762,x4766)) % 178.07/177.94 [477]~E(x4771,x4772)+E(f846(x4773,x4774,x4775,x4776,x4771),f846(x4773,x4774,x4775,x4776,x4772)) % 178.07/177.94 [478]~E(x4781,x4782)+E(f159(x4781,x4783),f159(x4782,x4783)) % 178.07/177.94 [479]~E(x4791,x4792)+E(f159(x4793,x4791),f159(x4793,x4792)) % 178.07/177.94 [480]~E(x4801,x4802)+E(f754(x4801,x4803,x4804),f754(x4802,x4803,x4804)) % 178.07/177.94 [481]~E(x4811,x4812)+E(f754(x4813,x4811,x4814),f754(x4813,x4812,x4814)) % 178.07/177.94 [482]~E(x4821,x4822)+E(f754(x4823,x4824,x4821),f754(x4823,x4824,x4822)) % 178.07/177.94 [483]~E(x4831,x4832)+E(f460(x4831,x4833,x4834),f460(x4832,x4833,x4834)) % 178.07/177.94 [484]~E(x4841,x4842)+E(f460(x4843,x4841,x4844),f460(x4843,x4842,x4844)) % 178.07/177.94 [485]~E(x4851,x4852)+E(f460(x4853,x4854,x4851),f460(x4853,x4854,x4852)) % 178.07/177.94 [486]~E(x4861,x4862)+E(f789(x4861,x4863,x4864),f789(x4862,x4863,x4864)) % 178.07/177.94 [487]~E(x4871,x4872)+E(f789(x4873,x4871,x4874),f789(x4873,x4872,x4874)) % 178.07/177.94 [488]~E(x4881,x4882)+E(f789(x4883,x4884,x4881),f789(x4883,x4884,x4882)) % 178.07/177.94 [489]~E(x4891,x4892)+E(f309(x4891,x4893,x4894),f309(x4892,x4893,x4894)) % 178.07/177.94 [490]~E(x4901,x4902)+E(f309(x4903,x4901,x4904),f309(x4903,x4902,x4904)) % 178.07/177.94 [491]~E(x4911,x4912)+E(f309(x4913,x4914,x4911),f309(x4913,x4914,x4912)) % 178.07/177.94 [492]~E(x4921,x4922)+E(f473(x4921,x4923,x4924),f473(x4922,x4923,x4924)) % 178.07/177.94 [493]~E(x4931,x4932)+E(f473(x4933,x4931,x4934),f473(x4933,x4932,x4934)) % 178.07/177.94 [494]~E(x4941,x4942)+E(f473(x4943,x4944,x4941),f473(x4943,x4944,x4942)) % 178.07/177.94 [495]~E(x4951,x4952)+E(f304(x4951),f304(x4952)) % 178.07/177.94 [496]~E(x4961,x4962)+E(f587(x4961,x4963,x4964,x4965),f587(x4962,x4963,x4964,x4965)) % 178.07/177.94 [497]~E(x4971,x4972)+E(f587(x4973,x4971,x4974,x4975),f587(x4973,x4972,x4974,x4975)) % 178.07/177.94 [498]~E(x4981,x4982)+E(f587(x4983,x4984,x4981,x4985),f587(x4983,x4984,x4982,x4985)) % 178.07/177.94 [499]~E(x4991,x4992)+E(f587(x4993,x4994,x4995,x4991),f587(x4993,x4994,x4995,x4992)) % 178.07/177.94 [500]~E(x5001,x5002)+E(f191(x5001),f191(x5002)) % 178.07/177.94 [501]~E(x5011,x5012)+E(f477(x5011,x5013,x5014),f477(x5012,x5013,x5014)) % 178.07/177.94 [502]~E(x5021,x5022)+E(f477(x5023,x5021,x5024),f477(x5023,x5022,x5024)) % 178.07/177.94 [503]~E(x5031,x5032)+E(f477(x5033,x5034,x5031),f477(x5033,x5034,x5032)) % 178.07/177.94 [504]~E(x5041,x5042)+E(f420(x5041,x5043,x5044,x5045),f420(x5042,x5043,x5044,x5045)) % 178.07/177.94 [505]~E(x5051,x5052)+E(f420(x5053,x5051,x5054,x5055),f420(x5053,x5052,x5054,x5055)) % 178.07/177.94 [506]~E(x5061,x5062)+E(f420(x5063,x5064,x5061,x5065),f420(x5063,x5064,x5062,x5065)) % 178.07/177.94 [507]~E(x5071,x5072)+E(f420(x5073,x5074,x5075,x5071),f420(x5073,x5074,x5075,x5072)) % 178.07/177.94 [508]~E(x5081,x5082)+E(f260(x5081,x5083),f260(x5082,x5083)) % 178.07/177.94 [509]~E(x5091,x5092)+E(f260(x5093,x5091),f260(x5093,x5092)) % 178.07/177.94 [510]~E(x5101,x5102)+E(f122(x5101,x5103,x5104),f122(x5102,x5103,x5104)) % 178.07/177.94 [511]~E(x5111,x5112)+E(f122(x5113,x5111,x5114),f122(x5113,x5112,x5114)) % 178.07/177.94 [512]~E(x5121,x5122)+E(f122(x5123,x5124,x5121),f122(x5123,x5124,x5122)) % 178.07/177.94 [513]~E(x5131,x5132)+E(f377(x5131),f377(x5132)) % 178.07/177.94 [514]~E(x5141,x5142)+E(f98(x5141,x5143,x5144),f98(x5142,x5143,x5144)) % 178.07/177.94 [515]~E(x5151,x5152)+E(f98(x5153,x5151,x5154),f98(x5153,x5152,x5154)) % 178.07/177.94 [516]~E(x5161,x5162)+E(f98(x5163,x5164,x5161),f98(x5163,x5164,x5162)) % 178.07/177.94 [517]~E(x5171,x5172)+E(f285(x5171,x5173),f285(x5172,x5173)) % 178.07/177.94 [518]~E(x5181,x5182)+E(f285(x5183,x5181),f285(x5183,x5182)) % 178.07/177.94 [519]~E(x5191,x5192)+E(f433(x5191,x5193),f433(x5192,x5193)) % 178.07/177.94 [520]~E(x5201,x5202)+E(f433(x5203,x5201),f433(x5203,x5202)) % 178.07/177.94 [521]~E(x5211,x5212)+E(f764(x5211,x5213,x5214,x5215,x5216),f764(x5212,x5213,x5214,x5215,x5216)) % 178.07/177.94 [522]~E(x5221,x5222)+E(f764(x5223,x5221,x5224,x5225,x5226),f764(x5223,x5222,x5224,x5225,x5226)) % 178.07/177.94 [523]~E(x5231,x5232)+E(f764(x5233,x5234,x5231,x5235,x5236),f764(x5233,x5234,x5232,x5235,x5236)) % 178.07/177.94 [524]~E(x5241,x5242)+E(f764(x5243,x5244,x5245,x5241,x5246),f764(x5243,x5244,x5245,x5242,x5246)) % 178.07/177.94 [525]~E(x5251,x5252)+E(f764(x5253,x5254,x5255,x5256,x5251),f764(x5253,x5254,x5255,x5256,x5252)) % 178.07/177.94 [526]~E(x5261,x5262)+E(f288(x5261,x5263),f288(x5262,x5263)) % 178.07/177.94 [527]~E(x5271,x5272)+E(f288(x5273,x5271),f288(x5273,x5272)) % 178.07/177.94 [528]~E(x5281,x5282)+E(f836(x5281,x5283,x5284,x5285),f836(x5282,x5283,x5284,x5285)) % 178.07/177.94 [529]~E(x5291,x5292)+E(f836(x5293,x5291,x5294,x5295),f836(x5293,x5292,x5294,x5295)) % 178.07/177.94 [530]~E(x5301,x5302)+E(f836(x5303,x5304,x5301,x5305),f836(x5303,x5304,x5302,x5305)) % 178.07/177.94 [531]~E(x5311,x5312)+E(f836(x5313,x5314,x5315,x5311),f836(x5313,x5314,x5315,x5312)) % 178.07/177.94 [532]~E(x5321,x5322)+E(f374(x5321,x5323,x5324,x5325,x5326),f374(x5322,x5323,x5324,x5325,x5326)) % 178.07/177.94 [533]~E(x5331,x5332)+E(f374(x5333,x5331,x5334,x5335,x5336),f374(x5333,x5332,x5334,x5335,x5336)) % 178.07/177.94 [534]~E(x5341,x5342)+E(f374(x5343,x5344,x5341,x5345,x5346),f374(x5343,x5344,x5342,x5345,x5346)) % 178.07/177.94 [535]~E(x5351,x5352)+E(f374(x5353,x5354,x5355,x5351,x5356),f374(x5353,x5354,x5355,x5352,x5356)) % 178.07/177.94 [536]~E(x5361,x5362)+E(f374(x5363,x5364,x5365,x5366,x5361),f374(x5363,x5364,x5365,x5366,x5362)) % 178.07/177.94 [537]~E(x5371,x5372)+E(f29(x5371,x5373,x5374),f29(x5372,x5373,x5374)) % 178.07/177.94 [538]~E(x5381,x5382)+E(f29(x5383,x5381,x5384),f29(x5383,x5382,x5384)) % 178.07/177.94 [539]~E(x5391,x5392)+E(f29(x5393,x5394,x5391),f29(x5393,x5394,x5392)) % 178.07/177.94 [540]~E(x5401,x5402)+E(f548(x5401,x5403,x5404),f548(x5402,x5403,x5404)) % 178.07/177.94 [541]~E(x5411,x5412)+E(f548(x5413,x5411,x5414),f548(x5413,x5412,x5414)) % 178.07/177.94 [542]~E(x5421,x5422)+E(f548(x5423,x5424,x5421),f548(x5423,x5424,x5422)) % 178.07/177.94 [543]~E(x5431,x5432)+E(f88(x5431),f88(x5432)) % 178.07/177.94 [544]~E(x5441,x5442)+E(f623(x5441,x5443,x5444),f623(x5442,x5443,x5444)) % 178.07/177.94 [545]~E(x5451,x5452)+E(f623(x5453,x5451,x5454),f623(x5453,x5452,x5454)) % 178.07/177.94 [546]~E(x5461,x5462)+E(f623(x5463,x5464,x5461),f623(x5463,x5464,x5462)) % 178.07/177.94 [547]~E(x5471,x5472)+E(f278(x5471,x5473,x5474,x5475),f278(x5472,x5473,x5474,x5475)) % 178.07/177.94 [548]~E(x5481,x5482)+E(f278(x5483,x5481,x5484,x5485),f278(x5483,x5482,x5484,x5485)) % 178.07/177.94 [549]~E(x5491,x5492)+E(f278(x5493,x5494,x5491,x5495),f278(x5493,x5494,x5492,x5495)) % 178.07/177.94 [550]~E(x5501,x5502)+E(f278(x5503,x5504,x5505,x5501),f278(x5503,x5504,x5505,x5502)) % 178.07/177.94 [551]~E(x5511,x5512)+E(f643(x5511,x5513,x5514),f643(x5512,x5513,x5514)) % 178.07/177.94 [552]~E(x5521,x5522)+E(f643(x5523,x5521,x5524),f643(x5523,x5522,x5524)) % 178.07/177.94 [553]~E(x5531,x5532)+E(f643(x5533,x5534,x5531),f643(x5533,x5534,x5532)) % 178.07/177.94 [554]~E(x5541,x5542)+E(f544(x5541,x5543,x5544),f544(x5542,x5543,x5544)) % 178.07/177.94 [555]~E(x5551,x5552)+E(f544(x5553,x5551,x5554),f544(x5553,x5552,x5554)) % 178.07/177.94 [556]~E(x5561,x5562)+E(f544(x5563,x5564,x5561),f544(x5563,x5564,x5562)) % 178.07/177.94 [557]~E(x5571,x5572)+E(f586(x5571,x5573,x5574,x5575),f586(x5572,x5573,x5574,x5575)) % 178.07/177.94 [558]~E(x5581,x5582)+E(f586(x5583,x5581,x5584,x5585),f586(x5583,x5582,x5584,x5585)) % 178.07/177.94 [559]~E(x5591,x5592)+E(f586(x5593,x5594,x5591,x5595),f586(x5593,x5594,x5592,x5595)) % 178.07/177.94 [560]~E(x5601,x5602)+E(f586(x5603,x5604,x5605,x5601),f586(x5603,x5604,x5605,x5602)) % 178.07/177.94 [561]~E(x5611,x5612)+E(f429(x5611,x5613,x5614,x5615),f429(x5612,x5613,x5614,x5615)) % 178.07/177.94 [562]~E(x5621,x5622)+E(f429(x5623,x5621,x5624,x5625),f429(x5623,x5622,x5624,x5625)) % 178.07/177.94 [563]~E(x5631,x5632)+E(f429(x5633,x5634,x5631,x5635),f429(x5633,x5634,x5632,x5635)) % 178.07/177.94 [564]~E(x5641,x5642)+E(f429(x5643,x5644,x5645,x5641),f429(x5643,x5644,x5645,x5642)) % 178.07/177.94 [565]~E(x5651,x5652)+E(f63(x5651,x5653,x5654),f63(x5652,x5653,x5654)) % 178.07/177.94 [566]~E(x5661,x5662)+E(f63(x5663,x5661,x5664),f63(x5663,x5662,x5664)) % 178.07/177.94 [567]~E(x5671,x5672)+E(f63(x5673,x5674,x5671),f63(x5673,x5674,x5672)) % 178.07/177.94 [568]~E(x5681,x5682)+E(f277(x5681,x5683),f277(x5682,x5683)) % 178.07/177.94 [569]~E(x5691,x5692)+E(f277(x5693,x5691),f277(x5693,x5692)) % 178.07/177.94 [570]~E(x5701,x5702)+E(f730(x5701,x5703,x5704),f730(x5702,x5703,x5704)) % 178.07/177.94 [571]~E(x5711,x5712)+E(f730(x5713,x5711,x5714),f730(x5713,x5712,x5714)) % 178.07/177.94 [572]~E(x5721,x5722)+E(f730(x5723,x5724,x5721),f730(x5723,x5724,x5722)) % 178.07/177.94 [573]~E(x5731,x5732)+E(f235(x5731,x5733),f235(x5732,x5733)) % 178.07/177.94 [574]~E(x5741,x5742)+E(f235(x5743,x5741),f235(x5743,x5742)) % 178.07/177.94 [575]~E(x5751,x5752)+E(f590(x5751,x5753,x5754,x5755,x5756,x5757,x5758),f590(x5752,x5753,x5754,x5755,x5756,x5757,x5758)) % 178.07/177.94 [576]~E(x5761,x5762)+E(f590(x5763,x5761,x5764,x5765,x5766,x5767,x5768),f590(x5763,x5762,x5764,x5765,x5766,x5767,x5768)) % 178.07/177.94 [577]~E(x5771,x5772)+E(f590(x5773,x5774,x5771,x5775,x5776,x5777,x5778),f590(x5773,x5774,x5772,x5775,x5776,x5777,x5778)) % 178.07/177.94 [578]~E(x5781,x5782)+E(f590(x5783,x5784,x5785,x5781,x5786,x5787,x5788),f590(x5783,x5784,x5785,x5782,x5786,x5787,x5788)) % 178.07/177.94 [579]~E(x5791,x5792)+E(f590(x5793,x5794,x5795,x5796,x5791,x5797,x5798),f590(x5793,x5794,x5795,x5796,x5792,x5797,x5798)) % 178.07/177.94 [580]~E(x5801,x5802)+E(f590(x5803,x5804,x5805,x5806,x5807,x5801,x5808),f590(x5803,x5804,x5805,x5806,x5807,x5802,x5808)) % 178.07/177.94 [581]~E(x5811,x5812)+E(f590(x5813,x5814,x5815,x5816,x5817,x5818,x5811),f590(x5813,x5814,x5815,x5816,x5817,x5818,x5812)) % 178.07/177.94 [582]~E(x5821,x5822)+E(f674(x5821,x5823,x5824,x5825),f674(x5822,x5823,x5824,x5825)) % 178.07/177.94 [583]~E(x5831,x5832)+E(f674(x5833,x5831,x5834,x5835),f674(x5833,x5832,x5834,x5835)) % 178.07/177.94 [584]~E(x5841,x5842)+E(f674(x5843,x5844,x5841,x5845),f674(x5843,x5844,x5842,x5845)) % 178.07/177.94 [585]~E(x5851,x5852)+E(f674(x5853,x5854,x5855,x5851),f674(x5853,x5854,x5855,x5852)) % 178.07/177.94 [586]~E(x5861,x5862)+E(f187(x5861,x5863,x5864,x5865),f187(x5862,x5863,x5864,x5865)) % 178.07/177.94 [587]~E(x5871,x5872)+E(f187(x5873,x5871,x5874,x5875),f187(x5873,x5872,x5874,x5875)) % 178.07/177.94 [588]~E(x5881,x5882)+E(f187(x5883,x5884,x5881,x5885),f187(x5883,x5884,x5882,x5885)) % 178.07/177.94 [589]~E(x5891,x5892)+E(f187(x5893,x5894,x5895,x5891),f187(x5893,x5894,x5895,x5892)) % 178.07/177.94 [590]~E(x5901,x5902)+E(f584(x5901,x5903,x5904),f584(x5902,x5903,x5904)) % 178.07/177.94 [591]~E(x5911,x5912)+E(f584(x5913,x5911,x5914),f584(x5913,x5912,x5914)) % 178.07/177.94 [592]~E(x5921,x5922)+E(f584(x5923,x5924,x5921),f584(x5923,x5924,x5922)) % 178.07/177.94 [593]~E(x5931,x5932)+E(f713(x5931,x5933),f713(x5932,x5933)) % 178.07/177.94 [594]~E(x5941,x5942)+E(f713(x5943,x5941),f713(x5943,x5942)) % 178.07/177.94 [595]~E(x5951,x5952)+E(f58(x5951),f58(x5952)) % 178.07/177.94 [596]~E(x5961,x5962)+E(f144(x5961,x5963),f144(x5962,x5963)) % 178.07/177.94 [597]~E(x5971,x5972)+E(f144(x5973,x5971),f144(x5973,x5972)) % 178.07/177.94 [598]~E(x5981,x5982)+E(f15(x5981,x5983),f15(x5982,x5983)) % 178.07/177.94 [599]~E(x5991,x5992)+E(f15(x5993,x5991),f15(x5993,x5992)) % 178.07/177.94 [600]~E(x6001,x6002)+E(f776(x6001),f776(x6002)) % 178.07/177.94 [601]~E(x6011,x6012)+E(f702(x6011,x6013,x6014,x6015,x6016,x6017,x6018),f702(x6012,x6013,x6014,x6015,x6016,x6017,x6018)) % 178.07/177.94 [602]~E(x6021,x6022)+E(f702(x6023,x6021,x6024,x6025,x6026,x6027,x6028),f702(x6023,x6022,x6024,x6025,x6026,x6027,x6028)) % 178.07/177.94 [603]~E(x6031,x6032)+E(f702(x6033,x6034,x6031,x6035,x6036,x6037,x6038),f702(x6033,x6034,x6032,x6035,x6036,x6037,x6038)) % 178.07/177.94 [604]~E(x6041,x6042)+E(f702(x6043,x6044,x6045,x6041,x6046,x6047,x6048),f702(x6043,x6044,x6045,x6042,x6046,x6047,x6048)) % 178.07/177.94 [605]~E(x6051,x6052)+E(f702(x6053,x6054,x6055,x6056,x6051,x6057,x6058),f702(x6053,x6054,x6055,x6056,x6052,x6057,x6058)) % 178.07/177.94 [606]~E(x6061,x6062)+E(f702(x6063,x6064,x6065,x6066,x6067,x6061,x6068),f702(x6063,x6064,x6065,x6066,x6067,x6062,x6068)) % 178.07/177.94 [607]~E(x6071,x6072)+E(f702(x6073,x6074,x6075,x6076,x6077,x6078,x6071),f702(x6073,x6074,x6075,x6076,x6077,x6078,x6072)) % 178.07/177.94 [608]~E(x6081,x6082)+E(f78(x6081,x6083,x6084,x6085),f78(x6082,x6083,x6084,x6085)) % 178.07/177.94 [609]~E(x6091,x6092)+E(f78(x6093,x6091,x6094,x6095),f78(x6093,x6092,x6094,x6095)) % 178.07/177.94 [610]~E(x6101,x6102)+E(f78(x6103,x6104,x6101,x6105),f78(x6103,x6104,x6102,x6105)) % 178.07/177.94 [611]~E(x6111,x6112)+E(f78(x6113,x6114,x6115,x6111),f78(x6113,x6114,x6115,x6112)) % 178.07/177.94 [612]~E(x6121,x6122)+E(f422(x6121,x6123,x6124,x6125),f422(x6122,x6123,x6124,x6125)) % 178.07/177.94 [613]~E(x6131,x6132)+E(f422(x6133,x6131,x6134,x6135),f422(x6133,x6132,x6134,x6135)) % 178.07/177.94 [614]~E(x6141,x6142)+E(f422(x6143,x6144,x6141,x6145),f422(x6143,x6144,x6142,x6145)) % 178.07/177.94 [615]~E(x6151,x6152)+E(f422(x6153,x6154,x6155,x6151),f422(x6153,x6154,x6155,x6152)) % 178.07/177.94 [616]~E(x6161,x6162)+E(f690(x6161,x6163,x6164,x6165,x6166,x6167,x6168),f690(x6162,x6163,x6164,x6165,x6166,x6167,x6168)) % 178.07/177.94 [617]~E(x6171,x6172)+E(f690(x6173,x6171,x6174,x6175,x6176,x6177,x6178),f690(x6173,x6172,x6174,x6175,x6176,x6177,x6178)) % 178.07/177.94 [618]~E(x6181,x6182)+E(f690(x6183,x6184,x6181,x6185,x6186,x6187,x6188),f690(x6183,x6184,x6182,x6185,x6186,x6187,x6188)) % 178.07/177.94 [619]~E(x6191,x6192)+E(f690(x6193,x6194,x6195,x6191,x6196,x6197,x6198),f690(x6193,x6194,x6195,x6192,x6196,x6197,x6198)) % 178.07/177.94 [620]~E(x6201,x6202)+E(f690(x6203,x6204,x6205,x6206,x6201,x6207,x6208),f690(x6203,x6204,x6205,x6206,x6202,x6207,x6208)) % 178.07/177.94 [621]~E(x6211,x6212)+E(f690(x6213,x6214,x6215,x6216,x6217,x6211,x6218),f690(x6213,x6214,x6215,x6216,x6217,x6212,x6218)) % 178.07/177.94 [622]~E(x6221,x6222)+E(f690(x6223,x6224,x6225,x6226,x6227,x6228,x6221),f690(x6223,x6224,x6225,x6226,x6227,x6228,x6222)) % 178.07/177.94 [623]~E(x6231,x6232)+E(f154(x6231,x6233,x6234),f154(x6232,x6233,x6234)) % 178.07/177.94 [624]~E(x6241,x6242)+E(f154(x6243,x6241,x6244),f154(x6243,x6242,x6244)) % 178.07/177.94 [625]~E(x6251,x6252)+E(f154(x6253,x6254,x6251),f154(x6253,x6254,x6252)) % 178.07/177.94 [626]~E(x6261,x6262)+E(f817(x6261,x6263,x6264),f817(x6262,x6263,x6264)) % 178.07/177.94 [627]~E(x6271,x6272)+E(f817(x6273,x6271,x6274),f817(x6273,x6272,x6274)) % 178.07/177.94 [628]~E(x6281,x6282)+E(f817(x6283,x6284,x6281),f817(x6283,x6284,x6282)) % 178.07/177.94 [629]~E(x6291,x6292)+E(f301(x6291),f301(x6292)) % 178.07/177.94 [630]~E(x6301,x6302)+E(f746(x6301,x6303,x6304),f746(x6302,x6303,x6304)) % 178.07/177.94 [631]~E(x6311,x6312)+E(f746(x6313,x6311,x6314),f746(x6313,x6312,x6314)) % 178.07/177.94 [632]~E(x6321,x6322)+E(f746(x6323,x6324,x6321),f746(x6323,x6324,x6322)) % 178.07/177.94 [633]~E(x6331,x6332)+E(f683(x6331,x6333),f683(x6332,x6333)) % 178.07/177.94 [634]~E(x6341,x6342)+E(f683(x6343,x6341),f683(x6343,x6342)) % 178.07/177.94 [635]~E(x6351,x6352)+E(f276(x6351,x6353),f276(x6352,x6353)) % 178.07/177.94 [636]~E(x6361,x6362)+E(f276(x6363,x6361),f276(x6363,x6362)) % 178.07/177.94 [637]~E(x6371,x6372)+E(f580(x6371,x6373,x6374),f580(x6372,x6373,x6374)) % 178.07/177.94 [638]~E(x6381,x6382)+E(f580(x6383,x6381,x6384),f580(x6383,x6382,x6384)) % 178.07/177.94 [639]~E(x6391,x6392)+E(f580(x6393,x6394,x6391),f580(x6393,x6394,x6392)) % 178.07/177.94 [640]~E(x6401,x6402)+E(f363(x6401,x6403,x6404),f363(x6402,x6403,x6404)) % 178.07/177.94 [641]~E(x6411,x6412)+E(f363(x6413,x6411,x6414),f363(x6413,x6412,x6414)) % 178.07/177.94 [642]~E(x6421,x6422)+E(f363(x6423,x6424,x6421),f363(x6423,x6424,x6422)) % 178.07/177.94 [643]~E(x6431,x6432)+E(f767(x6431,x6433,x6434,x6435,x6436),f767(x6432,x6433,x6434,x6435,x6436)) % 178.07/177.94 [644]~E(x6441,x6442)+E(f767(x6443,x6441,x6444,x6445,x6446),f767(x6443,x6442,x6444,x6445,x6446)) % 178.07/177.94 [645]~E(x6451,x6452)+E(f767(x6453,x6454,x6451,x6455,x6456),f767(x6453,x6454,x6452,x6455,x6456)) % 178.07/177.94 [646]~E(x6461,x6462)+E(f767(x6463,x6464,x6465,x6461,x6466),f767(x6463,x6464,x6465,x6462,x6466)) % 178.07/177.94 [647]~E(x6471,x6472)+E(f767(x6473,x6474,x6475,x6476,x6471),f767(x6473,x6474,x6475,x6476,x6472)) % 178.07/177.94 [648]~E(x6481,x6482)+E(f14(x6481,x6483),f14(x6482,x6483)) % 178.07/177.94 [649]~E(x6491,x6492)+E(f14(x6493,x6491),f14(x6493,x6492)) % 178.07/177.94 [650]~E(x6501,x6502)+E(f391(x6501,x6503,x6504),f391(x6502,x6503,x6504)) % 178.07/177.94 [651]~E(x6511,x6512)+E(f391(x6513,x6511,x6514),f391(x6513,x6512,x6514)) % 178.07/177.94 [652]~E(x6521,x6522)+E(f391(x6523,x6524,x6521),f391(x6523,x6524,x6522)) % 178.07/177.94 [653]~E(x6531,x6532)+E(f165(x6531),f165(x6532)) % 178.07/177.94 [654]~E(x6541,x6542)+E(f412(x6541,x6543),f412(x6542,x6543)) % 178.07/177.94 [655]~E(x6551,x6552)+E(f412(x6553,x6551),f412(x6553,x6552)) % 178.07/177.94 [656]~E(x6561,x6562)+E(f806(x6561,x6563,x6564),f806(x6562,x6563,x6564)) % 178.07/177.94 [657]~E(x6571,x6572)+E(f806(x6573,x6571,x6574),f806(x6573,x6572,x6574)) % 178.07/177.94 [658]~E(x6581,x6582)+E(f806(x6583,x6584,x6581),f806(x6583,x6584,x6582)) % 178.07/177.94 [659]~E(x6591,x6592)+E(f655(x6591,x6593),f655(x6592,x6593)) % 178.07/177.94 [660]~E(x6601,x6602)+E(f655(x6603,x6601),f655(x6603,x6602)) % 178.07/177.94 [661]~E(x6611,x6612)+E(f497(x6611,x6613,x6614,x6615,x6616,x6617),f497(x6612,x6613,x6614,x6615,x6616,x6617)) % 178.07/177.94 [662]~E(x6621,x6622)+E(f497(x6623,x6621,x6624,x6625,x6626,x6627),f497(x6623,x6622,x6624,x6625,x6626,x6627)) % 178.07/177.94 [663]~E(x6631,x6632)+E(f497(x6633,x6634,x6631,x6635,x6636,x6637),f497(x6633,x6634,x6632,x6635,x6636,x6637)) % 178.07/177.94 [664]~E(x6641,x6642)+E(f497(x6643,x6644,x6645,x6641,x6646,x6647),f497(x6643,x6644,x6645,x6642,x6646,x6647)) % 178.07/177.94 [665]~E(x6651,x6652)+E(f497(x6653,x6654,x6655,x6656,x6651,x6657),f497(x6653,x6654,x6655,x6656,x6652,x6657)) % 178.07/177.94 [666]~E(x6661,x6662)+E(f497(x6663,x6664,x6665,x6666,x6667,x6661),f497(x6663,x6664,x6665,x6666,x6667,x6662)) % 178.07/177.94 [667]~E(x6671,x6672)+E(f280(x6671,x6673),f280(x6672,x6673)) % 178.07/177.94 [668]~E(x6681,x6682)+E(f280(x6683,x6681),f280(x6683,x6682)) % 178.07/177.94 [669]~E(x6691,x6692)+E(f616(x6691,x6693,x6694,x6695,x6696,x6697,x6698,x6699),f616(x6692,x6693,x6694,x6695,x6696,x6697,x6698,x6699)) % 178.07/177.94 [670]~E(x6701,x6702)+E(f616(x6703,x6701,x6704,x6705,x6706,x6707,x6708,x6709),f616(x6703,x6702,x6704,x6705,x6706,x6707,x6708,x6709)) % 178.07/177.94 [671]~E(x6711,x6712)+E(f616(x6713,x6714,x6711,x6715,x6716,x6717,x6718,x6719),f616(x6713,x6714,x6712,x6715,x6716,x6717,x6718,x6719)) % 178.07/177.94 [672]~E(x6721,x6722)+E(f616(x6723,x6724,x6725,x6721,x6726,x6727,x6728,x6729),f616(x6723,x6724,x6725,x6722,x6726,x6727,x6728,x6729)) % 178.07/177.94 [673]~E(x6731,x6732)+E(f616(x6733,x6734,x6735,x6736,x6731,x6737,x6738,x6739),f616(x6733,x6734,x6735,x6736,x6732,x6737,x6738,x6739)) % 178.07/177.94 [674]~E(x6741,x6742)+E(f616(x6743,x6744,x6745,x6746,x6747,x6741,x6748,x6749),f616(x6743,x6744,x6745,x6746,x6747,x6742,x6748,x6749)) % 178.07/177.94 [675]~E(x6751,x6752)+E(f616(x6753,x6754,x6755,x6756,x6757,x6758,x6751,x6759),f616(x6753,x6754,x6755,x6756,x6757,x6758,x6752,x6759)) % 178.07/177.94 [676]~E(x6761,x6762)+E(f616(x6763,x6764,x6765,x6766,x6767,x6768,x6769,x6761),f616(x6763,x6764,x6765,x6766,x6767,x6768,x6769,x6762)) % 178.07/177.94 [677]~E(x6771,x6772)+E(f525(x6771,x6773),f525(x6772,x6773)) % 178.07/177.94 [678]~E(x6781,x6782)+E(f525(x6783,x6781),f525(x6783,x6782)) % 178.07/177.94 [679]~E(x6791,x6792)+E(f633(x6791,x6793,x6794,x6795),f633(x6792,x6793,x6794,x6795)) % 178.07/177.94 [680]~E(x6801,x6802)+E(f633(x6803,x6801,x6804,x6805),f633(x6803,x6802,x6804,x6805)) % 178.07/177.94 [681]~E(x6811,x6812)+E(f633(x6813,x6814,x6811,x6815),f633(x6813,x6814,x6812,x6815)) % 178.07/177.94 [682]~E(x6821,x6822)+E(f633(x6823,x6824,x6825,x6821),f633(x6823,x6824,x6825,x6822)) % 178.07/177.94 [683]~E(x6831,x6832)+E(f406(x6831,x6833,x6834,x6835,x6836),f406(x6832,x6833,x6834,x6835,x6836)) % 178.07/177.94 [684]~E(x6841,x6842)+E(f406(x6843,x6841,x6844,x6845,x6846),f406(x6843,x6842,x6844,x6845,x6846)) % 178.07/177.94 [685]~E(x6851,x6852)+E(f406(x6853,x6854,x6851,x6855,x6856),f406(x6853,x6854,x6852,x6855,x6856)) % 178.07/177.94 [686]~E(x6861,x6862)+E(f406(x6863,x6864,x6865,x6861,x6866),f406(x6863,x6864,x6865,x6862,x6866)) % 178.07/177.94 [687]~E(x6871,x6872)+E(f406(x6873,x6874,x6875,x6876,x6871),f406(x6873,x6874,x6875,x6876,x6872)) % 178.07/177.94 [688]~E(x6881,x6882)+E(f859(x6881,x6883),f859(x6882,x6883)) % 178.07/177.94 [689]~E(x6891,x6892)+E(f859(x6893,x6891),f859(x6893,x6892)) % 178.07/177.94 [690]~E(x6901,x6902)+E(f479(x6901,x6903,x6904,x6905),f479(x6902,x6903,x6904,x6905)) % 178.07/177.94 [691]~E(x6911,x6912)+E(f479(x6913,x6911,x6914,x6915),f479(x6913,x6912,x6914,x6915)) % 178.07/177.94 [692]~E(x6921,x6922)+E(f479(x6923,x6924,x6921,x6925),f479(x6923,x6924,x6922,x6925)) % 178.07/177.94 [693]~E(x6931,x6932)+E(f479(x6933,x6934,x6935,x6931),f479(x6933,x6934,x6935,x6932)) % 178.07/177.94 [694]~E(x6941,x6942)+E(f770(x6941,x6943,x6944,x6945,x6946),f770(x6942,x6943,x6944,x6945,x6946)) % 178.07/177.94 [695]~E(x6951,x6952)+E(f770(x6953,x6951,x6954,x6955,x6956),f770(x6953,x6952,x6954,x6955,x6956)) % 178.07/177.94 [696]~E(x6961,x6962)+E(f770(x6963,x6964,x6961,x6965,x6966),f770(x6963,x6964,x6962,x6965,x6966)) % 178.07/177.94 [697]~E(x6971,x6972)+E(f770(x6973,x6974,x6975,x6971,x6976),f770(x6973,x6974,x6975,x6972,x6976)) % 178.07/177.94 [698]~E(x6981,x6982)+E(f770(x6983,x6984,x6985,x6986,x6981),f770(x6983,x6984,x6985,x6986,x6982)) % 178.07/177.94 [699]~E(x6991,x6992)+E(f145(x6991,x6993),f145(x6992,x6993)) % 178.07/177.94 [700]~E(x7001,x7002)+E(f145(x7003,x7001),f145(x7003,x7002)) % 178.07/177.94 [701]~E(x7011,x7012)+E(f419(x7011,x7013,x7014),f419(x7012,x7013,x7014)) % 178.07/177.94 [702]~E(x7021,x7022)+E(f419(x7023,x7021,x7024),f419(x7023,x7022,x7024)) % 178.07/177.94 [703]~E(x7031,x7032)+E(f419(x7033,x7034,x7031),f419(x7033,x7034,x7032)) % 178.07/177.94 [704]~E(x7041,x7042)+E(f215(x7041,x7043,x7044,x7045,x7046,x7047,x7048),f215(x7042,x7043,x7044,x7045,x7046,x7047,x7048)) % 178.07/177.94 [705]~E(x7051,x7052)+E(f215(x7053,x7051,x7054,x7055,x7056,x7057,x7058),f215(x7053,x7052,x7054,x7055,x7056,x7057,x7058)) % 178.07/177.94 [706]~E(x7061,x7062)+E(f215(x7063,x7064,x7061,x7065,x7066,x7067,x7068),f215(x7063,x7064,x7062,x7065,x7066,x7067,x7068)) % 178.07/177.94 [707]~E(x7071,x7072)+E(f215(x7073,x7074,x7075,x7071,x7076,x7077,x7078),f215(x7073,x7074,x7075,x7072,x7076,x7077,x7078)) % 178.07/177.94 [708]~E(x7081,x7082)+E(f215(x7083,x7084,x7085,x7086,x7081,x7087,x7088),f215(x7083,x7084,x7085,x7086,x7082,x7087,x7088)) % 178.07/177.94 [709]~E(x7091,x7092)+E(f215(x7093,x7094,x7095,x7096,x7097,x7091,x7098),f215(x7093,x7094,x7095,x7096,x7097,x7092,x7098)) % 178.07/177.94 [710]~E(x7101,x7102)+E(f215(x7103,x7104,x7105,x7106,x7107,x7108,x7101),f215(x7103,x7104,x7105,x7106,x7107,x7108,x7102)) % 178.07/177.94 [711]~E(x7111,x7112)+E(f718(x7111,x7113,x7114),f718(x7112,x7113,x7114)) % 178.07/177.94 [712]~E(x7121,x7122)+E(f718(x7123,x7121,x7124),f718(x7123,x7122,x7124)) % 178.07/177.94 [713]~E(x7131,x7132)+E(f718(x7133,x7134,x7131),f718(x7133,x7134,x7132)) % 178.07/177.94 [714]~E(x7141,x7142)+E(f253(x7141,x7143,x7144),f253(x7142,x7143,x7144)) % 178.07/177.94 [715]~E(x7151,x7152)+E(f253(x7153,x7151,x7154),f253(x7153,x7152,x7154)) % 178.07/177.94 [716]~E(x7161,x7162)+E(f253(x7163,x7164,x7161),f253(x7163,x7164,x7162)) % 178.07/177.94 [717]~E(x7171,x7172)+E(f200(x7171,x7173),f200(x7172,x7173)) % 178.07/177.94 [718]~E(x7181,x7182)+E(f200(x7183,x7181),f200(x7183,x7182)) % 178.07/177.94 [719]~E(x7191,x7192)+E(f128(x7191),f128(x7192)) % 178.07/177.94 [720]~E(x7201,x7202)+E(f647(x7201,x7203),f647(x7202,x7203)) % 178.07/177.94 [721]~E(x7211,x7212)+E(f647(x7213,x7211),f647(x7213,x7212)) % 178.07/177.94 [722]~E(x7221,x7222)+E(f409(x7221,x7223,x7224,x7225,x7226,x7227),f409(x7222,x7223,x7224,x7225,x7226,x7227)) % 178.07/177.94 [723]~E(x7231,x7232)+E(f409(x7233,x7231,x7234,x7235,x7236,x7237),f409(x7233,x7232,x7234,x7235,x7236,x7237)) % 178.07/177.94 [724]~E(x7241,x7242)+E(f409(x7243,x7244,x7241,x7245,x7246,x7247),f409(x7243,x7244,x7242,x7245,x7246,x7247)) % 178.07/177.94 [725]~E(x7251,x7252)+E(f409(x7253,x7254,x7255,x7251,x7256,x7257),f409(x7253,x7254,x7255,x7252,x7256,x7257)) % 178.07/177.94 [726]~E(x7261,x7262)+E(f409(x7263,x7264,x7265,x7266,x7261,x7267),f409(x7263,x7264,x7265,x7266,x7262,x7267)) % 178.07/177.94 [727]~E(x7271,x7272)+E(f409(x7273,x7274,x7275,x7276,x7277,x7271),f409(x7273,x7274,x7275,x7276,x7277,x7272)) % 178.07/177.94 [728]~E(x7281,x7282)+E(f75(x7281,x7283),f75(x7282,x7283)) % 178.07/177.94 [729]~E(x7291,x7292)+E(f75(x7293,x7291),f75(x7293,x7292)) % 178.07/177.94 [730]~E(x7301,x7302)+E(f314(x7301),f314(x7302)) % 178.07/177.94 [731]~E(x7311,x7312)+E(f97(x7311,x7313,x7314,x7315),f97(x7312,x7313,x7314,x7315)) % 178.07/177.94 [732]~E(x7321,x7322)+E(f97(x7323,x7321,x7324,x7325),f97(x7323,x7322,x7324,x7325)) % 178.07/177.94 [733]~E(x7331,x7332)+E(f97(x7333,x7334,x7331,x7335),f97(x7333,x7334,x7332,x7335)) % 178.07/177.94 [734]~E(x7341,x7342)+E(f97(x7343,x7344,x7345,x7341),f97(x7343,x7344,x7345,x7342)) % 178.07/177.94 [735]~E(x7351,x7352)+E(f139(x7351,x7353,x7354),f139(x7352,x7353,x7354)) % 178.07/177.94 [736]~E(x7361,x7362)+E(f139(x7363,x7361,x7364),f139(x7363,x7362,x7364)) % 178.07/177.94 [737]~E(x7371,x7372)+E(f139(x7373,x7374,x7371),f139(x7373,x7374,x7372)) % 178.07/177.94 [738]~E(x7381,x7382)+E(f475(x7381,x7383,x7384),f475(x7382,x7383,x7384)) % 178.07/177.94 [739]~E(x7391,x7392)+E(f475(x7393,x7391,x7394),f475(x7393,x7392,x7394)) % 178.07/177.94 [740]~E(x7401,x7402)+E(f475(x7403,x7404,x7401),f475(x7403,x7404,x7402)) % 178.07/177.94 [741]~E(x7411,x7412)+E(f431(x7411,x7413,x7414),f431(x7412,x7413,x7414)) % 178.07/177.94 [742]~E(x7421,x7422)+E(f431(x7423,x7421,x7424),f431(x7423,x7422,x7424)) % 178.07/177.94 [743]~E(x7431,x7432)+E(f431(x7433,x7434,x7431),f431(x7433,x7434,x7432)) % 178.07/177.94 [744]~E(x7441,x7442)+E(f474(x7441,x7443,x7444),f474(x7442,x7443,x7444)) % 178.07/177.94 [745]~E(x7451,x7452)+E(f474(x7453,x7451,x7454),f474(x7453,x7452,x7454)) % 178.07/177.94 [746]~E(x7461,x7462)+E(f474(x7463,x7464,x7461),f474(x7463,x7464,x7462)) % 178.07/177.94 [747]~E(x7471,x7472)+E(f793(x7471,x7473),f793(x7472,x7473)) % 178.07/177.94 [748]~E(x7481,x7482)+E(f793(x7483,x7481),f793(x7483,x7482)) % 178.07/177.94 [749]~E(x7491,x7492)+E(f773(x7491,x7493,x7494,x7495),f773(x7492,x7493,x7494,x7495)) % 178.07/177.94 [750]~E(x7501,x7502)+E(f773(x7503,x7501,x7504,x7505),f773(x7503,x7502,x7504,x7505)) % 178.07/177.94 [751]~E(x7511,x7512)+E(f773(x7513,x7514,x7511,x7515),f773(x7513,x7514,x7512,x7515)) % 178.07/177.94 [752]~E(x7521,x7522)+E(f773(x7523,x7524,x7525,x7521),f773(x7523,x7524,x7525,x7522)) % 178.07/177.94 [753]~E(x7531,x7532)+E(f311(x7531,x7533,x7534),f311(x7532,x7533,x7534)) % 178.07/177.94 [754]~E(x7541,x7542)+E(f311(x7543,x7541,x7544),f311(x7543,x7542,x7544)) % 178.07/177.94 [755]~E(x7551,x7552)+E(f311(x7553,x7554,x7551),f311(x7553,x7554,x7552)) % 178.07/177.94 [756]~E(x7561,x7562)+E(f829(x7561,x7563,x7564,x7565,x7566),f829(x7562,x7563,x7564,x7565,x7566)) % 178.07/177.94 [757]~E(x7571,x7572)+E(f829(x7573,x7571,x7574,x7575,x7576),f829(x7573,x7572,x7574,x7575,x7576)) % 178.07/177.94 [758]~E(x7581,x7582)+E(f829(x7583,x7584,x7581,x7585,x7586),f829(x7583,x7584,x7582,x7585,x7586)) % 178.07/177.94 [759]~E(x7591,x7592)+E(f829(x7593,x7594,x7595,x7591,x7596),f829(x7593,x7594,x7595,x7592,x7596)) % 178.07/177.94 [760]~E(x7601,x7602)+E(f829(x7603,x7604,x7605,x7606,x7601),f829(x7603,x7604,x7605,x7606,x7602)) % 178.07/177.94 [761]~E(x7611,x7612)+E(f115(x7611),f115(x7612)) % 178.07/177.94 [762]~E(x7621,x7622)+E(f542(x7621,x7623),f542(x7622,x7623)) % 178.07/177.94 [763]~E(x7631,x7632)+E(f542(x7633,x7631),f542(x7633,x7632)) % 178.07/177.94 [764]~E(x7641,x7642)+E(f372(x7641,x7643,x7644,x7645,x7646),f372(x7642,x7643,x7644,x7645,x7646)) % 178.07/177.94 [765]~E(x7651,x7652)+E(f372(x7653,x7651,x7654,x7655,x7656),f372(x7653,x7652,x7654,x7655,x7656)) % 178.07/177.94 [766]~E(x7661,x7662)+E(f372(x7663,x7664,x7661,x7665,x7666),f372(x7663,x7664,x7662,x7665,x7666)) % 178.07/177.94 [767]~E(x7671,x7672)+E(f372(x7673,x7674,x7675,x7671,x7676),f372(x7673,x7674,x7675,x7672,x7676)) % 178.07/177.94 [768]~E(x7681,x7682)+E(f372(x7683,x7684,x7685,x7686,x7681),f372(x7683,x7684,x7685,x7686,x7682)) % 178.07/177.94 [769]~E(x7691,x7692)+E(f529(x7691,x7693,x7694),f529(x7692,x7693,x7694)) % 178.07/177.94 [770]~E(x7701,x7702)+E(f529(x7703,x7701,x7704),f529(x7703,x7702,x7704)) % 178.07/177.94 [771]~E(x7711,x7712)+E(f529(x7713,x7714,x7711),f529(x7713,x7714,x7712)) % 178.07/177.94 [772]~E(x7721,x7722)+E(f262(x7721,x7723),f262(x7722,x7723)) % 178.07/177.94 [773]~E(x7731,x7732)+E(f262(x7733,x7731),f262(x7733,x7732)) % 178.07/177.94 [774]~E(x7741,x7742)+E(f398(x7741,x7743,x7744),f398(x7742,x7743,x7744)) % 178.07/177.94 [775]~E(x7751,x7752)+E(f398(x7753,x7751,x7754),f398(x7753,x7752,x7754)) % 178.07/177.94 [776]~E(x7761,x7762)+E(f398(x7763,x7764,x7761),f398(x7763,x7764,x7762)) % 178.07/177.94 [777]~E(x7771,x7772)+E(f707(x7771),f707(x7772)) % 178.07/177.94 [778]~E(x7781,x7782)+E(f316(x7781,x7783,x7784,x7785),f316(x7782,x7783,x7784,x7785)) % 178.07/177.94 [779]~E(x7791,x7792)+E(f316(x7793,x7791,x7794,x7795),f316(x7793,x7792,x7794,x7795)) % 178.07/177.94 [780]~E(x7801,x7802)+E(f316(x7803,x7804,x7801,x7805),f316(x7803,x7804,x7802,x7805)) % 178.07/177.94 [781]~E(x7811,x7812)+E(f316(x7813,x7814,x7815,x7811),f316(x7813,x7814,x7815,x7812)) % 178.07/177.94 [782]~E(x7821,x7822)+E(f255(x7821,x7823,x7824),f255(x7822,x7823,x7824)) % 178.07/177.94 [783]~E(x7831,x7832)+E(f255(x7833,x7831,x7834),f255(x7833,x7832,x7834)) % 178.07/177.94 [784]~E(x7841,x7842)+E(f255(x7843,x7844,x7841),f255(x7843,x7844,x7842)) % 178.07/177.94 [785]~E(x7851,x7852)+E(f77(x7851,x7853,x7854,x7855,x7856),f77(x7852,x7853,x7854,x7855,x7856)) % 178.07/177.94 [786]~E(x7861,x7862)+E(f77(x7863,x7861,x7864,x7865,x7866),f77(x7863,x7862,x7864,x7865,x7866)) % 178.07/177.94 [787]~E(x7871,x7872)+E(f77(x7873,x7874,x7871,x7875,x7876),f77(x7873,x7874,x7872,x7875,x7876)) % 178.07/177.94 [788]~E(x7881,x7882)+E(f77(x7883,x7884,x7885,x7881,x7886),f77(x7883,x7884,x7885,x7882,x7886)) % 178.07/177.94 [789]~E(x7891,x7892)+E(f77(x7893,x7894,x7895,x7896,x7891),f77(x7893,x7894,x7895,x7896,x7892)) % 178.07/177.94 [790]~E(x7901,x7902)+E(f270(x7901,x7903,x7904,x7905),f270(x7902,x7903,x7904,x7905)) % 178.07/177.94 [791]~E(x7911,x7912)+E(f270(x7913,x7911,x7914,x7915),f270(x7913,x7912,x7914,x7915)) % 178.07/177.94 [792]~E(x7921,x7922)+E(f270(x7923,x7924,x7921,x7925),f270(x7923,x7924,x7922,x7925)) % 178.07/177.94 [793]~E(x7931,x7932)+E(f270(x7933,x7934,x7935,x7931),f270(x7933,x7934,x7935,x7932)) % 178.07/177.94 [794]~E(x7941,x7942)+E(f546(x7941,x7943,x7944,x7945,x7946,x7947,x7948),f546(x7942,x7943,x7944,x7945,x7946,x7947,x7948)) % 178.07/177.94 [795]~E(x7951,x7952)+E(f546(x7953,x7951,x7954,x7955,x7956,x7957,x7958),f546(x7953,x7952,x7954,x7955,x7956,x7957,x7958)) % 178.07/177.94 [796]~E(x7961,x7962)+E(f546(x7963,x7964,x7961,x7965,x7966,x7967,x7968),f546(x7963,x7964,x7962,x7965,x7966,x7967,x7968)) % 178.07/177.94 [797]~E(x7971,x7972)+E(f546(x7973,x7974,x7975,x7971,x7976,x7977,x7978),f546(x7973,x7974,x7975,x7972,x7976,x7977,x7978)) % 178.07/177.94 [798]~E(x7981,x7982)+E(f546(x7983,x7984,x7985,x7986,x7981,x7987,x7988),f546(x7983,x7984,x7985,x7986,x7982,x7987,x7988)) % 178.07/177.94 [799]~E(x7991,x7992)+E(f546(x7993,x7994,x7995,x7996,x7997,x7991,x7998),f546(x7993,x7994,x7995,x7996,x7997,x7992,x7998)) % 178.07/177.94 [800]~E(x8001,x8002)+E(f546(x8003,x8004,x8005,x8006,x8007,x8008,x8001),f546(x8003,x8004,x8005,x8006,x8007,x8008,x8002)) % 178.07/177.94 [801]~E(x8011,x8012)+E(f46(x8011,x8013),f46(x8012,x8013)) % 178.07/177.94 [802]~E(x8021,x8022)+E(f46(x8023,x8021),f46(x8023,x8022)) % 178.07/177.94 [803]~E(x8031,x8032)+E(f574(x8031,x8033,x8034,x8035,x8036,x8037),f574(x8032,x8033,x8034,x8035,x8036,x8037)) % 178.07/177.94 [804]~E(x8041,x8042)+E(f574(x8043,x8041,x8044,x8045,x8046,x8047),f574(x8043,x8042,x8044,x8045,x8046,x8047)) % 178.07/177.94 [805]~E(x8051,x8052)+E(f574(x8053,x8054,x8051,x8055,x8056,x8057),f574(x8053,x8054,x8052,x8055,x8056,x8057)) % 178.07/177.94 [806]~E(x8061,x8062)+E(f574(x8063,x8064,x8065,x8061,x8066,x8067),f574(x8063,x8064,x8065,x8062,x8066,x8067)) % 178.07/177.94 [807]~E(x8071,x8072)+E(f574(x8073,x8074,x8075,x8076,x8071,x8077),f574(x8073,x8074,x8075,x8076,x8072,x8077)) % 178.07/177.94 [808]~E(x8081,x8082)+E(f574(x8083,x8084,x8085,x8086,x8087,x8081),f574(x8083,x8084,x8085,x8086,x8087,x8082)) % 178.07/177.94 [809]~E(x8091,x8092)+E(f289(x8091,x8093),f289(x8092,x8093)) % 178.07/177.94 [810]~E(x8101,x8102)+E(f289(x8103,x8101),f289(x8103,x8102)) % 178.07/177.94 [811]~E(x8111,x8112)+E(f388(x8111,x8113),f388(x8112,x8113)) % 178.07/177.94 [812]~E(x8121,x8122)+E(f388(x8123,x8121),f388(x8123,x8122)) % 178.07/177.94 [813]~E(x8131,x8132)+E(f282(x8131),f282(x8132)) % 178.07/177.94 [814]~E(x8141,x8142)+E(f541(x8141,x8143,x8144,x8145),f541(x8142,x8143,x8144,x8145)) % 178.07/177.94 [815]~E(x8151,x8152)+E(f541(x8153,x8151,x8154,x8155),f541(x8153,x8152,x8154,x8155)) % 178.07/177.94 [816]~E(x8161,x8162)+E(f541(x8163,x8164,x8161,x8165),f541(x8163,x8164,x8162,x8165)) % 178.07/177.94 [817]~E(x8171,x8172)+E(f541(x8173,x8174,x8175,x8171),f541(x8173,x8174,x8175,x8172)) % 178.07/177.94 [818]~E(x8181,x8182)+E(f337(x8181),f337(x8182)) % 178.07/177.94 [819]~E(x8191,x8192)+E(f162(x8191,x8193,x8194,x8195),f162(x8192,x8193,x8194,x8195)) % 178.07/177.94 [820]~E(x8201,x8202)+E(f162(x8203,x8201,x8204,x8205),f162(x8203,x8202,x8204,x8205)) % 178.07/177.94 [821]~E(x8211,x8212)+E(f162(x8213,x8214,x8211,x8215),f162(x8213,x8214,x8212,x8215)) % 178.07/177.94 [822]~E(x8221,x8222)+E(f162(x8223,x8224,x8225,x8221),f162(x8223,x8224,x8225,x8222)) % 178.07/177.94 [823]~E(x8231,x8232)+E(f640(x8231,x8233,x8234),f640(x8232,x8233,x8234)) % 178.07/177.94 [824]~E(x8241,x8242)+E(f640(x8243,x8241,x8244),f640(x8243,x8242,x8244)) % 178.07/177.94 [825]~E(x8251,x8252)+E(f640(x8253,x8254,x8251),f640(x8253,x8254,x8252)) % 178.07/177.94 [826]~E(x8261,x8262)+E(f774(x8261,x8263,x8264,x8265),f774(x8262,x8263,x8264,x8265)) % 178.07/177.94 [827]~E(x8271,x8272)+E(f774(x8273,x8271,x8274,x8275),f774(x8273,x8272,x8274,x8275)) % 178.07/177.94 [828]~E(x8281,x8282)+E(f774(x8283,x8284,x8281,x8285),f774(x8283,x8284,x8282,x8285)) % 178.07/177.94 [829]~E(x8291,x8292)+E(f774(x8293,x8294,x8295,x8291),f774(x8293,x8294,x8295,x8292)) % 178.07/177.94 [830]~E(x8301,x8302)+E(f488(x8301,x8303),f488(x8302,x8303)) % 178.07/177.94 [831]~E(x8311,x8312)+E(f488(x8313,x8311),f488(x8313,x8312)) % 178.07/177.94 [832]~E(x8321,x8322)+E(f656(x8321,x8323,x8324),f656(x8322,x8323,x8324)) % 178.07/177.94 [833]~E(x8331,x8332)+E(f656(x8333,x8331,x8334),f656(x8333,x8332,x8334)) % 178.07/177.94 [834]~E(x8341,x8342)+E(f656(x8343,x8344,x8341),f656(x8343,x8344,x8342)) % 178.07/177.94 [835]~E(x8351,x8352)+E(f851(x8351,x8353,x8354),f851(x8352,x8353,x8354)) % 178.07/177.94 [836]~E(x8361,x8362)+E(f851(x8363,x8361,x8364),f851(x8363,x8362,x8364)) % 178.07/177.94 [837]~E(x8371,x8372)+E(f851(x8373,x8374,x8371),f851(x8373,x8374,x8372)) % 178.07/177.94 [838]~E(x8381,x8382)+E(f557(x8381),f557(x8382)) % 178.07/177.94 [839]~E(x8391,x8392)+E(f578(x8391,x8393),f578(x8392,x8393)) % 178.07/177.94 [840]~E(x8401,x8402)+E(f578(x8403,x8401),f578(x8403,x8402)) % 178.07/177.94 [841]~E(x8411,x8412)+E(f715(x8411,x8413,x8414,x8415),f715(x8412,x8413,x8414,x8415)) % 178.07/177.94 [842]~E(x8421,x8422)+E(f715(x8423,x8421,x8424,x8425),f715(x8423,x8422,x8424,x8425)) % 178.07/177.94 [843]~E(x8431,x8432)+E(f715(x8433,x8434,x8431,x8435),f715(x8433,x8434,x8432,x8435)) % 178.07/177.94 [844]~E(x8441,x8442)+E(f715(x8443,x8444,x8445,x8441),f715(x8443,x8444,x8445,x8442)) % 178.07/177.94 [845]~E(x8451,x8452)+E(f698(x8451,x8453,x8454),f698(x8452,x8453,x8454)) % 178.07/177.94 [846]~E(x8461,x8462)+E(f698(x8463,x8461,x8464),f698(x8463,x8462,x8464)) % 178.07/177.94 [847]~E(x8471,x8472)+E(f698(x8473,x8474,x8471),f698(x8473,x8474,x8472)) % 178.07/177.94 [848]~E(x8481,x8482)+E(f696(x8481,x8483),f696(x8482,x8483)) % 178.07/177.94 [849]~E(x8491,x8492)+E(f696(x8493,x8491),f696(x8493,x8492)) % 178.07/177.94 [850]~E(x8501,x8502)+E(f468(x8501,x8503,x8504),f468(x8502,x8503,x8504)) % 178.07/177.94 [851]~E(x8511,x8512)+E(f468(x8513,x8511,x8514),f468(x8513,x8512,x8514)) % 178.07/177.94 [852]~E(x8521,x8522)+E(f468(x8523,x8524,x8521),f468(x8523,x8524,x8522)) % 178.07/177.94 [853]~E(x8531,x8532)+E(f729(x8531,x8533,x8534),f729(x8532,x8533,x8534)) % 178.07/177.94 [854]~E(x8541,x8542)+E(f729(x8543,x8541,x8544),f729(x8543,x8542,x8544)) % 178.07/177.94 [855]~E(x8551,x8552)+E(f729(x8553,x8554,x8551),f729(x8553,x8554,x8552)) % 178.07/177.94 [856]~E(x8561,x8562)+E(f808(x8561,x8563,x8564),f808(x8562,x8563,x8564)) % 178.07/177.94 [857]~E(x8571,x8572)+E(f808(x8573,x8571,x8574),f808(x8573,x8572,x8574)) % 178.07/177.94 [858]~E(x8581,x8582)+E(f808(x8583,x8584,x8581),f808(x8583,x8584,x8582)) % 178.07/177.94 [859]~E(x8591,x8592)+E(f258(x8591,x8593,x8594),f258(x8592,x8593,x8594)) % 178.07/177.94 [860]~E(x8601,x8602)+E(f258(x8603,x8601,x8604),f258(x8603,x8602,x8604)) % 178.07/177.94 [861]~E(x8611,x8612)+E(f258(x8613,x8614,x8611),f258(x8613,x8614,x8612)) % 178.07/177.94 [862]~E(x8621,x8622)+E(f612(x8621,x8623,x8624),f612(x8622,x8623,x8624)) % 178.07/177.94 [863]~E(x8631,x8632)+E(f612(x8633,x8631,x8634),f612(x8633,x8632,x8634)) % 178.07/177.94 [864]~E(x8641,x8642)+E(f612(x8643,x8644,x8641),f612(x8643,x8644,x8642)) % 178.07/177.94 [865]~E(x8651,x8652)+E(f848(x8651,x8653),f848(x8652,x8653)) % 178.07/177.94 [866]~E(x8661,x8662)+E(f848(x8663,x8661),f848(x8663,x8662)) % 178.07/177.94 [867]~E(x8671,x8672)+E(f634(x8671,x8673,x8674,x8675),f634(x8672,x8673,x8674,x8675)) % 178.07/177.94 [868]~E(x8681,x8682)+E(f634(x8683,x8681,x8684,x8685),f634(x8683,x8682,x8684,x8685)) % 178.07/177.94 [869]~E(x8691,x8692)+E(f634(x8693,x8694,x8691,x8695),f634(x8693,x8694,x8692,x8695)) % 178.07/177.94 [870]~E(x8701,x8702)+E(f634(x8703,x8704,x8705,x8701),f634(x8703,x8704,x8705,x8702)) % 178.07/177.94 [871]~E(x8711,x8712)+E(f856(x8711,x8713,x8714,x8715,x8716,x8717),f856(x8712,x8713,x8714,x8715,x8716,x8717)) % 178.07/177.94 [872]~E(x8721,x8722)+E(f856(x8723,x8721,x8724,x8725,x8726,x8727),f856(x8723,x8722,x8724,x8725,x8726,x8727)) % 178.07/177.94 [873]~E(x8731,x8732)+E(f856(x8733,x8734,x8731,x8735,x8736,x8737),f856(x8733,x8734,x8732,x8735,x8736,x8737)) % 178.07/177.94 [874]~E(x8741,x8742)+E(f856(x8743,x8744,x8745,x8741,x8746,x8747),f856(x8743,x8744,x8745,x8742,x8746,x8747)) % 178.07/177.94 [875]~E(x8751,x8752)+E(f856(x8753,x8754,x8755,x8756,x8751,x8757),f856(x8753,x8754,x8755,x8756,x8752,x8757)) % 178.07/177.94 [876]~E(x8761,x8762)+E(f856(x8763,x8764,x8765,x8766,x8767,x8761),f856(x8763,x8764,x8765,x8766,x8767,x8762)) % 178.07/177.94 [877]~E(x8771,x8772)+E(f321(x8771,x8773,x8774,x8775),f321(x8772,x8773,x8774,x8775)) % 178.07/177.94 [878]~E(x8781,x8782)+E(f321(x8783,x8781,x8784,x8785),f321(x8783,x8782,x8784,x8785)) % 178.07/177.94 [879]~E(x8791,x8792)+E(f321(x8793,x8794,x8791,x8795),f321(x8793,x8794,x8792,x8795)) % 178.07/177.94 [880]~E(x8801,x8802)+E(f321(x8803,x8804,x8805,x8801),f321(x8803,x8804,x8805,x8802)) % 178.07/177.94 [881]~E(x8811,x8812)+E(f197(x8811,x8813),f197(x8812,x8813)) % 178.07/177.94 [882]~E(x8821,x8822)+E(f197(x8823,x8821),f197(x8823,x8822)) % 178.07/177.94 [883]~E(x8831,x8832)+E(f373(x8831,x8833,x8834,x8835,x8836),f373(x8832,x8833,x8834,x8835,x8836)) % 178.07/177.94 [884]~E(x8841,x8842)+E(f373(x8843,x8841,x8844,x8845,x8846),f373(x8843,x8842,x8844,x8845,x8846)) % 178.07/177.94 [885]~E(x8851,x8852)+E(f373(x8853,x8854,x8851,x8855,x8856),f373(x8853,x8854,x8852,x8855,x8856)) % 178.07/177.94 [886]~E(x8861,x8862)+E(f373(x8863,x8864,x8865,x8861,x8866),f373(x8863,x8864,x8865,x8862,x8866)) % 178.07/177.94 [887]~E(x8871,x8872)+E(f373(x8873,x8874,x8875,x8876,x8871),f373(x8873,x8874,x8875,x8876,x8872)) % 178.07/177.94 [888]~E(x8881,x8882)+E(f124(x8881,x8883),f124(x8882,x8883)) % 178.07/177.94 [889]~E(x8891,x8892)+E(f124(x8893,x8891),f124(x8893,x8892)) % 178.07/177.94 [890]~E(x8901,x8902)+E(f765(x8901,x8903,x8904,x8905,x8906),f765(x8902,x8903,x8904,x8905,x8906)) % 178.07/177.94 [891]~E(x8911,x8912)+E(f765(x8913,x8911,x8914,x8915,x8916),f765(x8913,x8912,x8914,x8915,x8916)) % 178.07/177.94 [892]~E(x8921,x8922)+E(f765(x8923,x8924,x8921,x8925,x8926),f765(x8923,x8924,x8922,x8925,x8926)) % 178.07/177.94 [893]~E(x8931,x8932)+E(f765(x8933,x8934,x8935,x8931,x8936),f765(x8933,x8934,x8935,x8932,x8936)) % 178.07/177.94 [894]~E(x8941,x8942)+E(f765(x8943,x8944,x8945,x8946,x8941),f765(x8943,x8944,x8945,x8946,x8942)) % 178.07/177.94 [895]~E(x8951,x8952)+E(f369(x8951,x8953,x8954),f369(x8952,x8953,x8954)) % 178.07/177.94 [896]~E(x8961,x8962)+E(f369(x8963,x8961,x8964),f369(x8963,x8962,x8964)) % 178.07/177.94 [897]~E(x8971,x8972)+E(f369(x8973,x8974,x8971),f369(x8973,x8974,x8972)) % 178.07/177.94 [898]~E(x8981,x8982)+E(f142(x8981,x8983),f142(x8982,x8983)) % 178.07/177.94 [899]~E(x8991,x8992)+E(f142(x8993,x8991),f142(x8993,x8992)) % 178.07/177.94 [900]~E(x9001,x9002)+E(f294(x9001,x9003,x9004,x9005,x9006),f294(x9002,x9003,x9004,x9005,x9006)) % 178.07/177.94 [901]~E(x9011,x9012)+E(f294(x9013,x9011,x9014,x9015,x9016),f294(x9013,x9012,x9014,x9015,x9016)) % 178.07/177.94 [902]~E(x9021,x9022)+E(f294(x9023,x9024,x9021,x9025,x9026),f294(x9023,x9024,x9022,x9025,x9026)) % 178.07/177.94 [903]~E(x9031,x9032)+E(f294(x9033,x9034,x9035,x9031,x9036),f294(x9033,x9034,x9035,x9032,x9036)) % 178.07/177.94 [904]~E(x9041,x9042)+E(f294(x9043,x9044,x9045,x9046,x9041),f294(x9043,x9044,x9045,x9046,x9042)) % 178.07/177.94 [905]~E(x9051,x9052)+E(f246(x9051,x9053),f246(x9052,x9053)) % 178.07/177.94 [906]~E(x9061,x9062)+E(f246(x9063,x9061),f246(x9063,x9062)) % 178.07/177.94 [907]~E(x9071,x9072)+E(f666(x9071,x9073),f666(x9072,x9073)) % 178.07/177.94 [908]~E(x9081,x9082)+E(f666(x9083,x9081),f666(x9083,x9082)) % 178.07/177.94 [909]~E(x9091,x9092)+E(f129(x9091,x9093,x9094),f129(x9092,x9093,x9094)) % 178.07/177.94 [910]~E(x9101,x9102)+E(f129(x9103,x9101,x9104),f129(x9103,x9102,x9104)) % 178.07/177.94 [911]~E(x9111,x9112)+E(f129(x9113,x9114,x9111),f129(x9113,x9114,x9112)) % 178.07/177.94 [912]~E(x9121,x9122)+E(f296(x9121,x9123,x9124,x9125),f296(x9122,x9123,x9124,x9125)) % 178.07/177.94 [913]~E(x9131,x9132)+E(f296(x9133,x9131,x9134,x9135),f296(x9133,x9132,x9134,x9135)) % 178.07/177.94 [914]~E(x9141,x9142)+E(f296(x9143,x9144,x9141,x9145),f296(x9143,x9144,x9142,x9145)) % 178.07/177.94 [915]~E(x9151,x9152)+E(f296(x9153,x9154,x9155,x9151),f296(x9153,x9154,x9155,x9152)) % 178.07/177.94 [916]~E(x9161,x9162)+E(f535(x9161,x9163,x9164),f535(x9162,x9163,x9164)) % 178.07/177.94 [917]~E(x9171,x9172)+E(f535(x9173,x9171,x9174),f535(x9173,x9172,x9174)) % 178.07/177.94 [918]~E(x9181,x9182)+E(f535(x9183,x9184,x9181),f535(x9183,x9184,x9182)) % 178.07/177.94 [919]~E(x9191,x9192)+E(f339(x9191),f339(x9192)) % 178.07/177.94 [920]~E(x9201,x9202)+E(f265(x9201,x9203,x9204,x9205,x9206),f265(x9202,x9203,x9204,x9205,x9206)) % 178.07/177.94 [921]~E(x9211,x9212)+E(f265(x9213,x9211,x9214,x9215,x9216),f265(x9213,x9212,x9214,x9215,x9216)) % 178.07/177.94 [922]~E(x9221,x9222)+E(f265(x9223,x9224,x9221,x9225,x9226),f265(x9223,x9224,x9222,x9225,x9226)) % 178.07/177.94 [923]~E(x9231,x9232)+E(f265(x9233,x9234,x9235,x9231,x9236),f265(x9233,x9234,x9235,x9232,x9236)) % 178.07/177.94 [924]~E(x9241,x9242)+E(f265(x9243,x9244,x9245,x9246,x9241),f265(x9243,x9244,x9245,x9246,x9242)) % 178.07/177.94 [925]~E(x9251,x9252)+E(f610(x9251,x9253,x9254,x9255,x9256),f610(x9252,x9253,x9254,x9255,x9256)) % 178.07/177.94 [926]~E(x9261,x9262)+E(f610(x9263,x9261,x9264,x9265,x9266),f610(x9263,x9262,x9264,x9265,x9266)) % 178.07/177.94 [927]~E(x9271,x9272)+E(f610(x9273,x9274,x9271,x9275,x9276),f610(x9273,x9274,x9272,x9275,x9276)) % 178.07/177.94 [928]~E(x9281,x9282)+E(f610(x9283,x9284,x9285,x9281,x9286),f610(x9283,x9284,x9285,x9282,x9286)) % 178.07/177.94 [929]~E(x9291,x9292)+E(f610(x9293,x9294,x9295,x9296,x9291),f610(x9293,x9294,x9295,x9296,x9292)) % 178.07/177.94 [930]~E(x9301,x9302)+E(f293(x9301,x9303,x9304,x9305),f293(x9302,x9303,x9304,x9305)) % 178.07/177.94 [931]~E(x9311,x9312)+E(f293(x9313,x9311,x9314,x9315),f293(x9313,x9312,x9314,x9315)) % 178.07/177.94 [932]~E(x9321,x9322)+E(f293(x9323,x9324,x9321,x9325),f293(x9323,x9324,x9322,x9325)) % 178.07/177.94 [933]~E(x9331,x9332)+E(f293(x9333,x9334,x9335,x9331),f293(x9333,x9334,x9335,x9332)) % 178.07/177.94 [934]~E(x9341,x9342)+E(f438(x9341,x9343,x9344,x9345),f438(x9342,x9343,x9344,x9345)) % 178.07/177.94 [935]~E(x9351,x9352)+E(f438(x9353,x9351,x9354,x9355),f438(x9353,x9352,x9354,x9355)) % 178.07/177.94 [936]~E(x9361,x9362)+E(f438(x9363,x9364,x9361,x9365),f438(x9363,x9364,x9362,x9365)) % 178.07/177.94 [937]~E(x9371,x9372)+E(f438(x9373,x9374,x9375,x9371),f438(x9373,x9374,x9375,x9372)) % 178.07/177.94 [938]~E(x9381,x9382)+E(f629(x9381,x9383,x9384,x9385),f629(x9382,x9383,x9384,x9385)) % 178.07/177.94 [939]~E(x9391,x9392)+E(f629(x9393,x9391,x9394,x9395),f629(x9393,x9392,x9394,x9395)) % 178.07/177.94 [940]~E(x9401,x9402)+E(f629(x9403,x9404,x9401,x9405),f629(x9403,x9404,x9402,x9405)) % 178.07/177.94 [941]~E(x9411,x9412)+E(f629(x9413,x9414,x9415,x9411),f629(x9413,x9414,x9415,x9412)) % 178.07/177.94 [942]~E(x9421,x9422)+E(f744(x9421,x9423,x9424),f744(x9422,x9423,x9424)) % 178.07/177.94 [943]~E(x9431,x9432)+E(f744(x9433,x9431,x9434),f744(x9433,x9432,x9434)) % 178.07/177.94 [944]~E(x9441,x9442)+E(f744(x9443,x9444,x9441),f744(x9443,x9444,x9442)) % 178.07/177.94 [945]~E(x9451,x9452)+E(f523(x9451,x9453,x9454,x9455),f523(x9452,x9453,x9454,x9455)) % 178.07/177.94 [946]~E(x9461,x9462)+E(f523(x9463,x9461,x9464,x9465),f523(x9463,x9462,x9464,x9465)) % 178.07/177.94 [947]~E(x9471,x9472)+E(f523(x9473,x9474,x9471,x9475),f523(x9473,x9474,x9472,x9475)) % 178.07/177.94 [948]~E(x9481,x9482)+E(f523(x9483,x9484,x9485,x9481),f523(x9483,x9484,x9485,x9482)) % 178.07/177.94 [949]~E(x9491,x9492)+E(f581(x9491,x9493),f581(x9492,x9493)) % 178.07/177.94 [950]~E(x9501,x9502)+E(f581(x9503,x9501),f581(x9503,x9502)) % 178.07/177.94 [951]~E(x9511,x9512)+E(f53(x9511,x9513),f53(x9512,x9513)) % 178.07/177.94 [952]~E(x9521,x9522)+E(f53(x9523,x9521),f53(x9523,x9522)) % 178.07/177.94 [953]~E(x9531,x9532)+E(f397(x9531,x9533,x9534,x9535,x9536,x9537,x9538,x9539),f397(x9532,x9533,x9534,x9535,x9536,x9537,x9538,x9539)) % 178.07/177.94 [954]~E(x9541,x9542)+E(f397(x9543,x9541,x9544,x9545,x9546,x9547,x9548,x9549),f397(x9543,x9542,x9544,x9545,x9546,x9547,x9548,x9549)) % 178.07/177.94 [955]~E(x9551,x9552)+E(f397(x9553,x9554,x9551,x9555,x9556,x9557,x9558,x9559),f397(x9553,x9554,x9552,x9555,x9556,x9557,x9558,x9559)) % 178.07/177.94 [956]~E(x9561,x9562)+E(f397(x9563,x9564,x9565,x9561,x9566,x9567,x9568,x9569),f397(x9563,x9564,x9565,x9562,x9566,x9567,x9568,x9569)) % 178.07/177.94 [957]~E(x9571,x9572)+E(f397(x9573,x9574,x9575,x9576,x9571,x9577,x9578,x9579),f397(x9573,x9574,x9575,x9576,x9572,x9577,x9578,x9579)) % 178.07/177.94 [958]~E(x9581,x9582)+E(f397(x9583,x9584,x9585,x9586,x9587,x9581,x9588,x9589),f397(x9583,x9584,x9585,x9586,x9587,x9582,x9588,x9589)) % 178.07/177.94 [959]~E(x9591,x9592)+E(f397(x9593,x9594,x9595,x9596,x9597,x9598,x9591,x9599),f397(x9593,x9594,x9595,x9596,x9597,x9598,x9592,x9599)) % 178.07/177.94 [960]~E(x9601,x9602)+E(f397(x9603,x9604,x9605,x9606,x9607,x9608,x9609,x9601),f397(x9603,x9604,x9605,x9606,x9607,x9608,x9609,x9602)) % 178.07/177.94 [961]~E(x9611,x9612)+E(f394(x9611,x9613,x9614,x9615),f394(x9612,x9613,x9614,x9615)) % 178.07/177.94 [962]~E(x9621,x9622)+E(f394(x9623,x9621,x9624,x9625),f394(x9623,x9622,x9624,x9625)) % 178.07/177.94 [963]~E(x9631,x9632)+E(f394(x9633,x9634,x9631,x9635),f394(x9633,x9634,x9632,x9635)) % 178.07/177.94 [964]~E(x9641,x9642)+E(f394(x9643,x9644,x9645,x9641),f394(x9643,x9644,x9645,x9642)) % 178.07/177.94 [965]~E(x9651,x9652)+E(f310(x9651,x9653),f310(x9652,x9653)) % 178.07/177.94 [966]~E(x9661,x9662)+E(f310(x9663,x9661),f310(x9663,x9662)) % 178.07/177.94 [967]~E(x9671,x9672)+E(f558(x9671,x9673,x9674),f558(x9672,x9673,x9674)) % 178.07/177.94 [968]~E(x9681,x9682)+E(f558(x9683,x9681,x9684),f558(x9683,x9682,x9684)) % 178.07/177.94 [969]~E(x9691,x9692)+E(f558(x9693,x9694,x9691),f558(x9693,x9694,x9692)) % 178.07/177.94 [970]~E(x9701,x9702)+E(f371(x9701,x9703,x9704,x9705,x9706),f371(x9702,x9703,x9704,x9705,x9706)) % 178.07/177.94 [971]~E(x9711,x9712)+E(f371(x9713,x9711,x9714,x9715,x9716),f371(x9713,x9712,x9714,x9715,x9716)) % 178.07/177.94 [972]~E(x9721,x9722)+E(f371(x9723,x9724,x9721,x9725,x9726),f371(x9723,x9724,x9722,x9725,x9726)) % 178.07/177.94 [973]~E(x9731,x9732)+E(f371(x9733,x9734,x9735,x9731,x9736),f371(x9733,x9734,x9735,x9732,x9736)) % 178.07/177.94 [974]~E(x9741,x9742)+E(f371(x9743,x9744,x9745,x9746,x9741),f371(x9743,x9744,x9745,x9746,x9742)) % 178.07/177.94 [975]~E(x9751,x9752)+E(f478(x9751,x9753,x9754),f478(x9752,x9753,x9754)) % 178.07/177.94 [976]~E(x9761,x9762)+E(f478(x9763,x9761,x9764),f478(x9763,x9762,x9764)) % 178.07/177.94 [977]~E(x9771,x9772)+E(f478(x9773,x9774,x9771),f478(x9773,x9774,x9772)) % 178.07/177.94 [978]~E(x9781,x9782)+E(f207(x9781,x9783),f207(x9782,x9783)) % 178.07/177.94 [979]~E(x9791,x9792)+E(f207(x9793,x9791),f207(x9793,x9792)) % 178.07/177.94 [980]~E(x9801,x9802)+E(f852(x9801,x9803,x9804),f852(x9802,x9803,x9804)) % 178.07/177.94 [981]~E(x9811,x9812)+E(f852(x9813,x9811,x9814),f852(x9813,x9812,x9814)) % 178.07/177.94 [982]~E(x9821,x9822)+E(f852(x9823,x9824,x9821),f852(x9823,x9824,x9822)) % 178.07/177.94 [983]~E(x9831,x9832)+E(f66(x9831,x9833,x9834),f66(x9832,x9833,x9834)) % 178.07/177.94 [984]~E(x9841,x9842)+E(f66(x9843,x9841,x9844),f66(x9843,x9842,x9844)) % 178.07/177.94 [985]~E(x9851,x9852)+E(f66(x9853,x9854,x9851),f66(x9853,x9854,x9852)) % 178.07/177.94 [986]~E(x9861,x9862)+E(f378(x9861,x9863),f378(x9862,x9863)) % 178.07/177.94 [987]~E(x9871,x9872)+E(f378(x9873,x9871),f378(x9873,x9872)) % 178.07/177.94 [988]~E(x9881,x9882)+E(f695(x9881,x9883,x9884,x9885),f695(x9882,x9883,x9884,x9885)) % 178.07/177.94 [989]~E(x9891,x9892)+E(f695(x9893,x9891,x9894,x9895),f695(x9893,x9892,x9894,x9895)) % 178.07/177.94 [990]~E(x9901,x9902)+E(f695(x9903,x9904,x9901,x9905),f695(x9903,x9904,x9902,x9905)) % 178.07/177.94 [991]~E(x9911,x9912)+E(f695(x9913,x9914,x9915,x9911),f695(x9913,x9914,x9915,x9912)) % 178.07/177.94 [992]~E(x9921,x9922)+E(f261(x9921,x9923),f261(x9922,x9923)) % 178.07/177.94 [993]~E(x9931,x9932)+E(f261(x9933,x9931),f261(x9933,x9932)) % 178.07/177.94 [994]~E(x9941,x9942)+E(f853(x9941,x9943,x9944,x9945),f853(x9942,x9943,x9944,x9945)) % 178.07/177.94 [995]~E(x9951,x9952)+E(f853(x9953,x9951,x9954,x9955),f853(x9953,x9952,x9954,x9955)) % 178.07/177.94 [996]~E(x9961,x9962)+E(f853(x9963,x9964,x9961,x9965),f853(x9963,x9964,x9962,x9965)) % 178.07/177.94 [997]~E(x9971,x9972)+E(f853(x9973,x9974,x9975,x9971),f853(x9973,x9974,x9975,x9972)) % 178.07/177.94 [998]~E(x9981,x9982)+E(f379(x9981,x9983,x9984,x9985,x9986),f379(x9982,x9983,x9984,x9985,x9986)) % 178.07/177.94 [999]~E(x9991,x9992)+E(f379(x9993,x9991,x9994,x9995,x9996),f379(x9993,x9992,x9994,x9995,x9996)) % 178.07/177.94 [1000]~E(x10001,x10002)+E(f379(x10003,x10004,x10001,x10005,x10006),f379(x10003,x10004,x10002,x10005,x10006)) % 178.07/177.94 [1001]~E(x10011,x10012)+E(f379(x10013,x10014,x10015,x10011,x10016),f379(x10013,x10014,x10015,x10012,x10016)) % 178.07/177.94 [1002]~E(x10021,x10022)+E(f379(x10023,x10024,x10025,x10026,x10021),f379(x10023,x10024,x10025,x10026,x10022)) % 178.07/177.94 [1003]~E(x10031,x10032)+E(f617(x10031,x10033,x10034),f617(x10032,x10033,x10034)) % 178.07/177.94 [1004]~E(x10041,x10042)+E(f617(x10043,x10041,x10044),f617(x10043,x10042,x10044)) % 178.07/177.94 [1005]~E(x10051,x10052)+E(f617(x10053,x10054,x10051),f617(x10053,x10054,x10052)) % 178.07/177.94 [1006]~E(x10061,x10062)+E(f370(x10061,x10063,x10064),f370(x10062,x10063,x10064)) % 178.07/177.94 [1007]~E(x10071,x10072)+E(f370(x10073,x10071,x10074),f370(x10073,x10072,x10074)) % 178.07/177.94 [1008]~E(x10081,x10082)+E(f370(x10083,x10084,x10081),f370(x10083,x10084,x10082)) % 178.07/177.94 [1009]~E(x10091,x10092)+E(f256(x10091,x10093,x10094),f256(x10092,x10093,x10094)) % 178.07/177.94 [1010]~E(x10101,x10102)+E(f256(x10103,x10101,x10104),f256(x10103,x10102,x10104)) % 178.07/177.94 [1011]~E(x10111,x10112)+E(f256(x10113,x10114,x10111),f256(x10113,x10114,x10112)) % 178.07/177.94 [1012]~E(x10121,x10122)+E(f217(x10121,x10123,x10124,x10125),f217(x10122,x10123,x10124,x10125)) % 178.07/177.94 [1013]~E(x10131,x10132)+E(f217(x10133,x10131,x10134,x10135),f217(x10133,x10132,x10134,x10135)) % 178.07/177.94 [1014]~E(x10141,x10142)+E(f217(x10143,x10144,x10141,x10145),f217(x10143,x10144,x10142,x10145)) % 178.07/177.94 [1015]~E(x10151,x10152)+E(f217(x10153,x10154,x10155,x10151),f217(x10153,x10154,x10155,x10152)) % 178.07/177.94 [1016]~E(x10161,x10162)+E(f202(x10161,x10163,x10164,x10165),f202(x10162,x10163,x10164,x10165)) % 178.07/177.94 [1017]~E(x10171,x10172)+E(f202(x10173,x10171,x10174,x10175),f202(x10173,x10172,x10174,x10175)) % 178.07/177.94 [1018]~E(x10181,x10182)+E(f202(x10183,x10184,x10181,x10185),f202(x10183,x10184,x10182,x10185)) % 178.07/177.94 [1019]~E(x10191,x10192)+E(f202(x10193,x10194,x10195,x10191),f202(x10193,x10194,x10195,x10192)) % 178.07/177.94 [1020]~E(x10201,x10202)+E(f756(x10201,x10203,x10204),f756(x10202,x10203,x10204)) % 178.07/177.94 [1021]~E(x10211,x10212)+E(f756(x10213,x10211,x10214),f756(x10213,x10212,x10214)) % 178.07/177.94 [1022]~E(x10221,x10222)+E(f756(x10223,x10224,x10221),f756(x10223,x10224,x10222)) % 178.07/177.94 [1023]~E(x10231,x10232)+E(f323(x10231,x10233,x10234),f323(x10232,x10233,x10234)) % 178.07/177.94 [1024]~E(x10241,x10242)+E(f323(x10243,x10241,x10244),f323(x10243,x10242,x10244)) % 178.07/177.94 [1025]~E(x10251,x10252)+E(f323(x10253,x10254,x10251),f323(x10253,x10254,x10252)) % 178.07/177.94 [1026]~E(x10261,x10262)+E(f646(x10261,x10263),f646(x10262,x10263)) % 178.07/177.94 [1027]~E(x10271,x10272)+E(f646(x10273,x10271),f646(x10273,x10272)) % 178.07/177.94 [1028]~E(x10281,x10282)+E(f614(x10281,x10283,x10284,x10285,x10286),f614(x10282,x10283,x10284,x10285,x10286)) % 178.07/177.94 [1029]~E(x10291,x10292)+E(f614(x10293,x10291,x10294,x10295,x10296),f614(x10293,x10292,x10294,x10295,x10296)) % 178.07/177.94 [1030]~E(x10301,x10302)+E(f614(x10303,x10304,x10301,x10305,x10306),f614(x10303,x10304,x10302,x10305,x10306)) % 178.07/177.94 [1031]~E(x10311,x10312)+E(f614(x10313,x10314,x10315,x10311,x10316),f614(x10313,x10314,x10315,x10312,x10316)) % 178.07/177.94 [1032]~E(x10321,x10322)+E(f614(x10323,x10324,x10325,x10326,x10321),f614(x10323,x10324,x10325,x10326,x10322)) % 178.07/177.94 [1033]~E(x10331,x10332)+E(f356(x10331,x10333),f356(x10332,x10333)) % 178.07/177.94 [1034]~E(x10341,x10342)+E(f356(x10343,x10341),f356(x10343,x10342)) % 178.07/177.94 [1035]~E(x10351,x10352)+E(f469(x10351,x10353,x10354),f469(x10352,x10353,x10354)) % 178.07/177.94 [1036]~E(x10361,x10362)+E(f469(x10363,x10361,x10364),f469(x10363,x10362,x10364)) % 178.07/177.94 [1037]~E(x10371,x10372)+E(f469(x10373,x10374,x10371),f469(x10373,x10374,x10372)) % 178.07/177.94 [1038]~E(x10381,x10382)+E(f621(x10381,x10383),f621(x10382,x10383)) % 178.07/177.94 [1039]~E(x10391,x10392)+E(f621(x10393,x10391),f621(x10393,x10392)) % 178.07/177.94 [1040]~E(x10401,x10402)+E(f786(x10401,x10403,x10404),f786(x10402,x10403,x10404)) % 178.07/177.94 [1041]~E(x10411,x10412)+E(f786(x10413,x10411,x10414),f786(x10413,x10412,x10414)) % 178.07/177.94 [1042]~E(x10421,x10422)+E(f786(x10423,x10424,x10421),f786(x10423,x10424,x10422)) % 178.07/177.94 [1043]~E(x10431,x10432)+E(f273(x10431,x10433),f273(x10432,x10433)) % 178.07/177.94 [1044]~E(x10441,x10442)+E(f273(x10443,x10441),f273(x10443,x10442)) % 178.07/177.94 [1045]~E(x10451,x10452)+E(f496(x10451,x10453,x10454,x10455),f496(x10452,x10453,x10454,x10455)) % 178.07/177.94 [1046]~E(x10461,x10462)+E(f496(x10463,x10461,x10464,x10465),f496(x10463,x10462,x10464,x10465)) % 178.07/177.94 [1047]~E(x10471,x10472)+E(f496(x10473,x10474,x10471,x10475),f496(x10473,x10474,x10472,x10475)) % 178.07/177.94 [1048]~E(x10481,x10482)+E(f496(x10483,x10484,x10485,x10481),f496(x10483,x10484,x10485,x10482)) % 178.07/177.94 [1049]~E(x10491,x10492)+E(f223(x10491,x10493),f223(x10492,x10493)) % 178.07/177.94 [1050]~E(x10501,x10502)+E(f223(x10503,x10501),f223(x10503,x10502)) % 178.07/177.94 [1051]~E(x10511,x10512)+E(f521(x10511,x10513,x10514),f521(x10512,x10513,x10514)) % 178.07/177.94 [1052]~E(x10521,x10522)+E(f521(x10523,x10521,x10524),f521(x10523,x10522,x10524)) % 178.07/177.94 [1053]~E(x10531,x10532)+E(f521(x10533,x10534,x10531),f521(x10533,x10534,x10532)) % 178.07/177.94 [1054]~E(x10541,x10542)+E(f649(x10541,x10543,x10544),f649(x10542,x10543,x10544)) % 178.07/177.94 [1055]~E(x10551,x10552)+E(f649(x10553,x10551,x10554),f649(x10553,x10552,x10554)) % 178.07/177.94 [1056]~E(x10561,x10562)+E(f649(x10563,x10564,x10561),f649(x10563,x10564,x10562)) % 178.07/177.94 [1057]~E(x10571,x10572)+E(f689(x10571,x10573,x10574,x10575,x10576),f689(x10572,x10573,x10574,x10575,x10576)) % 178.07/177.94 [1058]~E(x10581,x10582)+E(f689(x10583,x10581,x10584,x10585,x10586),f689(x10583,x10582,x10584,x10585,x10586)) % 178.07/177.94 [1059]~E(x10591,x10592)+E(f689(x10593,x10594,x10591,x10595,x10596),f689(x10593,x10594,x10592,x10595,x10596)) % 178.07/177.94 [1060]~E(x10601,x10602)+E(f689(x10603,x10604,x10605,x10601,x10606),f689(x10603,x10604,x10605,x10602,x10606)) % 178.07/177.94 [1061]~E(x10611,x10612)+E(f689(x10613,x10614,x10615,x10616,x10611),f689(x10613,x10614,x10615,x10616,x10612)) % 178.07/177.94 [1062]~E(x10621,x10622)+E(f424(x10621,x10623,x10624,x10625,x10626),f424(x10622,x10623,x10624,x10625,x10626)) % 178.07/177.94 [1063]~E(x10631,x10632)+E(f424(x10633,x10631,x10634,x10635,x10636),f424(x10633,x10632,x10634,x10635,x10636)) % 178.07/177.94 [1064]~E(x10641,x10642)+E(f424(x10643,x10644,x10641,x10645,x10646),f424(x10643,x10644,x10642,x10645,x10646)) % 178.07/177.94 [1065]~E(x10651,x10652)+E(f424(x10653,x10654,x10655,x10651,x10656),f424(x10653,x10654,x10655,x10652,x10656)) % 178.07/177.94 [1066]~E(x10661,x10662)+E(f424(x10663,x10664,x10665,x10666,x10661),f424(x10663,x10664,x10665,x10666,x10662)) % 178.07/177.94 [1067]~E(x10671,x10672)+E(f588(x10671,x10673,x10674,x10675),f588(x10672,x10673,x10674,x10675)) % 178.07/177.94 [1068]~E(x10681,x10682)+E(f588(x10683,x10681,x10684,x10685),f588(x10683,x10682,x10684,x10685)) % 178.07/177.94 [1069]~E(x10691,x10692)+E(f588(x10693,x10694,x10691,x10695),f588(x10693,x10694,x10692,x10695)) % 178.07/177.94 [1070]~E(x10701,x10702)+E(f588(x10703,x10704,x10705,x10701),f588(x10703,x10704,x10705,x10702)) % 178.07/177.94 [1071]~E(x10711,x10712)+E(f426(x10711,x10713,x10714,x10715),f426(x10712,x10713,x10714,x10715)) % 178.07/177.94 [1072]~E(x10721,x10722)+E(f426(x10723,x10721,x10724,x10725),f426(x10723,x10722,x10724,x10725)) % 178.07/177.94 [1073]~E(x10731,x10732)+E(f426(x10733,x10734,x10731,x10735),f426(x10733,x10734,x10732,x10735)) % 178.07/177.94 [1074]~E(x10741,x10742)+E(f426(x10743,x10744,x10745,x10741),f426(x10743,x10744,x10745,x10742)) % 178.07/177.94 [1075]~E(x10751,x10752)+E(f375(x10751),f375(x10752)) % 178.07/177.94 [1076]~E(x10761,x10762)+E(f608(x10761,x10763,x10764),f608(x10762,x10763,x10764)) % 178.07/177.94 [1077]~E(x10771,x10772)+E(f608(x10773,x10771,x10774),f608(x10773,x10772,x10774)) % 178.07/177.94 [1078]~E(x10781,x10782)+E(f608(x10783,x10784,x10781),f608(x10783,x10784,x10782)) % 178.07/177.94 [1079]~E(x10791,x10792)+E(f166(x10791,x10793,x10794),f166(x10792,x10793,x10794)) % 178.07/177.94 [1080]~E(x10801,x10802)+E(f166(x10803,x10801,x10804),f166(x10803,x10802,x10804)) % 178.07/177.94 [1081]~E(x10811,x10812)+E(f166(x10813,x10814,x10811),f166(x10813,x10814,x10812)) % 178.07/177.94 [1082]~E(x10821,x10822)+E(f768(x10821,x10823,x10824,x10825,x10826),f768(x10822,x10823,x10824,x10825,x10826)) % 178.07/177.94 [1083]~E(x10831,x10832)+E(f768(x10833,x10831,x10834,x10835,x10836),f768(x10833,x10832,x10834,x10835,x10836)) % 178.07/177.94 [1084]~E(x10841,x10842)+E(f768(x10843,x10844,x10841,x10845,x10846),f768(x10843,x10844,x10842,x10845,x10846)) % 178.07/177.94 [1085]~E(x10851,x10852)+E(f768(x10853,x10854,x10855,x10851,x10856),f768(x10853,x10854,x10855,x10852,x10856)) % 178.07/177.94 [1086]~E(x10861,x10862)+E(f768(x10863,x10864,x10865,x10866,x10861),f768(x10863,x10864,x10865,x10866,x10862)) % 178.07/177.94 [1087]~E(x10871,x10872)+E(f212(x10871),f212(x10872)) % 178.07/177.94 [1088]~E(x10881,x10882)+E(f728(x10881,x10883,x10884),f728(x10882,x10883,x10884)) % 178.07/177.94 [1089]~E(x10891,x10892)+E(f728(x10893,x10891,x10894),f728(x10893,x10892,x10894)) % 178.07/177.94 [1090]~E(x10901,x10902)+E(f728(x10903,x10904,x10901),f728(x10903,x10904,x10902)) % 178.07/177.94 [1091]~E(x10911,x10912)+E(f583(x10911,x10913,x10914,x10915,x10916),f583(x10912,x10913,x10914,x10915,x10916)) % 178.07/177.94 [1092]~E(x10921,x10922)+E(f583(x10923,x10921,x10924,x10925,x10926),f583(x10923,x10922,x10924,x10925,x10926)) % 178.07/177.94 [1093]~E(x10931,x10932)+E(f583(x10933,x10934,x10931,x10935,x10936),f583(x10933,x10934,x10932,x10935,x10936)) % 178.07/177.94 [1094]~E(x10941,x10942)+E(f583(x10943,x10944,x10945,x10941,x10946),f583(x10943,x10944,x10945,x10942,x10946)) % 178.07/177.94 [1095]~E(x10951,x10952)+E(f583(x10953,x10954,x10955,x10956,x10951),f583(x10953,x10954,x10955,x10956,x10952)) % 178.07/177.94 [1096]~E(x10961,x10962)+E(f561(x10961,x10963,x10964),f561(x10962,x10963,x10964)) % 178.07/177.94 [1097]~E(x10971,x10972)+E(f561(x10973,x10971,x10974),f561(x10973,x10972,x10974)) % 178.07/177.94 [1098]~E(x10981,x10982)+E(f561(x10983,x10984,x10981),f561(x10983,x10984,x10982)) % 178.07/177.94 [1099]~E(x10991,x10992)+E(f861(x10991,x10993,x10994),f861(x10992,x10993,x10994)) % 178.07/177.94 [1100]~E(x11001,x11002)+E(f861(x11003,x11001,x11004),f861(x11003,x11002,x11004)) % 178.07/177.94 [1101]~E(x11011,x11012)+E(f861(x11013,x11014,x11011),f861(x11013,x11014,x11012)) % 178.07/177.94 [1102]~E(x11021,x11022)+E(f594(x11021,x11023,x11024),f594(x11022,x11023,x11024)) % 178.07/177.94 [1103]~E(x11031,x11032)+E(f594(x11033,x11031,x11034),f594(x11033,x11032,x11034)) % 178.07/177.94 [1104]~E(x11041,x11042)+E(f594(x11043,x11044,x11041),f594(x11043,x11044,x11042)) % 178.07/177.94 [1105]~E(x11051,x11052)+E(f687(x11051,x11053,x11054,x11055,x11056),f687(x11052,x11053,x11054,x11055,x11056)) % 178.07/177.94 [1106]~E(x11061,x11062)+E(f687(x11063,x11061,x11064,x11065,x11066),f687(x11063,x11062,x11064,x11065,x11066)) % 178.07/177.94 [1107]~E(x11071,x11072)+E(f687(x11073,x11074,x11071,x11075,x11076),f687(x11073,x11074,x11072,x11075,x11076)) % 178.07/177.94 [1108]~E(x11081,x11082)+E(f687(x11083,x11084,x11085,x11081,x11086),f687(x11083,x11084,x11085,x11082,x11086)) % 178.07/177.94 [1109]~E(x11091,x11092)+E(f687(x11093,x11094,x11095,x11096,x11091),f687(x11093,x11094,x11095,x11096,x11092)) % 178.07/177.94 [1110]~E(x11101,x11102)+E(f677(x11101,x11103,x11104,x11105,x11106),f677(x11102,x11103,x11104,x11105,x11106)) % 178.07/177.94 [1111]~E(x11111,x11112)+E(f677(x11113,x11111,x11114,x11115,x11116),f677(x11113,x11112,x11114,x11115,x11116)) % 178.07/177.94 [1112]~E(x11121,x11122)+E(f677(x11123,x11124,x11121,x11125,x11126),f677(x11123,x11124,x11122,x11125,x11126)) % 178.07/177.94 [1113]~E(x11131,x11132)+E(f677(x11133,x11134,x11135,x11131,x11136),f677(x11133,x11134,x11135,x11132,x11136)) % 178.07/177.94 [1114]~E(x11141,x11142)+E(f677(x11143,x11144,x11145,x11146,x11141),f677(x11143,x11144,x11145,x11146,x11142)) % 178.07/177.94 [1115]~E(x11151,x11152)+E(f559(x11151,x11153,x11154),f559(x11152,x11153,x11154)) % 178.07/177.94 [1116]~E(x11161,x11162)+E(f559(x11163,x11161,x11164),f559(x11163,x11162,x11164)) % 178.07/177.94 [1117]~E(x11171,x11172)+E(f559(x11173,x11174,x11171),f559(x11173,x11174,x11172)) % 178.07/177.94 [1118]~E(x11181,x11182)+E(f392(x11181,x11183,x11184),f392(x11182,x11183,x11184)) % 178.07/177.94 [1119]~E(x11191,x11192)+E(f392(x11193,x11191,x11194),f392(x11193,x11192,x11194)) % 178.07/177.94 [1120]~E(x11201,x11202)+E(f392(x11203,x11204,x11201),f392(x11203,x11204,x11202)) % 178.07/177.94 [1121]~E(x11211,x11212)+E(f465(x11211,x11213,x11214),f465(x11212,x11213,x11214)) % 178.07/177.94 [1122]~E(x11221,x11222)+E(f465(x11223,x11221,x11224),f465(x11223,x11222,x11224)) % 178.07/177.94 [1123]~E(x11231,x11232)+E(f465(x11233,x11234,x11231),f465(x11233,x11234,x11232)) % 178.07/177.94 [1124]~E(x11241,x11242)+E(f436(x11241,x11243,x11244,x11245),f436(x11242,x11243,x11244,x11245)) % 178.07/177.94 [1125]~E(x11251,x11252)+E(f436(x11253,x11251,x11254,x11255),f436(x11253,x11252,x11254,x11255)) % 178.07/177.94 [1126]~E(x11261,x11262)+E(f436(x11263,x11264,x11261,x11265),f436(x11263,x11264,x11262,x11265)) % 178.07/177.94 [1127]~E(x11271,x11272)+E(f436(x11273,x11274,x11275,x11271),f436(x11273,x11274,x11275,x11272)) % 178.07/177.94 [1128]~E(x11281,x11282)+E(f830(x11281,x11283,x11284,x11285,x11286),f830(x11282,x11283,x11284,x11285,x11286)) % 178.07/177.94 [1129]~E(x11291,x11292)+E(f830(x11293,x11291,x11294,x11295,x11296),f830(x11293,x11292,x11294,x11295,x11296)) % 178.07/177.94 [1130]~E(x11301,x11302)+E(f830(x11303,x11304,x11301,x11305,x11306),f830(x11303,x11304,x11302,x11305,x11306)) % 178.07/177.94 [1131]~E(x11311,x11312)+E(f830(x11313,x11314,x11315,x11311,x11316),f830(x11313,x11314,x11315,x11312,x11316)) % 178.07/177.94 [1132]~E(x11321,x11322)+E(f830(x11323,x11324,x11325,x11326,x11321),f830(x11323,x11324,x11325,x11326,x11322)) % 178.07/177.94 [1133]~E(x11331,x11332)+E(f203(x11331,x11333,x11334,x11335),f203(x11332,x11333,x11334,x11335)) % 178.07/177.94 [1134]~E(x11341,x11342)+E(f203(x11343,x11341,x11344,x11345),f203(x11343,x11342,x11344,x11345)) % 178.07/177.94 [1135]~E(x11351,x11352)+E(f203(x11353,x11354,x11351,x11355),f203(x11353,x11354,x11352,x11355)) % 178.07/177.94 [1136]~E(x11361,x11362)+E(f203(x11363,x11364,x11365,x11361),f203(x11363,x11364,x11365,x11362)) % 178.07/177.94 [1137]~E(x11371,x11372)+E(f686(x11371,x11373,x11374,x11375,x11376),f686(x11372,x11373,x11374,x11375,x11376)) % 178.07/177.94 [1138]~E(x11381,x11382)+E(f686(x11383,x11381,x11384,x11385,x11386),f686(x11383,x11382,x11384,x11385,x11386)) % 178.07/177.94 [1139]~E(x11391,x11392)+E(f686(x11393,x11394,x11391,x11395,x11396),f686(x11393,x11394,x11392,x11395,x11396)) % 178.07/177.94 [1140]~E(x11401,x11402)+E(f686(x11403,x11404,x11405,x11401,x11406),f686(x11403,x11404,x11405,x11402,x11406)) % 178.07/177.94 [1141]~E(x11411,x11412)+E(f686(x11413,x11414,x11415,x11416,x11411),f686(x11413,x11414,x11415,x11416,x11412)) % 178.07/177.94 [1142]~E(x11421,x11422)+E(f857(x11421,x11423,x11424,x11425,x11426,x11427,x11428),f857(x11422,x11423,x11424,x11425,x11426,x11427,x11428)) % 178.07/177.94 [1143]~E(x11431,x11432)+E(f857(x11433,x11431,x11434,x11435,x11436,x11437,x11438),f857(x11433,x11432,x11434,x11435,x11436,x11437,x11438)) % 