TSTP Solution File: SWW386+1 by CSE---1.7
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%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SWW386+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 : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:09:02 EDT 2024
% Result : Theorem 162.26s 162.05s
% Output : CNFRefutation 162.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW386+1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 04:26:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 161.83/161.89 %-------------------------------------------
% 161.83/161.89 % File :CSE---1.7
% 161.83/161.89 % Problem :theBenchmark
% 161.83/161.89 % Transform :cnf
% 161.83/161.89 % Format :tptp:raw
% 161.83/161.89 % Command :java -jar mcs_scs.jar %d %s
% 161.83/161.89
% 161.83/161.89 % Result :Theorem 147.230000s
% 161.83/161.89 % Output :CNFRefutation 147.230000s
% 161.83/161.89 %-------------------------------------------
% 161.83/161.90 %------------------------------------------------------------------------------
% 161.83/161.90 % File : SWW386+1 : TPTP v8.2.0. Released v5.2.0.
% 161.83/161.90 % Domain : Software Verification
% 161.83/161.90 % Problem : Hoare's Logic with Procedures 435661, 5000 axioms selected
% 161.83/161.90 % Version : Especial.
% 161.83/161.90 % English :
% 161.83/161.90
% 161.83/161.90 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 161.83/161.90 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 161.83/161.90 % Source : [Bla11]
% 161.83/161.90 % Names : hoare_435661.5000.p [Bla11]
% 161.83/161.90
% 161.83/161.90 % Status : Theorem
% 161.83/161.90 % Rating : 0.56 v8.2.0, 0.50 v8.1.0, 0.56 v7.5.0, 0.53 v7.4.0, 0.57 v7.3.0, 0.59 v7.2.0, 0.55 v7.1.0, 0.61 v7.0.0, 0.63 v6.4.0, 0.62 v6.2.0, 0.76 v6.1.0, 0.80 v6.0.0, 0.70 v5.5.0, 0.74 v5.4.0, 0.79 v5.3.0, 0.85 v5.2.0
% 161.83/161.90 % Syntax : Number of formulae : 5248 (1735 unt; 0 def)
% 161.83/161.90 % Number of atoms : 12630 (4519 equ)
% 161.83/161.90 % Maximal formula atoms : 13 ( 2 avg)
% 161.83/161.90 % Number of connectives : 8402 (1020 ~; 155 |; 720 &)
% 161.83/161.90 % ( 891 <=>;5616 =>; 0 <=; 0 <~>)
% 161.83/161.90 % Maximal formula depth : 22 ( 6 avg)
% 161.83/161.90 % Maximal term depth : 19 ( 2 avg)
% 161.83/161.90 % Number of predicates : 147 ( 146 usr; 2 prp; 0-7 aty)
% 161.83/161.90 % Number of functors : 388 ( 388 usr; 58 con; 0-7 aty)
% 161.83/161.90 % Number of variables : 16655 (16510 !; 145 ?)
% 161.83/161.90 % SPC : FOF_THM_RFO_SEQ
% 161.83/161.90
% 161.83/161.90 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 161.83/161.90 % 2011-03-01 13:01:39
% 161.83/161.90 %------------------------------------------------------------------------------
% 161.83/161.90 %----Relevant facts (4986)
% 161.83/161.90 fof(fact_ext,axiom,
% 161.83/161.90 ! [V_g_2,V_f_2] :
% 161.83/161.90 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 161.83/161.90 => V_f_2 = V_g_2 ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_empty,axiom,
% 161.83/161.90 ! [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))) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 161.83/161.90 ! [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))) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_MGF,axiom,
% 161.83/161.90 ! [V_ca_2] :
% 161.83/161.90 ( c_Hoare__Mirabelle_Ostate__not__singleton
% 161.83/161.90 => ( c_Com_OWT__bodies
% 161.83/161.90 => ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
% 161.83/161.90 => 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)))) ) ) ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_cut,axiom,
% 161.83/161.90 ! [V_G_2,V_ts_2,V_G_H_2,T_a] :
% 161.83/161.90 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2)
% 161.83/161.90 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_G_H_2)
% 161.83/161.90 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_hoare__derivs_Oinsert,axiom,
% 161.83/161.90 ! [V_ts_2,V_t_2,V_G_2,T_a] :
% 161.83/161.90 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 161.83/161.90 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2)
% 161.83/161.90 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2)) ) ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_derivs__insertD,axiom,
% 161.83/161.90 ! [V_ts_2,V_t_2,V_G_2,T_a] :
% 161.83/161.90 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2))
% 161.83/161.90 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 161.83/161.90 & c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_WT__bodiesD,axiom,
% 161.83/161.90 ! [V_b,V_pn] :
% 161.83/161.90 ( c_Com_OWT__bodies
% 161.83/161.90 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b)
% 161.83/161.90 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_WT_Oequations_I7_J,axiom,
% 161.83/161.90 ! [V_a_2] :
% 161.83/161.90 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2)))
% 161.83/161.90 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_MGT__BodyN,axiom,
% 161.83/161.90 ! [V_G_2,V_pn_2] :
% 161.83/161.90 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,V_pn_2))),V_G_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
% 161.83/161.90 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_empty__not__insert,axiom,
% 161.83/161.90 ! [V_A_2,V_a_2,T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_insert__not__empty,axiom,
% 161.83/161.90 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_doubleton__eq__iff,axiom,
% 161.83/161.90 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 161.83/161.90 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_ca_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 161.83/161.90 <=> ( ( V_a_2 = V_ca_2
% 161.83/161.90 & V_b_2 = V_d_2 )
% 161.83/161.90 | ( V_a_2 = V_d_2
% 161.83/161.90 & V_b_2 = V_ca_2 ) ) ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_singleton__inject,axiom,
% 161.83/161.90 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.90 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
% 161.83/161.90 => V_a_2 = V_b_2 ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_bot__apply,axiom,
% 161.83/161.90 ! [V_x_2,T_b,T_a] :
% 161.83/161.90 ( class_Orderings_Obot(T_a)
% 161.83/161.90 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_MGF__lemma1,axiom,
% 161.83/161.90 ! [V_ca_2,V_G_2] :
% 161.83/161.90 ( c_Hoare__Mirabelle_Ostate__not__singleton
% 161.83/161.90 => ( ! [B_x] :
% 161.83/161.90 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))
% 161.83/161.90 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,B_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) )
% 161.83/161.90 => ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
% 161.83/161.90 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_WTs__elim__cases_I7_J,axiom,
% 161.83/161.90 ! [V_P] :
% 161.83/161.90 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P)))
% 161.83/161.90 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_Option_Oset_Osimps_I2_J,axiom,
% 161.83/161.90 ! [V_x_2,T_a] : c_Option_Oset(T_a,hAPP(c_Option_Ooption_OSome(T_a),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_com_Osimps_I6_J,axiom,
% 161.83/161.90 ! [V_pname_H_2,V_pname_2] :
% 161.83/161.90 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2)
% 161.83/161.90 <=> V_pname_2 = V_pname_H_2 ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_the_Osimps,axiom,
% 161.83/161.90 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ).
% 161.83/161.90
% 161.83/161.90 fof(fact_insert__code,axiom,
% 161.83/161.90 ! [V_x_2,V_A_2,V_y_2,T_a] :
% 161.83/161.90 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2),V_x_2))
% 161.83/161.90 <=> ( V_y_2 = V_x_2
% 161.83/161.90 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_insert__commute,axiom,
% 161.83/161.90 ! [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)) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_insert__absorb2,axiom,
% 161.83/161.90 ! [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) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_option_Oinject,axiom,
% 161.83/161.90 ! [V_a_H_2,V_a_2,T_a] :
% 161.83/161.90 ( hAPP(c_Option_Ooption_OSome(T_a),V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_a_H_2)
% 161.83/161.90 <=> V_a_2 = V_a_H_2 ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_insert__dom,axiom,
% 161.83/161.90 ! [T_b,V_y_2,T_a,V_x_2,V_f_2] :
% 161.83/161.90 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
% 161.83/161.90 => hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) = c_Map_Odom(T_b,T_a,V_f_2) ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_the__elem__eq,axiom,
% 161.83/161.90 ! [V_x_2,T_a] : c_Set_Othe__elem(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ).
% 161.83/161.90
% 161.83/161.90 fof(fact_BodyN,axiom,
% 161.83/161.90 ! [V_G_2,V_Q_2,V_pn_2,V_P_2,T_a] :
% 161.83/161.90 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),V_G_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 161.83/161.90 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_weak__Body,axiom,
% 161.83/161.90 ! [V_Q_2,V_pn_2,V_P_2,V_G_2,T_a] :
% 161.83/161.90 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 161.83/161.90 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_option_Osimps_I5_J,axiom,
% 161.83/161.90 ! [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) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_option_Orecs_I2_J,axiom,
% 161.83/161.90 ! [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) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_is__none__code_I2_J,axiom,
% 161.83/161.90 ! [V_x,T_b] : ~ c_Option_Ois__none(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x)) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_ospec,axiom,
% 161.83/161.90 ! [V_x_2,V_P_2,V_A_2,T_a] :
% 161.83/161.90 ( ! [B_x] :
% 161.83/161.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Option_Oset(T_a,V_A_2)))
% 161.83/161.90 => hBOOL(hAPP(V_P_2,B_x)) )
% 161.83/161.90 => ( V_A_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 161.83/161.90 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_WTs__elim__cases_I8_J,axiom,
% 161.83/161.90 ! [V_a_2,V_P_2,V_X_2] :
% 161.83/161.90 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2)))
% 161.83/161.90 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P_2))) ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_WT_OBody,axiom,
% 161.83/161.90 ! [V_pn] :
% 161.83/161.90 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom)
% 161.83/161.90 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ).
% 161.83/161.90
% 161.83/161.90 fof(fact_MGF__complete,axiom,
% 161.83/161.90 ! [V_Q_2,V_P_2,V_ca_2] :
% 161.83/161.91 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
% 161.83/161.91 => ( c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
% 161.83/161.91 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_finite__dom__body,axiom,
% 161.83/161.91 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_is__none__code_I1_J,axiom,
% 161.83/161.91 ! [T_a] : c_Option_Ois__none(T_a,c_Option_Ooption_ONone(T_a)) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_is__none__def,axiom,
% 161.83/161.91 ! [V_x_2,T_a] :
% 161.83/161.91 ( c_Option_Ois__none(T_a,V_x_2)
% 161.83/161.91 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_com_Osimps_I7_J,axiom,
% 161.83/161.91 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] :
% 161.83/161.91 ( 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)
% 161.83/161.91 <=> ( V_vname_2 = V_vname_H_2
% 161.83/161.91 & V_pname_2 = V_pname_H_2
% 161.83/161.91 & V_fun_2 = V_fun_H_2 ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_option_Orecs_I1_J,axiom,
% 161.83/161.91 ! [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 ).
% 161.83/161.91
% 161.83/161.91 fof(fact_option_Osimps_I4_J,axiom,
% 161.83/161.91 ! [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 ).