178.07/177.94 [1144]~E(x11441,x11442)+E(f857(x11443,x11444,x11441,x11445,x11446,x11447,x11448),f857(x11443,x11444,x11442,x11445,x11446,x11447,x11448)) % 178.07/177.94 [1145]~E(x11451,x11452)+E(f857(x11453,x11454,x11455,x11451,x11456,x11457,x11458),f857(x11453,x11454,x11455,x11452,x11456,x11457,x11458)) % 178.07/177.94 [1146]~E(x11461,x11462)+E(f857(x11463,x11464,x11465,x11466,x11461,x11467,x11468),f857(x11463,x11464,x11465,x11466,x11462,x11467,x11468)) % 178.07/177.94 [1147]~E(x11471,x11472)+E(f857(x11473,x11474,x11475,x11476,x11477,x11471,x11478),f857(x11473,x11474,x11475,x11476,x11477,x11472,x11478)) % 178.07/177.94 [1148]~E(x11481,x11482)+E(f857(x11483,x11484,x11485,x11486,x11487,x11488,x11481),f857(x11483,x11484,x11485,x11486,x11487,x11488,x11482)) % 178.07/177.94 [1149]~E(x11491,x11492)+E(f208(x11491,x11493),f208(x11492,x11493)) % 178.07/177.94 [1150]~E(x11501,x11502)+E(f208(x11503,x11501),f208(x11503,x11502)) % 178.07/177.94 [1151]~E(x11511,x11512)+E(f736(x11511,x11513,x11514),f736(x11512,x11513,x11514)) % 178.07/177.94 [1152]~E(x11521,x11522)+E(f736(x11523,x11521,x11524),f736(x11523,x11522,x11524)) % 178.07/177.94 [1153]~E(x11531,x11532)+E(f736(x11533,x11534,x11531),f736(x11533,x11534,x11532)) % 178.07/177.94 [1154]~E(x11541,x11542)+E(f766(x11541,x11543,x11544,x11545),f766(x11542,x11543,x11544,x11545)) % 178.07/177.94 [1155]~E(x11551,x11552)+E(f766(x11553,x11551,x11554,x11555),f766(x11553,x11552,x11554,x11555)) % 178.07/177.94 [1156]~E(x11561,x11562)+E(f766(x11563,x11564,x11561,x11565),f766(x11563,x11564,x11562,x11565)) % 178.07/177.94 [1157]~E(x11571,x11572)+E(f766(x11573,x11574,x11575,x11571),f766(x11573,x11574,x11575,x11572)) % 178.07/177.94 [1158]~E(x11581,x11582)+E(f632(x11581,x11583,x11584,x11585,x11586),f632(x11582,x11583,x11584,x11585,x11586)) % 178.07/177.94 [1159]~E(x11591,x11592)+E(f632(x11593,x11591,x11594,x11595,x11596),f632(x11593,x11592,x11594,x11595,x11596)) % 178.07/177.94 [1160]~E(x11601,x11602)+E(f632(x11603,x11604,x11601,x11605,x11606),f632(x11603,x11604,x11602,x11605,x11606)) % 178.07/177.94 [1161]~E(x11611,x11612)+E(f632(x11613,x11614,x11615,x11611,x11616),f632(x11613,x11614,x11615,x11612,x11616)) % 178.07/177.94 [1162]~E(x11621,x11622)+E(f632(x11623,x11624,x11625,x11626,x11621),f632(x11623,x11624,x11625,x11626,x11622)) % 178.07/177.94 [1163]~E(x11631,x11632)+E(f89(x11631),f89(x11632)) % 178.07/177.94 [1164]~E(x11641,x11642)+E(f556(x11641,x11643,x11644,x11645),f556(x11642,x11643,x11644,x11645)) % 178.07/177.94 [1165]~E(x11651,x11652)+E(f556(x11653,x11651,x11654,x11655),f556(x11653,x11652,x11654,x11655)) % 178.07/177.94 [1166]~E(x11661,x11662)+E(f556(x11663,x11664,x11661,x11665),f556(x11663,x11664,x11662,x11665)) % 178.07/177.94 [1167]~E(x11671,x11672)+E(f556(x11673,x11674,x11675,x11671),f556(x11673,x11674,x11675,x11672)) % 178.07/177.94 [1168]~E(x11681,x11682)+E(f509(x11681,x11683),f509(x11682,x11683)) % 178.07/177.94 [1169]~E(x11691,x11692)+E(f509(x11693,x11691),f509(x11693,x11692)) % 178.07/177.94 [1170]~E(x11701,x11702)+E(f428(x11701,x11703,x11704,x11705,x11706,x11707),f428(x11702,x11703,x11704,x11705,x11706,x11707)) % 178.07/177.94 [1171]~E(x11711,x11712)+E(f428(x11713,x11711,x11714,x11715,x11716,x11717),f428(x11713,x11712,x11714,x11715,x11716,x11717)) % 178.07/177.94 [1172]~E(x11721,x11722)+E(f428(x11723,x11724,x11721,x11725,x11726,x11727),f428(x11723,x11724,x11722,x11725,x11726,x11727)) % 178.07/177.94 [1173]~E(x11731,x11732)+E(f428(x11733,x11734,x11735,x11731,x11736,x11737),f428(x11733,x11734,x11735,x11732,x11736,x11737)) % 178.07/177.94 [1174]~E(x11741,x11742)+E(f428(x11743,x11744,x11745,x11746,x11741,x11747),f428(x11743,x11744,x11745,x11746,x11742,x11747)) % 178.07/177.94 [1175]~E(x11751,x11752)+E(f428(x11753,x11754,x11755,x11756,x11757,x11751),f428(x11753,x11754,x11755,x11756,x11757,x11752)) % 178.07/177.94 [1176]~E(x11761,x11762)+E(f661(x11761,x11763,x11764,x11765,x11766),f661(x11762,x11763,x11764,x11765,x11766)) % 178.07/177.94 [1177]~E(x11771,x11772)+E(f661(x11773,x11771,x11774,x11775,x11776),f661(x11773,x11772,x11774,x11775,x11776)) % 178.07/177.94 [1178]~E(x11781,x11782)+E(f661(x11783,x11784,x11781,x11785,x11786),f661(x11783,x11784,x11782,x11785,x11786)) % 178.07/177.94 [1179]~E(x11791,x11792)+E(f661(x11793,x11794,x11795,x11791,x11796),f661(x11793,x11794,x11795,x11792,x11796)) % 178.07/177.94 [1180]~E(x11801,x11802)+E(f661(x11803,x11804,x11805,x11806,x11801),f661(x11803,x11804,x11805,x11806,x11802)) % 178.07/177.94 [1181]~E(x11811,x11812)+E(f195(x11811,x11813,x11814,x11815),f195(x11812,x11813,x11814,x11815)) % 178.07/177.94 [1182]~E(x11821,x11822)+E(f195(x11823,x11821,x11824,x11825),f195(x11823,x11822,x11824,x11825)) % 178.07/177.94 [1183]~E(x11831,x11832)+E(f195(x11833,x11834,x11831,x11835),f195(x11833,x11834,x11832,x11835)) % 178.07/177.94 [1184]~E(x11841,x11842)+E(f195(x11843,x11844,x11845,x11841),f195(x11843,x11844,x11845,x11842)) % 178.07/177.94 [1185]~E(x11851,x11852)+E(f456(x11851,x11853,x11854,x11855),f456(x11852,x11853,x11854,x11855)) % 178.07/177.94 [1186]~E(x11861,x11862)+E(f456(x11863,x11861,x11864,x11865),f456(x11863,x11862,x11864,x11865)) % 178.07/177.94 [1187]~E(x11871,x11872)+E(f456(x11873,x11874,x11871,x11875),f456(x11873,x11874,x11872,x11875)) % 178.07/177.94 [1188]~E(x11881,x11882)+E(f456(x11883,x11884,x11885,x11881),f456(x11883,x11884,x11885,x11882)) % 178.07/177.94 [1189]~E(x11891,x11892)+E(f368(x11891,x11893,x11894,x11895),f368(x11892,x11893,x11894,x11895)) % 178.07/177.94 [1190]~E(x11901,x11902)+E(f368(x11903,x11901,x11904,x11905),f368(x11903,x11902,x11904,x11905)) % 178.07/177.94 [1191]~E(x11911,x11912)+E(f368(x11913,x11914,x11911,x11915),f368(x11913,x11914,x11912,x11915)) % 178.07/177.94 [1192]~E(x11921,x11922)+E(f368(x11923,x11924,x11925,x11921),f368(x11923,x11924,x11925,x11922)) % 178.07/177.94 [1193]~E(x11931,x11932)+E(f504(x11931,x11933,x11934),f504(x11932,x11933,x11934)) % 178.07/177.94 [1194]~E(x11941,x11942)+E(f504(x11943,x11941,x11944),f504(x11943,x11942,x11944)) % 178.07/177.94 [1195]~E(x11951,x11952)+E(f504(x11953,x11954,x11951),f504(x11953,x11954,x11952)) % 178.07/177.94 [1196]~E(x11961,x11962)+E(f352(x11961,x11963,x11964,x11965,x11966),f352(x11962,x11963,x11964,x11965,x11966)) % 178.07/177.94 [1197]~E(x11971,x11972)+E(f352(x11973,x11971,x11974,x11975,x11976),f352(x11973,x11972,x11974,x11975,x11976)) % 178.07/177.94 [1198]~E(x11981,x11982)+E(f352(x11983,x11984,x11981,x11985,x11986),f352(x11983,x11984,x11982,x11985,x11986)) % 178.07/177.94 [1199]~E(x11991,x11992)+E(f352(x11993,x11994,x11995,x11991,x11996),f352(x11993,x11994,x11995,x11992,x11996)) % 178.07/177.94 [1200]~E(x12001,x12002)+E(f352(x12003,x12004,x12005,x12006,x12001),f352(x12003,x12004,x12005,x12006,x12002)) % 178.07/177.94 [1201]~E(x12011,x12012)+E(f489(x12011,x12013),f489(x12012,x12013)) % 178.07/177.94 [1202]~E(x12021,x12022)+E(f489(x12023,x12021),f489(x12023,x12022)) % 178.07/177.94 [1203]~E(x12031,x12032)+E(f673(x12031,x12033,x12034),f673(x12032,x12033,x12034)) % 178.07/177.94 [1204]~E(x12041,x12042)+E(f673(x12043,x12041,x12044),f673(x12043,x12042,x12044)) % 178.07/177.94 [1205]~E(x12051,x12052)+E(f673(x12053,x12054,x12051),f673(x12053,x12054,x12052)) % 178.07/177.94 [1206]~E(x12061,x12062)+E(f554(x12061,x12063,x12064,x12065),f554(x12062,x12063,x12064,x12065)) % 178.07/177.94 [1207]~E(x12071,x12072)+E(f554(x12073,x12071,x12074,x12075),f554(x12073,x12072,x12074,x12075)) % 178.07/177.94 [1208]~E(x12081,x12082)+E(f554(x12083,x12084,x12081,x12085),f554(x12083,x12084,x12082,x12085)) % 178.07/177.94 [1209]~E(x12091,x12092)+E(f554(x12093,x12094,x12095,x12091),f554(x12093,x12094,x12095,x12092)) % 178.07/177.94 [1210]~E(x12101,x12102)+E(f513(x12101,x12103),f513(x12102,x12103)) % 178.07/177.94 [1211]~E(x12111,x12112)+E(f513(x12113,x12111),f513(x12113,x12112)) % 178.07/177.94 [1212]~E(x12121,x12122)+E(f334(x12121),f334(x12122)) % 178.07/177.94 [1213]~E(x12131,x12132)+E(f501(x12131,x12133,x12134),f501(x12132,x12133,x12134)) % 178.07/177.94 [1214]~E(x12141,x12142)+E(f501(x12143,x12141,x12144),f501(x12143,x12142,x12144)) % 178.07/177.94 [1215]~E(x12151,x12152)+E(f501(x12153,x12154,x12151),f501(x12153,x12154,x12152)) % 178.07/177.94 [1216]~E(x12161,x12162)+E(f360(x12161,x12163,x12164),f360(x12162,x12163,x12164)) % 178.07/177.94 [1217]~E(x12171,x12172)+E(f360(x12173,x12171,x12174),f360(x12173,x12172,x12174)) % 178.07/177.94 [1218]~E(x12181,x12182)+E(f360(x12183,x12184,x12181),f360(x12183,x12184,x12182)) % 178.07/177.94 [1219]~E(x12191,x12192)+E(f60(x12191,x12193,x12194,x12195),f60(x12192,x12193,x12194,x12195)) % 178.07/177.94 [1220]~E(x12201,x12202)+E(f60(x12203,x12201,x12204,x12205),f60(x12203,x12202,x12204,x12205)) % 178.07/177.94 [1221]~E(x12211,x12212)+E(f60(x12213,x12214,x12211,x12215),f60(x12213,x12214,x12212,x12215)) % 178.07/177.94 [1222]~E(x12221,x12222)+E(f60(x12223,x12224,x12225,x12221),f60(x12223,x12224,x12225,x12222)) % 178.07/177.94 [1223]~E(x12231,x12232)+E(f749(x12231,x12233,x12234,x12235,x12236,x12237,x12238,x12239),f749(x12232,x12233,x12234,x12235,x12236,x12237,x12238,x12239)) % 178.07/177.94 [1224]~E(x12241,x12242)+E(f749(x12243,x12241,x12244,x12245,x12246,x12247,x12248,x12249),f749(x12243,x12242,x12244,x12245,x12246,x12247,x12248,x12249)) % 178.07/177.94 [1225]~E(x12251,x12252)+E(f749(x12253,x12254,x12251,x12255,x12256,x12257,x12258,x12259),f749(x12253,x12254,x12252,x12255,x12256,x12257,x12258,x12259)) % 178.07/177.94 [1226]~E(x12261,x12262)+E(f749(x12263,x12264,x12265,x12261,x12266,x12267,x12268,x12269),f749(x12263,x12264,x12265,x12262,x12266,x12267,x12268,x12269)) % 178.07/177.94 [1227]~E(x12271,x12272)+E(f749(x12273,x12274,x12275,x12276,x12271,x12277,x12278,x12279),f749(x12273,x12274,x12275,x12276,x12272,x12277,x12278,x12279)) % 178.07/177.94 [1228]~E(x12281,x12282)+E(f749(x12283,x12284,x12285,x12286,x12287,x12281,x12288,x12289),f749(x12283,x12284,x12285,x12286,x12287,x12282,x12288,x12289)) % 178.07/177.94 [1229]~E(x12291,x12292)+E(f749(x12293,x12294,x12295,x12296,x12297,x12298,x12291,x12299),f749(x12293,x12294,x12295,x12296,x12297,x12298,x12292,x12299)) % 178.07/177.94 [1230]~E(x12301,x12302)+E(f749(x12303,x12304,x12305,x12306,x12307,x12308,x12309,x12301),f749(x12303,x12304,x12305,x12306,x12307,x12308,x12309,x12302)) % 178.07/177.94 [1231]~E(x12311,x12312)+E(f855(x12311,x12313,x12314),f855(x12312,x12313,x12314)) % 178.07/177.94 [1232]~E(x12321,x12322)+E(f855(x12323,x12321,x12324),f855(x12323,x12322,x12324)) % 178.07/177.94 [1233]~E(x12331,x12332)+E(f855(x12333,x12334,x12331),f855(x12333,x12334,x12332)) % 178.07/177.94 [1234]~E(x12341,x12342)+E(f862(x12341,x12343,x12344,x12345),f862(x12342,x12343,x12344,x12345)) % 178.07/177.94 [1235]~E(x12351,x12352)+E(f862(x12353,x12351,x12354,x12355),f862(x12353,x12352,x12354,x12355)) % 178.07/177.94 [1236]~E(x12361,x12362)+E(f862(x12363,x12364,x12361,x12365),f862(x12363,x12364,x12362,x12365)) % 178.07/177.94 [1237]~E(x12371,x12372)+E(f862(x12373,x12374,x12375,x12371),f862(x12373,x12374,x12375,x12372)) % 178.07/177.94 [1238]~E(x12381,x12382)+E(f493(x12381,x12383,x12384,x12385),f493(x12382,x12383,x12384,x12385)) % 178.07/177.94 [1239]~E(x12391,x12392)+E(f493(x12393,x12391,x12394,x12395),f493(x12393,x12392,x12394,x12395)) % 178.07/177.94 [1240]~E(x12401,x12402)+E(f493(x12403,x12404,x12401,x12405),f493(x12403,x12404,x12402,x12405)) % 178.07/177.94 [1241]~E(x12411,x12412)+E(f493(x12413,x12414,x12415,x12411),f493(x12413,x12414,x12415,x12412)) % 178.07/177.94 [1242]~E(x12421,x12422)+E(f752(x12421,x12423,x12424),f752(x12422,x12423,x12424)) % 178.07/177.94 [1243]~E(x12431,x12432)+E(f752(x12433,x12431,x12434),f752(x12433,x12432,x12434)) % 178.07/177.94 [1244]~E(x12441,x12442)+E(f752(x12443,x12444,x12441),f752(x12443,x12444,x12442)) % 178.07/177.94 [1245]~E(x12451,x12452)+E(f745(x12451,x12453,x12454),f745(x12452,x12453,x12454)) % 178.07/177.94 [1246]~E(x12461,x12462)+E(f745(x12463,x12461,x12464),f745(x12463,x12462,x12464)) % 178.07/177.94 [1247]~E(x12471,x12472)+E(f745(x12473,x12474,x12471),f745(x12473,x12474,x12472)) % 178.07/177.94 [1248]~E(x12481,x12482)+E(f172(x12481,x12483,x12484),f172(x12482,x12483,x12484)) % 178.07/177.94 [1249]~E(x12491,x12492)+E(f172(x12493,x12491,x12494),f172(x12493,x12492,x12494)) % 178.07/177.94 [1250]~E(x12501,x12502)+E(f172(x12503,x12504,x12501),f172(x12503,x12504,x12502)) % 178.07/177.94 [1251]~E(x12511,x12512)+E(f507(x12511,x12513,x12514,x12515),f507(x12512,x12513,x12514,x12515)) % 178.07/177.94 [1252]~E(x12521,x12522)+E(f507(x12523,x12521,x12524,x12525),f507(x12523,x12522,x12524,x12525)) % 178.07/177.94 [1253]~E(x12531,x12532)+E(f507(x12533,x12534,x12531,x12535),f507(x12533,x12534,x12532,x12535)) % 178.07/177.94 [1254]~E(x12541,x12542)+E(f507(x12543,x12544,x12545,x12541),f507(x12543,x12544,x12545,x12542)) % 178.07/177.94 [1255]~E(x12551,x12552)+E(f735(x12551,x12553,x12554,x12555,x12556,x12557,x12558),f735(x12552,x12553,x12554,x12555,x12556,x12557,x12558)) % 178.07/177.94 [1256]~E(x12561,x12562)+E(f735(x12563,x12561,x12564,x12565,x12566,x12567,x12568),f735(x12563,x12562,x12564,x12565,x12566,x12567,x12568)) % 178.07/177.94 [1257]~E(x12571,x12572)+E(f735(x12573,x12574,x12571,x12575,x12576,x12577,x12578),f735(x12573,x12574,x12572,x12575,x12576,x12577,x12578)) % 178.07/177.94 [1258]~E(x12581,x12582)+E(f735(x12583,x12584,x12585,x12581,x12586,x12587,x12588),f735(x12583,x12584,x12585,x12582,x12586,x12587,x12588)) % 178.07/177.94 [1259]~E(x12591,x12592)+E(f735(x12593,x12594,x12595,x12596,x12591,x12597,x12598),f735(x12593,x12594,x12595,x12596,x12592,x12597,x12598)) % 178.07/177.94 [1260]~E(x12601,x12602)+E(f735(x12603,x12604,x12605,x12606,x12607,x12601,x12608),f735(x12603,x12604,x12605,x12606,x12607,x12602,x12608)) % 178.07/177.94 [1261]~E(x12611,x12612)+E(f735(x12613,x12614,x12615,x12616,x12617,x12618,x12611),f735(x12613,x12614,x12615,x12616,x12617,x12618,x12612)) % 178.07/177.94 [1262]~E(x12621,x12622)+E(f784(x12621,x12623,x12624),f784(x12622,x12623,x12624)) % 178.07/177.94 [1263]~E(x12631,x12632)+E(f784(x12633,x12631,x12634),f784(x12633,x12632,x12634)) % 178.07/177.94 [1264]~E(x12641,x12642)+E(f784(x12643,x12644,x12641),f784(x12643,x12644,x12642)) % 178.07/177.94 [1265]~E(x12651,x12652)+E(f218(x12651,x12653,x12654,x12655),f218(x12652,x12653,x12654,x12655)) % 178.07/177.94 [1266]~E(x12661,x12662)+E(f218(x12663,x12661,x12664,x12665),f218(x12663,x12662,x12664,x12665)) % 178.07/177.94 [1267]~E(x12671,x12672)+E(f218(x12673,x12674,x12671,x12675),f218(x12673,x12674,x12672,x12675)) % 178.07/177.94 [1268]~E(x12681,x12682)+E(f218(x12683,x12684,x12685,x12681),f218(x12683,x12684,x12685,x12682)) % 178.07/177.94 [1269]~E(x12691,x12692)+E(f275(x12691,x12693),f275(x12692,x12693)) % 178.07/177.94 [1270]~E(x12701,x12702)+E(f275(x12703,x12701),f275(x12703,x12702)) % 178.07/177.94 [1271]~E(x12711,x12712)+E(f751(x12711,x12713,x12714,x12715,x12716),f751(x12712,x12713,x12714,x12715,x12716)) % 178.07/177.94 [1272]~E(x12721,x12722)+E(f751(x12723,x12721,x12724,x12725,x12726),f751(x12723,x12722,x12724,x12725,x12726)) % 178.07/177.94 [1273]~E(x12731,x12732)+E(f751(x12733,x12734,x12731,x12735,x12736),f751(x12733,x12734,x12732,x12735,x12736)) % 178.07/177.94 [1274]~E(x12741,x12742)+E(f751(x12743,x12744,x12745,x12741,x12746),f751(x12743,x12744,x12745,x12742,x12746)) % 178.07/177.94 [1275]~E(x12751,x12752)+E(f751(x12753,x12754,x12755,x12756,x12751),f751(x12753,x12754,x12755,x12756,x12752)) % 178.07/177.94 [1276]~E(x12761,x12762)+E(f631(x12761,x12763,x12764,x12765,x12766),f631(x12762,x12763,x12764,x12765,x12766)) % 178.07/177.94 [1277]~E(x12771,x12772)+E(f631(x12773,x12771,x12774,x12775,x12776),f631(x12773,x12772,x12774,x12775,x12776)) % 178.07/177.94 [1278]~E(x12781,x12782)+E(f631(x12783,x12784,x12781,x12785,x12786),f631(x12783,x12784,x12782,x12785,x12786)) % 178.07/177.94 [1279]~E(x12791,x12792)+E(f631(x12793,x12794,x12795,x12791,x12796),f631(x12793,x12794,x12795,x12792,x12796)) % 178.07/177.94 [1280]~E(x12801,x12802)+E(f631(x12803,x12804,x12805,x12806,x12801),f631(x12803,x12804,x12805,x12806,x12802)) % 178.07/177.94 [1281]~E(x12811,x12812)+E(f185(x12811,x12813,x12814),f185(x12812,x12813,x12814)) % 178.07/177.94 [1282]~E(x12821,x12822)+E(f185(x12823,x12821,x12824),f185(x12823,x12822,x12824)) % 178.07/177.94 [1283]~E(x12831,x12832)+E(f185(x12833,x12834,x12831),f185(x12833,x12834,x12832)) % 178.07/177.94 [1284]~E(x12841,x12842)+E(f297(x12841,x12843,x12844,x12845,x12846),f297(x12842,x12843,x12844,x12845,x12846)) % 178.07/177.94 [1285]~E(x12851,x12852)+E(f297(x12853,x12851,x12854,x12855,x12856),f297(x12853,x12852,x12854,x12855,x12856)) % 178.07/177.94 [1286]~E(x12861,x12862)+E(f297(x12863,x12864,x12861,x12865,x12866),f297(x12863,x12864,x12862,x12865,x12866)) % 178.07/177.94 [1287]~E(x12871,x12872)+E(f297(x12873,x12874,x12875,x12871,x12876),f297(x12873,x12874,x12875,x12872,x12876)) % 178.07/177.94 [1288]~E(x12881,x12882)+E(f297(x12883,x12884,x12885,x12886,x12881),f297(x12883,x12884,x12885,x12886,x12882)) % 178.07/177.94 [1289]~E(x12891,x12892)+E(f492(x12891,x12893,x12894,x12895,x12896),f492(x12892,x12893,x12894,x12895,x12896)) % 178.07/177.94 [1290]~E(x12901,x12902)+E(f492(x12903,x12901,x12904,x12905,x12906),f492(x12903,x12902,x12904,x12905,x12906)) % 178.07/177.94 [1291]~E(x12911,x12912)+E(f492(x12913,x12914,x12911,x12915,x12916),f492(x12913,x12914,x12912,x12915,x12916)) % 178.07/177.94 [1292]~E(x12921,x12922)+E(f492(x12923,x12924,x12925,x12921,x12926),f492(x12923,x12924,x12925,x12922,x12926)) % 178.07/177.94 [1293]~E(x12931,x12932)+E(f492(x12933,x12934,x12935,x12936,x12931),f492(x12933,x12934,x12935,x12936,x12932)) % 178.07/177.94 [1294]~E(x12941,x12942)+E(f416(x12941,x12943,x12944,x12945,x12946,x12947),f416(x12942,x12943,x12944,x12945,x12946,x12947)) % 178.07/177.94 [1295]~E(x12951,x12952)+E(f416(x12953,x12951,x12954,x12955,x12956,x12957),f416(x12953,x12952,x12954,x12955,x12956,x12957)) % 178.07/177.94 [1296]~E(x12961,x12962)+E(f416(x12963,x12964,x12961,x12965,x12966,x12967),f416(x12963,x12964,x12962,x12965,x12966,x12967)) % 178.07/177.94 [1297]~E(x12971,x12972)+E(f416(x12973,x12974,x12975,x12971,x12976,x12977),f416(x12973,x12974,x12975,x12972,x12976,x12977)) % 178.07/177.94 [1298]~E(x12981,x12982)+E(f416(x12983,x12984,x12985,x12986,x12981,x12987),f416(x12983,x12984,x12985,x12986,x12982,x12987)) % 178.07/177.94 [1299]~E(x12991,x12992)+E(f416(x12993,x12994,x12995,x12996,x12997,x12991),f416(x12993,x12994,x12995,x12996,x12997,x12992)) % 178.07/177.94 [1300]~E(x13001,x13002)+E(f569(x13001,x13003,x13004),f569(x13002,x13003,x13004)) % 178.07/177.94 [1301]~E(x13011,x13012)+E(f569(x13013,x13011,x13014),f569(x13013,x13012,x13014)) % 178.07/177.94 [1302]~E(x13021,x13022)+E(f569(x13023,x13024,x13021),f569(x13023,x13024,x13022)) % 178.07/177.94 [1303]~E(x13031,x13032)+E(f664(x13031,x13033,x13034),f664(x13032,x13033,x13034)) % 178.07/177.94 [1304]~E(x13041,x13042)+E(f664(x13043,x13041,x13044),f664(x13043,x13042,x13044)) % 178.07/177.94 [1305]~E(x13051,x13052)+E(f664(x13053,x13054,x13051),f664(x13053,x13054,x13052)) % 178.07/177.94 [1306]~E(x13061,x13062)+E(f572(x13061,x13063,x13064,x13065,x13066),f572(x13062,x13063,x13064,x13065,x13066)) % 178.07/177.94 [1307]~E(x13071,x13072)+E(f572(x13073,x13071,x13074,x13075,x13076),f572(x13073,x13072,x13074,x13075,x13076)) % 178.07/177.94 [1308]~E(x13081,x13082)+E(f572(x13083,x13084,x13081,x13085,x13086),f572(x13083,x13084,x13082,x13085,x13086)) % 178.07/177.94 [1309]~E(x13091,x13092)+E(f572(x13093,x13094,x13095,x13091,x13096),f572(x13093,x13094,x13095,x13092,x13096)) % 178.07/177.94 [1310]~E(x13101,x13102)+E(f572(x13103,x13104,x13105,x13106,x13101),f572(x13103,x13104,x13105,x13106,x13102)) % 178.07/177.94 [1311]~E(x13111,x13112)+E(f700(x13111,x13113,x13114,x13115),f700(x13112,x13113,x13114,x13115)) % 178.07/177.94 [1312]~E(x13121,x13122)+E(f700(x13123,x13121,x13124,x13125),f700(x13123,x13122,x13124,x13125)) % 178.07/177.94 [1313]~E(x13131,x13132)+E(f700(x13133,x13134,x13131,x13135),f700(x13133,x13134,x13132,x13135)) % 178.07/177.94 [1314]~E(x13141,x13142)+E(f700(x13143,x13144,x13145,x13141),f700(x13143,x13144,x13145,x13142)) % 178.07/177.94 [1315]~E(x13151,x13152)+E(f630(x13151,x13153,x13154,x13155),f630(x13152,x13153,x13154,x13155)) % 178.07/177.94 [1316]~E(x13161,x13162)+E(f630(x13163,x13161,x13164,x13165),f630(x13163,x13162,x13164,x13165)) % 178.07/177.94 [1317]~E(x13171,x13172)+E(f630(x13173,x13174,x13171,x13175),f630(x13173,x13174,x13172,x13175)) % 178.07/177.94 [1318]~E(x13181,x13182)+E(f630(x13183,x13184,x13185,x13181),f630(x13183,x13184,x13185,x13182)) % 178.07/177.94 [1319]~E(x13191,x13192)+E(f402(x13191),f402(x13192)) % 178.07/177.94 [1320]~E(x13201,x13202)+E(f761(x13201,x13203,x13204,x13205,x13206),f761(x13202,x13203,x13204,x13205,x13206)) % 178.07/177.94 [1321]~E(x13211,x13212)+E(f761(x13213,x13211,x13214,x13215,x13216),f761(x13213,x13212,x13214,x13215,x13216)) % 178.07/177.94 [1322]~E(x13221,x13222)+E(f761(x13223,x13224,x13221,x13225,x13226),f761(x13223,x13224,x13222,x13225,x13226)) % 178.07/177.94 [1323]~E(x13231,x13232)+E(f761(x13233,x13234,x13235,x13231,x13236),f761(x13233,x13234,x13235,x13232,x13236)) % 178.07/177.94 [1324]~E(x13241,x13242)+E(f761(x13243,x13244,x13245,x13246,x13241),f761(x13243,x13244,x13245,x13246,x13242)) % 178.07/177.94 [1325]~E(x13251,x13252)+E(f651(x13251,x13253,x13254),f651(x13252,x13253,x13254)) % 178.07/177.94 [1326]~E(x13261,x13262)+E(f651(x13263,x13261,x13264),f651(x13263,x13262,x13264)) % 178.07/177.94 [1327]~E(x13271,x13272)+E(f651(x13273,x13274,x13271),f651(x13273,x13274,x13272)) % 178.07/177.94 [1328]~E(x13281,x13282)+E(f708(x13281,x13283),f708(x13282,x13283)) % 178.07/177.94 [1329]~E(x13291,x13292)+E(f708(x13293,x13291),f708(x13293,x13292)) % 178.07/177.94 [1330]~E(x13301,x13302)+E(f571(x13301,x13303,x13304,x13305,x13306),f571(x13302,x13303,x13304,x13305,x13306)) % 178.07/177.94 [1331]~E(x13311,x13312)+E(f571(x13313,x13311,x13314,x13315,x13316),f571(x13313,x13312,x13314,x13315,x13316)) % 178.07/177.94 [1332]~E(x13321,x13322)+E(f571(x13323,x13324,x13321,x13325,x13326),f571(x13323,x13324,x13322,x13325,x13326)) % 178.07/177.94 [1333]~E(x13331,x13332)+E(f571(x13333,x13334,x13335,x13331,x13336),f571(x13333,x13334,x13335,x13332,x13336)) % 178.07/177.94 [1334]~E(x13341,x13342)+E(f571(x13343,x13344,x13345,x13346,x13341),f571(x13343,x13344,x13345,x13346,x13342)) % 178.07/177.94 [1335]~E(x13351,x13352)+E(f725(x13351,x13353,x13354,x13355),f725(x13352,x13353,x13354,x13355)) % 178.07/177.94 [1336]~E(x13361,x13362)+E(f725(x13363,x13361,x13364,x13365),f725(x13363,x13362,x13364,x13365)) % 178.07/177.94 [1337]~E(x13371,x13372)+E(f725(x13373,x13374,x13371,x13375),f725(x13373,x13374,x13372,x13375)) % 178.07/177.94 [1338]~E(x13381,x13382)+E(f725(x13383,x13384,x13385,x13381),f725(x13383,x13384,x13385,x13382)) % 178.07/177.94 [1339]~E(x13391,x13392)+E(f747(x13391,x13393,x13394,x13395,x13396,x13397,x13398,x13399),f747(x13392,x13393,x13394,x13395,x13396,x13397,x13398,x13399)) % 178.07/177.94 [1340]~E(x13401,x13402)+E(f747(x13403,x13401,x13404,x13405,x13406,x13407,x13408,x13409),f747(x13403,x13402,x13404,x13405,x13406,x13407,x13408,x13409)) % 178.07/177.94 [1341]~E(x13411,x13412)+E(f747(x13413,x13414,x13411,x13415,x13416,x13417,x13418,x13419),f747(x13413,x13414,x13412,x13415,x13416,x13417,x13418,x13419)) % 178.07/177.94 [1342]~E(x13421,x13422)+E(f747(x13423,x13424,x13425,x13421,x13426,x13427,x13428,x13429),f747(x13423,x13424,x13425,x13422,x13426,x13427,x13428,x13429)) % 178.07/177.94 [1343]~E(x13431,x13432)+E(f747(x13433,x13434,x13435,x13436,x13431,x13437,x13438,x13439),f747(x13433,x13434,x13435,x13436,x13432,x13437,x13438,x13439)) % 178.07/177.94 [1344]~E(x13441,x13442)+E(f747(x13443,x13444,x13445,x13446,x13447,x13441,x13448,x13449),f747(x13443,x13444,x13445,x13446,x13447,x13442,x13448,x13449)) % 178.07/177.94 [1345]~E(x13451,x13452)+E(f747(x13453,x13454,x13455,x13456,x13457,x13458,x13451,x13459),f747(x13453,x13454,x13455,x13456,x13457,x13458,x13452,x13459)) % 178.07/177.94 [1346]~E(x13461,x13462)+E(f747(x13463,x13464,x13465,x13466,x13467,x13468,x13469,x13461),f747(x13463,x13464,x13465,x13466,x13467,x13468,x13469,x13462)) % 178.07/177.94 [1347]~E(x13471,x13472)+E(f213(x13471,x13473,x13474,x13475),f213(x13472,x13473,x13474,x13475)) % 178.07/177.94 [1348]~E(x13481,x13482)+E(f213(x13483,x13481,x13484,x13485),f213(x13483,x13482,x13484,x13485)) % 178.07/177.94 [1349]~E(x13491,x13492)+E(f213(x13493,x13494,x13491,x13495),f213(x13493,x13494,x13492,x13495)) % 178.07/177.94 [1350]~E(x13501,x13502)+E(f213(x13503,x13504,x13505,x13501),f213(x13503,x13504,x13505,x13502)) % 178.07/177.94 [1351]~E(x13511,x13512)+E(f427(x13511,x13513,x13514,x13515),f427(x13512,x13513,x13514,x13515)) % 178.07/177.94 [1352]~E(x13521,x13522)+E(f427(x13523,x13521,x13524,x13525),f427(x13523,x13522,x13524,x13525)) % 178.07/177.94 [1353]~E(x13531,x13532)+E(f427(x13533,x13534,x13531,x13535),f427(x13533,x13534,x13532,x13535)) % 178.07/177.94 [1354]~E(x13541,x13542)+E(f427(x13543,x13544,x13545,x13541),f427(x13543,x13544,x13545,x13542)) % 178.07/177.94 [1355]~E(x13551,x13552)+E(f458(x13551,x13553,x13554,x13555,x13556),f458(x13552,x13553,x13554,x13555,x13556)) % 178.07/177.94 [1356]~E(x13561,x13562)+E(f458(x13563,x13561,x13564,x13565,x13566),f458(x13563,x13562,x13564,x13565,x13566)) % 178.07/177.94 [1357]~E(x13571,x13572)+E(f458(x13573,x13574,x13571,x13575,x13576),f458(x13573,x13574,x13572,x13575,x13576)) % 178.07/177.94 [1358]~E(x13581,x13582)+E(f458(x13583,x13584,x13585,x13581,x13586),f458(x13583,x13584,x13585,x13582,x13586)) % 178.07/177.94 [1359]~E(x13591,x13592)+E(f458(x13593,x13594,x13595,x13596,x13591),f458(x13593,x13594,x13595,x13596,x13592)) % 178.07/177.94 [1360]~E(x13601,x13602)+E(f798(x13601,x13603,x13604,x13605,x13606,x13607),f798(x13602,x13603,x13604,x13605,x13606,x13607)) % 178.07/177.94 [1361]~E(x13611,x13612)+E(f798(x13613,x13611,x13614,x13615,x13616,x13617),f798(x13613,x13612,x13614,x13615,x13616,x13617)) % 178.07/177.94 [1362]~E(x13621,x13622)+E(f798(x13623,x13624,x13621,x13625,x13626,x13627),f798(x13623,x13624,x13622,x13625,x13626,x13627)) % 178.07/177.94 [1363]~E(x13631,x13632)+E(f798(x13633,x13634,x13635,x13631,x13636,x13637),f798(x13633,x13634,x13635,x13632,x13636,x13637)) % 178.07/177.94 [1364]~E(x13641,x13642)+E(f798(x13643,x13644,x13645,x13646,x13641,x13647),f798(x13643,x13644,x13645,x13646,x13642,x13647)) % 178.07/177.94 [1365]~E(x13651,x13652)+E(f798(x13653,x13654,x13655,x13656,x13657,x13651),f798(x13653,x13654,x13655,x13656,x13657,x13652)) % 178.07/177.94 [1366]~E(x13661,x13662)+E(f508(x13661,x13663),f508(x13662,x13663)) % 178.07/177.94 [1367]~E(x13671,x13672)+E(f508(x13673,x13671),f508(x13673,x13672)) % 178.07/177.94 [1368]~E(x13681,x13682)+E(f799(x13681,x13683,x13684,x13685,x13686,x13687),f799(x13682,x13683,x13684,x13685,x13686,x13687)) % 178.07/177.94 [1369]~E(x13691,x13692)+E(f799(x13693,x13691,x13694,x13695,x13696,x13697),f799(x13693,x13692,x13694,x13695,x13696,x13697)) % 178.07/177.94 [1370]~E(x13701,x13702)+E(f799(x13703,x13704,x13701,x13705,x13706,x13707),f799(x13703,x13704,x13702,x13705,x13706,x13707)) % 178.07/177.94 [1371]~E(x13711,x13712)+E(f799(x13713,x13714,x13715,x13711,x13716,x13717),f799(x13713,x13714,x13715,x13712,x13716,x13717)) % 178.07/177.94 [1372]~E(x13721,x13722)+E(f799(x13723,x13724,x13725,x13726,x13721,x13727),f799(x13723,x13724,x13725,x13726,x13722,x13727)) % 178.07/177.94 [1373]~E(x13731,x13732)+E(f799(x13733,x13734,x13735,x13736,x13737,x13731),f799(x13733,x13734,x13735,x13736,x13737,x13732)) % 178.07/177.94 [1374]~E(x13741,x13742)+E(f840(x13741,x13743,x13744,x13745),f840(x13742,x13743,x13744,x13745)) % 178.07/177.94 [1375]~E(x13751,x13752)+E(f840(x13753,x13751,x13754,x13755),f840(x13753,x13752,x13754,x13755)) % 178.07/177.94 [1376]~E(x13761,x13762)+E(f840(x13763,x13764,x13761,x13765),f840(x13763,x13764,x13762,x13765)) % 178.07/177.94 [1377]~E(x13771,x13772)+E(f840(x13773,x13774,x13775,x13771),f840(x13773,x13774,x13775,x13772)) % 178.07/177.94 [1378]~E(x13781,x13782)+E(f669(x13781,x13783),f669(x13782,x13783)) % 178.07/177.94 [1379]~E(x13791,x13792)+E(f669(x13793,x13791),f669(x13793,x13792)) % 178.07/177.94 [1380]~E(x13801,x13802)+E(f439(x13801,x13803,x13804,x13805),f439(x13802,x13803,x13804,x13805)) % 178.07/177.94 [1381]~E(x13811,x13812)+E(f439(x13813,x13811,x13814,x13815),f439(x13813,x13812,x13814,x13815)) % 178.07/177.94 [1382]~E(x13821,x13822)+E(f439(x13823,x13824,x13821,x13825),f439(x13823,x13824,x13822,x13825)) % 178.07/177.94 [1383]~E(x13831,x13832)+E(f439(x13833,x13834,x13835,x13831),f439(x13833,x13834,x13835,x13832)) % 178.07/177.94 [1384]~E(x13841,x13842)+E(f99(x13841,x13843,x13844),f99(x13842,x13843,x13844)) % 178.07/177.94 [1385]~E(x13851,x13852)+E(f99(x13853,x13851,x13854),f99(x13853,x13852,x13854)) % 178.07/177.94 [1386]~E(x13861,x13862)+E(f99(x13863,x13864,x13861),f99(x13863,x13864,x13862)) % 178.07/177.94 [1387]~E(x13871,x13872)+E(f342(x13871,x13873,x13874),f342(x13872,x13873,x13874)) % 178.07/177.94 [1388]~E(x13881,x13882)+E(f342(x13883,x13881,x13884),f342(x13883,x13882,x13884)) % 178.07/177.94 [1389]~E(x13891,x13892)+E(f342(x13893,x13894,x13891),f342(x13893,x13894,x13892)) % 178.07/177.94 [1390]~E(x13901,x13902)+E(f467(x13901,x13903,x13904),f467(x13902,x13903,x13904)) % 178.07/177.94 [1391]~E(x13911,x13912)+E(f467(x13913,x13911,x13914),f467(x13913,x13912,x13914)) % 178.07/177.94 [1392]~E(x13921,x13922)+E(f467(x13923,x13924,x13921),f467(x13923,x13924,x13922)) % 178.07/177.94 [1393]~E(x13931,x13932)+E(f219(x13931,x13933,x13934,x13935,x13936,x13937,x13938),f219(x13932,x13933,x13934,x13935,x13936,x13937,x13938)) % 178.07/177.94 [1394]~E(x13941,x13942)+E(f219(x13943,x13941,x13944,x13945,x13946,x13947,x13948),f219(x13943,x13942,x13944,x13945,x13946,x13947,x13948)) % 178.07/177.94 [1395]~E(x13951,x13952)+E(f219(x13953,x13954,x13951,x13955,x13956,x13957,x13958),f219(x13953,x13954,x13952,x13955,x13956,x13957,x13958)) % 178.07/177.94 [1396]~E(x13961,x13962)+E(f219(x13963,x13964,x13965,x13961,x13966,x13967,x13968),f219(x13963,x13964,x13965,x13962,x13966,x13967,x13968)) % 178.07/177.94 [1397]~E(x13971,x13972)+E(f219(x13973,x13974,x13975,x13976,x13971,x13977,x13978),f219(x13973,x13974,x13975,x13976,x13972,x13977,x13978)) % 178.07/177.94 [1398]~E(x13981,x13982)+E(f219(x13983,x13984,x13985,x13986,x13987,x13981,x13988),f219(x13983,x13984,x13985,x13986,x13987,x13982,x13988)) % 178.07/177.94 [1399]~E(x13991,x13992)+E(f219(x13993,x13994,x13995,x13996,x13997,x13998,x13991),f219(x13993,x13994,x13995,x13996,x13997,x13998,x13992)) % 178.07/177.94 [1400]~E(x14001,x14002)+E(f55(x14001,x14003,x14004),f55(x14002,x14003,x14004)) % 178.07/177.94 [1401]~E(x14011,x14012)+E(f55(x14013,x14011,x14014),f55(x14013,x14012,x14014)) % 178.07/177.94 [1402]~E(x14021,x14022)+E(f55(x14023,x14024,x14021),f55(x14023,x14024,x14022)) % 178.07/177.94 [1403]~E(x14031,x14032)+E(f567(x14031,x14033),f567(x14032,x14033)) % 178.07/177.94 [1404]~E(x14041,x14042)+E(f567(x14043,x14041),f567(x14043,x14042)) % 178.07/177.94 [1405]~E(x14051,x14052)+E(f510(x14051,x14053),f510(x14052,x14053)) % 178.07/177.94 [1406]~E(x14061,x14062)+E(f510(x14063,x14061),f510(x14063,x14062)) % 178.07/177.94 [1407]~E(x14071,x14072)+E(f464(x14071,x14073,x14074,x14075),f464(x14072,x14073,x14074,x14075)) % 178.07/177.94 [1408]~E(x14081,x14082)+E(f464(x14083,x14081,x14084,x14085),f464(x14083,x14082,x14084,x14085)) % 178.07/177.94 [1409]~E(x14091,x14092)+E(f464(x14093,x14094,x14091,x14095),f464(x14093,x14094,x14092,x14095)) % 178.07/177.94 [1410]~E(x14101,x14102)+E(f464(x14103,x14104,x14105,x14101),f464(x14103,x14104,x14105,x14102)) % 178.07/177.94 [1411]~E(x14111,x14112)+E(f822(x14111,x14113,x14114),f822(x14112,x14113,x14114)) % 178.07/177.94 [1412]~E(x14121,x14122)+E(f822(x14123,x14121,x14124),f822(x14123,x14122,x14124)) % 178.07/177.94 [1413]~E(x14131,x14132)+E(f822(x14133,x14134,x14131),f822(x14133,x14134,x14132)) % 178.07/177.94 [1414]~E(x14141,x14142)+E(f600(x14141,x14143,x14144,x14145),f600(x14142,x14143,x14144,x14145)) % 178.07/177.94 [1415]~E(x14151,x14152)+E(f600(x14153,x14151,x14154,x14155),f600(x14153,x14152,x14154,x14155)) % 178.07/177.94 [1416]~E(x14161,x14162)+E(f600(x14163,x14164,x14161,x14165),f600(x14163,x14164,x14162,x14165)) % 178.07/177.94 [1417]~E(x14171,x14172)+E(f600(x14173,x14174,x14175,x14171),f600(x14173,x14174,x14175,x14172)) % 178.07/177.94 [1418]~E(x14181,x14182)+E(f821(x14181,x14183),f821(x14182,x14183)) % 178.07/177.94 [1419]~E(x14191,x14192)+E(f821(x14193,x14191),f821(x14193,x14192)) % 178.07/177.94 [1420]~E(x14201,x14202)+E(f237(x14201,x14203,x14204),f237(x14202,x14203,x14204)) % 178.07/177.94 [1421]~E(x14211,x14212)+E(f237(x14213,x14211,x14214),f237(x14213,x14212,x14214)) % 178.07/177.94 [1422]~E(x14221,x14222)+E(f237(x14223,x14224,x14221),f237(x14223,x14224,x14222)) % 178.07/177.94 [1423]~E(x14231,x14232)+E(f706(x14231,x14233,x14234,x14235,x14236,x14237,x14238,x14239),f706(x14232,x14233,x14234,x14235,x14236,x14237,x14238,x14239)) % 178.07/177.94 [1424]~E(x14241,x14242)+E(f706(x14243,x14241,x14244,x14245,x14246,x14247,x14248,x14249),f706(x14243,x14242,x14244,x14245,x14246,x14247,x14248,x14249)) % 178.07/177.94 [1425]~E(x14251,x14252)+E(f706(x14253,x14254,x14251,x14255,x14256,x14257,x14258,x14259),f706(x14253,x14254,x14252,x14255,x14256,x14257,x14258,x14259)) % 178.07/177.94 [1426]~E(x14261,x14262)+E(f706(x14263,x14264,x14265,x14261,x14266,x14267,x14268,x14269),f706(x14263,x14264,x14265,x14262,x14266,x14267,x14268,x14269)) % 178.07/177.94 [1427]~E(x14271,x14272)+E(f706(x14273,x14274,x14275,x14276,x14271,x14277,x14278,x14279),f706(x14273,x14274,x14275,x14276,x14272,x14277,x14278,x14279)) % 178.07/177.94 [1428]~E(x14281,x14282)+E(f706(x14283,x14284,x14285,x14286,x14287,x14281,x14288,x14289),f706(x14283,x14284,x14285,x14286,x14287,x14282,x14288,x14289)) % 178.07/177.94 [1429]~E(x14291,x14292)+E(f706(x14293,x14294,x14295,x14296,x14297,x14298,x14291,x14299),f706(x14293,x14294,x14295,x14296,x14297,x14298,x14292,x14299)) % 178.07/177.94 [1430]~E(x14301,x14302)+E(f706(x14303,x14304,x14305,x14306,x14307,x14308,x14309,x14301),f706(x14303,x14304,x14305,x14306,x14307,x14308,x14309,x14302)) % 178.07/177.94 [1431]~E(x14311,x14312)+E(f505(x14311,x14313,x14314),f505(x14312,x14313,x14314)) % 178.07/177.94 [1432]~E(x14321,x14322)+E(f505(x14323,x14321,x14324),f505(x14323,x14322,x14324)) % 178.07/177.94 [1433]~E(x14331,x14332)+E(f505(x14333,x14334,x14331),f505(x14333,x14334,x14332)) % 178.07/177.94 [1434]~E(x14341,x14342)+E(f657(x14341,x14343,x14344),f657(x14342,x14343,x14344)) % 178.07/177.94 [1435]~E(x14351,x14352)+E(f657(x14353,x14351,x14354),f657(x14353,x14352,x14354)) % 178.07/177.94 [1436]~E(x14361,x14362)+E(f657(x14363,x14364,x14361),f657(x14363,x14364,x14362)) % 178.07/177.94 [1437]~E(x14371,x14372)+E(f797(x14371,x14373,x14374,x14375,x14376,x14377),f797(x14372,x14373,x14374,x14375,x14376,x14377)) % 178.07/177.94 [1438]~E(x14381,x14382)+E(f797(x14383,x14381,x14384,x14385,x14386,x14387),f797(x14383,x14382,x14384,x14385,x14386,x14387)) % 178.07/177.94 [1439]~E(x14391,x14392)+E(f797(x14393,x14394,x14391,x14395,x14396,x14397),f797(x14393,x14394,x14392,x14395,x14396,x14397)) % 178.07/177.94 [1440]~E(x14401,x14402)+E(f797(x14403,x14404,x14405,x14401,x14406,x14407),f797(x14403,x14404,x14405,x14402,x14406,x14407)) % 178.07/177.94 [1441]~E(x14411,x14412)+E(f797(x14413,x14414,x14415,x14416,x14411,x14417),f797(x14413,x14414,x14415,x14416,x14412,x14417)) % 178.07/177.94 [1442]~E(x14421,x14422)+E(f797(x14423,x14424,x14425,x14426,x14427,x14421),f797(x14423,x14424,x14425,x14426,x14427,x14422)) % 178.07/177.94 [1443]~E(x14431,x14432)+E(f543(x14431,x14433,x14434),f543(x14432,x14433,x14434)) % 178.07/177.94 [1444]~E(x14441,x14442)+E(f543(x14443,x14441,x14444),f543(x14443,x14442,x14444)) % 178.07/177.94 [1445]~E(x14451,x14452)+E(f543(x14453,x14454,x14451),f543(x14453,x14454,x14452)) % 178.07/177.94 [1446]~E(x14461,x14462)+E(f362(x14461,x14463,x14464,x14465,x14466,x14467,x14468,x14469,x144610),f362(x14462,x14463,x14464,x14465,x14466,x14467,x14468,x14469,x144610)) % 178.07/177.94 [1447]~E(x14471,x14472)+E(f362(x14473,x14471,x14474,x14475,x14476,x14477,x14478,x14479,x144710),f362(x14473,x14472,x14474,x14475,x14476,x14477,x14478,x14479,x144710)) % 178.07/177.94 [1448]~E(x14481,x14482)+E(f362(x14483,x14484,x14481,x14485,x14486,x14487,x14488,x14489,x144810),f362(x14483,x14484,x14482,x14485,x14486,x14487,x14488,x14489,x144810)) % 178.07/177.94 [1449]~E(x14491,x14492)+E(f362(x14493,x14494,x14495,x14491,x14496,x14497,x14498,x14499,x144910),f362(x14493,x14494,x14495,x14492,x14496,x14497,x14498,x14499,x144910)) % 178.07/177.94 [1450]~E(x14501,x14502)+E(f362(x14503,x14504,x14505,x14506,x14501,x14507,x14508,x14509,x145010),f362(x14503,x14504,x14505,x14506,x14502,x14507,x14508,x14509,x145010)) % 178.07/177.94 [1451]~E(x14511,x14512)+E(f362(x14513,x14514,x14515,x14516,x14517,x14511,x14518,x14519,x145110),f362(x14513,x14514,x14515,x14516,x14517,x14512,x14518,x14519,x145110)) % 178.07/177.94 [1452]~E(x14521,x14522)+E(f362(x14523,x14524,x14525,x14526,x14527,x14528,x14521,x14529,x145210),f362(x14523,x14524,x14525,x14526,x14527,x14528,x14522,x14529,x145210)) % 178.07/177.94 [1453]~E(x14531,x14532)+E(f362(x14533,x14534,x14535,x14536,x14537,x14538,x14539,x14531,x145310),f362(x14533,x14534,x14535,x14536,x14537,x14538,x14539,x14532,x145310)) % 178.07/177.94 [1454]~E(x14541,x14542)+E(f362(x14543,x14544,x14545,x14546,x14547,x14548,x14549,x145410,x14541),f362(x14543,x14544,x14545,x14546,x14547,x14548,x14549,x145410,x14542)) % 178.07/177.94 [1455]~E(x14551,x14552)+E(f408(x14551,x14553,x14554,x14555,x14556,x14557),f408(x14552,x14553,x14554,x14555,x14556,x14557)) % 178.07/177.94 [1456]~E(x14561,x14562)+E(f408(x14563,x14561,x14564,x14565,x14566,x14567),f408(x14563,x14562,x14564,x14565,x14566,x14567)) % 178.07/177.94 [1457]~E(x14571,x14572)+E(f408(x14573,x14574,x14571,x14575,x14576,x14577),f408(x14573,x14574,x14572,x14575,x14576,x14577)) % 178.07/177.94 [1458]~E(x14581,x14582)+E(f408(x14583,x14584,x14585,x14581,x14586,x14587),f408(x14583,x14584,x14585,x14582,x14586,x14587)) % 178.07/177.94 [1459]~E(x14591,x14592)+E(f408(x14593,x14594,x14595,x14596,x14591,x14597),f408(x14593,x14594,x14595,x14596,x14592,x14597)) % 178.07/177.94 [1460]~E(x14601,x14602)+E(f408(x14603,x14604,x14605,x14606,x14607,x14601),f408(x14603,x14604,x14605,x14606,x14607,x14602)) % 178.07/177.94 [1461]~E(x14611,x14612)+E(f435(x14611,x14613,x14614,x14615),f435(x14612,x14613,x14614,x14615)) % 178.07/177.94 [1462]~E(x14621,x14622)+E(f435(x14623,x14621,x14624,x14625),f435(x14623,x14622,x14624,x14625)) % 178.07/177.94 [1463]~E(x14631,x14632)+E(f435(x14633,x14634,x14631,x14635),f435(x14633,x14634,x14632,x14635)) % 178.07/177.94 [1464]~E(x14641,x14642)+E(f435(x14643,x14644,x14645,x14641),f435(x14643,x14644,x14645,x14642)) % 178.07/177.94 [1465]~E(x14651,x14652)+E(f480(x14651,x14653,x14654,x14655,x14656),f480(x14652,x14653,x14654,x14655,x14656)) % 178.07/177.94 [1466]~E(x14661,x14662)+E(f480(x14663,x14661,x14664,x14665,x14666),f480(x14663,x14662,x14664,x14665,x14666)) % 178.07/177.94 [1467]~E(x14671,x14672)+E(f480(x14673,x14674,x14671,x14675,x14676),f480(x14673,x14674,x14672,x14675,x14676)) % 178.07/177.94 [1468]~E(x14681,x14682)+E(f480(x14683,x14684,x14685,x14681,x14686),f480(x14683,x14684,x14685,x14682,x14686)) % 178.07/177.94 [1469]~E(x14691,x14692)+E(f480(x14693,x14694,x14695,x14696,x14691),f480(x14693,x14694,x14695,x14696,x14692)) % 178.07/177.94 [1470]~E(x14701,x14702)+E(f620(x14701,x14703,x14704),f620(x14702,x14703,x14704)) % 178.07/177.94 [1471]~E(x14711,x14712)+E(f620(x14713,x14711,x14714),f620(x14713,x14712,x14714)) % 178.07/177.94 [1472]~E(x14721,x14722)+E(f620(x14723,x14724,x14721),f620(x14723,x14724,x14722)) % 178.07/177.94 [1473]~E(x14731,x14732)+E(f204(x14731,x14733,x14734,x14735),f204(x14732,x14733,x14734,x14735)) % 178.07/177.94 [1474]~E(x14741,x14742)+E(f204(x14743,x14741,x14744,x14745),f204(x14743,x14742,x14744,x14745)) % 178.07/177.94 [1475]~E(x14751,x14752)+E(f204(x14753,x14754,x14751,x14755),f204(x14753,x14754,x14752,x14755)) % 178.07/177.94 [1476]~E(x14761,x14762)+E(f204(x14763,x14764,x14765,x14761),f204(x14763,x14764,x14765,x14762)) % 178.07/177.94 [1477]~E(x14771,x14772)+E(f844(x14771,x14773),f844(x14772,x14773)) % 178.07/177.94 [1478]~E(x14781,x14782)+E(f844(x14783,x14781),f844(x14783,x14782)) % 178.07/177.94 [1479]~E(x14791,x14792)+E(f681(x14791,x14793,x14794),f681(x14792,x14793,x14794)) % 178.07/177.94 [1480]~E(x14801,x14802)+E(f681(x14803,x14801,x14804),f681(x14803,x14802,x14804)) % 178.07/177.94 [1481]~E(x14811,x14812)+E(f681(x14813,x14814,x14811),f681(x14813,x14814,x14812)) % 178.07/177.94 [1482]~E(x14821,x14822)+E(f365(x14821,x14823,x14824),f365(x14822,x14823,x14824)) % 178.07/177.94 [1483]~E(x14831,x14832)+E(f365(x14833,x14831,x14834),f365(x14833,x14832,x14834)) % 178.07/177.94 [1484]~E(x14841,x14842)+E(f365(x14843,x14844,x14841),f365(x14843,x14844,x14842)) % 178.07/177.94 [1485]~E(x14851,x14852)+E(f173(x14851,x14853,x14854),f173(x14852,x14853,x14854)) % 178.07/177.94 [1486]~E(x14861,x14862)+E(f173(x14863,x14861,x14864),f173(x14863,x14862,x14864)) % 178.07/177.94 [1487]~E(x14871,x14872)+E(f173(x14873,x14874,x14871),f173(x14873,x14874,x14872)) % 178.07/177.94 [1488]~E(x14881,x14882)+E(f432(x14881,x14883,x14884),f432(x14882,x14883,x14884)) % 178.07/177.94 [1489]~E(x14891,x14892)+E(f432(x14893,x14891,x14894),f432(x14893,x14892,x14894)) % 178.07/177.94 [1490]~E(x14901,x14902)+E(f432(x14903,x14904,x14901),f432(x14903,x14904,x14902)) % 178.07/177.94 [1491]~E(x14911,x14912)+E(f726(x14911,x14913,x14914,x14915,x14916),f726(x14912,x14913,x14914,x14915,x14916)) % 178.07/177.94 [1492]~E(x14921,x14922)+E(f726(x14923,x14921,x14924,x14925,x14926),f726(x14923,x14922,x14924,x14925,x14926)) % 178.07/177.94 [1493]~E(x14931,x14932)+E(f726(x14933,x14934,x14931,x14935,x14936),f726(x14933,x14934,x14932,x14935,x14936)) % 178.07/177.94 [1494]~E(x14941,x14942)+E(f726(x14943,x14944,x14945,x14941,x14946),f726(x14943,x14944,x14945,x14942,x14946)) % 178.07/177.94 [1495]~E(x14951,x14952)+E(f726(x14953,x14954,x14955,x14956,x14951),f726(x14953,x14954,x14955,x14956,x14952)) % 178.07/177.94 [1496]~E(x14961,x14962)+E(f291(x14961,x14963,x14964),f291(x14962,x14963,x14964)) % 178.07/177.94 [1497]~E(x14971,x14972)+E(f291(x14973,x14971,x14974),f291(x14973,x14972,x14974)) % 178.07/177.94 [1498]~E(x14981,x14982)+E(f291(x14983,x14984,x14981),f291(x14983,x14984,x14982)) % 178.07/177.94 [1499]~E(x14991,x14992)+E(f163(x14991,x14993,x14994,x14995),f163(x14992,x14993,x14994,x14995)) % 178.07/177.94 [1500]~E(x15001,x15002)+E(f163(x15003,x15001,x15004,x15005),f163(x15003,x15002,x15004,x15005)) % 178.07/177.94 [1501]~E(x15011,x15012)+E(f163(x15013,x15014,x15011,x15015),f163(x15013,x15014,x15012,x15015)) % 178.07/177.94 [1502]~E(x15021,x15022)+E(f163(x15023,x15024,x15025,x15021),f163(x15023,x15024,x15025,x15022)) % 178.07/177.94 [1503]~E(x15031,x15032)+E(f189(x15031,x15033,x15034),f189(x15032,x15033,x15034)) % 178.07/177.94 [1504]~E(x15041,x15042)+E(f189(x15043,x15041,x15044),f189(x15043,x15042,x15044)) % 178.07/177.94 [1505]~E(x15051,x15052)+E(f189(x15053,x15054,x15051),f189(x15053,x15054,x15052)) % 178.07/177.94 [1506]~E(x15061,x15062)+E(f575(x15061,x15063,x15064,x15065,x15066,x15067,x15068,x15069),f575(x15062,x15063,x15064,x15065,x15066,x15067,x15068,x15069)) % 178.07/177.94 [1507]~E(x15071,x15072)+E(f575(x15073,x15071,x15074,x15075,x15076,x15077,x15078,x15079),f575(x15073,x15072,x15074,x15075,x15076,x15077,x15078,x15079)) % 178.07/177.94 [1508]~E(x15081,x15082)+E(f575(x15083,x15084,x15081,x15085,x15086,x15087,x15088,x15089),f575(x15083,x15084,x15082,x15085,x15086,x15087,x15088,x15089)) % 178.07/177.94 [1509]~E(x15091,x15092)+E(f575(x15093,x15094,x15095,x15091,x15096,x15097,x15098,x15099),f575(x15093,x15094,x15095,x15092,x15096,x15097,x15098,x15099)) % 178.07/177.94 [1510]~E(x15101,x15102)+E(f575(x15103,x15104,x15105,x15106,x15101,x15107,x15108,x15109),f575(x15103,x15104,x15105,x15106,x15102,x15107,x15108,x15109)) % 178.07/177.94 [1511]~E(x15111,x15112)+E(f575(x15113,x15114,x15115,x15116,x15117,x15111,x15118,x15119),f575(x15113,x15114,x15115,x15116,x15117,x15112,x15118,x15119)) % 178.07/177.94 [1512]~E(x15121,x15122)+E(f575(x15123,x15124,x15125,x15126,x15127,x15128,x15121,x15129),f575(x15123,x15124,x15125,x15126,x15127,x15128,x15122,x15129)) % 178.07/177.94 [1513]~E(x15131,x15132)+E(f575(x15133,x15134,x15135,x15136,x15137,x15138,x15139,x15131),f575(x15133,x15134,x15135,x15136,x15137,x15138,x15139,x15132)) % 178.07/177.94 [1514]~E(x15141,x15142)+E(f417(x15141,x15143,x15144),f417(x15142,x15143,x15144)) % 178.07/177.94 [1515]~E(x15151,x15152)+E(f417(x15153,x15151,x15154),f417(x15153,x15152,x15154)) % 178.07/177.94 [1516]~E(x15161,x15162)+E(f417(x15163,x15164,x15161),f417(x15163,x15164,x15162)) % 178.07/177.94 [1517]~E(x15171,x15172)+E(f257(x15171,x15173),f257(x15172,x15173)) % 178.07/177.94 [1518]~E(x15181,x15182)+E(f257(x15183,x15181),f257(x15183,x15182)) % 178.07/177.94 [1519]~E(x15191,x15192)+E(f672(x15191,x15193,x15194,x15195),f672(x15192,x15193,x15194,x15195)) % 178.07/177.94 [1520]~E(x15201,x15202)+E(f672(x15203,x15201,x15204,x15205),f672(x15203,x15202,x15204,x15205)) % 178.07/177.94 [1521]~E(x15211,x15212)+E(f672(x15213,x15214,x15211,x15215),f672(x15213,x15214,x15212,x15215)) % 178.07/177.94 [1522]~E(x15221,x15222)+E(f672(x15223,x15224,x15225,x15221),f672(x15223,x15224,x15225,x15222)) % 178.07/177.94 [1523]~E(x15231,x15232)+E(f639(x15231,x15233,x15234),f639(x15232,x15233,x15234)) % 178.07/177.94 [1524]~E(x15241,x15242)+E(f639(x15243,x15241,x15244),f639(x15243,x15242,x15244)) % 178.07/177.94 [1525]~E(x15251,x15252)+E(f639(x15253,x15254,x15251),f639(x15253,x15254,x15252)) % 178.07/177.94 [1526]~E(x15261,x15262)+E(f101(x15261,x15263,x15264,x15265),f101(x15262,x15263,x15264,x15265)) % 178.07/177.94 [1527]~E(x15271,x15272)+E(f101(x15273,x15271,x15274,x15275),f101(x15273,x15272,x15274,x15275)) % 178.07/177.94 [1528]~E(x15281,x15282)+E(f101(x15283,x15284,x15281,x15285),f101(x15283,x15284,x15282,x15285)) % 178.07/177.94 [1529]~E(x15291,x15292)+E(f101(x15293,x15294,x15295,x15291),f101(x15293,x15294,x15295,x15292)) % 178.07/177.94 [1530]~E(x15301,x15302)+E(f385(x15301,x15303),f385(x15302,x15303)) % 178.07/177.94 [1531]~E(x15311,x15312)+E(f385(x15313,x15311),f385(x15313,x15312)) % 178.07/177.94 [1532]~E(x15321,x15322)+E(f444(x15321,x15323),f444(x15322,x15323)) % 178.07/177.94 [1533]~E(x15331,x15332)+E(f444(x15333,x15331),f444(x15333,x15332)) % 178.07/177.94 [1534]~E(x15341,x15342)+E(f229(x15341,x15343,x15344),f229(x15342,x15343,x15344)) % 178.07/177.94 [1535]~E(x15351,x15352)+E(f229(x15353,x15351,x15354),f229(x15353,x15352,x15354)) % 178.07/177.94 [1536]~E(x15361,x15362)+E(f229(x15363,x15364,x15361),f229(x15363,x15364,x15362)) % 178.07/177.94 [1537]~E(x15371,x15372)+E(f626(x15371,x15373,x15374,x15375,x15376,x15377),f626(x15372,x15373,x15374,x15375,x15376,x15377)) % 178.07/177.94 [1538]~E(x15381,x15382)+E(f626(x15383,x15381,x15384,x15385,x15386,x15387),f626(x15383,x15382,x15384,x15385,x15386,x15387)) % 178.07/177.94 [1539]~E(x15391,x15392)+E(f626(x15393,x15394,x15391,x15395,x15396,x15397),f626(x15393,x15394,x15392,x15395,x15396,x15397)) % 178.07/177.94 [1540]~E(x15401,x15402)+E(f626(x15403,x15404,x15405,x15401,x15406,x15407),f626(x15403,x15404,x15405,x15402,x15406,x15407)) % 178.07/177.94 [1541]~E(x15411,x15412)+E(f626(x15413,x15414,x15415,x15416,x15411,x15417),f626(x15413,x15414,x15415,x15416,x15412,x15417)) % 178.07/177.95 [1542]~E(x15421,x15422)+E(f626(x15423,x15424,x15425,x15426,x15427,x15421),f626(x15423,x15424,x15425,x15426,x15427,x15422)) % 178.07/177.95 [1543]~E(x15431,x15432)+E(f367(x15431,x15433,x15434),f367(x15432,x15433,x15434)) % 178.07/177.95 [1544]~E(x15441,x15442)+E(f367(x15443,x15441,x15444),f367(x15443,x15442,x15444)) % 178.07/177.95 [1545]~E(x15451,x15452)+E(f367(x15453,x15454,x15451),f367(x15453,x15454,x15452)) % 178.07/177.95 [1546]~E(x15461,x15462)+E(f245(x15461,x15463),f245(x15462,x15463)) % 178.07/177.95 [1547]~E(x15471,x15472)+E(f245(x15473,x15471),f245(x15473,x15472)) % 178.07/177.95 [1548]~E(x15481,x15482)+E(f769(x15481,x15483,x15484,x15485,x15486),f769(x15482,x15483,x15484,x15485,x15486)) % 178.07/177.95 [1549]~E(x15491,x15492)+E(f769(x15493,x15491,x15494,x15495,x15496),f769(x15493,x15492,x15494,x15495,x15496)) % 178.07/177.95 [1550]~E(x15501,x15502)+E(f769(x15503,x15504,x15501,x15505,x15506),f769(x15503,x15504,x15502,x15505,x15506)) % 178.07/177.95 [1551]~E(x15511,x15512)+E(f769(x15513,x15514,x15515,x15511,x15516),f769(x15513,x15514,x15515,x15512,x15516)) % 178.07/177.95 [1552]~E(x15521,x15522)+E(f769(x15523,x15524,x15525,x15526,x15521),f769(x15523,x15524,x15525,x15526,x15522)) % 178.07/177.95 [1553]~E(x15531,x15532)+E(f732(x15531,x15533,x15534,x15535,x15536),f732(x15532,x15533,x15534,x15535,x15536)) % 178.07/177.95 [1554]~E(x15541,x15542)+E(f732(x15543,x15541,x15544,x15545,x15546),f732(x15543,x15542,x15544,x15545,x15546)) % 178.07/177.95 [1555]~E(x15551,x15552)+E(f732(x15553,x15554,x15551,x15555,x15556),f732(x15553,x15554,x15552,x15555,x15556)) % 178.07/177.95 [1556]~E(x15561,x15562)+E(f732(x15563,x15564,x15565,x15561,x15566),f732(x15563,x15564,x15565,x15562,x15566)) % 178.07/177.95 [1557]~E(x15571,x15572)+E(f732(x15573,x15574,x15575,x15576,x15571),f732(x15573,x15574,x15575,x15576,x15572)) % 178.07/177.95 [1558]~E(x15581,x15582)+E(f678(x15581,x15583),f678(x15582,x15583)) % 178.07/177.95 [1559]~E(x15591,x15592)+E(f678(x15593,x15591),f678(x15593,x15592)) % 178.07/177.95 [1560]~E(x15601,x15602)+E(f576(x15601,x15603,x15604),f576(x15602,x15603,x15604)) % 178.07/177.95 [1561]~E(x15611,x15612)+E(f576(x15613,x15611,x15614),f576(x15613,x15612,x15614)) % 178.07/177.95 [1562]~E(x15621,x15622)+E(f576(x15623,x15624,x15621),f576(x15623,x15624,x15622)) % 178.07/177.95 [1563]~E(x15631,x15632)+E(f638(x15631,x15633,x15634,x15635,x15636),f638(x15632,x15633,x15634,x15635,x15636)) % 178.07/177.95 [1564]~E(x15641,x15642)+E(f638(x15643,x15641,x15644,x15645,x15646),f638(x15643,x15642,x15644,x15645,x15646)) % 178.07/177.95 [1565]~E(x15651,x15652)+E(f638(x15653,x15654,x15651,x15655,x15656),f638(x15653,x15654,x15652,x15655,x15656)) % 178.07/177.95 [1566]~E(x15661,x15662)+E(f638(x15663,x15664,x15665,x15661,x15666),f638(x15663,x15664,x15665,x15662,x15666)) % 178.07/177.95 [1567]~E(x15671,x15672)+E(f638(x15673,x15674,x15675,x15676,x15671),f638(x15673,x15674,x15675,x15676,x15672)) % 178.07/177.95 [1568]~E(x15681,x15682)+E(f347(x15681,x15683,x15684,x15685),f347(x15682,x15683,x15684,x15685)) % 178.07/177.95 [1569]~E(x15691,x15692)+E(f347(x15693,x15691,x15694,x15695),f347(x15693,x15692,x15694,x15695)) % 178.07/177.95 [1570]~E(x15701,x15702)+E(f347(x15703,x15704,x15701,x15705),f347(x15703,x15704,x15702,x15705)) % 178.07/177.95 [1571]~E(x15711,x15712)+E(f347(x15713,x15714,x15715,x15711),f347(x15713,x15714,x15715,x15712)) % 178.07/177.95 [1572]~E(x15721,x15722)+E(f818(x15721,x15723,x15724),f818(x15722,x15723,x15724)) % 178.07/177.95 [1573]~E(x15731,x15732)+E(f818(x15733,x15731,x15734),f818(x15733,x15732,x15734)) % 178.07/177.95 [1574]~E(x15741,x15742)+E(f818(x15743,x15744,x15741),f818(x15743,x15744,x15742)) % 178.07/177.95 [1575]~E(x15751,x15752)+E(f865(x15751,x15753,x15754),f865(x15752,x15753,x15754)) % 178.07/177.95 [1576]~E(x15761,x15762)+E(f865(x15763,x15761,x15764),f865(x15763,x15762,x15764)) % 178.07/177.95 [1577]~E(x15771,x15772)+E(f865(x15773,x15774,x15771),f865(x15773,x15774,x15772)) % 178.07/177.95 [1578]~E(x15781,x15782)+E(f864(x15781,x15783,x15784),f864(x15782,x15783,x15784)) % 178.07/177.95 [1579]~E(x15791,x15792)+E(f864(x15793,x15791,x15794),f864(x15793,x15792,x15794)) % 178.07/177.95 [1580]~E(x15801,x15802)+E(f864(x15803,x15804,x15801),f864(x15803,x15804,x15802)) % 178.07/177.95 [1581]~E(x15811,x15812)+E(f17(x15811,x15813,x15814,x15815),f17(x15812,x15813,x15814,x15815)) % 178.07/177.95 [1582]~E(x15821,x15822)+E(f17(x15823,x15821,x15824,x15825),f17(x15823,x15822,x15824,x15825)) % 178.07/177.95 [1583]~E(x15831,x15832)+E(f17(x15833,x15834,x15831,x15835),f17(x15833,x15834,x15832,x15835)) % 178.07/177.95 [1584]~E(x15841,x15842)+E(f17(x15843,x15844,x15845,x15841),f17(x15843,x15844,x15845,x15842)) % 178.07/177.95 [1585]~E(x15851,x15852)+E(f835(x15851,x15853,x15854,x15855),f835(x15852,x15853,x15854,x15855)) % 178.07/177.95 [1586]~E(x15861,x15862)+E(f835(x15863,x15861,x15864,x15865),f835(x15863,x15862,x15864,x15865)) % 178.07/177.95 [1587]~E(x15871,x15872)+E(f835(x15873,x15874,x15871,x15875),f835(x15873,x15874,x15872,x15875)) % 178.07/177.95 [1588]~E(x15881,x15882)+E(f835(x15883,x15884,x15885,x15881),f835(x15883,x15884,x15885,x15882)) % 178.07/177.95 [1589]~E(x15891,x15892)+E(f532(x15891,x15893,x15894,x15895,x15896,x15897),f532(x15892,x15893,x15894,x15895,x15896,x15897)) % 178.07/177.95 [1590]~E(x15901,x15902)+E(f532(x15903,x15901,x15904,x15905,x15906,x15907),f532(x15903,x15902,x15904,x15905,x15906,x15907)) % 178.07/177.95 [1591]~E(x15911,x15912)+E(f532(x15913,x15914,x15911,x15915,x15916,x15917),f532(x15913,x15914,x15912,x15915,x15916,x15917)) % 178.07/177.95 [1592]~E(x15921,x15922)+E(f532(x15923,x15924,x15925,x15921,x15926,x15927),f532(x15923,x15924,x15925,x15922,x15926,x15927)) % 178.07/177.95 [1593]~E(x15931,x15932)+E(f532(x15933,x15934,x15935,x15936,x15931,x15937),f532(x15933,x15934,x15935,x15936,x15932,x15937)) % 178.07/177.95 [1594]~E(x15941,x15942)+E(f532(x15943,x15944,x15945,x15946,x15947,x15941),f532(x15943,x15944,x15945,x15946,x15947,x15942)) % 178.07/177.95 [1595]~E(x15951,x15952)+E(f819(x15951,x15953,x15954,x15955,x15956),f819(x15952,x15953,x15954,x15955,x15956)) % 178.07/177.95 [1596]~E(x15961,x15962)+E(f819(x15963,x15961,x15964,x15965,x15966),f819(x15963,x15962,x15964,x15965,x15966)) % 178.07/177.95 [1597]~E(x15971,x15972)+E(f819(x15973,x15974,x15971,x15975,x15976),f819(x15973,x15974,x15972,x15975,x15976)) % 178.07/177.95 [1598]~E(x15981,x15982)+E(f819(x15983,x15984,x15985,x15981,x15986),f819(x15983,x15984,x15985,x15982,x15986)) % 178.07/177.95 [1599]~E(x15991,x15992)+E(f819(x15993,x15994,x15995,x15996,x15991),f819(x15993,x15994,x15995,x15996,x15992)) % 178.07/177.95 [1600]~E(x16001,x16002)+E(f361(x16001,x16003,x16004),f361(x16002,x16003,x16004)) % 178.07/177.95 [1601]~E(x16011,x16012)+E(f361(x16013,x16011,x16014),f361(x16013,x16012,x16014)) % 178.07/177.95 [1602]~E(x16021,x16022)+E(f361(x16023,x16024,x16021),f361(x16023,x16024,x16022)) % 178.07/177.95 [1603]~E(x16031,x16032)+E(f682(x16031,x16033,x16034,x16035),f682(x16032,x16033,x16034,x16035)) % 178.07/177.95 [1604]~E(x16041,x16042)+E(f682(x16043,x16041,x16044,x16045),f682(x16043,x16042,x16044,x16045)) % 178.07/177.95 [1605]~E(x16051,x16052)+E(f682(x16053,x16054,x16051,x16055),f682(x16053,x16054,x16052,x16055)) % 178.07/177.95 [1606]~E(x16061,x16062)+E(f682(x16063,x16064,x16065,x16061),f682(x16063,x16064,x16065,x16062)) % 178.07/177.95 [1607]~E(x16071,x16072)+E(f595(x16071,x16073,x16074,x16075),f595(x16072,x16073,x16074,x16075)) % 178.07/177.95 [1608]~E(x16081,x16082)+E(f595(x16083,x16081,x16084,x16085),f595(x16083,x16082,x16084,x16085)) % 178.07/177.95 [1609]~E(x16091,x16092)+E(f595(x16093,x16094,x16091,x16095),f595(x16093,x16094,x16092,x16095)) % 178.07/177.95 [1610]~E(x16101,x16102)+E(f595(x16103,x16104,x16105,x16101),f595(x16103,x16104,x16105,x16102)) % 178.07/177.95 [1611]~E(x16111,x16112)+E(f811(x16111,x16113),f811(x16112,x16113)) % 178.07/177.95 [1612]~E(x16121,x16122)+E(f811(x16123,x16121),f811(x16123,x16122)) % 178.07/177.95 [1613]~E(x16131,x16132)+E(f602(x16131,x16133,x16134,x16135),f602(x16132,x16133,x16134,x16135)) % 178.07/177.95 [1614]~E(x16141,x16142)+E(f602(x16143,x16141,x16144,x16145),f602(x16143,x16142,x16144,x16145)) % 178.07/177.95 [1615]~E(x16151,x16152)+E(f602(x16153,x16154,x16151,x16155),f602(x16153,x16154,x16152,x16155)) % 178.07/177.95 [1616]~E(x16161,x16162)+E(f602(x16163,x16164,x16165,x16161),f602(x16163,x16164,x16165,x16162)) % 178.07/177.95 [1617]~E(x16171,x16172)+E(f340(x16171,x16173),f340(x16172,x16173)) % 178.07/177.95 [1618]~E(x16181,x16182)+E(f340(x16183,x16181),f340(x16183,x16182)) % 178.07/177.95 [1619]~E(x16191,x16192)+E(f790(x16191,x16193,x16194),f790(x16192,x16193,x16194)) % 178.07/177.95 [1620]~E(x16201,x16202)+E(f790(x16203,x16201,x16204),f790(x16203,x16202,x16204)) % 178.07/177.95 [1621]~E(x16211,x16212)+E(f790(x16213,x16214,x16211),f790(x16213,x16214,x16212)) % 178.07/177.95 [1622]~E(x16221,x16222)+E(f831(x16221,x16223,x16224,x16225,x16226),f831(x16222,x16223,x16224,x16225,x16226)) % 178.07/177.95 [1623]~E(x16231,x16232)+E(f831(x16233,x16231,x16234,x16235,x16236),f831(x16233,x16232,x16234,x16235,x16236)) % 178.07/177.95 [1624]~E(x16241,x16242)+E(f831(x16243,x16244,x16241,x16245,x16246),f831(x16243,x16244,x16242,x16245,x16246)) % 178.07/177.95 [1625]~E(x16251,x16252)+E(f831(x16253,x16254,x16255,x16251,x16256),f831(x16253,x16254,x16255,x16252,x16256)) % 178.07/177.95 [1626]~E(x16261,x16262)+E(f831(x16263,x16264,x16265,x16266,x16261),f831(x16263,x16264,x16265,x16266,x16262)) % 178.07/177.95 [1627]~E(x16271,x16272)+E(f599(x16271,x16273,x16274,x16275),f599(x16272,x16273,x16274,x16275)) % 178.07/177.95 [1628]~E(x16281,x16282)+E(f599(x16283,x16281,x16284,x16285),f599(x16283,x16282,x16284,x16285)) % 178.07/177.95 [1629]~E(x16291,x16292)+E(f599(x16293,x16294,x16291,x16295),f599(x16293,x16294,x16292,x16295)) % 178.07/177.95 [1630]~E(x16301,x16302)+E(f599(x16303,x16304,x16305,x16301),f599(x16303,x16304,x16305,x16302)) % 178.07/177.95 [1631]~E(x16311,x16312)+E(f357(x16311),f357(x16312)) % 178.07/177.95 [1632]~E(x16321,x16322)+E(f401(x16321,x16323),f401(x16322,x16323)) % 178.07/177.95 [1633]~E(x16331,x16332)+E(f401(x16333,x16331),f401(x16333,x16332)) % 178.07/177.95 [1634]~E(x16341,x16342)+E(f405(x16341,x16343,x16344),f405(x16342,x16343,x16344)) % 178.07/177.95 [1635]~E(x16351,x16352)+E(f405(x16353,x16351,x16354),f405(x16353,x16352,x16354)) % 178.07/177.95 [1636]~E(x16361,x16362)+E(f405(x16363,x16364,x16361),f405(x16363,x16364,x16362)) % 178.07/177.95 [1637]~E(x16371,x16372)+E(f470(x16371,x16373,x16374),f470(x16372,x16373,x16374)) % 178.07/177.95 [1638]~E(x16381,x16382)+E(f470(x16383,x16381,x16384),f470(x16383,x16382,x16384)) % 178.07/177.95 [1639]~E(x16391,x16392)+E(f470(x16393,x16394,x16391),f470(x16393,x16394,x16392)) % 178.07/177.95 [1640]~E(x16401,x16402)+E(f563(x16401,x16403,x16404),f563(x16402,x16403,x16404)) % 178.07/177.95 [1641]~E(x16411,x16412)+E(f563(x16413,x16411,x16414),f563(x16413,x16412,x16414)) % 178.07/177.95 [1642]~E(x16421,x16422)+E(f563(x16423,x16424,x16421),f563(x16423,x16424,x16422)) % 178.07/177.95 [1643]~E(x16431,x16432)+E(f701(x16431,x16433,x16434,x16435),f701(x16432,x16433,x16434,x16435)) % 178.07/177.95 [1644]~E(x16441,x16442)+E(f701(x16443,x16441,x16444,x16445),f701(x16443,x16442,x16444,x16445)) % 178.07/177.95 [1645]~E(x16451,x16452)+E(f701(x16453,x16454,x16451,x16455),f701(x16453,x16454,x16452,x16455)) % 178.07/177.95 [1646]~E(x16461,x16462)+E(f701(x16463,x16464,x16465,x16461),f701(x16463,x16464,x16465,x16462)) % 178.07/177.95 [1647]~E(x16471,x16472)+E(f603(x16471,x16473,x16474,x16475),f603(x16472,x16473,x16474,x16475)) % 178.07/177.95 [1648]~E(x16481,x16482)+E(f603(x16483,x16481,x16484,x16485),f603(x16483,x16482,x16484,x16485)) % 178.07/177.95 [1649]~E(x16491,x16492)+E(f603(x16493,x16494,x16491,x16495),f603(x16493,x16494,x16492,x16495)) % 178.07/177.95 [1650]~E(x16501,x16502)+E(f603(x16503,x16504,x16505,x16501),f603(x16503,x16504,x16505,x16502)) % 178.07/177.95 [1651]~E(x16511,x16512)+E(f466(x16511,x16513,x16514,x16515,x16516),f466(x16512,x16513,x16514,x16515,x16516)) % 178.07/177.95 [1652]~E(x16521,x16522)+E(f466(x16523,x16521,x16524,x16525,x16526),f466(x16523,x16522,x16524,x16525,x16526)) % 178.07/177.95 [1653]~E(x16531,x16532)+E(f466(x16533,x16534,x16531,x16535,x16536),f466(x16533,x16534,x16532,x16535,x16536)) % 178.07/177.95 [1654]~E(x16541,x16542)+E(f466(x16543,x16544,x16545,x16541,x16546),f466(x16543,x16544,x16545,x16542,x16546)) % 178.07/177.95 [1655]~E(x16551,x16552)+E(f466(x16553,x16554,x16555,x16556,x16551),f466(x16553,x16554,x16555,x16556,x16552)) % 178.07/177.95 [1656]~E(x16561,x16562)+E(f125(x16561,x16563,x16564,x16565),f125(x16562,x16563,x16564,x16565)) % 178.07/177.95 [1657]~E(x16571,x16572)+E(f125(x16573,x16571,x16574,x16575),f125(x16573,x16572,x16574,x16575)) % 178.07/177.95 [1658]~E(x16581,x16582)+E(f125(x16583,x16584,x16581,x16585),f125(x16583,x16584,x16582,x16585)) % 178.07/177.95 [1659]~E(x16591,x16592)+E(f125(x16593,x16594,x16595,x16591),f125(x16593,x16594,x16595,x16592)) % 178.07/177.95 [1660]~E(x16601,x16602)+E(f741(x16601,x16603,x16604,x16605),f741(x16602,x16603,x16604,x16605)) % 178.07/177.95 [1661]~E(x16611,x16612)+E(f741(x16613,x16611,x16614,x16615),f741(x16613,x16612,x16614,x16615)) % 178.07/177.95 [1662]~E(x16621,x16622)+E(f741(x16623,x16624,x16621,x16625),f741(x16623,x16624,x16622,x16625)) % 178.07/177.95 [1663]~E(x16631,x16632)+E(f741(x16633,x16634,x16635,x16631),f741(x16633,x16634,x16635,x16632)) % 178.07/177.95 [1664]~E(x16641,x16642)+E(f512(x16641,x16643),f512(x16642,x16643)) % 178.07/177.95 [1665]~E(x16651,x16652)+E(f512(x16653,x16651),f512(x16653,x16652)) % 178.07/177.95 [1666]~E(x16661,x16662)+E(f748(x16661,x16663),f748(x16662,x16663)) % 178.07/177.95 [1667]~E(x16671,x16672)+E(f748(x16673,x16671),f748(x16673,x16672)) % 178.07/177.95 [1668]~E(x16681,x16682)+E(f828(x16681,x16683,x16684,x16685),f828(x16682,x16683,x16684,x16685)) % 178.07/177.95 [1669]~E(x16691,x16692)+E(f828(x16693,x16691,x16694,x16695),f828(x16693,x16692,x16694,x16695)) % 178.07/177.95 [1670]~E(x16701,x16702)+E(f828(x16703,x16704,x16701,x16705),f828(x16703,x16704,x16702,x16705)) % 178.07/177.95 [1671]~E(x16711,x16712)+E(f828(x16713,x16714,x16715,x16711),f828(x16713,x16714,x16715,x16712)) % 178.07/177.95 [1672]~E(x16721,x16722)+E(f210(x16721),f210(x16722)) % 178.07/177.95 [1673]~E(x16731,x16732)+E(f607(x16731,x16733,x16734,x16735),f607(x16732,x16733,x16734,x16735)) % 178.07/177.95 [1674]~E(x16741,x16742)+E(f607(x16743,x16741,x16744,x16745),f607(x16743,x16742,x16744,x16745)) % 178.07/177.95 [1675]~E(x16751,x16752)+E(f607(x16753,x16754,x16751,x16755),f607(x16753,x16754,x16752,x16755)) % 178.07/177.95 [1676]~E(x16761,x16762)+E(f607(x16763,x16764,x16765,x16761),f607(x16763,x16764,x16765,x16762)) % 178.07/177.95 [1677]~E(x16771,x16772)+E(f762(x16771,x16773,x16774,x16775,x16776),f762(x16772,x16773,x16774,x16775,x16776)) % 178.07/177.95 [1678]~E(x16781,x16782)+E(f762(x16783,x16781,x16784,x16785,x16786),f762(x16783,x16782,x16784,x16785,x16786)) % 178.07/177.95 [1679]~E(x16791,x16792)+E(f762(x16793,x16794,x16791,x16795,x16796),f762(x16793,x16794,x16792,x16795,x16796)) % 178.07/177.95 [1680]~E(x16801,x16802)+E(f762(x16803,x16804,x16805,x16801,x16806),f762(x16803,x16804,x16805,x16802,x16806)) % 178.07/177.95 [1681]~E(x16811,x16812)+E(f762(x16813,x16814,x16815,x16816,x16811),f762(x16813,x16814,x16815,x16816,x16812)) % 178.07/177.95 [1682]~E(x16821,x16822)+E(f759(x16821,x16823,x16824,x16825,x16826),f759(x16822,x16823,x16824,x16825,x16826)) % 178.07/177.95 [1683]~E(x16831,x16832)+E(f759(x16833,x16831,x16834,x16835,x16836),f759(x16833,x16832,x16834,x16835,x16836)) % 178.07/177.95 [1684]~E(x16841,x16842)+E(f759(x16843,x16844,x16841,x16845,x16846),f759(x16843,x16844,x16842,x16845,x16846)) % 178.07/177.95 [1685]~E(x16851,x16852)+E(f759(x16853,x16854,x16855,x16851,x16856),f759(x16853,x16854,x16855,x16852,x16856)) % 178.07/177.95 [1686]~E(x16861,x16862)+E(f759(x16863,x16864,x16865,x16866,x16861),f759(x16863,x16864,x16865,x16866,x16862)) % 178.07/177.95 [1687]~E(x16871,x16872)+E(f551(x16871,x16873,x16874),f551(x16872,x16873,x16874)) % 178.07/177.95 [1688]~E(x16881,x16882)+E(f551(x16883,x16881,x16884),f551(x16883,x16882,x16884)) % 178.07/177.95 [1689]~E(x16891,x16892)+E(f551(x16893,x16894,x16891),f551(x16893,x16894,x16892)) % 178.07/177.95 [1690]~E(x16901,x16902)+E(f484(x16901,x16903,x16904),f484(x16902,x16903,x16904)) % 178.07/177.95 [1691]~E(x16911,x16912)+E(f484(x16913,x16911,x16914),f484(x16913,x16912,x16914)) % 178.07/177.95 [1692]~E(x16921,x16922)+E(f484(x16923,x16924,x16921),f484(x16923,x16924,x16922)) % 178.07/177.95 [1693]~E(x16931,x16932)+E(f597(x16931,x16933,x16934),f597(x16932,x16933,x16934)) % 178.07/177.95 [1694]~E(x16941,x16942)+E(f597(x16943,x16941,x16944),f597(x16943,x16942,x16944)) % 178.07/177.95 [1695]~E(x16951,x16952)+E(f597(x16953,x16954,x16951),f597(x16953,x16954,x16952)) % 178.07/177.95 [1696]~E(x16961,x16962)+E(f692(x16961,x16963,x16964,x16965,x16966),f692(x16962,x16963,x16964,x16965,x16966)) % 178.07/177.95 [1697]~E(x16971,x16972)+E(f692(x16973,x16971,x16974,x16975,x16976),f692(x16973,x16972,x16974,x16975,x16976)) % 178.07/177.95 [1698]~E(x16981,x16982)+E(f692(x16983,x16984,x16981,x16985,x16986),f692(x16983,x16984,x16982,x16985,x16986)) % 178.07/177.95 [1699]~E(x16991,x16992)+E(f692(x16993,x16994,x16995,x16991,x16996),f692(x16993,x16994,x16995,x16992,x16996)) % 178.07/177.95 [1700]~E(x17001,x17002)+E(f692(x17003,x17004,x17005,x17006,x17001),f692(x17003,x17004,x17005,x17006,x17002)) % 178.07/177.95 [1701]~E(x17011,x17012)+E(f627(x17011,x17013,x17014,x17015,x17016,x17017),f627(x17012,x17013,x17014,x17015,x17016,x17017)) % 178.07/177.95 [1702]~E(x17021,x17022)+E(f627(x17023,x17021,x17024,x17025,x17026,x17027),f627(x17023,x17022,x17024,x17025,x17026,x17027)) % 178.07/177.95 [1703]~E(x17031,x17032)+E(f627(x17033,x17034,x17031,x17035,x17036,x17037),f627(x17033,x17034,x17032,x17035,x17036,x17037)) % 178.07/177.95 [1704]~E(x17041,x17042)+E(f627(x17043,x17044,x17045,x17041,x17046,x17047),f627(x17043,x17044,x17045,x17042,x17046,x17047)) % 178.07/177.95 [1705]~E(x17051,x17052)+E(f627(x17053,x17054,x17055,x17056,x17051,x17057),f627(x17053,x17054,x17055,x17056,x17052,x17057)) % 178.07/177.95 [1706]~E(x17061,x17062)+E(f627(x17063,x17064,x17065,x17066,x17067,x17061),f627(x17063,x17064,x17065,x17066,x17067,x17062)) % 178.07/177.95 [1707]~E(x17071,x17072)+E(f295(x17071,x17073,x17074),f295(x17072,x17073,x17074)) % 178.07/177.95 [1708]~E(x17081,x17082)+E(f295(x17083,x17081,x17084),f295(x17083,x17082,x17084)) % 178.07/177.95 [1709]~E(x17091,x17092)+E(f295(x17093,x17094,x17091),f295(x17093,x17094,x17092)) % 178.07/177.95 [1710]~E(x17101,x17102)+E(f281(x17101,x17103,x17104,x17105),f281(x17102,x17103,x17104,x17105)) % 178.07/177.95 [1711]~E(x17111,x17112)+E(f281(x17113,x17111,x17114,x17115),f281(x17113,x17112,x17114,x17115)) % 178.07/177.95 [1712]~E(x17121,x17122)+E(f281(x17123,x17124,x17121,x17125),f281(x17123,x17124,x17122,x17125)) % 178.07/177.95 [1713]~E(x17131,x17132)+E(f281(x17133,x17134,x17135,x17131),f281(x17133,x17134,x17135,x17132)) % 178.07/177.95 [1714]~E(x17141,x17142)+E(f522(x17141,x17143,x17144),f522(x17142,x17143,x17144)) % 178.07/177.95 [1715]~E(x17151,x17152)+E(f522(x17153,x17151,x17154),f522(x17153,x17152,x17154)) % 178.07/177.95 [1716]~E(x17161,x17162)+E(f522(x17163,x17164,x17161),f522(x17163,x17164,x17162)) % 178.07/177.95 [1717]~E(x17171,x17172)+E(f481(x17171),f481(x17172)) % 178.07/177.95 [1718]~E(x17181,x17182)+E(f809(x17181,x17183,x17184,x17185),f809(x17182,x17183,x17184,x17185)) % 178.07/177.95 [1719]~E(x17191,x17192)+E(f809(x17193,x17191,x17194,x17195),f809(x17193,x17192,x17194,x17195)) % 178.07/177.95 [1720]~E(x17201,x17202)+E(f809(x17203,x17204,x17201,x17205),f809(x17203,x17204,x17202,x17205)) % 178.07/177.95 [1721]~E(x17211,x17212)+E(f809(x17213,x17214,x17215,x17211),f809(x17213,x17214,x17215,x17212)) % 178.07/177.95 [1722]~E(x17221,x17222)+E(f407(x17221,x17223,x17224,x17225,x17226),f407(x17222,x17223,x17224,x17225,x17226)) % 178.07/177.95 [1723]~E(x17231,x17232)+E(f407(x17233,x17231,x17234,x17235,x17236),f407(x17233,x17232,x17234,x17235,x17236)) % 178.07/177.95 [1724]~E(x17241,x17242)+E(f407(x17243,x17244,x17241,x17245,x17246),f407(x17243,x17244,x17242,x17245,x17246)) % 178.07/177.95 [1725]~E(x17251,x17252)+E(f407(x17253,x17254,x17255,x17251,x17256),f407(x17253,x17254,x17255,x17252,x17256)) % 178.07/177.95 [1726]~E(x17261,x17262)+E(f407(x17263,x17264,x17265,x17266,x17261),f407(x17263,x17264,x17265,x17266,x17262)) % 178.07/177.95 [1727]~E(x17271,x17272)+E(f259(x17271,x17273,x17274),f259(x17272,x17273,x17274)) % 178.07/177.95 [1728]~E(x17281,x17282)+E(f259(x17283,x17281,x17284),f259(x17283,x17282,x17284)) % 178.07/177.95 [1729]~E(x17291,x17292)+E(f259(x17293,x17294,x17291),f259(x17293,x17294,x17292)) % 178.07/177.95 [1730]~E(x17301,x17302)+E(f133(x17301,x17303,x17304,x17305),f133(x17302,x17303,x17304,x17305)) % 178.07/177.95 [1731]~E(x17311,x17312)+E(f133(x17313,x17311,x17314,x17315),f133(x17313,x17312,x17314,x17315)) % 178.07/177.95 [1732]~E(x17321,x17322)+E(f133(x17323,x17324,x17321,x17325),f133(x17323,x17324,x17322,x17325)) % 178.07/177.95 [1733]~E(x17331,x17332)+E(f133(x17333,x17334,x17335,x17331),f133(x17333,x17334,x17335,x17332)) % 178.07/177.95 [1734]~E(x17341,x17342)+E(f359(x17341,x17343,x17344,x17345),f359(x17342,x17343,x17344,x17345)) % 178.07/177.95 [1735]~E(x17351,x17352)+E(f359(x17353,x17351,x17354,x17355),f359(x17353,x17352,x17354,x17355)) % 178.07/177.95 [1736]~E(x17361,x17362)+E(f359(x17363,x17364,x17361,x17365),f359(x17363,x17364,x17362,x17365)) % 178.07/177.95 [1737]~E(x17371,x17372)+E(f359(x17373,x17374,x17375,x17371),f359(x17373,x17374,x17375,x17372)) % 178.07/177.95 [1738]~E(x17381,x17382)+E(f500(x17381,x17383,x17384,x17385),f500(x17382,x17383,x17384,x17385)) % 178.07/177.95 [1739]~E(x17391,x17392)+E(f500(x17393,x17391,x17394,x17395),f500(x17393,x17392,x17394,x17395)) % 178.07/177.95 [1740]~E(x17401,x17402)+E(f500(x17403,x17404,x17401,x17405),f500(x17403,x17404,x17402,x17405)) % 178.07/177.95 [1741]~E(x17411,x17412)+E(f500(x17413,x17414,x17415,x17411),f500(x17413,x17414,x17415,x17412)) % 178.07/177.95 [1742]~E(x17421,x17422)+E(f555(x17421,x17423,x17424,x17425),f555(x17422,x17423,x17424,x17425)) % 178.07/177.95 [1743]~E(x17431,x17432)+E(f555(x17433,x17431,x17434,x17435),f555(x17433,x17432,x17434,x17435)) % 178.07/177.95 [1744]~E(x17441,x17442)+E(f555(x17443,x17444,x17441,x17445),f555(x17443,x17444,x17442,x17445)) % 178.07/177.95 [1745]~E(x17451,x17452)+E(f555(x17453,x17454,x17455,x17451),f555(x17453,x17454,x17455,x17452)) % 178.07/177.95 [1746]~E(x17461,x17462)+E(f566(x17461),f566(x17462)) % 178.07/177.95 [1747]~E(x17471,x17472)+E(f376(x17471),f376(x17472)) % 178.07/177.95 [1748]~E(x17481,x17482)+E(f824(x17481,x17483,x17484,x17485,x17486),f824(x17482,x17483,x17484,x17485,x17486)) % 178.07/177.95 [1749]~E(x17491,x17492)+E(f824(x17493,x17491,x17494,x17495,x17496),f824(x17493,x17492,x17494,x17495,x17496)) % 178.07/177.95 [1750]~E(x17501,x17502)+E(f824(x17503,x17504,x17501,x17505,x17506),f824(x17503,x17504,x17502,x17505,x17506)) % 178.07/177.95 [1751]~E(x17511,x17512)+E(f824(x17513,x17514,x17515,x17511,x17516),f824(x17513,x17514,x17515,x17512,x17516)) % 178.07/177.95 [1752]~E(x17521,x17522)+E(f824(x17523,x17524,x17525,x17526,x17521),f824(x17523,x17524,x17525,x17526,x17522)) % 178.07/177.95 [1753]~E(x17531,x17532)+E(f568(x17531,x17533,x17534),f568(x17532,x17533,x17534)) % 178.07/177.95 [1754]~E(x17541,x17542)+E(f568(x17543,x17541,x17544),f568(x17543,x17542,x17544)) % 178.07/177.95 [1755]~E(x17551,x17552)+E(f568(x17553,x17554,x17551),f568(x17553,x17554,x17552)) % 178.07/177.95 [1756]~E(x17561,x17562)+E(f733(x17561,x17563,x17564,x17565,x17566),f733(x17562,x17563,x17564,x17565,x17566)) % 178.07/177.95 [1757]~E(x17571,x17572)+E(f733(x17573,x17571,x17574,x17575,x17576),f733(x17573,x17572,x17574,x17575,x17576)) % 178.07/177.95 [1758]~E(x17581,x17582)+E(f733(x17583,x17584,x17581,x17585,x17586),f733(x17583,x17584,x17582,x17585,x17586)) % 178.07/177.95 [1759]~E(x17591,x17592)+E(f733(x17593,x17594,x17595,x17591,x17596),f733(x17593,x17594,x17595,x17592,x17596)) % 178.07/177.95 [1760]~E(x17601,x17602)+E(f733(x17603,x17604,x17605,x17606,x17601),f733(x17603,x17604,x17605,x17606,x17602)) % 178.07/177.95 [1761]~E(x17611,x17612)+E(f68(x17611,x17613,x17614),f68(x17612,x17613,x17614)) % 178.07/177.95 [1762]~E(x17621,x17622)+E(f68(x17623,x17621,x17624),f68(x17623,x17622,x17624)) % 178.07/177.95 [1763]~E(x17631,x17632)+E(f68(x17633,x17634,x17631),f68(x17633,x17634,x17632)) % 178.07/177.95 [1764]~E(x17641,x17642)+E(f693(x17641,x17643),f693(x17642,x17643)) % 178.07/177.95 [1765]~E(x17651,x17652)+E(f693(x17653,x17651),f693(x17653,x17652)) % 178.07/177.95 [1766]~E(x17661,x17662)+E(f662(x17661,x17663),f662(x17662,x17663)) % 178.07/177.95 [1767]~E(x17671,x17672)+E(f662(x17673,x17671),f662(x17673,x17672)) % 178.07/177.95 [1768]~E(x17681,x17682)+E(f680(x17681,x17683),f680(x17682,x17683)) % 178.07/177.95 [1769]~E(x17691,x17692)+E(f680(x17693,x17691),f680(x17693,x17692)) % 178.07/177.95 [1770]~E(x17701,x17702)+E(f527(x17701,x17703,x17704,x17705),f527(x17702,x17703,x17704,x17705)) % 178.07/177.95 [1771]~E(x17711,x17712)+E(f527(x17713,x17711,x17714,x17715),f527(x17713,x17712,x17714,x17715)) % 178.07/177.95 [1772]~E(x17721,x17722)+E(f527(x17723,x17724,x17721,x17725),f527(x17723,x17724,x17722,x17725)) % 178.07/177.95 [1773]~E(x17731,x17732)+E(f527(x17733,x17734,x17735,x17731),f527(x17733,x17734,x17735,x17732)) % 178.07/177.95 [1774]~E(x17741,x17742)+E(f364(x17741,x17743,x17744),f364(x17742,x17743,x17744)) % 178.07/177.95 [1775]~E(x17751,x17752)+E(f364(x17753,x17751,x17754),f364(x17753,x17752,x17754)) % 178.07/177.95 [1776]~E(x17761,x17762)+E(f364(x17763,x17764,x17761),f364(x17763,x17764,x17762)) % 178.07/177.95 [1777]~E(x17771,x17772)+E(f292(x17771,x17773,x17774),f292(x17772,x17773,x17774)) % 178.07/177.95 [1778]~E(x17781,x17782)+E(f292(x17783,x17781,x17784),f292(x17783,x17782,x17784)) % 178.07/177.95 [1779]~E(x17791,x17792)+E(f292(x17793,x17794,x17791),f292(x17793,x17794,x17792)) % 178.07/177.95 [1780]~E(x17801,x17802)+E(f333(x17801,x17803,x17804,x17805),f333(x17802,x17803,x17804,x17805)) % 178.07/177.95 [1781]~E(x17811,x17812)+E(f333(x17813,x17811,x17814,x17815),f333(x17813,x17812,x17814,x17815)) % 178.07/177.95 [1782]~E(x17821,x17822)+E(f333(x17823,x17824,x17821,x17825),f333(x17823,x17824,x17822,x17825)) % 178.07/177.95 [1783]~E(x17831,x17832)+E(f333(x17833,x17834,x17835,x17831),f333(x17833,x17834,x17835,x17832)) % 178.07/177.95 [1784]~E(x17841,x17842)+E(f516(x17841,x17843),f516(x17842,x17843)) % 178.07/177.95 [1785]~E(x17851,x17852)+E(f516(x17853,x17851),f516(x17853,x17852)) % 178.07/177.95 [1786]~E(x17861,x17862)+E(f274(x17861),f274(x17862)) % 178.07/177.95 [1787]~E(x17871,x17872)+E(f403(x17871,x17873,x17874),f403(x17872,x17873,x17874)) % 178.07/177.95 [1788]~E(x17881,x17882)+E(f403(x17883,x17881,x17884),f403(x17883,x17882,x17884)) % 178.07/177.95 [1789]~E(x17891,x17892)+E(f403(x17893,x17894,x17891),f403(x17893,x17894,x17892)) % 178.07/177.95 [1790]~E(x17901,x17902)+E(f613(x17901,x17903,x17904,x17905,x17906),f613(x17902,x17903,x17904,x17905,x17906)) % 178.07/177.95 [1791]~E(x17911,x17912)+E(f613(x17913,x17911,x17914,x17915,x17916),f613(x17913,x17912,x17914,x17915,x17916)) % 178.07/177.95 [1792]~E(x17921,x17922)+E(f613(x17923,x17924,x17921,x17925,x17926),f613(x17923,x17924,x17922,x17925,x17926)) % 178.07/177.95 [1793]~E(x17931,x17932)+E(f613(x17933,x17934,x17935,x17931,x17936),f613(x17933,x17934,x17935,x17932,x17936)) % 178.07/177.95 [1794]~E(x17941,x17942)+E(f613(x17943,x17944,x17945,x17946,x17941),f613(x17943,x17944,x17945,x17946,x17942)) % 178.07/177.95 [1795]~E(x17951,x17952)+E(f454(x17951,x17953,x17954),f454(x17952,x17953,x17954)) % 178.07/177.95 [1796]~E(x17961,x17962)+E(f454(x17963,x17961,x17964),f454(x17963,x17962,x17964)) % 178.07/177.95 [1797]~E(x17971,x17972)+E(f454(x17973,x17974,x17971),f454(x17973,x17974,x17972)) % 178.07/177.95 [1798]~E(x17981,x17982)+E(f95(x17981,x17983,x17984),f95(x17982,x17983,x17984)) % 178.07/177.95 [1799]~E(x17991,x17992)+E(f95(x17993,x17991,x17994),f95(x17993,x17992,x17994)) % 178.07/177.95 [1800]~E(x18001,x18002)+E(f95(x18003,x18004,x18001),f95(x18003,x18004,x18002)) % 178.07/177.95 [1801]~E(x18011,x18012)+E(f549(x18011,x18013),f549(x18012,x18013)) % 178.07/177.95 [1802]~E(x18021,x18022)+E(f549(x18023,x18021),f549(x18023,x18022)) % 178.07/177.95 [1803]~E(x18031,x18032)+E(f712(x18031,x18033),f712(x18032,x18033)) % 178.07/177.95 [1804]~E(x18041,x18042)+E(f712(x18043,x18041),f712(x18043,x18042)) % 178.07/177.95 [1805]~E(x18051,x18052)+E(f216(x18051),f216(x18052)) % 178.07/177.95 [1806]~E(x18061,x18062)+E(f348(x18061,x18063,x18064,x18065),f348(x18062,x18063,x18064,x18065)) % 178.07/177.95 [1807]~E(x18071,x18072)+E(f348(x18073,x18071,x18074,x18075),f348(x18073,x18072,x18074,x18075)) % 178.07/177.95 [1808]~E(x18081,x18082)+E(f348(x18083,x18084,x18081,x18085),f348(x18083,x18084,x18082,x18085)) % 178.07/177.95 [1809]~E(x18091,x18092)+E(f348(x18093,x18094,x18095,x18091),f348(x18093,x18094,x18095,x18092)) % 178.07/177.95 [1810]~E(x18101,x18102)+E(f462(x18101,x18103,x18104),f462(x18102,x18103,x18104)) % 178.07/177.95 [1811]~E(x18111,x18112)+E(f462(x18113,x18111,x18114),f462(x18113,x18112,x18114)) % 178.07/177.95 [1812]~E(x18121,x18122)+E(f462(x18123,x18124,x18121),f462(x18123,x18124,x18122)) % 178.07/177.95 [1813]~E(x18131,x18132)+E(f530(x18131,x18133,x18134),f530(x18132,x18133,x18134)) % 178.07/177.95 [1814]~E(x18141,x18142)+E(f530(x18143,x18141,x18144),f530(x18143,x18142,x18144)) % 178.07/177.95 [1815]~E(x18151,x18152)+E(f530(x18153,x18154,x18151),f530(x18153,x18154,x18152)) % 178.07/177.95 [1816]~E(x18161,x18162)+E(f722(x18161,x18163,x18164,x18165,x18166,x18167),f722(x18162,x18163,x18164,x18165,x18166,x18167)) % 178.07/177.95 [1817]~E(x18171,x18172)+E(f722(x18173,x18171,x18174,x18175,x18176,x18177),f722(x18173,x18172,x18174,x18175,x18176,x18177)) % 178.07/177.95 [1818]~E(x18181,x18182)+E(f722(x18183,x18184,x18181,x18185,x18186,x18187),f722(x18183,x18184,x18182,x18185,x18186,x18187)) % 178.07/177.95 [1819]~E(x18191,x18192)+E(f722(x18193,x18194,x18195,x18191,x18196,x18197),f722(x18193,x18194,x18195,x18192,x18196,x18197)) % 178.07/177.95 [1820]~E(x18201,x18202)+E(f722(x18203,x18204,x18205,x18206,x18201,x18207),f722(x18203,x18204,x18205,x18206,x18202,x18207)) % 178.07/177.95 [1821]~E(x18211,x18212)+E(f722(x18213,x18214,x18215,x18216,x18217,x18211),f722(x18213,x18214,x18215,x18216,x18217,x18212)) % 178.07/177.95 [1822]~E(x18221,x18222)+E(f688(x18221,x18223,x18224,x18225,x18226),f688(x18222,x18223,x18224,x18225,x18226)) % 178.07/177.95 [1823]~E(x18231,x18232)+E(f688(x18233,x18231,x18234,x18235,x18236),f688(x18233,x18232,x18234,x18235,x18236)) % 178.07/177.95 [1824]~E(x18241,x18242)+E(f688(x18243,x18244,x18241,x18245,x18246),f688(x18243,x18244,x18242,x18245,x18246)) % 178.07/177.95 [1825]~E(x18251,x18252)+E(f688(x18253,x18254,x18255,x18251,x18256),f688(x18253,x18254,x18255,x18252,x18256)) % 178.07/177.95 [1826]~E(x18261,x18262)+E(f688(x18263,x18264,x18265,x18266,x18261),f688(x18263,x18264,x18265,x18266,x18262)) % 178.07/177.95 [1827]~E(x18271,x18272)+E(f450(x18271),f450(x18272)) % 178.07/177.95 [1828]~E(x18281,x18282)+E(f344(x18281,x18283,x18284,x18285,x18286),f344(x18282,x18283,x18284,x18285,x18286)) % 178.07/177.95 [1829]~E(x18291,x18292)+E(f344(x18293,x18291,x18294,x18295,x18296),f344(x18293,x18292,x18294,x18295,x18296)) % 178.07/177.95 [1830]~E(x18301,x18302)+E(f344(x18303,x18304,x18301,x18305,x18306),f344(x18303,x18304,x18302,x18305,x18306)) % 178.07/177.95 [1831]~E(x18311,x18312)+E(f344(x18313,x18314,x18315,x18311,x18316),f344(x18313,x18314,x18315,x18312,x18316)) % 178.07/177.95 [1832]~E(x18321,x18322)+E(f344(x18323,x18324,x18325,x18326,x18321),f344(x18323,x18324,x18325,x18326,x18322)) % 178.07/177.95 [1833]~E(x18331,x18332)+E(f804(x18331,x18333,x18334,x18335),f804(x18332,x18333,x18334,x18335)) % 178.07/177.95 [1834]~E(x18341,x18342)+E(f804(x18343,x18341,x18344,x18345),f804(x18343,x18342,x18344,x18345)) % 178.07/177.95 [1835]~E(x18351,x18352)+E(f804(x18353,x18354,x18351,x18355),f804(x18353,x18354,x18352,x18355)) % 178.07/177.95 [1836]~E(x18361,x18362)+E(f804(x18363,x18364,x18365,x18361),f804(x18363,x18364,x18365,x18362)) % 178.07/177.95 [1837]~E(x18371,x18372)+E(f350(x18371,x18373,x18374,x18375,x18376),f350(x18372,x18373,x18374,x18375,x18376)) % 178.07/177.95 [1838]~E(x18381,x18382)+E(f350(x18383,x18381,x18384,x18385,x18386),f350(x18383,x18382,x18384,x18385,x18386)) % 178.07/177.95 [1839]~E(x18391,x18392)+E(f350(x18393,x18394,x18391,x18395,x18396),f350(x18393,x18394,x18392,x18395,x18396)) % 178.07/177.95 [1840]~E(x18401,x18402)+E(f350(x18403,x18404,x18405,x18401,x18406),f350(x18403,x18404,x18405,x18402,x18406)) % 178.07/177.95 [1841]~E(x18411,x18412)+E(f350(x18413,x18414,x18415,x18416,x18411),f350(x18413,x18414,x18415,x18416,x18412)) % 178.07/177.95 [1842]~E(x18421,x18422)+E(f833(x18421,x18423,x18424,x18425,x18426),f833(x18422,x18423,x18424,x18425,x18426)) % 178.07/177.95 [1843]~E(x18431,x18432)+E(f833(x18433,x18431,x18434,x18435,x18436),f833(x18433,x18432,x18434,x18435,x18436)) % 178.07/177.95 [1844]~E(x18441,x18442)+E(f833(x18443,x18444,x18441,x18445,x18446),f833(x18443,x18444,x18442,x18445,x18446)) % 178.07/177.95 [1845]~E(x18451,x18452)+E(f833(x18453,x18454,x18455,x18451,x18456),f833(x18453,x18454,x18455,x18452,x18456)) % 178.07/177.95 [1846]~E(x18461,x18462)+E(f833(x18463,x18464,x18465,x18466,x18461),f833(x18463,x18464,x18465,x18466,x18462)) % 178.07/177.95 [1847]~E(x18471,x18472)+E(f430(x18471,x18473,x18474,x18475),f430(x18472,x18473,x18474,x18475)) % 178.07/177.95 [1848]~E(x18481,x18482)+E(f430(x18483,x18481,x18484,x18485),f430(x18483,x18482,x18484,x18485)) % 178.07/177.95 [1849]~E(x18491,x18492)+E(f430(x18493,x18494,x18491,x18495),f430(x18493,x18494,x18492,x18495)) % 178.07/177.95 [1850]~E(x18501,x18502)+E(f430(x18503,x18504,x18505,x18501),f430(x18503,x18504,x18505,x18502)) % 178.07/177.95 [1851]~E(x18511,x18512)+E(f132(x18511,x18513,x18514,x18515,x18516),f132(x18512,x18513,x18514,x18515,x18516)) % 178.07/177.95 [1852]~E(x18521,x18522)+E(f132(x18523,x18521,x18524,x18525,x18526),f132(x18523,x18522,x18524,x18525,x18526)) % 178.07/177.95 [1853]~E(x18531,x18532)+E(f132(x18533,x18534,x18531,x18535,x18536),f132(x18533,x18534,x18532,x18535,x18536)) % 178.07/177.95 [1854]~E(x18541,x18542)+E(f132(x18543,x18544,x18545,x18541,x18546),f132(x18543,x18544,x18545,x18542,x18546)) % 178.07/177.95 [1855]~E(x18551,x18552)+E(f132(x18553,x18554,x18555,x18556,x18551),f132(x18553,x18554,x18555,x18556,x18552)) % 178.07/177.95 [1856]~E(x18561,x18562)+E(f471(x18561,x18563,x18564,x18565),f471(x18562,x18563,x18564,x18565)) % 178.07/177.95 [1857]~E(x18571,x18572)+E(f471(x18573,x18571,x18574,x18575),f471(x18573,x18572,x18574,x18575)) % 178.07/177.95 [1858]~E(x18581,x18582)+E(f471(x18583,x18584,x18581,x18585),f471(x18583,x18584,x18582,x18585)) % 178.07/177.95 [1859]~E(x18591,x18592)+E(f471(x18593,x18594,x18595,x18591),f471(x18593,x18594,x18595,x18592)) % 178.07/177.95 [1860]~E(x18601,x18602)+E(f346(x18601,x18603,x18604),f346(x18602,x18603,x18604)) % 178.07/177.95 [1861]~E(x18611,x18612)+E(f346(x18613,x18611,x18614),f346(x18613,x18612,x18614)) % 178.07/177.95 [1862]~E(x18621,x18622)+E(f346(x18623,x18624,x18621),f346(x18623,x18624,x18622)) % 178.07/177.95 [1863]~E(x18631,x18632)+E(f671(x18631,x18633,x18634),f671(x18632,x18633,x18634)) % 178.07/177.95 [1864]~E(x18641,x18642)+E(f671(x18643,x18641,x18644),f671(x18643,x18642,x18644)) % 178.07/177.95 [1865]~E(x18651,x18652)+E(f671(x18653,x18654,x18651),f671(x18653,x18654,x18652)) % 178.07/177.95 [1866]~E(x18661,x18662)+E(f734(x18661,x18663,x18664,x18665,x18666),f734(x18662,x18663,x18664,x18665,x18666)) % 178.07/177.95 [1867]~E(x18671,x18672)+E(f734(x18673,x18671,x18674,x18675,x18676),f734(x18673,x18672,x18674,x18675,x18676)) % 178.07/177.95 [1868]~E(x18681,x18682)+E(f734(x18683,x18684,x18681,x18685,x18686),f734(x18683,x18684,x18682,x18685,x18686)) % 178.07/177.95 [1869]~E(x18691,x18692)+E(f734(x18693,x18694,x18695,x18691,x18696),f734(x18693,x18694,x18695,x18692,x18696)) % 178.07/177.95 [1870]~E(x18701,x18702)+E(f734(x18703,x18704,x18705,x18706,x18701),f734(x18703,x18704,x18705,x18706,x18702)) % 178.07/177.95 [1871]~E(x18711,x18712)+E(f801(x18711,x18713,x18714),f801(x18712,x18713,x18714)) % 178.07/177.95 [1872]~E(x18721,x18722)+E(f801(x18723,x18721,x18724),f801(x18723,x18722,x18724)) % 178.07/177.95 [1873]~E(x18731,x18732)+E(f801(x18733,x18734,x18731),f801(x18733,x18734,x18732)) % 178.07/177.95 [1874]~E(x18741,x18742)+E(f533(x18741,x18743,x18744,x18745),f533(x18742,x18743,x18744,x18745)) % 178.07/177.95 [1875]~E(x18751,x18752)+E(f533(x18753,x18751,x18754,x18755),f533(x18753,x18752,x18754,x18755)) % 178.07/177.95 [1876]~E(x18761,x18762)+E(f533(x18763,x18764,x18761,x18765),f533(x18763,x18764,x18762,x18765)) % 178.07/177.95 [1877]~E(x18771,x18772)+E(f533(x18773,x18774,x18775,x18771),f533(x18773,x18774,x18775,x18772)) % 178.07/177.95 [1878]~E(x18781,x18782)+E(f399(x18781,x18783),f399(x18782,x18783)) % 178.07/177.95 [1879]~E(x18791,x18792)+E(f399(x18793,x18791),f399(x18793,x18792)) % 178.07/177.95 [1880]~E(x18801,x18802)+E(f445(x18801,x18803),f445(x18802,x18803)) % 178.07/177.95 [1881]~E(x18811,x18812)+E(f445(x18813,x18811),f445(x18813,x18812)) % 178.07/177.95 [1882]~E(x18821,x18822)+E(f710(x18821,x18823,x18824,x18825,x18826),f710(x18822,x18823,x18824,x18825,x18826)) % 178.07/177.95 [1883]~E(x18831,x18832)+E(f710(x18833,x18831,x18834,x18835,x18836),f710(x18833,x18832,x18834,x18835,x18836)) % 178.07/177.95 [1884]~E(x18841,x18842)+E(f710(x18843,x18844,x18841,x18845,x18846),f710(x18843,x18844,x18842,x18845,x18846)) % 178.07/177.95 [1885]~E(x18851,x18852)+E(f710(x18853,x18854,x18855,x18851,x18856),f710(x18853,x18854,x18855,x18852,x18856)) % 178.07/177.95 [1886]~E(x18861,x18862)+E(f710(x18863,x18864,x18865,x18866,x18861),f710(x18863,x18864,x18865,x18866,x18862)) % 178.07/177.95 [1887]~E(x18871,x18872)+E(f596(x18871,x18873,x18874),f596(x18872,x18873,x18874)) % 178.07/177.95 [1888]~E(x18881,x18882)+E(f596(x18883,x18881,x18884),f596(x18883,x18882,x18884)) % 178.07/177.95 [1889]~E(x18891,x18892)+E(f596(x18893,x18894,x18891),f596(x18893,x18894,x18892)) % 178.07/177.95 [1890]~E(x18901,x18902)+E(f341(x18901),f341(x18902)) % 178.07/177.95 [1891]~E(x18911,x18912)+E(f498(x18911,x18913,x18914,x18915),f498(x18912,x18913,x18914,x18915)) % 178.07/177.95 [1892]~E(x18921,x18922)+E(f498(x18923,x18921,x18924,x18925),f498(x18923,x18922,x18924,x18925)) % 178.07/177.95 [1893]~E(x18931,x18932)+E(f498(x18933,x18934,x18931,x18935),f498(x18933,x18934,x18932,x18935)) % 178.07/177.95 [1894]~E(x18941,x18942)+E(f498(x18943,x18944,x18945,x18941),f498(x18943,x18944,x18945,x18942)) % 178.07/177.95 [1895]~E(x18951,x18952)+E(f709(x18951,x18953,x18954,x18955),f709(x18952,x18953,x18954,x18955)) % 178.07/177.95 [1896]~E(x18961,x18962)+E(f709(x18963,x18961,x18964,x18965),f709(x18963,x18962,x18964,x18965)) % 178.07/177.95 [1897]~E(x18971,x18972)+E(f709(x18973,x18974,x18971,x18975),f709(x18973,x18974,x18972,x18975)) % 178.07/177.95 [1898]~E(x18981,x18982)+E(f709(x18983,x18984,x18985,x18981),f709(x18983,x18984,x18985,x18982)) % 178.07/177.95 [1899]~E(x18991,x18992)+E(f668(x18991,x18993),f668(x18992,x18993)) % 178.07/177.95 [1900]~E(x19001,x19002)+E(f668(x19003,x19001),f668(x19003,x19002)) % 178.07/177.95 [1901]~E(x19011,x19012)+E(f335(x19011),f335(x19012)) % 178.07/177.95 [1902]~E(x19021,x19022)+E(f721(x19021,x19023,x19024,x19025,x19026,x19027),f721(x19022,x19023,x19024,x19025,x19026,x19027)) % 178.07/177.95 [1903]~E(x19031,x19032)+E(f721(x19033,x19031,x19034,x19035,x19036,x19037),f721(x19033,x19032,x19034,x19035,x19036,x19037)) % 178.07/177.95 [1904]~E(x19041,x19042)+E(f721(x19043,x19044,x19041,x19045,x19046,x19047),f721(x19043,x19044,x19042,x19045,x19046,x19047)) % 178.07/177.95 [1905]~E(x19051,x19052)+E(f721(x19053,x19054,x19055,x19051,x19056,x19057),f721(x19053,x19054,x19055,x19052,x19056,x19057)) % 178.07/177.95 [1906]~E(x19061,x19062)+E(f721(x19063,x19064,x19065,x19066,x19061,x19067),f721(x19063,x19064,x19065,x19066,x19062,x19067)) % 178.07/177.95 [1907]~E(x19071,x19072)+E(f721(x19073,x19074,x19075,x19076,x19077,x19071),f721(x19073,x19074,x19075,x19076,x19077,x19072)) % 178.07/177.95 [1908]~E(x19081,x19082)+E(f476(x19081,x19083,x19084,x19085,x19086),f476(x19082,x19083,x19084,x19085,x19086)) % 178.07/177.95 [1909]~E(x19091,x19092)+E(f476(x19093,x19091,x19094,x19095,x19096),f476(x19093,x19092,x19094,x19095,x19096)) % 178.07/177.95 [1910]~E(x19101,x19102)+E(f476(x19103,x19104,x19101,x19105,x19106),f476(x19103,x19104,x19102,x19105,x19106)) % 178.07/177.95 [1911]~E(x19111,x19112)+E(f476(x19113,x19114,x19115,x19111,x19116),f476(x19113,x19114,x19115,x19112,x19116)) % 178.07/177.95 [1912]~E(x19121,x19122)+E(f476(x19123,x19124,x19125,x19126,x19121),f476(x19123,x19124,x19125,x19126,x19122)) % 178.07/177.95 [1913]~E(x19131,x19132)+E(f670(x19131,x19133),f670(x19132,x19133)) % 178.07/177.95 [1914]~E(x19141,x19142)+E(f670(x19143,x19141),f670(x19143,x19142)) % 178.07/177.95 [1915]~E(x19151,x19152)+E(f837(x19151,x19153,x19154,x19155,x19156,x19157,x19158),f837(x19152,x19153,x19154,x19155,x19156,x19157,x19158)) % 178.07/177.95 [1916]~E(x19161,x19162)+E(f837(x19163,x19161,x19164,x19165,x19166,x19167,x19168),f837(x19163,x19162,x19164,x19165,x19166,x19167,x19168)) % 178.07/177.95 [1917]~E(x19171,x19172)+E(f837(x19173,x19174,x19171,x19175,x19176,x19177,x19178),f837(x19173,x19174,x19172,x19175,x19176,x19177,x19178)) % 178.07/177.95 [1918]~E(x19181,x19182)+E(f837(x19183,x19184,x19185,x19181,x19186,x19187,x19188),f837(x19183,x19184,x19185,x19182,x19186,x19187,x19188)) % 178.07/177.95 [1919]~E(x19191,x19192)+E(f837(x19193,x19194,x19195,x19196,x19191,x19197,x19198),f837(x19193,x19194,x19195,x19196,x19192,x19197,x19198)) % 178.07/177.95 [1920]~E(x19201,x19202)+E(f837(x19203,x19204,x19205,x19206,x19207,x19201,x19208),f837(x19203,x19204,x19205,x19206,x19207,x19202,x19208)) % 178.07/177.95 [1921]~E(x19211,x19212)+E(f837(x19213,x19214,x19215,x19216,x19217,x19218,x19211),f837(x19213,x19214,x19215,x19216,x19217,x19218,x19212)) % 178.07/177.95 [1922]~E(x19221,x19222)+E(f100(x19221,x19223,x19224,x19225),f100(x19222,x19223,x19224,x19225)) % 178.07/177.95 [1923]~E(x19231,x19232)+E(f100(x19233,x19231,x19234,x19235),f100(x19233,x19232,x19234,x19235)) % 178.07/177.95 [1924]~E(x19241,x19242)+E(f100(x19243,x19244,x19241,x19245),f100(x19243,x19244,x19242,x19245)) % 178.07/177.95 [1925]~E(x19251,x19252)+E(f100(x19253,x19254,x19255,x19251),f100(x19253,x19254,x19255,x19252)) % 178.07/177.95 [1926]~E(x19261,x19262)+E(f518(x19261,x19263,x19264,x19265),f518(x19262,x19263,x19264,x19265)) % 178.07/177.95 [1927]~E(x19271,x19272)+E(f518(x19273,x19271,x19274,x19275),f518(x19273,x19272,x19274,x19275)) % 178.07/177.95 [1928]~E(x19281,x19282)+E(f518(x19283,x19284,x19281,x19285),f518(x19283,x19284,x19282,x19285)) % 178.07/177.95 [1929]~E(x19291,x19292)+E(f518(x19293,x19294,x19295,x19291),f518(x19293,x19294,x19295,x19292)) % 178.07/177.95 [1930]~E(x19301,x19302)+E(f637(x19301,x19303,x19304,x19305),f637(x19302,x19303,x19304,x19305)) % 178.07/177.95 [1931]~E(x19311,x19312)+E(f637(x19313,x19311,x19314,x19315),f637(x19313,x19312,x19314,x19315)) % 178.07/177.95 [1932]~E(x19321,x19322)+E(f637(x19323,x19324,x19321,x19325),f637(x19323,x19324,x19322,x19325)) % 178.07/177.95 [1933]~E(x19331,x19332)+E(f637(x19333,x19334,x19335,x19331),f637(x19333,x19334,x19335,x19332)) % 178.07/177.95 [1934]~E(x19341,x19342)+E(f224(x19341,x19343),f224(x19342,x19343)) % 178.07/177.95 [1935]~E(x19351,x19352)+E(f224(x19353,x19351),f224(x19353,x19352)) % 178.07/177.95 [1936]~E(x19361,x19362)+E(f827(x19361,x19363),f827(x19362,x19363)) % 178.07/177.95 [1937]~E(x19371,x19372)+E(f827(x19373,x19371),f827(x19373,x19372)) % 178.07/177.95 [1938]~E(x19381,x19382)+E(f650(x19381,x19383,x19384),f650(x19382,x19383,x19384)) % 178.07/177.95 [1939]~E(x19391,x19392)+E(f650(x19393,x19391,x19394),f650(x19393,x19392,x19394)) % 178.07/177.95 [1940]~E(x19401,x19402)+E(f650(x19403,x19404,x19401),f650(x19403,x19404,x19402)) % 178.07/177.95 [1941]~E(x19411,x19412)+E(f495(x19411,x19413,x19414,x19415),f495(x19412,x19413,x19414,x19415)) % 178.07/177.95 [1942]~E(x19421,x19422)+E(f495(x19423,x19421,x19424,x19425),f495(x19423,x19422,x19424,x19425)) % 178.07/177.95 [1943]~E(x19431,x19432)+E(f495(x19433,x19434,x19431,x19435),f495(x19433,x19434,x19432,x19435)) % 178.07/177.95 [1944]~E(x19441,x19442)+E(f495(x19443,x19444,x19445,x19441),f495(x19443,x19444,x19445,x19442)) % 178.07/177.95 [1945]~E(x19451,x19452)+E(f785(x19451,x19453,x19454),f785(x19452,x19453,x19454)) % 178.07/177.95 [1946]~E(x19461,x19462)+E(f785(x19463,x19461,x19464),f785(x19463,x19462,x19464)) % 178.07/177.95 [1947]~E(x19471,x19472)+E(f785(x19473,x19474,x19471),f785(x19473,x19474,x19472)) % 178.07/177.95 [1948]~E(x19481,x19482)+E(f395(x19481,x19483,x19484,x19485),f395(x19482,x19483,x19484,x19485)) % 178.07/177.95 [1949]~E(x19491,x19492)+E(f395(x19493,x19491,x19494,x19495),f395(x19493,x19492,x19494,x19495)) % 178.07/177.95 [1950]~E(x19501,x19502)+E(f395(x19503,x19504,x19501,x19505),f395(x19503,x19504,x19502,x19505)) % 178.07/177.95 [1951]~E(x19511,x19512)+E(f395(x19513,x19514,x19515,x19511),f395(x19513,x19514,x19515,x19512)) % 178.07/177.95 [1952]~E(x19521,x19522)+E(f161(x19521,x19523),f161(x19522,x19523)) % 178.07/177.95 [1953]~E(x19531,x19532)+E(f161(x19533,x19531),f161(x19533,x19532)) % 178.07/177.95 [1954]~E(x19541,x19542)+E(f228(x19541,x19543),f228(x19542,x19543)) % 178.07/177.95 [1955]~E(x19551,x19552)+E(f228(x19553,x19551),f228(x19553,x19552)) % 178.07/177.95 [1956]~E(x19561,x19562)+E(f825(x19561,x19563),f825(x19562,x19563)) % 178.07/177.95 [1957]~E(x19571,x19572)+E(f825(x19573,x19571),f825(x19573,x19572)) % 178.07/177.95 [1958]~E(x19581,x19582)+E(f820(x19581,x19583),f820(x19582,x19583)) % 178.07/177.95 [1959]~E(x19591,x19592)+E(f820(x19593,x19591),f820(x19593,x19592)) % 178.07/177.95 [1960]~E(x19601,x19602)+E(f514(x19601,x19603,x19604),f514(x19602,x19603,x19604)) % 178.07/177.95 [1961]~E(x19611,x19612)+E(f514(x19613,x19611,x19614),f514(x19613,x19612,x19614)) % 178.07/177.95 [1962]~E(x19621,x19622)+E(f514(x19623,x19624,x19621),f514(x19623,x19624,x19622)) % 178.07/177.95 [1963]~E(x19631,x19632)+E(f564(x19631,x19633,x19634,x19635,x19636),f564(x19632,x19633,x19634,x19635,x19636)) % 178.07/177.95 [1964]~E(x19641,x19642)+E(f564(x19643,x19641,x19644,x19645,x19646),f564(x19643,x19642,x19644,x19645,x19646)) % 178.07/177.95 [1965]~E(x19651,x19652)+E(f564(x19653,x19654,x19651,x19655,x19656),f564(x19653,x19654,x19652,x19655,x19656)) % 178.07/177.95 [1966]~E(x19661,x19662)+E(f564(x19663,x19664,x19665,x19661,x19666),f564(x19663,x19664,x19665,x19662,x19666)) % 178.07/177.95 [1967]~E(x19671,x19672)+E(f564(x19673,x19674,x19675,x19676,x19671),f564(x19673,x19674,x19675,x19676,x19672)) % 178.07/177.95 [1968]~E(x19681,x19682)+E(f724(x19681,x19683,x19684,x19685,x19686,x19687),f724(x19682,x19683,x19684,x19685,x19686,x19687)) % 178.07/177.95 [1969]~E(x19691,x19692)+E(f724(x19693,x19691,x19694,x19695,x19696,x19697),f724(x19693,x19692,x19694,x19695,x19696,x19697)) % 178.07/177.95 [1970]~E(x19701,x19702)+E(f724(x19703,x19704,x19701,x19705,x19706,x19707),f724(x19703,x19704,x19702,x19705,x19706,x19707)) % 178.07/177.95 [1971]~E(x19711,x19712)+E(f724(x19713,x19714,x19715,x19711,x19716,x19717),f724(x19713,x19714,x19715,x19712,x19716,x19717)) % 178.07/177.95 [1972]~E(x19721,x19722)+E(f724(x19723,x19724,x19725,x19726,x19721,x19727),f724(x19723,x19724,x19725,x19726,x19722,x19727)) % 178.07/177.95 [1973]~E(x19731,x19732)+E(f724(x19733,x19734,x19735,x19736,x19737,x19731),f724(x19733,x19734,x19735,x19736,x19737,x19732)) % 178.07/177.95 [1974]~E(x19741,x19742)+E(f211(x19741,x19743),f211(x19742,x19743)) % 178.07/177.95 [1975]~E(x19751,x19752)+E(f211(x19753,x19751),f211(x19753,x19752)) % 178.07/177.95 [1976]~E(x19761,x19762)+E(f624(x19761,x19763,x19764,x19765,x19766,x19767),f624(x19762,x19763,x19764,x19765,x19766,x19767)) % 178.07/177.95 [1977]~E(x19771,x19772)+E(f624(x19773,x19771,x19774,x19775,x19776,x19777),f624(x19773,x19772,x19774,x19775,x19776,x19777)) % 178.07/177.95 [1978]~E(x19781,x19782)+E(f624(x19783,x19784,x19781,x19785,x19786,x19787),f624(x19783,x19784,x19782,x19785,x19786,x19787)) % 178.07/177.95 [1979]~E(x19791,x19792)+E(f624(x19793,x19794,x19795,x19791,x19796,x19797),f624(x19793,x19794,x19795,x19792,x19796,x19797)) % 178.07/177.95 [1980]~E(x19801,x19802)+E(f624(x19803,x19804,x19805,x19806,x19801,x19807),f624(x19803,x19804,x19805,x19806,x19802,x19807)) % 178.07/177.95 [1981]~E(x19811,x19812)+E(f624(x19813,x19814,x19815,x19816,x19817,x19811),f624(x19813,x19814,x19815,x19816,x19817,x19812)) % 178.07/177.95 [1982]~E(x19821,x19822)+E(f812(x19821,x19823,x19824,x19825),f812(x19822,x19823,x19824,x19825)) % 178.07/177.95 [1983]~E(x19831,x19832)+E(f812(x19833,x19831,x19834,x19835),f812(x19833,x19832,x19834,x19835)) % 178.07/177.95 [1984]~E(x19841,x19842)+E(f812(x19843,x19844,x19841,x19845),f812(x19843,x19844,x19842,x19845)) % 178.07/177.95 [1985]~E(x19851,x19852)+E(f812(x19853,x19854,x19855,x19851),f812(x19853,x19854,x19855,x19852)) % 178.07/177.95 [1986]~E(x19861,x19862)+E(f679(x19861,x19863),f679(x19862,x19863)) % 178.07/177.95 [1987]~E(x19871,x19872)+E(f679(x19873,x19871),f679(x19873,x19872)) % 178.07/177.95 [1988]~E(x19881,x19882)+E(f667(x19881,x19883),f667(x19882,x19883)) % 178.07/177.95 [1989]~E(x19891,x19892)+E(f667(x19893,x19891),f667(x19893,x19892)) % 178.07/177.95 [1990]~E(x19901,x19902)+E(f850(x19901,x19903,x19904,x19905,x19906,x19907,x19908),f850(x19902,x19903,x19904,x19905,x19906,x19907,x19908)) % 178.07/177.95 [1991]~E(x19911,x19912)+E(f850(x19913,x19911,x19914,x19915,x19916,x19917,x19918),f850(x19913,x19912,x19914,x19915,x19916,x19917,x19918)) % 178.07/177.95 [1992]~E(x19921,x19922)+E(f850(x19923,x19924,x19921,x19925,x19926,x19927,x19928),f850(x19923,x19924,x19922,x19925,x19926,x19927,x19928)) % 178.07/177.95 [1993]~E(x19931,x19932)+E(f850(x19933,x19934,x19935,x19931,x19936,x19937,x19938),f850(x19933,x19934,x19935,x19932,x19936,x19937,x19938)) % 178.07/177.95 [1994]~E(x19941,x19942)+E(f850(x19943,x19944,x19945,x19946,x19941,x19947,x19948),f850(x19943,x19944,x19945,x19946,x19942,x19947,x19948)) % 178.07/177.95 [1995]~E(x19951,x19952)+E(f850(x19953,x19954,x19955,x19956,x19957,x19951,x19958),f850(x19953,x19954,x19955,x19956,x19957,x19952,x19958)) % 178.07/177.95 [1996]~E(x19961,x19962)+E(f850(x19963,x19964,x19965,x19966,x19967,x19968,x19961),f850(x19963,x19964,x19965,x19966,x19967,x19968,x19962)) % 178.07/177.95 [1997]~E(x19971,x19972)+E(f783(x19971,x19973,x19974),f783(x19972,x19973,x19974)) % 178.07/177.95 [1998]~E(x19981,x19982)+E(f783(x19983,x19981,x19984),f783(x19983,x19982,x19984)) % 178.07/177.95 [1999]~E(x19991,x19992)+E(f783(x19993,x19994,x19991),f783(x19993,x19994,x19992)) % 178.07/177.95 [2000]~E(x20001,x20002)+E(f720(x20001,x20003,x20004,x20005,x20006),f720(x20002,x20003,x20004,x20005,x20006)) % 178.07/177.95 [2001]~E(x20011,x20012)+E(f720(x20013,x20011,x20014,x20015,x20016),f720(x20013,x20012,x20014,x20015,x20016)) % 178.07/177.95 [2002]~E(x20021,x20022)+E(f720(x20023,x20024,x20021,x20025,x20026),f720(x20023,x20024,x20022,x20025,x20026)) % 178.07/177.95 [2003]~E(x20031,x20032)+E(f720(x20033,x20034,x20035,x20031,x20036),f720(x20033,x20034,x20035,x20032,x20036)) % 178.07/177.95 [2004]~E(x20041,x20042)+E(f720(x20043,x20044,x20045,x20046,x20041),f720(x20043,x20044,x20045,x20046,x20042)) % 178.07/177.95 [2005]~E(x20051,x20052)+E(f447(x20051,x20053,x20054,x20055,x20056),f447(x20052,x20053,x20054,x20055,x20056)) % 178.07/177.95 [2006]~E(x20061,x20062)+E(f447(x20063,x20061,x20064,x20065,x20066),f447(x20063,x20062,x20064,x20065,x20066)) % 178.07/177.95 [2007]~E(x20071,x20072)+E(f447(x20073,x20074,x20071,x20075,x20076),f447(x20073,x20074,x20072,x20075,x20076)) % 178.07/177.95 [2008]~E(x20081,x20082)+E(f447(x20083,x20084,x20085,x20081,x20086),f447(x20083,x20084,x20085,x20082,x20086)) % 178.07/177.95 [2009]~E(x20091,x20092)+E(f447(x20093,x20094,x20095,x20096,x20091),f447(x20093,x20094,x20095,x20096,x20092)) % 178.07/177.95 [2010]~E(x20101,x20102)+E(f795(x20101,x20103,x20104,x20105),f795(x20102,x20103,x20104,x20105)) % 178.07/177.95 [2011]~E(x20111,x20112)+E(f795(x20113,x20111,x20114,x20115),f795(x20113,x20112,x20114,x20115)) % 178.07/177.95 [2012]~E(x20121,x20122)+E(f795(x20123,x20124,x20121,x20125),f795(x20123,x20124,x20122,x20125)) % 178.07/177.95 [2013]~E(x20131,x20132)+E(f795(x20133,x20134,x20135,x20131),f795(x20133,x20134,x20135,x20132)) % 178.07/177.95 [2014]~E(x20141,x20142)+E(f434(x20141,x20143,x20144,x20145),f434(x20142,x20143,x20144,x20145)) % 178.07/177.95 [2015]~E(x20151,x20152)+E(f434(x20153,x20151,x20154,x20155),f434(x20153,x20152,x20154,x20155)) % 178.07/177.95 [2016]~E(x20161,x20162)+E(f434(x20163,x20164,x20161,x20165),f434(x20163,x20164,x20162,x20165)) % 178.07/177.95 [2017]~E(x20171,x20172)+E(f434(x20173,x20174,x20175,x20171),f434(x20173,x20174,x20175,x20172)) % 178.07/177.95 [2018]~E(x20181,x20182)+E(f781(x20181,x20183,x20184),f781(x20182,x20183,x20184)) % 178.07/177.95 [2019]~E(x20191,x20192)+E(f781(x20193,x20191,x20194),f781(x20193,x20192,x20194)) % 178.07/177.95 [2020]~E(x20201,x20202)+E(f781(x20203,x20204,x20201),f781(x20203,x20204,x20202)) % 178.07/177.95 [2021]~E(x20211,x20212)+E(f740(x20211,x20213,x20214),f740(x20212,x20213,x20214)) % 178.07/177.95 [2022]~E(x20221,x20222)+E(f740(x20223,x20221,x20224),f740(x20223,x20222,x20224)) % 178.07/177.95 [2023]~E(x20231,x20232)+E(f740(x20233,x20234,x20231),f740(x20233,x20234,x20232)) % 178.07/177.95 [2024]~E(x20241,x20242)+E(f440(x20241,x20243,x20244,x20245,x20246),f440(x20242,x20243,x20244,x20245,x20246)) % 178.07/177.95 [2025]~E(x20251,x20252)+E(f440(x20253,x20251,x20254,x20255,x20256),f440(x20253,x20252,x20254,x20255,x20256)) % 178.07/177.95 [2026]~E(x20261,x20262)+E(f440(x20263,x20264,x20261,x20265,x20266),f440(x20263,x20264,x20262,x20265,x20266)) % 178.07/177.95 [2027]~E(x20271,x20272)+E(f440(x20273,x20274,x20275,x20271,x20276),f440(x20273,x20274,x20275,x20272,x20276)) % 178.07/177.95 [2028]~E(x20281,x20282)+E(f440(x20283,x20284,x20285,x20286,x20281),f440(x20283,x20284,x20285,x20286,x20282)) % 178.07/177.95 [2029]~E(x20291,x20292)+E(f719(x20291,x20293,x20294,x20295),f719(x20292,x20293,x20294,x20295)) % 178.07/177.95 [2030]~E(x20301,x20302)+E(f719(x20303,x20301,x20304,x20305),f719(x20303,x20302,x20304,x20305)) % 178.07/177.95 [2031]~E(x20311,x20312)+E(f719(x20313,x20314,x20311,x20315),f719(x20313,x20314,x20312,x20315)) % 178.07/177.95 [2032]~E(x20321,x20322)+E(f719(x20323,x20324,x20325,x20321),f719(x20323,x20324,x20325,x20322)) % 178.07/177.95 [2033]~E(x20331,x20332)+E(f803(x20331,x20333,x20334),f803(x20332,x20333,x20334)) % 178.07/177.95 [2034]~E(x20341,x20342)+E(f803(x20343,x20341,x20344),f803(x20343,x20342,x20344)) % 178.07/177.95 [2035]~E(x20351,x20352)+E(f803(x20353,x20354,x20351),f803(x20353,x20354,x20352)) % 178.07/177.95 [2036]~E(x20361,x20362)+E(f775(x20361,x20363),f775(x20362,x20363)) % 178.07/177.95 [2037]~E(x20371,x20372)+E(f775(x20373,x20371),f775(x20373,x20372)) % 178.07/177.95 [2038]~E(x20381,x20382)+E(f390(x20381,x20383),f390(x20382,x20383)) % 178.07/177.95 [2039]~E(x20391,x20392)+E(f390(x20393,x20391),f390(x20393,x20392)) % 178.07/177.95 [2040]~E(x20401,x20402)+E(f622(x20401,x20403,x20404),f622(x20402,x20403,x20404)) % 178.07/177.95 [2041]~E(x20411,x20412)+E(f622(x20413,x20411,x20414),f622(x20413,x20412,x20414)) % 178.07/177.95 [2042]~E(x20421,x20422)+E(f622(x20423,x20424,x20421),f622(x20423,x20424,x20422)) % 178.07/177.95 [2043]~E(x20431,x20432)+E(f699(x20431,x20433,x20434,x20435),f699(x20432,x20433,x20434,x20435)) % 178.07/177.95 [2044]~E(x20441,x20442)+E(f699(x20443,x20441,x20444,x20445),f699(x20443,x20442,x20444,x20445)) % 178.07/177.95 [2045]~E(x20451,x20452)+E(f699(x20453,x20454,x20451,x20455),f699(x20453,x20454,x20452,x20455)) % 178.07/177.95 [2046]~E(x20461,x20462)+E(f699(x20463,x20464,x20465,x20461),f699(x20463,x20464,x20465,x20462)) % 178.07/177.95 [2047]~E(x20471,x20472)+E(f452(x20471,x20473,x20474,x20475),f452(x20472,x20473,x20474,x20475)) % 178.07/177.95 [2048]~E(x20481,x20482)+E(f452(x20483,x20481,x20484,x20485),f452(x20483,x20482,x20484,x20485)) % 178.07/177.95 [2049]~E(x20491,x20492)+E(f452(x20493,x20494,x20491,x20495),f452(x20493,x20494,x20492,x20495)) % 178.07/177.95 [2050]~E(x20501,x20502)+E(f452(x20503,x20504,x20505,x20501),f452(x20503,x20504,x20505,x20502)) % 178.07/177.95 [2051]~E(x20511,x20512)+E(f126(x20511),f126(x20512)) % 178.07/177.95 [2052]~E(x20521,x20522)+E(f826(x20521),f826(x20522)) % 178.07/177.95 [2053]~E(x20531,x20532)+E(f642(x20531,x20533,x20534),f642(x20532,x20533,x20534)) % 178.07/177.95 [2054]~E(x20541,x20542)+E(f642(x20543,x20541,x20544),f642(x20543,x20542,x20544)) % 178.07/177.95 [2055]~E(x20551,x20552)+E(f642(x20553,x20554,x20551),f642(x20553,x20554,x20552)) % 178.07/177.95 [2056]~E(x20561,x20562)+E(f534(x20561,x20563,x20564,x20565),f534(x20562,x20563,x20564,x20565)) % 178.07/177.95 [2057]~E(x20571,x20572)+E(f534(x20573,x20571,x20574,x20575),f534(x20573,x20572,x20574,x20575)) % 178.07/177.95 [2058]~E(x20581,x20582)+E(f534(x20583,x20584,x20581,x20585),f534(x20583,x20584,x20582,x20585)) % 178.07/177.95 [2059]~E(x20591,x20592)+E(f534(x20593,x20594,x20595,x20591),f534(x20593,x20594,x20595,x20592)) % 178.07/177.95 [2060]~E(x20601,x20602)+E(f805(x20601,x20603,x20604),f805(x20602,x20603,x20604)) % 178.07/177.95 [2061]~E(x20611,x20612)+E(f805(x20613,x20611,x20614),f805(x20613,x20612,x20614)) % 178.07/177.95 [2062]~E(x20621,x20622)+E(f805(x20623,x20624,x20621),f805(x20623,x20624,x20622)) % 178.07/177.95 [2063]~E(x20631,x20632)+E(f780(x20631,x20633),f780(x20632,x20633)) % 178.07/177.95 [2064]~E(x20641,x20642)+E(f780(x20643,x20641),f780(x20643,x20642)) % 178.07/177.95 [2065]~E(x20651,x20652)+E(f519(x20651,x20653,x20654),f519(x20652,x20653,x20654)) % 178.07/177.95 [2066]~E(x20661,x20662)+E(f519(x20663,x20661,x20664),f519(x20663,x20662,x20664)) % 178.07/177.95 [2067]~E(x20671,x20672)+E(f519(x20673,x20674,x20671),f519(x20673,x20674,x20672)) % 178.07/177.95 [2068]~E(x20681,x20682)+E(f21(x20681,x20683),f21(x20682,x20683)) % 178.07/177.95 [2069]~E(x20691,x20692)+E(f21(x20693,x20691),f21(x20693,x20692)) % 178.07/177.95 [2070]~E(x20701,x20702)+E(f867(x20701,x20703,x20704),f867(x20702,x20703,x20704)) % 178.07/177.95 [2071]~E(x20711,x20712)+E(f867(x20713,x20711,x20714),f867(x20713,x20712,x20714)) % 178.07/177.95 [2072]~E(x20721,x20722)+E(f867(x20723,x20724,x20721),f867(x20723,x20724,x20722)) % 178.07/177.95 [2073]~E(x20731,x20732)+E(f585(x20731,x20733,x20734,x20735),f585(x20732,x20733,x20734,x20735)) % 178.07/177.95 [2074]~E(x20741,x20742)+E(f585(x20743,x20741,x20744,x20745),f585(x20743,x20742,x20744,x20745)) % 178.07/177.95 [2075]~E(x20751,x20752)+E(f585(x20753,x20754,x20751,x20755),f585(x20753,x20754,x20752,x20755)) % 178.07/177.95 [2076]~E(x20761,x20762)+E(f585(x20763,x20764,x20765,x20761),f585(x20763,x20764,x20765,x20762)) % 178.07/177.95 [2077]~E(x20771,x20772)+E(f611(x20771,x20773,x20774),f611(x20772,x20773,x20774)) % 178.07/177.95 [2078]~E(x20781,x20782)+E(f611(x20783,x20781,x20784),f611(x20783,x20782,x20784)) % 178.07/177.95 [2079]~E(x20791,x20792)+E(f611(x20793,x20794,x20791),f611(x20793,x20794,x20792)) % 178.07/177.95 [2080]~E(x20801,x20802)+E(f343(x20801,x20803,x20804,x20805,x20806),f343(x20802,x20803,x20804,x20805,x20806)) % 178.07/177.95 [2081]~E(x20811,x20812)+E(f343(x20813,x20811,x20814,x20815,x20816),f343(x20813,x20812,x20814,x20815,x20816)) % 178.07/177.95 [2082]~E(x20821,x20822)+E(f343(x20823,x20824,x20821,x20825,x20826),f343(x20823,x20824,x20822,x20825,x20826)) % 178.07/177.95 [2083]~E(x20831,x20832)+E(f343(x20833,x20834,x20835,x20831,x20836),f343(x20833,x20834,x20835,x20832,x20836)) % 178.07/177.95 [2084]~E(x20841,x20842)+E(f343(x20843,x20844,x20845,x20846,x20841),f343(x20843,x20844,x20845,x20846,x20842)) % 178.07/177.95 [2085]~E(x20851,x20852)+E(f653(x20851,x20853,x20854),f653(x20852,x20853,x20854)) % 178.07/177.95 [2086]~E(x20861,x20862)+E(f653(x20863,x20861,x20864),f653(x20863,x20862,x20864)) % 178.07/177.95 [2087]~E(x20871,x20872)+E(f653(x20873,x20874,x20871),f653(x20873,x20874,x20872)) % 178.07/177.95 [2088]~E(x20881,x20882)+E(f520(x20881,x20883,x20884),f520(x20882,x20883,x20884)) % 178.07/177.95 [2089]~E(x20891,x20892)+E(f520(x20893,x20891,x20894),f520(x20893,x20892,x20894)) % 178.07/177.95 [2090]~E(x20901,x20902)+E(f520(x20903,x20904,x20901),f520(x20903,x20904,x20902)) % 178.07/177.95 [2091]~E(x20911,x20912)+E(f562(x20911),f562(x20912)) % 178.07/177.95 [2092]~E(x20921,x20922)+E(f731(x20921,x20923,x20924,x20925),f731(x20922,x20923,x20924,x20925)) % 178.07/177.95 [2093]~E(x20931,x20932)+E(f731(x20933,x20931,x20934,x20935),f731(x20933,x20932,x20934,x20935)) % 178.07/177.95 [2094]~E(x20941,x20942)+E(f731(x20943,x20944,x20941,x20945),f731(x20943,x20944,x20942,x20945)) % 178.07/177.95 [2095]~E(x20951,x20952)+E(f731(x20953,x20954,x20955,x20951),f731(x20953,x20954,x20955,x20952)) % 178.07/177.95 [2096]~E(x20961,x20962)+E(f491(x20961,x20963,x20964,x20965),f491(x20962,x20963,x20964,x20965)) % 178.07/177.95 [2097]~E(x20971,x20972)+E(f491(x20973,x20971,x20974,x20975),f491(x20973,x20972,x20974,x20975)) % 178.07/177.95 [2098]~E(x20981,x20982)+E(f491(x20983,x20984,x20981,x20985),f491(x20983,x20984,x20982,x20985)) % 178.07/177.95 [2099]~E(x20991,x20992)+E(f491(x20993,x20994,x20995,x20991),f491(x20993,x20994,x20995,x20992)) % 178.07/177.95 [2100]~E(x21001,x21002)+E(f459(x21001,x21003,x21004,x21005,x21006),f459(x21002,x21003,x21004,x21005,x21006)) % 178.07/177.95 [2101]~E(x21011,x21012)+E(f459(x21013,x21011,x21014,x21015,x21016),f459(x21013,x21012,x21014,x21015,x21016)) % 178.07/177.95 [2102]~E(x21021,x21022)+E(f459(x21023,x21024,x21021,x21025,x21026),f459(x21023,x21024,x21022,x21025,x21026)) % 178.07/177.95 [2103]~E(x21031,x21032)+E(f459(x21033,x21034,x21035,x21031,x21036),f459(x21033,x21034,x21035,x21032,x21036)) % 178.07/177.95 [2104]~E(x21041,x21042)+E(f459(x21043,x21044,x21045,x21046,x21041),f459(x21043,x21044,x21045,x21046,x21042)) % 178.07/177.95 [2105]~E(x21051,x21052)+E(f755(x21051,x21053,x21054),f755(x21052,x21053,x21054)) % 178.07/177.95 [2106]~E(x21061,x21062)+E(f755(x21063,x21061,x21064),f755(x21063,x21062,x21064)) % 178.07/177.95 [2107]~E(x21071,x21072)+E(f755(x21073,x21074,x21071),f755(x21073,x21074,x21072)) % 178.07/177.95 [2108]~E(x21081,x21082)+E(f750(x21081,x21083,x21084),f750(x21082,x21083,x21084)) % 178.07/177.95 [2109]~E(x21091,x21092)+E(f750(x21093,x21091,x21094),f750(x21093,x21092,x21094)) % 178.07/177.95 [2110]~E(x21101,x21102)+E(f750(x21103,x21104,x21101),f750(x21103,x21104,x21102)) % 178.07/177.95 [2111]~E(x21111,x21112)+E(f619(x21111,x21113),f619(x21112,x21113)) % 178.07/177.95 [2112]~E(x21121,x21122)+E(f619(x21123,x21121),f619(x21123,x21122)) % 178.07/177.95 [2113]~E(x21131,x21132)+E(f592(x21131,x21133,x21134),f592(x21132,x21133,x21134)) % 178.07/177.95 [2114]~E(x21141,x21142)+E(f592(x21143,x21141,x21144),f592(x21143,x21142,x21144)) % 178.07/177.95 [2115]~E(x21151,x21152)+E(f592(x21153,x21154,x21151),f592(x21153,x21154,x21152)) % 178.07/177.95 [2116]~E(x21161,x21162)+E(f579(x21161,x21163,x21164,x21165,x21166,x21167),f579(x21162,x21163,x21164,x21165,x21166,x21167)) % 178.07/177.95 [2117]~E(x21171,x21172)+E(f579(x21173,x21171,x21174,x21175,x21176,x21177),f579(x21173,x21172,x21174,x21175,x21176,x21177)) % 178.07/177.95 [2118]~E(x21181,x21182)+E(f579(x21183,x21184,x21181,x21185,x21186,x21187),f579(x21183,x21184,x21182,x21185,x21186,x21187)) % 178.07/177.95 [2119]~E(x21191,x21192)+E(f579(x21193,x21194,x21195,x21191,x21196,x21197),f579(x21193,x21194,x21195,x21192,x21196,x21197)) % 178.07/177.95 [2120]~E(x21201,x21202)+E(f579(x21203,x21204,x21205,x21206,x21201,x21207),f579(x21203,x21204,x21205,x21206,x21202,x21207)) % 178.07/177.95 [2121]~E(x21211,x21212)+E(f579(x21213,x21214,x21215,x21216,x21217,x21211),f579(x21213,x21214,x21215,x21216,x21217,x21212)) % 178.07/177.95 [2122]~E(x21221,x21222)+E(f345(x21221,x21223,x21224,x21225,x21226),f345(x21222,x21223,x21224,x21225,x21226)) % 178.07/177.95 [2123]~E(x21231,x21232)+E(f345(x21233,x21231,x21234,x21235,x21236),f345(x21233,x21232,x21234,x21235,x21236)) % 178.07/177.95 [2124]~E(x21241,x21242)+E(f345(x21243,x21244,x21241,x21245,x21246),f345(x21243,x21244,x21242,x21245,x21246)) % 178.07/177.95 [2125]~E(x21251,x21252)+E(f345(x21253,x21254,x21255,x21251,x21256),f345(x21253,x21254,x21255,x21252,x21256)) % 178.07/177.95 [2126]~E(x21261,x21262)+E(f345(x21263,x21264,x21265,x21266,x21261),f345(x21263,x21264,x21265,x21266,x21262)) % 178.07/177.95 [2127]~E(x21271,x21272)+E(f415(x21271,x21273),f415(x21272,x21273)) % 178.07/177.95 [2128]~E(x21281,x21282)+E(f415(x21283,x21281),f415(x21283,x21282)) % 178.07/177.95 [2129]~E(x21291,x21292)+E(f758(x21291,x21293),f758(x21292,x21293)) % 178.07/177.95 [2130]~E(x21301,x21302)+E(f758(x21303,x21301),f758(x21303,x21302)) % 178.07/177.95 [2131]~E(x21311,x21312)+E(f757(x21311,x21313),f757(x21312,x21313)) % 178.07/177.95 [2132]~E(x21321,x21322)+E(f757(x21323,x21321),f757(x21323,x21322)) % 178.07/177.95 [2133]~E(x21331,x21332)+E(f782(x21331,x21333,x21334),f782(x21332,x21333,x21334)) % 178.07/177.95 [2134]~E(x21341,x21342)+E(f782(x21343,x21341,x21344),f782(x21343,x21342,x21344)) % 178.07/177.95 [2135]~E(x21351,x21352)+E(f782(x21353,x21354,x21351),f782(x21353,x21354,x21352)) % 178.07/177.95 [2136]~E(x21361,x21362)+E(f598(x21361,x21363,x21364),f598(x21362,x21363,x21364)) % 178.07/177.95 [2137]~E(x21371,x21372)+E(f598(x21373,x21371,x21374),f598(x21373,x21372,x21374)) % 178.07/177.95 [2138]~E(x21381,x21382)+E(f598(x21383,x21384,x21381),f598(x21383,x21384,x21382)) % 178.07/177.95 [2139]~E(x21391,x21392)+E(f272(x21391,x21393,x21394,x21395,x21396),f272(x21392,x21393,x21394,x21395,x21396)) % 178.07/177.95 [2140]~E(x21401,x21402)+E(f272(x21403,x21401,x21404,x21405,x21406),f272(x21403,x21402,x21404,x21405,x21406)) % 178.07/177.95 [2141]~E(x21411,x21412)+E(f272(x21413,x21414,x21411,x21415,x21416),f272(x21413,x21414,x21412,x21415,x21416)) % 178.07/177.95 [2142]~E(x21421,x21422)+E(f272(x21423,x21424,x21425,x21421,x21426),f272(x21423,x21424,x21425,x21422,x21426)) % 178.07/177.95 [2143]~E(x21431,x21432)+E(f272(x21433,x21434,x21435,x21436,x21431),f272(x21433,x21434,x21435,x21436,x21432)) % 178.07/177.95 [2144]~E(x21441,x21442)+E(f383(x21441),f383(x21442)) % 178.07/177.95 [2145]~E(x21451,x21452)+E(f545(x21451,x21453,x21454,x21455,x21456,x21457,x21458),f545(x21452,x21453,x21454,x21455,x21456,x21457,x21458)) % 178.07/177.95 [2146]~E(x21461,x21462)+E(f545(x21463,x21461,x21464,x21465,x21466,x21467,x21468),f545(x21463,x21462,x21464,x21465,x21466,x21467,x21468)) % 178.07/177.95 [2147]~E(x21471,x21472)+E(f545(x21473,x21474,x21471,x21475,x21476,x21477,x21478),f545(x21473,x21474,x21472,x21475,x21476,x21477,x21478)) % 178.07/177.95 [2148]~E(x21481,x21482)+E(f545(x21483,x21484,x21485,x21481,x21486,x21487,x21488),f545(x21483,x21484,x21485,x21482,x21486,x21487,x21488)) % 178.07/177.95 [2149]~E(x21491,x21492)+E(f545(x21493,x21494,x21495,x21496,x21491,x21497,x21498),f545(x21493,x21494,x21495,x21496,x21492,x21497,x21498)) % 178.07/177.95 [2150]~E(x21501,x21502)+E(f545(x21503,x21504,x21505,x21506,x21507,x21501,x21508),f545(x21503,x21504,x21505,x21506,x21507,x21502,x21508)) % 178.07/177.95 [2151]~E(x21511,x21512)+E(f545(x21513,x21514,x21515,x21516,x21517,x21518,x21511),f545(x21513,x21514,x21515,x21516,x21517,x21518,x21512)) % 178.07/177.95 [2152]~E(x21521,x21522)+E(f606(x21521,x21523,x21524,x21525),f606(x21522,x21523,x21524,x21525)) % 178.07/177.95 [2153]~E(x21531,x21532)+E(f606(x21533,x21531,x21534,x21535),f606(x21533,x21532,x21534,x21535)) % 178.07/177.95 [2154]~E(x21541,x21542)+E(f606(x21543,x21544,x21541,x21545),f606(x21543,x21544,x21542,x21545)) % 178.07/177.95 [2155]~E(x21551,x21552)+E(f606(x21553,x21554,x21555,x21551),f606(x21553,x21554,x21555,x21552)) % 178.07/177.95 [2156]~E(x21561,x21562)+E(f788(x21561,x21563,x21564),f788(x21562,x21563,x21564)) % 178.07/177.95 [2157]~E(x21571,x21572)+E(f788(x21573,x21571,x21574),f788(x21573,x21572,x21574)) % 178.07/177.95 [2158]~E(x21581,x21582)+E(f788(x21583,x21584,x21581),f788(x21583,x21584,x21582)) % 178.07/177.95 [2159]~E(x21591,x21592)+E(f654(x21591,x21593),f654(x21592,x21593)) % 178.07/177.95 [2160]~E(x21601,x21602)+E(f654(x21603,x21601),f654(x21603,x21602)) % 178.07/177.95 [2161]~E(x21611,x21612)+E(f717(x21611,x21613,x21614),f717(x21612,x21613,x21614)) % 178.07/177.95 [2162]~E(x21621,x21622)+E(f717(x21623,x21621,x21624),f717(x21623,x21622,x21624)) % 178.07/177.95 [2163]~E(x21631,x21632)+E(f717(x21633,x21634,x21631),f717(x21633,x21634,x21632)) % 178.07/177.95 [2164]~E(x21641,x21642)+E(f714(x21641,x21643),f714(x21642,x21643)) % 178.07/177.95 [2165]~E(x21651,x21652)+E(f714(x21653,x21651),f714(x21653,x21652)) % 178.07/177.95 [2166]~E(x21661,x21662)+E(f742(x21661,x21663,x21664,x21665),f742(x21662,x21663,x21664,x21665)) % 178.07/177.95 [2167]~E(x21671,x21672)+E(f742(x21673,x21671,x21674,x21675),f742(x21673,x21672,x21674,x21675)) % 178.07/177.95 [2168]~E(x21681,x21682)+E(f742(x21683,x21684,x21681,x21685),f742(x21683,x21684,x21682,x21685)) % 178.07/177.95 [2169]~E(x21691,x21692)+E(f742(x21693,x21694,x21695,x21691),f742(x21693,x21694,x21695,x21692)) % 178.07/177.95 [2170]~E(x21701,x21702)+E(f389(x21701),f389(x21702)) % 178.07/177.95 [2171]~E(x21711,x21712)+E(f565(x21711),f565(x21712)) % 178.07/177.95 [2172]~E(x21721,x21722)+E(f443(x21721,x21723),f443(x21722,x21723)) % 178.07/177.95 [2173]~E(x21731,x21732)+E(f443(x21733,x21731),f443(x21733,x21732)) % 178.07/177.95 [2174]~E(x21741,x21742)+E(f660(x21741,x21743,x21744),f660(x21742,x21743,x21744)) % 178.07/177.95 [2175]~E(x21751,x21752)+E(f660(x21753,x21751,x21754),f660(x21753,x21752,x21754)) % 178.07/177.95 [2176]~E(x21761,x21762)+E(f660(x21763,x21764,x21761),f660(x21763,x21764,x21762)) % 178.07/177.95 [2177]~E(x21771,x21772)+E(f838(x21771,x21773,x21774),f838(x21772,x21773,x21774)) % 178.07/177.95 [2178]~E(x21781,x21782)+E(f838(x21783,x21781,x21784),f838(x21783,x21782,x21784)) % 178.07/177.95 [2179]~E(x21791,x21792)+E(f838(x21793,x21794,x21791),f838(x21793,x21794,x21792)) % 178.07/177.95 [2180]~E(x21801,x21802)+E(f866(x21801,x21803,x21804),f866(x21802,x21803,x21804)) % 178.07/177.95 [2181]~E(x21811,x21812)+E(f866(x21813,x21811,x21814),f866(x21813,x21812,x21814)) % 178.07/177.95 [2182]~E(x21821,x21822)+E(f866(x21823,x21824,x21821),f866(x21823,x21824,x21822)) % 178.07/177.95 [2183]~E(x21831,x21832)+E(f380(x21831,x21833,x21834,x21835,x21836),f380(x21832,x21833,x21834,x21835,x21836)) % 178.07/177.95 [2184]~E(x21841,x21842)+E(f380(x21843,x21841,x21844,x21845,x21846),f380(x21843,x21842,x21844,x21845,x21846)) % 178.07/177.95 [2185]~E(x21851,x21852)+E(f380(x21853,x21854,x21851,x21855,x21856),f380(x21853,x21854,x21852,x21855,x21856)) % 178.07/177.95 [2186]~E(x21861,x21862)+E(f380(x21863,x21864,x21865,x21861,x21866),f380(x21863,x21864,x21865,x21862,x21866)) % 178.07/177.95 [2187]~E(x21871,x21872)+E(f380(x21873,x21874,x21875,x21876,x21871),f380(x21873,x21874,x21875,x21876,x21872)) % 178.07/177.95 [2188]~E(x21881,x21882)+E(f54(x21881,x21883),f54(x21882,x21883)) % 178.07/177.95 [2189]~E(x21891,x21892)+E(f54(x21893,x21891),f54(x21893,x21892)) % 178.07/177.95 [2190]~E(x21901,x21902)+E(f771(x21901,x21903,x21904,x21905,x21906),f771(x21902,x21903,x21904,x21905,x21906)) % 178.07/177.95 [2191]~E(x21911,x21912)+E(f771(x21913,x21911,x21914,x21915,x21916),f771(x21913,x21912,x21914,x21915,x21916)) % 178.07/177.95 [2192]~E(x21921,x21922)+E(f771(x21923,x21924,x21921,x21925,x21926),f771(x21923,x21924,x21922,x21925,x21926)) % 178.07/177.95 [2193]~E(x21931,x21932)+E(f771(x21933,x21934,x21935,x21931,x21936),f771(x21933,x21934,x21935,x21932,x21936)) % 178.07/177.95 [2194]~E(x21941,x21942)+E(f771(x21943,x21944,x21945,x21946,x21941),f771(x21943,x21944,x21945,x21946,x21942)) % 178.07/177.95 [2195]~E(x21951,x21952)+E(f778(x21951,x21953,x21954),f778(x21952,x21953,x21954)) % 178.07/177.95 [2196]~E(x21961,x21962)+E(f778(x21963,x21961,x21964),f778(x21963,x21962,x21964)) % 178.07/177.95 [2197]~E(x21971,x21972)+E(f778(x21973,x21974,x21971),f778(x21973,x21974,x21972)) % 178.07/177.95 [2198]~E(x21981,x21982)+E(f382(x21981),f382(x21982)) % 178.07/177.95 [2199]~E(x21991,x21992)+E(f515(x21991,x21993),f515(x21992,x21993)) % 178.07/177.95 [2200]~E(x22001,x22002)+E(f515(x22003,x22001),f515(x22003,x22002)) % 178.07/177.95 [2201]~E(x22011,x22012)+E(f214(x22011,x22013,x22014,x22015),f214(x22012,x22013,x22014,x22015)) % 178.07/177.95 [2202]~E(x22021,x22022)+E(f214(x22023,x22021,x22024,x22025),f214(x22023,x22022,x22024,x22025)) % 178.07/177.95 [2203]~E(x22031,x22032)+E(f214(x22033,x22034,x22031,x22035),f214(x22033,x22034,x22032,x22035)) % 178.07/177.95 [2204]~E(x22041,x22042)+E(f214(x22043,x22044,x22045,x22041),f214(x22043,x22044,x22045,x22042)) % 178.07/177.95 [2205]~E(x22051,x22052)+E(f233(x22051,x22053,x22054),f233(x22052,x22053,x22054)) % 178.07/177.95 [2206]~E(x22061,x22062)+E(f233(x22063,x22061,x22064),f233(x22063,x22062,x22064)) % 178.07/177.95 [2207]~E(x22071,x22072)+E(f233(x22073,x22074,x22071),f233(x22073,x22074,x22072)) % 178.07/177.95 [2208]~E(x22081,x22082)+E(f279(x22081,x22083,x22084),f279(x22082,x22083,x22084)) % 178.07/177.95 [2209]~E(x22091,x22092)+E(f279(x22093,x22091,x22094),f279(x22093,x22092,x22094)) % 178.07/177.95 [2210]~E(x22101,x22102)+E(f279(x22103,x22104,x22101),f279(x22103,x22104,x22102)) % 178.07/177.95 [2211]~E(x22111,x22112)+E(f526(x22111,x22113,x22114),f526(x22112,x22113,x22114)) % 178.07/177.95 [2212]~E(x22121,x22122)+E(f526(x22123,x22121,x22124),f526(x22123,x22122,x22124)) % 178.07/177.95 [2213]~E(x22131,x22132)+E(f526(x22133,x22134,x22131),f526(x22133,x22134,x22132)) % 178.07/177.95 [2214]~E(x22141,x22142)+E(f517(x22141,x22143,x22144),f517(x22142,x22143,x22144)) % 178.07/177.95 [2215]~E(x22151,x22152)+E(f517(x22153,x22151,x22154),f517(x22153,x22152,x22154)) % 178.07/177.95 [2216]~E(x22161,x22162)+E(f517(x22163,x22164,x22161),f517(x22163,x22164,x22162)) % 178.07/177.95 [2217]~E(x22171,x22172)+E(f644(x22171,x22173,x22174),f644(x22172,x22173,x22174)) % 178.07/177.95 [2218]~E(x22181,x22182)+E(f644(x22183,x22181,x22184),f644(x22183,x22182,x22184)) % 178.07/177.95 [2219]~E(x22191,x22192)+E(f644(x22193,x22194,x22191),f644(x22193,x22194,x22192)) % 178.07/177.95 [2220]~E(x22201,x22202)+E(f794(x22201,x22203,x22204,x22205,x22206),f794(x22202,x22203,x22204,x22205,x22206)) % 178.07/177.95 [2221]~E(x22211,x22212)+E(f794(x22213,x22211,x22214,x22215,x22216),f794(x22213,x22212,x22214,x22215,x22216)) % 178.07/177.95 [2222]~E(x22221,x22222)+E(f794(x22223,x22224,x22221,x22225,x22226),f794(x22223,x22224,x22222,x22225,x22226)) % 178.07/177.95 [2223]~E(x22231,x22232)+E(f794(x22233,x22234,x22235,x22231,x22236),f794(x22233,x22234,x22235,x22232,x22236)) % 178.07/177.95 [2224]~E(x22241,x22242)+E(f794(x22243,x22244,x22245,x22246,x22241),f794(x22243,x22244,x22245,x22246,x22242)) % 178.07/177.95 [2225]~E(x22251,x22252)+E(f384(x22251,x22253,x22254,x22255,x22256),f384(x22252,x22253,x22254,x22255,x22256)) % 178.07/177.95 [2226]~E(x22261,x22262)+E(f384(x22263,x22261,x22264,x22265,x22266),f384(x22263,x22262,x22264,x22265,x22266)) % 178.07/177.95 [2227]~E(x22271,x22272)+E(f384(x22273,x22274,x22271,x22275,x22276),f384(x22273,x22274,x22272,x22275,x22276)) % 178.07/177.95 [2228]~E(x22281,x22282)+E(f384(x22283,x22284,x22285,x22281,x22286),f384(x22283,x22284,x22285,x22282,x22286)) % 178.07/177.95 [2229]~E(x22291,x22292)+E(f384(x22293,x22294,x22295,x22296,x22291),f384(x22293,x22294,x22295,x22296,x22292)) % 178.07/177.95 [2230]~E(x22301,x22302)+E(f180(x22301),f180(x22302)) % 178.07/177.95 [2231]~E(x22311,x22312)+E(f494(x22311,x22313,x22314,x22315),f494(x22312,x22313,x22314,x22315)) % 178.07/177.95 [2232]~E(x22321,x22322)+E(f494(x22323,x22321,x22324,x22325),f494(x22323,x22322,x22324,x22325)) % 178.07/177.95 [2233]~E(x22331,x22332)+E(f494(x22333,x22334,x22331,x22335),f494(x22333,x22334,x22332,x22335)) % 178.07/177.95 [2234]~E(x22341,x22342)+E(f494(x22343,x22344,x22345,x22341),f494(x22343,x22344,x22345,x22342)) % 178.07/177.95 [2235]~E(x22351,x22352)+E(f528(x22351,x22353,x22354,x22355),f528(x22352,x22353,x22354,x22355)) % 178.07/177.95 [2236]~E(x22361,x22362)+E(f528(x22363,x22361,x22364,x22365),f528(x22363,x22362,x22364,x22365)) % 178.07/177.95 [2237]~E(x22371,x22372)+E(f528(x22373,x22374,x22371,x22375),f528(x22373,x22374,x22372,x22375)) % 178.07/177.95 [2238]~E(x22381,x22382)+E(f528(x22383,x22384,x22385,x22381),f528(x22383,x22384,x22385,x22382)) % 178.07/177.95 [2239]~E(x22391,x22392)+E(f404(x22391,x22393,x22394),f404(x22392,x22393,x22394)) % 178.07/177.95 [2240]~E(x22401,x22402)+E(f404(x22403,x22401,x22404),f404(x22403,x22402,x22404)) % 178.07/177.95 [2241]~E(x22411,x22412)+E(f404(x22413,x22414,x22411),f404(x22413,x22414,x22412)) % 178.07/177.95 [2242]~E(x22421,x22422)+E(f589(x22421,x22423,x22424,x22425),f589(x22422,x22423,x22424,x22425)) % 178.07/177.95 [2243]~E(x22431,x22432)+E(f589(x22433,x22431,x22434,x22435),f589(x22433,x22432,x22434,x22435)) % 178.07/177.95 [2244]~E(x22441,x22442)+E(f589(x22443,x22444,x22441,x22445),f589(x22443,x22444,x22442,x22445)) % 178.07/177.95 [2245]~E(x22451,x22452)+E(f589(x22453,x22454,x22455,x22451),f589(x22453,x22454,x22455,x22452)) % 178.07/177.95 [2246]~E(x22461,x22462)+E(f482(x22461,x22463),f482(x22462,x22463)) % 178.07/177.95 [2247]~E(x22471,x22472)+E(f482(x22473,x22471),f482(x22473,x22472)) % 178.07/177.95 [2248]~E(x22481,x22482)+E(f423(x22481,x22483,x22484,x22485),f423(x22482,x22483,x22484,x22485)) % 178.07/177.95 [2249]~E(x22491,x22492)+E(f423(x22493,x22491,x22494,x22495),f423(x22493,x22492,x22494,x22495)) % 178.07/177.95 [2250]~E(x22501,x22502)+E(f423(x22503,x22504,x22501,x22505),f423(x22503,x22504,x22502,x22505)) % 178.07/177.95 [2251]~E(x22511,x22512)+E(f423(x22513,x22514,x22515,x22511),f423(x22513,x22514,x22515,x22512)) % 178.07/177.95 [2252]~E(x22521,x22522)+E(f763(x22521,x22523),f763(x22522,x22523)) % 178.07/177.95 [2253]~E(x22531,x22532)+E(f763(x22533,x22531),f763(x22533,x22532)) % 178.07/177.95 [2254]~E(x22541,x22542)+E(f573(x22541,x22543,x22544,x22545,x22546,x22547),f573(x22542,x22543,x22544,x22545,x22546,x22547)) % 178.07/177.95 [2255]~E(x22551,x22552)+E(f573(x22553,x22551,x22554,x22555,x22556,x22557),f573(x22553,x22552,x22554,x22555,x22556,x22557)) % 178.07/177.95 [2256]~E(x22561,x22562)+E(f573(x22563,x22564,x22561,x22565,x22566,x22567),f573(x22563,x22564,x22562,x22565,x22566,x22567)) % 178.07/177.95 [2257]~E(x22571,x22572)+E(f573(x22573,x22574,x22575,x22571,x22576,x22577),f573(x22573,x22574,x22575,x22572,x22576,x22577)) % 178.07/177.95 [2258]~E(x22581,x22582)+E(f573(x22583,x22584,x22585,x22586,x22581,x22587),f573(x22583,x22584,x22585,x22586,x22582,x22587)) % 178.07/177.95 [2259]~E(x22591,x22592)+E(f573(x22593,x22594,x22595,x22596,x22597,x22591),f573(x22593,x22594,x22595,x22596,x22597,x22592)) % 178.07/177.95 [2260]~E(x22601,x22602)+E(f832(x22601,x22603,x22604,x22605,x22606,x22607,x22608),f832(x22602,x22603,x22604,x22605,x22606,x22607,x22608)) % 178.07/177.95 [2261]~E(x22611,x22612)+E(f832(x22613,x22611,x22614,x22615,x22616,x22617,x22618),f832(x22613,x22612,x22614,x22615,x22616,x22617,x22618)) % 178.07/177.95 [2262]~E(x22621,x22622)+E(f832(x22623,x22624,x22621,x22625,x22626,x22627,x22628),f832(x22623,x22624,x22622,x22625,x22626,x22627,x22628)) % 178.07/177.95 [2263]~E(x22631,x22632)+E(f832(x22633,x22634,x22635,x22631,x22636,x22637,x22638),f832(x22633,x22634,x22635,x22632,x22636,x22637,x22638)) % 178.07/177.95 [2264]~E(x22641,x22642)+E(f832(x22643,x22644,x22645,x22646,x22641,x22647,x22648),f832(x22643,x22644,x22645,x22646,x22642,x22647,x22648)) % 178.07/177.95 [2265]~E(x22651,x22652)+E(f832(x22653,x22654,x22655,x22656,x22657,x22651,x22658),f832(x22653,x22654,x22655,x22656,x22657,x22652,x22658)) % 178.07/177.95 [2266]~E(x22661,x22662)+E(f832(x22663,x22664,x22665,x22666,x22667,x22668,x22661),f832(x22663,x22664,x22665,x22666,x22667,x22668,x22662)) % 178.07/177.95 [2267]~E(x22671,x22672)+E(f421(x22671,x22673,x22674,x22675),f421(x22672,x22673,x22674,x22675)) % 178.07/177.95 [2268]~E(x22681,x22682)+E(f421(x22683,x22681,x22684,x22685),f421(x22683,x22682,x22684,x22685)) % 178.07/177.95 [2269]~E(x22691,x22692)+E(f421(x22693,x22694,x22691,x22695),f421(x22693,x22694,x22692,x22695)) % 178.07/177.95 [2270]~E(x22701,x22702)+E(f421(x22703,x22704,x22705,x22701),f421(x22703,x22704,x22705,x22702)) % 178.07/177.95 [2271]~E(x22711,x22712)+E(f354(x22711,x22713,x22714,x22715,x22716),f354(x22712,x22713,x22714,x22715,x22716)) % 178.07/177.95 [2272]~E(x22721,x22722)+E(f354(x22723,x22721,x22724,x22725,x22726),f354(x22723,x22722,x22724,x22725,x22726)) % 178.07/177.95 [2273]~E(x22731,x22732)+E(f354(x22733,x22734,x22731,x22735,x22736),f354(x22733,x22734,x22732,x22735,x22736)) % 178.07/177.95 [2274]~E(x22741,x22742)+E(f354(x22743,x22744,x22745,x22741,x22746),f354(x22743,x22744,x22745,x22742,x22746)) % 178.07/177.95 [2275]~E(x22751,x22752)+E(f354(x22753,x22754,x22755,x22756,x22751),f354(x22753,x22754,x22755,x22756,x22752)) % 178.07/177.95 [2276]~E(x22761,x22762)+E(f511(x22761,x22763),f511(x22762,x22763)) % 178.07/177.95 [2277]~E(x22771,x22772)+E(f511(x22773,x22771),f511(x22773,x22772)) % 178.07/177.95 [2278]~E(x22781,x22782)+E(f400(x22781),f400(x22782)) % 178.07/177.95 [2279]~E(x22791,x22792)+E(f792(x22791,x22793,x22794),f792(x22792,x22793,x22794)) % 178.07/177.95 [2280]~E(x22801,x22802)+E(f792(x22803,x22801,x22804),f792(x22803,x22802,x22804)) % 178.07/177.95 [2281]~E(x22811,x22812)+E(f792(x22813,x22814,x22811),f792(x22813,x22814,x22812)) % 178.07/177.95 [2282]~E(x22821,x22822)+E(f209(x22821),f209(x22822)) % 178.07/177.95 [2283]~E(x22831,x22832)+E(f739(x22831,x22833,x22834,x22835,x22836,x22837,x22838),f739(x22832,x22833,x22834,x22835,x22836,x22837,x22838)) % 178.07/177.95 [2284]~E(x22841,x22842)+E(f739(x22843,x22841,x22844,x22845,x22846,x22847,x22848),f739(x22843,x22842,x22844,x22845,x22846,x22847,x22848)) % 178.07/177.95 [2285]~E(x22851,x22852)+E(f739(x22853,x22854,x22851,x22855,x22856,x22857,x22858),f739(x22853,x22854,x22852,x22855,x22856,x22857,x22858)) % 178.07/177.95 [2286]~E(x22861,x22862)+E(f739(x22863,x22864,x22865,x22861,x22866,x22867,x22868),f739(x22863,x22864,x22865,x22862,x22866,x22867,x22868)) % 178.07/177.95 [2287]~E(x22871,x22872)+E(f739(x22873,x22874,x22875,x22876,x22871,x22877,x22878),f739(x22873,x22874,x22875,x22876,x22872,x22877,x22878)) % 178.07/177.95 [2288]~E(x22881,x22882)+E(f739(x22883,x22884,x22885,x22886,x22887,x22881,x22888),f739(x22883,x22884,x22885,x22886,x22887,x22882,x22888)) % 178.07/177.95 [2289]~E(x22891,x22892)+E(f739(x22893,x22894,x22895,x22896,x22897,x22898,x22891),f739(x22893,x22894,x22895,x22896,x22897,x22898,x22892)) % 178.07/177.95 [2290]~E(x22901,x22902)+E(f349(x22901,x22903,x22904,x22905),f349(x22902,x22903,x22904,x22905)) % 178.07/177.95 [2291]~E(x22911,x22912)+E(f349(x22913,x22911,x22914,x22915),f349(x22913,x22912,x22914,x22915)) % 178.07/177.95 [2292]~E(x22921,x22922)+E(f349(x22923,x22924,x22921,x22925),f349(x22923,x22924,x22922,x22925)) % 178.07/177.95 [2293]~E(x22931,x22932)+E(f349(x22933,x22934,x22935,x22931),f349(x22933,x22934,x22935,x22932)) % 178.07/177.95 [2294]~E(x22941,x22942)+E(f800(x22941,x22943,x22944,x22945),f800(x22942,x22943,x22944,x22945)) % 178.07/177.95 [2295]~E(x22951,x22952)+E(f800(x22953,x22951,x22954,x22955),f800(x22953,x22952,x22954,x22955)) % 178.07/177.95 [2296]~E(x22961,x22962)+E(f800(x22963,x22964,x22961,x22965),f800(x22963,x22964,x22962,x22965)) % 178.07/177.95 [2297]~E(x22971,x22972)+E(f800(x22973,x22974,x22975,x22971),f800(x22973,x22974,x22975,x22972)) % 178.07/177.95 [2298]~E(x22981,x22982)+E(f845(x22981,x22983,x22984,x22985,x22986),f845(x22982,x22983,x22984,x22985,x22986)) % 178.07/177.95 [2299]~E(x22991,x22992)+E(f845(x22993,x22991,x22994,x22995,x22996),f845(x22993,x22992,x22994,x22995,x22996)) % 178.07/177.95 [2300]~E(x23001,x23002)+E(f845(x23003,x23004,x23001,x23005,x23006),f845(x23003,x23004,x23002,x23005,x23006)) % 178.07/177.95 [2301]~E(x23011,x23012)+E(f845(x23013,x23014,x23015,x23011,x23016),f845(x23013,x23014,x23015,x23012,x23016)) % 178.07/177.95 [2302]~E(x23021,x23022)+E(f845(x23023,x23024,x23025,x23026,x23021),f845(x23023,x23024,x23025,x23026,x23022)) % 178.07/177.95 [2303]~E(x23031,x23032)+E(f222(x23031,x23033),f222(x23032,x23033)) % 178.07/177.95 [2304]~E(x23041,x23042)+E(f222(x23043,x23041),f222(x23043,x23042)) % 178.07/177.95 [2305]~E(x23051,x23052)+E(f483(x23051,x23053,x23054),f483(x23052,x23053,x23054)) % 178.07/177.95 [2306]~E(x23061,x23062)+E(f483(x23063,x23061,x23064),f483(x23063,x23062,x23064)) % 178.07/177.95 [2307]~E(x23071,x23072)+E(f483(x23073,x23074,x23071),f483(x23073,x23074,x23072)) % 178.07/177.95 [2308]~E(x23081,x23082)+E(f727(x23081,x23083,x23084),f727(x23082,x23083,x23084)) % 178.07/177.95 [2309]~E(x23091,x23092)+E(f727(x23093,x23091,x23094),f727(x23093,x23092,x23094)) % 178.07/177.95 [2310]~E(x23101,x23102)+E(f727(x23103,x23104,x23101),f727(x23103,x23104,x23102)) % 178.07/177.95 [2311]~E(x23111,x23112)+E(f239(x23111,x23113,x23114,x23115,x23116),f239(x23112,x23113,x23114,x23115,x23116)) % 178.07/177.95 [2312]~E(x23121,x23122)+E(f239(x23123,x23121,x23124,x23125,x23126),f239(x23123,x23122,x23124,x23125,x23126)) % 178.07/177.95 [2313]~E(x23131,x23132)+E(f239(x23133,x23134,x23131,x23135,x23136),f239(x23133,x23134,x23132,x23135,x23136)) % 178.07/177.95 [2314]~E(x23141,x23142)+E(f239(x23143,x23144,x23145,x23141,x23146),f239(x23143,x23144,x23145,x23142,x23146)) % 178.07/177.95 [2315]~E(x23151,x23152)+E(f239(x23153,x23154,x23155,x23156,x23151),f239(x23153,x23154,x23155,x23156,x23152)) % 178.07/177.95 [2316]~E(x23161,x23162)+E(f676(x23161,x23163,x23164,x23165,x23166),f676(x23162,x23163,x23164,x23165,x23166)) % 178.07/177.95 [2317]~E(x23171,x23172)+E(f676(x23173,x23171,x23174,x23175,x23176),f676(x23173,x23172,x23174,x23175,x23176)) % 178.07/177.95 [2318]~E(x23181,x23182)+E(f676(x23183,x23184,x23181,x23185,x23186),f676(x23183,x23184,x23182,x23185,x23186)) % 178.07/177.95 [2319]~E(x23191,x23192)+E(f676(x23193,x23194,x23195,x23191,x23196),f676(x23193,x23194,x23195,x23192,x23196)) % 178.07/177.95 [2320]~E(x23201,x23202)+E(f676(x23203,x23204,x23205,x23206,x23201),f676(x23203,x23204,x23205,x23206,x23202)) % 178.07/177.95 [2321]~E(x23211,x23212)+E(f386(x23211,x23213),f386(x23212,x23213)) % 178.07/177.95 [2322]~E(x23221,x23222)+E(f386(x23223,x23221),f386(x23223,x23222)) % 178.07/177.95 [2323]~E(x23231,x23232)+E(f411(x23231,x23233),f411(x23232,x23233)) % 178.07/177.95 [2324]~E(x23241,x23242)+E(f411(x23243,x23241),f411(x23243,x23242)) % 178.07/177.95 [2325]~E(x23251,x23252)+E(f863(x23251,x23253,x23254,x23255),f863(x23252,x23253,x23254,x23255)) % 178.07/177.95 [2326]~E(x23261,x23262)+E(f863(x23263,x23261,x23264,x23265),f863(x23263,x23262,x23264,x23265)) % 178.07/177.95 [2327]~E(x23271,x23272)+E(f863(x23273,x23274,x23271,x23275),f863(x23273,x23274,x23272,x23275)) % 