% 161.83/161.91
% 161.83/161.91 fof(fact_triple_Oinject,axiom,
% 161.83/161.91 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_a] :
% 161.83/161.91 ( 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)
% 161.83/161.91 <=> ( V_fun1_2 = V_fun1_H_2
% 161.83/161.91 & V_com_2 = V_com_H_2
% 161.83/161.91 & V_fun2_2 = V_fun2_H_2 ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_option_Osimps_I2_J,axiom,
% 161.83/161.91 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_option_Osimps_I3_J,axiom,
% 161.83/161.91 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_not__Some__eq,axiom,
% 161.83/161.91 ! [T_a,V_x_2] :
% 161.83/161.91 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_a),B_y)
% 161.83/161.91 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_not__None__eq,axiom,
% 161.83/161.91 ! [T_a,V_x_2] :
% 161.83/161.91 ( V_x_2 != c_Option_Ooption_ONone(T_a)
% 161.83/161.91 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_a),B_y) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_com_Osimps_I62_J,axiom,
% 161.83/161.91 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_pname_2] : hAPP(c_Com_Ocom_OBODY,V_pname_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_com_Osimps_I63_J,axiom,
% 161.83/161.91 ! [V_pname_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != hAPP(c_Com_Ocom_OBODY,V_pname_2) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_Option_Oset_Osimps_I1_J,axiom,
% 161.83/161.91 ! [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)) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_set__empty__eq,axiom,
% 161.83/161.91 ! [V_xo_2,T_a] :
% 161.83/161.91 ( c_Option_Oset(T_a,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.91 <=> V_xo_2 = c_Option_Ooption_ONone(T_a) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_WT_Oequations_I8_J,axiom,
% 161.83/161.91 ! [V_a3_2,V_a1_2,V_a2_2] :
% 161.83/161.91 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2)))
% 161.83/161.91 <=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_WT_OCall,axiom,
% 161.83/161.91 ! [V_a_2,V_X_2,V_pn_2] :
% 161.83/161.91 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn_2)))
% 161.83/161.91 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2))) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_hoare__sound,axiom,
% 161.83/161.91 ! [V_ts_2,V_G_2,T_a] :
% 161.83/161.91 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2)
% 161.83/161.91 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,V_ts_2) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_finite_OinsertI,axiom,
% 161.83/161.91 ! [V_a_2,V_A_2,T_a] :
% 161.83/161.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_finite_OemptyI,axiom,
% 161.83/161.91 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_triple_Osimps_I2_J,axiom,
% 161.83/161.91 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_triple_Orecs,axiom,
% 161.83/161.91 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_finite__insert,axiom,
% 161.83/161.91 ! [V_A_2,V_a_2,T_a] :
% 161.83/161.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)))
% 161.83/161.91 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_finite_Oequations_I1_J,axiom,
% 161.83/161.91 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_hoare__derivs_OSkip,axiom,
% 161.83/161.91 ! [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)))) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_hoare__derivs_Oequations_I7_J,axiom,
% 161.83/161.91 ! [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)))) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_conseq2,axiom,
% 161.83/161.91 ! [V_Q_2,V_Q_H_2,V_ca_2,V_P_2,V_G_2,T_a] :
% 161.83/161.91 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 161.83/161.91 => ( ! [B_Z,B_s] :
% 161.83/161.91 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s))
% 161.83/161.91 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) )
% 161.83/161.91 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_conseq1,axiom,
% 161.83/161.91 ! [V_P_2,V_Q_2,V_ca_2,V_P_H_2,V_G_2,T_a] :
% 161.83/161.91 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_H_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 161.83/161.91 => ( ! [B_Z,B_s] :
% 161.83/161.91 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 161.83/161.91 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) )
% 161.83/161.91 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_Comp,axiom,
% 161.83/161.91 ! [V_R_2,V_d_2,V_Q_2,V_ca_2,V_P_2,V_G_2,T_a] :
% 161.83/161.91 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 161.83/161.91 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_Q_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 161.83/161.91 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),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)))) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_map__comp__None__iff,axiom,
% 161.83/161.91 ! [V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] :
% 161.83/161.91 ( 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)
% 161.83/161.91 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 161.83/161.91 | ? [B_k_H] :
% 161.83/161.91 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H)
% 161.83/161.91 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_a) ) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_WTs__elim__cases_I4_J,axiom,
% 161.83/161.91 ! [V_c2,V_c1] :
% 161.83/161.91 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2)))
% 161.83/161.91 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 161.83/161.91 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_com_Osimps_I3_J,axiom,
% 161.83/161.91 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
% 161.83/161.91 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
% 161.83/161.91 <=> ( V_com1_2 = V_com1_H_2
% 161.83/161.91 & V_com2_2 = V_com2_H_2 ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_com_Osimps_I13_J,axiom,
% 161.83/161.91 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
% 161.83/161.91
% 161.83/161.91 fof(fact_com_Osimps_I12_J,axiom,
% 161.83/161.91 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_com_Osimps_I48_J,axiom,
% 161.83/161.91 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_com_Osimps_I49_J,axiom,
% 161.83/161.91 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_WT_OSemi,axiom,
% 161.83/161.91 ! [V_c1,V_c0] :
% 161.83/161.91 ( hBOOL(hAPP(c_Com_OWT,V_c0))
% 161.83/161.91 => ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 161.83/161.91 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_WT_Oequations_I4_J,axiom,
% 161.83/161.91 ! [V_a2_2,V_a1_2] :
% 161.83/161.91 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2)))
% 161.83/161.91 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 161.83/161.91 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_com_Osimps_I51_J,axiom,
% 161.83/161.91 ! [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) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_com_Osimps_I50_J,axiom,
% 161.83/161.91 ! [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) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_com_Osimps_I19_J,axiom,
% 161.83/161.91 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ).
% 161.83/161.91
% 161.83/161.91 fof(fact_com_Osimps_I18_J,axiom,
% 161.83/161.91 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_WT_Oequations_I1_J,axiom,
% 161.83/161.91 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_WT_OSkip,axiom,
% 161.83/161.91 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_com_Osimps_I21_J,axiom,
% 161.83/161.91 ! [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 ).
% 161.83/161.91
% 161.83/161.91 fof(fact_com_Osimps_I20_J,axiom,
% 161.83/161.91 ! [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) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_map__comp__simps_I1_J,axiom,
% 161.83/161.91 ! [V_m1_2,T_b,T_c,T_a,V_k_2,V_m2_2] :
% 161.83/161.91 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 161.83/161.91 => 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) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_map__comp__simps_I2_J,axiom,
% 161.83/161.91 ! [V_m1_2,T_b,T_c,V_k_H_2,T_a,V_k_2,V_m2_2] :
% 161.83/161.91 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_k_H_2)
% 161.83/161.91 => 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) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_map__comp__Some__iff,axiom,
% 161.83/161.91 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] :
% 161.83/161.91 ( 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)
% 161.83/161.91 <=> ? [B_k_H] :
% 161.83/161.91 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H)
% 161.83/161.91 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_finite,axiom,
% 161.83/161.91 ! [V_A_2,T_a] :
% 161.83/161.91 ( class_Finite__Set_Ofinite(T_a)
% 161.83/161.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_finite__code,axiom,
% 161.83/161.91 ! [V_A_2,T_a] :
% 161.83/161.91 ( class_Finite__Set_Ofinite(T_a)
% 161.83/161.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 161.83/161.91 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 161.83/161.91 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 161.83/161.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.91 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.91 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 161.83/161.91 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 161.83/161.91 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 161.83/161.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 161.83/161.91 => 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)) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_folding__one_Osingleton,axiom,
% 161.83/161.91 ! [V_x_2,V_F_2,V_f_2,T_a] :
% 161.83/161.91 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 161.83/161.91 => 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 ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_fold1Set__sing,axiom,
% 161.83/161.91 ! [V_b_2,V_a_2,V_f_2,T_a] :
% 161.83/161.91 ( 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))
% 161.83/161.91 <=> V_a_2 = V_b_2 ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_finite_Osimps,axiom,
% 161.83/161.91 ! [V_a_2,T_a] :
% 161.83/161.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a_2))
% 161.83/161.91 <=> ( V_a_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.91 | ? [B_A] :
% 161.83/161.91 ( ? [B_a] : V_a_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A)
% 161.83/161.91 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A)) ) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_dom__minus,axiom,
% 161.83/161.91 ! [V_A_2,T_b,T_a,V_x_2,V_f_2] :
% 161.83/161.91 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_a)
% 161.83/161.91 => 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) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_evalc_OBody,axiom,
% 161.83/161.91 ! [V_s1,V_s0,V_pn] :
% 161.83/161.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1))
% 161.83/161.91 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_evalc__elim__cases_I6_J,axiom,
% 161.83/161.91 ! [V_s1,V_s,V_P] :
% 161.83/161.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1))
% 161.83/161.91 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_Body__triple__valid__Suc,axiom,
% 161.83/161.91 ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_a] :
% 161.83/161.91 ( 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))
% 161.83/161.91 <=> 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)) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_elem__set,axiom,
% 161.83/161.91 ! [V_xo_2,V_x_2,T_a] :
% 161.83/161.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Option_Oset(T_a,V_xo_2)))
% 161.83/161.91 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_option_Oexhaust,axiom,
% 161.83/161.91 ! [T_a,V_y] :
% 161.83/161.91 ( V_y != c_Option_Ooption_ONone(T_a)
% 161.83/161.91 => ~ ! [B_a] : V_y != hAPP(c_Option_Ooption_OSome(T_a),B_a) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_conseq12,axiom,
% 161.83/161.91 ! [V_Q_2,V_P_2,V_Q_H_2,V_ca_2,V_P_H_2,V_G_2,T_a] :
% 161.83/161.91 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_H_2),V_ca_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 161.83/161.91 => ( ! [B_Z,B_s] :
% 161.83/161.91 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 161.83/161.91 => ! [B_s_H] :
% 161.83/161.91 ( ! [B_Z_H] :
% 161.83/161.91 ( hBOOL(hAPP(hAPP(V_P_H_2,B_Z_H),B_s))
% 161.83/161.91 => hBOOL(hAPP(hAPP(V_Q_H_2,B_Z_H),B_s_H)) )
% 161.83/161.91 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) )
% 161.83/161.91 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_equalityCE,axiom,
% 161.83/161.91 ! [V_ca_2,T_a,V_B_2,V_A_2] :
% 161.83/161.91 ( V_A_2 = V_B_2
% 161.83/161.91 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 161.83/161.91 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) )
% 161.83/161.91 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 161.83/161.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_emptyE,axiom,
% 161.83/161.91 ! [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)))) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_insertE,axiom,
% 161.83/161.91 ! [V_A_2,V_b_2,V_a_2,T_a] :
% 161.83/161.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)))
% 161.83/161.91 => ( V_a_2 != V_b_2
% 161.83/161.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_insertCI,axiom,
% 161.83/161.91 ! [V_b_2,V_B_2,V_a_2,T_a] :
% 161.83/161.91 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
% 161.83/161.91 => V_a_2 = V_b_2 )
% 161.83/161.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_DiffI,axiom,
% 161.83/161.91 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 161.83/161.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 161.83/161.91 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
% 161.83/161.91 => 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))) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_DiffE,axiom,
% 161.83/161.91 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 161.83/161.91 ( 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)))
% 161.83/161.91 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 161.83/161.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_finite__Diff,axiom,
% 161.83/161.91 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.91 => 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))) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_evalc_OSemi,axiom,
% 161.83/161.91 ! [V_s2,V_c1,V_s1,V_s0,V_c0] :
% 161.83/161.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1))
% 161.83/161.91 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2))
% 161.83/161.91 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_evalc__elim__cases_I1_J,axiom,
% 161.83/161.91 ! [V_t,V_s] :
% 161.83/161.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t))
% 161.83/161.91 => V_t = V_s ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_evalc_OSkip,axiom,
% 161.83/161.91 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_mem__def,axiom,
% 161.83/161.91 ! [V_A_2,V_x_2,T_a] :
% 161.83/161.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.91 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_Diff__iff,axiom,
% 161.83/161.91 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 161.83/161.91 ( 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)))
% 161.83/161.91 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 161.83/161.91 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_Diff__idemp,axiom,
% 161.83/161.91 ! [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) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_eqset__imp__iff,axiom,
% 161.83/161.91 ! [V_x_2,T_a,V_B_2,V_A_2] :
% 161.83/161.91 ( V_A_2 = V_B_2
% 161.83/161.91 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.91 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_eqelem__imp__iff,axiom,
% 161.83/161.91 ! [V_A_2,T_a,V_y_2,V_x_2] :
% 161.83/161.91 ( V_x_2 = V_y_2
% 161.83/161.91 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.91 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_eq__mem__trans,axiom,
% 161.83/161.91 ! [V_A_2,T_a,V_b_2,V_a_2] :
% 161.83/161.91 ( V_a_2 = V_b_2
% 161.83/161.91 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 161.83/161.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_DiffD1,axiom,
% 161.83/161.91 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 161.83/161.91 ( 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)))
% 161.83/161.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_DiffD2,axiom,
% 161.83/161.91 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 161.83/161.91 ( 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)))
% 161.83/161.91 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_com__det,axiom,
% 161.83/161.91 ! [V_u,V_t,V_s,V_c] :
% 161.83/161.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
% 161.83/161.91 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u))
% 161.83/161.91 => V_u = V_t ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_triple__valid__Suc,axiom,
% 161.83/161.91 ! [V_t,V_n,T_a] :
% 161.83/161.91 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t)
% 161.83/161.91 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_insert__Diff1,axiom,
% 161.83/161.91 ! [V_A_2,V_B_2,V_x_2,T_a] :
% 161.83/161.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 161.83/161.91 => 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) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_insert__Diff__if,axiom,
% 161.83/161.91 ! [V_A_2,V_B_2,V_x_2,T_a] :