178.07/177.95 [2328]~E(x23281,x23282)+E(f863(x23283,x23284,x23285,x23281),f863(x23283,x23284,x23285,x23282)) % 178.07/177.95 [2329]~E(x23291,x23292)+E(f834(x23291,x23293,x23294,x23295,x23296,x23297,x23298),f834(x23292,x23293,x23294,x23295,x23296,x23297,x23298)) % 178.07/177.95 [2330]~E(x23301,x23302)+E(f834(x23303,x23301,x23304,x23305,x23306,x23307,x23308),f834(x23303,x23302,x23304,x23305,x23306,x23307,x23308)) % 178.07/177.95 [2331]~E(x23311,x23312)+E(f834(x23313,x23314,x23311,x23315,x23316,x23317,x23318),f834(x23313,x23314,x23312,x23315,x23316,x23317,x23318)) % 178.07/177.95 [2332]~E(x23321,x23322)+E(f834(x23323,x23324,x23325,x23321,x23326,x23327,x23328),f834(x23323,x23324,x23325,x23322,x23326,x23327,x23328)) % 178.07/177.95 [2333]~E(x23331,x23332)+E(f834(x23333,x23334,x23335,x23336,x23331,x23337,x23338),f834(x23333,x23334,x23335,x23336,x23332,x23337,x23338)) % 178.07/177.95 [2334]~E(x23341,x23342)+E(f834(x23343,x23344,x23345,x23346,x23347,x23341,x23348),f834(x23343,x23344,x23345,x23346,x23347,x23342,x23348)) % 178.07/177.95 [2335]~E(x23351,x23352)+E(f834(x23353,x23354,x23355,x23356,x23357,x23358,x23351),f834(x23353,x23354,x23355,x23356,x23357,x23358,x23352)) % 178.07/177.95 [2336]~E(x23361,x23362)+E(f641(x23361,x23363,x23364),f641(x23362,x23363,x23364)) % 178.07/177.95 [2337]~E(x23371,x23372)+E(f641(x23373,x23371,x23374),f641(x23373,x23372,x23374)) % 178.07/177.95 [2338]~E(x23381,x23382)+E(f641(x23383,x23384,x23381),f641(x23383,x23384,x23382)) % 178.07/177.95 [2339]~E(x23391,x23392)+E(f854(x23391,x23393,x23394),f854(x23392,x23393,x23394)) % 178.07/177.95 [2340]~E(x23401,x23402)+E(f854(x23403,x23401,x23404),f854(x23403,x23402,x23404)) % 178.07/177.95 [2341]~E(x23411,x23412)+E(f854(x23413,x23414,x23411),f854(x23413,x23414,x23412)) % 178.07/177.95 [2342]~E(x23421,x23422)+E(f779(x23421,x23423),f779(x23422,x23423)) % 178.07/177.95 [2343]~E(x23431,x23432)+E(f779(x23433,x23431),f779(x23433,x23432)) % 178.07/177.95 [2344]~E(x23441,x23442)+E(f506(x23441,x23443,x23444,x23445),f506(x23442,x23443,x23444,x23445)) % 178.07/177.95 [2345]~E(x23451,x23452)+E(f506(x23453,x23451,x23454,x23455),f506(x23453,x23452,x23454,x23455)) % 178.07/177.95 [2346]~E(x23461,x23462)+E(f506(x23463,x23464,x23461,x23465),f506(x23463,x23464,x23462,x23465)) % 178.07/177.95 [2347]~E(x23471,x23472)+E(f506(x23473,x23474,x23475,x23471),f506(x23473,x23474,x23475,x23472)) % 178.07/177.95 [2348]~E(x23481,x23482)+E(f601(x23481,x23483,x23484),f601(x23482,x23483,x23484)) % 178.07/177.95 [2349]~E(x23491,x23492)+E(f601(x23493,x23491,x23494),f601(x23493,x23492,x23494)) % 178.07/177.95 [2350]~E(x23501,x23502)+E(f601(x23503,x23504,x23501),f601(x23503,x23504,x23502)) % 178.07/177.95 [2351]~E(x23511,x23512)+E(f738(x23511,x23513,x23514,x23515,x23516,x23517),f738(x23512,x23513,x23514,x23515,x23516,x23517)) % 178.07/177.95 [2352]~E(x23521,x23522)+E(f738(x23523,x23521,x23524,x23525,x23526,x23527),f738(x23523,x23522,x23524,x23525,x23526,x23527)) % 178.07/177.95 [2353]~E(x23531,x23532)+E(f738(x23533,x23534,x23531,x23535,x23536,x23537),f738(x23533,x23534,x23532,x23535,x23536,x23537)) % 178.07/177.95 [2354]~E(x23541,x23542)+E(f738(x23543,x23544,x23545,x23541,x23546,x23547),f738(x23543,x23544,x23545,x23542,x23546,x23547)) % 178.07/177.95 [2355]~E(x23551,x23552)+E(f738(x23553,x23554,x23555,x23556,x23551,x23557),f738(x23553,x23554,x23555,x23556,x23552,x23557)) % 178.07/177.95 [2356]~E(x23561,x23562)+E(f738(x23563,x23564,x23565,x23566,x23567,x23561),f738(x23563,x23564,x23565,x23566,x23567,x23562)) % 178.07/177.95 [2357]~E(x23571,x23572)+E(f743(x23571,x23573,x23574,x23575,x23576),f743(x23572,x23573,x23574,x23575,x23576)) % 178.07/177.95 [2358]~E(x23581,x23582)+E(f743(x23583,x23581,x23584,x23585,x23586),f743(x23583,x23582,x23584,x23585,x23586)) % 178.07/177.95 [2359]~E(x23591,x23592)+E(f743(x23593,x23594,x23591,x23595,x23596),f743(x23593,x23594,x23592,x23595,x23596)) % 178.07/177.95 [2360]~E(x23601,x23602)+E(f743(x23603,x23604,x23605,x23601,x23606),f743(x23603,x23604,x23605,x23602,x23606)) % 178.07/177.95 [2361]~E(x23611,x23612)+E(f743(x23613,x23614,x23615,x23616,x23611),f743(x23613,x23614,x23615,x23616,x23612)) % 178.07/177.95 [2362]~E(x23621,x23622)+E(f472(x23621,x23623,x23624),f472(x23622,x23623,x23624)) % 178.07/177.95 [2363]~E(x23631,x23632)+E(f472(x23633,x23631,x23634),f472(x23633,x23632,x23634)) % 178.07/177.95 [2364]~E(x23641,x23642)+E(f472(x23643,x23644,x23641),f472(x23643,x23644,x23642)) % 178.07/177.95 [2365]~E(x23651,x23652)+E(f226(x23651,x23653),f226(x23652,x23653)) % 178.07/177.95 [2366]~E(x23661,x23662)+E(f226(x23663,x23661),f226(x23663,x23662)) % 178.07/177.95 [2367]~E(x23671,x23672)+E(f552(x23671,x23673,x23674),f552(x23672,x23673,x23674)) % 178.07/177.95 [2368]~E(x23681,x23682)+E(f552(x23683,x23681,x23684),f552(x23683,x23682,x23684)) % 178.07/177.95 [2369]~E(x23691,x23692)+E(f552(x23693,x23694,x23691),f552(x23693,x23694,x23692)) % 178.07/177.95 [2370]~E(x23701,x23702)+E(f560(x23701,x23703,x23704),f560(x23702,x23703,x23704)) % 178.07/177.95 [2371]~E(x23711,x23712)+E(f560(x23713,x23711,x23714),f560(x23713,x23712,x23714)) % 178.07/177.95 [2372]~E(x23721,x23722)+E(f560(x23723,x23724,x23721),f560(x23723,x23724,x23722)) % 178.07/177.95 [2373]~E(x23731,x23732)+E(f524(x23731,x23733),f524(x23732,x23733)) % 178.07/177.95 [2374]~E(x23741,x23742)+E(f524(x23743,x23741),f524(x23743,x23742)) % 178.07/177.95 [2375]~E(x23751,x23752)+E(f777(x23751,x23753),f777(x23752,x23753)) % 178.07/177.95 [2376]~E(x23761,x23762)+E(f777(x23763,x23761),f777(x23763,x23762)) % 178.07/177.95 [2377]~E(x23771,x23772)+E(f123(x23771,x23773,x23774),f123(x23772,x23773,x23774)) % 178.07/177.95 [2378]~E(x23781,x23782)+E(f123(x23783,x23781,x23784),f123(x23783,x23782,x23784)) % 178.07/177.95 [2379]~E(x23791,x23792)+E(f123(x23793,x23794,x23791),f123(x23793,x23794,x23792)) % 178.07/177.95 [2380]~E(x23801,x23802)+E(f841(x23801,x23803,x23804,x23805,x23806),f841(x23802,x23803,x23804,x23805,x23806)) % 178.07/177.95 [2381]~E(x23811,x23812)+E(f841(x23813,x23811,x23814,x23815,x23816),f841(x23813,x23812,x23814,x23815,x23816)) % 178.07/177.95 [2382]~E(x23821,x23822)+E(f841(x23823,x23824,x23821,x23825,x23826),f841(x23823,x23824,x23822,x23825,x23826)) % 178.07/177.95 [2383]~E(x23831,x23832)+E(f841(x23833,x23834,x23835,x23831,x23836),f841(x23833,x23834,x23835,x23832,x23836)) % 178.07/177.95 [2384]~E(x23841,x23842)+E(f841(x23843,x23844,x23845,x23846,x23841),f841(x23843,x23844,x23845,x23846,x23842)) % 178.07/177.95 [2385]~E(x23851,x23852)+E(f697(x23851,x23853,x23854,x23855),f697(x23852,x23853,x23854,x23855)) % 178.07/177.95 [2386]~E(x23861,x23862)+E(f697(x23863,x23861,x23864,x23865),f697(x23863,x23862,x23864,x23865)) % 178.07/177.95 [2387]~E(x23871,x23872)+E(f697(x23873,x23874,x23871,x23875),f697(x23873,x23874,x23872,x23875)) % 178.07/177.95 [2388]~E(x23881,x23882)+E(f697(x23883,x23884,x23885,x23881),f697(x23883,x23884,x23885,x23882)) % 178.07/177.95 [2389]~E(x23891,x23892)+E(f387(x23891,x23893),f387(x23892,x23893)) % 178.07/177.95 [2390]~E(x23901,x23902)+E(f387(x23903,x23901),f387(x23903,x23902)) % 178.07/177.95 [2391]~E(x23911,x23912)+E(f205(x23911,x23913,x23914,x23915),f205(x23912,x23913,x23914,x23915)) % 178.07/177.95 [2392]~E(x23921,x23922)+E(f205(x23923,x23921,x23924,x23925),f205(x23923,x23922,x23924,x23925)) % 178.07/177.95 [2393]~E(x23931,x23932)+E(f205(x23933,x23934,x23931,x23935),f205(x23933,x23934,x23932,x23935)) % 178.07/177.95 [2394]~E(x23941,x23942)+E(f205(x23943,x23944,x23945,x23941),f205(x23943,x23944,x23945,x23942)) % 178.07/177.95 [2395]~E(x23951,x23952)+E(f453(x23951,x23953,x23954,x23955),f453(x23952,x23953,x23954,x23955)) % 178.07/177.95 [2396]~E(x23961,x23962)+E(f453(x23963,x23961,x23964,x23965),f453(x23963,x23962,x23964,x23965)) % 178.07/177.95 [2397]~E(x23971,x23972)+E(f453(x23973,x23974,x23971,x23975),f453(x23973,x23974,x23972,x23975)) % 178.07/177.95 [2398]~E(x23981,x23982)+E(f453(x23983,x23984,x23985,x23981),f453(x23983,x23984,x23985,x23982)) % 178.07/177.95 [2399]~E(x23991,x23992)+E(f538(x23991,x23993,x23994,x23995,x23996,x23997,x23998),f538(x23992,x23993,x23994,x23995,x23996,x23997,x23998)) % 178.07/177.95 [2400]~E(x24001,x24002)+E(f538(x24003,x24001,x24004,x24005,x24006,x24007,x24008),f538(x24003,x24002,x24004,x24005,x24006,x24007,x24008)) % 178.07/177.95 [2401]~E(x24011,x24012)+E(f538(x24013,x24014,x24011,x24015,x24016,x24017,x24018),f538(x24013,x24014,x24012,x24015,x24016,x24017,x24018)) % 178.07/177.95 [2402]~E(x24021,x24022)+E(f538(x24023,x24024,x24025,x24021,x24026,x24027,x24028),f538(x24023,x24024,x24025,x24022,x24026,x24027,x24028)) % 178.07/177.95 [2403]~E(x24031,x24032)+E(f538(x24033,x24034,x24035,x24036,x24031,x24037,x24038),f538(x24033,x24034,x24035,x24036,x24032,x24037,x24038)) % 178.07/177.95 [2404]~E(x24041,x24042)+E(f538(x24043,x24044,x24045,x24046,x24047,x24041,x24048),f538(x24043,x24044,x24045,x24046,x24047,x24042,x24048)) % 178.07/177.95 [2405]~E(x24051,x24052)+E(f538(x24053,x24054,x24055,x24056,x24057,x24058,x24051),f538(x24053,x24054,x24055,x24056,x24057,x24058,x24052)) % 178.07/177.95 [2406]~E(x24061,x24062)+E(f396(x24061,x24063,x24064,x24065,x24066,x24067),f396(x24062,x24063,x24064,x24065,x24066,x24067)) % 178.07/177.95 [2407]~E(x24071,x24072)+E(f396(x24073,x24071,x24074,x24075,x24076,x24077),f396(x24073,x24072,x24074,x24075,x24076,x24077)) % 178.07/177.95 [2408]~E(x24081,x24082)+E(f396(x24083,x24084,x24081,x24085,x24086,x24087),f396(x24083,x24084,x24082,x24085,x24086,x24087)) % 178.07/177.95 [2409]~E(x24091,x24092)+E(f396(x24093,x24094,x24095,x24091,x24096,x24097),f396(x24093,x24094,x24095,x24092,x24096,x24097)) % 178.07/177.95 [2410]~E(x24101,x24102)+E(f396(x24103,x24104,x24105,x24106,x24101,x24107),f396(x24103,x24104,x24105,x24106,x24102,x24107)) % 178.07/177.95 [2411]~E(x24111,x24112)+E(f396(x24113,x24114,x24115,x24116,x24117,x24111),f396(x24113,x24114,x24115,x24116,x24117,x24112)) % 178.07/177.95 [2412]~E(x24121,x24122)+E(f486(x24121,x24123),f486(x24122,x24123)) % 178.07/177.95 [2413]~E(x24131,x24132)+E(f486(x24133,x24131),f486(x24133,x24132)) % 178.07/177.95 [2414]~E(x24141,x24142)+E(f393(x24141,x24143,x24144),f393(x24142,x24143,x24144)) % 178.07/177.95 [2415]~E(x24151,x24152)+E(f393(x24153,x24151,x24154),f393(x24153,x24152,x24154)) % 178.07/177.95 [2416]~E(x24161,x24162)+E(f393(x24163,x24164,x24161),f393(x24163,x24164,x24162)) % 178.07/177.95 [2417]~E(x24171,x24172)+E(f290(x24171,x24173,x24174),f290(x24172,x24173,x24174)) % 178.07/177.95 [2418]~E(x24181,x24182)+E(f290(x24183,x24181,x24184),f290(x24183,x24182,x24184)) % 178.07/177.95 [2419]~E(x24191,x24192)+E(f290(x24193,x24194,x24191),f290(x24193,x24194,x24192)) % 178.07/177.95 [2420]~E(x24201,x24202)+E(f410(x24201,x24203,x24204),f410(x24202,x24203,x24204)) % 178.07/177.95 [2421]~E(x24211,x24212)+E(f410(x24213,x24211,x24214),f410(x24213,x24212,x24214)) % 178.07/177.95 [2422]~E(x24221,x24222)+E(f410(x24223,x24224,x24221),f410(x24223,x24224,x24222)) % 178.07/177.95 [2423]~E(x24231,x24232)+E(f645(x24231,x24233,x24234,x24235),f645(x24232,x24233,x24234,x24235)) % 178.07/177.95 [2424]~E(x24241,x24242)+E(f645(x24243,x24241,x24244,x24245),f645(x24243,x24242,x24244,x24245)) % 178.07/177.95 [2425]~E(x24251,x24252)+E(f645(x24253,x24254,x24251,x24255),f645(x24253,x24254,x24252,x24255)) % 178.07/177.95 [2426]~E(x24261,x24262)+E(f645(x24263,x24264,x24265,x24261),f645(x24263,x24264,x24265,x24262)) % 178.07/177.95 [2427]~E(x24271,x24272)+E(f441(x24271,x24273,x24274,x24275),f441(x24272,x24273,x24274,x24275)) % 178.07/177.95 [2428]~E(x24281,x24282)+E(f441(x24283,x24281,x24284,x24285),f441(x24283,x24282,x24284,x24285)) % 178.07/177.95 [2429]~E(x24291,x24292)+E(f441(x24293,x24294,x24291,x24295),f441(x24293,x24294,x24292,x24295)) % 178.07/177.95 [2430]~E(x24301,x24302)+E(f441(x24303,x24304,x24305,x24301),f441(x24303,x24304,x24305,x24302)) % 178.07/177.95 [2431]~E(x24311,x24312)+E(f609(x24311,x24313,x24314,x24315,x24316),f609(x24312,x24313,x24314,x24315,x24316)) % 178.07/177.95 [2432]~E(x24321,x24322)+E(f609(x24323,x24321,x24324,x24325,x24326),f609(x24323,x24322,x24324,x24325,x24326)) % 178.07/177.95 [2433]~E(x24331,x24332)+E(f609(x24333,x24334,x24331,x24335,x24336),f609(x24333,x24334,x24332,x24335,x24336)) % 178.07/177.95 [2434]~E(x24341,x24342)+E(f609(x24343,x24344,x24345,x24341,x24346),f609(x24343,x24344,x24345,x24342,x24346)) % 178.07/177.95 [2435]~E(x24351,x24352)+E(f609(x24353,x24354,x24355,x24356,x24351),f609(x24353,x24354,x24355,x24356,x24352)) % 178.07/177.95 [2436]~E(x24361,x24362)+E(f487(x24361,x24363,x24364),f487(x24362,x24363,x24364)) % 178.07/177.95 [2437]~E(x24371,x24372)+E(f487(x24373,x24371,x24374),f487(x24373,x24372,x24374)) % 178.07/177.95 [2438]~E(x24381,x24382)+E(f487(x24383,x24384,x24381),f487(x24383,x24384,x24382)) % 178.07/177.95 [2439]~E(x24391,x24392)+E(f485(x24391,x24393,x24394),f485(x24392,x24393,x24394)) % 178.07/177.95 [2440]~E(x24401,x24402)+E(f485(x24403,x24401,x24404),f485(x24403,x24402,x24404)) % 178.07/177.95 [2441]~E(x24411,x24412)+E(f485(x24413,x24414,x24411),f485(x24413,x24414,x24412)) % 178.07/177.95 [2442]~E(x24421,x24422)+E(f313(x24421,x24423,x24424),f313(x24422,x24423,x24424)) % 178.07/177.95 [2443]~E(x24431,x24432)+E(f313(x24433,x24431,x24434),f313(x24433,x24432,x24434)) % 178.07/177.95 [2444]~E(x24441,x24442)+E(f313(x24443,x24444,x24441),f313(x24443,x24444,x24442)) % 178.07/177.95 [2445]~E(x24451,x24452)+E(f413(x24451,x24453),f413(x24452,x24453)) % 178.07/177.95 [2446]~E(x24461,x24462)+E(f413(x24463,x24461),f413(x24463,x24462)) % 178.07/177.95 [2447]~E(x24471,x24472)+E(f490(x24471,x24473,x24474,x24475),f490(x24472,x24473,x24474,x24475)) % 178.07/177.95 [2448]~E(x24481,x24482)+E(f490(x24483,x24481,x24484,x24485),f490(x24483,x24482,x24484,x24485)) % 178.07/177.95 [2449]~E(x24491,x24492)+E(f490(x24493,x24494,x24491,x24495),f490(x24493,x24494,x24492,x24495)) % 178.07/177.95 [2450]~E(x24501,x24502)+E(f490(x24503,x24504,x24505,x24501),f490(x24503,x24504,x24505,x24502)) % 178.07/177.95 [2451]~E(x24511,x24512)+E(f772(x24511,x24513,x24514,x24515),f772(x24512,x24513,x24514,x24515)) % 178.07/177.95 [2452]~E(x24521,x24522)+E(f772(x24523,x24521,x24524,x24525),f772(x24523,x24522,x24524,x24525)) % 178.07/177.95 [2453]~E(x24531,x24532)+E(f772(x24533,x24534,x24531,x24535),f772(x24533,x24534,x24532,x24535)) % 178.07/177.95 [2454]~E(x24541,x24542)+E(f772(x24543,x24544,x24545,x24541),f772(x24543,x24544,x24545,x24542)) % 178.07/177.95 [2455]~E(x24551,x24552)+E(f847(x24551,x24553,x24554,x24555,x24556),f847(x24552,x24553,x24554,x24555,x24556)) % 178.07/177.95 [2456]~E(x24561,x24562)+E(f847(x24563,x24561,x24564,x24565,x24566),f847(x24563,x24562,x24564,x24565,x24566)) % 178.07/177.95 [2457]~E(x24571,x24572)+E(f847(x24573,x24574,x24571,x24575,x24576),f847(x24573,x24574,x24572,x24575,x24576)) % 178.07/177.95 [2458]~E(x24581,x24582)+E(f847(x24583,x24584,x24585,x24581,x24586),f847(x24583,x24584,x24585,x24582,x24586)) % 178.07/177.95 [2459]~E(x24591,x24592)+E(f847(x24593,x24594,x24595,x24596,x24591),f847(x24593,x24594,x24595,x24596,x24592)) % 178.07/177.95 [2460]~E(x24601,x24602)+E(f791(x24601,x24603,x24604),f791(x24602,x24603,x24604)) % 178.07/177.95 [2461]~E(x24611,x24612)+E(f791(x24613,x24611,x24614),f791(x24613,x24612,x24614)) % 178.07/177.95 [2462]~E(x24621,x24622)+E(f791(x24623,x24624,x24621),f791(x24623,x24624,x24622)) % 178.07/177.95 [2463]~E(x24631,x24632)+E(f351(x24631,x24633,x24634,x24635,x24636),f351(x24632,x24633,x24634,x24635,x24636)) % 178.07/177.95 [2464]~E(x24641,x24642)+E(f351(x24643,x24641,x24644,x24645,x24646),f351(x24643,x24642,x24644,x24645,x24646)) % 178.07/177.95 [2465]~E(x24651,x24652)+E(f351(x24653,x24654,x24651,x24655,x24656),f351(x24653,x24654,x24652,x24655,x24656)) % 178.07/177.95 [2466]~E(x24661,x24662)+E(f351(x24663,x24664,x24665,x24661,x24666),f351(x24663,x24664,x24665,x24662,x24666)) % 178.07/177.95 [2467]~E(x24671,x24672)+E(f351(x24673,x24674,x24675,x24676,x24671),f351(x24673,x24674,x24675,x24676,x24672)) % 178.07/177.95 [2468]~E(x24681,x24682)+E(f591(x24681),f591(x24682)) % 178.07/177.95 [2469]~E(x24691,x24692)+E(f615(x24691,x24693,x24694,x24695,x24696,x24697,x24698,x24699),f615(x24692,x24693,x24694,x24695,x24696,x24697,x24698,x24699)) % 178.07/177.95 [2470]~E(x24701,x24702)+E(f615(x24703,x24701,x24704,x24705,x24706,x24707,x24708,x24709),f615(x24703,x24702,x24704,x24705,x24706,x24707,x24708,x24709)) % 178.07/177.95 [2471]~E(x24711,x24712)+E(f615(x24713,x24714,x24711,x24715,x24716,x24717,x24718,x24719),f615(x24713,x24714,x24712,x24715,x24716,x24717,x24718,x24719)) % 178.07/177.95 [2472]~E(x24721,x24722)+E(f615(x24723,x24724,x24725,x24721,x24726,x24727,x24728,x24729),f615(x24723,x24724,x24725,x24722,x24726,x24727,x24728,x24729)) % 178.07/177.95 [2473]~E(x24731,x24732)+E(f615(x24733,x24734,x24735,x24736,x24731,x24737,x24738,x24739),f615(x24733,x24734,x24735,x24736,x24732,x24737,x24738,x24739)) % 178.07/177.95 [2474]~E(x24741,x24742)+E(f615(x24743,x24744,x24745,x24746,x24747,x24741,x24748,x24749),f615(x24743,x24744,x24745,x24746,x24747,x24742,x24748,x24749)) % 178.07/177.95 [2475]~E(x24751,x24752)+E(f615(x24753,x24754,x24755,x24756,x24757,x24758,x24751,x24759),f615(x24753,x24754,x24755,x24756,x24757,x24758,x24752,x24759)) % 178.07/177.95 [2476]~E(x24761,x24762)+E(f615(x24763,x24764,x24765,x24766,x24767,x24768,x24769,x24761),f615(x24763,x24764,x24765,x24766,x24767,x24768,x24769,x24762)) % 178.07/177.95 [2477]~E(x24771,x24772)+E(f843(x24771,x24773,x24774,x24775,x24776),f843(x24772,x24773,x24774,x24775,x24776)) % 178.07/177.95 [2478]~E(x24781,x24782)+E(f843(x24783,x24781,x24784,x24785,x24786),f843(x24783,x24782,x24784,x24785,x24786)) % 178.07/177.95 [2479]~E(x24791,x24792)+E(f843(x24793,x24794,x24791,x24795,x24796),f843(x24793,x24794,x24792,x24795,x24796)) % 178.07/177.95 [2480]~E(x24801,x24802)+E(f843(x24803,x24804,x24805,x24801,x24806),f843(x24803,x24804,x24805,x24802,x24806)) % 178.07/177.95 [2481]~E(x24811,x24812)+E(f843(x24813,x24814,x24815,x24816,x24811),f843(x24813,x24814,x24815,x24816,x24812)) % 178.07/177.95 [2482]~E(x24821,x24822)+E(f582(x24821,x24823),f582(x24822,x24823)) % 178.07/177.95 [2483]~E(x24831,x24832)+E(f582(x24833,x24831),f582(x24833,x24832)) % 178.07/177.95 [2484]~E(x24841,x24842)+E(f842(x24841,x24843),f842(x24842,x24843)) % 178.07/177.95 [2485]~E(x24851,x24852)+E(f842(x24853,x24851),f842(x24853,x24852)) % 178.07/177.95 [2486]~E(x24861,x24862)+E(f694(x24861,x24863),f694(x24862,x24863)) % 178.07/177.95 [2487]~E(x24871,x24872)+E(f694(x24873,x24871),f694(x24873,x24872)) % 178.07/177.95 [2488]~E(x24881,x24882)+E(f537(x24881,x24883,x24884,x24885,x24886),f537(x24882,x24883,x24884,x24885,x24886)) % 178.07/177.95 [2489]~E(x24891,x24892)+E(f537(x24893,x24891,x24894,x24895,x24896),f537(x24893,x24892,x24894,x24895,x24896)) % 178.07/177.95 [2490]~E(x24901,x24902)+E(f537(x24903,x24904,x24901,x24905,x24906),f537(x24903,x24904,x24902,x24905,x24906)) % 178.07/177.95 [2491]~E(x24911,x24912)+E(f537(x24913,x24914,x24915,x24911,x24916),f537(x24913,x24914,x24915,x24912,x24916)) % 178.07/177.95 [2492]~E(x24921,x24922)+E(f537(x24923,x24924,x24925,x24926,x24921),f537(x24923,x24924,x24925,x24926,x24922)) % 178.07/177.95 [2493]~E(x24931,x24932)+E(f451(x24931,x24933,x24934,x24935),f451(x24932,x24933,x24934,x24935)) % 178.07/177.95 [2494]~E(x24941,x24942)+E(f451(x24943,x24941,x24944,x24945),f451(x24943,x24942,x24944,x24945)) % 178.07/177.95 [2495]~E(x24951,x24952)+E(f451(x24953,x24954,x24951,x24955),f451(x24953,x24954,x24952,x24955)) % 178.07/177.95 [2496]~E(x24961,x24962)+E(f451(x24963,x24964,x24965,x24961),f451(x24963,x24964,x24965,x24962)) % 178.07/177.95 [2497]~E(x24971,x24972)+E(f723(x24971,x24973,x24974,x24975,x24976,x24977),f723(x24972,x24973,x24974,x24975,x24976,x24977)) % 178.07/177.95 [2498]~E(x24981,x24982)+E(f723(x24983,x24981,x24984,x24985,x24986,x24987),f723(x24983,x24982,x24984,x24985,x24986,x24987)) % 178.07/177.95 [2499]~E(x24991,x24992)+E(f723(x24993,x24994,x24991,x24995,x24996,x24997),f723(x24993,x24994,x24992,x24995,x24996,x24997)) % 178.07/177.95 [2500]~E(x25001,x25002)+E(f723(x25003,x25004,x25005,x25001,x25006,x25007),f723(x25003,x25004,x25005,x25002,x25006,x25007)) % 178.07/177.95 [2501]~E(x25011,x25012)+E(f723(x25013,x25014,x25015,x25016,x25011,x25017),f723(x25013,x25014,x25015,x25016,x25012,x25017)) % 178.07/177.95 [2502]~E(x25021,x25022)+E(f723(x25023,x25024,x25025,x25026,x25027,x25021),f723(x25023,x25024,x25025,x25026,x25027,x25022)) % 178.07/177.95 [2503]~E(x25031,x25032)+E(f531(x25031,x25033,x25034),f531(x25032,x25033,x25034)) % 178.07/177.95 [2504]~E(x25041,x25042)+E(f531(x25043,x25041,x25044),f531(x25043,x25042,x25044)) % 178.07/177.95 [2505]~E(x25051,x25052)+E(f531(x25053,x25054,x25051),f531(x25053,x25054,x25052)) % 178.07/177.95 [2506]~E(x25061,x25062)+E(f547(x25061,x25063,x25064),f547(x25062,x25063,x25064)) % 178.07/177.95 [2507]~E(x25071,x25072)+E(f547(x25073,x25071,x25074),f547(x25073,x25072,x25074)) % 178.07/177.95 [2508]~E(x25081,x25082)+E(f547(x25083,x25084,x25081),f547(x25083,x25084,x25082)) % 178.07/177.95 [2509]~E(x25091,x25092)+E(f823(x25091,x25093,x25094,x25095,x25096),f823(x25092,x25093,x25094,x25095,x25096)) % 178.07/177.95 [2510]~E(x25101,x25102)+E(f823(x25103,x25101,x25104,x25105,x25106),f823(x25103,x25102,x25104,x25105,x25106)) % 178.07/177.95 [2511]~E(x25111,x25112)+E(f823(x25113,x25114,x25111,x25115,x25116),f823(x25113,x25114,x25112,x25115,x25116)) % 178.07/177.95 [2512]~E(x25121,x25122)+E(f823(x25123,x25124,x25125,x25121,x25126),f823(x25123,x25124,x25125,x25122,x25126)) % 178.07/177.95 [2513]~E(x25131,x25132)+E(f823(x25133,x25134,x25135,x25136,x25131),f823(x25133,x25134,x25135,x25136,x25132)) % 178.07/177.95 [2514]~E(x25141,x25142)+E(f442(x25141,x25143,x25144,x25145),f442(x25142,x25143,x25144,x25145)) % 178.07/177.95 [2515]~E(x25151,x25152)+E(f442(x25153,x25151,x25154,x25155),f442(x25153,x25152,x25154,x25155)) % 178.07/177.95 [2516]~E(x25161,x25162)+E(f442(x25163,x25164,x25161,x25165),f442(x25163,x25164,x25162,x25165)) % 178.07/177.95 [2517]~E(x25171,x25172)+E(f442(x25173,x25174,x25175,x25171),f442(x25173,x25174,x25175,x25172)) % 178.07/177.95 [2518]~E(x25181,x25182)+E(f605(x25181,x25183,x25184,x25185),f605(x25182,x25183,x25184,x25185)) % 178.07/177.95 [2519]~E(x25191,x25192)+E(f605(x25193,x25191,x25194,x25195),f605(x25193,x25192,x25194,x25195)) % 178.07/177.95 [2520]~E(x25201,x25202)+E(f605(x25203,x25204,x25201,x25205),f605(x25203,x25204,x25202,x25205)) % 178.07/177.95 [2521]~E(x25211,x25212)+E(f605(x25213,x25214,x25215,x25211),f605(x25213,x25214,x25215,x25212)) % 178.07/177.95 [2522]~E(x25221,x25222)+E(f868(x25221,x25223,x25224,x25225,x25226),f868(x25222,x25223,x25224,x25225,x25226)) % 178.07/177.95 [2523]~E(x25231,x25232)+E(f868(x25233,x25231,x25234,x25235,x25236),f868(x25233,x25232,x25234,x25235,x25236)) % 178.07/177.95 [2524]~E(x25241,x25242)+E(f868(x25243,x25244,x25241,x25245,x25246),f868(x25243,x25244,x25242,x25245,x25246)) % 178.07/177.95 [2525]~E(x25251,x25252)+E(f868(x25253,x25254,x25255,x25251,x25256),f868(x25253,x25254,x25255,x25252,x25256)) % 178.07/177.95 [2526]~E(x25261,x25262)+E(f868(x25263,x25264,x25265,x25266,x25261),f868(x25263,x25264,x25265,x25266,x25262)) % 178.07/177.95 [2527]~E(x25271,x25272)+E(f96(x25271),f96(x25272)) % 178.07/177.95 [2528]~E(x25281,x25282)+E(f336(x25281),f336(x25282)) % 178.07/177.95 [2529]~E(x25291,x25292)+E(f271(x25291,x25293,x25294,x25295,x25296),f271(x25292,x25293,x25294,x25295,x25296)) % 178.07/177.95 [2530]~E(x25301,x25302)+E(f271(x25303,x25301,x25304,x25305,x25306),f271(x25303,x25302,x25304,x25305,x25306)) % 178.07/177.95 [2531]~E(x25311,x25312)+E(f271(x25313,x25314,x25311,x25315,x25316),f271(x25313,x25314,x25312,x25315,x25316)) % 178.07/177.95 [2532]~E(x25321,x25322)+E(f271(x25323,x25324,x25325,x25321,x25326),f271(x25323,x25324,x25325,x25322,x25326)) % 178.07/177.95 [2533]~E(x25331,x25332)+E(f271(x25333,x25334,x25335,x25336,x25331),f271(x25333,x25334,x25335,x25336,x25332)) % 178.07/177.95 [2534]~E(x25341,x25342)+E(f849(x25341,x25343,x25344,x25345,x25346),f849(x25342,x25343,x25344,x25345,x25346)) % 178.07/177.95 [2535]~E(x25351,x25352)+E(f849(x25353,x25351,x25354,x25355,x25356),f849(x25353,x25352,x25354,x25355,x25356)) % 178.07/177.95 [2536]~E(x25361,x25362)+E(f849(x25363,x25364,x25361,x25365,x25366),f849(x25363,x25364,x25362,x25365,x25366)) % 178.07/177.95 [2537]~E(x25371,x25372)+E(f849(x25373,x25374,x25375,x25371,x25376),f849(x25373,x25374,x25375,x25372,x25376)) % 178.07/177.95 [2538]~E(x25381,x25382)+E(f849(x25383,x25384,x25385,x25386,x25381),f849(x25383,x25384,x25385,x25386,x25382)) % 178.07/177.95 [2539]~E(x25391,x25392)+E(f457(x25391,x25393,x25394,x25395,x25396),f457(x25392,x25393,x25394,x25395,x25396)) % 178.07/177.95 [2540]~E(x25401,x25402)+E(f457(x25403,x25401,x25404,x25405,x25406),f457(x25403,x25402,x25404,x25405,x25406)) % 178.07/177.95 [2541]~E(x25411,x25412)+E(f457(x25413,x25414,x25411,x25415,x25416),f457(x25413,x25414,x25412,x25415,x25416)) % 178.07/177.95 [2542]~E(x25421,x25422)+E(f457(x25423,x25424,x25425,x25421,x25426),f457(x25423,x25424,x25425,x25422,x25426)) % 178.07/177.95 [2543]~E(x25431,x25432)+E(f457(x25433,x25434,x25435,x25436,x25431),f457(x25433,x25434,x25435,x25436,x25432)) % 178.07/177.95 [2544]~E(x25441,x25442)+E(f787(x25441,x25443,x25444),f787(x25442,x25443,x25444)) % 178.07/177.95 [2545]~E(x25451,x25452)+E(f787(x25453,x25451,x25454),f787(x25453,x25452,x25454)) % 178.07/177.95 [2546]~E(x25461,x25462)+E(f787(x25463,x25464,x25461),f787(x25463,x25464,x25462)) % 178.07/177.95 [2547]~E(x25471,x25472)+E(f536(x25471,x25473,x25474),f536(x25472,x25473,x25474)) % 178.07/177.95 [2548]~E(x25481,x25482)+E(f536(x25483,x25481,x25484),f536(x25483,x25482,x25484)) % 178.07/177.95 [2549]~E(x25491,x25492)+E(f536(x25493,x25494,x25491),f536(x25493,x25494,x25492)) % 178.07/177.95 [2550]~E(x25501,x25502)+E(f658(x25501,x25503,x25504),f658(x25502,x25503,x25504)) % 178.07/177.95 [2551]~E(x25511,x25512)+E(f658(x25513,x25511,x25514),f658(x25513,x25512,x25514)) % 178.07/177.95 [2552]~E(x25521,x25522)+E(f658(x25523,x25524,x25521),f658(x25523,x25524,x25522)) % 178.07/177.95 [2553]~E(x25531,x25532)+E(f737(x25531,x25533,x25534,x25535,x25536),f737(x25532,x25533,x25534,x25535,x25536)) % 178.07/177.95 [2554]~E(x25541,x25542)+E(f737(x25543,x25541,x25544,x25545,x25546),f737(x25543,x25542,x25544,x25545,x25546)) % 178.07/177.95 [2555]~E(x25551,x25552)+E(f737(x25553,x25554,x25551,x25555,x25556),f737(x25553,x25554,x25552,x25555,x25556)) % 178.07/177.95 [2556]~E(x25561,x25562)+E(f737(x25563,x25564,x25565,x25561,x25566),f737(x25563,x25564,x25565,x25562,x25566)) % 178.07/177.95 [2557]~E(x25571,x25572)+E(f737(x25573,x25574,x25575,x25576,x25571),f737(x25573,x25574,x25575,x25576,x25572)) % 178.07/177.95 [2558]~E(x25581,x25582)+E(f312(x25581,x25583,x25584),f312(x25582,x25583,x25584)) % 178.07/177.95 [2559]~E(x25591,x25592)+E(f312(x25593,x25591,x25594),f312(x25593,x25592,x25594)) % 178.07/177.95 [2560]~E(x25601,x25602)+E(f312(x25603,x25604,x25601),f312(x25603,x25604,x25602)) % 178.07/177.95 [2561]~E(x25611,x25612)+E(f414(x25611,x25613),f414(x25612,x25613)) % 178.07/177.95 [2562]~E(x25621,x25622)+E(f414(x25623,x25621),f414(x25623,x25622)) % 178.07/177.95 [2563]~E(x25631,x25632)+E(f802(x25631,x25633,x25634),f802(x25632,x25633,x25634)) % 178.07/177.95 [2564]~E(x25641,x25642)+E(f802(x25643,x25641,x25644),f802(x25643,x25642,x25644)) % 178.07/177.95 [2565]~E(x25651,x25652)+E(f802(x25653,x25654,x25651),f802(x25653,x25654,x25652)) % 178.07/177.95 [2566]~E(x25661,x25662)+E(f353(x25661,x25663,x25664,x25665,x25666),f353(x25662,x25663,x25664,x25665,x25666)) % 178.07/177.95 [2567]~E(x25671,x25672)+E(f353(x25673,x25671,x25674,x25675,x25676),f353(x25673,x25672,x25674,x25675,x25676)) % 178.07/177.95 [2568]~E(x25681,x25682)+E(f353(x25683,x25684,x25681,x25685,x25686),f353(x25683,x25684,x25682,x25685,x25686)) % 178.07/177.95 [2569]~E(x25691,x25692)+E(f353(x25693,x25694,x25695,x25691,x25696),f353(x25693,x25694,x25695,x25692,x25696)) % 178.07/177.95 [2570]~E(x25701,x25702)+E(f353(x25703,x25704,x25705,x25706,x25701),f353(x25703,x25704,x25705,x25706,x25702)) % 178.07/177.95 [2571]~E(x25711,x25712)+E(f230(x25711,x25713,x25714,x25715),f230(x25712,x25713,x25714,x25715)) % 178.07/177.95 [2572]~E(x25721,x25722)+E(f230(x25723,x25721,x25724,x25725),f230(x25723,x25722,x25724,x25725)) % 178.07/177.95 [2573]~E(x25731,x25732)+E(f230(x25733,x25734,x25731,x25735),f230(x25733,x25734,x25732,x25735)) % 178.07/177.95 [2574]~E(x25741,x25742)+E(f230(x25743,x25744,x25745,x25741),f230(x25743,x25744,x25745,x25742)) % 178.07/177.95 [2575]~E(x25751,x25752)+E(f449(x25751,x25753),f449(x25752,x25753)) % 178.07/177.95 [2576]~E(x25761,x25762)+E(f449(x25763,x25761),f449(x25763,x25762)) % 178.07/177.95 [2577]~E(x25771,x25772)+E(f691(x25771,x25773,x25774,x25775),f691(x25772,x25773,x25774,x25775)) % 178.07/177.95 [2578]~E(x25781,x25782)+E(f691(x25783,x25781,x25784,x25785),f691(x25783,x25782,x25784,x25785)) % 178.07/177.95 [2579]~E(x25791,x25792)+E(f691(x25793,x25794,x25791,x25795),f691(x25793,x25794,x25792,x25795)) % 178.07/177.95 [2580]~E(x25801,x25802)+E(f691(x25803,x25804,x25805,x25801),f691(x25803,x25804,x25805,x25802)) % 178.07/177.95 [2581]~E(x25811,x25812)+E(f448(x25811,x25813),f448(x25812,x25813)) % 178.07/177.95 [2582]~E(x25821,x25822)+E(f448(x25823,x25821),f448(x25823,x25822)) % 178.07/177.95 [2583]~E(x25831,x25832)+E(f130(x25831),f130(x25832)) % 178.07/177.95 [2584]~E(x25841,x25842)+E(f703(x25841,x25843,x25844,x25845),f703(x25842,x25843,x25844,x25845)) % 178.07/177.95 [2585]~E(x25851,x25852)+E(f703(x25853,x25851,x25854,x25855),f703(x25853,x25852,x25854,x25855)) % 178.07/177.95 [2586]~E(x25861,x25862)+E(f703(x25863,x25864,x25861,x25865),f703(x25863,x25864,x25862,x25865)) % 178.07/177.95 [2587]~E(x25871,x25872)+E(f703(x25873,x25874,x25875,x25871),f703(x25873,x25874,x25875,x25872)) % 178.07/177.95 [2588]~E(x25881,x25882)+E(f502(x25881,x25883,x25884),f502(x25882,x25883,x25884)) % 178.07/177.95 [2589]~E(x25891,x25892)+E(f502(x25893,x25891,x25894),f502(x25893,x25892,x25894)) % 178.07/177.95 [2590]~E(x25901,x25902)+E(f502(x25903,x25904,x25901),f502(x25903,x25904,x25902)) % 178.07/177.95 [2591]~E(x25911,x25912)+E(f704(x25911,x25913,x25914,x25915),f704(x25912,x25913,x25914,x25915)) % 178.07/177.95 [2592]~E(x25921,x25922)+E(f704(x25923,x25921,x25924,x25925),f704(x25923,x25922,x25924,x25925)) % 178.07/177.95 [2593]~E(x25931,x25932)+E(f704(x25933,x25934,x25931,x25935),f704(x25933,x25934,x25932,x25935)) % 178.07/177.95 [2594]~E(x25941,x25942)+E(f704(x25943,x25944,x25945,x25941),f704(x25943,x25944,x25945,x25942)) % 178.07/177.95 [2595]~E(x25951,x25952)+E(f570(x25951,x25953,x25954,x25955,x25956),f570(x25952,x25953,x25954,x25955,x25956)) % 178.07/177.95 [2596]~E(x25961,x25962)+E(f570(x25963,x25961,x25964,x25965,x25966),f570(x25963,x25962,x25964,x25965,x25966)) % 178.07/177.95 [2597]~E(x25971,x25972)+E(f570(x25973,x25974,x25971,x25975,x25976),f570(x25973,x25974,x25972,x25975,x25976)) % 178.07/177.95 [2598]~E(x25981,x25982)+E(f570(x25983,x25984,x25985,x25981,x25986),f570(x25983,x25984,x25985,x25982,x25986)) % 178.07/177.95 [2599]~E(x25991,x25992)+E(f570(x25993,x25994,x25995,x25996,x25991),f570(x25993,x25994,x25995,x25996,x25992)) % 178.07/177.95 [2600]~P1(x26001)+P1(x26002)+~E(x26001,x26002) % 178.07/177.95 [2601]~P4(x26011)+P4(x26012)+~E(x26011,x26012) % 178.07/177.95 [2602]~P24(x26021)+P24(x26022)+~E(x26021,x26022) % 178.07/177.95 [2603]~P25(x26031)+P25(x26032)+~E(x26031,x26032) % 178.07/177.95 [2604]~P105(x26041)+P105(x26042)+~E(x26041,x26042) % 178.07/177.95 [2605]~P26(x26051)+P26(x26052)+~E(x26051,x26052) % 178.07/177.95 [2606]P29(x26062,x26063)+~E(x26061,x26062)+~P29(x26061,x26063) % 178.07/177.95 [2607]P29(x26073,x26072)+~E(x26071,x26072)+~P29(x26073,x26071) % 178.07/177.95 [2608]~P63(x26081)+P63(x26082)+~E(x26081,x26082) % 178.07/177.95 [2609]~P86(x26091)+P86(x26092)+~E(x26091,x26092) % 178.07/177.95 [2610]~P117(x26101)+P117(x26102)+~E(x26101,x26102) % 178.07/177.95 [2611]~P64(x26111)+P64(x26112)+~E(x26111,x26112) % 178.07/177.95 [2612]~P99(x26121)+P99(x26122)+~E(x26121,x26122) % 178.07/177.95 [2613]~P62(x26131)+P62(x26132)+~E(x26131,x26132) % 178.07/177.95 [2614]~P77(x26141)+P77(x26142)+~E(x26141,x26142) % 178.07/177.95 [2615]~P65(x26151)+P65(x26152)+~E(x26151,x26152) % 178.07/177.95 [2616]~P27(x26161)+P27(x26162)+~E(x26161,x26162) % 178.07/177.95 [2617]~P107(x26171)+P107(x26172)+~E(x26171,x26172) % 178.07/177.95 [2618]~P92(x26181)+P92(x26182)+~E(x26181,x26182) % 178.07/177.95 [2619]P33(x26192,x26193,x26194,x26195)+~E(x26191,x26192)+~P33(x26191,x26193,x26194,x26195) % 178.07/177.95 [2620]P33(x26203,x26202,x26204,x26205)+~E(x26201,x26202)+~P33(x26203,x26201,x26204,x26205) % 178.07/177.95 [2621]P33(x26213,x26214,x26212,x26215)+~E(x26211,x26212)+~P33(x26213,x26214,x26211,x26215) % 178.07/177.95 [2622]P33(x26223,x26224,x26225,x26222)+~E(x26221,x26222)+~P33(x26223,x26224,x26225,x26221) % 178.07/177.95 [2623]~P81(x26231)+P81(x26232)+~E(x26231,x26232) % 178.07/177.95 [2624]~P83(x26241)+P83(x26242)+~E(x26241,x26242) % 178.07/177.95 [2625]~P89(x26251)+P89(x26252)+~E(x26251,x26252) % 178.07/177.95 [2626]~P100(x26261)+P100(x26262)+~E(x26261,x26262) % 178.07/177.95 [2627]~P93(x26271)+P93(x26272)+~E(x26271,x26272) % 178.07/177.95 [2628]~P61(x26281)+P61(x26282)+~E(x26281,x26282) % 178.07/177.95 [2629]~P97(x26291)+P97(x26292)+~E(x26291,x26292) % 178.07/177.95 [2630]P38(x26302,x26303)+~E(x26301,x26302)+~P38(x26301,x26303) % 178.07/177.95 [2631]P38(x26313,x26312)+~E(x26311,x26312)+~P38(x26313,x26311) % 178.07/177.95 [2632]P53(x26322,x26323)+~E(x26321,x26322)+~P53(x26321,x26323) % 178.07/177.95 [2633]P53(x26333,x26332)+~E(x26331,x26332)+~P53(x26333,x26331) % 178.07/177.95 [2634]~P66(x26341)+P66(x26342)+~E(x26341,x26342) % 178.07/177.95 [2635]~P103(x26351)+P103(x26352)+~E(x26351,x26352) % 178.07/177.95 [2636]~P98(x26361)+P98(x26362)+~E(x26361,x26362) % 178.07/177.95 [2637]~P67(x26371)+P67(x26372)+~E(x26371,x26372) % 178.07/177.95 [2638]~P108(x26381)+P108(x26382)+~E(x26381,x26382) % 178.07/177.95 [2639]~P68(x26391)+P68(x26392)+~E(x26391,x26392) % 178.07/177.95 [2640]~P39(x26401)+P39(x26402)+~E(x26401,x26402) % 178.07/177.95 [2641]~P75(x26411)+P75(x26412)+~E(x26411,x26412) % 178.07/177.95 [2642]~P70(x26421)+P70(x26422)+~E(x26421,x26422) % 178.07/177.95 [2643]P21(x26432,x26433,x26434,x26435)+~E(x26431,x26432)+~P21(x26431,x26433,x26434,x26435) % 178.07/177.95 [2644]P21(x26443,x26442,x26444,x26445)+~E(x26441,x26442)+~P21(x26443,x26441,x26444,x26445) % 178.07/177.95 [2645]P21(x26453,x26454,x26452,x26455)+~E(x26451,x26452)+~P21(x26453,x26454,x26451,x26455) % 178.07/177.95 [2646]P21(x26463,x26464,x26465,x26462)+~E(x26461,x26462)+~P21(x26463,x26464,x26465,x26461) % 178.07/177.95 [2647]P12(x26472,x26473,x26474)+~E(x26471,x26472)+~P12(x26471,x26473,x26474) % 178.07/177.95 [2648]P12(x26483,x26482,x26484)+~E(x26481,x26482)+~P12(x26483,x26481,x26484) % 178.07/177.95 [2649]P12(x26493,x26494,x26492)+~E(x26491,x26492)+~P12(x26493,x26494,x26491) % 178.07/177.95 [2650]~P134(x26501)+P134(x26502)+~E(x26501,x26502) % 178.07/177.95 [2651]P5(x26512,x26513)+~E(x26511,x26512)+~P5(x26511,x26513) % 178.07/177.95 [2652]P5(x26523,x26522)+~E(x26521,x26522)+~P5(x26523,x26521) % 178.07/177.95 [2653]P35(x26532,x26533,x26534,x26535,x26536)+~E(x26531,x26532)+~P35(x26531,x26533,x26534,x26535,x26536) % 178.07/177.95 [2654]P35(x26543,x26542,x26544,x26545,x26546)+~E(x26541,x26542)+~P35(x26543,x26541,x26544,x26545,x26546) % 178.07/177.95 [2655]P35(x26553,x26554,x26552,x26555,x26556)+~E(x26551,x26552)+~P35(x26553,x26554,x26551,x26555,x26556) % 178.07/177.95 [2656]P35(x26563,x26564,x26565,x26562,x26566)+~E(x26561,x26562)+~P35(x26563,x26564,x26565,x26561,x26566) % 178.07/177.95 [2657]P35(x26573,x26574,x26575,x26576,x26572)+~E(x26571,x26572)+~P35(x26573,x26574,x26575,x26576,x26571) % 178.07/177.95 [2658]~P109(x26581)+P109(x26582)+~E(x26581,x26582) % 178.07/177.95 [2659]P144(x26592,x26593,x26594)+~E(x26591,x26592)+~P144(x26591,x26593,x26594) % 178.07/177.95 [2660]P144(x26603,x26602,x26604)+~E(x26601,x26602)+~P144(x26603,x26601,x26604) % 178.07/177.95 [2661]P144(x26613,x26614,x26612)+~E(x26611,x26612)+~P144(x26613,x26614,x26611) % 178.07/177.95 [2662]~P74(x26621)+P74(x26622)+~E(x26621,x26622) % 178.07/177.95 [2663]~P80(x26631)+P80(x26632)+~E(x26631,x26632) % 178.07/177.95 [2664]~P104(x26641)+P104(x26642)+~E(x26641,x26642) % 178.07/177.95 [2665]~P78(x26651)+P78(x26652)+~E(x26651,x26652) % 178.07/177.95 [2666]~P123(x26661)+P123(x26662)+~E(x26661,x26662) % 178.07/177.95 [2667]~P132(x26671)+P132(x26672)+~E(x26671,x26672) % 178.07/177.95 [2668]~P69(x26681)+P69(x26682)+~E(x26681,x26682) % 178.07/177.95 [2669]~P59(x26691)+P59(x26692)+~E(x26691,x26692) % 178.07/177.95 [2670]P22(x26702,x26703)+~E(x26701,x26702)+~P22(x26701,x26703) % 178.07/177.95 [2671]P22(x26713,x26712)+~E(x26711,x26712)+~P22(x26713,x26711) % 178.07/177.95 [2672]~P71(x26721)+P71(x26722)+~E(x26721,x26722) % 178.07/177.95 [2673]~P58(x26731)+P58(x26732)+~E(x26731,x26732) % 178.07/177.95 [2674]P2(x26742,x26743,x26744)+~E(x26741,x26742)+~P2(x26741,x26743,x26744) % 178.07/177.95 [2675]P2(x26753,x26752,x26754)+~E(x26751,x26752)+~P2(x26753,x26751,x26754) % 178.07/177.95 [2676]P2(x26763,x26764,x26762)+~E(x26761,x26762)+~P2(x26763,x26764,x26761) % 178.07/177.95 [2677]~P72(x26771)+P72(x26772)+~E(x26771,x26772) % 178.07/177.95 [2678]P50(x26782,x26783,x26784)+~E(x26781,x26782)+~P50(x26781,x26783,x26784) % 178.07/177.95 [2679]P50(x26793,x26792,x26794)+~E(x26791,x26792)+~P50(x26793,x26791,x26794) % 178.07/177.95 [2680]P50(x26803,x26804,x26802)+~E(x26801,x26802)+~P50(x26803,x26804,x26801) % 178.07/177.95 [2681]~P137(x26811)+P137(x26812)+~E(x26811,x26812) % 178.07/177.95 [2682]~P135(x26821)+P135(x26822)+~E(x26821,x26822) % 178.07/177.95 [2683]P34(x26832,x26833,x26834)+~E(x26831,x26832)+~P34(x26831,x26833,x26834) % 178.07/177.95 [2684]P34(x26843,x26842,x26844)+~E(x26841,x26842)+~P34(x26843,x26841,x26844) % 178.07/177.95 [2685]P34(x26853,x26854,x26852)+~E(x26851,x26852)+~P34(x26853,x26854,x26851) % 178.07/177.95 [2686]~P118(x26861)+P118(x26862)+~E(x26861,x26862) % 178.07/177.95 [2687]~P110(x26871)+P110(x26872)+~E(x26871,x26872) % 178.07/177.95 [2688]P14(x26882,x26883,x26884)+~E(x26881,x26882)+~P14(x26881,x26883,x26884) % 178.07/177.95 [2689]P14(x26893,x26892,x26894)+~E(x26891,x26892)+~P14(x26893,x26891,x26894) % 178.07/177.95 [2690]P14(x26903,x26904,x26902)+~E(x26901,x26902)+~P14(x26903,x26904,x26901) % 178.07/177.95 [2691]P6(x26912,x26913,x26914)+~E(x26911,x26912)+~P6(x26911,x26913,x26914) % 178.07/177.95 [2692]P6(x26923,x26922,x26924)+~E(x26921,x26922)+~P6(x26923,x26921,x26924) % 178.07/177.95 [2693]P6(x26933,x26934,x26932)+~E(x26931,x26932)+~P6(x26933,x26934,x26931) % 178.07/177.95 [2694]~P79(x26941)+P79(x26942)+~E(x26941,x26942) % 178.07/177.95 [2695]P54(x26952,x26953,x26954,x26955)+~E(x26951,x26952)+~P54(x26951,x26953,x26954,x26955) % 178.07/177.95 [2696]P54(x26963,x26962,x26964,x26965)+~E(x26961,x26962)+~P54(x26963,x26961,x26964,x26965) % 178.07/177.95 [2697]P54(x26973,x26974,x26972,x26975)+~E(x26971,x26972)+~P54(x26973,x26974,x26971,x26975) % 178.07/177.95 [2698]P54(x26983,x26984,x26985,x26982)+~E(x26981,x26982)+~P54(x26983,x26984,x26985,x26981) % 178.07/177.95 [2699]~P113(x26991)+P113(x26992)+~E(x26991,x26992) % 178.07/177.95 [2700]~P136(x27001)+P136(x27002)+~E(x27001,x27002) % 178.07/177.95 [2701]~P111(x27011)+P111(x27012)+~E(x27011,x27012) % 178.07/177.95 [2702]~P114(x27021)+P114(x27022)+~E(x27021,x27022) % 178.07/177.95 [2703]P40(x27032,x27033,x27034)+~E(x27031,x27032)+~P40(x27031,x27033,x27034) % 178.07/177.95 [2704]P40(x27043,x27042,x27044)+~E(x27041,x27042)+~P40(x27043,x27041,x27044) % 178.07/177.95 [2705]P40(x27053,x27054,x27052)+~E(x27051,x27052)+~P40(x27053,x27054,x27051) % 178.07/177.95 [2706]P52(x27062,x27063,x27064,x27065,x27066)+~E(x27061,x27062)+~P52(x27061,x27063,x27064,x27065,x27066) % 178.07/177.95 [2707]P52(x27073,x27072,x27074,x27075,x27076)+~E(x27071,x27072)+~P52(x27073,x27071,x27074,x27075,x27076) % 178.07/177.95 [2708]P52(x27083,x27084,x27082,x27085,x27086)+~E(x27081,x27082)+~P52(x27083,x27084,x27081,x27085,x27086) % 178.07/177.95 [2709]P52(x27093,x27094,x27095,x27092,x27096)+~E(x27091,x27092)+~P52(x27093,x27094,x27095,x27091,x27096) % 178.07/177.95 [2710]P52(x27103,x27104,x27105,x27106,x27102)+~E(x27101,x27102)+~P52(x27103,x27104,x27105,x27106,x27101) % 178.07/177.95 [2711]~P139(x27111)+P139(x27112)+~E(x27111,x27112) % 178.07/177.95 [2712]P32(x27122,x27123,x27124)+~E(x27121,x27122)+~P32(x27121,x27123,x27124) % 178.07/177.95 [2713]P32(x27133,x27132,x27134)+~E(x27131,x27132)+~P32(x27133,x27131,x27134) % 178.07/177.95 [2714]P32(x27143,x27144,x27142)+~E(x27141,x27142)+~P32(x27143,x27144,x27141) % 178.07/177.95 [2715]~P120(x27151)+P120(x27152)+~E(x27151,x27152) % 178.07/177.95 [2716]~P56(x27161)+P56(x27162)+~E(x27161,x27162) % 178.07/177.95 [2717]~P121(x27171)+P121(x27172)+~E(x27171,x27172) % 178.07/177.95 [2718]~P129(x27181)+P129(x27182)+~E(x27181,x27182) % 178.07/177.95 [2719]~P82(x27191)+P82(x27192)+~E(x27191,x27192) % 178.07/177.95 [2720]P36(x27202,x27203,x27204)+~E(x27201,x27202)+~P36(x27201,x27203,x27204) % 178.07/177.95 [2721]P36(x27213,x27212,x27214)+~E(x27211,x27212)+~P36(x27213,x27211,x27214) % 178.07/177.95 [2722]P36(x27223,x27224,x27222)+~E(x27221,x27222)+~P36(x27223,x27224,x27221) % 178.07/177.95 [2723]P49(x27232,x27233)+~E(x27231,x27232)+~P49(x27231,x27233) % 178.07/177.95 [2724]P49(x27243,x27242)+~E(x27241,x27242)+~P49(x27243,x27241) % 178.07/177.95 [2725]~P106(x27251)+P106(x27252)+~E(x27251,x27252) % 178.07/177.95 [2726]P30(x27262,x27263,x27264)+~E(x27261,x27262)+~P30(x27261,x27263,x27264) % 178.07/177.95 [2727]P30(x27273,x27272,x27274)+~E(x27271,x27272)+~P30(x27273,x27271,x27274) % 178.07/177.95 [2728]P30(x27283,x27284,x27282)+~E(x27281,x27282)+~P30(x27283,x27284,x27281) % 178.07/177.95 [2729]P13(x27292,x27293,x27294)+~E(x27291,x27292)+~P13(x27291,x27293,x27294) % 178.07/177.95 [2730]P13(x27303,x27302,x27304)+~E(x27301,x27302)+~P13(x27303,x27301,x27304) % 178.07/177.95 [2731]P13(x27313,x27314,x27312)+~E(x27311,x27312)+~P13(x27313,x27314,x27311) % 178.07/177.95 [2732]P20(x27322,x27323,x27324)+~E(x27321,x27322)+~P20(x27321,x27323,x27324) % 178.07/177.95 [2733]P20(x27333,x27332,x27334)+~E(x27331,x27332)+~P20(x27333,x27331,x27334) % 178.07/177.95 [2734]P20(x27343,x27344,x27342)+~E(x27341,x27342)+~P20(x27343,x27344,x27341) % 178.07/177.95 [2735]P9(x27352,x27353,x27354,x27355)+~E(x27351,x27352)+~P9(x27351,x27353,x27354,x27355) % 178.07/177.95 [2736]P9(x27363,x27362,x27364,x27365)+~E(x27361,x27362)+~P9(x27363,x27361,x27364,x27365) % 178.07/177.95 [2737]P9(x27373,x27374,x27372,x27375)+~E(x27371,x27372)+~P9(x27373,x27374,x27371,x27375) % 178.07/177.95 [2738]P9(x27383,x27384,x27385,x27382)+~E(x27381,x27382)+~P9(x27383,x27384,x27385,x27381) % 178.07/177.95 [2739]P7(x27392,x27393,x27394)+~E(x27391,x27392)+~P7(x27391,x27393,x27394) % 178.07/177.95 [2740]P7(x27403,x27402,x27404)+~E(x27401,x27402)+~P7(x27403,x27401,x27404) % 178.07/177.95 [2741]P7(x27413,x27414,x27412)+~E(x27411,x27412)+~P7(x27413,x27414,x27411) % 178.07/177.95 [2742]P43(x27422,x27423,x27424,x27425,x27426,x27427)+~E(x27421,x27422)+~P43(x27421,x27423,x27424,x27425,x27426,x27427) % 178.07/177.95 [2743]P43(x27433,x27432,x27434,x27435,x27436,x27437)+~E(x27431,x27432)+~P43(x27433,x27431,x27434,x27435,x27436,x27437) % 178.07/177.95 [2744]P43(x27443,x27444,x27442,x27445,x27446,x27447)+~E(x27441,x27442)+~P43(x27443,x27444,x27441,x27445,x27446,x27447) % 178.07/177.95 [2745]P43(x27453,x27454,x27455,x27452,x27456,x27457)+~E(x27451,x27452)+~P43(x27453,x27454,x27455,x27451,x27456,x27457) % 178.07/177.95 [2746]P43(x27463,x27464,x27465,x27466,x27462,x27467)+~E(x27461,x27462)+~P43(x27463,x27464,x27465,x27466,x27461,x27467) % 178.07/177.95 [2747]P43(x27473,x27474,x27475,x27476,x27477,x27472)+~E(x27471,x27472)+~P43(x27473,x27474,x27475,x27476,x27477,x27471) % 178.07/177.95 [2748]~P91(x27481)+P91(x27482)+~E(x27481,x27482) % 178.07/177.95 [2749]P31(x27492,x27493)+~E(x27491,x27492)+~P31(x27491,x27493) % 178.07/177.95 [2750]P31(x27503,x27502)+~E(x27501,x27502)+~P31(x27503,x27501) % 178.07/177.95 [2751]P11(x27512,x27513,x27514)+~E(x27511,x27512)+~P11(x27511,x27513,x27514) % 178.07/177.95 [2752]P11(x27523,x27522,x27524)+~E(x27521,x27522)+~P11(x27523,x27521,x27524) % 178.07/177.95 [2753]P11(x27533,x27534,x27532)+~E(x27531,x27532)+~P11(x27533,x27534,x27531) % 178.07/177.95 [2754]P17(x27542,x27543,x27544,x27545,x27546)+~E(x27541,x27542)+~P17(x27541,x27543,x27544,x27545,x27546) % 178.07/177.95 [2755]P17(x27553,x27552,x27554,x27555,x27556)+~E(x27551,x27552)+~P17(x27553,x27551,x27554,x27555,x27556) % 178.07/177.95 [2756]P17(x27563,x27564,x27562,x27565,x27566)+~E(x27561,x27562)+~P17(x27563,x27564,x27561,x27565,x27566) % 178.07/177.95 [2757]P17(x27573,x27574,x27575,x27572,x27576)+~E(x27571,x27572)+~P17(x27573,x27574,x27575,x27571,x27576) % 178.07/177.95 [2758]P17(x27583,x27584,x27585,x27586,x27582)+~E(x27581,x27582)+~P17(x27583,x27584,x27585,x27586,x27581) % 178.07/177.95 [2759]~P126(x27591)+P126(x27592)+~E(x27591,x27592) % 178.07/177.95 [2760]P143(x27602,x27603,x27604)+~E(x27601,x27602)+~P143(x27601,x27603,x27604) % 178.07/177.95 [2761]P143(x27613,x27612,x27614)+~E(x27611,x27612)+~P143(x27613,x27611,x27614) % 178.07/177.95 [2762]P143(x27623,x27624,x27622)+~E(x27621,x27622)+~P143(x27623,x27624,x27621) % 178.07/177.95 [2763]P8(x27632,x27633,x27634)+~E(x27631,x27632)+~P8(x27631,x27633,x27634) % 178.07/177.95 [2764]P8(x27643,x27642,x27644)+~E(x27641,x27642)+~P8(x27643,x27641,x27644) % 178.07/177.95 [2765]P8(x27653,x27654,x27652)+~E(x27651,x27652)+~P8(x27653,x27654,x27651) % 178.07/177.95 [2766]~P112(x27661)+P112(x27662)+~E(x27661,x27662) % 178.07/177.95 [2767]~P84(x27671)+P84(x27672)+~E(x27671,x27672) % 178.07/177.95 [2768]P23(x27682,x27683,x27684)+~E(x27681,x27682)+~P23(x27681,x27683,x27684) % 178.07/177.95 [2769]P23(x27693,x27692,x27694)+~E(x27691,x27692)+~P23(x27693,x27691,x27694) % 178.07/177.95 [2770]P23(x27703,x27704,x27702)+~E(x27701,x27702)+~P23(x27703,x27704,x27701) % 178.07/177.95 [2771]~P115(x27711)+P115(x27712)+~E(x27711,x27712) % 178.07/177.95 [2772]~P96(x27721)+P96(x27722)+~E(x27721,x27722) % 178.07/177.95 [2773]~P60(x27731)+P60(x27732)+~E(x27731,x27732) % 178.07/177.95 [2774]~P131(x27741)+P131(x27742)+~E(x27741,x27742) % 178.07/177.95 [2775]~P124(x27751)+P124(x27752)+~E(x27751,x27752) % 178.07/177.95 [2776]~P85(x27761)+P85(x27762)+~E(x27761,x27762) % 178.07/177.95 [2777]P15(x27772,x27773,x27774,x27775)+~E(x27771,x27772)+~P15(x27771,x27773,x27774,x27775) % 178.07/177.95 [2778]P15(x27783,x27782,x27784,x27785)+~E(x27781,x27782)+~P15(x27783,x27781,x27784,x27785) % 178.07/177.95 [2779]P15(x27793,x27794,x27792,x27795)+~E(x27791,x27792)+~P15(x27793,x27794,x27791,x27795) % 178.07/177.95 [2780]P15(x27803,x27804,x27805,x27802)+~E(x27801,x27802)+~P15(x27803,x27804,x27805,x27801) % 178.07/177.95 [2781]~P94(x27811)+P94(x27812)+~E(x27811,x27812) % 178.07/177.95 [2782]P19(x27822,x27823,x27824,x27825,x27826,x27827)+~E(x27821,x27822)+~P19(x27821,x27823,x27824,x27825,x27826,x27827) % 178.07/177.95 [2783]P19(x27833,x27832,x27834,x27835,x27836,x27837)+~E(x27831,x27832)+~P19(x27833,x27831,x27834,x27835,x27836,x27837) % 178.07/177.95 [2784]P19(x27843,x27844,x27842,x27845,x27846,x27847)+~E(x27841,x27842)+~P19(x27843,x27844,x27841,x27845,x27846,x27847) % 178.07/177.95 [2785]P19(x27853,x27854,x27855,x27852,x27856,x27857)+~E(x27851,x27852)+~P19(x27853,x27854,x27855,x27851,x27856,x27857) % 178.07/177.95 [2786]P19(x27863,x27864,x27865,x27866,x27862,x27867)+~E(x27861,x27862)+~P19(x27863,x27864,x27865,x27866,x27861,x27867) % 178.07/177.95 [2787]P19(x27873,x27874,x27875,x27876,x27877,x27872)+~E(x27871,x27872)+~P19(x27873,x27874,x27875,x27876,x27877,x27871) % 178.07/177.95 [2788]~P87(x27881)+P87(x27882)+~E(x27881,x27882) % 178.07/177.95 [2789]P18(x27892,x27893,x27894,x27895,x27896,x27897)+~E(x27891,x27892)+~P18(x27891,x27893,x27894,x27895,x27896,x27897) % 178.07/177.95 [2790]P18(x27903,x27902,x27904,x27905,x27906,x27907)+~E(x27901,x27902)+~P18(x27903,x27901,x27904,x27905,x27906,x27907) % 178.07/177.95 [2791]P18(x27913,x27914,x27912,x27915,x27916,x27917)+~E(x27911,x27912)+~P18(x27913,x27914,x27911,x27915,x27916,x27917) % 178.07/177.95 [2792]P18(x27923,x27924,x27925,x27922,x27926,x27927)+~E(x27921,x27922)+~P18(x27923,x27924,x27925,x27921,x27926,x27927) % 178.07/177.95 [2793]P18(x27933,x27934,x27935,x27936,x27932,x27937)+~E(x27931,x27932)+~P18(x27933,x27934,x27935,x27936,x27931,x27937) % 178.07/177.95 [2794]P18(x27943,x27944,x27945,x27946,x27947,x27942)+~E(x27941,x27942)+~P18(x27943,x27944,x27945,x27946,x27947,x27941) % 178.07/177.95 [2795]~P141(x27951)+P141(x27952)+~E(x27951,x27952) % 178.07/177.95 [2796]P3(x27962,x27963,x27964,x27965,x27966)+~E(x27961,x27962)+~P3(x27961,x27963,x27964,x27965,x27966) % 178.07/177.95 [2797]P3(x27973,x27972,x27974,x27975,x27976)+~E(x27971,x27972)+~P3(x27973,x27971,x27974,x27975,x27976) % 178.07/177.95 [2798]P3(x27983,x27984,x27982,x27985,x27986)+~E(x27981,x27982)+~P3(x27983,x27984,x27981,x27985,x27986) % 178.07/177.95 [2799]P3(x27993,x27994,x27995,x27992,x27996)+~E(x27991,x27992)+~P3(x27993,x27994,x27995,x27991,x27996) % 178.07/177.95 [2800]P3(x28003,x28004,x28005,x28006,x28002)+~E(x28001,x28002)+~P3(x28003,x28004,x28005,x28006,x28001) % 178.07/177.95 [2801]P51(x28012,x28013,x28014)+~E(x28011,x28012)+~P51(x28011,x28013,x28014) % 178.07/177.95 [2802]P51(x28023,x28022,x28024)+~E(x28021,x28022)+~P51(x28023,x28021,x28024) % 178.07/177.95 [2803]P51(x28033,x28034,x28032)+~E(x28031,x28032)+~P51(x28033,x28034,x28031) % 178.07/177.95 [2804]P16(x28042,x28043,x28044,x28045)+~E(x28041,x28042)+~P16(x28041,x28043,x28044,x28045) % 178.07/177.95 [2805]P16(x28053,x28052,x28054,x28055)+~E(x28051,x28052)+~P16(x28053,x28051,x28054,x28055) % 178.07/177.95 [2806]P16(x28063,x28064,x28062,x28065)+~E(x28061,x28062)+~P16(x28063,x28064,x28061,x28065) % 178.07/177.95 [2807]P16(x28073,x28074,x28075,x28072)+~E(x28071,x28072)+~P16(x28073,x28074,x28075,x28071) % 178.07/177.95 [2808]~P140(x28081)+P140(x28082)+~E(x28081,x28082) % 178.07/177.95 [2809]~P28(x28091)+P28(x28092)+~E(x28091,x28092) % 178.07/177.95 [2810]P41(x28102,x28103,x28104,x28105)+~E(x28101,x28102)+~P41(x28101,x28103,x28104,x28105) % 178.07/177.95 [2811]P41(x28113,x28112,x28114,x28115)+~E(x28111,x28112)+~P41(x28113,x28111,x28114,x28115) % 178.07/177.95 [2812]P41(x28123,x28124,x28122,x28125)+~E(x28121,x28122)+~P41(x28123,x28124,x28121,x28125) % 178.07/177.95 [2813]P41(x28133,x28134,x28135,x28132)+~E(x28131,x28132)+~P41(x28133,x28134,x28135,x28131) % 178.07/177.95 [2814]~P90(x28141)+P90(x28142)+~E(x28141,x28142) % 178.07/177.95 [2815]~P128(x28151)+P128(x28152)+~E(x28151,x28152) % 178.07/177.95 [2816]~P116(x28161)+P116(x28162)+~E(x28161,x28162) % 178.07/177.95 [2817]P10(x28172,x28173,x28174,x28175,x28176,x28177)+~E(x28171,x28172)+~P10(x28171,x28173,x28174,x28175,x28176,x28177) % 178.07/177.95 [2818]P10(x28183,x28182,x28184,x28185,x28186,x28187)+~E(x28181,x28182)+~P10(x28183,x28181,x28184,x28185,x28186,x28187) % 178.07/177.95 [2819]P10(x28193,x28194,x28192,x28195,x28196,x28197)+~E(x28191,x28192)+~P10(x28193,x28194,x28191,x28195,x28196,x28197) % 178.07/177.95 [2820]P10(x28203,x28204,x28205,x28202,x28206,x28207)+~E(x28201,x28202)+~P10(x28203,x28204,x28205,x28201,x28206,x28207) % 178.07/177.95 [2821]P10(x28213,x28214,x28215,x28216,x28212,x28217)+~E(x28211,x28212)+~P10(x28213,x28214,x28215,x28216,x28211,x28217) % 178.07/177.95 [2822]P10(x28223,x28224,x28225,x28226,x28227,x28222)+~E(x28221,x28222)+~P10(x28223,x28224,x28225,x28226,x28227,x28221) % 178.07/177.95 [2823]P55(x28232,x28233)+~E(x28231,x28232)+~P55(x28231,x28233) % 178.07/177.95 [2824]P55(x28243,x28242)+~E(x28241,x28242)+~P55(x28243,x28241) % 178.07/177.95 [2825]~P127(x28251)+P127(x28252)+~E(x28251,x28252) % 178.07/177.95 [2826]~P122(x28261)+P122(x28262)+~E(x28261,x28262) % 178.07/177.95 [2827]~P138(x28271)+P138(x28272)+~E(x28271,x28272) % 178.07/177.95 [2828]P42(x28282,x28283)+~E(x28281,x28282)+~P42(x28281,x28283) % 178.07/177.95 [2829]P42(x28293,x28292)+~E(x28291,x28292)+~P42(x28293,x28291) % 178.07/177.95 [2830]~P95(x28301)+P95(x28302)+~E(x28301,x28302) % 178.07/177.95 [2831]~P125(x28311)+P125(x28312)+~E(x28311,x28312) % 178.07/177.95 [2832]~P130(x28321)+P130(x28322)+~E(x28321,x28322) % 178.07/177.95 [2833]~P101(x28331)+P101(x28332)+~E(x28331,x28332) % 178.07/177.95 [2834]~P102(x28341)+P102(x28342)+~E(x28341,x28342) % 178.07/177.95 [2835]~P37(x28351)+P37(x28352)+~E(x28351,x28352) % 178.07/177.95 [2836]P48(x28362,x28363,x28364)+~E(x28361,x28362)+~P48(x28361,x28363,x28364) % 178.07/177.95 [2837]P48(x28373,x28372,x28374)+~E(x28371,x28372)+~P48(x28373,x28371,x28374) % 178.07/177.95 [2838]P48(x28383,x28384,x28382)+~E(x28381,x28382)+~P48(x28383,x28384,x28381) % 178.07/177.95 [2839]~P88(x28391)+P88(x28392)+~E(x28391,x28392) % 178.07/177.95 [2840]~P45(x28401)+P45(x28402)+~E(x28401,x28402) % 178.07/177.95 [2841]~P142(x28411)+P142(x28412)+~E(x28411,x28412) % 178.07/177.95 [2842]P44(x28422,x28423)+~E(x28421,x28422)+~P44(x28421,x28423) % 178.07/177.95 [2843]P44(x28433,x28432)+~E(x28431,x28432)+~P44(x28433,x28431) % 178.07/177.95 [2844]~P57(x28441)+P57(x28442)+~E(x28441,x28442) % 178.07/177.95 [2845]~P73(x28451)+P73(x28452)+~E(x28451,x28452) % 178.07/177.95 [2846]P46(x28462,x28463)+~E(x28461,x28462)+~P46(x28461,x28463) % 178.07/177.95 [2847]P46(x28473,x28472)+~E(x28471,x28472)+~P46(x28473,x28471) % 178.07/177.95 [2848]~P76(x28481)+P76(x28482)+~E(x28481,x28482) % 178.07/177.95 [2849]~P133(x28491)+P133(x28492)+~E(x28491,x28492) % 178.07/177.95 [2850]P47(x28502,x28503,x28504)+~E(x28501,x28502)+~P47(x28501,x28503,x28504) % 178.07/177.95 [2851]P47(x28513,x28512,x28514)+~E(x28511,x28512)+~P47(x28513,x28511,x28514) % 178.07/177.95 [2852]P47(x28523,x28524,x28522)+~E(x28521,x28522)+~P47(x28523,x28524,x28521) % 178.07/177.95 [2853]~P119(x28531)+P119(x28532)+~E(x28531,x28532) % 178.07/177.95 % 178.07/177.95 %------------------------------------------- % 178.17/178.00 cnf(10189,plain, % 178.17/178.00 (~E(f329(a118,x101891),x101891)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(10192,plain, % 178.17/178.00 (E(f329(f260(x101921,x101921),f261(x101921,x101922)),x101922)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(10199,plain, % 178.17/178.00 (~E(f329(a118,x101991),x101991)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(10210,plain, % 178.17/178.00 (~E(f329(a118,x102101),x102101)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(10215,plain, % 178.17/178.00 (~P24(f329(f63(x102151,x102152,f193(f883(x102151,a869))),x102153))), % 178.17/178.00 inference(rename_variables,[],[4539])). % 178.17/178.00 cnf(10218,plain, % 178.17/178.00 (~P24(f329(f63(x102181,x102182,f193(f883(x102181,a869))),x102183))), % 178.17/178.00 inference(rename_variables,[],[4539])). % 178.17/178.00 cnf(10221,plain, % 178.17/178.00 (~E(f329(a118,x102211),x102211)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(10224,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x102241),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(10227,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x102271),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(10240,plain, % 178.17/178.00 (~P24(f329(f193(f883(x102401,a869)),x102402))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,2855,3055,3224,3098,3160,3106,3250,4515,10224,4512,4462,4522,3241,4505,4539,10215,4543,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014])). % 178.17/178.00 cnf(10244,plain, % 178.17/178.00 (~P24(f329(f329(f243(a875),f329(a118,x102441)),x102441))), % 178.17/178.00 inference(rename_variables,[],[4524])). % 178.17/178.00 cnf(10247,plain, % 178.17/178.00 (~E(f329(f329(f150(x102471),x102472),x102473),x102473)), % 178.17/178.00 inference(rename_variables,[],[4467])). % 178.17/178.00 cnf(10253,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x102531),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(10255,plain, % 178.17/178.00 (E(f45(a875,f329(f260(x102551,x102551),f261(x102551,f329(f329(f82(a875),x102552),x102553))),x102552),f2(a875))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,2855,3055,3224,10192,3098,3160,3127,3106,4467,3250,4515,10224,10227,4512,4462,4524,4522,3241,4505,4539,10215,4543,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041])). % 178.17/178.00 cnf(10256,plain, % 178.17/178.00 (E(f329(f260(x102561,x102561),f261(x102561,x102562)),x102562)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(10259,plain, % 178.17/178.00 (E(f329(f260(x102591,x102591),f261(x102591,x102592)),x102592)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(10263,plain, % 178.17/178.00 (~P24(f329(a198,a84))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,2855,3055,3224,10192,10256,3098,3160,3127,3106,4467,3250,4515,10224,10227,4512,4462,4524,4522,3241,4505,4539,10215,4543,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088])). % 178.17/178.00 cnf(10266,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),f329(f329(f81(a875),x102661),x102662)),x102662))), % 178.17/178.00 inference(rename_variables,[],[4541])). % 178.17/178.00 cnf(10269,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),f329(f329(f81(a875),x102691),x102692)),x102692))), % 178.17/178.00 inference(rename_variables,[],[4541])). % 178.17/178.00 cnf(10276,plain, % 178.17/178.00 (~E(x102761,f329(a118,x102761))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,2855,3055,3224,10192,10256,3098,3160,3127,3106,4467,3339,3250,4515,10224,10227,4512,4462,4524,4094,4522,3241,4505,4539,10215,4543,4541,10266,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155])). % 178.17/178.00 cnf(10290,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x102901),x102901))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(10293,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),f45(a875,x102931,x102932)),x102931))), % 178.17/178.00 inference(rename_variables,[],[3726])). % 178.17/178.00 cnf(10314,plain, % 178.17/178.00 (E(f329(f38(a875),f329(f250(a875),x103141)),x103141)), % 178.17/178.00 inference(rename_variables,[],[3158])). % 178.17/178.00 cnf(10322,plain, % 178.17/178.00 (~E(f329(a118,x103221),x103221)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(10325,plain, % 178.17/178.00 (~E(f329(a118,x103251),x103251)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(10328,plain, % 178.17/178.00 (~E(f329(a118,x103281),x103281)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(10330,plain, % 178.17/178.00 (P24(f329(a198,a103))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,10221,10322,10325,2855,3055,3224,10192,10256,3098,3160,3127,3106,3195,4467,3158,4549,3178,3339,3250,4515,10224,10227,3854,3271,4512,4462,4511,10290,3365,3787,3726,4524,10244,4094,4522,4501,3241,4505,4506,4539,10215,4543,4541,10266,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299])). % 178.17/178.00 cnf(10333,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x103331),f329(a118,x103331)))), % 178.17/178.00 inference(rename_variables,[],[3339])). % 178.17/178.00 cnf(10342,plain, % 178.17/178.00 (P24(f329(f329(f199(a24),x103421),x103421))), % 178.17/178.00 inference(rename_variables,[],[3267])). % 178.17/178.00 cnf(10349,plain, % 178.17/178.00 (E(f329(f260(x103491,x103491),f261(x103491,x103492)),x103492)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(10352,plain, % 178.17/178.00 (E(f329(f260(x103521,x103521),f261(x103521,x103522)),x103522)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(10371,plain, % 178.17/178.00 (P24(f329(f329(f243(a1),x103711),x103711))), % 178.17/178.00 inference(rename_variables,[],[3269])). % 178.17/178.00 cnf(10380,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x103801),x103801))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(10385,plain, % 178.17/178.00 (~E(f329(f329(f329(f73(x103851,f879(x103852)),x103853),x103854),f329(f236(x103852),x103855)),f329(f16(f879(x103852),x103851),f206(x103852)))), % 178.17/178.00 inference(rename_variables,[],[4536])). % 178.17/178.00 cnf(10412,plain, % 178.17/178.00 (~E(f329(f329(f150(x104121),x104122),x104123),x104123)), % 178.17/178.00 inference(rename_variables,[],[4467])). % 178.17/178.00 cnf(10415,plain, % 178.17/178.00 (~E(f329(a26,x104151),f34(x104152,x104153))), % 178.17/178.00 inference(rename_variables,[],[4457])). % 178.17/178.00 cnf(10426,plain, % 178.17/178.00 (P24(f329(f329(f243(a1),x104261),x104261))), % 178.17/178.00 inference(rename_variables,[],[3269])). % 178.17/178.00 cnf(10431,plain, % 178.17/178.00 (~E(f329(a118,x104311),x104311)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(10438,plain, % 178.17/178.00 (P24(f329(f329(f199(a24),x104381),x104381))), % 178.17/178.00 inference(rename_variables,[],[3267])). % 178.17/178.00 cnf(10451,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x104511),f329(a118,x104511)))), % 178.17/178.00 inference(rename_variables,[],[3339])). % 178.17/178.00 cnf(10456,plain, % 178.17/178.00 (E(f329(f329(f127(x104561),f119(x104561)),x104562),x104562)), % 178.17/178.00 inference(rename_variables,[],[3219])). % 178.17/178.00 cnf(10474,plain, % 178.17/178.00 (~P24(f329(f63(x104741,x104742,f193(f883(x104741,a869))),x104743))), % 178.17/178.00 inference(rename_variables,[],[4539])). % 178.17/178.00 cnf(10493,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x104931),x104931))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(10505,plain, % 178.17/178.00 (E(f329(f329(f254(a875),f329(f109(a875),a103)),x105051),f329(f329(f254(a875),f2(a875)),x105051))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,10221,10322,10325,10328,4457,2855,3055,3224,10192,10256,10259,10349,3098,3160,3127,3106,3195,3219,10456,4536,4467,10247,3158,4050,4549,3178,3632,3339,10333,10451,3250,4515,10224,10227,10253,4531,3708,3854,3296,3297,3271,4512,4462,4003,3267,10342,3268,3269,10371,3270,4511,10290,10380,3365,3787,3726,10293,4524,10244,4094,4522,4501,3241,3242,4502,4505,4506,4539,10215,10218,4543,3747,4541,10266,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802])). % 178.17/178.00 cnf(10508,plain, % 178.17/178.00 (~E(f329(a26,x105081),f34(x105082,x105083))), % 178.17/178.00 inference(rename_variables,[],[4457])). % 178.17/178.00 cnf(10517,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x105171),x105171))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(10522,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x105221),f329(a118,x105221)))), % 178.17/178.00 inference(rename_variables,[],[3339])). % 178.17/178.00 cnf(10525,plain, % 178.17/178.00 (~P24(f329(f63(x105251,x105252,f193(f883(x105251,a869))),x105253))), % 178.17/178.00 inference(rename_variables,[],[4539])). % 178.17/178.00 cnf(10528,plain, % 178.17/178.00 (~P24(f329(f63(x105281,x105282,f193(f883(x105281,a869))),x105283))), % 178.17/178.00 inference(rename_variables,[],[4539])). % 178.17/178.00 cnf(10533,plain, % 178.17/178.00 (~P24(f329(f63(x105331,x105332,f193(f883(x105331,a869))),x105333))), % 178.17/178.00 inference(rename_variables,[],[4539])). % 178.17/178.00 cnf(10543,plain, % 178.17/178.00 (~E(f329(f168(x105431),f329(a118,f329(f329(f127(x105431),f329(f168(x105431),x105432)),f329(f329(f150(x105431),x105433),f119(x105431))))),f329(f329(f150(x105431),x105433),x105432))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,10221,10322,10325,10328,10431,4457,10415,2855,3055,3224,10192,10256,10259,10349,3098,3160,3127,3106,3195,3219,10456,4536,4467,10247,3158,4050,4549,3178,3632,3339,10333,10451,10522,3250,4515,10224,10227,10253,4531,3708,3854,3296,3297,3271,4512,4462,4003,3267,10342,3268,3269,10371,3270,4511,10290,10380,10493,3365,3787,3726,10293,4524,10244,4094,4522,4501,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,4543,3747,4541,10266,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980])). % 178.17/178.00 cnf(10544,plain, % 178.17/178.00 (~E(f329(a118,x105441),x105441)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(10558,plain, % 178.17/178.00 (P24(f329(f329(f244(a105),f329(a3,x105581)),f329(a3,f329(a118,x105581))))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,10221,10322,10325,10328,10431,4457,10415,2855,3055,3224,10192,10256,10259,10349,3098,3160,3127,3106,3195,3219,10456,4536,4467,10247,3158,4050,4549,3178,3632,3339,10333,10451,10522,3721,3250,4515,10224,10227,10253,4531,3708,3854,3296,3297,3271,4512,4462,4003,3267,10342,3268,3269,10371,3270,4511,10290,10380,10493,3365,3787,3726,10293,4524,10244,4094,4522,4501,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,4543,3747,4541,10266,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060])). % 178.17/178.00 cnf(10569,plain, % 178.17/178.00 (P24(f329(f329(f199(a24),x105691),x105691))), % 178.17/178.00 inference(rename_variables,[],[3267])). % 178.17/178.00 cnf(10572,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x105721),f329(a118,f329(f329(f81(a875),x105722),x105721))))), % 178.17/178.00 inference(rename_variables,[],[3719])). % 178.17/178.00 cnf(10574,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x105741),f329(f329(f82(a875),f329(a118,x105741)),f329(a118,x105741))))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,10221,10322,10325,10328,10431,4457,10415,2855,3055,3224,10192,10256,10259,10349,3098,3160,3127,3106,3195,3219,10456,4536,4467,10247,3158,4050,4549,3178,3632,3339,10333,10451,10522,3721,3250,4515,10224,10227,10253,4531,3708,3854,3296,3297,3271,4512,4462,4003,3267,10342,10438,3268,3269,10371,3270,4511,10290,10380,10493,3365,3787,3726,10293,4524,10244,4094,4522,4501,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,3537,4543,3747,4541,10266,3719,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085])). % 178.17/178.00 cnf(10575,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x105751),f329(f329(f82(a875),x105751),x105751)))), % 178.17/178.00 inference(rename_variables,[],[3537])). % 178.17/178.00 cnf(10578,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x105781),f329(f329(f82(a875),x105781),x105781)))), % 178.17/178.00 inference(rename_variables,[],[3537])). % 178.17/178.00 cnf(10583,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x105831),f329(a118,x105831)))), % 178.17/178.00 inference(rename_variables,[],[3339])). % 178.17/178.00 cnf(10586,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x105861),f329(a118,x105861)))), % 178.17/178.00 inference(rename_variables,[],[3339])). % 178.17/178.00 cnf(10589,plain, % 178.17/178.00 (P24(f329(f329(f331(x105891),x105892),f252(f883(x105891,a869))))), % 178.17/178.00 inference(rename_variables,[],[3428])). % 178.17/178.00 cnf(10604,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),f329(f329(f81(a875),x106041),x106042)),x106042))), % 178.17/178.00 inference(rename_variables,[],[4541])). % 178.17/178.00 cnf(10607,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),f329(f329(f81(a875),x106071),x106072)),x106072))), % 178.17/178.00 inference(rename_variables,[],[4541])). % 178.17/178.00 cnf(10610,plain, % 178.17/178.00 (~P24(f329(f329(f243(a875),f329(a118,x106101)),x106101))), % 178.17/178.00 inference(rename_variables,[],[4524])). % 178.17/178.00 cnf(10613,plain, % 178.17/178.00 (~P24(f329(f329(f243(a875),f329(a118,x106131)),x106131))), % 178.17/178.00 inference(rename_variables,[],[4524])). % 178.17/178.00 cnf(10616,plain, % 178.17/178.00 (P24(f329(f252(f883(x106161,a869)),x106162))), % 178.17/178.00 inference(rename_variables,[],[3333])). % 178.17/178.00 cnf(10619,plain, % 178.17/178.00 (E(f329(f38(a875),f329(f250(a875),x106191)),x106191)), % 178.17/178.00 inference(rename_variables,[],[3158])). % 178.17/178.00 cnf(10622,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x106221),f329(a118,x106221)))), % 178.17/178.00 inference(rename_variables,[],[3339])). % 178.17/178.00 cnf(10629,plain, % 178.17/178.00 (P24(f329(f329(f199(a24),x106291),x106291))), % 178.17/178.00 inference(rename_variables,[],[3267])). % 178.17/178.00 cnf(10634,plain, % 178.17/178.00 (P24(f329(f329(f243(a1),x106341),x106341))), % 178.17/178.00 inference(rename_variables,[],[3269])). % 178.17/178.00 cnf(10643,plain, % 178.17/178.00 (E(f329(f260(x106431,x106431),f261(x106431,x106432)),x106432)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(10646,plain, % 178.17/178.00 (P24(f329(f252(f883(x106461,a869)),x106462))), % 178.17/178.00 inference(rename_variables,[],[3333])). % 178.17/178.00 cnf(10649,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),f2(a875)),x106491))), % 178.17/178.00 inference(rename_variables,[],[3290])). % 178.17/178.00 cnf(10652,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x106521,a869)),f193(f883(x106521,a869))),x106522))), % 178.17/178.00 inference(rename_variables,[],[3717])). % 178.17/178.00 cnf(10655,plain, % 178.17/178.00 (P24(f329(f252(f883(x106551,a869)),x106552))), % 178.17/178.00 inference(rename_variables,[],[3333])). % 178.17/178.00 cnf(10657,plain, % 178.17/178.00 (~P24(f329(f329(f243(a875),f329(f329(f82(a875),f329(a118,x106571)),f329(a118,x106571))),x106571))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,10221,10322,10325,10328,10431,4457,10415,2855,3055,3224,10192,10256,10259,10349,10352,3098,3160,3127,3106,3195,3219,10456,4536,4467,10247,3158,10314,4050,4549,3178,3632,3573,3339,10333,10451,10522,10583,10586,3721,3250,4515,10224,10227,10253,4531,3708,3481,3854,3296,3297,3271,4512,4462,4003,3267,10342,10438,10569,3268,3269,10371,10426,3270,4511,10290,10380,10493,3428,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,3290,4094,4522,4501,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,4547,3717,3537,10575,10578,4543,3747,4541,10266,10269,10604,3719,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296])). % 178.17/178.00 cnf(10658,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x106581),f329(f329(f82(a875),x106581),x106581)))), % 178.17/178.00 inference(rename_variables,[],[3537])). % 178.17/178.00 cnf(10662,plain, % 178.17/178.00 (E(f329(f168(x106621),f172(x106622,f329(f329(f127(x106621),f329(f168(x106621),x106623)),f329(f329(f150(x106621),x106624),f119(x106621))),f119(x106622))),f329(f329(f150(x106621),x106624),x106623))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,10221,10322,10325,10328,10431,4457,10415,2855,3055,3224,10192,10256,10259,10349,10352,3202,3098,3160,3127,3106,3195,3219,10456,4536,4467,10247,3158,10314,4050,4549,3178,3632,3573,3339,10333,10451,10522,10583,10586,3721,3250,4515,10224,10227,10253,4531,3708,3481,3854,3296,3297,3271,4512,4462,4003,3267,10342,10438,10569,3268,3269,10371,10426,3270,4511,10290,10380,10493,3428,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,3290,4094,4522,4501,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,4547,3717,3537,10575,10578,4543,3747,4541,10266,10269,10604,3719,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337])). % 178.17/178.00 cnf(10663,plain, % 178.17/178.00 (E(f172(x106631,x106632,f119(x106631)),x106632)), % 178.17/178.00 inference(rename_variables,[],[3202])). % 178.17/178.00 cnf(10675,plain, % 178.17/178.00 (~P24(f329(f329(f243(a875),f329(a118,f329(a118,f329(f329(f81(a875),x106751),x106752)))),f329(a118,x106752)))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,10221,10322,10325,10328,10431,4457,10415,2855,3055,3224,10192,10256,10259,10349,10352,3202,3098,3160,3127,3106,3195,3219,10456,4536,4467,10247,3158,10314,4050,4549,3178,3632,3573,3339,10333,10451,10522,10583,10586,10622,3721,3250,4515,10224,10227,10253,4531,3708,3481,3854,3296,3297,3271,4512,4462,4003,3267,10342,10438,10569,3268,3269,10371,10426,3270,4511,10290,10380,10493,3428,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,3290,4094,4522,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,4547,3717,3537,10575,10578,4543,3747,4541,10266,10269,10604,3719,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345])). % 178.17/178.00 cnf(10698,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x106981),x106981))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(10709,plain, % 178.17/178.00 (~P24(f329(f329(f193(f883(x107091,f883(x107092,a869))),x107093),x107094))), % 178.17/178.00 inference(rename_variables,[],[4544])). % 178.17/178.00 cnf(10716,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x107161),f329(a118,x107161)))), % 178.17/178.00 inference(rename_variables,[],[3339])). % 178.17/178.00 cnf(10718,plain, % 178.17/178.00 (P24(f329(f329(f244(a1),f329(f329(f22(a1),x107181),f79(a1))),x107181))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,10221,10322,10325,10328,10431,4457,10415,2855,3055,3224,10192,10256,10259,10349,10352,3202,3098,3160,3127,3106,3195,3219,10456,4536,4467,10247,3158,10314,4050,3905,4549,3178,3632,3573,3339,10333,10451,10522,10583,10586,10622,3721,3250,4515,10224,10227,10253,4531,3708,3481,3854,3296,3297,3271,4512,4462,4003,3267,10342,10438,10569,3268,10698,3269,10371,10426,10634,3270,4511,10290,10380,10493,3428,4527,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,10613,3290,4094,4522,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,4547,3717,3537,10575,10578,4543,4544,3747,4541,10266,10269,10604,3719,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600])). % 178.17/178.00 cnf(10719,plain, % 178.17/178.00 (P24(f329(f329(f243(a1),x107191),x107191))), % 178.17/178.00 inference(rename_variables,[],[3269])). % 178.17/178.00 cnf(10724,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x107241),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(10737,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x107371),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(10740,plain, % 178.17/178.00 (~P24(f329(f329(f244(f883(x107401,a869)),x107402),f193(f883(x107401,a869))))), % 178.17/178.00 inference(rename_variables,[],[4537])). % 178.17/178.00 cnf(10743,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x107431),x107431))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(10746,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x107461),x107461))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(10760,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x107601),f329(f329(f22(a875),x107601),x107602)))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,10221,10322,10325,10328,10431,4457,10415,2855,3055,3224,10192,10256,10259,10349,10352,3202,3098,3160,3127,3106,3195,3219,10456,4536,4467,10247,3158,10314,4050,3905,4549,3178,3632,3573,3339,10333,10451,10522,10583,10586,10622,3721,3250,4515,10224,10227,10253,10724,4531,3708,3481,3854,3296,3297,3271,4512,4462,4014,4003,4537,3267,10342,10438,10569,3268,10698,10743,10746,3269,10371,10426,10634,3270,4511,10290,10380,10493,10517,3428,4527,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,10613,3290,4094,4522,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,4547,3717,3537,10575,10578,4543,4544,3747,4541,10266,10269,10604,3719,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763])). % 178.17/178.00 cnf(10761,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x107611),x107611))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(10770,plain, % 178.17/178.00 (~P24(f329(f329(f331(x107701),x107702),f193(f883(x107701,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(10779,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x107791),x107791))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(10782,plain, % 178.17/178.00 (~P24(f329(f329(f331(x107821),x107822),f193(f883(x107821,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(10785,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x107851,a869)),f329(f308(x107852,x107851,x107853),f329(f309(x107852,x107851,x107853),x107854))),x107854))), % 178.17/178.00 inference(rename_variables,[],[4154])). % 178.17/178.00 cnf(10792,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x107921,a869)),f329(f171(x107921),f329(f135(x107921,x107922),x107923))),f329(f171(x107921),x107923)))), % 178.17/178.00 inference(rename_variables,[],[3915])). % 178.17/178.00 cnf(10795,plain, % 178.17/178.00 (E(f329(f308(x107951,x107951,f5(x107951)),x107952),x107952)), % 178.17/178.00 inference(rename_variables,[],[3329])). % 178.17/178.00 cnf(10800,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),f2(a875)),x108001))), % 178.17/178.00 inference(rename_variables,[],[3290])). % 178.17/178.00 cnf(10803,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x108031),x108031))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(10806,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x108061),x108061))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(10809,plain, % 178.17/178.00 (~P24(f329(f329(f193(f883(x108091,f883(x108092,a869))),x108093),x108094))), % 178.17/178.00 inference(rename_variables,[],[4544])). % 178.17/178.00 cnf(10816,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x108161),x108161))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(10827,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x108271),f329(a118,f329(f329(f81(a875),x108272),x108271))))), % 178.17/178.00 inference(rename_variables,[],[3719])). % 178.17/178.00 cnf(10830,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x108301),f329(f329(f82(a875),x108301),x108301)))), % 178.17/178.00 inference(rename_variables,[],[3537])). % 178.17/178.00 cnf(10840,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x108401),x108401))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(10843,plain, % 178.17/178.00 (P24(f329(f329(f243(a1),x108431),x108431))), % 178.17/178.00 inference(rename_variables,[],[3269])). % 178.17/178.00 cnf(10846,plain, % 178.17/178.00 (~E(f329(a118,x108461),x108461)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(10851,plain, % 178.17/178.00 (P24(f329(f329(f331(x108511),x108512),f252(f883(x108511,a869))))), % 178.17/178.00 inference(rename_variables,[],[3428])). % 178.17/178.00 cnf(10856,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x108561),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(10871,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),f2(a875)),x108711))), % 178.17/178.00 inference(rename_variables,[],[3290])). % 178.17/178.00 cnf(10878,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x108781),x108781))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(10887,plain, % 178.17/178.00 (~P24(f329(f329(f331(x108871),x108872),f193(f883(x108871,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(10889,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x108891,a869)),f41(f883(x108891,a869),f329(f306(x108891),x108892))),x108892))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,4457,10415,2855,3055,3224,10192,10256,10259,10349,10352,3202,3098,3160,3127,3106,3329,3195,3219,10456,4536,4467,10247,3158,10314,4050,3905,4549,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,3721,3250,4515,10224,10227,10253,10724,10737,4531,3708,3481,3854,3296,3297,3271,4512,4462,4014,3915,10792,3633,4003,4537,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,4527,10770,10782,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,10613,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,4547,3717,3537,10575,10578,10658,10830,4543,4544,10709,4154,3747,4541,10266,10269,10604,3719,10572,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749])). % 178.17/178.00 cnf(10891,plain, % 178.17/178.00 (E(f329(f329(f107(f883(x108911,a869)),f329(f329(f107(f883(x108911,a869)),x108912),f329(f80(f883(x108911,a869)),x108913))),x108913),f193(f883(x108911,a869)))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,4457,10415,2855,3055,3224,10192,10256,10259,10349,10352,3202,3098,3160,3127,3106,3329,3195,3219,10456,4536,4467,10247,3158,10314,4050,3905,4549,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,3721,3250,4515,10224,10227,10253,10724,10737,4531,3708,3481,3854,3296,3297,3271,4512,4462,4014,3915,10792,3633,4003,4537,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,4527,10770,10782,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,10613,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,4547,3717,3537,10575,10578,10658,10830,4543,4544,10709,4154,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751])). % 178.17/178.00 cnf(10894,plain, % 178.17/178.00 (P24(f329(f329(f331(f876(x108941)),x108942),f160(x108941,f252(f883(x108941,a869)))))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,4457,10415,2855,3055,3224,10192,10256,10259,10349,10352,3202,3098,3160,3127,3106,3329,3195,3219,10456,4536,4467,10247,3158,10314,4050,3905,4549,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,3721,3250,4515,10224,10227,10253,10724,10737,4531,3708,3481,3854,3296,3297,3271,4512,4462,4014,3915,10792,3633,4003,4537,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,4527,10770,10782,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,10613,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,4547,3717,3537,10575,10578,10658,10830,4543,4544,10709,4154,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759])). % 178.17/178.00 cnf(10895,plain, % 178.17/178.00 (P24(f329(f329(f331(x108951),x108952),f252(f883(x108951,a869))))), % 178.17/178.00 inference(rename_variables,[],[3428])). % 178.17/178.00 cnf(10898,plain, % 178.17/178.00 (~P24(f329(f329(f331(f882(f876(x108981),f876(x108981))),f329(f329(f264(f876(x108981),f876(x108981)),x108982),f119(x108981))),f146(x108981,x108983)))), % 178.17/178.00 inference(rename_variables,[],[4549])). % 178.17/178.00 cnf(10904,plain, % 178.17/178.00 (~P24(f329(f329(f331(f882(x109041,x109041)),x109042),f261(x109041,f193(f883(x109041,a869)))))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,4457,10415,2855,3055,3224,10192,10256,10259,10349,10352,3202,3098,3160,3127,3106,3329,3195,3219,10456,4536,4467,10247,3158,10314,4050,3905,4549,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,3721,3250,4515,10224,10227,10253,10724,10737,4531,3708,3481,3854,3296,3297,3271,4512,4462,4014,3915,10792,3633,4003,4537,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,4527,10770,10782,10887,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,10613,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,4547,3717,3537,10575,10578,10658,10830,4543,4544,10709,4154,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890])). % 178.17/178.00 cnf(10905,plain, % 178.17/178.00 (~P24(f329(f329(f331(x109051),x109052),f193(f883(x109051,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(10907,plain, % 178.17/178.00 (~P24(f329(f329(f331(x109071),x109072),f329(f309(x109071,x109073,x109074),f193(f883(x109073,a869)))))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,4457,10415,2855,3055,3224,10192,10256,10259,10349,10352,3202,3098,3160,3127,3106,3329,3195,3219,10456,4536,4467,10247,3158,10314,4050,3905,4549,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,3721,3250,4515,10224,10227,10253,10724,10737,4531,3708,3481,3854,3296,3297,3271,4512,4462,4014,3915,10792,3633,4003,4537,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,4527,10770,10782,10887,10905,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,10613,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,4547,3717,3537,10575,10578,10658,10830,4543,4544,10709,4154,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924])). % 178.17/178.00 cnf(10908,plain, % 178.17/178.00 (~P24(f329(f329(f331(x109081),x109082),f193(f883(x109081,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(10911,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x109111,a869)),x109112),f329(f329(f307(x109111),x109113),x109112)))), % 178.17/178.00 inference(rename_variables,[],[3715])). % 178.17/178.00 cnf(10914,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x109141),x109141))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(10917,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x109171,a869)),x109172),f329(f329(f307(x109171),x109173),x109172)))), % 178.17/178.00 inference(rename_variables,[],[3715])). % 178.17/178.00 cnf(10919,plain, % 178.17/178.00 (P35(x109191,x109192,x109193,f120(x109191,f119(x109191)),f119(x109192))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,4457,10415,2855,3055,3108,3224,10192,10256,10259,10349,10352,3202,3098,3160,3127,3106,3329,3195,3219,10456,4536,4467,10247,3158,10314,4050,3905,4549,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,3721,3250,4515,10224,10227,10253,10724,10737,4531,3708,3481,3854,3296,3297,3271,4512,4462,4014,3915,10792,3633,4003,4537,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,4527,10770,10782,10887,10905,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,10613,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,4547,3715,10911,3717,3537,10575,10578,10658,10830,4543,4544,10709,4154,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035])). % 178.17/178.00 cnf(10932,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x109321,a869)),x109322),f329(f329(f307(x109321),x109323),x109322)))), % 178.17/178.00 inference(rename_variables,[],[3715])). % 178.17/178.00 cnf(10937,plain, % 178.17/178.00 (~P24(f329(f63(x109371,x109372,f193(f883(x109371,a869))),x109373))), % 178.17/178.00 inference(rename_variables,[],[4539])). % 178.17/178.00 cnf(10941,plain, % 178.17/178.00 (~P24(f329(f329(f331(f882(a875,a875)),f329(f329(f264(a875,a875),f329(a118,x109411)),x109411)),f305(a875,a319)))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,4457,10415,2855,3055,3108,3224,10192,10256,10259,10349,10352,3202,3098,3160,3127,3106,3329,3195,3219,10456,4536,4467,10247,3158,10314,4050,3905,4549,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,3721,3250,4515,10224,10227,10253,10724,10737,4531,3708,3481,3854,3296,3297,3271,4512,4462,4014,3915,10792,3633,4003,4537,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,10895,4527,10770,10782,10887,10905,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,10613,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,10533,4547,3871,3715,10911,10917,3717,3537,10575,10578,10658,10830,4543,4544,10709,4154,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357])). % 178.17/178.00 cnf(10950,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x109501),f329(a118,x109501)))), % 178.17/178.00 inference(rename_variables,[],[3339])). % 178.17/178.00 cnf(10960,plain, % 178.17/178.00 (~E(f329(f308(x109601,f883(x109601,a869),x109602),x109603),f329(f306(x109601),x109603))), % 178.17/178.00 inference(rename_variables,[],[4525])). % 178.17/178.00 cnf(10963,plain, % 178.17/178.00 (~P24(f329(f329(f331(x109631),x109632),f193(f883(x109631,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(10966,plain, % 178.17/178.00 (P24(f329(f329(f331(f882(x109661,x109661)),f329(f329(f264(x109661,x109661),x109662),x109662)),f305(x109661,x109663)))), % 178.17/178.00 inference(rename_variables,[],[3905])). % 178.17/178.00 cnf(10969,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x109691,a869)),f329(f171(x109691),f169(x109691,x109692,x109693))),f329(f171(x109691),x109693)))), % 178.17/178.00 inference(rename_variables,[],[3966])). % 178.17/178.00 cnf(10972,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x109721,a869)),x109722),f252(f883(x109721,a869))))), % 178.17/178.00 inference(rename_variables,[],[3651])). % 178.17/178.00 cnf(10988,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x109881,a869)),f193(f883(x109881,a869))),x109882))), % 178.17/178.00 inference(rename_variables,[],[3717])). % 178.17/178.00 cnf(10999,plain, % 178.17/178.00 (~P24(f329(f329(f331(f882(f876(x109991),f876(x109991))),f329(f329(f264(f876(x109991),f876(x109991)),x109992),f119(x109991))),f146(x109991,x109993)))), % 178.17/178.00 inference(rename_variables,[],[4549])). % 178.17/178.00 cnf(11010,plain, % 178.17/178.00 (~E(f329(a118,x110101),x110101)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(11013,plain, % 178.17/178.00 (~E(f329(a118,x110131),x110131)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(11015,plain, % 178.17/178.00 (P24(f329(f329(f331(f882(f876(x110151),f876(x110151))),f329(f329(f264(f876(x110151),f876(x110151)),f119(x110151)),f119(x110151))),f329(f329(f286(f876(x110151),f876(x110151),f876(x110151)),f157(x110151,x110152)),f305(f876(x110151),f157(x110151,x110152)))))), % 178.17/178.00 inference(scs_inference,[],[4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,4457,10415,2855,3055,3108,3224,10192,10256,10259,10349,10352,3202,3729,3098,3160,3127,3106,3329,3195,3219,10456,4536,3903,4467,10247,4525,3158,10314,4050,3905,10966,4549,10898,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,3721,3250,4515,10224,10227,10253,10724,10737,10856,4531,3708,3481,3854,3296,3297,3271,4512,4462,4014,3915,10792,3966,3633,4003,3651,4537,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,10895,4527,10770,10782,10887,10905,10908,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,10613,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,10533,4547,3871,3715,10911,10917,3717,10652,3537,10575,10578,10658,10830,4543,4544,10709,4154,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589])). % 178.17/178.00 cnf(11025,plain, % 178.17/178.00 (P21(x110251,x110251,f5(x110251),x110252)), % 178.17/178.00 inference(rename_variables,[],[3511])). % 178.17/178.00 cnf(11030,plain, % 178.17/178.00 (~E(f329(f308(x110301,f883(x110301,a869),x110302),x110303),f329(f306(x110301),x110303))), % 178.17/178.00 inference(rename_variables,[],[4525])). % 178.17/178.00 cnf(11035,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x110351,a869)),x110352),f252(f883(x110351,a869))))), % 178.17/178.00 inference(rename_variables,[],[3651])). % 178.17/178.00 cnf(11049,plain, % 178.17/178.00 (~P24(f329(f329(f331(x110491),x110492),f193(f883(x110491,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(11052,plain, % 178.17/178.00 (~P24(f329(f329(f243(a875),f329(a118,x110521)),x110521))), % 178.17/178.00 inference(rename_variables,[],[4524])). % 178.17/178.00 cnf(11057,plain, % 178.17/178.00 (~P24(f329(f329(f331(x110571),x110572),f193(f883(x110571,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(11069,plain, % 178.17/178.00 (~P24(f329(f329(f331(a875),f329(a118,f329(f141(a875,a875,f81(a875),f2(a875)),x110691))),f329(f171(a875),x110691)))), % 178.17/178.00 inference(scs_inference,[],[3511,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,4457,10415,10508,2855,3055,3108,3224,10192,10256,10259,10349,10352,3202,3729,3098,3160,3127,3106,3329,3195,3219,10456,4536,3903,4467,10247,4525,10960,3376,3158,10314,4050,3905,10966,4549,10898,10999,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,3250,4515,10224,10227,10253,10724,10737,10856,4531,3708,3481,3854,3296,3297,3271,4512,4462,4014,3915,10792,3966,3633,4003,3651,10972,4537,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,10895,4527,10770,10782,10887,10905,10908,10963,11049,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,10613,11052,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,10533,4547,3871,3715,10911,10917,3717,10652,3537,10575,10578,10658,10830,4543,4544,10709,4154,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807])). % 178.17/178.00 cnf(11070,plain, % 178.17/178.00 (~P24(f329(f329(f243(a875),f329(a118,x110701)),x110701))), % 178.17/178.00 inference(rename_variables,[],[4524])). % 178.17/178.00 cnf(11073,plain, % 178.17/178.00 (~P24(f329(f329(f331(x110731),x110732),f193(f883(x110731,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(11083,plain, % 178.17/178.00 (E(f329(x110831,f676(f329(x110831,x110832),f329(f236(x110833),x110832),x110831,x110834,x110833)),f329(x110831,x110832))), % 178.17/178.00 inference(scs_inference,[],[3511,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,4457,10415,10508,2855,3055,3108,3224,10192,10256,10259,10349,10352,3202,3729,3098,3160,3127,3106,3329,3195,3219,10456,3375,4536,3903,4467,10247,4525,10960,3376,3158,10314,4050,3905,10966,4549,10898,10999,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,3250,4515,10224,10227,10253,10724,10737,10856,4531,3708,3481,3854,3296,3297,3271,4512,4462,4014,3915,10792,3966,3633,4003,3651,10972,4537,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,10895,4527,10770,10782,10887,10905,10908,10963,11049,11057,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,10613,11052,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,10533,4547,3871,3715,10911,10917,3717,10652,3537,10575,10578,10658,10830,4543,4544,10709,4154,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882])). % 178.17/178.00 cnf(11092,plain, % 178.17/178.00 (P24(f329(f329(f331(f882(x110921,x110921)),f329(f329(f264(x110921,x110921),x110922),x110922)),f305(x110921,x110923)))), % 178.17/178.00 inference(rename_variables,[],[3905])). % 178.17/178.00 cnf(11097,plain, % 178.17/178.00 (~P24(f329(f329(f331(f882(f876(x110971),f876(x110971))),f329(f329(f264(f876(x110971),f876(x110971)),x110972),f119(x110971))),f146(x110971,x110973)))), % 178.17/178.00 inference(rename_variables,[],[4549])). % 178.17/178.00 cnf(11100,plain, % 178.17/178.00 (~P24(f329(f329(f331(f882(f876(x111001),f876(x111001))),f329(f329(f264(f876(x111001),f876(x111001)),x111002),f119(x111001))),f144(x111001,x111003)))), % 178.17/178.00 inference(rename_variables,[],[4550])). % 178.17/178.00 cnf(11103,plain, % 178.17/178.00 (~P24(f329(f329(f331(f882(f876(x111031),f876(x111031))),f329(f329(f264(f876(x111031),f876(x111031)),x111032),f119(x111031))),f156(x111031,x111033)))), % 178.17/178.00 inference(rename_variables,[],[4551])). % 178.17/178.00 cnf(11108,plain, % 178.17/178.00 (~P24(f329(f329(f244(f883(x111081,a869)),x111082),f193(f883(x111081,a869))))), % 178.17/178.00 inference(rename_variables,[],[4537])). % 178.17/178.00 cnf(11111,plain, % 178.17/178.00 (~P24(f329(f329(f331(x111111),x111112),f193(f883(x111111,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(11115,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x111151,a869)),x111152),f329(f329(f116(f883(x111151,a869)),x111153),f252(f883(x111151,a869)))))), % 178.17/178.00 inference(scs_inference,[],[3511,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,4457,10415,10508,2855,3055,3108,3224,10192,10256,10259,10349,10352,3202,3729,3098,3160,3127,3106,3329,3195,3219,10456,3375,4536,3903,4467,10247,4525,10960,3376,3158,10314,4050,3905,10966,4549,10898,10999,11097,4550,4551,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,3250,4515,10224,10227,10253,10724,10737,10856,4531,3708,3481,3854,3296,3297,3271,4512,4462,4014,3915,10792,3966,3633,4003,3651,10972,11035,4537,10740,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,10895,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,10613,11052,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,10533,4547,3871,3715,10911,10917,3717,10652,3537,10575,10578,10658,10830,4543,4544,10709,4154,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081])). % 178.17/178.00 cnf(11116,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x111161,a869)),x111162),f252(f883(x111161,a869))))), % 178.17/178.00 inference(rename_variables,[],[3651])). % 178.17/178.00 cnf(11119,plain, % 178.17/178.00 (~P24(f329(f329(f193(f883(x111191,f883(x111192,a869))),x111193),x111194))), % 178.17/178.00 inference(rename_variables,[],[4544])). % 178.17/178.00 cnf(11128,plain, % 178.17/178.00 (~P24(f329(f329(f331(x111281),x111282),f193(f883(x111281,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(11131,plain, % 178.17/178.00 (~P24(f329(f329(f331(f882(x111311,x111311)),f329(f329(f264(x111311,x111311),x111312),x111313)),f152(x111311,f119(f883(x111311,a875)))))), % 178.17/178.00 inference(rename_variables,[],[4547])). % 178.17/178.00 cnf(11134,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x111341,a869)),x111342),x111342))), % 178.17/178.00 inference(rename_variables,[],[3569])). % 178.17/178.00 cnf(11137,plain, % 178.17/178.00 (~P24(f329(f329(f331(x111371),x111372),f193(f883(x111371,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(11139,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x111391,a869)),f329(f283(x111392,x111391,f193(f883(f882(x111392,x111391),a869))),x111393)),x111394))), % 178.17/178.00 inference(scs_inference,[],[3511,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,4457,10415,10508,2855,3055,3108,3224,10192,10256,10259,10349,10352,3202,3729,3098,3160,3127,3106,3329,3195,3219,10456,3375,4536,3903,4467,10247,4525,10960,3376,3158,10314,4050,3905,10966,4549,10898,10999,11097,4550,4551,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,3250,4515,10224,10227,10253,10724,10737,10856,4531,3708,3481,3854,3296,3297,3271,4512,4462,4014,3915,10792,3966,3633,4003,3651,10972,11035,4537,10740,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,10895,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,10613,11052,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,10533,4547,3871,3715,10911,10917,3569,3717,10652,10988,3537,10575,10578,10658,10830,4543,4544,10709,10809,4154,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253])). % 178.17/178.00 cnf(11140,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x111401,a869)),f193(f883(x111401,a869))),x111402))), % 178.17/178.00 inference(rename_variables,[],[3717])). % 178.17/178.00 cnf(11143,plain, % 178.17/178.00 (P24(f329(f329(f331(f882(x111431,x111431)),f329(f329(f264(x111431,x111431),x111432),x111432)),f305(x111431,x111433)))), % 178.17/178.00 inference(rename_variables,[],[3905])). % 178.17/178.00 cnf(11145,plain, % 178.17/178.00 (~P35(x111451,x111452,x111453,f329(f329(f153(x111454,x111451),x111455),f329(a118,f119(x111454))),f119(x111452))), % 178.17/178.00 inference(scs_inference,[],[3511,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,4457,10415,10508,2855,3055,3108,3224,10192,10256,10259,10349,10352,3202,3729,3098,3160,3127,3106,3329,3195,3219,10456,3375,4536,3903,4467,10247,4525,10960,3376,3158,10314,4050,3905,10966,11092,4549,10898,10999,11097,4550,4551,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,3250,4515,10224,10227,10253,10724,10737,10856,4531,3708,3481,3854,3296,3297,3271,4512,4462,4014,3915,10792,3966,3633,4003,3651,10972,11035,4537,10740,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,10895,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,10613,11052,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,10533,4547,3871,3715,10911,10917,3569,3717,10652,10988,3537,10575,10578,10658,10830,4543,4544,10709,10809,4154,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262])). % 178.17/178.00 cnf(11147,plain, % 178.17/178.00 (~E(f329(f329(f107(f883(f882(f876(x111471),f876(x111471)),a869)),f329(f284(f876(x111471),f876(x111471)),f157(x111471,x111472))),f305(f876(x111471),f157(x111471,x111472))),f193(f883(f882(f876(x111471),f876(x111471)),a869)))), % 178.17/178.00 inference(scs_inference,[],[3511,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,4457,10415,10508,2855,3055,3108,3224,10192,10256,10259,10349,10352,3202,3729,3098,3160,3127,3106,3329,3195,3219,10456,3375,4536,3903,4467,10247,4525,10960,3376,3158,10314,4050,3905,10966,11092,4549,10898,10999,11097,4550,4551,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,3250,4515,10224,10227,10253,10724,10737,10856,4531,3708,3481,3854,3296,3297,3271,4512,4462,4014,3915,10792,3966,3633,4003,3651,10972,11035,4537,10740,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,10895,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,10613,11052,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,10533,4547,3871,3715,10911,10917,3569,3717,10652,10988,3537,10575,10578,10658,10830,4543,4544,10709,10809,4154,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284])). % 178.17/178.00 cnf(11149,plain, % 178.17/178.00 (P35(x111491,x111492,x111493,f329(f329(f153(x111494,x111491),x111495),f120(x111494,f119(x111494))),f119(x111492))), % 178.17/178.00 inference(scs_inference,[],[3511,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,4457,10415,10508,2855,3055,3108,3224,10192,10256,10259,10349,10352,3202,3729,3098,3160,3127,3106,3329,3195,3219,10456,3375,4536,3903,4467,10247,4525,10960,3376,3158,10314,4050,3905,10966,11092,4549,10898,10999,11097,4550,4551,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,3250,4515,10224,10227,10253,10724,10737,10856,4531,3708,3481,3854,3296,3297,3271,4512,4462,4014,3915,10792,3966,3633,4003,3651,10972,11035,4537,10740,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,10895,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,10613,11052,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,10533,4547,3871,3715,10911,10917,3569,3717,10652,10988,3537,10575,10578,10658,10830,4543,4544,10709,10809,4154,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285])). % 178.17/178.00 cnf(11154,plain, % 178.17/178.00 (~P24(f329(f329(f331(f882(f876(x111541),f876(x111541))),f329(f329(f264(f876(x111541),f876(x111541)),x111542),f119(x111541))),f156(x111541,x111543)))), % 178.17/178.00 inference(rename_variables,[],[4551])). % 178.17/178.00 cnf(11157,plain, % 178.17/178.00 (~P24(f329(f329(f331(f882(f876(x111571),f876(x111571))),f329(f329(f264(f876(x111571),f876(x111571)),f119(x111571)),x111572)),f144(x111571,x111573)))), % 178.17/178.00 inference(rename_variables,[],[4552])). % 178.17/178.00 cnf(11162,plain, % 178.17/178.00 (~P24(f329(f329(f331(f882(f883(x111621,a869),f883(x111621,a869))),f329(f329(f264(f883(x111621,a869),f883(x111621,a869)),x111622),f193(f883(x111621,a869)))),f304(x111621)))), % 178.17/178.00 inference(scs_inference,[],[3511,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,4457,10415,10508,2855,3055,3108,3224,10192,10256,10259,10349,10352,3202,3729,3098,3160,3127,3106,3329,3195,3219,10456,3375,4536,3903,4467,10247,4525,10960,3376,3158,10314,4050,3905,10966,11092,4549,10898,10999,11097,4550,4551,11103,4552,4553,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,3250,4515,10224,10227,10253,10724,10737,10856,4531,3708,3481,3854,3296,3297,3271,4512,4462,4014,3915,10792,3966,3633,4003,3651,10972,11035,4537,10740,11108,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,10895,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,10613,11052,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,10533,4547,3871,3715,10911,10917,3569,3717,10652,10988,3537,10575,10578,10658,10830,4543,4544,10709,10809,4154,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411])). % 178.17/178.00 cnf(11165,plain, % 178.17/178.00 (P24(f329(f329(f331(x111651),x111652),f252(f883(x111651,a869))))), % 178.17/178.00 inference(rename_variables,[],[3428])). % 178.17/178.00 cnf(11170,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x111701,a869)),f193(f883(x111701,a869))),x111702))), % 178.17/178.00 inference(rename_variables,[],[3717])). % 178.17/178.00 cnf(11173,plain, % 178.17/178.00 (~P24(f329(f329(f331(x111731),x111732),f193(f883(x111731,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(11176,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x111761,a869)),x111762),f252(f883(x111761,a869))))), % 178.17/178.00 inference(rename_variables,[],[3651])). % 178.17/178.00 cnf(11180,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x111801,a869)),f329(f283(x111802,x111801,x111803),f193(f883(x111802,a869)))),x111804))), % 178.17/178.00 inference(scs_inference,[],[3511,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,4457,10415,10508,2855,3055,3108,3224,10192,10256,10259,10349,10352,3202,3729,3098,3160,3127,3106,3329,3195,3219,10456,3375,4536,3903,4467,10247,4525,10960,3376,3158,10314,4050,3905,10966,11092,4549,10898,10999,11097,4550,4551,11103,4552,4553,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,3250,4515,10224,10227,10253,10724,10737,10856,4531,3708,3481,3854,3296,3297,3271,4512,4462,4014,3915,10792,3966,3633,4003,3651,10972,11035,11116,4537,10740,11108,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,10895,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,10613,11052,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,10533,4547,3871,3715,10911,10917,3569,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,4544,10709,10809,4154,4055,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516])). % 178.17/178.00 cnf(11181,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x111811,a869)),f193(f883(x111811,a869))),x111812))), % 178.17/178.00 inference(rename_variables,[],[3717])). % 178.17/178.00 cnf(11183,plain, % 178.17/178.00 (~P24(f329(f67(a875,x111831,x111832,x111833,f252(f883(a875,a869))),x111834))), % 178.17/178.00 inference(scs_inference,[],[3511,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,4457,10415,10508,2855,3055,3108,3224,10192,10256,10259,10349,10352,3202,3729,3098,3160,3127,3106,3329,3195,3219,10456,3375,4536,3903,4467,10247,4525,10960,3376,3158,10314,4050,3905,10966,11092,4549,10898,10999,11097,4550,4551,11103,4552,4553,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,3250,4515,10224,10227,10253,10724,10737,10856,4531,3708,3481,3854,3296,3297,3271,4512,4462,4014,3915,10792,3966,3633,4003,3651,10972,11035,11116,4537,10740,11108,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,10895,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,3333,10616,10646,3365,3787,3726,10293,4524,10244,10610,10613,11052,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,10533,4547,3871,3715,10911,10917,3569,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,4544,10709,10809,4154,4055,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538])). % 178.17/178.00 cnf(11194,plain, % 178.17/178.00 (P24(f329(f252(f883(x111941,a869)),x111942))), % 178.17/178.00 inference(rename_variables,[],[3333])). % 178.17/178.00 cnf(11202,plain, % 178.17/178.00 (~P24(f329(f329(f331(f882(f876(x112021),f876(x112021))),f329(f329(f264(f876(x112021),f876(x112021)),x112022),f119(x112021))),f146(x112021,x112023)))), % 178.17/178.00 inference(rename_variables,[],[4549])). % 178.17/178.00 cnf(11205,plain, % 178.17/178.00 (~P24(f329(f329(f331(f882(f876(x112051),f876(x112051))),f329(f329(f264(f876(x112051),f876(x112051)),x112052),f119(x112051))),f144(x112051,x112053)))), % 178.17/178.00 inference(rename_variables,[],[4550])). % 178.17/178.00 cnf(11208,plain, % 178.17/178.00 (~E(f329(f329(f150(x112081),x112082),x112083),x112083)), % 178.17/178.00 inference(rename_variables,[],[4467])). % 178.17/178.00 cnf(11211,plain, % 178.17/178.00 (~E(f329(a118,x112111),x112111)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(11214,plain, % 178.17/178.00 (~P24(f329(f329(f331(x112141),x112142),f193(f883(x112141,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(11219,plain, % 178.17/178.00 (P24(f329(f329(f331(f882(f876(x112191),f876(x112191))),f329(f329(f264(f876(x112191),f876(x112191)),x112192),x112192)),f157(x112191,f305(x112191,x112193))))), % 178.17/178.00 inference(rename_variables,[],[4044])). % 178.17/178.00 cnf(11224,plain, % 178.17/178.00 (~P24(f329(f329(f331(f882(f876(x112241),f876(x112241))),f329(f329(f264(f876(x112241),f876(x112241)),x112242),f119(x112241))),f146(x112241,x112243)))), % 178.17/178.00 inference(rename_variables,[],[4549])). % 178.17/178.00 cnf(11228,plain, % 178.17/178.00 (E(f329(f329(f150(x112281),f609(f305(x112281,x112282),f329(f329(f150(x112281),x112283),x112284),x112284,x112283,x112281)),f610(f305(x112281,x112282),f329(f329(f150(x112281),x112283),x112284),x112284,x112283,x112281)),f329(f329(f150(x112281),x112283),x112284))), % 178.17/178.00 inference(scs_inference,[],[3511,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,4457,10415,10508,2855,3055,3108,3224,10192,10256,10259,10349,10352,3202,3729,3098,3160,3127,3106,3329,3195,3219,10456,3375,4536,3903,4467,10247,10412,4525,10960,3376,3158,10314,4050,3905,10966,11092,4549,10898,10999,11097,11202,4550,11100,4551,11103,4552,11157,4553,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,3250,4515,10224,10227,10253,10724,10737,10856,4531,3708,3481,3854,3296,3297,3271,4512,4462,4044,11219,4014,3915,10792,3966,3633,4003,3651,10972,11035,11116,4537,10740,11108,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,10895,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,3333,10616,10646,10655,3365,3787,3726,10293,4524,10244,10610,10613,11052,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,10533,4547,3871,3715,10911,10917,3569,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,4544,10709,10809,4154,4055,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708])). % 178.17/178.00 cnf(11233,plain, % 178.17/178.00 (~P24(f329(f329(f331(x112331),x112332),f185(x112333,x112331,f187(x112333,x112331,x112334,f193(f883(x112333,a869))))))), % 178.17/178.00 inference(scs_inference,[],[3511,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,4457,10415,10508,2855,3055,3108,3224,10192,10256,10259,10349,10352,3202,3729,3098,3160,3127,3106,3329,3195,3219,10456,3375,4536,3903,4467,10247,10412,4525,10960,3376,3158,10314,4050,3905,10966,11092,4549,10898,10999,11097,11202,4550,11100,4551,11103,4552,11157,4553,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,3250,4515,10224,10227,10253,10724,10737,10856,4531,3708,3481,3854,3296,3297,3271,4512,4462,4044,11219,4014,3915,10792,3966,3633,4003,3651,10972,11035,11116,4537,10740,11108,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,10895,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,3333,10616,10646,10655,3365,3787,3726,10293,4524,10244,10610,10613,11052,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,10533,4547,3871,3715,10911,10917,3569,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,4544,10709,10809,4154,4055,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731])). % 178.17/178.00 cnf(11234,plain, % 178.17/178.00 (~P24(f329(f329(f331(x112341),x112342),f193(f883(x112341,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(11237,plain, % 178.17/178.00 (~P24(f329(f329(f331(x112371),x112372),f193(f883(x112371,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(11240,plain, % 178.17/178.00 (~P24(f329(f329(f331(x112401),x112402),f193(f883(x112401,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(11243,plain, % 178.17/178.00 (P24(f329(f329(f331(x112431),x112432),f252(f883(x112431,a869))))), % 178.17/178.00 inference(rename_variables,[],[3428])). % 178.17/178.00 cnf(11246,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x112461),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(11251,plain, % 178.17/178.00 (~P24(f329(f329(f331(f882(x112511,x112511)),f329(f329(f264(x112511,x112511),x112512),x112513)),f152(x112511,f119(f883(x112511,a875)))))), % 178.17/178.00 inference(rename_variables,[],[4547])). % 178.17/178.00 cnf(11254,plain, % 178.17/178.00 (~E(f329(f308(x112541,f883(x112541,a869),x112542),x112543),f329(f306(x112541),x112543))), % 178.17/178.00 inference(rename_variables,[],[4525])). % 178.17/178.00 cnf(11257,plain, % 178.17/178.00 (~E(f329(f308(x112571,f883(x112571,a869),x112572),x112573),f329(f306(x112571),x112573))), % 178.17/178.00 inference(rename_variables,[],[4525])). % 178.17/178.00 cnf(11259,plain, % 178.17/178.00 (E(f329(f329(f264(a875,a875),f797(f305(a875,a319),a319,a875,f329(f329(f264(a875,a875),x112591),f329(a118,x112591)),a875,a875)),f798(f305(a875,a319),a319,a875,f329(f329(f264(a875,a875),x112591),f329(a118,x112591)),a875,a875)),f329(f329(f264(a875,a875),x112591),f329(a118,x112591)))), % 178.17/178.00 inference(scs_inference,[],[3511,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,4457,10415,10508,2855,3055,3108,3224,10192,10256,10259,10349,10352,3202,3729,3098,3160,3127,3106,3329,3195,3219,10456,3375,4536,3903,4467,10247,10412,4525,10960,11030,11254,3376,3158,10314,4050,3905,10966,11092,4549,10898,10999,11097,11202,4550,11100,4551,11103,4552,11157,4553,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,3250,4515,10224,10227,10253,10724,10737,10856,4531,3708,3481,3854,3296,3297,3271,4512,4462,4044,11219,4014,3915,10792,3966,3633,4003,3651,10972,11035,11116,4537,10740,11108,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,10895,11165,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,3333,10616,10646,10655,3365,3787,3726,10293,4524,10244,10610,10613,11052,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,10533,4547,11131,3871,3715,10911,10917,3569,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,4544,10709,10809,4154,4055,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902])). % 178.17/178.00 cnf(11262,plain, % 178.17/178.00 (~P24(f329(f329(f331(f882(f876(x112621),f876(x112621))),f329(f329(f264(f876(x112621),f876(x112621)),x112622),f119(x112621))),f146(x112621,x112623)))), % 178.17/178.00 inference(rename_variables,[],[4549])). % 178.17/178.00 cnf(11268,plain, % 178.17/178.00 (~P24(f329(f329(f331(f882(f876(x112681),f876(x112681))),f329(f329(f264(f876(x112681),f876(x112681)),x112682),f119(x112681))),f146(x112681,x112683)))), % 178.17/178.00 inference(rename_variables,[],[4549])). % 178.17/178.00 cnf(11271,plain, % 178.17/178.00 (~P24(f329(f329(f331(x112711),x112712),f193(f883(x112711,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(11275,plain, % 178.17/178.00 (P24(f329(f329(f331(f882(x112751,x112752)),f329(f329(f264(x112751,x112752),f329(x112753,x112754)),f329(x112755,x112754))),f329(f308(f882(x112756,x112756),f882(x112751,x112752),f269(x112756,x112751,x112756,x112752,x112753,x112755)),f305(x112756,x112757))))), % 178.17/178.00 inference(scs_inference,[],[3511,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,4457,10415,10508,2855,3055,3108,3224,10192,10256,10259,10349,10352,3202,3729,3098,3160,3127,3106,3329,3195,3219,10456,3375,4536,3903,4467,10247,10412,4525,10960,11030,11254,3376,3158,10314,4050,3905,10966,11092,11143,4549,10898,10999,11097,11202,11224,11262,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,3632,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,3250,4515,10224,10227,10253,10724,10737,10856,4531,3708,3481,3854,3296,3297,3271,4512,4462,4044,11219,4014,3915,10792,3966,3633,4003,3651,10972,11035,11116,4537,10740,11108,3267,10342,10438,10569,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,10895,11165,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,3333,10616,10646,10655,3365,3787,3726,10293,4524,10244,10610,10613,11052,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4539,10215,10218,10474,10525,10528,10533,4547,11131,3871,3715,10911,10917,3569,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,4544,10709,10809,4154,4055,3747,4541,10266,10269,10604,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030])). % 178.17/178.00 cnf(11278,plain, % 178.17/178.00 (~P24(f329(f329(f331(x112781),x112782),f193(f883(x112781,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(11281,plain, % 178.17/178.00 (~P24(f329(f329(f331(x112811),x112812),f193(f883(x112811,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(11284,plain, % 178.17/178.00 (P24(f329(f329(f331(x112841),f329(x112842,x112843)),f329(f308(x112844,x112841,x112842),f252(f883(x112844,a869)))))), % 178.17/178.00 inference(rename_variables,[],[3871])). % 178.17/178.00 cnf(11287,plain, % 178.17/178.00 (~P24(f329(f329(f331(f882(x112871,x112871)),f329(f329(f264(x112871,x112871),x112872),x112873)),f152(x112871,f119(f883(x112871,a875)))))), % 178.17/178.00 inference(rename_variables,[],[4547])). % 178.17/178.00 cnf(11295,plain, % 178.17/178.00 (E(f120(x112951,f119(x112951)),f119(x112951))), % 178.17/178.00 inference(rename_variables,[],[3108])). % 178.17/178.00 cnf(11298,plain, % 178.17/178.00 (~E(f329(a118,x112981),x112981)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(11305,plain, % 178.17/178.00 (~E(f329(a118,x113051),x113051)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(11310,plain, % 178.17/178.00 (E(f329(f260(x113101,x113101),f261(x113101,x113102)),x113102)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(11313,plain, % 178.17/178.00 (E(f329(f260(x113131,x113131),f261(x113131,x113132)),x113132)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(11319,plain, % 178.17/178.00 (~E(f329(a118,x113191),x113191)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(11326,plain, % 178.17/178.00 (~E(f329(f329(f81(a1),x113261),x113261),a103)), % 178.17/178.00 inference(rename_variables,[],[4465])). % 178.17/178.00 cnf(11335,plain, % 178.17/178.00 (E(f329(f329(f22(a875),f2(a875)),x113351),f2(a875))), % 178.17/178.00 inference(rename_variables,[],[3179])). % 178.17/178.00 cnf(11338,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x113381),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(11345,plain, % 178.17/178.00 (E(f329(f329(f81(a1),f329(f329(f82(a1),x113451),f329(f329(f39(a1),x113452),x113451))),f45(a1,x113452,x113451)),x113452)), % 178.17/178.00 inference(rename_variables,[],[3819])). % 178.17/178.00 cnf(11369,plain, % 178.17/178.00 (~E(f329(a118,x113691),x113691)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(11372,plain, % 178.17/178.00 (~E(f329(a118,x113721),x113721)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(11398,plain, % 178.17/178.00 (~P24(f329(f63(x113981,x113982,f193(f883(x113981,a869))),x113983))), % 178.17/178.00 inference(rename_variables,[],[4539])). % 178.17/178.00 cnf(11401,plain, % 178.17/178.00 (~P24(f329(f329(f193(f883(x114011,f883(x114012,a869))),x114013),x114014))), % 178.17/178.00 inference(rename_variables,[],[4544])). % 178.17/178.00 cnf(11404,plain, % 178.17/178.00 (P24(f329(f329(f331(x114041),x114042),f252(f883(x114041,a869))))), % 178.17/178.00 inference(rename_variables,[],[3428])). % 178.17/178.00 cnf(11416,plain, % 178.17/178.00 (P24(f329(f329(f199(a24),x114161),x114161))), % 178.17/178.00 inference(rename_variables,[],[3267])). % 178.17/178.00 cnf(11423,plain, % 178.17/178.00 (P24(f329(f67(x114231,x114232,x114233,x114234,f193(f883(x114231,a869))),x114234))), % 178.17/178.00 inference(rename_variables,[],[4193])). % 178.17/178.00 cnf(11424,plain, % 178.17/178.00 (E(f329(f260(x114241,x114241),f261(x114241,x114242)),x114242)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(11429,plain, % 178.17/178.00 (~P24(f329(f329(f193(f883(x114291,f883(x114292,a869))),x114293),x114294))), % 178.17/178.00 inference(rename_variables,[],[4544])). % 178.17/178.00 cnf(11440,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),f329(f329(f81(a875),x114401),x114402)),x114402))), % 178.17/178.00 inference(rename_variables,[],[4541])). % 178.17/178.00 cnf(11443,plain, % 178.17/178.00 (~P24(f329(f329(f244(a1),f329(f106(a1),x114431)),f2(a1)))), % 178.17/178.00 inference(rename_variables,[],[4531])). % 178.17/178.00 cnf(11459,plain, % 178.17/178.00 (~E(f329(f329(f107(a875),f329(a118,x114591)),x114591),f329(a118,x114591))), % 178.17/178.00 inference(scs_inference,[],[3511,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,4457,10415,10508,3183,2855,2865,2869,2878,2880,2885,2888,2893,2901,2910,2930,2931,2934,2939,2947,2948,2950,2961,2980,3010,3011,3021,3034,3041,3055,4438,3108,11295,3224,10192,10256,10259,10349,10352,10643,11310,11313,3202,3729,3098,3819,11345,3160,3127,3106,3329,3195,3219,10456,3375,4536,3903,4467,10247,10412,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3077,3179,11335,4050,3905,10966,11092,11143,4549,10898,10999,11097,11202,11224,11262,11268,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,3632,4465,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,3250,4515,10224,10227,10253,10724,10737,10856,11246,11338,4531,3708,3481,3854,3296,3297,3271,4512,4462,3465,4532,4044,11219,3592,4014,3915,10792,3966,3633,4003,3651,10972,11035,11116,4537,10740,11108,3267,10342,10438,10569,10629,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,3270,4511,10290,10380,10493,10517,10761,10806,3428,10589,10851,10895,11165,11243,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,3333,10616,10646,10655,3365,3787,3726,10293,4524,10244,10610,10613,11052,11070,3290,10649,10800,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,4193,4539,10215,10218,10474,10525,10528,10533,10937,4547,11131,11251,3871,3715,10911,10917,3569,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,4533,4544,10709,10809,11119,11401,4154,4055,3747,4541,10266,10269,10604,10607,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345])). % 178.17/178.00 cnf(11466,plain, % 178.17/178.00 (E(f329(f260(x114661,x114661),f261(x114661,x114662)),x114662)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(11471,plain, % 178.17/178.00 (E(f329(f260(x114711,x114711),f261(x114711,x114712)),x114712)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(11474,plain, % 178.17/178.00 (~P24(f329(f329(f244(a1),f329(f106(a1),x114741)),f2(a1)))), % 178.17/178.00 inference(rename_variables,[],[4531])). % 178.17/178.00 cnf(11479,plain, % 178.17/178.00 (~E(f329(a118,x114791),x114791)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(11488,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x114881),x114881))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(11509,plain, % 178.17/178.00 (~P24(f329(f329(f244(a1),f329(f106(a1),x115091)),f2(a1)))), % 178.17/178.00 inference(rename_variables,[],[4531])). % 178.17/178.00 cnf(11522,plain, % 178.17/178.00 (P24(f329(f329(f243(a1),x115221),x115221))), % 178.17/178.00 inference(rename_variables,[],[3269])). % 178.17/178.00 cnf(11525,plain, % 178.17/178.00 (~P24(f329(f329(f243(a875),f329(a118,x115251)),x115251))), % 178.17/178.00 inference(rename_variables,[],[4524])). % 178.17/178.00 cnf(11526,plain, % 178.17/178.00 (~E(f329(a118,x115261),x115261)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(11536,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),f329(f329(f81(a875),x115361),x115362)),x115361))), % 178.17/178.00 inference(rename_variables,[],[4542])). % 178.17/178.00 cnf(11539,plain, % 178.17/178.00 (~P24(f329(f329(f244(a1),f329(f106(a1),x115391)),f2(a1)))), % 178.17/178.00 inference(rename_variables,[],[4531])). % 178.17/178.00 cnf(11542,plain, % 178.17/178.00 (~E(f329(a118,x115421),x115421)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(11555,plain, % 178.17/178.00 (P24(f329(f329(f331(x115551),x115552),f329(f329(f307(x115551),x115552),x115553)))), % 178.17/178.00 inference(rename_variables,[],[3582])). % 178.17/178.00 cnf(11556,plain, % 178.17/178.00 (~P24(f329(f329(f243(a1),f2(a1)),f329(f80(a1),f329(f106(a1),f329(a118,x115561)))))), % 178.17/178.00 inference(rename_variables,[],[4543])). % 178.17/178.00 cnf(11559,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),f329(f329(f22(a875),x115591),x115592)),f329(a118,x115591)))), % 178.17/178.00 inference(rename_variables,[],[3721])). % 178.17/178.00 cnf(11562,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),f45(a875,x115621,x115622)),x115621))), % 178.17/178.00 inference(rename_variables,[],[3726])). % 178.17/178.00 cnf(11568,plain, % 178.17/178.00 (E(f329(f329(f127(x115681),x115682),f119(x115681)),x115682)), % 178.17/178.00 inference(rename_variables,[],[3196])). % 178.17/178.00 cnf(11571,plain, % 178.17/178.00 (E(f329(f260(x115711,x115711),f261(x115711,x115712)),x115712)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(11574,plain, % 178.17/178.00 (E(f172(x115741,x115742,f119(x115741)),x115742)), % 178.17/178.00 inference(rename_variables,[],[3202])). % 178.17/178.00 cnf(11580,plain, % 178.17/178.00 (~P24(f329(f329(f243(a875),f329(a118,x115801)),x115801))), % 178.17/178.00 inference(rename_variables,[],[4524])). % 178.17/178.00 cnf(11589,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x115891),x115891))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(11592,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),f45(a875,x115921,x115922)),x115921))), % 178.17/178.00 inference(rename_variables,[],[3726])). % 178.17/178.00 cnf(11593,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),f2(a875)),x115931))), % 178.17/178.00 inference(rename_variables,[],[3290])). % 178.17/178.00 cnf(11595,plain, % 178.17/178.00 (~P24(f329(f329(f243(a1),f79(a1)),f2(a1)))), % 178.17/178.00 inference(scs_inference,[],[3511,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,4457,10415,10508,3183,2855,2865,2869,2870,2878,2880,2881,2885,2888,2893,2901,2910,2930,2931,2933,2934,2939,2940,2947,2948,2950,2961,2980,3010,3011,3019,3021,3034,3041,3055,4438,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,3196,11568,3202,10663,11574,3729,3098,3819,11345,3160,3127,3122,3106,3107,3329,3195,3219,10456,3375,4536,3903,4467,10247,10412,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,3905,10966,11092,11143,4549,10898,10999,11097,11202,11224,11262,11268,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,3632,4333,4334,4465,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,3250,4515,10224,10227,10253,10724,10737,10856,11246,11338,4531,11443,11474,11509,3708,3481,3854,3296,3297,3271,4512,4462,3465,4532,4044,11219,3592,4014,3915,10792,3966,3633,4003,3651,10972,11035,11116,4537,10740,11108,3267,10342,10438,10569,10629,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,10843,3270,4511,10290,10380,10493,10517,10761,10806,10816,11488,3428,10589,10851,10895,11165,11243,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,3333,10616,10646,10655,3371,3365,3787,3726,10293,11562,4524,10244,10610,10613,11052,11070,11525,3290,10649,10800,10871,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,3582,4193,4539,10215,10218,10474,10525,10528,10533,10937,4547,11131,11251,3871,3715,10911,10917,3569,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,4533,4544,10709,10809,11119,11401,4154,4055,3747,4541,10266,10269,10604,10607,4542,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781])). % 178.17/178.00 cnf(11610,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x116101),x116101))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(11613,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x116131),x116131))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(11616,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x116161),x116161))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(11619,plain, % 178.17/178.00 (P24(f329(f329(f331(x116191),f329(x116192,x116193)),f329(f308(x116194,x116191,x116192),f252(f883(x116194,a869)))))), % 178.17/178.00 inference(rename_variables,[],[3871])). % 178.17/178.00 cnf(11620,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),f329(f329(f81(a875),x116201),x116202)),x116202))), % 178.17/178.00 inference(rename_variables,[],[4541])). % 178.17/178.00 cnf(11623,plain, % 178.17/178.00 (P24(f329(f329(f331(x116231),f329(x116232,x116233)),f329(f308(x116234,x116231,x116232),f252(f883(x116234,a869)))))), % 178.17/178.00 inference(rename_variables,[],[3871])). % 178.17/178.00 cnf(11624,plain, % 178.17/178.00 (~P24(f329(f329(f243(a875),f329(a118,x116241)),x116241))), % 178.17/178.00 inference(rename_variables,[],[4524])). % 178.17/178.00 cnf(11629,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),f329(f329(f81(a875),x116291),x116292)),x116291))), % 178.17/178.00 inference(rename_variables,[],[4542])). % 178.17/178.00 cnf(11632,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x116321),x116321))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(11635,plain, % 178.17/178.00 (P24(f329(f329(f199(a24),x116351),x116351))), % 178.17/178.00 inference(rename_variables,[],[3267])). % 178.17/178.00 cnf(11641,plain, % 178.17/178.00 (~P36(x116411,x116412,f119(x116411))), % 178.17/178.00 inference(rename_variables,[],[4478])). % 178.17/178.00 cnf(11644,plain, % 178.17/178.00 (P24(f329(f329(f331(x116441),x116442),f252(f883(x116441,a869))))), % 178.17/178.00 inference(rename_variables,[],[3428])). % 178.17/178.00 cnf(11645,plain, % 178.17/178.00 (~P24(f329(f329(f243(a875),f329(a118,x116451)),x116451))), % 178.17/178.00 inference(rename_variables,[],[4524])). % 178.17/178.00 cnf(11648,plain, % 178.17/178.00 (~P24(f329(f63(x116481,x116482,f193(f883(x116481,a869))),x116483))), % 178.17/178.00 inference(rename_variables,[],[4539])). % 178.17/178.00 cnf(11661,plain, % 178.17/178.00 (~P24(f329(f329(f331(x116611),x116612),f193(f883(x116611,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(11664,plain, % 178.17/178.00 (E(f329(f329(f16(x116641,x116642),x116643),x116644),x116643)), % 178.17/178.00 inference(rename_variables,[],[3257])). % 178.17/178.00 cnf(11667,plain, % 178.17/178.00 (E(f329(f329(f16(x116671,x116672),x116673),x116674),x116673)), % 178.17/178.00 inference(rename_variables,[],[3257])). % 178.17/178.00 cnf(11679,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),f2(a875)),f329(a118,x116791)))), % 178.17/178.00 inference(rename_variables,[],[3351])). % 178.17/178.00 cnf(11682,plain, % 178.17/178.00 (P24(f329(f329(f199(a24),x116821),x116821))), % 178.17/178.00 inference(rename_variables,[],[3267])). % 178.17/178.00 cnf(11685,plain, % 178.17/178.00 (P24(f329(f329(f331(x116851),f329(x116852,x116853)),f329(f308(x116854,x116851,x116852),f252(f883(x116854,a869)))))), % 178.17/178.00 inference(rename_variables,[],[3871])). % 178.17/178.00 cnf(11688,plain, % 178.17/178.00 (P24(f329(f62(x116881),f329(f171(x116881),x116882)))), % 178.17/178.00 inference(rename_variables,[],[3311])). % 178.17/178.00 cnf(11691,plain, % 178.17/178.00 (P24(f329(f62(x116911),f329(f171(x116911),x116912)))), % 178.17/178.00 inference(rename_variables,[],[3311])). % 178.17/178.00 cnf(11694,plain, % 178.17/178.00 (P24(f329(f329(f243(a1),f329(f80(a1),f329(f106(a1),x116941))),f329(f106(a1),x116942)))), % 178.17/178.00 inference(rename_variables,[],[3748])). % 178.17/178.00 cnf(11697,plain, % 178.17/178.00 (~P24(f329(f329(f331(x116971),x116972),f193(f883(x116971,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(11707,plain, % 178.17/178.00 (~P24(f329(f329(f331(a875),f2(a875)),f329(f301(a875),x117071)))), % 178.17/178.00 inference(scs_inference,[],[3511,4477,4478,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,4457,10415,10508,3183,2855,2865,2869,2870,2878,2880,2881,2885,2888,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2943,2947,2948,2950,2961,2980,3010,3011,3019,3021,3034,3041,3055,4438,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,3196,11568,3202,10663,11574,3729,3098,3819,11345,3160,3127,3122,3106,3107,3329,3195,3219,10456,3375,4536,3903,4467,10247,10412,3257,11664,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,3905,10966,11092,11143,4549,10898,10999,11097,11202,11224,11262,11268,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,3632,4333,4334,4465,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,11559,3250,3351,4515,10224,10227,10253,10724,10737,10856,11246,11338,4531,11443,11474,11509,3708,3481,3854,3296,3297,3271,4512,4462,3465,4532,4044,11219,3592,3311,11688,4014,3915,10792,3966,3633,4003,3651,10972,11035,11116,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,10843,3270,3347,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,3428,10589,10851,10895,11165,11243,11404,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,3333,10616,10646,10655,3371,3365,3787,3726,10293,11562,4524,10244,10610,10613,11052,11070,11525,11580,11624,3290,10649,10800,10871,3748,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,3582,4193,4539,10215,10218,10474,10525,10528,10533,10937,11398,4547,11131,11251,3980,3871,11284,11619,11623,3715,10911,10917,3569,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,11556,4533,4544,10709,10809,11119,11401,4154,4055,3747,3695,4541,10266,10269,10604,10607,11440,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114])). % 178.17/178.00 cnf(11709,plain, % 178.17/178.00 (~P24(f329(f329(f331(a875),x117091),f329(f250(a875),f2(a875))))), % 178.17/178.00 inference(scs_inference,[],[3511,4477,4478,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,4457,10415,10508,3183,2855,2865,2869,2870,2878,2880,2881,2885,2888,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2943,2947,2948,2950,2961,2980,3010,3011,3019,3021,3034,3041,3055,4438,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,3196,11568,3202,10663,11574,3729,3098,3819,11345,3160,3127,3122,3106,3107,3329,3195,3219,10456,3375,4536,3903,4467,10247,10412,3257,11664,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,3905,10966,11092,11143,4549,10898,10999,11097,11202,11224,11262,11268,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,3632,4333,4334,4465,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,11559,3250,3351,4515,10224,10227,10253,10724,10737,10856,11246,11338,4531,11443,11474,11509,3708,3481,3854,3296,3297,3271,4512,4462,3465,4532,4044,11219,3592,3311,11688,4014,3915,10792,3966,3633,4003,3651,10972,11035,11116,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,10843,3270,3347,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,3428,10589,10851,10895,11165,11243,11404,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,3333,10616,10646,10655,3371,3365,3787,3726,10293,11562,4524,10244,10610,10613,11052,11070,11525,11580,11624,3290,10649,10800,10871,3748,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,3582,4193,4539,10215,10218,10474,10525,10528,10533,10937,11398,4547,11131,11251,3980,3871,11284,11619,11623,3715,10911,10917,3569,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,11556,4533,4544,10709,10809,11119,11401,4154,4055,3747,3695,4541,10266,10269,10604,10607,11440,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115])). % 178.17/178.00 cnf(11716,plain, % 178.17/178.00 (P24(f329(f329(f199(a24),x117161),x117161))), % 178.17/178.00 inference(rename_variables,[],[3267])). % 178.17/178.00 cnf(11719,plain, % 178.17/178.00 (P24(f329(f329(f243(a1),x117191),x117191))), % 178.17/178.00 inference(rename_variables,[],[3269])). % 178.17/178.00 cnf(11728,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x117281),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(11731,plain, % 178.17/178.00 (P24(f329(f329(f243(a1),x117311),x117311))), % 178.17/178.00 inference(rename_variables,[],[3269])). % 178.17/178.00 cnf(11736,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x117361),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(11743,plain, % 178.17/178.00 (P24(f329(f252(f883(x117431,a869)),x117432))), % 178.17/178.00 inference(rename_variables,[],[3333])). % 178.17/178.00 cnf(11748,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),f2(a875)),x117481))), % 178.17/178.00 inference(rename_variables,[],[3290])). % 178.17/178.00 cnf(11749,plain, % 178.17/178.00 (~P24(f329(f329(f243(a875),f329(a118,x117491)),x117491))), % 178.17/178.00 inference(rename_variables,[],[4524])). % 178.17/178.00 cnf(11752,plain, % 178.17/178.00 (~P24(f329(f63(x117521,x117522,f193(f883(x117521,a869))),x117523))), % 178.17/178.00 inference(rename_variables,[],[4539])). % 178.17/178.00 cnf(11765,plain, % 178.17/178.00 (~P24(f329(f329(f244(a1),f329(f106(a1),f329(a118,x117651))),f329(f80(a1),f2(a1))))), % 178.17/178.00 