% 161.83/161.91 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 161.83/161.91 => 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) )
% 161.83/161.91 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 161.83/161.91 => 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)) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_folding__one__idem_Oidem,axiom,
% 161.83/161.91 ! [V_x_2,V_F_2,V_f_2,T_a] :
% 161.83/161.91 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 161.83/161.91 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 161.83/161.91 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 161.83/161.91 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 161.83/161.91 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_folding__one__idem_Oin__idem,axiom,
% 161.83/161.91 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 161.83/161.91 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 161.83/161.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.91 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.91 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_evalc_Oequations_I4_J,axiom,
% 161.83/161.91 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] :
% 161.83/161.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2))
% 161.83/161.91 <=> ? [B_s1] :
% 161.83/161.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1))
% 161.83/161.91 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_evalc_Oequations_I1_J,axiom,
% 161.83/161.91 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 161.83/161.91 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 161.83/161.91 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 161.83/161.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 161.83/161.91 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 161.83/161.91 => 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) ) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_Diff__insert__absorb,axiom,
% 161.83/161.91 ! [V_A_2,V_x_2,T_a] :
% 161.83/161.91 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.91 => 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 ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_insert__Diff,axiom,
% 161.83/161.91 ! [V_A_2,V_a_2,T_a] :
% 161.83/161.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 161.83/161.91 => 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 ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_folding__one_Oremove,axiom,
% 161.83/161.91 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 161.83/161.91 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 161.83/161.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.91 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.91 => ( ( 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))
% 161.83/161.91 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 161.83/161.91 & ( 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))
% 161.83/161.91 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_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)))))) ) ) ) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_empty__Diff,axiom,
% 161.83/161.91 ! [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)) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_Diff__empty,axiom,
% 161.83/161.91 ! [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 ).
% 161.83/161.91
% 161.83/161.91 fof(fact_Diff__cancel,axiom,
% 161.83/161.91 ! [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)) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_finite__Diff2,axiom,
% 161.83/161.91 ! [V_A_2,V_B_2,T_a] :
% 161.83/161.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 161.83/161.91 => ( 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)))
% 161.83/161.91 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_all__not__in__conv,axiom,
% 161.83/161.91 ! [V_A_2,T_a] :
% 161.83/161.91 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 161.83/161.91 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_ex__in__conv,axiom,
% 161.83/161.91 ! [V_A_2,T_a] :
% 161.83/161.91 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 161.83/161.91 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_empty__iff,axiom,
% 161.83/161.91 ! [V_ca_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_equals0D,axiom,
% 161.83/161.91 ! [V_a_2,T_a,V_A_2] :
% 161.83/161.91 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.91 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_insertI1,axiom,
% 161.83/161.91 ! [V_B_2,V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_insert__iff,axiom,
% 161.83/161.91 ! [V_A_2,V_b_2,V_a_2,T_a] :
% 161.83/161.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)))
% 161.83/161.91 <=> ( V_a_2 = V_b_2
% 161.83/161.91 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_insert__ident,axiom,
% 161.83/161.91 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 161.83/161.91 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.91 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 161.83/161.91 => ( hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2)
% 161.83/161.91 <=> V_A_2 = V_B_2 ) ) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_insertI2,axiom,
% 161.83/161.91 ! [V_b_2,V_B_2,V_a_2,T_a] :
% 161.83/161.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
% 161.83/161.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_insert__absorb,axiom,
% 161.83/161.91 ! [V_A_2,V_a_2,T_a] :
% 161.83/161.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 161.83/161.91 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = V_A_2 ) ).
% 161.83/161.91
% 161.83/161.91 fof(fact_folding__one_Oinsert__remove,axiom,
% 161.83/161.91 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 161.83/161.91 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 161.83/161.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.91 => ( ( 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))
% 161.83/161.91 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 161.83/161.92 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.92 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_folding__one_Oinsert,axiom,
% 161.83/161.92 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 161.83/161.92 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 161.83/161.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.92 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_Diff__insert,axiom,
% 161.83/161.92 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_Diff__insert2,axiom,
% 161.83/161.92 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_insert__Diff__single,axiom,
% 161.83/161.92 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_finite__Diff__insert,axiom,
% 161.83/161.92 ! [V_B_2,V_a_2,V_A_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))))
% 161.83/161.92 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_empty__fold1SetE,axiom,
% 161.83/161.92 ! [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)) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_fold1Set__nonempty,axiom,
% 161.83/161.92 ! [V_x_2,V_A_2,V_f_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),V_x_2))
% 161.83/161.92 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_singleton__iff,axiom,
% 161.83/161.92 ! [V_a_2,V_b_2,T_a] :
% 161.83/161.92 ( 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)))))
% 161.83/161.92 <=> V_b_2 = V_a_2 ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_singletonE,axiom,
% 161.83/161.92 ! [V_a_2,V_b_2,T_a] :
% 161.83/161.92 ( 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)))))
% 161.83/161.92 => V_b_2 = V_a_2 ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_domIff,axiom,
% 161.83/161.92 ! [V_m_2,T_b,V_a_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2)))
% 161.83/161.92 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_b) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_domI,axiom,
% 161.83/161.92 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] :
% 161.83/161.92 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2)
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2))) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_evalc_Oequations_I9_J,axiom,
% 161.83/161.92 ! [V_a3_2,V_a2_2,V_a1_2] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2))
% 161.83/161.92 <=> 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)) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_folding__image__simple_Oremove,axiom,
% 161.83/161.92 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 161.83/161.92 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 161.83/161.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 161.83/161.92 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 161.83/161.92 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 161.83/161.92 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 161.83/161.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 161.83/161.92 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_minus__apply,axiom,
% 161.83/161.92 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 161.83/161.92 ( class_Groups_Ominus(T_a)
% 161.83/161.92 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_folding__one_Oclosed,axiom,
% 161.83/161.92 ! [V_A_2,V_F_2,V_f_2,T_a] :
% 161.83/161.92 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 161.83/161.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.92 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_finite__empty__induct,axiom,
% 161.83/161.92 ! [V_P_2,V_A_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.92 => ( hBOOL(hAPP(V_P_2,V_A_2))
% 161.83/161.92 => ( ! [B_a,B_A] :
% 161.83/161.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A))
% 161.83/161.92 => ( hBOOL(hAPP(V_P_2,B_A))
% 161.83/161.92 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_a),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) )
% 161.83/161.92 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_card__Suc__Diff1,axiom,
% 161.83/161.92 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.92 => 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) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_evaln_OBody,axiom,
% 161.83/161.92 ! [V_s1,V_n,V_s0,V_pn] :
% 161.83/161.92 ( 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))
% 161.83/161.92 => 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)) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_folding__image__simple_Oinsert,axiom,
% 161.83/161.92 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 161.83/161.92 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 161.83/161.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 161.83/161.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 161.83/161.92 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_fold1Set_Ointros,axiom,
% 161.83/161.92 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2),V_x_2))
% 161.83/161.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 161.83/161.92 => 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)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_dom__fun__upd,axiom,
% 161.83/161.92 ! [V_x_2,V_f_2,T_b,T_a,V_y_2] :
% 161.83/161.92 ( ( V_y_2 = c_Option_Ooption_ONone(T_a)
% 161.83/161.92 => c_Map_Odom(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) )
% 161.83/161.92 & ( V_y_2 != c_Option_Ooption_ONone(T_a)
% 161.83/161.92 => c_Map_Odom(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_evaln_OSemi,axiom,
% 161.83/161.92 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0),V_s0),V_n),V_s1))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s1),V_n),V_s2))
% 161.83/161.92 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_n),V_s2)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_evaln_OSkip,axiom,
% 161.83/161.92 ! [V_n,V_s] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_s)) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_evaln__elim__cases_I1_J,axiom,
% 161.83/161.92 ! [V_t,V_n,V_s] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_t))
% 161.83/161.92 => V_t = V_s ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_evaln__Suc,axiom,
% 161.83/161.92 ! [V_s_H,V_n,V_s,V_c] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_s_H))
% 161.83/161.92 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),hAPP(c_Nat_OSuc,V_n)),V_s_H)) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_map__upd__eqD1,axiom,
% 161.83/161.92 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_b,T_a] :
% 161.83/161.92 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_n_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))
% 161.83/161.92 => V_x_2 = V_y_2 ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_map__upd__triv,axiom,
% 161.83/161.92 ! [T_b,V_x_2,T_a,V_k_2,V_t_2] :
% 161.83/161.92 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 161.83/161.92 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_a),V_x_2)) = V_t_2 ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_map__upd__Some__unfold,axiom,
% 161.83/161.92 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_a,T_b] :
% 161.83/161.92 ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
% 161.83/161.92 <=> ( ( V_x_2 = V_a_2
% 161.83/161.92 & V_b_2 = V_y_2 )
% 161.83/161.92 | ( V_x_2 != V_a_2
% 161.83/161.92 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_eval__eq,axiom,
% 161.83/161.92 ! [V_t_2,V_s_2,V_ca_2] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s_2),V_t_2))
% 161.83/161.92 <=> ? [B_n] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s_2),B_n),V_t_2)) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_evaln__evalc,axiom,
% 161.83/161.92 ! [V_t,V_n,V_s,V_c] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_evaln_Oequations_I4_J,axiom,
% 161.83/161.92 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] :
% 161.83/161.92 ( 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))
% 161.83/161.92 <=> ? [B_s1] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a1_2),V_a2_2),V_a3_2),B_s1))
% 161.83/161.92 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a5_2),B_s1),V_a3_2),V_a6_2)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_evaln_Oequations_I1_J,axiom,
% 161.83/161.92 ! [V_a2,V_a1] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_a1),V_a2),V_a1)) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_empty__fold__graphE,axiom,
% 161.83/161.92 ! [V_x_2,V_z_2,V_f_2,T_b,T_a] :
% 161.83/161.92 ( 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))
% 161.83/161.92 => V_x_2 = V_z_2 ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_fold__graph_OemptyI,axiom,
% 161.83/161.92 ! [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)) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 161.83/161.92 ! [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)) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_fold__graph__imp__finite,axiom,
% 161.83/161.92 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2))
% 161.83/161.92 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_folding__image__simple_Oempty,axiom,
% 161.83/161.92 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 161.83/161.92 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 161.83/161.92 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_fold__graph_OinsertI,axiom,
% 161.83/161.92 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 161.83/161.92 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.92 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
% 161.83/161.92 => 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))) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_triple__valid__def2,axiom,
% 161.83/161.92 ! [V_Q_2,V_ca_2,V_P_2,V_n_2,T_a] :
% 161.83/161.92 ( 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))
% 161.83/161.92 <=> ! [B_Z,B_s] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 161.83/161.92 => ! [B_s_H] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),B_s),V_n_2),B_s_H))
% 161.83/161.92 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_card__insert__disjoint,axiom,
% 161.83/161.92 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.92 => 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)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_card__insert__if,axiom,
% 161.83/161.92 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.92 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.92 => 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) )
% 161.83/161.92 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.92 => 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)) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_evaln_Oequations_I9_J,axiom,
% 161.83/161.92 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] :
% 161.83/161.92 ( 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))
% 161.83/161.92 <=> 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)) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_card__insert,axiom,
% 161.83/161.92 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.92 => 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)))))) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_Diff1__fold__graph,axiom,
% 161.83/161.92 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 161.83/161.92 ( 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))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.92 => 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))) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_fun__upd__triv,axiom,
% 161.83/161.92 ! [V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),hAPP(V_f_2,V_x_2)) = V_f_2 ).