inference(scs_inference,[],[3511,4477,4478,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,4457,10415,10508,3183,2855,2865,2869,2870,2875,2878,2880,2881,2885,2888,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2943,2947,2948,2950,2957,2961,2980,3010,3011,3019,3021,3025,3034,3041,3055,4438,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,3196,11568,3202,10663,11574,3729,3098,3819,11345,3160,3127,3122,3106,3107,3329,3195,3219,10456,3375,4536,3903,4467,10247,10412,3257,11664,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,3905,10966,11092,11143,4549,10898,10999,11097,11202,11224,11262,11268,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,3632,4333,4334,4465,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,11559,3250,3351,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,4531,11443,11474,11509,11539,3708,3481,3854,3296,3297,3271,4512,4462,3465,4532,4044,11219,3592,3311,11688,4014,3915,10792,3966,3633,4003,3651,10972,11035,11116,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,10843,11522,11719,3270,3347,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,3428,10589,10851,10895,11165,11243,11404,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,3333,10616,10646,10655,11194,3371,3365,3787,3726,10293,11562,11592,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,3290,10649,10800,10871,11593,3748,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,3582,4193,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,3980,3871,11284,11619,11623,3715,10911,10917,3569,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,11556,4533,4544,10709,10809,11119,11401,4154,4055,3747,3695,4541,10266,10269,10604,10607,11440,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406])). % 178.17/178.00 cnf(11769,plain, % 178.17/178.00 (P24(f329(f329(f244(a1),f329(f80(a1),f79(a1))),f2(a1)))), % 178.17/178.00 inference(scs_inference,[],[3511,4477,4478,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,4457,10415,10508,3183,2855,2865,2869,2870,2875,2878,2880,2881,2885,2888,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2943,2947,2948,2950,2957,2961,2980,3010,3011,3019,3021,3025,3034,3041,3055,4438,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,3196,11568,3202,10663,11574,3729,3098,3819,11345,3160,3127,3122,3106,3107,3329,3195,3219,10456,3375,4536,3903,4467,10247,10412,3257,11664,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,3905,10966,11092,11143,4549,10898,10999,11097,11202,11224,11262,11268,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,3632,4333,4334,4465,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,11559,3250,3351,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,4531,11443,11474,11509,11539,3708,3481,3854,3296,3297,3271,4512,4462,3465,4532,4044,11219,3592,3311,11688,4014,3915,10792,3966,3633,4003,3651,10972,11035,11116,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,10843,11522,11719,3270,3347,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,3428,10589,10851,10895,11165,11243,11404,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,3333,10616,10646,10655,11194,3371,3365,3787,3726,10293,11562,11592,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,3290,10649,10800,10871,11593,3748,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,3582,4193,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,3980,3871,11284,11619,11623,3715,10911,10917,3569,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,11556,4533,4544,10709,10809,11119,11401,4154,4055,3747,3695,4541,10266,10269,10604,10607,11440,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423])). % 178.17/178.00 cnf(11774,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x117741),x117741))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(11777,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x117771),x117771))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(11780,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x117801),x117801))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(11783,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x117831),x117831))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(11786,plain, % 178.17/178.00 (~P24(f329(f329(f243(a875),f329(a118,x117861)),x117861))), % 178.17/178.00 inference(rename_variables,[],[4524])). % 178.17/178.00 cnf(11789,plain, % 178.17/178.00 (~P24(f329(f329(f243(a875),f329(a118,x117891)),x117891))), % 178.17/178.00 inference(rename_variables,[],[4524])). % 178.17/178.00 cnf(11792,plain, % 178.17/178.00 (~P24(f329(f329(f243(a875),f329(a118,x117921)),x117921))), % 178.17/178.00 inference(rename_variables,[],[4524])). % 178.17/178.00 cnf(11795,plain, % 178.17/178.00 (~P24(f329(f329(f243(a875),f329(a118,x117951)),x117951))), % 178.17/178.00 inference(rename_variables,[],[4524])). % 178.17/178.00 cnf(11811,plain, % 178.17/178.00 (P24(f329(f329(f199(a24),f329(f329(f22(a875),x118111),f329(a118,x118111))),f2(a875)))), % 178.17/178.00 inference(scs_inference,[],[3511,4477,4478,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,4457,10415,10508,3183,2855,2865,2869,2870,2875,2878,2880,2881,2885,2888,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2943,2947,2948,2950,2957,2961,2980,3010,3011,3019,3021,3025,3034,3041,3055,4438,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,3196,11568,3202,10663,11574,3729,3098,3819,11345,3160,3127,3122,3106,3107,3329,3195,3219,10456,3375,4536,3903,4467,10247,10412,3257,11664,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,3905,10966,11092,11143,4549,10898,10999,11097,11202,11224,11262,11268,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,3632,4333,4334,4465,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,11559,3250,3351,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,4531,11443,11474,11509,11539,3708,3481,3854,3296,3297,3271,4512,4462,3465,4532,4044,11219,3592,3311,11688,4014,3915,10792,3966,3633,4003,3651,10972,11035,11116,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,10843,11522,11719,3270,3347,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,3428,10589,10851,10895,11165,11243,11404,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,3333,10616,10646,10655,11194,3371,3365,3787,3726,10293,11562,11592,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,3290,10649,10800,10871,11593,3748,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,3582,4193,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,3980,3871,11284,11619,11623,3715,10911,10917,3569,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,11556,4533,4544,10709,10809,11119,11401,4154,4055,3747,3695,4541,10266,10269,10604,10607,11440,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500])). % 178.17/178.00 cnf(11812,plain, % 178.17/178.00 (P24(f329(f329(f199(a24),x118121),x118121))), % 178.17/178.00 inference(rename_variables,[],[3267])). % 178.17/178.00 cnf(11817,plain, % 178.17/178.00 (P24(f329(f329(f243(a1),x118171),f329(f76(a1),x118171)))), % 178.17/178.00 inference(scs_inference,[],[3511,4477,4478,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,4457,10415,10508,3480,3183,2855,2865,2869,2870,2875,2878,2880,2881,2885,2888,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2943,2947,2948,2950,2957,2961,2980,3010,3011,3019,3021,3025,3034,3041,3055,4438,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,3196,11568,3202,10663,11574,3729,3098,3819,11345,3160,3127,3122,3106,3107,3329,3195,3219,10456,3375,4536,3903,4467,10247,10412,3257,11664,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,3905,10966,11092,11143,4549,10898,10999,11097,11202,11224,11262,11268,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,3632,4333,4334,4465,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,3721,11559,3250,3351,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,4531,11443,11474,11509,11539,3708,3481,3854,3296,3297,3271,4512,4462,3465,4532,4044,11219,3592,3311,11688,4014,3915,10792,3966,3633,4003,3651,10972,11035,11116,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,3268,10698,10743,10746,10779,10803,10840,10878,3269,10371,10426,10634,10719,10843,11522,11719,11731,3270,3347,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,3428,10589,10851,10895,11165,11243,11404,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,3333,10616,10646,10655,11194,3371,3365,3787,3726,10293,11562,11592,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,3290,10649,10800,10871,11593,3748,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,3582,4193,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,3980,3871,11284,11619,11623,3715,10911,10917,3569,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,11556,4533,4544,10709,10809,11119,11401,4154,4055,3747,3695,4541,10266,10269,10604,10607,11440,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520])). % 178.17/178.00 cnf(11818,plain, % 178.17/178.00 (P24(f329(f329(f243(a1),x118181),x118181))), % 178.17/178.00 inference(rename_variables,[],[3269])). % 178.17/178.00 cnf(11829,plain, % 178.17/178.00 (P24(f329(f329(f243(a1),x118291),x118291))), % 178.17/178.00 inference(rename_variables,[],[3269])). % 178.17/178.00 cnf(11832,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(f882(f876(x118321),f876(x118321)),a869)),f157(x118321,x118322)),f305(f876(x118321),f156(x118321,x118322))))), % 178.17/178.00 inference(rename_variables,[],[3971])). % 178.17/178.00 cnf(11839,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x118391),f329(a118,x118391)))), % 178.17/178.00 inference(rename_variables,[],[3339])). % 178.17/178.00 cnf(11842,plain, % 178.17/178.00 (P24(f329(f329(f331(f883(x118421,a869)),x118422),f329(f306(x118421),x118422)))), % 178.17/178.00 inference(rename_variables,[],[3633])). % 178.17/178.00 cnf(11843,plain, % 178.17/178.00 (~E(f329(a118,x118431),x118431)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(11850,plain, % 178.17/178.00 (P24(f329(f329(f243(a1),x118501),x118501))), % 178.17/178.00 inference(rename_variables,[],[3269])). % 178.17/178.00 cnf(11855,plain, % 178.17/178.00 (P24(f329(f329(f243(a1),x118551),x118551))), % 178.17/178.00 inference(rename_variables,[],[3269])). % 178.17/178.00 cnf(11864,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x118641,a869)),x118642),f329(f329(f307(x118641),x118643),x118642)))), % 178.17/178.00 inference(rename_variables,[],[3715])). % 178.17/178.00 cnf(11867,plain, % 178.17/178.00 (P24(f329(f329(f199(a24),x118671),x118671))), % 178.17/178.00 inference(rename_variables,[],[3267])). % 178.17/178.00 cnf(11868,plain, % 178.17/178.00 (~E(f329(a118,x118681),x118681)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(11879,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x118791),x118791))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(11880,plain, % 178.17/178.00 (~E(f329(a118,x118801),x118801)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(11883,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x118831),x118831))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(11886,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x118861),x118861))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(11889,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x118891),x118891))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(11892,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x118921),x118921))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(11894,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),f329(a110,f2(a1))),f329(a118,x118941)))), % 178.17/178.00 inference(scs_inference,[],[3511,4477,4478,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,4457,10415,10508,3480,3183,2855,2865,2869,2870,2875,2878,2880,2881,2885,2888,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2943,2947,2948,2950,2957,2961,2980,3010,3011,3019,3021,3025,3034,3041,3055,4438,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,3196,11568,3202,10663,11574,3729,3098,3819,11345,3160,3127,3122,3106,3107,3329,3195,3219,10456,3375,4536,3903,4467,10247,10412,3257,11664,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,3905,10966,11092,11143,4549,10898,10999,11097,11202,11224,11262,11268,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,3632,4333,4334,4465,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,3721,11559,3250,3351,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,4531,11443,11474,11509,11539,3708,3481,3854,3296,3297,3271,4512,4462,3465,4532,4044,11219,3592,3311,11688,4014,3971,3915,10792,3966,3633,4003,3651,10972,11035,11116,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,3270,3347,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,3428,10589,10851,10895,11165,11243,11404,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,3333,10616,10646,10655,11194,3371,3365,3787,3726,10293,11562,11592,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,3290,10649,10800,10871,11593,3748,4094,4522,3795,4501,4503,3241,3242,4502,4505,4506,3582,4193,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,3980,3871,11284,11619,11623,3715,10911,10917,10932,3569,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,11556,4533,4544,10709,10809,11119,11401,4154,4055,3747,3695,4541,10266,10269,10604,10607,11440,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764])). % 178.17/178.00 cnf(11895,plain, % 178.17/178.00 (P24(f329(f329(f243(a1),x118951),x118951))), % 178.17/178.00 inference(rename_variables,[],[3269])). % 178.17/178.00 cnf(11898,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x118981),x118981))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(11901,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x119011),x119011))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(11902,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x119021),f329(a118,x119021)))), % 178.17/178.00 inference(rename_variables,[],[3339])). % 178.17/178.00 cnf(11911,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x119111),x119111))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(11912,plain, % 178.17/178.00 (~E(f329(a118,x119121),x119121)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(11917,plain, % 178.17/178.00 (P24(f329(f329(f243(a1),x119171),x119171))), % 178.17/178.00 inference(rename_variables,[],[3269])). % 178.17/178.00 cnf(11932,plain, % 178.17/178.00 (P24(f329(f329(f243(a1),x119321),x119321))), % 178.17/178.00 inference(rename_variables,[],[3269])). % 178.17/178.00 cnf(11937,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),f2(a875)),x119371))), % 178.17/178.00 inference(rename_variables,[],[3290])). % 178.17/178.00 cnf(11954,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x119541),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(11957,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x119571),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(11960,plain, % 178.17/178.00 (~P24(f329(f329(f331(x119601),x119602),f193(f883(x119601,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(11963,plain, % 178.17/178.00 (~P24(f329(f329(f331(x119631),x119632),f193(f883(x119631,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(11966,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x119661),x119661))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(11968,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x119681),f329(f329(f107(a875),x119681),x119682)))), % 178.17/178.00 inference(scs_inference,[],[3511,4477,4478,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,4457,10415,10508,3480,3183,2855,2865,2869,2870,2875,2878,2880,2881,2885,2888,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2943,2947,2948,2950,2957,2961,2980,3010,3011,3019,3021,3025,3034,3041,3055,4438,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,3196,11568,3202,10663,11574,3209,3729,3963,3098,3819,11345,3160,3127,3122,3106,3107,3329,3195,3219,10456,3375,4536,3903,4467,10247,10412,3257,11664,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,3905,10966,11092,11143,4549,10898,10999,11097,11202,11224,11262,11268,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,3632,4333,4334,4465,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,3721,11559,3250,3351,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,4531,11443,11474,11509,11539,3708,3481,3854,3296,3297,3271,4512,4462,3465,4532,4044,11219,3592,3311,11688,4014,3971,3915,10792,3966,3633,4003,3651,10972,11035,11116,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,3270,3347,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,3428,10589,10851,10895,11165,11243,11404,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,3333,10616,10646,10655,11194,3371,3365,3787,3726,10293,11562,11592,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,3290,10649,10800,10871,11593,11748,3748,4094,4522,3759,3795,4501,4503,3241,3242,4502,4505,4506,3766,3582,4193,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,3980,3871,11284,11619,11623,3715,10911,10917,10932,3569,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,11556,4533,4544,10709,10809,11119,11401,4154,4055,3747,3695,4541,10266,10269,10604,10607,11440,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998])). % 178.17/178.00 cnf(11969,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x119691),x119691))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(11972,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x119721),x119721))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(11975,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x119751),x119751))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(11978,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x119781),f329(a118,x119781)))), % 178.17/178.00 inference(rename_variables,[],[3339])). % 178.17/178.00 cnf(11985,plain, % 178.17/178.00 (P24(f329(f329(f331(f883(x119851,a869)),x119852),f329(f306(x119851),x119852)))), % 178.17/178.00 inference(rename_variables,[],[3633])). % 178.17/178.00 cnf(11989,plain, % 178.17/178.00 (~P24(f329(f329(f331(a875),f329(a118,f329(f141(a875,a875,f81(a875),f2(a875)),x119891))),f329(f171(a875),f329(f135(a875,x119892),x119891))))), % 178.17/178.00 inference(scs_inference,[],[3511,4477,4478,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,4457,10415,10508,3480,3183,2855,2865,2869,2870,2875,2878,2880,2881,2885,2888,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2943,2947,2948,2950,2957,2961,2980,3010,3011,3019,3021,3025,3034,3041,3055,4438,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,3196,11568,3202,10663,11574,3209,3729,3963,3098,3819,11345,3160,3127,3122,3106,3107,3329,3195,3219,10456,3375,4536,3903,4467,10247,10412,3257,11664,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,3905,10966,11092,11143,4549,10898,10999,11097,11202,11224,11262,11268,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,3632,4333,4334,4465,3573,3783,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,3721,11559,3250,3351,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,4531,11443,11474,11509,11539,3708,3481,3854,3296,3297,3271,4512,4462,3465,4532,4044,11219,3592,3311,11688,4014,3971,3915,10792,3966,3633,11842,4003,3651,10972,11035,11116,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,3270,3347,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,3428,10589,10851,10895,11165,11243,11404,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,3333,10616,10646,10655,11194,3371,3365,3787,3726,10293,11562,11592,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,3290,10649,10800,10871,11593,11748,3748,4094,4522,3759,3795,4501,4503,3241,3242,4502,4505,4506,3766,3582,4193,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,3980,3871,11284,11619,11623,3715,10911,10917,10932,3569,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,11556,4533,4544,10709,10809,11119,11401,4154,4055,3747,3695,4541,10266,10269,10604,10607,11440,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098])). % 178.17/178.00 cnf(11990,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x119901,a869)),f329(f171(x119901),f329(f135(x119901,x119902),x119903))),f329(f171(x119901),x119903)))), % 178.17/178.00 inference(rename_variables,[],[3915])). % 178.17/178.00 cnf(11997,plain, % 178.17/178.00 (~P24(f329(f329(f331(x119971),x119972),f193(f883(x119971,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(12002,plain, % 178.17/178.00 (E(f329(f194(f876(x120021)),f329(f167(x120021),x120022)),f329(f194(f876(x120021)),x120022))), % 178.17/178.00 inference(rename_variables,[],[3281])). % 178.17/178.00 cnf(12009,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x120091,a869)),x120092),f252(f883(x120091,a869))))), % 178.17/178.00 inference(rename_variables,[],[3651])). % 178.17/178.00 cnf(12010,plain, % 178.17/178.00 (~E(f329(a118,x120101),x120101)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(12013,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x120131,a869)),f329(f171(x120131),f329(f135(x120131,x120132),x120133))),f329(f171(x120131),x120133)))), % 178.17/178.00 inference(rename_variables,[],[3915])). % 178.17/178.00 cnf(12019,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x120191),f329(a118,x120191)))), % 178.17/178.00 inference(rename_variables,[],[3339])). % 178.17/178.00 cnf(12027,plain, % 178.17/178.00 (~P24(f329(f329(f331(f882(x120271,x120271)),x120272),f152(x120271,f119(f883(x120271,a875)))))), % 178.17/178.00 inference(scs_inference,[],[3511,4477,4478,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,4457,10415,10508,3480,3183,2855,2865,2869,2870,2875,2878,2880,2881,2885,2888,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2942,2943,2947,2948,2950,2957,2961,2980,3010,3011,3019,3021,3025,3034,3041,3055,4438,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,3196,11568,3202,10663,11574,3209,3729,3963,3098,3819,11345,3160,3127,3122,3106,3107,3281,3329,3195,3219,10456,3375,4536,3903,4467,10247,10412,3257,11664,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,3905,10966,11092,11143,4549,10898,10999,11097,11202,11224,11262,11268,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,3632,4333,4334,4465,3573,3783,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,3721,11559,3250,3351,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,4531,11443,11474,11509,11539,3708,3481,3854,3296,3297,3271,4512,4462,3465,4532,4044,11219,3592,3311,11688,4014,3971,3915,10792,11990,3966,3633,11842,4003,3651,10972,11035,11116,11176,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,3270,3347,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,3428,10589,10851,10895,11165,11243,11404,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,3333,10616,10646,10655,11194,3371,3365,3787,3726,10293,11562,11592,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,3290,10649,10800,10871,11593,11748,3748,4094,4522,3759,3795,4501,4503,3241,3242,4502,4505,4506,3766,3582,4193,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,3980,3871,11284,11619,11623,3715,10911,10917,10932,3569,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,11556,4533,4544,10709,10809,11119,11401,4154,4055,3747,3695,4541,10266,10269,10604,10607,11440,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220])). % 178.17/178.00 cnf(12028,plain, % 178.17/178.00 (E(f329(f260(x120281,x120281),f261(x120281,x120282)),x120282)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(12039,plain, % 178.17/178.00 (P24(f329(f62(x120391),f193(f883(x120391,a869))))), % 178.17/178.00 inference(rename_variables,[],[3347])). % 178.17/178.00 cnf(12040,plain, % 178.17/178.00 (~P24(f329(f329(f331(x120401),x120402),f193(f883(x120401,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(12045,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x120451),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(12046,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x120461),x120461))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(12051,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x120511,a869)),f329(f171(x120511),f169(x120511,x120512,x120513))),f329(f171(x120511),x120513)))), % 178.17/178.00 inference(rename_variables,[],[3966])). % 178.17/178.00 cnf(12054,plain, % 178.17/178.00 (P21(x120541,x120541,f5(x120541),x120542)), % 178.17/178.00 inference(rename_variables,[],[3511])). % 178.17/178.00 cnf(12059,plain, % 178.17/178.00 (P24(f329(f329(f331(f883(x120591,a869)),x120592),f329(f306(x120591),x120592)))), % 178.17/178.00 inference(rename_variables,[],[3633])). % 178.17/178.00 cnf(12066,plain, % 178.17/178.00 (P24(f329(f329(f199(a24),x120661),x120661))), % 178.17/178.00 inference(rename_variables,[],[3267])). % 178.17/178.00 cnf(12069,plain, % 178.17/178.00 (~P24(f329(f329(f331(x120691),x120692),f193(f883(x120691,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(12072,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x120721,a869)),x120722),f329(f329(f307(x120721),x120723),x120722)))), % 178.17/178.00 inference(rename_variables,[],[3715])). % 178.17/178.00 cnf(12073,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x120731,a869)),x120732),f252(f883(x120731,a869))))), % 178.17/178.00 inference(rename_variables,[],[3651])). % 178.17/178.00 cnf(12080,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x120801),f329(a118,x120801)))), % 178.17/178.00 inference(rename_variables,[],[3339])). % 178.17/178.00 cnf(12083,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x120831),f329(a118,x120831)))), % 178.17/178.00 inference(rename_variables,[],[3339])). % 178.17/178.00 cnf(12086,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x120861),x120861))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(12089,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x120891),x120891))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(12092,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x120921),x120921))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(12095,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x120951),x120951))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(12098,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x120981,a869)),x120982),x120982))), % 178.17/178.00 inference(rename_variables,[],[3569])). % 178.17/178.00 cnf(12102,plain, % 178.17/178.00 (~P24(f329(f329(f243(a1),f329(f329(f22(a1),a84),a103)),f2(a1)))), % 178.17/178.00 inference(scs_inference,[],[3511,11025,4477,4478,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,4457,10415,10508,3480,3183,2855,2865,2869,2870,2875,2878,2880,2881,2885,2888,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2942,2943,2946,2947,2948,2950,2957,2961,2980,3010,3011,3019,3021,3025,3034,3041,3055,4438,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,3196,11568,3202,10663,11574,3209,3729,3963,3098,3819,11345,3160,3127,3122,3106,3107,3281,3329,3195,3219,10456,3375,4536,3903,4467,10247,10412,3257,11664,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,3905,10966,11092,11143,4549,10898,10999,11097,11202,11224,11262,11268,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,3632,4333,4334,4465,3573,3783,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,3721,11559,3250,3351,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,4531,11443,11474,11509,11539,3708,3481,3854,3296,3297,3271,4512,4462,3465,4532,4044,11219,3592,3311,11688,11691,4014,3971,3915,10792,11990,3966,10969,3633,11842,11985,4003,3651,10972,11035,11116,11176,12009,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,3270,3347,12039,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,3428,10589,10851,10895,11165,11243,11404,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,3333,10616,10646,10655,11194,3371,3365,3787,3726,10293,11562,11592,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,3290,10649,10800,10871,11593,11748,3748,4094,4522,3759,3795,4501,4503,3241,3242,4502,4505,4506,3766,3582,4193,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,3980,3871,11284,11619,11623,3715,10911,10917,10932,11864,3569,11134,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,11556,4533,4544,10709,10809,11119,11401,4154,4055,3747,3695,4541,10266,10269,10604,10607,11440,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7386,7400,7417,7450,7453,7479,7503,7520,7523,7524,7534,7552,7553,7555,7557,7559,7561,7587,7612,7613])). % 178.17/178.00 cnf(12105,plain, % 178.17/178.00 (P24(f329(f329(f331(f883(x121051,a869)),x121052),f329(f306(x121051),x121052)))), % 178.17/178.00 inference(rename_variables,[],[3633])). % 178.17/178.00 cnf(12109,plain, % 178.17/178.00 (~P24(f329(f329(f244(a1),f329(f329(f81(a1),a84),a84)),f2(a1)))), % 178.17/178.00 inference(scs_inference,[],[3511,11025,4477,4478,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,4457,10415,10508,3480,3183,2855,2865,2869,2870,2875,2878,2880,2881,2885,2888,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2942,2943,2946,2947,2948,2950,2957,2961,2980,3010,3011,3019,3021,3025,3034,3041,3055,4438,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,3196,11568,3202,10663,11574,3209,3729,3963,3098,3819,11345,3160,3127,3122,3106,3107,3281,3329,3195,3219,10456,3375,4536,3903,4467,10247,10412,3257,11664,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,3905,10966,11092,11143,4549,10898,10999,11097,11202,11224,11262,11268,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,3632,4333,4334,4465,3573,3783,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,3721,11559,3250,3351,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,4531,11443,11474,11509,11539,3708,3481,3854,3296,3297,3271,4512,4462,3465,4532,4044,11219,3592,3311,11688,11691,4014,3971,3915,10792,11990,3966,10969,3633,11842,11985,12059,4003,3651,10972,11035,11116,11176,12009,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,3270,3347,12039,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,3428,10589,10851,10895,11165,11243,11404,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,3333,10616,10646,10655,11194,3371,3365,3787,3726,10293,11562,11592,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,3290,10649,10800,10871,11593,11748,3748,4094,4522,3759,3795,4501,4503,3241,3242,4502,4505,4506,3766,3582,4193,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,3980,3871,11284,11619,11623,3715,10911,10917,10932,11864,3569,11134,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,11556,4533,4544,10709,10809,11119,11401,4154,4055,3747,3695,4541,10266,10269,10604,10607,11440,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7386,7400,7417,7450,7453,7479,7503,7520,7523,7524,7534,7552,7553,7555,7557,7559,7561,7587,7612,7613,7645,7647,7648])). % 178.17/178.00 cnf(12114,plain, % 178.17/178.00 (~E(f329(a118,x121141),x121141)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(12115,plain, % 178.17/178.00 (E(f329(f308(x121151,x121151,f5(x121151)),x121152),x121152)), % 178.17/178.00 inference(rename_variables,[],[3329])). % 178.17/178.00 cnf(12118,plain, % 178.17/178.00 (P33(x121181,x121182,f119(x121181),f119(x121181))), % 178.17/178.00 inference(rename_variables,[],[3520])). % 178.17/178.00 cnf(12121,plain, % 178.17/178.00 (~E(f329(a118,x121211),x121211)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(12124,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x121241,a869)),f329(f171(x121241),f169(x121241,x121242,x121243))),f329(f171(x121241),x121243)))), % 178.17/178.00 inference(rename_variables,[],[3966])). % 178.17/178.00 cnf(12125,plain, % 178.17/178.00 (P24(f329(f62(x121251),f329(f171(x121251),x121252)))), % 178.17/178.00 inference(rename_variables,[],[3311])). % 178.17/178.00 cnf(12136,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x121361),x121361))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(12139,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x121391),x121391))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(12144,plain, % 178.17/178.00 (E(f329(f194(f876(x121441)),f329(f167(x121441),x121442)),f329(f194(f876(x121441)),x121442))), % 178.17/178.00 inference(rename_variables,[],[3281])). % 178.17/178.00 cnf(12151,plain, % 178.17/178.00 (P29(a875,f329(f168(a875),f329(f329(f153(f876(x121511),a875),f194(f876(x121511))),f179(x121511,x121512))))), % 178.17/178.00 inference(rename_variables,[],[3829])). % 178.17/178.00 cnf(12154,plain, % 178.17/178.00 (P21(x121541,x121541,f5(x121541),x121542)), % 178.17/178.00 inference(rename_variables,[],[3511])). % 178.17/178.00 cnf(12157,plain, % 178.17/178.00 (P24(f329(f329(f331(f876(x121571)),f119(x121571)),f160(x121571,x121572)))), % 178.17/178.00 inference(rename_variables,[],[3473])). % 178.17/178.00 cnf(12160,plain, % 178.17/178.00 (~P24(f329(f329(f193(f883(x121601,f883(x121602,a869))),x121603),x121604))), % 178.17/178.00 inference(rename_variables,[],[4544])). % 178.17/178.00 cnf(12162,plain, % 178.17/178.00 (P24(f329(f329(f244(f883(x121621,a869)),f329(a118,f252(f883(x121621,a869)))),f329(f329(f307(x121621),x121622),f252(f883(x121621,a869)))))), % 178.17/178.00 inference(scs_inference,[],[4546,3511,11025,12054,3520,4477,4478,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,4457,10415,10508,3480,3183,2855,2865,2869,2870,2875,2878,2880,2881,2885,2888,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2942,2943,2946,2947,2948,2950,2957,2961,2980,3010,3011,3019,3021,3025,3034,3041,3055,4438,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,3196,11568,3202,10663,11574,3209,3729,3963,3098,3819,11345,3160,3127,3122,3106,3107,3112,3142,3281,12002,3329,10795,3195,3219,10456,3375,4536,3903,4467,10247,10412,3257,11664,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,3905,10966,11092,11143,4549,10898,10999,11097,11202,11224,11262,11268,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,3632,4333,4334,4465,3573,3783,3829,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,3721,11559,3250,3351,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,4531,11443,11474,11509,11539,3708,3481,3854,3296,3297,3271,4512,4462,3465,4532,4044,11219,3592,3311,11688,11691,4014,3971,3915,10792,11990,3966,10969,12051,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,3270,3347,12039,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,3428,10589,10851,10895,11165,11243,11404,11644,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,3333,10616,10646,10655,11194,3371,3365,3787,3726,10293,11562,11592,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,3290,10649,10800,10871,11593,11748,3748,4094,4522,3759,3795,4501,4503,3241,3242,4502,4505,4506,3766,3582,4193,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,3980,3871,11284,11619,11623,3715,10911,10917,10932,11864,3569,11134,3717,10652,10988,11140,11170,3537,10575,10578,10658,10830,4543,11556,4533,4544,10709,10809,11119,11401,11429,4154,4055,3747,3695,4541,10266,10269,10604,10607,11440,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7386,7400,7417,7450,7453,7479,7503,7520,7523,7524,7534,7552,7553,7555,7557,7559,7561,7587,7612,7613,7645,7647,7648,7649,7654,7675,7684,7695,7700,7706,7708,7714,7725,7726,7728,7748,7757,7780,7845,7846,7893,7901,7902])). % 178.17/178.00 cnf(12165,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x121651),x121651))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(12166,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),f2(a875)),x121661))), % 178.17/178.00 inference(rename_variables,[],[3290])). % 178.17/178.00 cnf(12169,plain, % 178.17/178.00 (~P24(f329(f329(f193(f883(x121691,f883(x121692,a869))),x121693),x121694))), % 178.17/178.00 inference(rename_variables,[],[4544])). % 178.17/178.00 cnf(12172,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(f882(f876(x121721),f876(x121721)),a869)),f157(x121721,x121722)),f305(f876(x121721),f156(x121721,x121722))))), % 178.17/178.00 inference(rename_variables,[],[3971])). % 178.17/178.00 cnf(12177,plain, % 178.17/178.00 (P24(f329(f329(f244(f883(x121771,a869)),f193(f883(x121771,a869))),f252(f883(x121771,a869))))), % 178.17/178.00 inference(scs_inference,[],[4546,3511,11025,12054,3520,4477,4478,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,4457,10415,10508,3480,3183,2855,2865,2869,2870,2875,2878,2880,2881,2885,2888,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2942,2943,2946,2947,2948,2950,2957,2961,2980,3010,3011,3019,3021,3025,3034,3041,3055,4438,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,3196,11568,3202,10663,11574,3209,3729,3963,3098,3819,11345,3160,3127,3122,3106,3107,3112,3142,3281,12002,3329,10795,3195,3219,10456,3375,4536,3903,4467,10247,10412,3257,11664,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,3905,10966,11092,11143,4549,10898,10999,11097,11202,11224,11262,11268,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,3632,4333,4334,4465,3573,3783,3829,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,3721,11559,3250,3351,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,4531,11443,11474,11509,11539,3708,3481,3854,3296,3297,3271,4512,4462,3465,4532,4044,11219,3592,3311,11688,11691,4014,3971,11832,12172,3915,10792,11990,3966,10969,12051,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,12095,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,3270,3347,12039,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,3428,10589,10851,10895,11165,11243,11404,11644,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,3333,10616,10646,10655,11194,3371,3365,3787,3726,10293,11562,11592,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,3290,10649,10800,10871,11593,11748,11937,3748,4094,4522,3759,3795,4501,4503,3241,3242,4502,4505,4506,3766,3582,4193,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,3980,3871,11284,11619,11623,3715,10911,10917,10932,11864,3569,11134,3717,10652,10988,11140,11170,11181,3537,10575,10578,10658,10830,4543,11556,4533,4544,10709,10809,11119,11401,11429,12160,4154,4055,3747,3695,4541,10266,10269,10604,10607,11440,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7386,7400,7417,7450,7453,7479,7503,7520,7523,7524,7534,7552,7553,7555,7557,7559,7561,7587,7612,7613,7645,7647,7648,7649,7654,7675,7684,7695,7700,7706,7708,7714,7725,7726,7728,7748,7757,7780,7845,7846,7893,7901,7902,7926,7927,7944,7945,8011])). % 178.17/178.00 cnf(12178,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x121781,a869)),f193(f883(x121781,a869))),x121782))), % 178.17/178.00 inference(rename_variables,[],[3717])). % 178.17/178.00 cnf(12181,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x121811,a869)),f329(f308(x121812,x121811,x121813),f329(f309(x121812,x121811,x121813),x121814))),x121814))), % 178.17/178.00 inference(rename_variables,[],[4154])). % 178.17/178.00 cnf(12184,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x121841,a869)),f329(f171(x121841),f169(x121841,x121842,x121843))),f329(f171(x121841),x121843)))), % 178.17/178.00 inference(rename_variables,[],[3966])). % 178.17/178.00 cnf(12185,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x121851,a869)),f329(f171(x121851),f329(f135(x121851,x121852),x121853))),f329(f171(x121851),x121853)))), % 178.17/178.00 inference(rename_variables,[],[3915])). % 178.17/178.00 cnf(12188,plain, % 178.17/178.00 (P21(x121881,f879(x121881),f236(x121881),x121882)), % 178.17/178.00 inference(rename_variables,[],[3521])). % 178.17/178.00 cnf(12193,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x121931,a869)),f329(f308(x121932,x121931,x121933),f329(f309(x121932,x121931,x121933),x121934))),x121934))), % 178.17/178.00 inference(rename_variables,[],[4154])). % 178.17/178.00 cnf(12196,plain, % 178.17/178.00 (P24(f329(f62(f879(x121961)),f329(f308(x121962,f879(x121961),f329(f177(x121962,x121961),x121963)),f252(f883(x121962,a869)))))), % 178.17/178.00 inference(rename_variables,[],[3980])). % 178.17/178.00 cnf(12201,plain, % 178.17/178.00 (P24(f329(f329(f331(f876(x122011)),f119(x122011)),f160(x122011,x122012)))), % 178.17/178.00 inference(rename_variables,[],[3473])). % 178.17/178.00 cnf(12204,plain, % 178.17/178.00 (~P24(f329(f329(f331(f882(f876(x122041),f876(x122041))),f329(f329(f264(f876(x122041),f876(x122041)),x122042),f119(x122041))),f146(x122041,x122043)))), % 178.17/178.00 inference(rename_variables,[],[4549])). % 178.17/178.00 cnf(12207,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x122071),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(12209,plain, % 178.17/178.00 (~P24(f329(f62(x122091),f252(f883(x122091,a869))))), % 178.17/178.00 inference(scs_inference,[],[4546,3511,11025,12054,3520,3521,3235,4477,4478,3136,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,4457,10415,10508,3480,3183,2855,2865,2869,2870,2875,2878,2880,2881,2885,2888,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2942,2943,2946,2947,2948,2950,2951,2957,2961,2980,3010,3011,3019,3021,3025,3034,3041,3055,4438,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,3196,11568,3202,10663,11574,3209,3729,3963,3098,3819,11345,3160,3127,3122,3106,3107,3112,3142,3281,12002,3329,10795,3195,3219,10456,3375,4536,3903,4467,10247,10412,3257,11664,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,3905,10966,11092,11143,4549,10898,10999,11097,11202,11224,11262,11268,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,12157,12201,3632,4333,4334,4465,3573,3783,3829,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,3721,11559,3250,3351,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,4531,11443,11474,11509,11539,3708,3481,3854,3296,3297,3271,4512,4462,3465,4532,4044,11219,3592,3311,11688,11691,4014,3971,11832,12172,3915,10792,11990,12013,3966,10969,12051,12124,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,12095,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,3270,3347,12039,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,3428,10589,10851,10895,11165,11243,11404,11644,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,3333,10616,10646,10655,11194,3371,3365,3787,3726,10293,11562,11592,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,3290,10649,10800,10871,11593,11748,11937,3748,4094,4522,3759,3795,4501,4503,3241,3242,4502,4505,4506,3766,3582,4193,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,3980,3871,11284,11619,11623,3715,10911,10917,10932,11864,3569,11134,12098,3717,10652,10988,11140,11170,11181,3537,10575,10578,10658,10830,4543,11556,4533,4544,10709,10809,11119,11401,11429,12160,4154,10785,12181,4055,3747,3695,4541,10266,10269,10604,10607,11440,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7386,7400,7417,7450,7453,7479,7503,7520,7523,7524,7534,7552,7553,7555,7557,7559,7561,7587,7612,7613,7645,7647,7648,7649,7654,7675,7684,7695,7700,7706,7708,7714,7725,7726,7728,7748,7757,7780,7845,7846,7893,7901,7902,7926,7927,7944,7945,8011,8012,8013,8038,8071,8078,8080,8089,8101,8133,8139,8146])). % 178.17/178.00 cnf(12210,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x122101,a869)),x122102),x122102))), % 178.17/178.00 inference(rename_variables,[],[3569])). % 178.17/178.00 cnf(12213,plain, % 178.17/178.00 (~P24(f329(f329(f331(x122131),x122132),f193(f883(x122131,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(12216,plain, % 178.17/178.00 (~P24(f329(f329(f193(f883(x122161,f883(x122162,a869))),x122163),x122164))), % 178.17/178.00 inference(rename_variables,[],[4544])). % 178.17/178.00 cnf(12219,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x122191,a869)),f329(f308(x122192,x122191,x122193),f329(f309(x122192,x122191,x122193),x122194))),x122194))), % 178.17/178.00 inference(rename_variables,[],[4154])). % 178.17/178.00 cnf(12220,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x122201,a869)),x122202),x122202))), % 178.17/178.00 inference(rename_variables,[],[3569])). % 178.17/178.00 cnf(12225,plain, % 178.17/178.00 (E(f329(f260(x122251,x122251),f261(x122251,x122252)),x122252)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(12228,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x122281,a869)),f329(f171(x122281),f169(x122281,x122282,x122283))),f329(f171(x122281),x122283)))), % 178.17/178.00 inference(rename_variables,[],[3966])). % 178.17/178.00 cnf(12229,plain, % 178.17/178.00 (P24(f329(f62(x122291),f329(f171(x122291),x122292)))), % 178.17/178.00 inference(rename_variables,[],[3311])). % 178.17/178.00 cnf(12232,plain, % 178.17/178.00 (P24(f329(f329(f199(a24),x122321),x122321))), % 178.17/178.00 inference(rename_variables,[],[3267])). % 178.17/178.00 cnf(12235,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x122351),x122351))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(12238,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x122381),x122381))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(12249,plain, % 178.17/178.00 (P21(x122491,x122491,f5(x122491),x122492)), % 178.17/178.00 inference(rename_variables,[],[3511])). % 178.17/178.00 cnf(12256,plain, % 178.17/178.00 (~P24(f329(f329(f331(x122561),x122562),f193(f883(x122561,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(12259,plain, % 178.17/178.00 (P24(f329(f329(f331(f882(x122591,x122591)),f329(f329(f264(x122591,x122591),x122592),x122592)),f305(x122591,x122593)))), % 178.17/178.00 inference(rename_variables,[],[3905])). % 178.17/178.00 cnf(12262,plain, % 178.17/178.00 (~P24(f329(f329(f331(x122621),x122622),f193(f883(x122621,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(12265,plain, % 178.17/178.00 (P24(f329(f329(f331(f882(x122651,x122651)),f329(f329(f264(x122651,x122651),x122652),x122652)),f305(x122651,x122653)))), % 178.17/178.00 inference(rename_variables,[],[3905])). % 178.17/178.00 cnf(12275,plain, % 178.17/178.00 (~E(f329(f329(f150(x122751),x122752),x122753),x122753)), % 178.17/178.00 inference(rename_variables,[],[4467])). % 178.17/178.00 cnf(12278,plain, % 178.17/178.00 (P24(f329(f329(f331(x122781),x122782),f252(f883(x122781,a869))))), % 178.17/178.00 inference(rename_variables,[],[3428])). % 178.17/178.00 cnf(12279,plain, % 178.17/178.00 (~E(f329(a118,x122791),x122791)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(12282,plain, % 178.17/178.00 (P24(f329(f329(f331(f876(x122821)),f119(x122821)),f160(x122821,x122822)))), % 178.17/178.00 inference(rename_variables,[],[3473])). % 178.17/178.00 cnf(12283,plain, % 178.17/178.00 (~E(f329(f329(f150(x122831),x122832),x122833),f119(x122831))), % 178.17/178.00 inference(rename_variables,[],[4476])). % 178.17/178.00 cnf(12286,plain, % 178.17/178.00 (P24(f329(f329(f331(x122861),f329(x122862,x122863)),f329(f308(x122864,x122861,x122862),f252(f883(x122864,a869)))))), % 178.17/178.00 inference(rename_variables,[],[3871])). % 178.17/178.00 cnf(12287,plain, % 178.17/178.00 (P21(x122871,x122871,f5(x122871),x122872)), % 178.17/178.00 inference(rename_variables,[],[3511])). % 178.17/178.00 cnf(12290,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x122901,a869)),f193(f883(x122901,a869))),x122902))), % 178.17/178.00 inference(rename_variables,[],[3717])). % 178.17/178.00 cnf(12291,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x122911,a869)),x122912),x122912))), % 178.17/178.00 inference(rename_variables,[],[3569])). % 178.17/178.00 cnf(12294,plain, % 178.17/178.00 (P24(f329(f329(f331(x122941),f329(x122942,x122943)),f329(f308(x122944,x122941,x122942),f252(f883(x122944,a869)))))), % 178.17/178.00 inference(rename_variables,[],[3871])). % 178.17/178.00 cnf(12295,plain, % 178.17/178.00 (P21(x122951,x122951,f5(x122951),x122952)), % 178.17/178.00 inference(rename_variables,[],[3511])). % 178.17/178.00 cnf(12298,plain, % 178.17/178.00 (P24(f329(f329(f331(f882(f876(x122981),f876(x122981))),f329(f329(f264(f876(x122981),f876(x122981)),f119(x122981)),f119(x122981))),f157(x122981,x122982)))), % 178.17/178.00 inference(rename_variables,[],[4050])). % 178.17/178.00 cnf(12301,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x123011),x123011))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(12302,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x123021),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(12308,plain, % 178.17/178.00 (P21(x123081,x123081,f5(x123081),x123082)), % 178.17/178.00 inference(rename_variables,[],[3511])). % 178.17/178.00 cnf(12311,plain, % 178.17/178.00 (E(f329(f329(f127(x123111),x123112),f119(x123111)),x123112)), % 178.17/178.00 inference(rename_variables,[],[3196])). % 178.17/178.00 cnf(12312,plain, % 178.17/178.00 (~E(f329(f329(f150(x123121),x123122),x123123),x123123)), % 178.17/178.00 inference(rename_variables,[],[4467])). % 178.17/178.00 cnf(12315,plain, % 178.17/178.00 (E(f329(f329(f127(x123151),x123152),f119(x123151)),x123152)), % 178.17/178.00 inference(rename_variables,[],[3196])). % 178.17/178.00 cnf(12316,plain, % 178.17/178.00 (~E(f329(f329(f150(x123161),x123162),x123163),x123163)), % 178.17/178.00 inference(rename_variables,[],[4467])). % 178.17/178.00 cnf(12319,plain, % 178.17/178.00 (E(f329(f329(f127(x123191),x123192),f119(x123191)),x123192)), % 178.17/178.00 inference(rename_variables,[],[3196])). % 178.17/178.00 cnf(12328,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x123281,a869)),x123282),f252(f883(x123281,a869))))), % 178.17/178.00 inference(rename_variables,[],[3651])). % 178.17/178.00 cnf(12332,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x123321),x123321))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(12333,plain, % 178.17/178.00 (~E(f329(a118,x123331),x123331)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(12336,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x123361,a869)),f193(f883(x123361,a869))),x123362))), % 178.17/178.00 inference(rename_variables,[],[3717])). % 178.17/178.00 cnf(12339,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x123391),x123391))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(12342,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x123421,a869)),x123422),x123422))), % 178.17/178.00 inference(rename_variables,[],[3569])). % 178.17/178.00 cnf(12347,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x123471,a869)),x123472),f329(f329(f307(x123471),x123473),x123472)))), % 178.17/178.00 inference(rename_variables,[],[3715])). % 178.17/178.00 cnf(12350,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x123501,a869)),x123502),x123502))), % 178.17/178.00 inference(rename_variables,[],[3569])). % 178.17/178.00 cnf(12351,plain, % 178.17/178.00 (~P24(f329(f329(f331(x123511),x123512),f193(f883(x123511,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(12354,plain, % 178.17/178.00 (~P24(f329(f329(f331(x123541),x123542),f193(f883(x123541,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(12363,plain, % 178.17/178.00 (P21(x123631,x123631,f5(x123631),x123632)), % 178.17/178.00 inference(rename_variables,[],[3511])). % 178.17/178.00 cnf(12366,plain, % 178.17/178.00 (E(f329(f194(f876(x123661)),f329(f167(x123661),x123662)),f329(f194(f876(x123661)),x123662))), % 178.17/178.00 inference(rename_variables,[],[3281])). % 178.17/178.00 cnf(12369,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x123691),x123691))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(12370,plain, % 178.17/178.00 (P24(f329(f252(f883(x123701,a869)),x123702))), % 178.17/178.00 inference(rename_variables,[],[3333])). % 178.17/178.00 cnf(12373,plain, % 178.17/178.00 (~P24(f329(f329(f331(x123731),x123732),f193(f883(x123731,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(12376,plain, % 178.17/178.00 (P24(f329(f329(f331(x123761),f329(x123762,x123763)),f329(f308(x123764,x123761,x123762),f252(f883(x123764,a869)))))), % 178.17/178.00 inference(rename_variables,[],[3871])). % 178.17/178.00 cnf(12377,plain, % 178.17/178.00 (P24(f329(f329(f331(f882(x123771,x123771)),f329(f329(f264(x123771,x123771),x123772),x123772)),f305(x123771,x123773)))), % 178.17/178.00 inference(rename_variables,[],[3905])). % 178.17/178.00 cnf(12380,plain, % 178.17/178.00 (P24(f329(f329(f331(f882(x123801,x123801)),f329(f329(f264(x123801,x123801),x123802),x123802)),f305(x123801,x123803)))), % 178.17/178.00 inference(rename_variables,[],[3905])). % 178.17/178.00 cnf(12383,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x123831),x123831))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(12384,plain, % 178.17/178.00 (P24(f329(f252(f883(x123841,a869)),x123842))), % 178.17/178.00 inference(rename_variables,[],[3333])). % 178.17/178.00 cnf(12387,plain, % 178.17/178.00 (P24(f329(f62(x123871),f329(f171(x123871),x123872)))), % 178.17/178.00 inference(rename_variables,[],[3311])). % 178.17/178.00 cnf(12392,plain, % 178.17/178.00 (P24(f329(f329(f331(f882(f876(x123921),f876(x123921))),f329(f329(f264(f876(x123921),f876(x123921)),f119(x123921)),f119(x123921))),f329(f329(f286(f876(x123921),f876(x123921),f876(x123921)),f157(x123921,x123922)),f157(x123921,x123922))))), % 178.17/178.00 inference(scs_inference,[],[4546,3511,11025,12054,12154,12249,12287,12295,12308,3520,3521,3235,4477,4478,3136,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,12121,12279,4457,10415,10508,3328,3480,3183,2855,2865,2869,2870,2875,2878,2880,2881,2885,2888,2889,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2942,2943,2946,2947,2948,2950,2951,2957,2961,2980,3010,3011,3019,3021,3025,3034,3041,3055,4438,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,12028,3196,11568,12311,12315,12319,3202,10663,11574,3209,3729,3963,3098,4454,3819,11345,3160,3127,3122,3106,3107,3112,3142,3281,12002,12144,3329,10795,12115,3194,3195,3219,10456,3375,4536,3903,4467,10247,10412,11208,12275,12312,4476,12283,3257,11664,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,12298,3905,10966,11092,11143,12259,12265,12377,4549,10898,10999,11097,11202,11224,11262,11268,12204,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,12157,12201,12282,3632,4333,4334,4465,11326,3573,3783,3829,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,12083,3721,11559,3250,3351,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,12207,4531,11443,11474,11509,11539,3708,3481,3854,3296,3297,3271,4512,4462,3660,3465,4532,4044,11219,3592,3311,11688,11691,12125,12229,4014,3971,11832,12172,3915,10792,11990,12013,3966,10969,12051,12124,12184,12228,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,12073,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,12066,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,12095,12165,12339,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,3270,3347,12039,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,12139,12235,12238,12301,12332,3428,10589,10851,10895,11165,11243,11404,11644,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,12069,12213,12256,12262,12351,12354,3333,10616,10646,10655,11194,11743,12370,3371,3365,3787,3726,10293,11562,11592,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,3290,10649,10800,10871,11593,11748,11937,3748,4094,4522,3759,3795,4501,4503,3241,3242,4502,4505,4506,3766,3582,4193,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,11287,3980,3871,11284,11619,11623,11685,12286,12294,3715,10911,10917,10932,11864,12072,3569,11134,12098,12210,12220,12291,12342,3717,10652,10988,11140,11170,11181,12178,12290,3537,10575,10578,10658,10830,4543,11556,4533,4544,10709,10809,11119,11401,11429,12160,12169,4154,10785,12181,12193,4055,3747,3695,4541,10266,10269,10604,10607,11440,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7386,7400,7417,7450,7453,7479,7503,7520,7523,7524,7534,7552,7553,7555,7557,7559,7561,7587,7612,7613,7645,7647,7648,7649,7654,7675,7684,7695,7700,7706,7708,7714,7725,7726,7728,7748,7757,7780,7845,7846,7893,7901,7902,7926,7927,7944,7945,8011,8012,8013,8038,8071,8078,8080,8089,8101,8133,8139,8146,8159,8178,8184,8206,8249,8279,8291,8309,8312,8342,8365,8429,8430,8433,8435,8454,8539,8540,8541,8542,8568,8597,8625,8670,8688,8743,8788,8791,8804,8811,8848,8868,8895,8896,8913,8914,9054,9058,9078,9088,9111,9113,9116,9120,9123,9124,9137,9138,9158,9164,9176,9224,9243,9297,9298,9305,9366,9371,9406])). % 178.17/178.00 cnf(12394,plain, % 178.17/178.00 (P24(f329(f329(f331(f882(x123941,x123941)),f329(f329(f264(x123941,x123941),x123942),x123942)),f329(f329(f286(x123941,x123941,x123941),f305(x123941,x123943)),f305(x123941,f305(x123941,x123943)))))), % 178.17/178.00 inference(scs_inference,[],[4546,3511,11025,12054,12154,12249,12287,12295,12308,3520,3521,3235,4477,4478,3136,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,12121,12279,4457,10415,10508,3328,3480,3183,2855,2865,2869,2870,2875,2878,2880,2881,2885,2888,2889,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2942,2943,2946,2947,2948,2950,2951,2957,2961,2980,3010,3011,3019,3021,3025,3034,3041,3055,4438,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,12028,3196,11568,12311,12315,12319,3202,10663,11574,3209,3729,3963,3098,4454,3819,11345,3160,3127,3122,3106,3107,3112,3142,3281,12002,12144,3329,10795,12115,3194,3195,3219,10456,3375,4536,3903,4467,10247,10412,11208,12275,12312,4476,12283,3257,11664,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,12298,3905,10966,11092,11143,12259,12265,12377,12380,4549,10898,10999,11097,11202,11224,11262,11268,12204,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,12157,12201,12282,3632,4333,4334,4465,11326,3573,3783,3829,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,12083,3721,11559,3250,3351,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,12207,4531,11443,11474,11509,11539,3708,3481,3854,3296,3297,3271,4512,4462,3660,3465,4532,4044,11219,3592,3311,11688,11691,12125,12229,4014,3971,11832,12172,3915,10792,11990,12013,3966,10969,12051,12124,12184,12228,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,12073,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,12066,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,12095,12165,12339,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,3270,3347,12039,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,12139,12235,12238,12301,12332,3428,10589,10851,10895,11165,11243,11404,11644,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,12069,12213,12256,12262,12351,12354,3333,10616,10646,10655,11194,11743,12370,3371,3365,3787,3726,10293,11562,11592,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,3290,10649,10800,10871,11593,11748,11937,3748,4094,4522,3759,3795,4501,4503,3241,3242,4502,4505,4506,3766,3582,4193,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,11287,3980,3871,11284,11619,11623,11685,12286,12294,3715,10911,10917,10932,11864,12072,3569,11134,12098,12210,12220,12291,12342,3717,10652,10988,11140,11170,11181,12178,12290,3537,10575,10578,10658,10830,4543,11556,4533,4544,10709,10809,11119,11401,11429,12160,12169,4154,10785,12181,12193,4055,3747,3695,4541,10266,10269,10604,10607,11440,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7386,7400,7417,7450,7453,7479,7503,7520,7523,7524,7534,7552,7553,7555,7557,7559,7561,7587,7612,7613,7645,7647,7648,7649,7654,7675,7684,7695,7700,7706,7708,7714,7725,7726,7728,7748,7757,7780,7845,7846,7893,7901,7902,7926,7927,7944,7945,8011,8012,8013,8038,8071,8078,8080,8089,8101,8133,8139,8146,8159,8178,8184,8206,8249,8279,8291,8309,8312,8342,8365,8429,8430,8433,8435,8454,8539,8540,8541,8542,8568,8597,8625,8670,8688,8743,8788,8791,8804,8811,8848,8868,8895,8896,8913,8914,9054,9058,9078,9088,9111,9113,9116,9120,9123,9124,9137,9138,9158,9164,9176,9224,9243,9297,9298,9305,9366,9371,9406,9413])). % 178.17/178.00 cnf(12397,plain, % 178.17/178.00 (~P24(f329(f329(f193(f883(x123971,f883(x123972,a869))),x123973),x123974))), % 178.17/178.00 inference(rename_variables,[],[4544])). % 178.17/178.00 cnf(12400,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x124001,a869)),x124002),f252(f883(x124001,a869))))), % 178.17/178.00 inference(rename_variables,[],[3651])). % 178.17/178.00 cnf(12403,plain, % 178.17/178.00 (P24(f329(f329(f331(f882(x124031,x124031)),f329(f329(f264(x124031,x124031),x124032),x124032)),f305(x124031,x124033)))), % 178.17/178.00 inference(rename_variables,[],[3905])). % 178.17/178.00 cnf(12406,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),f329(f329(f81(a875),x124061),x124062)),x124062))), % 178.17/178.00 inference(rename_variables,[],[4541])). % 178.17/178.00 cnf(12407,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x124071),f329(a118,x124071)))), % 178.17/178.00 inference(rename_variables,[],[3339])). % 178.17/178.00 cnf(12410,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x124101,a869)),f329(f171(x124101),f329(f135(x124101,x124102),x124103))),f329(f171(x124101),x124103)))), % 178.17/178.00 inference(rename_variables,[],[3915])). % 178.17/178.00 cnf(12413,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x124131,a869)),x124132),f252(f883(x124131,a869))))), % 178.17/178.00 inference(rename_variables,[],[3651])). % 178.17/178.00 cnf(12416,plain, % 178.17/178.00 (E(f329(f260(x124161,x124161),f261(x124161,x124162)),x124162)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(12423,plain, % 178.17/178.00 (P24(f329(f329(f331(f882(f882(f876(x124231),f876(x124231)),f882(f876(x124231),f876(x124231)))),f598(f305(f882(f876(x124231),f876(x124231)),x124232),f146(x124231,x124233),f882(f876(x124231),f876(x124231)))),f305(f882(f876(x124231),f876(x124231)),x124232)))), % 178.17/178.00 inference(scs_inference,[],[4546,3511,11025,12054,12154,12249,12287,12295,12308,3520,3521,3235,4477,4478,3136,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,12121,12279,4457,10415,10508,3328,3480,3183,2855,2865,2869,2870,2875,2878,2880,2881,2885,2888,2889,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2942,2943,2946,2947,2948,2950,2951,2957,2961,2980,3010,3011,3019,3021,3025,3034,3041,3055,4438,3607,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,12028,12225,3196,11568,12311,12315,12319,3202,10663,11574,3209,3729,3963,3098,4454,3819,11345,3160,3127,3122,3106,3107,3112,3142,3281,12002,12144,3329,10795,12115,3194,3195,3219,10456,3375,4536,3903,4467,10247,10412,11208,12275,12312,4476,12283,3257,11664,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,12298,3905,10966,11092,11143,12259,12265,12377,12380,12403,4549,10898,10999,11097,11202,11224,11262,11268,12204,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,12157,12201,12282,3632,4333,4334,4465,11326,3573,3783,3829,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,12083,3721,11559,3250,3351,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,12207,4531,11443,11474,11509,11539,3708,3481,3854,3296,3297,3271,4512,4462,3660,4187,3465,4532,4044,11219,3592,3311,11688,11691,12125,12229,4014,3971,11832,12172,3915,10792,11990,12013,12185,3966,10969,12051,12124,12184,12228,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,12073,12328,12400,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,12066,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,12095,12165,12339,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,3270,3347,12039,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,12139,12235,12238,12301,12332,3428,10589,10851,10895,11165,11243,11404,11644,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,12069,12213,12256,12262,12351,12354,3333,10616,10646,10655,11194,11743,12370,3371,3365,3787,3726,10293,11562,11592,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,3290,10649,10800,10871,11593,11748,11937,3748,4094,4522,3759,3795,4501,4503,3241,3242,4502,4505,4506,3766,3582,4193,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,11287,3980,3871,11284,11619,11623,11685,12286,12294,3715,10911,10917,10932,11864,12072,3569,11134,12098,12210,12220,12291,12342,4048,3717,10652,10988,11140,11170,11181,12178,12290,3537,10575,10578,10658,10830,4543,11556,4533,4544,10709,10809,11119,11401,11429,12160,12169,12216,4154,10785,12181,12193,4055,3747,3695,4541,10266,10269,10604,10607,11440,11620,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7386,7400,7417,7450,7453,7479,7503,7520,7523,7524,7534,7552,7553,7555,7557,7559,7561,7587,7612,7613,7645,7647,7648,7649,7654,7675,7684,7695,7700,7706,7708,7714,7725,7726,7728,7748,7757,7780,7845,7846,7893,7901,7902,7926,7927,7944,7945,8011,8012,8013,8038,8071,8078,8080,8089,8101,8133,8139,8146,8159,8178,8184,8206,8249,8279,8291,8309,8312,8342,8365,8429,8430,8433,8435,8454,8539,8540,8541,8542,8568,8597,8625,8670,8688,8743,8788,8791,8804,8811,8848,8868,8895,8896,8913,8914,9054,9058,9078,9088,9111,9113,9116,9120,9123,9124,9137,9138,9158,9164,9176,9224,9243,9297,9298,9305,9366,9371,9406,9413,9416,9419,9420,9435,9451,9460,9472,9482,9483,9486])). % 178.17/178.00 cnf(12427,plain, % 178.17/178.00 (~P24(f329(f329(f331(x124271),x124272),f193(f883(x124271,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(12428,plain, % 178.17/178.00 (P24(f329(f329(f331(f882(f876(x124281),f876(x124281))),f329(f329(f264(f876(x124281),f876(x124281)),f119(x124281)),f119(x124281))),f157(x124281,x124282)))), % 178.17/178.00 inference(rename_variables,[],[4050])). % 178.17/178.00 cnf(12430,plain, % 178.17/178.00 (P24(f329(f329(f331(f882(a875,a875)),f329(f329(f264(a875,a875),f329(a118,x124301)),f329(a118,f329(a118,x124301)))),f329(f329(f286(a875,a875,a875),f305(a875,a319)),f305(a875,f305(a875,a319)))))), % 178.17/178.00 inference(scs_inference,[],[4546,3511,11025,12054,12154,12249,12287,12295,12308,3520,3521,3235,4477,4478,3136,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,12121,12279,4457,10415,10508,3328,3480,3183,2855,2865,2869,2870,2875,2878,2880,2881,2885,2888,2889,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2942,2943,2946,2947,2948,2950,2951,2957,2961,2980,3010,3011,3019,3021,3025,3034,3041,3055,4438,3607,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,12028,12225,3196,11568,12311,12315,12319,3202,10663,11574,3209,3729,3963,3098,4454,3819,11345,3160,3127,3122,3106,3107,3112,3142,3281,12002,12144,3329,10795,12115,3194,3195,3219,10456,3375,4536,3903,4467,10247,10412,11208,12275,12312,4476,12283,3257,11664,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,12298,3905,10966,11092,11143,12259,12265,12377,12380,12403,4549,10898,10999,11097,11202,11224,11262,11268,12204,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,12157,12201,12282,3632,4333,4334,4465,11326,3573,3783,3829,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,12083,3721,11559,3250,3351,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,12207,4531,11443,11474,11509,11539,3708,3481,3854,3296,3297,3271,4512,4462,3660,4187,3465,4532,4044,11219,3592,3311,11688,11691,12125,12229,4014,3971,11832,12172,3915,10792,11990,12013,12185,3966,10969,12051,12124,12184,12228,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,12073,12328,12400,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,12066,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,12095,12165,12339,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,3270,3347,12039,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,12139,12235,12238,12301,12332,3428,10589,10851,10895,11165,11243,11404,11644,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,12069,12213,12256,12262,12351,12354,12373,3333,10616,10646,10655,11194,11743,12370,3371,3365,3787,3726,10293,11562,11592,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,3290,10649,10800,10871,11593,11748,11937,3748,4094,4522,3759,3795,4501,4503,3241,3242,4502,4505,4506,3766,3582,4193,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,11287,3980,3871,11284,11619,11623,11685,12286,12294,3715,10911,10917,10932,11864,12072,3569,11134,12098,12210,12220,12291,12342,4048,3717,10652,10988,11140,11170,11181,12178,12290,3537,10575,10578,10658,10830,4543,11556,4533,4544,10709,10809,11119,11401,11429,12160,12169,12216,4154,10785,12181,12193,4055,3747,3695,4541,10266,10269,10604,10607,11440,11620,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7386,7400,7417,7450,7453,7479,7503,7520,7523,7524,7534,7552,7553,7555,7557,7559,7561,7587,7612,7613,7645,7647,7648,7649,7654,7675,7684,7695,7700,7706,7708,7714,7725,7726,7728,7748,7757,7780,7845,7846,7893,7901,7902,7926,7927,7944,7945,8011,8012,8013,8038,8071,8078,8080,8089,8101,8133,8139,8146,8159,8178,8184,8206,8249,8279,8291,8309,8312,8342,8365,8429,8430,8433,8435,8454,8539,8540,8541,8542,8568,8597,8625,8670,8688,8743,8788,8791,8804,8811,8848,8868,8895,8896,8913,8914,9054,9058,9078,9088,9111,9113,9116,9120,9123,9124,9137,9138,9158,9164,9176,9224,9243,9297,9298,9305,9366,9371,9406,9413,9416,9419,9420,9435,9451,9460,9472,9482,9483,9486,9488,9514])). % 