% 161.83/161.92
% 161.83/161.92 fof(fact_evaln__elim__cases_I6_J,axiom,
% 161.83/161.92 ! [V_s1,V_n,V_s,V_P] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_n),V_s1))
% 161.83/161.92 => ~ ! [B_n] :
% 161.83/161.92 ( V_n = hAPP(c_Nat_OSuc,B_n)
% 161.83/161.92 => ~ 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)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_ran__map__upd,axiom,
% 161.83/161.92 ! [V_b_2,T_b,T_a,V_a_2,V_m_2] :
% 161.83/161.92 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_a)
% 161.83/161.92 => c_Map_Oran(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2)) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_fun__upd__None__restrict,axiom,
% 161.83/161.92 ! [V_m_2,T_b,V_D_2,V_x_2,T_a] :
% 161.83/161.92 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 161.83/161.92 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) )
% 161.83/161.92 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 161.83/161.92 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_fun__upd__restrict__conv,axiom,
% 161.83/161.92 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 161.83/161.92 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_restrict__fun__upd,axiom,
% 161.83/161.92 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] :
% 161.83/161.92 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 161.83/161.92 => c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) )
% 161.83/161.92 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 161.83/161.92 => c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_card__Diff__singleton__if,axiom,
% 161.83/161.92 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.92 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.92 => 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)) )
% 161.83/161.92 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.92 => 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) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_card__Diff__singleton,axiom,
% 161.83/161.92 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.92 => 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)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_card__Diff2__less,axiom,
% 161.83/161.92 ! [V_y_2,V_x_2,V_A_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 161.83/161.92 => 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))) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_card__Diff1__less,axiom,
% 161.83/161.92 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.92 => 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))) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_fold1Set_Oequations,axiom,
% 161.83/161.92 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a] :
% 161.83/161.92 ( 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))
% 161.83/161.92 <=> ? [B_a,B_A] :
% 161.83/161.92 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A)
% 161.83/161.92 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_a3_2))
% 161.83/161.92 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_order__less__irrefl,axiom,
% 161.83/161.92 ! [V_x,T_a] :
% 161.83/161.92 ( class_Orderings_Opreorder(T_a)
% 161.83/161.92 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_linorder__neq__iff,axiom,
% 161.83/161.92 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.92 ( class_Orderings_Olinorder(T_a)
% 161.83/161.92 => ( V_x_2 != V_y_2
% 161.83/161.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 161.83/161.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_not__less__iff__gr__or__eq,axiom,
% 161.83/161.92 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.92 ( class_Orderings_Olinorder(T_a)
% 161.83/161.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 161.83/161.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
% 161.83/161.92 | V_x_2 = V_y_2 ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_linorder__less__linear,axiom,
% 161.83/161.92 ! [V_y,V_x,T_a] :
% 161.83/161.92 ( class_Orderings_Olinorder(T_a)
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 161.83/161.92 | V_x = V_y
% 161.83/161.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_linorder__antisym__conv3,axiom,
% 161.83/161.92 ! [V_x_2,V_y_2,T_a] :
% 161.83/161.92 ( class_Orderings_Olinorder(T_a)
% 161.83/161.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
% 161.83/161.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 161.83/161.92 <=> V_x_2 = V_y_2 ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_linorder__neqE,axiom,
% 161.83/161.92 ! [V_y,V_x,T_a] :
% 161.83/161.92 ( class_Orderings_Olinorder(T_a)
% 161.83/161.92 => ( V_x != V_y
% 161.83/161.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_less__imp__neq,axiom,
% 161.83/161.92 ! [V_y,V_x,T_a] :
% 161.83/161.92 ( class_Orderings_Oorder(T_a)
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 161.83/161.92 => V_x != V_y ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_order__less__not__sym,axiom,
% 161.83/161.92 ! [V_y,V_x,T_a] :
% 161.83/161.92 ( class_Orderings_Opreorder(T_a)
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 161.83/161.92 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_order__less__imp__not__less,axiom,
% 161.83/161.92 ! [V_y,V_x,T_a] :
% 161.83/161.92 ( class_Orderings_Opreorder(T_a)
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 161.83/161.92 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_order__less__imp__not__eq,axiom,
% 161.83/161.92 ! [V_y,V_x,T_a] :
% 161.83/161.92 ( class_Orderings_Oorder(T_a)
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 161.83/161.92 => V_x != V_y ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_order__less__imp__not__eq2,axiom,
% 161.83/161.92 ! [V_y,V_x,T_a] :
% 161.83/161.92 ( class_Orderings_Oorder(T_a)
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 161.83/161.92 => V_y != V_x ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_order__less__asym_H,axiom,
% 161.83/161.92 ! [V_b,V_a,T_a] :
% 161.83/161.92 ( class_Orderings_Opreorder(T_a)
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 161.83/161.92 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_xt1_I9_J,axiom,
% 161.83/161.92 ! [V_a,V_b,T_a] :
% 161.83/161.92 ( class_Orderings_Oorder(T_a)
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 161.83/161.92 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_ord__eq__less__trans,axiom,
% 161.83/161.92 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.92 ( class_Orderings_Oord(T_a)
% 161.83/161.92 => ( V_a = V_b
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_xt1_I1_J,axiom,
% 161.83/161.92 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.92 ( class_Orderings_Oorder(T_a)
% 161.83/161.92 => ( V_a = V_b
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_ord__less__eq__trans,axiom,
% 161.83/161.92 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.92 ( class_Orderings_Oord(T_a)
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 161.83/161.92 => ( V_b = V_c
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_xt1_I2_J,axiom,
% 161.83/161.92 ! [V_c,V_a,V_b,T_a] :
% 161.83/161.92 ( class_Orderings_Oorder(T_a)
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 161.83/161.92 => ( V_b = V_c
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_order__less__trans,axiom,
% 161.83/161.92 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.92 ( class_Orderings_Opreorder(T_a)
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_xt1_I10_J,axiom,
% 161.83/161.92 ! [V_z,V_x,V_y,T_a] :
% 161.83/161.92 ( class_Orderings_Oorder(T_a)
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_order__less__asym,axiom,
% 161.83/161.92 ! [V_y,V_x,T_a] :
% 161.83/161.92 ( class_Orderings_Opreorder(T_a)
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 161.83/161.92 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_linorder__cases,axiom,
% 161.83/161.92 ! [V_y,V_x,T_a] :
% 161.83/161.92 ( class_Orderings_Olinorder(T_a)
% 161.83/161.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 161.83/161.92 => ( V_x != V_y
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 161.83/161.92 ! [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) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_restrict__in,axiom,
% 161.83/161.92 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.92 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_restrict__out,axiom,
% 161.83/161.92 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 161.83/161.92 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.92 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_restrict__map__insert,axiom,
% 161.83/161.92 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_f_2,V_A_2)),V_a_2),hAPP(V_f_2,V_a_2)) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_fun__upd__idem,axiom,
% 161.83/161.92 ! [T_a,T_b,V_y_2,V_x_2,V_f_2] :
% 161.83/161.92 ( hAPP(V_f_2,V_x_2) = V_y_2
% 161.83/161.92 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2) = V_f_2 ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_fun__upd__other,axiom,
% 161.83/161.92 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] :
% 161.83/161.92 ( V_z_2 != V_x_2
% 161.83/161.92 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_fun__upd__twist,axiom,
% 161.83/161.92 ! [V_d_2,V_b_2,V_m_2,T_b,T_a,V_ca_2,V_a_2] :
% 161.83/161.92 ( V_a_2 != V_ca_2
% 161.83/161.92 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_a_2),V_b_2)),V_ca_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_ca_2),V_d_2)),V_a_2),V_b_2) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_fun__upd__apply,axiom,
% 161.83/161.92 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] :
% 161.83/161.92 ( ( V_z_2 = V_x_2
% 161.83/161.92 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = V_y_2 )
% 161.83/161.92 & ( V_z_2 != V_x_2
% 161.83/161.92 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_fun__upd__same,axiom,
% 161.83/161.92 ! [V_y_2,V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2),V_x_2) = V_y_2 ).
% 161.83/161.92
% 161.83/161.92 fof(fact_fun__upd__upd,axiom,
% 161.83/161.92 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_x_2),V_z_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_z_2) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_fun__upd__idem__iff,axiom,
% 161.83/161.92 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 161.83/161.92 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2) = V_f_2
% 161.83/161.92 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_ranI,axiom,
% 161.83/161.92 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] :
% 161.83/161.92 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2)
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2))) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_fun__upd__restrict,axiom,
% 161.83/161.92 ! [V_y_2,V_x_2,V_D_2,V_m_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_card__Diff__insert,axiom,
% 161.83/161.92 ! [V_B_2,V_a_2,V_A_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 161.83/161.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
% 161.83/161.92 => 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)) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_Suc__mono,axiom,
% 161.83/161.92 ! [V_n,V_m] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_lessI,axiom,
% 161.83/161.92 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_diff__Suc__1,axiom,
% 161.83/161.92 ! [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 ).
% 161.83/161.92
% 161.83/161.92 fof(fact_diff__less__Suc,axiom,
% 161.83/161.92 ! [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))) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_card_Oremove,axiom,
% 161.83/161.92 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.92 => 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)))))) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_diff__less__mono2,axiom,
% 161.83/161.92 ! [V_l,V_n,V_m] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 161.83/161.92 => 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))) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_less__imp__diff__less,axiom,
% 161.83/161.92 ! [V_n,V_k,V_j] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 161.83/161.92 => 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)) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_Suc__diff__diff,axiom,
% 161.83/161.92 ! [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) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_diff__Suc__Suc,axiom,
% 161.83/161.92 ! [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) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_Suc__less__SucD,axiom,
% 161.83/161.92 ! [V_n,V_m] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_Suc__lessD,axiom,
% 161.83/161.92 ! [V_n,V_m] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_nat__add__commute,axiom,
% 161.83/161.92 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_nat__add__left__commute,axiom,
% 161.83/161.92 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_nat__add__assoc,axiom,
% 161.83/161.92 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_nat__add__left__cancel,axiom,
% 161.83/161.92 ! [V_n_2,V_m_2,V_k_2] :
% 161.83/161.92 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)
% 161.83/161.92 <=> V_m_2 = V_n_2 ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_nat__add__right__cancel,axiom,
% 161.83/161.92 ! [V_n_2,V_k_2,V_m_2] :
% 161.83/161.92 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)
% 161.83/161.92 <=> V_m_2 = V_n_2 ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_add__Suc__right,axiom,
% 161.83/161.92 ! [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)) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_add__Suc,axiom,
% 161.83/161.92 ! [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)) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_add__Suc__shift,axiom,
% 161.83/161.92 ! [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)) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_not__add__less1,axiom,
% 161.83/161.92 ! [V_j,V_i] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_not__add__less2,axiom,
% 161.83/161.92 ! [V_i,V_j] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_nat__add__left__cancel__less,axiom,
% 161.83/161.92 ! [V_n_2,V_m_2,V_k_2] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
% 161.83/161.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_trans__less__add1,axiom,
% 161.83/161.92 ! [V_m,V_j,V_i] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_trans__less__add2,axiom,
% 161.83/161.92 ! [V_m,V_j,V_i] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_add__less__mono1,axiom,
% 161.83/161.92 ! [V_k,V_j,V_i] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_add__less__mono,axiom,
% 161.83/161.92 ! [V_l,V_k,V_j,V_i] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_less__add__eq__less,axiom,
% 161.83/161.92 ! [V_n,V_m,V_l,V_k] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 161.83/161.92 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_add__lessD1,axiom,
% 161.83/161.92 ! [V_k,V_j,V_i] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_diff__add__inverse2,axiom,
% 161.83/161.92 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ).
% 161.83/161.92
% 161.83/161.92 fof(fact_diff__add__inverse,axiom,
% 161.83/161.92 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ).
% 161.83/161.92
% 161.83/161.92 fof(fact_diff__diff__left,axiom,
% 161.83/161.92 ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_diff__cancel,axiom,
% 161.83/161.92 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_diff__cancel2,axiom,
% 161.83/161.92 ! [V_n,V_k,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_psubsetD,axiom,
% 161.83/161.92 ! [V_ca_2,V_B_2,V_A_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_not__psubset__empty,axiom,
% 161.83/161.92 ! [V_A_2,T_a] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_less__iff__Suc__add,axiom,
% 161.83/161.92 ! [V_n_2,V_m_2] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 161.83/161.92 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_less__add__Suc2,axiom,
% 161.83/161.92 ! [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)))) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_less__add__Suc1,axiom,
% 161.83/161.92 ! [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)))) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_less__diff__conv,axiom,
% 161.83/161.92 ! [V_k_2,V_j_2,V_i_2] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))
% 161.83/161.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_add__diff__inverse,axiom,
% 161.83/161.92 ! [V_n,V_m] :
% 161.83/161.92 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 161.83/161.92 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_Suc__eq__plus1,axiom,
% 161.83/161.92 ! [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)) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_Suc__eq__plus1__left,axiom,
% 161.83/161.92 ! [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) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_psubset__card__mono,axiom,
% 161.83/161.92 ! [V_A_2,V_B_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.92 => 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))) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_n__not__Suc__n,axiom,
% 161.83/161.92 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_Suc__n__not__n,axiom,
% 161.83/161.92 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 161.83/161.92
% 161.83/161.92 fof(fact_nat_Oinject,axiom,
% 161.83/161.92 ! [V_nat_H_2,V_nat_2] :
% 161.83/161.92 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 161.83/161.92 <=> V_nat_2 = V_nat_H_2 ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_Suc__inject,axiom,
% 161.83/161.92 ! [V_y,V_x] :
% 161.83/161.92 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 161.83/161.92 => V_x = V_y ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_less__not__refl,axiom,
% 161.83/161.92 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_nat__neq__iff,axiom,
% 161.83/161.92 ! [V_n_2,V_m_2] :
% 161.83/161.92 ( V_m_2 != V_n_2
% 161.83/161.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 161.83/161.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_linorder__neqE__nat,axiom,
% 161.83/161.92 ! [V_y,V_x] :
% 161.83/161.92 ( V_x != V_y
% 161.83/161.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_less__irrefl__nat,axiom,
% 161.83/161.92 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_less__not__refl2,axiom,
% 161.83/161.92 ! [V_m,V_n] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 161.83/161.92 => V_m != V_n ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_less__not__refl3,axiom,
% 161.83/161.92 ! [V_t,V_s] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 161.83/161.92 => V_s != V_t ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_nat__less__cases,axiom,
% 161.83/161.92 ! [V_P_2,V_n_2,V_m_2] :
% 161.83/161.92 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 161.83/161.92 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 161.83/161.92 => ( ( V_m_2 = V_n_2
% 161.83/161.92 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 161.83/161.92 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 161.83/161.92 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 161.83/161.92 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_diff__commute,axiom,
% 161.83/161.92 ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_card_Oinsert,axiom,
% 161.83/161.92 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.92 => 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)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_card_Oinsert__remove,axiom,
% 161.83/161.92 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.92 => 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)))))) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_not__less__eq,axiom,
% 161.83/161.92 ! [V_n_2,V_m_2] :
% 161.83/161.92 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 161.83/161.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_less__Suc__eq,axiom,
% 161.83/161.92 ! [V_n_2,V_m_2] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 161.83/161.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 161.83/161.92 | V_m_2 = V_n_2 ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_Suc__less__eq,axiom,
% 161.83/161.92 ! [V_n_2,V_m_2] :
% 161.83/161.92 ( 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)))
% 161.83/161.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_not__less__less__Suc__eq,axiom,
% 161.83/161.92 ! [V_m_2,V_n_2] :
% 161.83/161.92 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 161.83/161.92 <=> V_n_2 = V_m_2 ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_less__antisym,axiom,
% 161.83/161.92 ! [V_m,V_n] :
% 161.83/161.92 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 161.83/161.92 => V_m = V_n ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_less__SucI,axiom,
% 161.83/161.92 ! [V_n,V_m] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_Suc__lessI,axiom,
% 161.83/161.92 ! [V_n,V_m] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 161.83/161.92 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_less__trans__Suc,axiom,
% 161.83/161.92 ! [V_k,V_j,V_i] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_less__SucE,axiom,
% 161.83/161.92 ! [V_n,V_m] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 161.83/161.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 161.83/161.92 => V_m = V_n ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_less__add__one,axiom,
% 161.83/161.92 ! [V_a,T_a] :
% 161.83/161.92 ( class_Rings_Olinordered__semidom(T_a)
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_termination__basic__simps_I1_J,axiom,
% 161.83/161.92 ! [V_z,V_y,V_x] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_termination__basic__simps_I2_J,axiom,
% 161.83/161.92 ! [V_y,V_z,V_x] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_diff__add__cancel,axiom,
% 161.83/161.92 ! [V_b,V_a,T_a] :
% 161.83/161.92 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.92 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_add__diff__cancel,axiom,
% 161.83/161.92 ! [V_b,V_a,T_a] :
% 161.83/161.92 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.92 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_diff__eq__diff__less,axiom,
% 161.83/161.92 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 161.83/161.92 ( class_Groups_Oordered__ab__group__add(T_a)
% 161.83/161.92 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_ca_2),V_d_2)
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 161.83/161.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_add__less__cancel__right,axiom,
% 161.83/161.92 ! [V_b_2,V_ca_2,V_a_2,T_a] :
% 161.83/161.92 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 161.83/161.92 => ( 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)))
% 161.83/161.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_add__less__cancel__left,axiom,
% 161.83/161.92 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 161.83/161.92 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 161.83/161.92 => ( 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)))
% 161.83/161.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_add__strict__right__mono,axiom,
% 161.83/161.92 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.92 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_add__strict__left__mono,axiom,
% 161.83/161.92 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.92 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_add__strict__mono,axiom,
% 161.83/161.92 ! [V_d,V_c,V_b,V_a,T_a] :
% 161.83/161.92 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_psubset__trans,axiom,
% 161.83/161.92 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 161.83/161.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_linorder__neqE__linordered__idom,axiom,
% 161.83/161.92 ! [V_y,V_x,T_a] :
% 161.83/161.92 ( class_Rings_Olinordered__idom(T_a)
% 161.83/161.92 => ( V_x != V_y
% 161.83/161.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_add__right__imp__eq,axiom,
% 161.83/161.92 ! [V_c,V_a,V_b,T_a] :
% 161.83/161.92 ( class_Groups_Ocancel__semigroup__add(T_a)
% 161.83/161.92 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)
% 161.83/161.92 => V_b = V_c ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_add__imp__eq,axiom,
% 161.83/161.92 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.92 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 161.83/161.92 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
% 161.83/161.92 => V_b = V_c ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_add__left__imp__eq,axiom,
% 161.83/161.92 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.92 ( class_Groups_Ocancel__semigroup__add(T_a)
% 161.83/161.92 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
% 161.83/161.92 => V_b = V_c ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_add__right__cancel,axiom,
% 161.83/161.92 ! [V_ca_2,V_a_2,V_b_2,T_a] :
% 161.83/161.92 ( class_Groups_Ocancel__semigroup__add(T_a)
% 161.83/161.92 => ( 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)
% 161.83/161.92 <=> V_b_2 = V_ca_2 ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_add__left__cancel,axiom,
% 161.83/161.92 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 161.83/161.92 ( class_Groups_Ocancel__semigroup__add(T_a)
% 161.83/161.92 => ( 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)
% 161.83/161.92 <=> V_b_2 = V_ca_2 ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 161.83/161.92 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.92 ( class_Groups_Oab__semigroup__add(T_a)
% 161.83/161.92 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_diff__eq__diff__eq,axiom,
% 161.83/161.92 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 161.83/161.92 ( class_Groups_Oab__group__add(T_a)