178.17/178.00 cnf(12433,plain, % 178.17/178.00 (~P24(f329(f329(f331(x124331),x124332),f193(f883(x124331,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(12436,plain, % 178.17/178.00 (P32(x124361,x124362,f119(x124361))), % 178.17/178.00 inference(rename_variables,[],[3201])). % 178.17/178.00 cnf(12439,plain, % 178.17/178.00 (E(f329(f194(f876(x124391)),f329(f167(x124391),x124392)),f329(f194(f876(x124391)),x124392))), % 178.17/178.00 inference(rename_variables,[],[3281])). % 178.17/178.00 cnf(12442,plain, % 178.17/178.00 (~P24(f329(f329(f331(x124421),x124422),f193(f883(x124421,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(12448,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x124481),x124481))), % 178.17/178.00 inference(rename_variables,[],[4511])). % 178.17/178.00 cnf(12450,plain, % 178.17/178.00 (P24(f329(f329(f331(f882(f876(x124501),f876(x124501))),f329(f329(f264(f876(x124501),f876(x124501)),f329(f167(x124501),x124502)),x124502)),f157(x124501,f252(f883(f882(x124501,x124501),a869)))))), % 178.17/178.00 inference(scs_inference,[],[4546,3511,11025,12054,12154,12249,12287,12295,12308,3520,3521,3235,3201,4477,4478,3136,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,12121,12279,4457,10415,10508,3328,3480,3183,2855,2865,2869,2870,2875,2878,2880,2881,2885,2888,2889,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2942,2943,2946,2947,2948,2950,2951,2957,2961,2980,3010,3011,3019,3021,3025,3034,3041,3055,4438,3607,3108,11295,3312,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,12028,12225,3196,11568,12311,12315,12319,3202,10663,11574,3209,3729,3963,3098,4454,3819,11345,3160,3127,3122,3106,3107,3112,3142,3281,12002,12144,12366,12439,3329,10795,12115,3194,3195,3219,10456,3375,4536,3903,4467,10247,10412,11208,12275,12312,4476,12283,3257,11664,4525,10960,11030,11254,11257,3376,3157,3158,10314,10619,3433,3077,3179,11335,4050,12298,12428,3905,10966,11092,11143,12259,12265,12377,12380,12403,4549,10898,10999,11097,11202,11224,11262,11268,12204,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,12157,12201,12282,3632,4333,4334,4465,11326,3573,3783,3829,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,12083,3721,11559,3250,3351,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,12207,4531,11443,11474,11509,11539,3708,3481,3854,3296,3297,3271,4512,4462,3660,4187,3465,4532,4044,11219,3592,3311,11688,11691,12125,12229,4014,3971,11832,12172,3915,10792,11990,12013,12185,3966,10969,12051,12124,12184,12228,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,12073,12328,12400,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,12066,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,12095,12165,12339,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,3270,3347,12039,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,12139,12235,12238,12301,12332,12369,3428,10589,10851,10895,11165,11243,11404,11644,12278,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,12069,12213,12256,12262,12351,12354,12373,12427,12433,3333,10616,10646,10655,11194,11743,12370,3371,3365,3787,3726,10293,11562,11592,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,3290,10649,10800,10871,11593,11748,11937,3748,4094,4522,3759,3795,4501,4503,3241,3242,4502,4505,4506,3766,3582,4193,11423,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,11287,3980,3871,11284,11619,11623,11685,12286,12294,3715,10911,10917,10932,11864,12072,3569,11134,12098,12210,12220,12291,12342,4048,3717,10652,10988,11140,11170,11181,12178,12290,3537,10575,10578,10658,10830,4543,11556,4533,4544,10709,10809,11119,11401,11429,12160,12169,12216,4154,10785,12181,12193,4055,3747,3695,4541,10266,10269,10604,10607,11440,11620,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8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% 178.17/178.00 cnf(12451,plain, % 178.17/178.00 (P24(f329(f329(f331(x124511),x124512),f252(f883(x124511,a869))))), % 178.17/178.00 inference(rename_variables,[],[3428])). % 178.17/178.00 cnf(12455,plain, % 178.17/178.00 (P20(x124551,x124552,f329(f329(f307(f874(x124551)),f329(f329(f329(f93(x124551),f329(f329(f7(x124551,f883(a871,a869),f883(a871,a869)),f329(f329(f8(f883(a871,f883(a869,a869)),f883(f883(a871,a869),f883(a871,a869)),x124551),f18(a871,a869,a869)),f329(f329(f8(f883(a871,a869),f883(a871,f883(a869,a869)),x124551),f329(f8(a869,f883(a869,a869),a871),a327)),x124553))),f329(f329(f8(a869,a869,a871),a324),x124554))),f33(x124554,x124555)),x124553)),f193(f883(f874(x124551),a869))))), % 178.17/178.00 inference(rename_variables,[],[4421])). % 178.17/178.00 cnf(12458,plain, % 178.17/178.00 (P24(f329(f329(f243(f883(x124581,a869)),x124582),x124582))), % 178.17/178.00 inference(rename_variables,[],[3569])). % 178.17/178.00 cnf(12461,plain, % 178.17/178.00 (~P24(f329(f329(f331(x124611),x124612),f193(f883(x124611,a869))))), % 178.17/178.00 inference(rename_variables,[],[4527])). % 178.17/178.00 cnf(12464,plain, % 178.17/178.00 (P24(f329(f329(f243(a1),f2(a1)),f329(f329(f254(a1),f329(f76(a1),x124641)),x124642)))), % 178.17/178.00 inference(rename_variables,[],[3747])). % 178.17/178.00 cnf(12467,plain, % 178.17/178.00 (~E(f329(a118,x124671),x124671)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(12469,plain, % 178.17/178.00 (E(f329(f260(x124691,x124691),f261(x124691,x124692)),x124692)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(12471,plain, % 178.17/178.00 (E(f329(f260(x124711,x124711),f261(x124711,x124712)),x124712)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(12475,plain, % 178.17/178.00 (E(f329(f260(x124751,x124751),f261(x124751,x124752)),x124752)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(12477,plain, % 178.17/178.00 (E(f329(f260(x124771,x124771),f261(x124771,x124772)),x124772)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(12479,plain, % 178.17/178.00 (E(f329(f260(x124791,x124791),f261(x124791,x124792)),x124792)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(12481,plain, % 178.17/178.00 (P33(x124811,x124812,f119(x124811),f119(x124811))), % 178.17/178.00 inference(rename_variables,[],[3520])). % 178.17/178.00 cnf(12483,plain, % 178.17/178.00 (P33(x124831,x124832,f119(x124831),f119(x124831))), % 178.17/178.00 inference(rename_variables,[],[3520])). % 178.17/178.00 cnf(12487,plain, % 178.17/178.00 (P38(x124871,f152(x124871,x124872))), % 178.17/178.00 inference(rename_variables,[],[3136])). % 178.17/178.00 cnf(12491,plain, % 178.17/178.00 (E(f329(f260(x124911,x124911),f261(x124911,x124912)),x124912)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(12493,plain, % 178.17/178.00 (E(f329(f260(x124931,x124931),f261(x124931,x124932)),x124932)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(12495,plain, % 178.17/178.00 (E(f329(f260(x124951,x124951),f261(x124951,x124952)),x124952)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(12497,plain, % 178.17/178.00 (E(f329(f260(x124971,x124971),f261(x124971,x124972)),x124972)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(12499,plain, % 178.17/178.00 (P21(x124991,x124991,f5(x124991),x124992)), % 178.17/178.00 inference(rename_variables,[],[3511])). % 178.17/178.00 cnf(12501,plain, % 178.17/178.00 (P21(x125011,x125011,f5(x125011),x125012)), % 178.17/178.00 inference(rename_variables,[],[3511])). % 178.17/178.00 cnf(12516,plain, % 178.17/178.00 (P50(x125161,x125161,f261(x125161,x125162))), % 178.17/178.00 inference(rename_variables,[],[3235])). % 178.17/178.00 cnf(12524,plain, % 178.17/178.00 (E(f193(f883(f882(x125241,x125241),a869)),f261(x125241,f193(f883(x125241,a869))))), % 178.17/178.00 inference(rename_variables,[],[3342])). % 178.17/178.00 cnf(12526,plain, % 178.17/178.00 (P40(x125261,x125262,f261(x125261,x125262))), % 178.17/178.00 inference(rename_variables,[],[3234])). % 178.17/178.00 cnf(12528,plain, % 178.17/178.00 (P40(x125281,x125282,f261(x125281,x125282))), % 178.17/178.00 inference(rename_variables,[],[3234])). % 178.17/178.00 cnf(12542,plain, % 178.17/178.00 (P30(x125421,f2(a875),f329(f329(f329(f93(x125421),x125422),f329(a26,x125423)),x125424))), % 178.17/178.00 inference(rename_variables,[],[3644])). % 178.17/178.00 cnf(12556,plain, % 178.17/178.00 (P43(x125561,x125562,x125563,x125564,f193(f883(x125561,a869)),x125564)), % 178.17/178.00 inference(rename_variables,[],[4217])). % 178.17/178.00 cnf(12559,plain, % 178.17/178.00 (P43(x125591,x125592,x125593,x125594,f193(f883(x125591,a869)),x125594)), % 178.17/178.00 inference(rename_variables,[],[4217])). % 178.17/178.00 cnf(12564,plain, % 178.17/178.00 (P11(x125641,f883(x125641,a869),f307(x125641))), % 178.17/178.00 inference(rename_variables,[],[3238])). % 178.17/178.00 cnf(12572,plain, % 178.17/178.00 (P51(x125721,f193(f883(x125721,a869)),x125722)), % 178.17/178.00 inference(rename_variables,[],[3288])). % 178.17/178.00 cnf(12576,plain, % 178.17/178.00 (E(f329(f260(x125761,x125761),f261(x125761,x125762)),x125762)), % 178.17/178.00 inference(rename_variables,[],[3224])). % 178.17/178.00 cnf(12584,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),f2(a875)),f329(a118,x125841)))), % 178.17/178.00 inference(rename_variables,[],[3351])). % 178.17/178.00 cnf(12585,plain, % 178.17/178.00 (~E(f329(a118,x125851),x125851)), % 178.17/178.00 inference(rename_variables,[],[4442])). % 178.17/178.00 cnf(12591,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x125911),f329(a118,x125911)))), % 178.17/178.00 inference(rename_variables,[],[3339])). % 178.17/178.00 cnf(12596,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x125961),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(12599,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x125991),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(12606,plain, % 178.17/178.00 (~P24(f329(f329(f244(a1),f329(f106(a1),x126061)),f329(f80(a1),f329(f106(a1),x126062))))), % 178.17/178.00 inference(rename_variables,[],[4538])). % 178.17/178.00 cnf(12616,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x126161),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(12619,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x126191),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(12622,plain, % 178.17/178.00 (P24(f329(f62(a875),f302(a875,x126221,x126222)))), % 178.17/178.00 inference(rename_variables,[],[3482])). % 178.17/178.00 cnf(12625,plain, % 178.17/178.00 (P24(f329(f62(a875),f302(a875,x126251,x126252)))), % 178.17/178.00 inference(rename_variables,[],[3482])). % 178.17/178.00 cnf(12628,plain, % 178.17/178.00 (P24(f329(f62(a875),f302(a875,x126281,x126282)))), % 178.17/178.00 inference(rename_variables,[],[3482])). % 178.17/178.00 cnf(12631,plain, % 178.17/178.00 (P24(f329(f62(a875),f302(a875,x126311,x126312)))), % 178.17/178.00 inference(rename_variables,[],[3482])). % 178.17/178.00 cnf(12638,plain, % 178.17/178.00 (P24(f329(f329(f243(a1),f329(f80(a1),f329(f106(a1),x126381))),f329(f106(a1),x126382)))), % 178.17/178.00 inference(rename_variables,[],[3748])). % 178.17/178.00 cnf(12641,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x126411),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(12642,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x126421),x126421))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(12649,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x126491),f329(a118,x126491)))), % 178.17/178.00 inference(rename_variables,[],[3339])). % 178.17/178.00 cnf(12652,plain, % 178.17/178.00 (P24(f329(f329(f331(x126521),f329(x126522,x126523)),f329(f308(x126524,x126521,x126522),f252(f883(x126524,a869)))))), % 178.17/178.00 inference(rename_variables,[],[3871])). % 178.17/178.00 cnf(12653,plain, % 178.17/178.00 (~E(f329(a118,x126531),f2(a875))), % 178.17/178.00 inference(rename_variables,[],[4452])). % 178.17/178.00 cnf(12655,plain, % 178.17/178.00 (~P24(f329(f329(f244(a1),f2(a1)),f329(f109(a1),f2(a1))))), % 178.17/178.00 inference(scs_inference,[],[4546,3511,11025,12054,12154,12249,12287,12295,12308,12363,12499,3520,12118,12481,12483,3521,12188,3234,12526,12528,3235,12516,3201,12436,4477,4478,11641,4217,12556,12559,3238,12564,3076,3136,12487,3571,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,12121,12279,12333,12467,4457,10415,10508,3328,3288,12572,3480,3183,4452,2855,2865,2869,2870,2875,2878,2880,2881,2885,2888,2889,2893,2900,2901,2910,2930,2931,2933,2934,2939,2940,2942,2943,2946,2947,2948,2950,2951,2957,2961,2980,3010,3011,3018,3019,3021,3025,3034,3041,4437,3055,3135,4438,3607,3108,11295,3248,3312,3221,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,12028,12225,12416,12469,12471,12475,12477,12479,12491,12493,12495,12497,3196,11568,12311,12315,12319,3202,10663,11574,3209,3729,3963,3098,4454,3819,11345,3327,3160,3127,3304,3644,12542,3122,3937,3649,4421,12455,3106,3107,3086,3112,3142,3281,12002,12144,12366,12439,3329,10795,12115,3194,3195,3219,10456,3375,4536,10385,3903,4467,10247,10412,11208,12275,12312,4476,12283,3257,11664,4525,10960,11030,11254,11257,3352,3376,3593,3342,12524,3157,3158,10314,10619,3433,3150,3077,3179,11335,4050,12298,12428,3905,10966,11092,11143,12259,12265,12377,12380,12403,4549,10898,10999,11097,11202,11224,11262,11268,12204,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,12157,12201,12282,3632,4333,4334,4465,11326,3573,3610,3783,3829,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,12083,12407,12591,3721,11559,3250,3351,11679,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,12207,12302,12596,12599,12616,12619,4531,11443,11474,11509,11539,3708,3481,3482,12622,12625,12628,3854,3296,3297,3271,4512,3156,4462,3660,4187,3972,3465,4532,4044,11219,3592,3311,11688,11691,12125,12229,4014,3971,11832,12172,3915,10792,11990,12013,12185,3966,10969,12051,12124,12184,12228,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,12073,12328,12400,12413,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,12066,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,12095,12165,12339,12383,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,3270,3347,12039,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,12139,12235,12238,12301,12332,12369,3428,10589,10851,10895,11165,11243,11404,11644,12278,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,12069,12213,12256,12262,12351,12354,12373,12427,12433,12442,3333,10616,10646,10655,11194,11743,12370,3371,3365,3787,3726,10293,11562,11592,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,3290,10649,10800,10871,11593,11748,11937,3748,11694,4094,3487,4522,3759,3795,4501,4503,4504,3241,3242,4502,4505,4506,3766,3582,4193,11423,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,11287,3980,12196,3871,11284,11619,11623,11685,12286,12294,12376,3715,10911,10917,10932,11864,12072,3569,11134,12098,12210,12220,12291,12342,12350,4048,3717,10652,10988,11140,11170,11181,12178,12290,3537,10575,10578,10658,10830,3539,4543,11556,4533,4538,12606,4544,10709,10809,11119,11401,11429,12160,12169,12216,12397,4154,10785,12181,12193,4055,3747,3695,3696,4541,10266,10269,10604,10607,11440,11620,4542,11536,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855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% 178.17/178.00 cnf(12658,plain, % 178.17/178.00 (P24(f329(f329(f243(a1),x126581),x126581))), % 178.17/178.00 inference(rename_variables,[],[3269])). % 178.17/178.00 cnf(12661,plain, % 178.17/178.00 (P24(f329(f62(a875),f302(a875,x126611,x126612)))), % 178.17/178.00 inference(rename_variables,[],[3482])). % 178.17/178.00 cnf(12664,plain, % 178.17/178.00 (P24(f329(f62(a875),f302(a875,x126641,x126642)))), % 178.17/178.00 inference(rename_variables,[],[3482])). % 178.17/178.00 cnf(12667,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),x126671),x126671))), % 178.17/178.00 inference(rename_variables,[],[3268])). % 178.17/178.00 cnf(12680,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x126801),f329(a118,x126801)))), % 178.17/178.00 inference(rename_variables,[],[3339])). % 178.17/178.00 cnf(12685,plain, % 178.17/178.00 (P24(f329(f329(f243(a875),f45(a875,x126851,x126852)),x126851))), % 178.17/178.00 inference(rename_variables,[],[3726])). % 178.17/178.00 cnf(12692,plain, % 178.17/178.00 (P24(f329(f329(f244(a875),x126921),f329(a118,x126921)))), % 178.17/178.00 inference(rename_variables,[],[3339])). % 178.17/178.00 cnf(12693,plain, % 178.17/178.00 (~P24(f329(f329(f244(a875),x126931),f2(a875)))), % 178.17/178.00 inference(rename_variables,[],[4515])). % 178.17/178.00 cnf(12702,plain, % 178.17/178.00 (~P24(f329(f329(f244(a1),f329(f106(a1),x127021)),f2(a1)))), % 178.17/178.00 inference(rename_variables,[],[4531])). % 178.17/178.00 cnf(12703,plain, % 178.17/178.00 (P24(f329(f252(f883(x127031,a869)),x127032))), % 178.17/178.00 inference(rename_variables,[],[3333])). % 178.17/178.00 cnf(12706,plain, % 178.17/178.01 (~P24(f329(f329(f244(a1),f329(f106(a1),x127061)),f2(a1)))), % 178.17/178.01 inference(rename_variables,[],[4531])). % 178.17/178.01 cnf(12707,plain, % 178.17/178.01 (P24(f329(f252(f883(x127071,a869)),x127072))), % 178.17/178.01 inference(rename_variables,[],[3333])). % 178.17/178.01 cnf(12710,plain, % 178.17/178.01 (P24(f329(f252(f883(x127101,a869)),x127102))), % 178.17/178.01 inference(rename_variables,[],[3333])). % 178.17/178.01 cnf(12721,plain, % 178.17/178.01 (~P24(f329(f329(f331(x127211),x127212),f193(f883(x127211,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(12722,plain, % 178.17/178.01 (P24(f329(f62(x127221),f193(f883(x127221,a869))))), % 178.17/178.01 inference(rename_variables,[],[3347])). % 178.17/178.01 cnf(12731,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),f2(a875)),x127311))), % 178.17/178.01 inference(rename_variables,[],[3290])). % 178.17/178.01 cnf(12734,plain, % 178.17/178.01 (P24(f329(f329(f244(a875),x127341),f329(a118,x127341)))), % 178.17/178.01 inference(rename_variables,[],[3339])). % 178.17/178.01 cnf(12735,plain, % 178.17/178.01 (~E(f329(a118,x127351),x127351)), % 178.17/178.01 inference(rename_variables,[],[4442])). % 178.17/178.01 cnf(12738,plain, % 178.17/178.01 (~P24(f329(f329(f331(x127381),x127382),f193(f883(x127381,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(12741,plain, % 178.17/178.01 (~P24(f329(f329(f331(x127411),x127412),f193(f883(x127411,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(12744,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x127441),x127441))), % 178.17/178.01 inference(rename_variables,[],[3268])). % 178.17/178.01 cnf(12751,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x127511),x127511))), % 178.17/178.01 inference(rename_variables,[],[3268])). % 178.17/178.01 cnf(12755,plain, % 178.17/178.01 (P24(f329(f329(f244(a875),x127551),f329(a118,x127551)))), % 178.17/178.01 inference(rename_variables,[],[3339])). % 178.17/178.01 cnf(12758,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x127581),x127581))), % 178.17/178.01 inference(rename_variables,[],[3268])). % 178.17/178.01 cnf(12763,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x127631),x127631))), % 178.17/178.01 inference(rename_variables,[],[3268])). % 178.17/178.01 cnf(12766,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x127661),x127661))), % 178.17/178.01 inference(rename_variables,[],[3268])). % 178.17/178.01 cnf(12769,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x127691),x127691))), % 178.17/178.01 inference(rename_variables,[],[3268])). % 178.17/178.01 cnf(12772,plain, % 178.17/178.01 (E(f329(f329(f22(f883(x127721,a869)),f193(f883(x127721,a869))),x127722),f193(f883(x127721,a869)))), % 178.17/178.01 inference(rename_variables,[],[3542])). % 178.17/178.01 cnf(12773,plain, % 178.17/178.01 (P24(f329(f62(x127731),f193(f883(x127731,a869))))), % 178.17/178.01 inference(rename_variables,[],[3347])). % 178.17/178.01 cnf(12776,plain, % 178.17/178.01 (E(f329(f329(f22(f883(x127761,a869)),f193(f883(x127761,a869))),x127762),f193(f883(x127761,a869)))), % 178.17/178.01 inference(rename_variables,[],[3542])). % 178.17/178.01 cnf(12777,plain, % 178.17/178.01 (P24(f329(f62(x127771),f193(f883(x127771,a869))))), % 178.17/178.01 inference(rename_variables,[],[3347])). % 178.17/178.01 cnf(12780,plain, % 178.17/178.01 (E(f329(f329(f22(f883(x127801,a869)),f193(f883(x127801,a869))),x127802),f193(f883(x127801,a869)))), % 178.17/178.01 inference(rename_variables,[],[3542])). % 178.17/178.01 cnf(12781,plain, % 178.17/178.01 (P24(f329(f62(x127811),f193(f883(x127811,a869))))), % 178.17/178.01 inference(rename_variables,[],[3347])). % 178.17/178.01 cnf(12784,plain, % 178.17/178.01 (E(f329(f329(f22(f883(x127841,a869)),f193(f883(x127841,a869))),x127842),f193(f883(x127841,a869)))), % 178.17/178.01 inference(rename_variables,[],[3542])). % 178.17/178.01 cnf(12785,plain, % 178.17/178.01 (P24(f329(f62(x127851),f193(f883(x127851,a869))))), % 178.17/178.01 inference(rename_variables,[],[3347])). % 178.17/178.01 cnf(12789,plain, % 178.17/178.01 (E(f329(f260(x127891,x127891),f261(x127891,x127892)),x127892)), % 178.17/178.01 inference(rename_variables,[],[3224])). % 178.17/178.01 cnf(12794,plain, % 178.17/178.01 (E(f329(f329(f22(f883(x127941,a869)),f193(f883(x127941,a869))),x127942),f193(f883(x127941,a869)))), % 178.17/178.01 inference(rename_variables,[],[3542])). % 178.17/178.01 cnf(12795,plain, % 178.17/178.01 (P24(f329(f62(x127951),f193(f883(x127951,a869))))), % 178.17/178.01 inference(rename_variables,[],[3347])). % 178.17/178.01 cnf(12799,plain, % 178.17/178.01 (P24(f329(f62(x127991),f193(f883(x127991,a869))))), % 178.17/178.01 inference(rename_variables,[],[3347])). % 178.17/178.01 cnf(12802,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x128021),x128021))), % 178.17/178.01 inference(rename_variables,[],[3268])). % 178.17/178.01 cnf(12808,plain, % 178.17/178.01 (P24(f329(f329(f243(a1),x128081),x128081))), % 178.17/178.01 inference(rename_variables,[],[3269])). % 178.17/178.01 cnf(12811,plain, % 178.17/178.01 (P24(f329(f329(f244(a875),x128111),f329(a118,x128111)))), % 178.17/178.01 inference(rename_variables,[],[3339])). % 178.17/178.01 cnf(12814,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x128141),x128141))), % 178.17/178.01 inference(rename_variables,[],[3268])). % 178.17/178.01 cnf(12817,plain, % 178.17/178.01 (P24(f329(f329(f244(a875),x128171),f329(a118,x128171)))), % 178.17/178.01 inference(rename_variables,[],[3339])). % 178.17/178.01 cnf(12832,plain, % 178.17/178.01 (P24(f329(f329(f243(a1),x128321),x128321))), % 178.17/178.01 inference(rename_variables,[],[3269])). % 178.17/178.01 cnf(12837,plain, % 178.17/178.01 (~P24(f329(f329(f331(x128371),x128372),f193(f883(x128371,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(12848,plain, % 178.17/178.01 (P24(f329(f329(f331(x128481),x128482),f252(f883(x128481,a869))))), % 178.17/178.01 inference(rename_variables,[],[3428])). % 178.17/178.01 cnf(12854,plain, % 178.17/178.01 (P24(f329(f329(f243(f883(x128541,a869)),f329(f171(x128541),f329(f135(x128541,x128542),x128543))),f329(f171(x128541),x128543)))), % 178.17/178.01 inference(rename_variables,[],[3915])). % 178.17/178.01 cnf(12860,plain, % 178.17/178.01 (~P24(f329(f329(f244(a875),x128601),f2(a875)))), % 178.17/178.01 inference(rename_variables,[],[4515])). % 178.17/178.01 cnf(12861,plain, % 178.17/178.01 (P24(f329(f329(f243(a1),x128611),x128611))), % 178.17/178.01 inference(rename_variables,[],[3269])). % 178.17/178.01 cnf(12865,plain, % 178.17/178.01 (~P24(f329(f329(f244(a875),x128651),f2(a875)))), % 178.17/178.01 inference(rename_variables,[],[4515])). % 178.17/178.01 cnf(12866,plain, % 178.17/178.01 (P24(f329(f329(f243(a1),x128661),x128661))), % 178.17/178.01 inference(rename_variables,[],[3269])). % 178.17/178.01 cnf(12875,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x128751),x128751))), % 178.17/178.01 inference(rename_variables,[],[3268])). % 178.17/178.01 cnf(12882,plain, % 178.17/178.01 (E(f329(f329(f16(x128821,x128822),x128823),x128824),x128823)), % 178.17/178.01 inference(rename_variables,[],[3257])). % 178.17/178.01 cnf(12885,plain, % 178.17/178.01 (P24(f329(f329(f243(f883(x128851,a869)),f329(f171(x128851),f169(x128851,x128852,x128853))),f329(f171(x128851),x128853)))), % 178.17/178.01 inference(rename_variables,[],[3966])). % 178.17/178.01 cnf(12887,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),f473(f329(x128871,f2(a875)),x128871,f2(a875))),f2(a875)))), % 178.17/178.01 inference(scs_inference,[],[4546,3511,11025,12054,12154,12249,12287,12295,12308,12363,12499,3520,12118,12481,12483,3521,12188,3234,12526,12528,3235,12516,3201,12436,4477,4478,11641,4217,12556,12559,3238,12564,3076,3136,12487,3571,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,12121,12279,12333,12467,12585,4457,10415,10508,3328,3288,12572,3480,3183,4452,2855,2864,2865,2869,2870,2875,2878,2880,2881,2885,2888,2889,2890,2893,2900,2901,2910,2930,2931,2933,2934,2936,2939,2940,2942,2943,2946,2947,2948,2950,2951,2957,2961,2980,2982,2986,2994,3000,3010,3011,3018,3019,3020,3021,3025,3026,3034,3041,4437,3055,3135,4438,3607,3108,11295,3248,3312,3221,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,12028,12225,12416,12469,12471,12475,12477,12479,12491,12493,12495,12497,12576,3594,3845,3196,11568,12311,12315,12319,3202,10663,11574,3209,3729,3963,3098,4454,3819,11345,3327,3160,3127,3304,3644,12542,3122,3937,3649,4421,12455,3106,3107,3086,3112,3142,3281,12002,12144,12366,12439,3329,10795,12115,3194,3195,3219,10456,3375,4536,10385,3903,4467,10247,10412,11208,12275,12312,4476,12283,3257,11664,11667,4525,10960,11030,11254,11257,3352,3376,3593,3342,12524,3157,3158,10314,10619,3433,3150,3077,3179,11335,4050,12298,12428,3905,10966,11092,11143,12259,12265,12377,12380,12403,4549,10898,10999,11097,11202,11224,11262,11268,12204,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,12157,12201,12282,3632,4333,4334,4465,11326,3573,3610,3783,3542,12772,12776,12780,12784,12794,3829,12151,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,12083,12407,12591,12649,12680,12692,12734,12755,12811,12817,3721,11559,3250,3351,11679,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,12207,12302,12596,12599,12616,12619,12641,12693,12860,12865,4531,11443,11474,11509,11539,12702,12706,3708,3481,3482,12622,12625,12628,12631,12661,3854,3296,3297,3271,4512,3156,4462,3660,4187,3972,3465,4532,4044,11219,3592,3311,11688,11691,12125,12229,12387,4014,3971,11832,12172,3915,10792,11990,12013,12185,12410,3966,10969,12051,12124,12184,12228,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,12073,12328,12400,12413,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,12066,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,12095,12165,12339,12383,12642,12667,12744,12751,12758,12763,12766,12769,12802,12814,12875,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,11932,12658,12808,12832,12861,12866,3270,3347,12039,12722,12773,12777,12781,12785,12795,12799,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,12139,12235,12238,12301,12332,12369,12448,3428,10589,10851,10895,11165,11243,11404,11644,12278,12451,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,12069,12213,12256,12262,12351,12354,12373,12427,12433,12442,12461,12721,12738,12741,3333,10616,10646,10655,11194,11743,12370,12384,12703,12707,12710,3371,3365,3787,3726,10293,11562,11592,12685,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,3290,10649,10800,10871,11593,11748,11937,12166,3748,11694,12638,4094,3487,4522,3759,3795,4501,4503,4504,3241,3242,4502,4505,4506,3766,3582,4193,11423,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,11287,3980,12196,3871,11284,11619,11623,11685,12286,12294,12376,3715,10911,10917,10932,11864,12072,3569,11134,12098,12210,12220,12291,12342,12350,3605,4048,3717,10652,10988,11140,11170,11181,12178,12290,3537,10575,10578,10658,10830,3539,4543,11556,4533,4538,12606,4544,10709,10809,11119,11401,11429,12160,12169,12216,12397,4154,10785,12181,12193,4055,3747,12464,3695,3696,4541,10266,10269,10604,10607,11440,11620,12406,4542,11536,11629,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,606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% 178.17/178.01 cnf(12889,plain, % 178.17/178.01 (~P24(f329(f329(f244(a875),x128891),f2(a875)))), % 178.17/178.01 inference(rename_variables,[],[4515])). % 178.17/178.01 cnf(12890,plain, % 178.17/178.01 (P24(f329(f329(f243(a1),x128901),x128901))), % 178.17/178.01 inference(rename_variables,[],[3269])). % 178.17/178.01 cnf(12894,plain, % 178.17/178.01 (~P24(f329(f329(f244(a875),x128941),f2(a875)))), % 178.17/178.01 inference(rename_variables,[],[4515])). % 178.17/178.01 cnf(12899,plain, % 178.17/178.01 (~P24(f329(f329(f244(f883(a875,a869)),f300(a875,f329(a118,x128991),f329(a118,x128991))),f300(a875,x128992,x128991)))), % 178.17/178.01 inference(scs_inference,[],[4546,3511,11025,12054,12154,12249,12287,12295,12308,12363,12499,3520,12118,12481,12483,3521,12188,3234,12526,12528,3235,12516,3201,12436,4477,4478,11641,4217,12556,12559,3238,12564,3076,3136,12487,3571,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,12121,12279,12333,12467,12585,4457,10415,10508,3328,3288,12572,3480,3183,4452,2855,2864,2865,2869,2870,2875,2878,2880,2881,2885,2888,2889,2890,2893,2900,2901,2910,2930,2931,2933,2934,2936,2939,2940,2942,2943,2946,2947,2948,2950,2951,2957,2961,2980,2982,2986,2994,3000,3010,3011,3018,3019,3020,3021,3025,3026,3034,3041,4437,3055,3135,4438,3607,3108,11295,3248,3312,3221,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,12028,12225,12416,12469,12471,12475,12477,12479,12491,12493,12495,12497,12576,3594,3845,3196,11568,12311,12315,12319,3202,10663,11574,3209,3729,3963,3098,4454,3819,11345,3327,3160,3127,3304,3644,12542,3122,3937,3649,4421,12455,3106,3107,3086,3112,3142,3281,12002,12144,12366,12439,3329,10795,12115,3194,3195,3219,10456,3375,4536,10385,3903,4467,10247,10412,11208,12275,12312,4476,12283,3257,11664,11667,4525,10960,11030,11254,11257,3352,3376,3593,3342,12524,3157,3158,10314,10619,3433,3150,3077,3179,11335,4050,12298,12428,3905,10966,11092,11143,12259,12265,12377,12380,12403,4549,10898,10999,11097,11202,11224,11262,11268,12204,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,12157,12201,12282,3632,4333,4334,4465,11326,3573,3610,3783,3542,12772,12776,12780,12784,12794,3829,12151,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,12083,12407,12591,12649,12680,12692,12734,12755,12811,12817,3721,11559,3250,3351,11679,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,12207,12302,12596,12599,12616,12619,12641,12693,12860,12865,12889,4531,11443,11474,11509,11539,12702,12706,3708,3481,3482,12622,12625,12628,12631,12661,3854,3296,3297,3271,4512,3156,4462,3660,4187,3972,3465,4532,4044,11219,3592,3311,11688,11691,12125,12229,12387,4014,3971,11832,12172,3915,10792,11990,12013,12185,12410,3966,10969,12051,12124,12184,12228,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,12073,12328,12400,12413,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,12066,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,12095,12165,12339,12383,12642,12667,12744,12751,12758,12763,12766,12769,12802,12814,12875,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,11932,12658,12808,12832,12861,12866,12890,3270,3347,12039,12722,12773,12777,12781,12785,12795,12799,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,12139,12235,12238,12301,12332,12369,12448,3428,10589,10851,10895,11165,11243,11404,11644,12278,12451,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,12069,12213,12256,12262,12351,12354,12373,12427,12433,12442,12461,12721,12738,12741,3333,10616,10646,10655,11194,11743,12370,12384,12703,12707,12710,3371,3365,3787,3726,10293,11562,11592,12685,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,3290,10649,10800,10871,11593,11748,11937,12166,3748,11694,12638,4094,3487,4522,3759,3795,4501,4503,4504,3241,3242,4502,4505,4506,3766,3582,4193,11423,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,11287,3980,12196,3871,11284,11619,11623,11685,12286,12294,12376,3715,10911,10917,10932,11864,12072,3569,11134,12098,12210,12220,12291,12342,12350,3605,4048,3717,10652,10988,11140,11170,11181,12178,12290,3537,10575,10578,10658,10830,3539,4543,11556,4533,4538,12606,4544,10709,10809,11119,11401,11429,12160,12169,12216,12397,4154,10785,12181,12193,4055,3747,12464,3695,3696,4541,10266,10269,10604,10607,11440,11620,12406,4542,11536,11629,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7386,7400,7417,7450,7453,7479,7503,7520,7523,7524,7534,7552,7553,7555,7557,7559,7561,7587,7612,7613,7645,7647,7648,7649,7654,7675,7684,7695,7700,7706,7708,7714,7725,7726,7728,7748,7757,7780,7845,7846,7893,7901,7902,7926,7927,7944,7945,8011,8012,8013,8038,8071,8078,8080,8089,8101,8133,8139,8146,8159,8178,8184,8206,8249,8279,8291,8309,8312,8342,8365,8429,8430,8433,8435,8454,8539,8540,8541,8542,8568,8597,8625,8670,8688,8743,8788,8791,8804,8811,8848,8868,8895,8896,8913,8914,9054,9058,9078,9088,9111,9113,9116,9120,9123,9124,9137,9138,9158,9164,9176,9224,9243,9297,9298,9305,9366,9371,9406,9413,9416,9419,9420,9435,9451,9460,9472,9482,9483,9486,9488,9514,9637,9681,9682,9724,9769,9885,9942,10006,10081,10094,10099,3,2602,2605,2607,2610,2614,2616,2619,2621,2622,2630,2631,2634,2635,2637,2640,2643,2644,2645,2646,2652,2653,2654,2656,2657,2659,2660,2661,2678,2679,2680,2691,2692,2693,2703,2704,2705,2708,2709,2712,2713,2714,2720,2721,2722,2726,2727,2728,2732,2733,2734,2735,2737,2742,2745,2746,2747,2750,2751,2753,2760,2761,2762,2768,2801,2802,2809,2823,2828,2829,2846,5206,5268,5364,5450,5451,5452,5527,5623,5654,5687,5703,5705,5711,5774,5775,5776,5777,5783,5816,5949,5995,6018,6055,6095,6240,6247,6281,6282,6302,6305,6307,6314,6315,6316,6317,6318,6319,6320,6321,6402,6470,6471,6556,6590,6591,6632,6633,6771,6786,6858,6859,6866,6888,6911,6919,6921,6968,6993,6994,7010,7011,7012,7048,7092,7093,7190,7251,7252,7253,7254,7268,7301,7357,7358,7367,7374,7376,7388,7420,7421,7422,7423,7567,7568,7575,7577,7578,7579,7788,7790,7791,7805,7843,7922,7964,8022,8043,8044,8059,8118,8220,8289,8290,8292,8327,8389,8390,8462,8483])). % 178.17/178.01 cnf(12900,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x129001),x129001))), % 178.17/178.01 inference(rename_variables,[],[3268])). % 178.17/178.01 cnf(12902,plain, % 178.17/178.01 (~P24(f329(f329(f243(f883(a875,a869)),f300(a875,f329(a118,x129021),f329(a118,x129021))),f300(a875,x129022,x129021)))), % 178.17/178.01 inference(scs_inference,[],[4546,3511,11025,12054,12154,12249,12287,12295,12308,12363,12499,3520,12118,12481,12483,3521,12188,3234,12526,12528,3235,12516,3201,12436,4477,4478,11641,4217,12556,12559,3238,12564,3076,3136,12487,3571,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,12121,12279,12333,12467,12585,4457,10415,10508,3328,3288,12572,3480,3183,4452,2855,2864,2865,2869,2870,2875,2878,2880,2881,2885,2888,2889,2890,2893,2900,2901,2910,2930,2931,2933,2934,2936,2939,2940,2942,2943,2946,2947,2948,2950,2951,2957,2961,2980,2982,2986,2994,3000,3010,3011,3018,3019,3020,3021,3025,3026,3034,3041,4437,3055,3135,4438,3607,3108,11295,3248,3312,3221,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,12028,12225,12416,12469,12471,12475,12477,12479,12491,12493,12495,12497,12576,3594,3845,3196,11568,12311,12315,12319,3202,10663,11574,3209,3729,3963,3098,4454,3819,11345,3327,3160,3127,3304,3644,12542,3122,3937,3649,4421,12455,3106,3107,3086,3112,3142,3281,12002,12144,12366,12439,3329,10795,12115,3194,3195,3219,10456,3375,4536,10385,3903,4467,10247,10412,11208,12275,12312,4476,12283,3257,11664,11667,4525,10960,11030,11254,11257,3352,3376,3593,3342,12524,3157,3158,10314,10619,3433,3150,3077,3179,11335,4050,12298,12428,3905,10966,11092,11143,12259,12265,12377,12380,12403,4549,10898,10999,11097,11202,11224,11262,11268,12204,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,12157,12201,12282,3632,4333,4334,4465,11326,3573,3610,3783,3542,12772,12776,12780,12784,12794,3829,12151,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,12083,12407,12591,12649,12680,12692,12734,12755,12811,12817,3721,11559,3250,3351,11679,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,12207,12302,12596,12599,12616,12619,12641,12693,12860,12865,12889,4531,11443,11474,11509,11539,12702,12706,3708,3481,3482,12622,12625,12628,12631,12661,3854,3296,3297,3271,4512,3156,4462,3660,4187,3972,3465,4532,4044,11219,3592,3311,11688,11691,12125,12229,12387,4014,3971,11832,12172,3915,10792,11990,12013,12185,12410,3966,10969,12051,12124,12184,12228,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,12073,12328,12400,12413,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,12066,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,12095,12165,12339,12383,12642,12667,12744,12751,12758,12763,12766,12769,12802,12814,12875,12900,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,11932,12658,12808,12832,12861,12866,12890,3270,3347,12039,12722,12773,12777,12781,12785,12795,12799,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,12139,12235,12238,12301,12332,12369,12448,3428,10589,10851,10895,11165,11243,11404,11644,12278,12451,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,12069,12213,12256,12262,12351,12354,12373,12427,12433,12442,12461,12721,12738,12741,3333,10616,10646,10655,11194,11743,12370,12384,12703,12707,12710,3371,3365,3787,3726,10293,11562,11592,12685,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,3290,10649,10800,10871,11593,11748,11937,12166,3748,11694,12638,4094,3487,4522,3759,3795,4501,4503,4504,3241,3242,4502,4505,4506,3766,3582,4193,11423,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,11287,3980,12196,3871,11284,11619,11623,11685,12286,12294,12376,3715,10911,10917,10932,11864,12072,3569,11134,12098,12210,12220,12291,12342,12350,3605,4048,3717,10652,10988,11140,11170,11181,12178,12290,3537,10575,10578,10658,10830,3539,4543,11556,4533,4538,12606,4544,10709,10809,11119,11401,11429,12160,12169,12216,12397,4154,10785,12181,12193,4055,3747,12464,3695,3696,4541,10266,10269,10604,10607,11440,11620,12406,4542,11536,11629,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7386,7400,7417,7450,7453,7479,7503,7520,7523,7524,7534,7552,7553,7555,7557,7559,7561,7587,7612,7613,7645,7647,7648,7649,7654,7675,7684,7695,7700,7706,7708,7714,7725,7726,7728,7748,7757,7780,7845,7846,7893,7901,7902,7926,7927,7944,7945,8011,8012,8013,8038,8071,8078,8080,8089,8101,8133,8139,8146,8159,8178,8184,8206,8249,8279,8291,8309,8312,8342,8365,8429,8430,8433,8435,8454,8539,8540,8541,8542,8568,8597,8625,8670,8688,8743,8788,8791,8804,8811,8848,8868,8895,8896,8913,8914,9054,9058,9078,9088,9111,9113,9116,9120,9123,9124,9137,9138,9158,9164,9176,9224,9243,9297,9298,9305,9366,9371,9406,9413,9416,9419,9420,9435,9451,9460,9472,9482,9483,9486,9488,9514,9637,9681,9682,9724,9769,9885,9942,10006,10081,10094,10099,3,2602,2605,2607,2610,2614,2616,2619,2621,2622,2630,2631,2634,2635,2637,2640,2643,2644,2645,2646,2652,2653,2654,2656,2657,2659,2660,2661,2678,2679,2680,2691,2692,2693,2703,2704,2705,2708,2709,2712,2713,2714,2720,2721,2722,2726,2727,2728,2732,2733,2734,2735,2737,2742,2745,2746,2747,2750,2751,2753,2760,2761,2762,2768,2801,2802,2809,2823,2828,2829,2846,5206,5268,5364,5450,5451,5452,5527,5623,5654,5687,5703,5705,5711,5774,5775,5776,5777,5783,5816,5949,5995,6018,6055,6095,6240,6247,6281,6282,6302,6305,6307,6314,6315,6316,6317,6318,6319,6320,6321,6402,6470,6471,6556,6590,6591,6632,6633,6771,6786,6858,6859,6866,6888,6911,6919,6921,6968,6993,6994,7010,7011,7012,7048,7092,7093,7190,7251,7252,7253,7254,7268,7301,7357,7358,7367,7374,7376,7388,7420,7421,7422,7423,7567,7568,7575,7577,7578,7579,7788,7790,7791,7805,7843,7922,7964,8022,8043,8044,8059,8118,8220,8289,8290,8292,8327,8389,8390,8462,8483,8484])). % 178.17/178.01 cnf(12903,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x129031),x129031))), % 178.17/178.01 inference(rename_variables,[],[3268])). % 178.17/178.01 cnf(12906,plain, % 178.17/178.01 (~P24(f329(f329(f243(a875),f329(a118,x129061)),x129061))), % 178.17/178.01 inference(rename_variables,[],[4524])). % 178.17/178.01 cnf(12911,plain, % 178.17/178.01 (E(x129111,f812(f329(f5(x129112),f329(f5(x129112),x129111)),f5(x129112),x129112,x129112))), % 178.17/178.01 inference(scs_inference,[],[4546,3511,11025,12054,12154,12249,12287,12295,12308,12363,12499,12501,3520,12118,12481,12483,3521,12188,3234,12526,12528,3235,12516,3201,12436,4477,4478,11641,4217,12556,12559,3238,12564,3076,3136,12487,3571,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,12121,12279,12333,12467,12585,4457,10415,10508,3328,3288,12572,3480,3183,4452,2855,2864,2865,2869,2870,2875,2878,2880,2881,2885,2888,2889,2890,2893,2900,2901,2910,2930,2931,2933,2934,2936,2939,2940,2942,2943,2946,2947,2948,2950,2951,2957,2961,2980,2982,2986,2994,3000,3010,3011,3018,3019,3020,3021,3025,3026,3034,3041,4437,3055,3135,4438,3607,3108,11295,3248,3312,3221,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,12028,12225,12416,12469,12471,12475,12477,12479,12491,12493,12495,12497,12576,3594,3845,3196,11568,12311,12315,12319,3202,10663,11574,3209,3729,3963,3097,3098,4454,3819,11345,3327,3160,3127,3304,3644,12542,3122,3937,3649,4421,12455,3106,3107,3086,3112,3142,3281,12002,12144,12366,12439,3329,10795,12115,3194,3195,3219,10456,3375,4536,10385,3903,4467,10247,10412,11208,12275,12312,4476,12283,3257,11664,11667,4525,10960,11030,11254,11257,3352,3376,3593,3342,12524,3157,3158,10314,10619,3433,3150,3077,3179,11335,4050,12298,12428,3905,10966,11092,11143,12259,12265,12377,12380,12403,4549,10898,10999,11097,11202,11224,11262,11268,12204,4550,11100,11205,4551,11103,4552,11157,4553,3178,3473,12157,12201,12282,3632,4333,4334,4465,11326,3573,3610,3783,3542,12772,12776,12780,12784,12794,3829,12151,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,12083,12407,12591,12649,12680,12692,12734,12755,12811,12817,3721,11559,3250,3351,11679,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,12207,12302,12596,12599,12616,12619,12641,12693,12860,12865,12889,4531,11443,11474,11509,11539,12702,12706,3708,3481,3482,12622,12625,12628,12631,12661,3854,3296,3297,3271,4512,3156,4462,3660,4187,3972,3465,4532,4044,11219,3592,3311,11688,11691,12125,12229,12387,4014,3971,11832,12172,3915,10792,11990,12013,12185,12410,3966,10969,12051,12124,12184,12228,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,12073,12328,12400,12413,4537,10740,11108,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,12066,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,12095,12165,12339,12383,12642,12667,12744,12751,12758,12763,12766,12769,12802,12814,12875,12900,12903,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,11932,12658,12808,12832,12861,12866,12890,3270,3347,12039,12722,12773,12777,12781,12785,12795,12799,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,12139,12235,12238,12301,12332,12369,12448,3428,10589,10851,10895,11165,11243,11404,11644,12278,12451,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,12069,12213,12256,12262,12351,12354,12373,12427,12433,12442,12461,12721,12738,12741,3333,10616,10646,10655,11194,11743,12370,12384,12703,12707,12710,3371,3365,3787,3726,10293,11562,11592,12685,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,12906,3290,10649,10800,10871,11593,11748,11937,12166,3748,11694,12638,4094,3487,4522,3759,3795,4501,4503,4504,3241,3242,4502,4505,4506,3766,3582,4193,11423,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,11287,3980,12196,3871,11284,11619,11623,11685,12286,12294,12376,12652,3715,10911,10917,10932,11864,12072,3569,11134,12098,12210,12220,12291,12342,12350,3605,4048,3717,10652,10988,11140,11170,11181,12178,12290,3537,10575,10578,10658,10830,3539,4543,11556,4533,4538,12606,4544,10709,10809,11119,11401,11429,12160,12169,12216,12397,4154,10785,12181,12193,4055,3747,12464,3695,3696,4541,10266,10269,10604,10607,11440,11620,12406,4542,11536,11629,3719,10572,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7386,7400,7417,7450,7453,7479,7503,7520,7523,7524,7534,7552,7553,7555,7557,7559,7561,7587,7612,7613,7645,7647,7648,7649,7654,7675,7684,7695,7700,7706,7708,7714,7725,7726,7728,7748,7757,7780,7845,7846,7893,7901,7902,7926,7927,7944,7945,8011,8012,8013,8038,8071,8078,8080,8089,8101,8133,8139,8146,8159,8178,8184,8206,8249,8279,8291,8309,8312,8342,8365,8429,8430,8433,8435,8454,8539,8540,8541,8542,8568,8597,8625,8670,8688,8743,8788,8791,8804,8811,8848,8868,8895,8896,8913,8914,9054,9058,9078,9088,9111,9113,9116,9120,9123,9124,9137,9138,9158,9164,9176,9224,9243,9297,9298,9305,9366,9371,9406,9413,9416,9419,9420,9435,9451,9460,9472,9482,9483,9486,9488,9514,9637,9681,9682,9724,9769,9885,9942,10006,10081,10094,10099,3,2602,2605,2607,2610,2614,2616,2619,2621,2622,2630,2631,2634,2635,2637,2640,2643,2644,2645,2646,2652,2653,2654,2656,2657,2659,2660,2661,2678,2679,2680,2691,2692,2693,2703,2704,2705,2708,2709,2712,2713,2714,2720,2721,2722,2726,2727,2728,2732,2733,2734,2735,2737,2742,2745,2746,2747,2750,2751,2753,2760,2761,2762,2768,2801,2802,2809,2823,2828,2829,2846,5206,5268,5364,5450,5451,5452,5527,5623,5654,5687,5703,5705,5711,5774,5775,5776,5777,5783,5816,5949,5995,6018,6055,6095,6240,6247,6281,6282,6302,6305,6307,6314,6315,6316,6317,6318,6319,6320,6321,6402,6470,6471,6556,6590,6591,6632,6633,6771,6786,6858,6859,6866,6888,6911,6919,6921,6968,6993,6994,7010,7011,7012,7048,7092,7093,7190,7251,7252,7253,7254,7268,7301,7357,7358,7367,7374,7376,7388,7420,7421,7422,7423,7567,7568,7575,7577,7578,7579,7788,7790,7791,7805,7843,7922,7964,8022,8043,8044,8059,8118,8220,8289,8290,8292,8327,8389,8390,8462,8483,8484,8485,8486,8629])). % 178.17/178.01 cnf(12912,plain, % 178.17/178.01 (P24(f329(f329(f331(x129121),f329(x129122,x129123)),f329(f308(x129124,x129121,x129122),f252(f883(x129124,a869)))))), % 178.17/178.01 inference(rename_variables,[],[3871])). % 178.17/178.01 cnf(12913,plain, % 178.17/178.01 (P21(x129131,x129131,f5(x129131),x129132)), % 178.17/178.01 inference(rename_variables,[],[3511])). % 178.17/178.01 cnf(12917,plain, % 178.17/178.01 (P24(f329(f329(f331(x129171),x129172),f252(f883(x129171,a869))))), % 178.17/178.01 inference(rename_variables,[],[3428])). % 178.17/178.01 cnf(12918,plain, % 178.17/178.01 (~P24(f329(f329(f331(x129181),x129182),f193(f883(x129181,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(12922,plain, % 178.17/178.01 (P24(f329(f329(f243(f883(x129221,a869)),x129222),f252(f883(x129221,a869))))), % 178.17/178.01 inference(rename_variables,[],[3651])). % 178.17/178.01 cnf(12923,plain, % 178.17/178.01 (P21(x129231,x129231,f5(x129231),x129232)), % 178.17/178.01 inference(rename_variables,[],[3511])). % 178.17/178.01 cnf(12927,plain, % 178.17/178.01 (P24(f329(f329(f243(f883(x129271,a869)),x129272),f252(f883(x129271,a869))))), % 178.17/178.01 inference(rename_variables,[],[3651])). % 178.17/178.01 cnf(12928,plain, % 178.17/178.01 (P21(x129281,x129281,f5(x129281),x129282)), % 178.17/178.01 inference(rename_variables,[],[3511])). % 178.17/178.01 cnf(12931,plain, % 178.17/178.01 (P24(f329(f329(f243(f883(x129311,a869)),f329(f308(x129312,x129311,x129313),f329(f309(x129312,x129311,x129313),x129314))),x129314))), % 178.17/178.01 inference(rename_variables,[],[4154])). % 178.17/178.01 cnf(12932,plain, % 178.17/178.01 (P21(x129321,x129321,f5(x129321),x129322)), % 178.17/178.01 inference(rename_variables,[],[3511])). % 178.17/178.01 cnf(12935,plain, % 178.17/178.01 (~P24(f329(f329(f244(f883(x129351,a869)),x129352),f193(f883(x129351,a869))))), % 178.17/178.01 inference(rename_variables,[],[4537])). % 178.17/178.01 cnf(12938,plain, % 178.17/178.01 (P21(x129381,x129381,f5(x129381),x129382)), % 178.17/178.01 inference(rename_variables,[],[3511])). % 178.17/178.01 cnf(12941,plain, % 178.17/178.01 (P21(x129411,x129411,f5(x129411),x129412)), % 178.17/178.01 inference(rename_variables,[],[3511])). % 178.17/178.01 cnf(12944,plain, % 178.17/178.01 (P24(f329(f329(f331(x129441),x129442),f329(f329(f307(x129441),x129442),x129443)))), % 178.17/178.01 inference(rename_variables,[],[3582])). % 178.17/178.01 cnf(12952,plain, % 178.17/178.01 (P24(f329(f329(f243(f883(x129521,a869)),f193(f883(x129521,a869))),x129522))), % 178.17/178.01 inference(rename_variables,[],[3717])). % 178.17/178.01 cnf(12956,plain, % 178.17/178.01 (E(f329(f260(x129561,x129561),f261(x129561,x129562)),x129562)), % 178.17/178.01 inference(rename_variables,[],[3224])). % 178.17/178.01 cnf(12960,plain, % 178.17/178.01 (~P24(f329(f329(f331(x129601),x129602),f193(f883(x129601,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(12964,plain, % 178.17/178.01 (P24(f329(f329(f331(x129641),f329(x129642,x129643)),f329(f308(x129644,x129641,x129642),f252(f883(x129644,a869)))))), % 178.17/178.01 inference(rename_variables,[],[3871])). % 178.17/178.01 cnf(12965,plain, % 178.17/178.01 (P21(x129651,x129651,f5(x129651),x129652)), % 178.17/178.01 inference(rename_variables,[],[3511])). % 178.17/178.01 cnf(12968,plain, % 178.17/178.01 (P24(f329(f329(f331(x129681),x129682),f252(f883(x129681,a869))))), % 178.17/178.01 inference(rename_variables,[],[3428])). % 178.17/178.01 cnf(12975,plain, % 178.17/178.01 (~P24(f329(f329(f331(x129751),x129752),f193(f883(x129751,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(12978,plain, % 178.17/178.01 (~P24(f329(f329(f331(x129781),x129782),f193(f883(x129781,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(12982,plain, % 178.17/178.01 (E(f329(f329(f16(x129821,x129822),x129823),x129824),x129823)), % 178.17/178.01 inference(rename_variables,[],[3257])). % 178.17/178.01 cnf(12985,plain, % 178.17/178.01 (P24(f329(f329(f244(a875),x129851),f329(a118,x129851)))), % 178.17/178.01 inference(rename_variables,[],[3339])). % 178.17/178.01 cnf(12986,plain, % 178.17/178.01 (~E(f329(a118,x129861),x129861)), % 178.17/178.01 inference(rename_variables,[],[4442])). % 178.17/178.01 cnf(12989,plain, % 178.17/178.01 (P24(f329(f329(f244(a875),x129891),f329(a118,f329(f329(f81(a875),x129892),x129891))))), % 178.17/178.01 inference(rename_variables,[],[3719])). % 178.17/178.01 cnf(12990,plain, % 178.17/178.01 (P24(f329(f329(f244(a875),x129901),f329(a118,x129901)))), % 178.17/178.01 inference(rename_variables,[],[3339])). % 178.17/178.01 cnf(12992,plain, % 178.17/178.01 (~E(f329(f329(f82(a875),f329(a118,f2(a875))),a884),f329(f329(f82(a875),f329(a118,f2(a875))),f329(f308(a872,f874(a871),f329(f329(f8(a870,f874(a871),a872),a94),a26)),f183(a872,a870,a28))))), % 178.17/178.01 inference(scs_inference,[],[4546,3511,11025,12054,12154,12249,12287,12295,12308,12363,12499,12501,12913,12923,12928,12932,12938,12941,3520,12118,12481,12483,3521,12188,3234,12526,12528,3235,12516,3201,12436,4477,4478,11641,4217,12556,12559,3238,12564,3076,3136,12487,3571,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,12121,12279,12333,12467,12585,12735,12986,4457,10415,10508,3328,3288,12572,3480,3183,4452,2855,2864,2865,2869,2870,2875,2878,2880,2881,2885,2888,2889,2890,2893,2900,2901,2910,2927,2930,2931,2933,2934,2936,2939,2940,2942,2943,2946,2947,2948,2950,2951,2957,2961,2980,2982,2986,2994,3000,3010,3011,3018,3019,3020,3021,3025,3026,3034,3041,4437,3055,3135,4438,3607,3108,11295,3248,3312,3221,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,12028,12225,12416,12469,12471,12475,12477,12479,12491,12493,12495,12497,12576,12789,3594,3845,3196,11568,12311,12315,12319,3202,10663,11574,3209,3729,3963,3097,3098,4454,3819,11345,3327,3160,3127,3304,3644,12542,3122,3937,3143,3649,4421,12455,3106,3107,3086,3112,3142,3281,12002,12144,12366,12439,3329,10795,12115,3194,3195,3219,10456,3375,4536,10385,3903,4467,10247,10412,11208,12275,12312,12316,4476,12283,3257,11664,11667,12882,4525,10960,11030,11254,11257,3352,3254,3376,3593,3342,12524,3157,3158,10314,10619,4509,3433,3150,3077,3179,11335,4050,12298,12428,3905,10966,11092,11143,12259,12265,12377,12380,12403,4549,10898,10999,11097,11202,11224,11262,11268,12204,4550,11100,11205,4551,11103,11154,4552,11157,4553,3178,3473,12157,12201,12282,3632,4333,4334,4465,11326,3573,3610,3783,3542,12772,12776,12780,12784,12794,3829,12151,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,12083,12407,12591,12649,12680,12692,12734,12755,12811,12817,12985,3721,11559,3250,3351,11679,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,12207,12302,12596,12599,12616,12619,12641,12693,12860,12865,12889,4531,11443,11474,11509,11539,12702,12706,3708,3481,3482,12622,12625,12628,12631,12661,3854,3296,3297,3271,4512,3156,4462,3660,4187,3972,3465,4532,4044,11219,3592,3311,11688,11691,12125,12229,12387,4014,3971,11832,12172,3915,10792,11990,12013,12185,12410,3966,10969,12051,12124,12184,12228,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,12073,12328,12400,12413,12922,12927,4537,10740,11108,12935,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,12066,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,12095,12165,12339,12383,12642,12667,12744,12751,12758,12763,12766,12769,12802,12814,12875,12900,12903,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,11932,12658,12808,12832,12861,12866,12890,3270,3347,12039,12722,12773,12777,12781,12785,12795,12799,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,12139,12235,12238,12301,12332,12369,12448,3428,10589,10851,10895,11165,11243,11404,11644,12278,12451,12848,12917,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,12069,12213,12256,12262,12351,12354,12373,12427,12433,12442,12461,12721,12738,12741,12837,12918,12960,12975,3333,10616,10646,10655,11194,11743,12370,12384,12703,12707,12710,3371,3365,3787,3726,10293,11562,11592,12685,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,12906,3290,10649,10800,10871,11593,11748,11937,12166,3748,11694,12638,4094,3487,4522,3759,3795,4501,4503,4504,3241,3242,4502,4505,4506,3766,3582,11555,4193,11423,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,11287,3980,12196,3871,11284,11619,11623,11685,12286,12294,12376,12652,12912,12964,3715,10911,10917,10932,11864,12072,12347,3569,11134,12098,12210,12220,12291,12342,12350,3605,4048,3717,10652,10988,11140,11170,11181,12178,12290,12336,3537,10575,10578,10658,10830,3539,4543,11556,4533,4538,12606,4544,10709,10809,11119,11401,11429,12160,12169,12216,12397,4154,10785,12181,12193,12219,4055,3747,12464,3695,3696,4541,10266,10269,10604,10607,11440,11620,12406,4542,11536,11629,3719,10572,10827,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7386,7400,7417,7450,7453,7479,7503,7520,7523,7524,7534,7552,7553,7555,7557,7559,7561,7587,7612,7613,7645,7647,7648,7649,7654,7675,7684,7695,7700,7706,7708,7714,7725,7726,7728,7748,7757,7780,7845,7846,7893,7901,7902,7926,7927,7944,7945,8011,8012,8013,8038,8071,8078,8080,8089,8101,8133,8139,8146,8159,8178,8184,8206,8249,8279,8291,8309,8312,8342,8365,8429,8430,8433,8435,8454,8539,8540,8541,8542,8568,8597,8625,8670,8688,8743,8788,8791,8804,8811,8848,8868,8895,8896,8913,8914,9054,9058,9078,9088,9111,9113,9116,9120,9123,9124,9137,9138,9158,9164,9176,9224,9243,9297,9298,9305,9366,9371,9406,9413,9416,9419,9420,9435,9451,9460,9472,9482,9483,9486,9488,9514,9637,9681,9682,9724,9769,9885,9942,10006,10081,10094,10099,3,2602,2605,2607,2610,2614,2616,2619,2621,2622,2630,2631,2634,2635,2637,2640,2643,2644,2645,2646,2652,2653,2654,2656,2657,2659,2660,2661,2678,2679,2680,2691,2692,2693,2703,2704,2705,2708,2709,2712,2713,2714,2720,2721,2722,2726,2727,2728,2732,2733,2734,2735,2737,2742,2745,2746,2747,2750,2751,2753,2760,2761,2762,2768,2801,2802,2809,2823,2828,2829,2846,5206,5268,5364,5450,5451,5452,5527,5623,5654,5687,5703,5705,5711,5774,5775,5776,5777,5783,5816,5949,5995,6018,6055,6095,6240,6247,6281,6282,6302,6305,6307,6314,6315,6316,6317,6318,6319,6320,6321,6402,6470,6471,6556,6590,6591,6632,6633,6771,6786,6858,6859,6866,6888,6911,6919,6921,6968,6993,6994,7010,7011,7012,7048,7092,7093,7190,7251,7252,7253,7254,7268,7301,7357,7358,7367,7374,7376,7388,7420,7421,7422,7423,7567,7568,7575,7577,7578,7579,7788,7790,7791,7805,7843,7922,7964,8022,8043,8044,8059,8118,8220,8289,8290,8292,8327,8389,8390,8462,8483,8484,8485,8486,8629,8841,8865,8866,8945,8959,9015,9016,9132,9168,9191,9225,9267,9458,9718,9911,9967,9969,6013,6385,6386,6473])). % 178.17/178.01 cnf(12994,plain, % 178.17/178.01 (~E(f329(a118,x129941),x129941)), % 178.17/178.01 inference(rename_variables,[],[4442])). % 178.17/178.01 cnf(12999,plain, % 178.17/178.01 (P24(f329(f329(f243(a1),f2(a1)),f329(f106(a1),x129991)))), % 178.17/178.01 inference(rename_variables,[],[3371])). % 178.17/178.01 cnf(13002,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),f2(a875)),x130021))), % 178.17/178.01 inference(rename_variables,[],[3290])). % 178.17/178.01 cnf(13003,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x130031),x130031))), % 178.17/178.01 inference(rename_variables,[],[3268])). % 178.17/178.01 cnf(13006,plain, % 178.17/178.01 (~E(f329(a118,x130061),f2(a875))), % 178.17/178.01 inference(rename_variables,[],[4452])). % 178.17/178.01 cnf(13011,plain, % 178.17/178.01 (P24(f329(f329(f331(x130111),x130112),f252(f883(x130111,a869))))), % 178.17/178.01 inference(rename_variables,[],[3428])). % 178.17/178.01 cnf(13015,plain, % 178.17/178.01 (~P24(f329(f329(f331(x130151),x130152),f193(f883(x130151,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(13018,plain, % 178.17/178.01 (P24(f329(f62(a875),f302(a875,x130181,x130182)))), % 178.17/178.01 inference(rename_variables,[],[3482])). % 178.17/178.01 cnf(13019,plain, % 178.17/178.01 (E(f329(f329(f241(a875),f329(a118,x130191)),f329(a118,x130192)),f329(a118,f329(f329(f241(a875),x130191),x130192)))), % 178.17/178.01 inference(rename_variables,[],[3445])). % 178.17/178.01 cnf(13022,plain, % 178.17/178.01 (P24(f329(f62(a875),f302(a875,x130221,x130222)))), % 178.17/178.01 inference(rename_variables,[],[3482])). % 178.17/178.01 cnf(13023,plain, % 178.17/178.01 (E(f329(f329(f242(a875),f329(a118,x130231)),f329(a118,x130232)),f329(a118,f329(f329(f242(a875),x130231),x130232)))), % 178.17/178.01 inference(rename_variables,[],[3446])). % 178.17/178.01 cnf(13026,plain, % 178.17/178.01 (P24(f329(f62(a875),f302(a875,x130261,x130262)))), % 178.17/178.01 inference(rename_variables,[],[3482])). % 178.17/178.01 cnf(13030,plain, % 178.17/178.01 (P24(f329(f62(a875),f302(a875,x130301,x130302)))), % 178.17/178.01 inference(rename_variables,[],[3482])). % 178.17/178.01 cnf(13034,plain, % 178.17/178.01 (P24(f329(f329(f243(f883(x130341,a869)),f329(f171(x130341),f329(f135(x130341,x130342),x130343))),f329(f171(x130341),x130343)))), % 178.17/178.01 inference(rename_variables,[],[3915])). % 178.17/178.01 cnf(13035,plain, % 178.17/178.01 (E(f329(f329(f16(x130351,x130352),x130353),x130354),x130353)), % 178.17/178.01 inference(rename_variables,[],[3257])). % 178.17/178.01 cnf(13038,plain, % 178.17/178.01 (P24(f329(f329(f243(f883(x130381,a869)),f329(f171(x130381),f329(f329(f174(x130381),x130382),x130383))),f329(f171(x130381),x130383)))), % 178.17/178.01 inference(rename_variables,[],[3960])). % 178.17/178.01 cnf(13039,plain, % 178.17/178.01 (E(f329(f329(f16(x130391,x130392),x130393),x130394),x130393)), % 178.17/178.01 inference(rename_variables,[],[3257])). % 178.17/178.01 cnf(13043,plain, % 178.17/178.01 (E(f329(f329(f16(x130431,x130432),x130433),x130434),x130433)), % 178.17/178.01 inference(rename_variables,[],[3257])). % 178.17/178.01 cnf(13056,plain, % 178.17/178.01 (P24(f329(f329(f243(a1),f2(a1)),f329(f106(a1),x130561)))), % 178.17/178.01 inference(rename_variables,[],[3371])). % 178.17/178.01 cnf(13059,plain, % 178.17/178.01 (~P24(f329(f329(f331(x130591),x130592),f193(f883(x130591,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(13062,plain, % 178.17/178.01 (~P24(f329(f329(f331(x130621),x130622),f193(f883(x130621,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(13063,plain, % 178.17/178.01 (E(f329(f260(x130631,x130631),f261(x130631,x130632)),x130632)), % 178.17/178.01 inference(rename_variables,[],[3224])). % 178.17/178.01 cnf(13064,plain, % 178.17/178.01 (P21(x130641,x130641,f5(x130641),x130642)), % 178.17/178.01 inference(rename_variables,[],[3511])). % 178.17/178.01 cnf(13068,plain, % 178.17/178.01 (E(f329(f260(x130681,x130681),f261(x130681,x130682)),x130682)), % 178.17/178.01 inference(rename_variables,[],[3224])). % 178.17/178.01 cnf(13074,plain, % 178.17/178.01 (P24(f329(f329(f244(a875),x130741),f329(a118,x130741)))), % 178.17/178.01 inference(rename_variables,[],[3339])). % 178.17/178.01 cnf(13076,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x130761),x130761))), % 178.17/178.01 inference(rename_variables,[],[3268])). % 178.17/178.01 cnf(13077,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),f2(a875)),x130771))), % 178.17/178.01 inference(rename_variables,[],[3290])). % 178.17/178.01 cnf(13080,plain, % 178.17/178.01 (P24(f329(f329(f244(a875),x130801),f329(a118,x130801)))), % 178.17/178.01 inference(rename_variables,[],[3339])). % 178.17/178.01 cnf(13082,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x130821),x130821))), % 178.17/178.01 inference(rename_variables,[],[3268])). % 178.17/178.01 cnf(13083,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),f2(a875)),x130831))), % 178.17/178.01 inference(rename_variables,[],[3290])). % 178.17/178.01 cnf(13087,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),f2(a875)),x130871))), % 178.17/178.01 inference(rename_variables,[],[3290])). % 178.17/178.01 cnf(13088,plain, % 178.17/178.01 (P24(f329(f329(f244(a875),f2(a875)),f329(a118,x130881)))), % 178.17/178.01 inference(rename_variables,[],[3351])). % 178.17/178.01 cnf(13089,plain, % 178.17/178.01 (E(f329(f260(x130891,x130891),f261(x130891,x130892)),x130892)), % 178.17/178.01 inference(rename_variables,[],[3224])). % 178.17/178.01 cnf(13092,plain, % 178.17/178.01 (P24(f329(f48(f329(f260(x130921,x130921),f261(x130921,f329(f329(f81(a875),f329(f329(f82(a875),f329(f263(a875,a875),f329(f329(f264(a875,a875),f2(a875)),x130922))),f329(a118,f329(f329(f81(a875),x130923),f329(f267(a875,a875),f329(f329(f264(a875,a875),f2(a875)),x130922)))))),f329(f267(a875,a875),f329(f329(f264(a875,a875),f2(a875)),x130922))))),f329(a118,f329(f329(f81(a875),x130923),f329(f267(a875,a875),f329(f329(f264(a875,a875),f2(a875)),x130922))))),f329(f329(f264(a875,a875),f2(a875)),x130922)))), % 178.17/178.01 inference(scs_inference,[],[4546,3511,11025,12054,12154,12249,12287,12295,12308,12363,12499,12501,12913,12923,12928,12932,12938,12941,12965,13064,3520,12118,12481,12483,3521,12188,3234,12526,12528,3235,12516,3201,12436,4477,4478,11641,4217,12556,12559,3238,12564,3076,3136,12487,3571,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,12121,12279,12333,12467,12585,12735,12986,4457,10415,10508,3328,3288,12572,3480,3183,4452,12653,13006,2855,2864,2865,2869,2870,2875,2878,2880,2881,2885,2888,2889,2890,2893,2900,2901,2910,2927,2930,2931,2933,2934,2936,2939,2940,2942,2943,2946,2947,2948,2950,2951,2957,2961,2968,2980,2982,2983,2986,2994,3000,3010,3011,3018,3019,3020,3021,3025,3026,3034,3041,4437,3055,3135,4438,3607,3108,11295,3248,3312,3221,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,12028,12225,12416,12469,12471,12475,12477,12479,12491,12493,12495,12497,12576,12789,12956,13063,13068,13089,3594,3845,3196,11568,12311,12315,12319,3202,10663,11574,3209,3729,3963,3097,3098,4454,3819,11345,3327,3160,3127,3304,3644,12542,3122,3937,3143,3649,4421,12455,3106,3107,3086,3112,3142,3281,12002,12144,12366,12439,3329,10795,12115,3194,3195,3219,10456,3375,4536,10385,3903,4467,10247,10412,11208,12275,12312,12316,4476,12283,3257,11664,11667,12882,12982,13035,13039,13043,4525,10960,11030,11254,11257,3352,3254,3376,3593,3368,3342,12524,3157,3158,10314,10619,4509,3433,3150,3077,3262,3179,11335,4050,12298,12428,3905,10966,11092,11143,12259,12265,12377,12380,12403,4549,10898,10999,11097,11202,11224,11262,11268,12204,4550,11100,11205,4551,11103,11154,4552,11157,4553,3178,3473,12157,12201,12282,3632,4333,4334,3456,4465,11326,3573,3610,3783,3542,12772,12776,12780,12784,12794,3829,12151,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,12083,12407,12591,12649,12680,12692,12734,12755,12811,12817,12985,12990,13074,13080,3721,11559,3250,3351,11679,12584,13088,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,12207,12302,12596,12599,12616,12619,12641,12693,12860,12865,12889,4531,11443,11474,11509,11539,12702,12706,3708,3481,3482,12622,12625,12628,12631,12661,12664,13018,13022,13026,3854,3445,13019,3446,13023,3296,3297,3271,4512,3156,4462,3660,4187,3972,3465,4532,4044,11219,3592,3311,11688,11691,12125,12229,12387,4014,3971,11832,12172,3915,10792,11990,12013,12185,12410,12854,13034,3960,13038,3966,10969,12051,12124,12184,12228,12885,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,12073,12328,12400,12413,12922,12927,4537,10740,11108,12935,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,12066,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,12095,12165,12339,12383,12642,12667,12744,12751,12758,12763,12766,12769,12802,12814,12875,12900,12903,13003,13076,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,11932,12658,12808,12832,12861,12866,12890,3270,3347,12039,12722,12773,12777,12781,12785,12795,12799,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,12139,12235,12238,12301,12332,12369,12448,3428,10589,10851,10895,11165,11243,11404,11644,12278,12451,12848,12917,12968,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,12069,12213,12256,12262,12351,12354,12373,12427,12433,12442,12461,12721,12738,12741,12837,12918,12960,12975,12978,13015,13059,13062,3333,10616,10646,10655,11194,11743,12370,12384,12703,12707,12710,3371,12999,3365,3787,3726,10293,11562,11592,12685,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,12906,3290,10649,10800,10871,11593,11748,11937,12166,12731,13002,13077,13083,13087,3748,11694,12638,4094,3487,4522,3759,3795,4501,4503,4504,3241,3242,4502,4505,4506,4270,3766,3582,11555,4193,11423,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,11287,3980,12196,3871,11284,11619,11623,11685,12286,12294,12376,12652,12912,12964,3715,10911,10917,10932,11864,12072,12347,3569,11134,12098,12210,12220,12291,12342,12350,12458,3605,4048,3717,10652,10988,11140,11170,11181,12178,12290,12336,12952,3537,10575,10578,10658,10830,3539,4543,11556,4533,4538,12606,4544,10709,10809,11119,11401,11429,12160,12169,12216,12397,4154,10785,12181,12193,12219,4055,3747,12464,3695,3696,4541,10266,10269,10604,10607,11440,11620,12406,4542,11536,11629,3719,10572,10827,12989,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7386,7400,7417,7450,7453,7479,7503,7520,7523,7524,7534,7552,7553,7555,7557,7559,7561,7587,7612,7613,7645,7647,7648,7649,7654,7675,7684,7695,7700,7706,7708,7714,7725,7726,7728,7748,7757,7780,7845,7846,7893,7901,7902,7926,7927,7944,7945,8011,8012,8013,8038,8071,8078,8080,8089,8101,8133,8139,8146,8159,8178,8184,8206,8249,8279,8291,8309,8312,8342,8365,8429,8430,8433,8435,8454,8539,8540,8541,8542,8568,8597,8625,8670,8688,8743,8788,8791,8804,8811,8848,8868,8895,8896,8913,8914,9054,9058,9078,9088,9111,9113,9116,9120,9123,9124,9137,9138,9158,9164,9176,9224,9243,9297,9298,9305,9366,9371,9406,9413,9416,9419,9420,9435,9451,9460,9472,9482,9483,9486,9488,9514,9637,9681,9682,9724,9769,9885,9942,10006,10081,10094,10099,3,2602,2605,2607,2610,2614,2616,2619,2621,2622,2630,2631,2634,2635,2637,2640,2643,2644,2645,2646,2652,2653,2654,2656,2657,2659,2660,2661,2678,2679,2680,2691,2692,2693,2703,2704,2705,2708,2709,2712,2713,2714,2720,2721,2722,2726,2727,2728,2732,2733,2734,2735,2737,2742,2745,2746,2747,2750,2751,2753,2760,2761,2762,2768,2801,2802,2809,2823,2828,2829,2846,5206,5268,5364,5450,5451,5452,5527,5623,5654,5687,5703,5705,5711,5774,5775,5776,5777,5783,5816,5949,5995,6018,6055,6095,6240,6247,6281,6282,6302,6305,6307,6314,6315,6316,6317,6318,6319,6320,6321,6402,6470,6471,6556,6590,6591,6632,6633,6771,6786,6858,6859,6866,6888,6911,6919,6921,6968,6993,6994,7010,7011,7012,7048,7092,7093,7190,7251,7252,7253,7254,7268,7301,7357,7358,7367,7374,7376,7388,7420,7421,7422,7423,7567,7568,7575,7577,7578,7579,7788,7790,7791,7805,7843,7922,7964,8022,8043,8044,8059,8118,8220,8289,8290,8292,8327,8389,8390,8462,8483,8484,8485,8486,8629,8841,8865,8866,8945,8959,9015,9016,9132,9168,9191,9225,9267,9458,9718,9911,9967,9969,6013,6385,6386,6473,6493,6494,6910,7128,8554,8587,8782,8971,8972,9043,9044,9315,9316,9317,9318,9517,9789,10090,10141,10142,6455,8380,8381,8831,8849])). % 