% 161.83/161.92 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_ca_2),V_d_2)
% 161.83/161.92 => ( V_a_2 = V_b_2
% 161.83/161.92 <=> V_ca_2 = V_d_2 ) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_one__reorient,axiom,
% 161.83/161.92 ! [V_x_2,T_a] :
% 161.83/161.92 ( class_Groups_Oone(T_a)
% 161.83/161.92 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 161.83/161.92 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_add__less__imp__less__left,axiom,
% 161.83/161.92 ! [V_b,V_a,V_c,T_a] :
% 161.83/161.92 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_add__less__imp__less__right,axiom,
% 161.83/161.92 ! [V_b,V_c,V_a,T_a] :
% 161.83/161.92 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 161.83/161.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
% 161.83/161.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 161.83/161.92
% 161.83/161.92 fof(fact_ran__restrictD,axiom,
% 161.83/161.92 ! [V_A_2,V_m_2,T_b,V_y_2,T_a] :
% 161.83/161.93 ( 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))))
% 161.83/161.93 => ? [B_x] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 161.83/161.93 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_insert__fold1SetE,axiom,
% 161.83/161.93 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_a] :
% 161.83/161.93 ( 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))
% 161.83/161.93 => ~ ! [B_a,B_A] :
% 161.83/161.93 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A)
% 161.83/161.93 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_x_2))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_psubset__insert__iff,axiom,
% 161.83/161.93 ! [V_B_2,V_x_2,V_A_2,T_a] :
% 161.83/161.93 ( 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)))
% 161.83/161.93 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 161.83/161.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 161.83/161.93 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.93 => 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)) )
% 161.83/161.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_restrict__upd__same,axiom,
% 161.83/161.93 ! [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))))) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_restrict__complement__singleton__eq,axiom,
% 161.83/161.93 ! [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)) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_card__Diff1__le,axiom,
% 161.83/161.93 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_fold__graph__permute__diff,axiom,
% 161.83/161.93 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_a] :
% 161.83/161.93 ( class_Groups_Oab__semigroup__mult(T_a)
% 161.83/161.93 => ( 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))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 161.83/161.93 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 161.83/161.93 => 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)) ) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_card__Plus,axiom,
% 161.83/161.93 ! [V_B_2,T_b,V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 161.83/161.93 => 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)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_map__add__upd__left,axiom,
% 161.83/161.93 ! [V_u1_2,V_e1_2,V_e2_2,T_b,V_m_2,T_a] :
% 161.83/161.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_e2_2)))
% 161.83/161.93 => c_Map_Omap__add(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_e1_2),V_m_2),hAPP(c_Option_Ooption_OSome(T_b),V_u1_2)),V_e2_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__add(T_a,T_b,V_e1_2,V_e2_2)),V_m_2),hAPP(c_Option_Ooption_OSome(T_b),V_u1_2)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_finite__induct,axiom,
% 161.83/161.93 ! [V_P_2,V_F_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 161.83/161.93 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 161.83/161.93 => ( ! [B_x,B_F] :
% 161.83/161.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F))
% 161.83/161.93 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_F))
% 161.83/161.93 => ( hBOOL(hAPP(V_P_2,B_F))
% 161.83/161.93 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_x),B_F))) ) ) )
% 161.83/161.93 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_order__refl,axiom,
% 161.83/161.93 ! [V_x,T_a] :
% 161.83/161.93 ( class_Orderings_Opreorder(T_a)
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_equalityI,axiom,
% 161.83/161.93 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 161.83/161.93 => V_A_2 = V_B_2 ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_subsetD,axiom,
% 161.83/161.93 ! [V_ca_2,V_B_2,V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_empty__subsetI,axiom,
% 161.83/161.93 ! [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)) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_ComplI,axiom,
% 161.83/161.93 ! [V_A_2,V_ca_2,T_a] :
% 161.83/161.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 161.83/161.93 => 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))) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__imp__neg__le,axiom,
% 161.83/161.93 ! [V_b,V_a,T_a] :
% 161.83/161.93 ( class_Groups_Oordered__ab__group__add(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 161.83/161.93 => 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))) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_square__eq__iff,axiom,
% 161.83/161.93 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.93 ( class_Rings_Oidom(T_a)
% 161.83/161.93 => ( 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)
% 161.83/161.93 <=> ( V_a_2 = V_b_2
% 161.83/161.93 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 161.83/161.93 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.93 ( class_Groups_Oab__semigroup__mult(T_a)
% 161.83/161.93 => 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)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_neg__le__iff__le,axiom,
% 161.83/161.93 ! [V_a_2,V_b_2,T_a] :
% 161.83/161.93 ( class_Groups_Oordered__ab__group__add(T_a)
% 161.83/161.93 => ( 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)))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_minus__mult__minus,axiom,
% 161.83/161.93 ! [V_b,V_a,T_a] :
% 161.83/161.93 ( class_Rings_Oring(T_a)
% 161.83/161.93 => 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) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_neg__equal__iff__equal,axiom,
% 161.83/161.93 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.93 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.93 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
% 161.83/161.93 <=> V_a_2 = V_b_2 ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_minus__le__iff,axiom,
% 161.83/161.93 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.93 ( class_Groups_Oordered__ab__group__add(T_a)
% 161.83/161.93 => ( 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))
% 161.83/161.93 <=> 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)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_minus__equation__iff,axiom,
% 161.83/161.93 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.93 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.93 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_b_2
% 161.83/161.93 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) = V_a_2 ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_minus__mult__commute,axiom,
% 161.83/161.93 ! [V_b,V_a,T_a] :
% 161.83/161.93 ( class_Rings_Oring(T_a)
% 161.83/161.93 => 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)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__minus__iff,axiom,
% 161.83/161.93 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.93 ( class_Groups_Oordered__ab__group__add(T_a)
% 161.83/161.93 => ( 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)))
% 161.83/161.93 <=> 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))) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_equation__minus__iff,axiom,
% 161.83/161.93 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.93 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.93 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
% 161.83/161.93 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_minus__mult__left,axiom,
% 161.83/161.93 ! [V_b,V_a,T_a] :
% 161.83/161.93 ( class_Rings_Oring(T_a)
% 161.83/161.93 => 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) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_minus__mult__right,axiom,
% 161.83/161.93 ! [V_b,V_a,T_a] :
% 161.83/161.93 ( class_Rings_Oring(T_a)
% 161.83/161.93 => 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)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_minus__minus,axiom,
% 161.83/161.93 ! [V_a,T_a] :
% 161.83/161.93 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.93 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_square__eq__1__iff,axiom,
% 161.83/161.93 ! [V_x_2,T_a] :
% 161.83/161.93 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 161.83/161.93 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 161.83/161.93 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a)
% 161.83/161.93 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_map__add__assoc,axiom,
% 161.83/161.93 ! [V_m3_2,V_m2_2,V_m1_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m1_2,c_Map_Omap__add(T_a,T_b,V_m2_2,V_m3_2)) = c_Map_Omap__add(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2),V_m3_2) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_linorder__le__cases,axiom,
% 161.83/161.93 ! [V_y,V_x,T_a] :
% 161.83/161.93 ( class_Orderings_Olinorder(T_a)
% 161.83/161.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__funE,axiom,
% 161.83/161.93 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 161.83/161.93 ( class_Orderings_Oord(T_b)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 161.83/161.93 => 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))) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_equalityE,axiom,
% 161.83/161.93 ! [T_a,V_B_2,V_A_2] :
% 161.83/161.93 ( V_A_2 = V_B_2
% 161.83/161.93 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_xt1_I6_J,axiom,
% 161.83/161.93 ! [V_z,V_x,V_y,T_a] :
% 161.83/161.93 ( class_Orderings_Oorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_xt1_I5_J,axiom,
% 161.83/161.93 ! [V_x,V_y,T_a] :
% 161.83/161.93 ( class_Orderings_Oorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 161.83/161.93 => V_x = V_y ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_order__trans,axiom,
% 161.83/161.93 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.93 ( class_Orderings_Opreorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_order__antisym,axiom,
% 161.83/161.93 ! [V_y,V_x,T_a] :
% 161.83/161.93 ( class_Orderings_Oorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 161.83/161.93 => V_x = V_y ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_xt1_I4_J,axiom,
% 161.83/161.93 ! [V_c,V_a,V_b,T_a] :
% 161.83/161.93 ( class_Orderings_Oorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 161.83/161.93 => ( V_b = V_c
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_ord__le__eq__trans,axiom,
% 161.83/161.93 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.93 ( class_Orderings_Oord(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 161.83/161.93 => ( V_b = V_c
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_subset__trans,axiom,
% 161.83/161.93 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_xt1_I3_J,axiom,
% 161.83/161.93 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.93 ( class_Orderings_Oorder(T_a)
% 161.83/161.93 => ( V_a = V_b
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_ord__eq__le__trans,axiom,
% 161.83/161.93 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.93 ( class_Orderings_Oord(T_a)
% 161.83/161.93 => ( V_a = V_b
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_order__antisym__conv,axiom,
% 161.83/161.93 ! [V_x_2,V_y_2,T_a] :
% 161.83/161.93 ( class_Orderings_Oorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 161.83/161.93 <=> V_x_2 = V_y_2 ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__funD,axiom,
% 161.83/161.93 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 161.83/161.93 ( class_Orderings_Oord(T_b)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 161.83/161.93 => 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))) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_Compl__anti__mono,axiom,
% 161.83/161.93 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_order__eq__refl,axiom,
% 161.83/161.93 ! [V_y,V_x,T_a] :
% 161.83/161.93 ( class_Orderings_Opreorder(T_a)
% 161.83/161.93 => ( V_x = V_y
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_equalityD2,axiom,
% 161.83/161.93 ! [T_a,V_B_2,V_A_2] :
% 161.83/161.93 ( V_A_2 = V_B_2
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_equalityD1,axiom,
% 161.83/161.93 ! [T_a,V_B_2,V_A_2] :
% 161.83/161.93 ( V_A_2 = V_B_2
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_Compl__subset__Compl__iff,axiom,
% 161.83/161.93 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_Compl__eq__Compl__iff,axiom,
% 161.83/161.93 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.93 ( 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)
% 161.83/161.93 <=> V_A_2 = V_B_2 ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_order__eq__iff,axiom,
% 161.83/161.93 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.93 ( class_Orderings_Oorder(T_a)
% 161.83/161.93 => ( V_x_2 = V_y_2
% 161.83/161.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 161.83/161.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_set__eq__subset,axiom,
% 161.83/161.93 ! [T_a,V_B_2,V_A_2] :
% 161.83/161.93 ( V_A_2 = V_B_2
% 161.83/161.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_linorder__linear,axiom,
% 161.83/161.93 ! [V_y,V_x,T_a] :
% 161.83/161.93 ( class_Orderings_Olinorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 161.83/161.93 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__fun__def,axiom,
% 161.83/161.93 ! [V_g_2,V_f_2,T_a,T_b] :
% 161.83/161.93 ( class_Orderings_Oord(T_b)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 161.83/161.93 <=> ! [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))) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_double__complement,axiom,
% 161.83/161.93 ! [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 ).
% 161.83/161.93
% 161.83/161.93 fof(fact_subset__refl,axiom,
% 161.83/161.93 ! [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)) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_compl__mono,axiom,
% 161.83/161.93 ! [V_y,V_x,T_a] :
% 161.83/161.93 ( class_Lattices_Oboolean__algebra(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 161.83/161.93 => 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))) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_compl__le__compl__iff,axiom,
% 161.83/161.93 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.93 ( class_Lattices_Oboolean__algebra(T_a)
% 161.83/161.93 => ( 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)))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_compl__eq__compl__iff,axiom,
% 161.83/161.93 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.93 ( class_Lattices_Oboolean__algebra(T_a)
% 161.83/161.93 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)
% 161.83/161.93 <=> V_x_2 = V_y_2 ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_mult__left__idem,axiom,
% 161.83/161.93 ! [V_b,V_a,T_a] :
% 161.83/161.93 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 161.83/161.93 => 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) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_uminus__apply,axiom,
% 161.83/161.93 ! [V_x_2,V_A_2,T_b,T_a] :
% 161.83/161.93 ( class_Groups_Ouminus(T_a)
% 161.83/161.93 => 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)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_mult__idem,axiom,
% 161.83/161.93 ! [V_x,T_a] :
% 161.83/161.93 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 161.83/161.93 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_times_Oidem,axiom,
% 161.83/161.93 ! [V_a,T_a] :
% 161.83/161.93 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 161.83/161.93 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_double__compl,axiom,
% 161.83/161.93 ! [V_x,T_a] :
% 161.83/161.93 ( class_Lattices_Oboolean__algebra(T_a)
% 161.83/161.93 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_mult__le__mono,axiom,
% 161.83/161.93 ! [V_l,V_k,V_j,V_i] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 161.83/161.93 => 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))) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__antisym,axiom,
% 161.83/161.93 ! [V_n,V_m] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 161.83/161.93 => V_m = V_n ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__trans,axiom,
% 161.83/161.93 ! [V_k,V_j,V_i] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_mult__le__mono2,axiom,
% 161.83/161.93 ! [V_k,V_j,V_i] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 161.83/161.93 => 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))) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_mult__le__mono1,axiom,
% 161.83/161.93 ! [V_k,V_j,V_i] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 161.83/161.93 => 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))) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_eq__imp__le,axiom,
% 161.83/161.93 ! [V_n,V_m] :
% 161.83/161.93 ( V_m = V_n
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_nat__le__linear,axiom,
% 161.83/161.93 ! [V_n,V_m] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 161.83/161.93 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__cube,axiom,
% 161.83/161.93 ! [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)))) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__square,axiom,
% 161.83/161.93 ! [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))) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__refl,axiom,
% 161.83/161.93 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_subset__Compl__self__eq,axiom,
% 161.83/161.93 ! [V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
% 161.83/161.93 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_Suc__mult__le__cancel1,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2,V_k_2] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__add__iff1,axiom,
% 161.83/161.93 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 161.83/161.93 ( class_Rings_Oordered__ring(T_a)
% 161.83/161.93 => ( 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)))
% 161.83/161.93 <=> 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)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__add__iff2,axiom,
% 161.83/161.93 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 161.83/161.93 ( class_Rings_Oordered__ring(T_a)
% 161.83/161.93 => ( 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)))
% 161.83/161.93 <=> 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))) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_card__mono,axiom,
% 161.83/161.93 ! [V_A_2,V_B_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_card__seteq,axiom,
% 161.83/161.93 ! [V_A_2,V_B_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)))
% 161.83/161.93 => V_A_2 = V_B_2 ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_less__minus__iff,axiom,
% 161.83/161.93 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.93 ( class_Groups_Oordered__ab__group__add(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_minus__less__iff,axiom,
% 161.83/161.93 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.93 ( class_Groups_Oordered__ab__group__add(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_neg__less__iff__less,axiom,
% 161.83/161.93 ! [V_a_2,V_b_2,T_a] :
% 161.83/161.93 ( class_Groups_Oordered__ab__group__add(T_a)
% 161.83/161.93 => ( 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)))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_minus__add__distrib,axiom,
% 161.83/161.93 ! [V_b,V_a,T_a] :
% 161.83/161.93 ( class_Groups_Oab__group__add(T_a)
% 161.83/161.93 => 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)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_minus__add,axiom,
% 161.83/161.93 ! [V_b,V_a,T_a] :
% 161.83/161.93 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.93 => 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)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_add__minus__cancel,axiom,
% 161.83/161.93 ! [V_b,V_a,T_a] :
% 161.83/161.93 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.93 => 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 ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_minus__add__cancel,axiom,
% 161.83/161.93 ! [V_b,V_a,T_a] :
% 161.83/161.93 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.93 => 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 ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_ComplE,axiom,
% 161.83/161.93 ! [V_A_2,V_ca_2,T_a] :
% 161.83/161.93 ( 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)))
% 161.83/161.93 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_ComplD,axiom,
% 161.83/161.93 ! [V_A_2,V_ca_2,T_a] :
% 161.83/161.93 ( 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)))
% 161.83/161.93 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_Compl__iff,axiom,
% 161.83/161.93 ! [V_A_2,V_ca_2,T_a] :
% 161.83/161.93 ( 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)))
% 161.83/161.93 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_minus__diff__eq,axiom,
% 161.83/161.93 ! [V_b,V_a,T_a] :
% 161.83/161.93 ( class_Groups_Oab__group__add(T_a)
% 161.83/161.93 => 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) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_comm__semiring__class_Odistrib,axiom,
% 161.83/161.93 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.93 ( class_Rings_Ocomm__semiring(T_a)
% 161.83/161.93 => 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)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_combine__common__factor,axiom,
% 161.83/161.93 ! [V_c,V_b,V_e,V_a,T_a] :
% 161.83/161.93 ( class_Rings_Osemiring(T_a)
% 161.83/161.93 => 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) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_xt1_I8_J,axiom,
% 161.83/161.93 ! [V_z,V_x,V_y,T_a] :
% 161.83/161.93 ( class_Orderings_Oorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_order__le__less__trans,axiom,
% 161.83/161.93 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.93 ( class_Orderings_Opreorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_xt1_I7_J,axiom,
% 161.83/161.93 ! [V_z,V_x,V_y,T_a] :
% 161.83/161.93 ( class_Orderings_Oorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_order__less__le__trans,axiom,
% 161.83/161.93 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.93 ( class_Orderings_Opreorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_xt1_I11_J,axiom,
% 161.83/161.93 ! [V_a,V_b,T_a] :
% 161.83/161.93 ( class_Orderings_Oorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 161.83/161.93 => ( V_a != V_b
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_order__le__neq__trans,axiom,
% 161.83/161.93 ! [V_b,V_a,T_a] :
% 161.83/161.93 ( class_Orderings_Oorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 161.83/161.93 => ( V_a != V_b
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_order__le__imp__less__or__eq,axiom,
% 161.83/161.93 ! [V_y,V_x,T_a] :
% 161.83/161.93 ( class_Orderings_Oorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 161.83/161.93 | V_x = V_y ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_linorder__antisym__conv2,axiom,
% 161.83/161.93 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.93 ( class_Orderings_Olinorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 161.83/161.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 161.83/161.93 <=> V_x_2 = V_y_2 ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_order__less__imp__le,axiom,
% 161.83/161.93 ! [V_y,V_x,T_a] :
% 161.83/161.93 ( class_Orderings_Opreorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_leD,axiom,
% 161.83/161.93 ! [V_x,V_y,T_a] :
% 161.83/161.93 ( class_Orderings_Olinorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 161.83/161.93 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_xt1_I12_J,axiom,
% 161.83/161.93 ! [V_b,V_a,T_a] :
% 161.83/161.93 ( class_Orderings_Oorder(T_a)
% 161.83/161.93 => ( V_a != V_b
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_order__neq__le__trans,axiom,
% 161.83/161.93 ! [V_b,V_a,T_a] :
% 161.83/161.93 ( class_Orderings_Oorder(T_a)
% 161.83/161.93 => ( V_a != V_b
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_linorder__antisym__conv1,axiom,
% 161.83/161.93 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.93 ( class_Orderings_Olinorder(T_a)
% 161.83/161.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 161.83/161.93 <=> V_x_2 = V_y_2 ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_not__leE,axiom,
% 161.83/161.93 ! [V_x,V_y,T_a] :
% 161.83/161.93 ( class_Orderings_Olinorder(T_a)
% 161.83/161.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_leI,axiom,
% 161.83/161.93 ! [V_y,V_x,T_a] :
% 161.83/161.93 ( class_Orderings_Olinorder(T_a)
% 161.83/161.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_order__le__less,axiom,
% 161.83/161.93 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.93 ( class_Orderings_Oorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 161.83/161.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 161.83/161.93 | V_x_2 = V_y_2 ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_less__le__not__le,axiom,
% 161.83/161.93 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.93 ( class_Orderings_Opreorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 161.83/161.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 161.83/161.93 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_order__less__le,axiom,
% 161.83/161.93 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.93 ( class_Orderings_Oorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 161.83/161.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 161.83/161.93 & V_x_2 != V_y_2 ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_linorder__le__less__linear,axiom,
% 161.83/161.93 ! [V_y,V_x,T_a] :
% 161.83/161.93 ( class_Orderings_Olinorder(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 161.83/161.93 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_linorder__not__le,axiom,
% 161.83/161.93 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.93 ( class_Orderings_Olinorder(T_a)
% 161.83/161.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_linorder__not__less,axiom,
% 161.83/161.93 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.93 ( class_Orderings_Olinorder(T_a)
% 161.83/161.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_set__mp,axiom,
% 161.83/161.93 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_set__rev__mp,axiom,
% 161.83/161.93 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_in__mono,axiom,
% 161.83/161.93 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_add__le__cancel__right,axiom,
% 161.83/161.93 ! [V_b_2,V_ca_2,V_a_2,T_a] :
% 161.83/161.93 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 161.83/161.93 => ( 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)))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_add__le__cancel__left,axiom,
% 161.83/161.93 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 161.83/161.93 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 161.83/161.93 => ( 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)))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_add__right__mono,axiom,
% 161.83/161.93 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.93 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 161.83/161.93 => 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))) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_add__left__mono,axiom,
% 161.83/161.93 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.93 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 161.83/161.93 => 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))) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_add__mono,axiom,
% 161.83/161.93 ! [V_d,V_c,V_b,V_a,T_a] :
% 161.83/161.93 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 161.83/161.93 => 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))) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_add__le__imp__le__right,axiom,
% 161.83/161.93 ! [V_b,V_c,V_a,T_a] :
% 161.83/161.93 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 161.83/161.93 => ( 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)))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_add__le__imp__le__left,axiom,
% 161.83/161.93 ! [V_b,V_a,V_c,T_a] :
% 161.83/161.93 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 161.83/161.93 => ( 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)))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_mult__1__left,axiom,
% 161.83/161.93 ! [V_a,T_a] :
% 161.83/161.93 ( class_Groups_Omonoid__mult(T_a)
% 161.83/161.93 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_mult__1,axiom,
% 161.83/161.93 ! [V_a,T_a] :
% 161.83/161.93 ( class_Groups_Ocomm__monoid__mult(T_a)
% 161.83/161.93 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_mult__1__right,axiom,
% 161.83/161.93 ! [V_a,T_a] :
% 161.83/161.93 ( class_Groups_Omonoid__mult(T_a)
% 161.83/161.93 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_mult_Ocomm__neutral,axiom,
% 161.83/161.93 ! [V_a,T_a] :
% 161.83/161.93 ( class_Groups_Ocomm__monoid__mult(T_a)
% 161.83/161.93 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_bot__least,axiom,
% 161.83/161.93 ! [V_x,T_a] :
% 161.83/161.93 ( class_Orderings_Obot(T_a)
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_diff__eq__diff__less__eq,axiom,
% 161.83/161.93 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 161.83/161.93 ( class_Groups_Oordered__ab__group__add(T_a)
% 161.83/161.93 => ( 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)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_subset__empty,axiom,
% 161.83/161.93 ! [V_A_2,T_a] :
% 161.83/161.93 ( 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))))
% 161.83/161.93 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_Suc__mult__cancel1,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2,V_k_2] :
% 161.83/161.93 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)
% 161.83/161.93 <=> V_m_2 = V_n_2 ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_rev__finite__subset,axiom,
% 161.83/161.93 ! [V_A_2,V_B_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_finite__subset,axiom,
% 161.83/161.93 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 161.83/161.93 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_insert__mono,axiom,
% 161.83/161.93 ! [V_a_2,V_D_2,V_C_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))
% 161.83/161.93 => 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))) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_subset__insertI2,axiom,
% 161.83/161.93 ! [V_b_2,V_B_2,V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 => 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))) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_subset__insertI,axiom,
% 161.83/161.93 ! [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))) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_add__mult__distrib2,axiom,
% 161.83/161.93 ! [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)) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_add__mult__distrib,axiom,
% 161.83/161.93 ! [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)) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_Suc__n__not__le__n,axiom,
% 161.83/161.93 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_not__less__eq__eq,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2] :