178.17/178.01 cnf(13108,plain, % 178.17/178.01 (E(f329(f329(f81(a875),f2(a875)),f860(f329(a118,f2(a875)),f2(a875))),f2(a875))), % 178.17/178.01 inference(scs_inference,[],[4546,3511,11025,12054,12154,12249,12287,12295,12308,12363,12499,12501,12913,12923,12928,12932,12938,12941,12965,13064,3520,12118,12481,12483,3521,12188,3234,12526,12528,3235,12516,3201,12436,4477,4478,11641,4217,12556,12559,3238,12564,3076,3136,12487,3571,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,12121,12279,12333,12467,12585,12735,12986,4457,10415,10508,3328,3288,12572,3480,3183,4452,12653,13006,2855,2864,2865,2869,2870,2875,2878,2880,2881,2885,2888,2889,2890,2893,2894,2900,2901,2910,2927,2930,2931,2933,2934,2936,2939,2940,2942,2943,2946,2947,2948,2950,2951,2955,2957,2961,2968,2980,2982,2983,2986,2994,3000,3010,3011,3018,3019,3020,3021,3025,3026,3034,3041,4437,3055,3135,4438,3607,3108,11295,3248,3312,3221,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,12028,12225,12416,12469,12471,12475,12477,12479,12491,12493,12495,12497,12576,12789,12956,13063,13068,13089,3594,3845,3196,11568,12311,12315,12319,3202,10663,11574,3209,3729,3963,3097,3098,4454,3819,11345,3327,3160,3127,3304,3644,12542,3122,3937,3143,3649,4421,12455,3106,3107,3086,3112,3142,3281,12002,12144,12366,12439,3329,10795,12115,3194,3195,3219,10456,3375,4536,10385,3903,4467,10247,10412,11208,12275,12312,12316,4476,12283,3257,11664,11667,12882,12982,13035,13039,13043,4525,10960,11030,11254,11257,3352,3254,3376,3593,3368,3342,12524,3157,3158,10314,10619,4509,3433,3150,3077,3262,3179,11335,4050,12298,12428,3905,10966,11092,11143,12259,12265,12377,12380,12403,4549,10898,10999,11097,11202,11224,11262,11268,12204,4550,11100,11205,4551,11103,11154,4552,11157,4553,3178,3473,12157,12201,12282,3632,4333,4334,3456,4465,11326,3573,3610,3783,3542,12772,12776,12780,12784,12794,3829,12151,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,12083,12407,12591,12649,12680,12692,12734,12755,12811,12817,12985,12990,13074,13080,3721,11559,3250,3351,11679,12584,13088,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,12207,12302,12596,12599,12616,12619,12641,12693,12860,12865,12889,12894,4531,11443,11474,11509,11539,12702,12706,3708,3481,3482,12622,12625,12628,12631,12661,12664,13018,13022,13026,3854,3445,13019,3446,13023,3296,3297,3271,4512,3156,4462,3660,4187,3972,3465,4532,4044,11219,3592,3311,11688,11691,12125,12229,12387,4014,3971,11832,12172,3915,10792,11990,12013,12185,12410,12854,13034,3960,13038,3966,10969,12051,12124,12184,12228,12885,3967,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,12073,12328,12400,12413,12922,12927,4537,10740,11108,12935,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,12066,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,12095,12165,12339,12383,12642,12667,12744,12751,12758,12763,12766,12769,12802,12814,12875,12900,12903,13003,13076,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,11932,12658,12808,12832,12861,12866,12890,3270,3347,12039,12722,12773,12777,12781,12785,12795,12799,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,12139,12235,12238,12301,12332,12369,12448,3428,10589,10851,10895,11165,11243,11404,11644,12278,12451,12848,12917,12968,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,12069,12213,12256,12262,12351,12354,12373,12427,12433,12442,12461,12721,12738,12741,12837,12918,12960,12975,12978,13015,13059,13062,3333,10616,10646,10655,11194,11743,12370,12384,12703,12707,12710,3371,12999,13056,3365,3787,3726,10293,11562,11592,12685,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,12906,3290,10649,10800,10871,11593,11748,11937,12166,12731,13002,13077,13083,13087,3748,11694,12638,4094,3487,4522,3759,3795,4501,4503,4504,3241,3242,4502,4505,4506,4270,3766,3582,11555,4193,11423,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,11287,3980,12196,3871,11284,11619,11623,11685,12286,12294,12376,12652,12912,12964,3715,10911,10917,10932,11864,12072,12347,3569,11134,12098,12210,12220,12291,12342,12350,12458,3605,4048,3717,10652,10988,11140,11170,11181,12178,12290,12336,12952,3537,10575,10578,10658,10830,3539,4543,11556,4533,4538,12606,4544,10709,10809,11119,11401,11429,12160,12169,12216,12397,4154,10785,12181,12193,12219,4055,3747,12464,3695,3696,4541,10266,10269,10604,10607,11440,11620,12406,4542,11536,11629,3719,10572,10827,12989,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7386,7400,7417,7450,7453,7479,7503,7520,7523,7524,7534,7552,7553,7555,7557,7559,7561,7587,7612,7613,7645,7647,7648,7649,7654,7675,7684,7695,7700,7706,7708,7714,7725,7726,7728,7748,7757,7780,7845,7846,7893,7901,7902,7926,7927,7944,7945,8011,8012,8013,8038,8071,8078,8080,8089,8101,8133,8139,8146,8159,8178,8184,8206,8249,8279,8291,8309,8312,8342,8365,8429,8430,8433,8435,8454,8539,8540,8541,8542,8568,8597,8625,8670,8688,8743,8788,8791,8804,8811,8848,8868,8895,8896,8913,8914,9054,9058,9078,9088,9111,9113,9116,9120,9123,9124,9137,9138,9158,9164,9176,9224,9243,9297,9298,9305,9366,9371,9406,9413,9416,9419,9420,9435,9451,9460,9472,9482,9483,9486,9488,9514,9637,9681,9682,9724,9769,9885,9942,10006,10081,10094,10099,3,2602,2605,2607,2610,2614,2616,2619,2621,2622,2630,2631,2634,2635,2637,2640,2643,2644,2645,2646,2652,2653,2654,2656,2657,2659,2660,2661,2678,2679,2680,2691,2692,2693,2703,2704,2705,2708,2709,2712,2713,2714,2720,2721,2722,2726,2727,2728,2732,2733,2734,2735,2737,2742,2745,2746,2747,2750,2751,2753,2760,2761,2762,2768,2801,2802,2809,2823,2828,2829,2846,5206,5268,5364,5450,5451,5452,5527,5623,5654,5687,5703,5705,5711,5774,5775,5776,5777,5783,5816,5949,5995,6018,6055,6095,6240,6247,6281,6282,6302,6305,6307,6314,6315,6316,6317,6318,6319,6320,6321,6402,6470,6471,6556,6590,6591,6632,6633,6771,6786,6858,6859,6866,6888,6911,6919,6921,6968,6993,6994,7010,7011,7012,7048,7092,7093,7190,7251,7252,7253,7254,7268,7301,7357,7358,7367,7374,7376,7388,7420,7421,7422,7423,7567,7568,7575,7577,7578,7579,7788,7790,7791,7805,7843,7922,7964,8022,8043,8044,8059,8118,8220,8289,8290,8292,8327,8389,8390,8462,8483,8484,8485,8486,8629,8841,8865,8866,8945,8959,9015,9016,9132,9168,9191,9225,9267,9458,9718,9911,9967,9969,6013,6385,6386,6473,6493,6494,6910,7128,8554,8587,8782,8971,8972,9043,9044,9315,9316,9317,9318,9517,9789,10090,10141,10142,6455,8380,8381,8831,8849,9790,10140,4633,4635])). % 178.17/178.01 cnf(13162,plain, % 178.17/178.01 (P24(f329(f329(f244(a1),f2(a1)),f329(f76(a1),f79(a1))))), % 178.17/178.01 inference(scs_inference,[],[4546,3511,11025,12054,12154,12249,12287,12295,12308,12363,12499,12501,12913,12923,12928,12932,12938,12941,12965,13064,3520,12118,12481,12483,3521,12188,3234,12526,12528,3235,12516,3201,12436,4477,4478,11641,4217,12556,12559,3238,12564,3076,3136,12487,3571,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,12121,12279,12333,12467,12585,12735,12986,4457,10415,10508,3328,3288,12572,3480,3183,4452,12653,13006,2855,2864,2865,2869,2870,2875,2878,2880,2881,2885,2888,2889,2890,2893,2894,2900,2901,2910,2927,2930,2931,2933,2934,2936,2939,2940,2942,2943,2946,2947,2948,2950,2951,2955,2957,2961,2968,2980,2982,2983,2986,2994,3000,3010,3011,3018,3019,3020,3021,3025,3026,3034,3041,4437,3055,3135,4438,3607,3108,11295,3248,3312,3221,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,12028,12225,12416,12469,12471,12475,12477,12479,12491,12493,12495,12497,12576,12789,12956,13063,13068,13089,3594,3845,3196,11568,12311,12315,12319,3202,10663,11574,3209,3729,3963,3097,3098,4454,3819,11345,3327,3160,3127,3304,3644,12542,3122,3937,3143,3649,4421,12455,3106,3107,3086,3112,3142,3281,12002,12144,12366,12439,3329,10795,12115,3194,3195,3219,10456,3375,4536,10385,3903,4467,10247,10412,11208,12275,12312,12316,4476,12283,3257,11664,11667,12882,12982,13035,13039,13043,4525,10960,11030,11254,11257,3352,3254,3376,3593,3368,3342,12524,3157,3158,10314,10619,4509,3433,3150,3077,3262,3179,11335,4050,12298,12428,3905,10966,11092,11143,12259,12265,12377,12380,12403,4549,10898,10999,11097,11202,11224,11262,11268,12204,4550,11100,11205,4551,11103,11154,4552,11157,4553,3178,3473,12157,12201,12282,3632,4333,4334,3456,4465,11326,3573,3610,3783,3542,12772,12776,12780,12784,12794,3829,12151,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,12083,12407,12591,12649,12680,12692,12734,12755,12811,12817,12985,12990,13074,13080,3721,11559,3250,3351,11679,12584,13088,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,12207,12302,12596,12599,12616,12619,12641,12693,12860,12865,12889,12894,4531,11443,11474,11509,11539,12702,12706,3708,3481,3482,12622,12625,12628,12631,12661,12664,13018,13022,13026,3854,3445,13019,3446,13023,3296,3297,3271,4512,3156,4462,3660,4187,3972,3465,4532,4044,11219,3592,3311,11688,11691,12125,12229,12387,4014,3971,11832,12172,3915,10792,11990,12013,12185,12410,12854,13034,3960,13038,3966,10969,12051,12124,12184,12228,12885,3967,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,12073,12328,12400,12413,12922,12927,4537,10740,11108,12935,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,12066,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,12095,12165,12339,12383,12642,12667,12744,12751,12758,12763,12766,12769,12802,12814,12875,12900,12903,13003,13076,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,11932,12658,12808,12832,12861,12866,12890,3270,3347,12039,12722,12773,12777,12781,12785,12795,12799,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,12139,12235,12238,12301,12332,12369,12448,3428,10589,10851,10895,11165,11243,11404,11644,12278,12451,12848,12917,12968,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,12069,12213,12256,12262,12351,12354,12373,12427,12433,12442,12461,12721,12738,12741,12837,12918,12960,12975,12978,13015,13059,13062,3333,10616,10646,10655,11194,11743,12370,12384,12703,12707,12710,3371,12999,13056,3365,3787,3726,10293,11562,11592,12685,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,12906,3290,10649,10800,10871,11593,11748,11937,12166,12731,13002,13077,13083,13087,3748,11694,12638,4094,3487,4522,3759,3795,4501,4503,4504,3241,3242,4502,4505,4506,4270,3766,3582,11555,4193,11423,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,11287,3980,12196,3871,11284,11619,11623,11685,12286,12294,12376,12652,12912,12964,3715,10911,10917,10932,11864,12072,12347,3569,11134,12098,12210,12220,12291,12342,12350,12458,3605,4048,3717,10652,10988,11140,11170,11181,12178,12290,12336,12952,3537,10575,10578,10658,10830,3539,4543,11556,4533,4538,12606,4544,10709,10809,11119,11401,11429,12160,12169,12216,12397,4154,10785,12181,12193,12219,4055,3747,12464,3695,3696,4541,10266,10269,10604,10607,11440,11620,12406,4542,11536,11629,3719,10572,10827,12989,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7386,7400,7417,7450,7453,7479,7503,7520,7523,7524,7534,7552,7553,7555,7557,7559,7561,7587,7612,7613,7645,7647,7648,7649,7654,7675,7684,7695,7700,7706,7708,7714,7725,7726,7728,7748,7757,7780,7845,7846,7893,7901,7902,7926,7927,7944,7945,8011,8012,8013,8038,8071,8078,8080,8089,8101,8133,8139,8146,8159,8178,8184,8206,8249,8279,8291,8309,8312,8342,8365,8429,8430,8433,8435,8454,8539,8540,8541,8542,8568,8597,8625,8670,8688,8743,8788,8791,8804,8811,8848,8868,8895,8896,8913,8914,9054,9058,9078,9088,9111,9113,9116,9120,9123,9124,9137,9138,9158,9164,9176,9224,9243,9297,9298,9305,9366,9371,9406,9413,9416,9419,9420,9435,9451,9460,9472,9482,9483,9486,9488,9514,9637,9681,9682,9724,9769,9885,9942,10006,10081,10094,10099,3,2602,2605,2607,2610,2614,2616,2619,2621,2622,2630,2631,2634,2635,2637,2640,2643,2644,2645,2646,2652,2653,2654,2656,2657,2659,2660,2661,2678,2679,2680,2691,2692,2693,2703,2704,2705,2708,2709,2712,2713,2714,2720,2721,2722,2726,2727,2728,2732,2733,2734,2735,2737,2742,2745,2746,2747,2750,2751,2753,2760,2761,2762,2768,2801,2802,2809,2823,2828,2829,2846,5206,5268,5364,5450,5451,5452,5527,5623,5654,5687,5703,5705,5711,5774,5775,5776,5777,5783,5816,5949,5995,6018,6055,6095,6240,6247,6281,6282,6302,6305,6307,6314,6315,6316,6317,6318,6319,6320,6321,6402,6470,6471,6556,6590,6591,6632,6633,6771,6786,6858,6859,6866,6888,6911,6919,6921,6968,6993,6994,7010,7011,7012,7048,7092,7093,7190,7251,7252,7253,7254,7268,7301,7357,7358,7367,7374,7376,7388,7420,7421,7422,7423,7567,7568,7575,7577,7578,7579,7788,7790,7791,7805,7843,7922,7964,8022,8043,8044,8059,8118,8220,8289,8290,8292,8327,8389,8390,8462,8483,8484,8485,8486,8629,8841,8865,8866,8945,8959,9015,9016,9132,9168,9191,9225,9267,9458,9718,9911,9967,9969,6013,6385,6386,6473,6493,6494,6910,7128,8554,8587,8782,8971,8972,9043,9044,9315,9316,9317,9318,9517,9789,10090,10141,10142,6455,8380,8381,8831,8849,9790,10140,4633,4635,4636,4691,4699,4836,4852,4853,4881,4882,4911,4966,5028,5085,5135,5163,5199,5202,5207,5209,5210,5236,5311,5332,5466,5532,5533,5534,5650])). % 178.17/178.01 cnf(13182,plain, % 178.17/178.01 (~P24(f329(f329(f244(a875),f329(a118,f329(f329(f81(a875),x131821),x131822))),f329(a118,x131822)))), % 178.17/178.01 inference(scs_inference,[],[4546,3511,11025,12054,12154,12249,12287,12295,12308,12363,12499,12501,12913,12923,12928,12932,12938,12941,12965,13064,3520,12118,12481,12483,3521,12188,3234,12526,12528,3235,12516,3201,12436,4477,4478,11641,4217,12556,12559,3238,12564,3076,3136,12487,3571,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,12121,12279,12333,12467,12585,12735,12986,4457,10415,10508,3328,3288,12572,3480,3183,4452,12653,13006,2855,2864,2865,2869,2870,2875,2878,2880,2881,2885,2888,2889,2890,2893,2894,2900,2901,2910,2927,2930,2931,2933,2934,2936,2939,2940,2942,2943,2946,2947,2948,2950,2951,2955,2957,2961,2968,2980,2982,2983,2986,2994,3000,3010,3011,3018,3019,3020,3021,3025,3026,3034,3041,4437,3055,3135,4438,3607,3108,11295,3248,3312,3221,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,12028,12225,12416,12469,12471,12475,12477,12479,12491,12493,12495,12497,12576,12789,12956,13063,13068,13089,3594,3845,3196,11568,12311,12315,12319,3202,10663,11574,3209,3729,3963,3097,3098,4454,3819,11345,3327,3160,3127,3304,3644,12542,3122,3937,3143,3649,4421,12455,3106,3107,3086,3112,3142,3281,12002,12144,12366,12439,3329,10795,12115,3194,3195,3219,10456,3375,4536,10385,3903,4467,10247,10412,11208,12275,12312,12316,4476,12283,3257,11664,11667,12882,12982,13035,13039,13043,4525,10960,11030,11254,11257,3352,3254,3376,3593,3368,3342,12524,3157,3158,10314,10619,4509,3433,3150,3077,3262,3179,11335,4050,12298,12428,3905,10966,11092,11143,12259,12265,12377,12380,12403,4549,10898,10999,11097,11202,11224,11262,11268,12204,4550,11100,11205,4551,11103,11154,4552,11157,4553,3178,3473,12157,12201,12282,3632,4333,4334,3456,4465,11326,3573,3610,3783,3542,12772,12776,12780,12784,12794,3829,12151,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,12083,12407,12591,12649,12680,12692,12734,12755,12811,12817,12985,12990,13074,13080,3721,11559,3250,3351,11679,12584,13088,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,12207,12302,12596,12599,12616,12619,12641,12693,12860,12865,12889,12894,4531,11443,11474,11509,11539,12702,12706,3708,3481,3482,12622,12625,12628,12631,12661,12664,13018,13022,13026,3854,3445,13019,3446,13023,3296,3297,3271,4512,3156,4462,3660,4187,3972,3465,4532,4044,11219,3592,3311,11688,11691,12125,12229,12387,4014,3971,11832,12172,3915,10792,11990,12013,12185,12410,12854,13034,3960,13038,3966,10969,12051,12124,12184,12228,12885,3967,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,12073,12328,12400,12413,12922,12927,4537,10740,11108,12935,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,12066,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,12095,12165,12339,12383,12642,12667,12744,12751,12758,12763,12766,12769,12802,12814,12875,12900,12903,13003,13076,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,11932,12658,12808,12832,12861,12866,12890,3270,3347,12039,12722,12773,12777,12781,12785,12795,12799,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,12139,12235,12238,12301,12332,12369,12448,3428,10589,10851,10895,11165,11243,11404,11644,12278,12451,12848,12917,12968,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,12069,12213,12256,12262,12351,12354,12373,12427,12433,12442,12461,12721,12738,12741,12837,12918,12960,12975,12978,13015,13059,13062,3333,10616,10646,10655,11194,11743,12370,12384,12703,12707,12710,3371,12999,13056,3365,3787,3726,10293,11562,11592,12685,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,12906,3290,10649,10800,10871,11593,11748,11937,12166,12731,13002,13077,13083,13087,3748,11694,12638,4094,3487,4522,3759,3795,4501,4503,4504,3241,3242,4502,4505,4506,4270,3766,3582,11555,4193,11423,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,11287,3980,12196,3871,11284,11619,11623,11685,12286,12294,12376,12652,12912,12964,3715,10911,10917,10932,11864,12072,12347,3569,11134,12098,12210,12220,12291,12342,12350,12458,3605,4048,3717,10652,10988,11140,11170,11181,12178,12290,12336,12952,3537,10575,10578,10658,10830,3539,4543,11556,4533,4538,12606,4544,10709,10809,11119,11401,11429,12160,12169,12216,12397,4154,10785,12181,12193,12219,4055,3747,12464,3695,3696,4541,10266,10269,10604,10607,11440,11620,12406,4542,11536,11629,3719,10572,10827,12989,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7386,7400,7417,7450,7453,7479,7503,7520,7523,7524,7534,7552,7553,7555,7557,7559,7561,7587,7612,7613,7645,7647,7648,7649,7654,7675,7684,7695,7700,7706,7708,7714,7725,7726,7728,7748,7757,7780,7845,7846,7893,7901,7902,7926,7927,7944,7945,8011,8012,8013,8038,8071,8078,8080,8089,8101,8133,8139,8146,8159,8178,8184,8206,8249,8279,8291,8309,8312,8342,8365,8429,8430,8433,8435,8454,8539,8540,8541,8542,8568,8597,8625,8670,8688,8743,8788,8791,8804,8811,8848,8868,8895,8896,8913,8914,9054,9058,9078,9088,9111,9113,9116,9120,9123,9124,9137,9138,9158,9164,9176,9224,9243,9297,9298,9305,9366,9371,9406,9413,9416,9419,9420,9435,9451,9460,9472,9482,9483,9486,9488,9514,9637,9681,9682,9724,9769,9885,9942,10006,10081,10094,10099,3,2602,2605,2607,2610,2614,2616,2619,2621,2622,2630,2631,2634,2635,2637,2640,2643,2644,2645,2646,2652,2653,2654,2656,2657,2659,2660,2661,2678,2679,2680,2691,2692,2693,2703,2704,2705,2708,2709,2712,2713,2714,2720,2721,2722,2726,2727,2728,2732,2733,2734,2735,2737,2742,2745,2746,2747,2750,2751,2753,2760,2761,2762,2768,2801,2802,2809,2823,2828,2829,2846,5206,5268,5364,5450,5451,5452,5527,5623,5654,5687,5703,5705,5711,5774,5775,5776,5777,5783,5816,5949,5995,6018,6055,6095,6240,6247,6281,6282,6302,6305,6307,6314,6315,6316,6317,6318,6319,6320,6321,6402,6470,6471,6556,6590,6591,6632,6633,6771,6786,6858,6859,6866,6888,6911,6919,6921,6968,6993,6994,7010,7011,7012,7048,7092,7093,7190,7251,7252,7253,7254,7268,7301,7357,7358,7367,7374,7376,7388,7420,7421,7422,7423,7567,7568,7575,7577,7578,7579,7788,7790,7791,7805,7843,7922,7964,8022,8043,8044,8059,8118,8220,8289,8290,8292,8327,8389,8390,8462,8483,8484,8485,8486,8629,8841,8865,8866,8945,8959,9015,9016,9132,9168,9191,9225,9267,9458,9718,9911,9967,9969,6013,6385,6386,6473,6493,6494,6910,7128,8554,8587,8782,8971,8972,9043,9044,9315,9316,9317,9318,9517,9789,10090,10141,10142,6455,8380,8381,8831,8849,9790,10140,4633,4635,4636,4691,4699,4836,4852,4853,4881,4882,4911,4966,5028,5085,5135,5163,5199,5202,5207,5209,5210,5236,5311,5332,5466,5532,5533,5534,5650,5651,5676,5677,5681,5734,5740,5742,5751,5757,5829])). % 178.17/178.01 cnf(13188,plain, % 178.17/178.01 (~E(f329(f187(x131881,f883(x131882,a869),x131883,f193(f883(x131881,a869))),x131884),f329(f236(f883(x131882,a869)),f329(f329(f43(f45(a1,x131885,x131885),f883(x131882,a869)),x131886),a118)))), % 178.17/178.01 inference(scs_inference,[],[4546,3511,11025,12054,12154,12249,12287,12295,12308,12363,12499,12501,12913,12923,12928,12932,12938,12941,12965,13064,3520,12118,12481,12483,3521,12188,3234,12526,12528,3235,12516,3201,12436,4477,4478,11641,4217,12556,12559,3238,12564,3076,3136,12487,3571,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,12121,12279,12333,12467,12585,12735,12986,4457,10415,10508,3328,3288,12572,3480,3183,4452,12653,13006,2855,2864,2865,2869,2870,2875,2878,2880,2881,2885,2888,2889,2890,2893,2894,2900,2901,2910,2927,2930,2931,2933,2934,2936,2939,2940,2942,2943,2946,2947,2948,2950,2951,2955,2957,2961,2968,2980,2982,2983,2986,2994,3000,3010,3011,3018,3019,3020,3021,3025,3026,3034,3041,4437,3055,3135,4438,3607,3108,11295,3248,3312,3221,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,12028,12225,12416,12469,12471,12475,12477,12479,12491,12493,12495,12497,12576,12789,12956,13063,13068,13089,3594,3845,3196,11568,12311,12315,12319,3202,10663,11574,3209,3729,3963,3097,3098,4454,3819,11345,3327,3160,3127,3304,3644,12542,3122,3937,3143,3649,4421,12455,3106,3107,3086,3112,3142,3281,12002,12144,12366,12439,3329,10795,12115,3194,3195,3219,10456,3375,4536,10385,3903,4467,10247,10412,11208,12275,12312,12316,4476,12283,3257,11664,11667,12882,12982,13035,13039,13043,4525,10960,11030,11254,11257,3352,3254,3376,3593,3368,3342,12524,3157,3158,10314,10619,4509,3433,3150,3077,3262,3179,11335,4050,12298,12428,3905,10966,11092,11143,12259,12265,12377,12380,12403,4549,10898,10999,11097,11202,11224,11262,11268,12204,4550,11100,11205,4551,11103,11154,4552,11157,4553,3178,3473,12157,12201,12282,3632,4333,4334,3456,4465,11326,3573,3610,3783,3542,12772,12776,12780,12784,12794,3829,12151,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,12083,12407,12591,12649,12680,12692,12734,12755,12811,12817,12985,12990,13074,13080,3721,11559,3250,3351,11679,12584,13088,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,12207,12302,12596,12599,12616,12619,12641,12693,12860,12865,12889,12894,4531,11443,11474,11509,11539,12702,12706,3708,3481,3482,12622,12625,12628,12631,12661,12664,13018,13022,13026,3854,3445,13019,3446,13023,3296,3297,3271,4512,3156,4462,3660,4187,3972,3465,4532,4044,11219,3592,3311,11688,11691,12125,12229,12387,4014,3971,11832,12172,3915,10792,11990,12013,12185,12410,12854,13034,3960,13038,3966,10969,12051,12124,12184,12228,12885,3967,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,12073,12328,12400,12413,12922,12927,4537,10740,11108,12935,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,12066,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,12095,12165,12339,12383,12642,12667,12744,12751,12758,12763,12766,12769,12802,12814,12875,12900,12903,13003,13076,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,11932,12658,12808,12832,12861,12866,12890,3270,3347,12039,12722,12773,12777,12781,12785,12795,12799,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,12139,12235,12238,12301,12332,12369,12448,3428,10589,10851,10895,11165,11243,11404,11644,12278,12451,12848,12917,12968,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,12069,12213,12256,12262,12351,12354,12373,12427,12433,12442,12461,12721,12738,12741,12837,12918,12960,12975,12978,13015,13059,13062,3333,10616,10646,10655,11194,11743,12370,12384,12703,12707,12710,3371,12999,13056,3365,3787,3726,10293,11562,11592,12685,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,12906,3290,10649,10800,10871,11593,11748,11937,12166,12731,13002,13077,13083,13087,3748,11694,12638,4094,3487,4522,3759,3795,4501,4503,4504,3241,3242,4502,4505,4506,4270,3766,3582,11555,4193,11423,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,11287,3980,12196,3871,11284,11619,11623,11685,12286,12294,12376,12652,12912,12964,3715,10911,10917,10932,11864,12072,12347,3569,11134,12098,12210,12220,12291,12342,12350,12458,3605,4048,3717,10652,10988,11140,11170,11181,12178,12290,12336,12952,3537,10575,10578,10658,10830,3539,4543,11556,4533,4538,12606,4544,10709,10809,11119,11401,11429,12160,12169,12216,12397,4154,10785,12181,12193,12219,4055,3747,12464,3695,3696,4541,10266,10269,10604,10607,11440,11620,12406,4542,11536,11629,3719,10572,10827,12989,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7386,7400,7417,7450,7453,7479,7503,7520,7523,7524,7534,7552,7553,7555,7557,7559,7561,7587,7612,7613,7645,7647,7648,7649,7654,7675,7684,7695,7700,7706,7708,7714,7725,7726,7728,7748,7757,7780,7845,7846,7893,7901,7902,7926,7927,7944,7945,8011,8012,8013,8038,8071,8078,8080,8089,8101,8133,8139,8146,8159,8178,8184,8206,8249,8279,8291,8309,8312,8342,8365,8429,8430,8433,8435,8454,8539,8540,8541,8542,8568,8597,8625,8670,8688,8743,8788,8791,8804,8811,8848,8868,8895,8896,8913,8914,9054,9058,9078,9088,9111,9113,9116,9120,9123,9124,9137,9138,9158,9164,9176,9224,9243,9297,9298,9305,9366,9371,9406,9413,9416,9419,9420,9435,9451,9460,9472,9482,9483,9486,9488,9514,9637,9681,9682,9724,9769,9885,9942,10006,10081,10094,10099,3,2602,2605,2607,2610,2614,2616,2619,2621,2622,2630,2631,2634,2635,2637,2640,2643,2644,2645,2646,2652,2653,2654,2656,2657,2659,2660,2661,2678,2679,2680,2691,2692,2693,2703,2704,2705,2708,2709,2712,2713,2714,2720,2721,2722,2726,2727,2728,2732,2733,2734,2735,2737,2742,2745,2746,2747,2750,2751,2753,2760,2761,2762,2768,2801,2802,2809,2823,2828,2829,2846,5206,5268,5364,5450,5451,5452,5527,5623,5654,5687,5703,5705,5711,5774,5775,5776,5777,5783,5816,5949,5995,6018,6055,6095,6240,6247,6281,6282,6302,6305,6307,6314,6315,6316,6317,6318,6319,6320,6321,6402,6470,6471,6556,6590,6591,6632,6633,6771,6786,6858,6859,6866,6888,6911,6919,6921,6968,6993,6994,7010,7011,7012,7048,7092,7093,7190,7251,7252,7253,7254,7268,7301,7357,7358,7367,7374,7376,7388,7420,7421,7422,7423,7567,7568,7575,7577,7578,7579,7788,7790,7791,7805,7843,7922,7964,8022,8043,8044,8059,8118,8220,8289,8290,8292,8327,8389,8390,8462,8483,8484,8485,8486,8629,8841,8865,8866,8945,8959,9015,9016,9132,9168,9191,9225,9267,9458,9718,9911,9967,9969,6013,6385,6386,6473,6493,6494,6910,7128,8554,8587,8782,8971,8972,9043,9044,9315,9316,9317,9318,9517,9789,10090,10141,10142,6455,8380,8381,8831,8849,9790,10140,4633,4635,4636,4691,4699,4836,4852,4853,4881,4882,4911,4966,5028,5085,5135,5163,5199,5202,5207,5209,5210,5236,5311,5332,5466,5532,5533,5534,5650,5651,5676,5677,5681,5734,5740,5742,5751,5757,5829,5907,5971,6036])). % 178.17/178.01 cnf(13192,plain, % 178.17/178.01 (~P24(f329(f62(x131921),f40(f883(x131921,a869),f252(f883(f883(x131921,a869),a869)))))), % 178.17/178.01 inference(scs_inference,[],[4546,3511,11025,12054,12154,12249,12287,12295,12308,12363,12499,12501,12913,12923,12928,12932,12938,12941,12965,13064,3520,12118,12481,12483,3521,12188,3234,12526,12528,3235,12516,3201,12436,4477,4478,11641,4217,12556,12559,3238,12564,3076,3136,12487,3571,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,12121,12279,12333,12467,12585,12735,12986,4457,10415,10508,3328,3288,12572,3480,3183,4452,12653,13006,2855,2864,2865,2869,2870,2875,2878,2880,2881,2885,2888,2889,2890,2893,2894,2900,2901,2910,2927,2930,2931,2933,2934,2936,2939,2940,2942,2943,2946,2947,2948,2950,2951,2955,2957,2961,2968,2980,2982,2983,2986,2994,3000,3010,3011,3018,3019,3020,3021,3025,3026,3034,3041,4437,3055,3135,4438,3607,3108,11295,3248,3312,3221,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,12028,12225,12416,12469,12471,12475,12477,12479,12491,12493,12495,12497,12576,12789,12956,13063,13068,13089,3594,3845,3196,11568,12311,12315,12319,3202,10663,11574,3209,3729,3963,3097,3098,4454,3819,11345,3327,3160,3127,3304,3644,12542,3122,3937,3143,3649,4421,12455,3106,3107,3086,3112,3142,3281,12002,12144,12366,12439,3329,10795,12115,3194,3195,3219,10456,3375,4536,10385,3903,4467,10247,10412,11208,12275,12312,12316,4476,12283,3257,11664,11667,12882,12982,13035,13039,13043,4525,10960,11030,11254,11257,3352,3254,3376,3593,3368,3342,12524,3157,3158,10314,10619,4509,3433,3150,3077,3262,3179,11335,4050,12298,12428,3905,10966,11092,11143,12259,12265,12377,12380,12403,4549,10898,10999,11097,11202,11224,11262,11268,12204,4550,11100,11205,4551,11103,11154,4552,11157,4553,3178,3473,12157,12201,12282,3632,4333,4334,3456,4465,11326,3573,3610,3783,3542,12772,12776,12780,12784,12794,3829,12151,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,12083,12407,12591,12649,12680,12692,12734,12755,12811,12817,12985,12990,13074,13080,3721,11559,3250,3351,11679,12584,13088,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,12207,12302,12596,12599,12616,12619,12641,12693,12860,12865,12889,12894,4531,11443,11474,11509,11539,12702,12706,3708,3481,3482,12622,12625,12628,12631,12661,12664,13018,13022,13026,3854,3445,13019,3446,13023,3296,3297,3271,4512,3156,4462,3660,4187,3972,3465,4532,4044,11219,3592,3311,11688,11691,12125,12229,12387,4014,3971,11832,12172,3915,10792,11990,12013,12185,12410,12854,13034,3960,13038,3966,10969,12051,12124,12184,12228,12885,3967,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,12073,12328,12400,12413,12922,12927,4537,10740,11108,12935,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,12066,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,12095,12165,12339,12383,12642,12667,12744,12751,12758,12763,12766,12769,12802,12814,12875,12900,12903,13003,13076,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,11932,12658,12808,12832,12861,12866,12890,3270,3347,12039,12722,12773,12777,12781,12785,12795,12799,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,12139,12235,12238,12301,12332,12369,12448,3428,10589,10851,10895,11165,11243,11404,11644,12278,12451,12848,12917,12968,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,12069,12213,12256,12262,12351,12354,12373,12427,12433,12442,12461,12721,12738,12741,12837,12918,12960,12975,12978,13015,13059,13062,3333,10616,10646,10655,11194,11743,12370,12384,12703,12707,12710,3371,12999,13056,3365,3787,3726,10293,11562,11592,12685,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,12906,3290,10649,10800,10871,11593,11748,11937,12166,12731,13002,13077,13083,13087,3748,11694,12638,4094,3487,4522,3759,3795,4501,4503,4504,3241,3242,4502,4505,4506,4270,3766,3582,11555,4193,11423,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,11287,3980,12196,3871,11284,11619,11623,11685,12286,12294,12376,12652,12912,12964,3715,10911,10917,10932,11864,12072,12347,3569,11134,12098,12210,12220,12291,12342,12350,12458,3605,4048,3717,10652,10988,11140,11170,11181,12178,12290,12336,12952,3537,10575,10578,10658,10830,3539,4543,11556,4533,4538,12606,4544,10709,10809,11119,11401,11429,12160,12169,12216,12397,4154,10785,12181,12193,12219,4055,3747,12464,3695,3696,4541,10266,10269,10604,10607,11440,11620,12406,4542,11536,11629,3719,10572,10827,12989,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7386,7400,7417,7450,7453,7479,7503,7520,7523,7524,7534,7552,7553,7555,7557,7559,7561,7587,7612,7613,7645,7647,7648,7649,7654,7675,7684,7695,7700,7706,7708,7714,7725,7726,7728,7748,7757,7780,7845,7846,7893,7901,7902,7926,7927,7944,7945,8011,8012,8013,8038,8071,8078,8080,8089,8101,8133,8139,8146,8159,8178,8184,8206,8249,8279,8291,8309,8312,8342,8365,8429,8430,8433,8435,8454,8539,8540,8541,8542,8568,8597,8625,8670,8688,8743,8788,8791,8804,8811,8848,8868,8895,8896,8913,8914,9054,9058,9078,9088,9111,9113,9116,9120,9123,9124,9137,9138,9158,9164,9176,9224,9243,9297,9298,9305,9366,9371,9406,9413,9416,9419,9420,9435,9451,9460,9472,9482,9483,9486,9488,9514,9637,9681,9682,9724,9769,9885,9942,10006,10081,10094,10099,3,2602,2605,2607,2610,2614,2616,2619,2621,2622,2630,2631,2634,2635,2637,2640,2643,2644,2645,2646,2652,2653,2654,2656,2657,2659,2660,2661,2678,2679,2680,2691,2692,2693,2703,2704,2705,2708,2709,2712,2713,2714,2720,2721,2722,2726,2727,2728,2732,2733,2734,2735,2737,2742,2745,2746,2747,2750,2751,2753,2760,2761,2762,2768,2801,2802,2809,2823,2828,2829,2846,5206,5268,5364,5450,5451,5452,5527,5623,5654,5687,5703,5705,5711,5774,5775,5776,5777,5783,5816,5949,5995,6018,6055,6095,6240,6247,6281,6282,6302,6305,6307,6314,6315,6316,6317,6318,6319,6320,6321,6402,6470,6471,6556,6590,6591,6632,6633,6771,6786,6858,6859,6866,6888,6911,6919,6921,6968,6993,6994,7010,7011,7012,7048,7092,7093,7190,7251,7252,7253,7254,7268,7301,7357,7358,7367,7374,7376,7388,7420,7421,7422,7423,7567,7568,7575,7577,7578,7579,7788,7790,7791,7805,7843,7922,7964,8022,8043,8044,8059,8118,8220,8289,8290,8292,8327,8389,8390,8462,8483,8484,8485,8486,8629,8841,8865,8866,8945,8959,9015,9016,9132,9168,9191,9225,9267,9458,9718,9911,9967,9969,6013,6385,6386,6473,6493,6494,6910,7128,8554,8587,8782,8971,8972,9043,9044,9315,9316,9317,9318,9517,9789,10090,10141,10142,6455,8380,8381,8831,8849,9790,10140,4633,4635,4636,4691,4699,4836,4852,4853,4881,4882,4911,4966,5028,5085,5135,5163,5199,5202,5207,5209,5210,5236,5311,5332,5466,5532,5533,5534,5650,5651,5676,5677,5681,5734,5740,5742,5751,5757,5829,5907,5971,6036,6059,6227])). % 178.17/178.01 cnf(13237,plain, % 178.17/178.01 (~E(f329(a118,x132371),x132371)), % 178.17/178.01 inference(rename_variables,[],[4442])). % 178.17/178.01 cnf(13276,plain, % 178.17/178.01 (~P24(f329(f329(f243(a875),f329(a118,f2(a875))),f329(f329(f22(a875),f329(f329(f81(a875),x132761),f2(a875))),f329(f329(f81(a875),x132761),f2(a875)))))), % 178.17/178.01 inference(scs_inference,[],[4546,3511,11025,12054,12154,12249,12287,12295,12308,12363,12499,12501,12913,12923,12928,12932,12938,12941,12965,13064,3520,12118,12481,12483,3521,12188,3234,12526,12528,3235,12516,3201,12436,4477,4478,11641,4217,12556,12559,3238,12564,3076,3136,12487,3571,4442,10189,10199,10210,10221,10322,10325,10328,10431,10544,10846,11010,11013,11211,11298,11305,11319,11369,11372,11479,11526,11542,11843,11868,11880,11912,12010,12114,12121,12279,12333,12467,12585,12735,12986,12994,13237,4457,10415,10508,3328,3288,12572,3480,3183,4452,12653,13006,2855,2864,2865,2869,2870,2875,2878,2880,2881,2885,2888,2889,2890,2893,2894,2900,2901,2910,2927,2930,2931,2933,2934,2936,2939,2940,2942,2943,2946,2947,2948,2950,2951,2955,2957,2961,2968,2980,2982,2983,2986,2994,3000,3010,3011,3018,3019,3020,3021,3025,3026,3034,3041,4437,3055,3135,4438,3607,3108,11295,3248,3312,3221,3224,10192,10256,10259,10349,10352,10643,11310,11313,11424,11466,11471,11571,12028,12225,12416,12469,12471,12475,12477,12479,12491,12493,12495,12497,12576,12789,12956,13063,13068,13089,3594,3845,3196,11568,12311,12315,12319,3202,10663,11574,3209,3729,3963,3097,3098,4454,3819,11345,3327,3160,3162,3636,3127,3304,3644,12542,3122,3937,3143,3649,4421,12455,3106,3107,3086,3112,3142,3281,12002,12144,12366,12439,3329,10795,12115,3194,3195,3219,10456,3375,4536,10385,3903,4467,10247,10412,11208,12275,12312,12316,4476,12283,3257,11664,11667,12882,12982,13035,13039,13043,4525,10960,11030,11254,11257,3352,3254,3376,3593,3368,3342,12524,3157,3158,10314,10619,4509,3433,3150,3077,3262,3179,11335,4050,12298,12428,3905,10966,11092,11143,12259,12265,12377,12380,12403,4549,10898,10999,11097,11202,11224,11262,11268,12204,4550,11100,11205,4551,11103,11154,4552,11157,4553,3178,3473,12157,12201,12282,3632,4333,4334,3456,4465,11326,3573,3610,3783,3542,12772,12776,12780,12784,12794,3829,12151,3459,3710,3339,10333,10451,10522,10583,10586,10622,10716,10950,11839,11902,11978,12019,12080,12083,12407,12591,12649,12680,12692,12734,12755,12811,12817,12985,12990,13074,13080,3721,11559,3250,3351,11679,12584,13088,3536,4515,10224,10227,10253,10724,10737,10856,11246,11338,11728,11736,11954,11957,12045,12207,12302,12596,12599,12616,12619,12641,12693,12860,12865,12889,12894,4531,11443,11474,11509,11539,12702,12706,3708,3481,3482,12622,12625,12628,12631,12661,12664,13018,13022,13026,13030,3483,3854,3445,13019,3446,13023,3296,3297,3271,4512,3156,4462,3660,4187,3972,3465,4532,4044,11219,3592,3311,11688,11691,12125,12229,12387,4014,3971,11832,12172,3915,10792,11990,12013,12185,12410,12854,13034,3960,13038,3966,10969,12051,12124,12184,12228,12885,3967,3633,11842,11985,12059,12105,4003,3651,10972,11035,11116,11176,12009,12073,12328,12400,12413,12922,12927,4537,10740,11108,12935,3267,10342,10438,10569,10629,11416,11635,11682,11716,11812,11867,12066,12232,3268,10698,10743,10746,10779,10803,10840,10878,10914,11883,11886,11889,11892,12086,12089,12092,12095,12165,12339,12383,12642,12667,12744,12751,12758,12763,12766,12769,12802,12814,12875,12900,12903,13003,13076,13082,3269,10371,10426,10634,10719,10843,11522,11719,11731,11818,11829,11850,11855,11895,11917,11932,12658,12808,12832,12861,12866,12890,3270,3347,12039,12722,12773,12777,12781,12785,12795,12799,4511,10290,10380,10493,10517,10761,10806,10816,11488,11589,11610,11613,11616,11632,11774,11777,11780,11783,11879,11898,11901,11911,11966,11969,11972,11975,12046,12136,12139,12235,12238,12301,12332,12369,12448,3428,10589,10851,10895,11165,11243,11404,11644,12278,12451,12848,12917,12968,13011,4527,10770,10782,10887,10905,10908,10963,11049,11057,11073,11111,11128,11137,11173,11214,11234,11237,11240,11271,11278,11281,11661,11697,11960,11963,11997,12040,12069,12213,12256,12262,12351,12354,12373,12427,12433,12442,12461,12721,12738,12741,12837,12918,12960,12975,12978,13015,13059,13062,3333,10616,10646,10655,11194,11743,12370,12384,12703,12707,12710,3371,12999,13056,3365,3787,3726,10293,11562,11592,12685,4524,10244,10610,10613,11052,11070,11525,11580,11624,11645,11749,11786,11789,11792,11795,12906,3290,10649,10800,10871,11593,11748,11937,12166,12731,13002,13077,13083,13087,3748,11694,12638,4094,3487,4522,3759,3795,4501,4503,4504,3241,3242,4502,4505,4506,4270,3766,3582,11555,12944,4193,11423,4539,10215,10218,10474,10525,10528,10533,10937,11398,11648,11752,4547,11131,11251,11287,3980,12196,3871,11284,11619,11623,11685,12286,12294,12376,12652,12912,12964,3715,10911,10917,10932,11864,12072,12347,3569,11134,12098,12210,12220,12291,12342,12350,12458,3605,4048,3717,10652,10988,11140,11170,11181,12178,12290,12336,12952,3537,10575,10578,10658,10830,3539,4543,11556,4533,4538,12606,4544,10709,10809,11119,11401,11429,12160,12169,12216,12397,4154,10785,12181,12193,12219,12931,4055,3747,12464,3695,3696,4541,10266,10269,10604,10607,11440,11620,12406,4542,11536,11629,3719,10572,10827,12989,3987,4558,4566,4592,4641,4643,4673,4690,4697,4698,4737,4767,4773,4858,4883,4884,4919,4944,4945,4967,4968,4981,4985,5007,5014,5031,5034,5035,5036,5041,5042,5063,5088,5089,5099,5104,5110,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5217,5224,5227,5228,5229,5233,5270,5283,5290,5292,5293,5297,5298,5299,5307,5310,5314,5315,5316,5323,5327,5328,5329,5337,5341,5342,5343,5348,5361,5370,5382,5384,5392,5393,5397,5401,5426,5432,5442,5443,5458,5470,5492,5498,5514,5515,5518,5537,5545,5546,5551,5552,5562,5563,5575,5579,5588,5589,5591,5606,5611,5621,5622,5634,5641,5655,5659,5662,5668,5669,5670,5673,5678,5715,5716,5719,5721,5724,5725,5726,5728,5730,5732,5737,5744,5759,5773,5778,5779,5792,5793,5798,5802,5804,5809,5850,5862,5871,5875,5886,5890,5891,5899,5913,5919,5937,5940,5952,5980,5994,6019,6039,6040,6043,6058,6060,6061,6063,6076,6077,6080,6082,6085,6086,6098,6104,6105,6106,6108,6110,6153,6154,6161,6170,6206,6208,6210,6212,6221,6223,6225,6231,6233,6239,6242,6250,6257,6258,6259,6264,6286,6287,6288,6290,6296,6301,6337,6338,6341,6342,6343,6344,6345,6346,6347,6354,6387,6388,6397,6418,6419,6439,6442,6453,6454,6460,6490,6492,6506,6544,6546,6547,6600,6625,6667,6687,6696,6697,6698,6699,6718,6719,6725,6738,6741,6743,6745,6746,6747,6749,6763,6774,6776,6777,6790,6793,6844,6855,6857,6861,6878,6879,6915,6927,6958,6992,7046,7074,7129,7150,7159,7162,7217,7225,7283,7285,7300,7308,7311,7312,7331,7337,7339,7389,7399,7402,7418,7470,7471,7475,7518,7519,7537,7604,7623,7646,7668,7683,7699,7709,7717,7718,7746,7749,7751,7759,7797,7807,7832,7890,7924,7956,8003,8019,8035,8036,8111,8164,8183,8207,8227,8251,8349,8351,8357,8373,8377,8393,8415,8426,8428,8443,8449,8453,8476,8490,8491,8507,8509,8513,8514,8515,8516,8517,8535,8536,8537,8545,8559,8561,8573,8577,8579,8580,8581,8589,8594,8621,8622,8654,8667,8671,8689,8711,8712,8713,8714,8726,8727,8749,8759,8769,8770,8771,8772,8774,8795,8796,8807,8851,8857,8863,8875,8880,8882,8885,8886,8890,8899,8981,9012,9013,9014,9029,9046,9052,9080,9081,9122,9125,9151,9196,9197,9198,9213,9239,9253,9259,9262,9284,9285,9313,9374,9409,9410,9411,9436,9437,9455,9473,9479,9493,9516,9538,9546,9547,9548,9549,9564,9566,9571,9602,9603,9609,9610,9654,9655,9686,9695,9705,9707,9708,9717,9731,9734,9762,9795,9797,9801,9858,9899,9900,9902,9912,9913,9933,9938,9979,10030,10102,10103,10156,10172,2,8,9,4579,4580,4598,4629,4630,4632,4659,4665,4666,4677,4726,4728,4758,4772,4802,4898,4899,4912,4932,4988,4989,4992,4993,4995,4997,4998,5010,5011,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5087,5095,5098,5105,5170,5176,5177,5184,5214,5225,5231,5249,5269,5276,5277,5278,5287,5296,5303,5305,5306,5312,5319,5320,5333,5334,5335,5336,5338,5339,5344,5345,5346,5347,5378,5379,5380,5388,5389,5390,5391,5437,5439,5441,5477,5479,5480,5482,5483,5485,5486,5488,5497,5502,5504,5505,5506,5507,5508,5509,5516,5526,5529,5540,5556,5557,5560,5569,5571,5572,5573,5598,5608,5624,5625,5635,5636,5638,5640,5645,5680,5684,5686,5746,5780,5781,5785,5791,5794,5795,5796,5797,5803,5814,5815,5817,5818,5826,5847,5878,5894,5897,5898,5900,5909,5930,5931,5932,5935,5936,5954,5965,5966,5996,5997,6001,6021,6024,6028,6047,6052,6053,6078,6081,6089,6097,6103,6107,6114,6115,6116,6117,6156,6171,6224,6260,6262,6283,6284,6289,6292,6293,6297,6303,6312,6330,6349,6350,6355,6365,6380,6400,6406,6408,6423,6424,6427,6428,6430,6432,6433,6434,6436,6438,6441,6447,6448,6449,6450,6456,6458,6500,6505,6520,6521,6522,6523,6558,6563,6565,6570,6571,6579,6583,6596,6621,6622,6623,6624,6635,6641,6657,6661,6680,6713,6714,6715,6720,6734,6755,6757,6759,6761,6764,6770,6772,6787,6794,6830,6833,6834,6847,6848,6849,6850,6869,6870,6887,6913,6935,6946,6948,6949,6951,6953,6954,6989,6990,6995,6996,6997,6998,7000,7002,7027,7036,7037,7049,7059,7098,7108,7112,7119,7130,7131,7136,7138,7144,7153,7166,7183,7201,7203,7220,7269,7271,7272,7273,7279,7284,7307,7352,7386,7400,7417,7450,7453,7479,7503,7520,7523,7524,7534,7552,7553,7555,7557,7559,7561,7587,7612,7613,7645,7647,7648,7649,7654,7675,7684,7695,7700,7706,7708,7714,7725,7726,7728,7748,7757,7780,7845,7846,7893,7901,7902,7926,7927,7944,7945,8011,8012,8013,8038,8071,8078,8080,8089,8101,8133,8139,8146,8159,8178,8184,8206,8249,8279,8291,8309,8312,8342,8365,8429,8430,8433,8435,8454,8539,8540,8541,8542,8568,8597,8625,8670,8688,8743,8788,8791,8804,8811,8848,8868,8895,8896,8913,8914,9054,9058,9078,9088,9111,9113,9116,9120,9123,9124,9137,9138,9158,9164,9176,9224,9243,9297,9298,9305,9366,9371,9406,9413,9416,9419,9420,9435,9451,9460,9472,9482,9483,9486,9488,9514,9637,9681,9682,9724,9769,9885,9942,10006,10081,10094,10099,3,2602,2605,2607,2610,2614,2616,2619,2621,2622,2630,2631,2634,2635,2637,2640,2643,2644,2645,2646,2652,2653,2654,2656,2657,2659,2660,2661,2678,2679,2680,2691,2692,2693,2703,2704,2705,2708,2709,2712,2713,2714,2720,2721,2722,2726,2727,2728,2732,2733,2734,2735,2737,2742,2745,2746,2747,2750,2751,2753,2760,2761,2762,2768,2801,2802,2809,2823,2828,2829,2846,5206,5268,5364,5450,5451,5452,5527,5623,5654,5687,5703,5705,5711,5774,5775,5776,5777,5783,5816,5949,5995,6018,6055,6095,6240,6247,6281,6282,6302,6305,6307,6314,6315,6316,6317,6318,6319,6320,6321,6402,6470,6471,6556,6590,6591,6632,6633,6771,6786,6858,6859,6866,6888,6911,6919,6921,6968,6993,6994,7010,7011,7012,7048,7092,7093,7190,7251,7252,7253,7254,7268,7301,7357,7358,7367,7374,7376,7388,7420,7421,7422,7423,7567,7568,7575,7577,7578,7579,7788,7790,7791,7805,7843,7922,7964,8022,8043,8044,8059,8118,8220,8289,8290,8292,8327,8389,8390,8462,8483,8484,8485,8486,8629,8841,8865,8866,8945,8959,9015,9016,9132,9168,9191,9225,9267,9458,9718,9911,9967,9969,6013,6385,6386,6473,6493,6494,6910,7128,8554,8587,8782,8971,8972,9043,9044,9315,9316,9317,9318,9517,9789,10090,10141,10142,6455,8380,8381,8831,8849,9790,10140,4633,4635,4636,4691,4699,4836,4852,4853,4881,4882,4911,4966,5028,5085,5135,5163,5199,5202,5207,5209,5210,5236,5311,5332,5466,5532,5533,5534,5650,5651,5676,5677,5681,5734,5740,5742,5751,5757,5829,5907,5971,6036,6059,6227,6348,6503,6705,6706,6856,6922,6961,7134,7359,7429,7764,7765,7859,7935,7937,7938,8020,8789,9047,9281,9552,4866,4913,5052,5911,5975,5988,6009,6023,6280,6708,7109,7152,7317,7385,7462,7752])). % 178.17/178.01 cnf(13331,plain, % 178.17/178.01 (~P24(f329(f329(f331(x133311),x133312),f193(f883(x133311,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(13336,plain, % 178.17/178.01 (P24(f329(f329(f331(x133361),f329(x133362,x133363)),f329(f308(x133364,x133361,x133362),f252(f883(x133364,a869)))))), % 178.17/178.01 inference(rename_variables,[],[3871])). % 178.17/178.01 cnf(13345,plain, % 178.17/178.01 (P24(f329(f329(f331(x133451),f329(x133452,x133453)),f329(f308(x133454,x133451,x133452),f252(f883(x133454,a869)))))), % 178.17/178.01 inference(rename_variables,[],[3871])). % 178.17/178.01 cnf(13352,plain, % 178.17/178.01 (~P24(f329(f329(f331(a875),x133521),f329(f250(a875),f2(a875))))), % 178.17/178.01 inference(rename_variables,[],[11709])). % 178.17/178.01 cnf(13362,plain, % 178.17/178.01 (~P24(f329(f329(f331(x133621),x133622),f193(f883(x133621,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(13371,plain, % 178.17/178.01 (~P24(f329(f329(f331(f882(x133711,x133711)),x133712),f261(x133711,f193(f883(x133711,a869)))))), % 178.17/178.01 inference(rename_variables,[],[10904])). % 178.17/178.01 cnf(13381,plain, % 178.17/178.01 (E(f329(f329(f127(x133811),x133812),f119(x133811)),x133812)), % 178.17/178.01 inference(rename_variables,[],[3196])). % 178.17/178.01 cnf(13399,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x133991),f329(f329(f82(a875),x133991),x133991)))), % 178.17/178.01 inference(rename_variables,[],[3537])). % 178.17/178.01 cnf(13402,plain, % 178.17/178.01 (~P24(f329(f329(f331(x134021),x134022),f329(f309(x134021,x134023,x134024),f193(f883(x134023,a869)))))), % 178.17/178.01 inference(rename_variables,[],[10907])). % 178.17/178.01 cnf(13405,plain, % 178.17/178.01 (~P24(f329(f329(f331(x134051),x134052),f193(f883(x134051,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(13412,plain, % 178.17/178.01 (~P24(f329(f329(f243(a875),f329(f329(f82(a875),f329(a118,x134121)),f329(a118,x134121))),x134121))), % 178.17/178.01 inference(rename_variables,[],[10657])). % 178.17/178.01 cnf(13418,plain, % 178.17/178.01 (E(f329(f329(f127(x134181),x134182),f119(x134181)),x134182)), % 178.17/178.01 inference(rename_variables,[],[3196])). % 178.17/178.01 cnf(13423,plain, % 178.17/178.01 (P24(f329(f329(f243(f883(x134231,a869)),x134232),x134232))), % 178.17/178.01 inference(rename_variables,[],[3569])). % 178.17/178.01 cnf(13426,plain, % 178.17/178.01 (~P24(f329(f329(f244(a875),f329(f329(f81(a875),x134261),x134262)),x134261))), % 178.17/178.01 inference(rename_variables,[],[4542])). % 178.17/178.01 cnf(13429,plain, % 178.17/178.01 (~E(f329(a118,x134291),f2(a875))), % 178.17/178.01 inference(rename_variables,[],[4452])). % 178.17/178.01 cnf(13434,plain, % 178.17/178.01 (~P24(f329(f329(f244(a875),f329(f329(f81(a875),x134341),x134342)),x134342))), % 178.17/178.01 inference(rename_variables,[],[4541])). % 178.17/178.01 cnf(13451,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x134511),f329(f329(f82(a875),x134511),x134511)))), % 178.17/178.01 inference(rename_variables,[],[3537])). % 178.17/178.01 cnf(13456,plain, % 178.17/178.01 (~P24(f329(f329(f244(a875),f329(f329(f81(a875),x134561),x134562)),x134561))), % 178.17/178.01 inference(rename_variables,[],[4542])). % 178.17/178.01 cnf(13465,plain, % 178.17/178.01 (P24(f329(f329(f243(f883(x134651,a869)),f329(f171(x134651),f169(x134651,x134652,x134653))),f329(f171(x134651),x134653)))), % 178.17/178.01 inference(rename_variables,[],[3966])). % 178.17/178.01 cnf(13468,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),f2(a875)),x134681))), % 178.17/178.01 inference(rename_variables,[],[3290])). % 178.17/178.01 cnf(13477,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),f45(a875,x134771,x134772)),x134771))), % 178.17/178.01 inference(rename_variables,[],[3726])). % 178.17/178.01 cnf(13480,plain, % 178.17/178.01 (~E(f329(f329(f150(x134801),x134802),x134803),x134803)), % 178.17/178.01 inference(rename_variables,[],[4467])). % 178.17/178.01 cnf(13483,plain, % 178.17/178.01 (~E(f329(f329(f150(x134831),x134832),x134833),x134833)), % 178.17/178.01 inference(rename_variables,[],[4467])). % 178.17/178.01 cnf(13488,plain, % 178.17/178.01 (P24(f329(f329(f244(a875),x134881),f329(f329(f82(a875),f329(a118,x134881)),f329(a118,x134881))))), % 178.17/178.01 inference(rename_variables,[],[10574])). % 178.17/178.01 cnf(13497,plain, % 178.17/178.01 (~P24(f329(f329(f331(x134971),x134972),f193(f883(x134971,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(13502,plain, % 178.17/178.01 (E(f329(f329(f127(x135021),x135022),f119(x135021)),x135022)), % 178.17/178.01 inference(rename_variables,[],[3196])). % 178.17/178.01 cnf(13506,plain, % 178.17/178.01 (P24(f329(f329(f243(f883(x135061,a869)),f329(f171(x135061),f169(x135061,x135062,x135063))),f329(f171(x135061),x135063)))), % 178.17/178.01 inference(rename_variables,[],[3966])). % 178.17/178.01 cnf(13513,plain, % 178.17/178.01 (E(f329(f329(f127(x135131),x135132),f119(x135131)),x135132)), % 178.17/178.01 inference(rename_variables,[],[3196])). % 178.17/178.01 cnf(13516,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x135161),f329(f329(f82(a875),x135161),x135161)))), % 178.17/178.01 inference(rename_variables,[],[3537])). % 178.17/178.01 cnf(13523,plain, % 178.17/178.01 (~P24(f329(f329(f331(x135231),x135232),f193(f883(x135231,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(13526,plain, % 178.17/178.01 (~P24(f329(f329(f331(x135261),x135262),f193(f883(x135261,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(13537,plain, % 178.17/178.01 (E(f329(f260(x135371,x135371),f261(x135371,x135372)),x135372)), % 178.17/178.01 inference(rename_variables,[],[3224])). % 178.17/178.01 cnf(13545,plain, % 178.17/178.01 (E(f329(x135451,f676(f329(x135451,x135452),f329(f236(x135453),x135452),x135451,x135454,x135453)),f329(x135451,x135452))), % 178.17/178.01 inference(rename_variables,[],[11083])). % 178.17/178.01 cnf(13548,plain, % 178.17/178.01 (E(f329(x135481,f676(f329(x135481,x135482),f329(f236(x135483),x135482),x135481,x135484,x135483)),f329(x135481,x135482))), % 178.17/178.01 inference(rename_variables,[],[11083])). % 178.17/178.01 cnf(13551,plain, % 178.17/178.01 (~P24(f329(f329(f331(f882(x135511,x135511)),x135512),f261(x135511,f193(f883(x135511,a869)))))), % 178.17/178.01 inference(rename_variables,[],[10904])). % 178.17/178.01 cnf(13565,plain, % 178.17/178.01 (P24(f329(f329(f244(a1),f329(f329(f22(a1),x135651),f79(a1))),x135651))), % 178.17/178.01 inference(rename_variables,[],[10718])). % 178.17/178.01 cnf(13568,plain, % 178.17/178.01 (~P24(f329(f329(f331(a875),x135681),f329(f250(a875),f2(a875))))), % 178.17/178.01 inference(rename_variables,[],[11709])). % 178.17/178.01 cnf(13574,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x135741),f329(f329(f82(a875),x135741),x135741)))), % 178.17/178.01 inference(rename_variables,[],[3537])). % 178.17/178.01 cnf(13583,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x135831),x135831))), % 178.17/178.01 inference(rename_variables,[],[3268])). % 178.17/178.01 cnf(13592,plain, % 178.17/178.01 (~P24(f329(f329(f331(x135921),x135922),f329(f309(x135921,x135923,x135924),f193(f883(x135923,a869)))))), % 178.17/178.01 inference(rename_variables,[],[10907])). % 178.17/178.01 cnf(13595,plain, % 178.17/178.01 (~P24(f329(f329(f331(x135951),x135952),f193(f883(x135951,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(13604,plain, % 178.17/178.01 (~P24(f329(f329(f244(a875),x136041),x136041))), % 178.17/178.01 inference(rename_variables,[],[4511])). % 178.17/178.01 cnf(13607,plain, % 178.17/178.01 (P24(f329(f329(f331(x136071),f329(x136072,x136073)),f329(f308(x136074,x136071,x136072),f252(f883(x136074,a869)))))), % 178.17/178.01 inference(rename_variables,[],[3871])). % 178.17/178.01 cnf(13610,plain, % 178.17/178.01 (~P24(f329(f329(f331(a875),x136101),f329(f250(a875),f2(a875))))), % 178.17/178.01 inference(rename_variables,[],[11709])). % 178.17/178.01 cnf(13619,plain, % 178.17/178.01 (~P24(f329(f329(f193(f883(x136191,f883(x136192,a869))),x136193),x136194))), % 178.17/178.01 inference(rename_variables,[],[4544])). % 178.17/178.01 cnf(13629,plain, % 178.17/178.01 (E(f329(x136291,f676(f329(x136291,x136292),f329(f236(x136293),x136292),x136291,x136294,x136293)),f329(x136291,x136292))), % 178.17/178.01 inference(rename_variables,[],[11083])). % 178.17/178.01 cnf(13632,plain, % 178.17/178.01 (~P24(f329(f329(f331(x136321),x136322),f193(f883(x136321,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(13641,plain, % 178.17/178.01 (~P24(f329(f329(f331(a875),x136411),f329(f250(a875),f2(a875))))), % 178.17/178.01 inference(rename_variables,[],[11709])). % 178.17/178.01 cnf(13648,plain, % 178.17/178.01 (~P24(f329(f329(f331(f882(x136481,x136481)),x136482),f261(x136481,f193(f883(x136481,a869)))))), % 178.17/178.01 inference(rename_variables,[],[10904])). % 178.17/178.01 cnf(13651,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x136511),f329(f329(f81(a875),x136511),x136512)))), % 178.17/178.01 inference(rename_variables,[],[3539])). % 178.17/178.01 cnf(13662,plain, % 178.17/178.01 (~P24(f329(f329(f244(a875),f329(f329(f81(a875),x136621),x136622)),x136621))), % 178.17/178.01 inference(rename_variables,[],[4542])). % 178.17/178.01 cnf(13667,plain, % 178.17/178.01 (E(f329(f260(x136671,x136671),f261(x136671,x136672)),x136672)), % 178.17/178.01 inference(rename_variables,[],[3224])). % 178.17/178.01 cnf(13674,plain, % 178.17/178.01 (~P24(f329(f329(f331(f882(f876(x136741),f876(x136741))),f329(f329(f264(f876(x136741),f876(x136741)),f119(x136741)),x136742)),f156(x136741,x136743)))), % 178.17/178.01 inference(rename_variables,[],[4553])). % 178.17/178.01 cnf(13677,plain, % 178.17/178.01 (~E(f329(f329(f150(x136771),x136772),x136773),x136773)), % 178.17/178.01 inference(rename_variables,[],[4467])). % 178.17/178.01 cnf(13680,plain, % 178.17/178.01 (E(f329(x136801,f676(f329(x136801,x136802),f329(f236(x136803),x136802),x136801,x136804,x136803)),f329(x136801,x136802))), % 178.17/178.01 inference(rename_variables,[],[11083])). % 178.17/178.01 cnf(13688,plain, % 178.17/178.01 (~P24(f329(f329(f243(a875),f329(a118,x136881)),x136881))), % 178.17/178.01 inference(rename_variables,[],[4524])). % 178.17/178.01 cnf(13695,plain, % 178.17/178.01 (E(f329(x136951,f676(f329(x136951,x136952),f329(f236(x136953),x136952),x136951,x136954,x136953)),f329(x136951,x136952))), % 178.17/178.01 inference(rename_variables,[],[11083])). % 178.17/178.01 cnf(13700,plain, % 178.17/178.01 (~E(f329(f329(f150(x137001),x137002),x137003),x137003)), % 178.17/178.01 inference(rename_variables,[],[4467])). % 178.17/178.01 cnf(13709,plain, % 178.17/178.01 (~P24(f329(f329(f331(a875),x137091),f329(f250(a875),f2(a875))))), % 178.17/178.01 inference(rename_variables,[],[11709])). % 178.17/178.01 cnf(13726,plain, % 178.17/178.01 (P24(f329(f329(f243(f883(x137261,a869)),x137262),f329(f329(f307(x137261),x137263),x137262)))), % 178.17/178.01 inference(rename_variables,[],[3715])). % 178.17/178.01 cnf(13732,plain, % 178.17/178.01 (P24(f329(f329(f331(x137321),f329(x137322,x137323)),f329(f308(x137324,x137321,x137322),f252(f883(x137324,a869)))))), % 178.17/178.01 inference(rename_variables,[],[3871])). % 178.17/178.01 cnf(13753,plain, % 178.17/178.01 (~P24(f329(f329(f331(a875),x137531),f329(f250(a875),f2(a875))))), % 178.17/178.01 inference(rename_variables,[],[11709])). % 178.17/178.01 cnf(13763,plain, % 178.17/178.01 (E(f329(f260(x137631,x137631),f261(x137631,x137632)),x137632)), % 178.17/178.01 inference(rename_variables,[],[3224])). % 178.17/178.01 cnf(13779,plain, % 178.17/178.01 (~E(f329(f329(f150(x137791),x137792),x137793),x137793)), % 178.17/178.01 inference(rename_variables,[],[4467])). % 178.17/178.01 cnf(13801,plain, % 178.17/178.01 (~P24(f329(f329(f331(f882(f876(x138011),f876(x138011))),f329(f329(f264(f876(x138011),f876(x138011)),x138012),f119(x138011))),f156(x138011,x138013)))), % 178.17/178.01 inference(rename_variables,[],[4551])). % 178.17/178.01 cnf(13817,plain, % 178.17/178.01 (~E(f329(f329(f150(x138171),x138172),x138173),x138173)), % 178.17/178.01 inference(rename_variables,[],[4467])). % 178.17/178.01 cnf(13820,plain, % 178.17/178.01 (~P24(f329(f329(f331(f882(x138201,x138201)),x138202),f261(x138201,f193(f883(x138201,a869)))))), % 178.17/178.01 inference(rename_variables,[],[10904])). % 178.17/178.01 cnf(13830,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x138301),x138301))), % 178.17/178.01 inference(rename_variables,[],[3268])). % 178.17/178.01 cnf(13844,plain, % 178.17/178.01 (~P24(f329(f329(f331(f882(x138441,x138441)),x138442),f261(x138441,f193(f883(x138441,a869)))))), % 178.17/178.01 inference(rename_variables,[],[10904])). % 178.17/178.01 cnf(13859,plain, % 178.17/178.01 (~E(f329(f329(f150(x138591),x138592),x138593),x138593)), % 178.17/178.01 inference(rename_variables,[],[4467])). % 178.17/178.01 cnf(13873,plain, % 178.17/178.01 (~P24(f329(f329(f243(a875),f329(a118,x138731)),x138731))), % 178.17/178.01 inference(rename_variables,[],[4524])). % 178.17/178.01 cnf(13876,plain, % 178.17/178.01 (P24(f329(f329(f244(a1),f329(f329(f22(a1),x138761),f79(a1))),x138761))), % 178.17/178.01 inference(rename_variables,[],[10718])). % 178.17/178.01 cnf(13892,plain, % 178.17/178.01 (~E(f329(f329(f150(x138921),x138922),x138923),x138923)), % 178.17/178.01 inference(rename_variables,[],[4467])). % 178.17/178.01 cnf(13902,plain, % 178.17/178.01 (~P24(f329(f329(f331(f882(x139021,x139021)),x139022),f261(x139021,f193(f883(x139021,a869)))))), % 178.17/178.01 inference(rename_variables,[],[10904])). % 178.17/178.01 cnf(13913,plain, % 178.17/178.01 (~P35(x139131,x139132,x139133,f329(f329(f153(x139134,x139131),x139135),f329(a118,f119(x139134))),f119(x139132))), % 178.17/178.01 inference(rename_variables,[],[11145])). % 178.17/178.01 cnf(13916,plain, % 178.17/178.01 (~E(f329(f329(f150(x139161),x139162),x139163),x139163)), % 178.17/178.01 inference(rename_variables,[],[4467])). % 178.17/178.01 cnf(13921,plain, % 178.17/178.01 (P24(f329(f329(f243(f883(x139211,a869)),f329(f171(x139211),f169(x139211,x139212,x139213))),f329(f171(x139211),x139213)))), % 178.17/178.01 inference(rename_variables,[],[3966])). % 178.17/178.01 cnf(13924,plain, % 178.17/178.01 (~P24(f329(f329(f331(x139241),x139242),f329(f309(x139241,x139243,x139244),f193(f883(x139243,a869)))))), % 178.17/178.01 inference(rename_variables,[],[10907])). % 178.17/178.01 cnf(13927,plain, % 178.17/178.01 (~P24(f329(f329(f243(a875),f329(a118,x139271)),x139271))), % 178.17/178.01 inference(rename_variables,[],[4524])). % 178.17/178.01 cnf(13974,plain, % 178.17/178.01 (P24(f329(f329(f243(a1),x139741),x139741))), % 178.17/178.01 inference(rename_variables,[],[3269])). % 178.17/178.01 cnf(13982,plain, % 178.17/178.01 (P24(f329(f329(f331(f882(x139821,x139821)),f329(f329(f264(x139821,x139821),x139822),x139822)),f305(x139821,x139823)))), % 178.17/178.01 inference(rename_variables,[],[3905])). % 178.17/178.01 cnf(13990,plain, % 178.17/178.01 (P24(f329(f329(f244(a875),x139901),f329(a118,f329(f329(f81(a875),x139902),x139901))))), % 178.17/178.01 inference(rename_variables,[],[3719])). % 178.17/178.01 cnf(13995,plain, % 178.17/178.01 (~P24(f329(f329(f331(x139951),x139952),f193(f883(x139951,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(14000,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x140001),x140001))), % 178.17/178.01 inference(rename_variables,[],[3268])). % 178.17/178.01 cnf(14007,plain, % 178.17/178.01 (~P24(f329(f329(f331(f882(x140071,x140071)),x140072),f261(x140071,f193(f883(x140071,a869)))))), % 178.17/178.01 inference(rename_variables,[],[10904])). % 178.17/178.01 cnf(14010,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x140101),f329(f329(f81(a875),x140101),x140102)))), % 178.17/178.01 inference(rename_variables,[],[3539])). % 178.17/178.01 cnf(14028,plain, % 178.17/178.01 (~P24(f329(f329(f331(x140281),x140282),f193(f883(x140281,a869))))), % 178.17/178.01 inference(rename_variables,[],[4527])). % 178.17/178.01 cnf(14031,plain, % 178.17/178.01 (~P24(f329(f329(f331(a875),x140311),f329(f250(a875),f2(a875))))), % 178.17/178.01 inference(rename_variables,[],[11709])). % 178.17/178.01 cnf(14034,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x140341),f329(f329(f81(a875),x140341),x140342)))), % 178.17/178.01 inference(rename_variables,[],[3539])). % 178.17/178.01 cnf(14044,plain, % 178.17/178.01 (~P24(f329(f329(f331(f882(x140441,x140441)),x140442),f152(x140441,f119(f883(x140441,a875)))))), % 178.17/178.01 inference(rename_variables,[],[12027])). % 178.17/178.01 cnf(14056,plain, % 178.17/178.01 (E(f329(x140561,f676(f329(x140561,x140562),f329(f236(x140563),x140562),x140561,x140564,x140563)),f329(x140561,x140562))), % 178.17/178.01 inference(rename_variables,[],[11083])). % 178.17/178.01 cnf(14063,plain, % 178.17/178.01 (P24(f329(f329(f243(f883(x140631,a869)),f329(f171(x140631),f169(x140631,x140632,x140633))),f329(f171(x140631),x140633)))), % 178.17/178.01 inference(rename_variables,[],[3966])). % 178.17/178.01 cnf(14069,plain, % 178.17/178.01 (~P24(f329(f329(f331(f882(f876(x140691),f876(x140691))),f329(f329(f264(f876(x140691),f876(x140691)),x140692),f119(x140691))),f146(x140691,x140693)))), % 178.17/178.01 inference(rename_variables,[],[4549])). % 178.17/178.01 cnf(14091,plain, % 178.17/178.01 (P24(f329(f329(f244(a1),f329(f329(f22(a1),x140911),f79(a1))),x140911))), % 178.17/178.01 inference(rename_variables,[],[10718])). % 178.17/178.01 cnf(14096,plain, % 178.17/178.01 (~P24(f329(f329(f331(f882(x140961,x140961)),x140962),f261(x140961,f193(f883(x140961,a869)))))), % 178.17/178.01 inference(rename_variables,[],[10904])). % 178.17/178.01 cnf(14107,plain, % 178.17/178.01 (P24(f329(f329(f244(a875),x141071),f329(a118,f329(f329(f81(a875),x141072),x141071))))), % 178.17/178.01 inference(rename_variables,[],[3719])). % 178.17/178.01 cnf(14132,plain, % 178.17/178.01 (~P24(f329(f329(f193(f883(x141321,f883(x141322,a869))),x141323),x141324))), % 178.17/178.01 inference(rename_variables,[],[4544])). % 178.17/178.01 cnf(14140,plain, % 178.17/178.01 (~P24(f329(f329(f331(f882(f876(x141401),f876(x141401))),f329(f329(f264(f876(x141401),f876(x141401)),x141402),f119(x141401))),f144(x141401,x141403)))), % 178.17/178.01 inference(rename_variables,[],[4550])). % 178.17/178.01 cnf(14171,plain, % 178.17/178.01 (P24(f329(f329(f243(a875),x141711),f329(f329(f82(a875),x141711),x141711)))), % 178.17/178.01 inference(rename_variables,[],[3537])). % 178.17/178.01 cnf(14202,plain, % 178.17/178.01 ($false), % 178.17/178.01 inference(scs_inference,[],[3297,3296,3708,4014,3854,4050,3055,4543,3268,13583,13830,14000,3271,4531,3242,4512,3905,13982,3347,4549,14069,4502,3365,3721,4527,13331,13362,13405,13497,13523,13526,13595,13632,13995,14028,3351,3966,13465,13506,13921,14063,3871,13336,13345,13607,13732,3375,4457,4452,13429,4467,13480,13483,13677,13700,13779,13817,13859,13892,13916,4465,3250,4044,3915,3269,13974,3726,13477,3290,13468,3715,13726,3569,13423,3717,3537,13399,13451,13516,13574,14171,3539,13651,14010,14034,4154,3719,13990,14107,3224,13537,13667,13763,3196,13381,13418,13502,13513,3107,3632,4550,14140,4551,13801,4553,13674,4511,13604,4524,13688,13873,13927,4533,4538,4544,13619,14132,4541,13434,4542,13426,13456,13662,3480,11459,10276,10543,12992,11147,13188,10330,11894,11769,11811,12887,12392,11275,13162,12177,10574,13488,11817,10558,11015,12394,12423,12430,10894,13092,11115,12162,10718,13565,13876,14091,4276,3635,12450,10889,11180,11139,4281,11083,13545,13548,13629,13680,13695,14056,13108,10255,12911,10891,11259,11228,10662,10505,3330,3208,10263,11162,10941,12899,12902,13182,10675,11595,12109,12102,12209,10240,11707,11709,13352,13568,13610,13641,13709,13753,14031,11765,12655,11069,10904,13371,13551,13648,13820,13844,13902,14007,14096,12027,14044,10907,13402,13592,13924,13276,11183,10657,13412,10760,11968,11989,11233,13192,11145,13913,10919,11149,2862,3820,9,8,5952,7283,6719,5470,7749,8857,4737,8515,7418,6108,7807,8770,9899,6387,8207,9912,5662,5994,8535,8851,10030,4858,4691,5041,8517,5466,4911,5829,5563,6060,6105,6857,7746,9012,6741,5310,8759,7759,5329,8774,9253,5089,5552,6242,7129,8726,6547,4698,5210,5314,5744,6036,6725,6774,6208,5311,5937,6077,8796,6221,5283,5940,6354,6453,8581,5293,6058,6082,5292,7956,9603,5670,6264,2,6927,8577,7832,5328,7074,9047,9695,6667,9797,5227,5384,5719,7159,8036,9284,5634,8443,4635,9196,5668,6419,6490,7470,8476,5726,8771,7859,8003,9411,6019,5327,5621,6076,6844,7162,6861,9933,6856,7718,5779,7471,7475,6790,8537,5757,5180,5724,4967,7935,7389,4636,4944,5759,6341,6746,9731,5742,5732,10102,7312,6492,6878,5890,6206,5721,6337,6418,7717,9374,4690,5207,9014,5676,5773,7924,6348,4633,4641,4773,9902,5299,6154,6705,6342,6777,8875,8899,5514,6454,9479,9609,9259,5323,6223,8981,5155,5164,7300,9436,5007,5716,8789,6104,9801,4852,8035,4697,4945,7518,8428,8622,5270,5297,5798,5850,6776,7339,5217,6039,6161,7150,6503,9602,9610,5035,6855,6301,6227,4592,9858,5042,5135,5875,6080,6546,6915,8654,6063,6696,8453,7668,8885,8890,9795,6697,7134,4919,6439,9239,6698,7337,5224,5871,5492,5498,5515,8536,8711,5546,8667,5980,7938,8183,8490,10103,6343,7751,9213,9717,5591,5458,8393,9762,7217,8164,9285,9979,5099,5156,6763,6212,6170,8377,8594,5532,5028,5229,5401,7429,9197,9564,5579,9262,9571,6992,4566,6043,6225,6442,8689,5088,5316,7285,8426,9734,6296,9046,5202,9686,9547,5677,5751,5669,7797,9654,6086,6110,6879,8111,6706,6085,7519,5228,5862,5209,5382,6388,8491,8769,9938,6345,6958,8509,9548,9549,5740,5737,7890,6397,8514,10172,4767,8545,9913,8415,5673,6239,5518,5442,5734,5545,8772,9546,5361,5899,5891,4643,8580,9705,5728,5163,5201,5533,6793,9313,5348,6747,6749,5659,5192,5793,6233,6738,7402,4884,5655,5715,5341,6922,5562,9080,10156,9081,9566,5681,8579,4673]), % 178.17/178.01 ['proof']). % 178.17/178.02 % SZS output end Proof % 178.17/178.02 % Total time :163.680000s %------------------------------------------------------------------------------