% 161.83/161.93 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__Suc__eq,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 161.83/161.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 161.83/161.93 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_Suc__le__mono,axiom,
% 161.83/161.93 ! [V_m_2,V_n_2] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2)))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__SucI,axiom,
% 161.83/161.93 ! [V_n,V_m] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__SucE,axiom,
% 161.83/161.93 ! [V_n,V_m] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 161.83/161.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 161.83/161.93 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_Suc__leD,axiom,
% 161.83/161.93 ! [V_n,V_m] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_nat__less__le,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 161.83/161.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 161.83/161.93 & V_m_2 != V_n_2 ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__eq__less__or__eq,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 161.83/161.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 161.83/161.93 | V_m_2 = V_n_2 ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_less__imp__le__nat,axiom,
% 161.83/161.93 ! [V_n,V_m] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__neq__implies__less,axiom,
% 161.83/161.93 ! [V_n,V_m] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 161.83/161.93 => ( V_m != V_n
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_less__or__eq__imp__le,axiom,
% 161.83/161.93 ! [V_n,V_m] :
% 161.83/161.93 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 161.83/161.93 | V_m = V_n )
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_termination__basic__simps_I5_J,axiom,
% 161.83/161.93 ! [V_y,V_x] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__add2,axiom,
% 161.83/161.93 ! [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))) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__add1,axiom,
% 161.83/161.93 ! [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))) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__iff__add,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 161.83/161.93 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_nat__add__left__cancel__le,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2,V_k_2] :
% 161.83/161.93 ( 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)))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_trans__le__add1,axiom,
% 161.83/161.93 ! [V_m,V_j,V_i] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 161.83/161.93 => 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))) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_trans__le__add2,axiom,
% 161.83/161.93 ! [V_m,V_j,V_i] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 161.83/161.93 => 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))) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_add__le__mono1,axiom,
% 161.83/161.93 ! [V_k,V_j,V_i] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 161.83/161.93 => 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))) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_add__le__mono,axiom,
% 161.83/161.93 ! [V_l,V_k,V_j,V_i] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 161.83/161.93 => 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))) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_add__leD2,axiom,
% 161.83/161.93 ! [V_n,V_k,V_m] :
% 161.83/161.93 ( 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))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_add__leD1,axiom,
% 161.83/161.93 ! [V_n,V_k,V_m] :
% 161.83/161.93 ( 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))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_add__leE,axiom,
% 161.83/161.93 ! [V_n,V_k,V_m] :
% 161.83/161.93 ( 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))
% 161.83/161.93 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 161.83/161.93 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_termination__basic__simps_I3_J,axiom,
% 161.83/161.93 ! [V_z,V_y,V_x] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 161.83/161.93 => 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))) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_termination__basic__simps_I4_J,axiom,
% 161.83/161.93 ! [V_y,V_z,V_x] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 161.83/161.93 => 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))) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_diff__mult__distrib2,axiom,
% 161.83/161.93 ! [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)) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_diff__mult__distrib,axiom,
% 161.83/161.93 ! [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)) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_double__diff,axiom,
% 161.83/161.93 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 161.83/161.93 => 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 ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_Diff__mono,axiom,
% 161.83/161.93 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_D_2),V_B_2))
% 161.83/161.93 => 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))) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_Diff__subset,axiom,
% 161.83/161.93 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_diff__le__self,axiom,
% 161.83/161.93 ! [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)) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_diff__le__mono2,axiom,
% 161.83/161.93 ! [V_l,V_n,V_m] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 161.83/161.93 => 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))) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_diff__le__mono,axiom,
% 161.83/161.93 ! [V_l,V_n,V_m] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 161.83/161.93 => 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))) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_diff__diff__cancel,axiom,
% 161.83/161.93 ! [V_n,V_i] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 161.83/161.93 => 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 ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_eq__diff__iff,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2,V_k_2] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 161.83/161.93 => ( 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)
% 161.83/161.93 <=> V_m_2 = V_n_2 ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_Nat_Odiff__diff__eq,axiom,
% 161.83/161.93 ! [V_n,V_m,V_k] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 161.83/161.93 => 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) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__diff__iff,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2,V_k_2] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 161.83/161.93 => ( 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)))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_nat__mult__1,axiom,
% 161.83/161.93 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 161.83/161.93
% 161.83/161.93 fof(fact_nat__1__eq__mult__iff,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2] :
% 161.83/161.93 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 161.83/161.93 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 161.83/161.93 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_nat__mult__1__right,axiom,
% 161.83/161.93 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 161.83/161.93
% 161.83/161.93 fof(fact_nat__mult__eq__1__iff,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2] :
% 161.83/161.93 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 161.83/161.93 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 161.83/161.93 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_less__fun__def,axiom,
% 161.83/161.93 ! [V_g_2,V_f_2,T_a,T_b] :
% 161.83/161.93 ( class_Orderings_Oord(T_b)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 161.83/161.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 161.83/161.93 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_g_2),V_f_2)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_evaln__nonstrict,axiom,
% 161.83/161.93 ! [V_m,V_t,V_n,V_s,V_c] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 161.83/161.93 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_m),V_t)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_thin,axiom,
% 161.83/161.93 ! [V_G_2,V_ts_2,V_G_H_2,T_a] :
% 161.83/161.93 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2)
% 161.83/161.93 => ( 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))
% 161.83/161.93 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_weaken,axiom,
% 161.83/161.93 ! [V_ts_2,V_ts_H_2,V_G_2,T_a] :
% 161.83/161.93 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_H_2)
% 161.83/161.93 => ( 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))
% 161.83/161.93 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_asm,axiom,
% 161.83/161.93 ! [V_G_2,V_ts_2,T_a] :
% 161.83/161.93 ( 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))
% 161.83/161.93 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_subset__psubset__trans,axiom,
% 161.83/161.93 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_psubset__subset__trans,axiom,
% 161.83/161.93 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_psubset__imp__subset,axiom,
% 161.83/161.93 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_subset__iff__psubset__eq,axiom,
% 161.83/161.93 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 | V_A_2 = V_B_2 ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_psubset__eq,axiom,
% 161.83/161.93 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 & V_A_2 != V_B_2 ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_map__add__None,axiom,
% 161.83/161.93 ! [V_k_2,V_n_2,V_m_2,T_a,T_b] :
% 161.83/161.93 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_a)
% 161.83/161.93 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 161.83/161.93 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_a) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_map__add__find__right,axiom,
% 161.83/161.93 ! [V_m_2,T_b,V_xx_2,T_a,V_k_2,V_n_2] :
% 161.83/161.93 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2)
% 161.83/161.93 => hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_finite__Plus__iff,axiom,
% 161.83/161.93 ! [V_B_2,V_A_2,T_b,T_a] :
% 161.83/161.93 ( 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)))
% 161.83/161.93 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.93 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_finite__Plus,axiom,
% 161.83/161.93 ! [V_B_2,T_b,V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 161.83/161.93 => 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))) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_finite__PlusD_I1_J,axiom,
% 161.83/161.93 ! [V_B_2,V_A_2,T_b,T_a] :
% 161.83/161.93 ( 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)))
% 161.83/161.93 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_finite__PlusD_I2_J,axiom,
% 161.83/161.93 ! [V_B_2,V_A_2,T_b,T_a] :
% 161.83/161.93 ( 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)))
% 161.83/161.93 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_diff__minus__eq__add,axiom,
% 161.83/161.93 ! [V_b,V_a,T_a] :
% 161.83/161.93 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.93 => 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) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_ab__diff__minus,axiom,
% 161.83/161.93 ! [V_b,V_a,T_a] :
% 161.83/161.93 ( class_Groups_Oab__group__add(T_a)
% 161.83/161.93 => 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)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_diff__def,axiom,
% 161.83/161.93 ! [V_b,V_a,T_a] :
% 161.83/161.93 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.93 => 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)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_less__1__mult,axiom,
% 161.83/161.93 ! [V_n,V_m,T_a] :
% 161.83/161.93 ( class_Rings_Olinordered__semidom(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 161.83/161.93 => 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))) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_eq__add__iff1,axiom,
% 161.83/161.93 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 161.83/161.93 ( class_Rings_Oring(T_a)
% 161.83/161.93 => ( 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)
% 161.83/161.93 <=> 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 ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_eq__add__iff2,axiom,
% 161.83/161.93 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 161.83/161.93 ( class_Rings_Oring(T_a)
% 161.83/161.93 => ( 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)
% 161.83/161.93 <=> 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) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_add__le__less__mono,axiom,
% 161.83/161.93 ! [V_d,V_c,V_b,V_a,T_a] :
% 161.83/161.93 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 161.83/161.93 => 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))) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_add__less__le__mono,axiom,
% 161.83/161.93 ! [V_d,V_c,V_b,V_a,T_a] :
% 161.83/161.93 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 161.83/161.93 => 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))) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_insert__subset,axiom,
% 161.83/161.93 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 161.83/161.93 ( 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))
% 161.83/161.93 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 161.83/161.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_subset__insert,axiom,
% 161.83/161.93 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 161.83/161.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.93 => ( 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)))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_Suc__mult__less__cancel1,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2,V_k_2] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_subset__singletonD,axiom,
% 161.83/161.93 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.93 ( 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)))))
% 161.83/161.93 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.93 | 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))) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_mult__Suc,axiom,
% 161.83/161.93 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_mult__Suc__right,axiom,
% 161.83/161.93 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_Suc__le__lessD,axiom,
% 161.83/161.93 ! [V_n,V_m] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__less__Suc__eq,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 161.83/161.93 <=> V_n_2 = V_m_2 ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_Suc__leI,axiom,
% 161.83/161.93 ! [V_n,V_m] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__imp__less__Suc,axiom,
% 161.83/161.93 ! [V_n,V_m] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_Suc__le__eq,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_less__Suc__eq__le,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_less__eq__Suc__le,axiom,
% 161.83/161.93 ! [V_m_2,V_n_2] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_Suc__diff__le,axiom,
% 161.83/161.93 ! [V_m,V_n] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 161.83/161.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_diff__less__mono,axiom,
% 161.83/161.93 ! [V_c,V_b,V_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c))) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_less__diff__iff,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2,V_k_2] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_diff__add__assoc2,axiom,
% 161.83/161.93 ! [V_i,V_j,V_k] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 161.83/161.93 => 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) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_add__diff__assoc2,axiom,
% 161.83/161.93 ! [V_i,V_j,V_k] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 161.83/161.93 => 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) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_diff__add__assoc,axiom,
% 161.83/161.93 ! [V_i,V_j,V_k] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 161.83/161.93 => 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)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__imp__diff__is__add,axiom,
% 161.83/161.93 ! [V_k_2,V_j_2,V_i_2] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 161.83/161.93 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 161.83/161.93 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__add__diff__inverse2,axiom,
% 161.83/161.93 ! [V_m,V_n] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 161.83/161.93 => 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 ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__diff__conv2,axiom,
% 161.83/161.93 ! [V_i_2,V_j_2,V_k_2] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 161.83/161.93 => ( 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)))
% 161.83/161.93 <=> 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)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_add__diff__assoc,axiom,
% 161.83/161.93 ! [V_i,V_j,V_k] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 161.83/161.93 => 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) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__add__diff__inverse,axiom,
% 161.83/161.93 ! [V_m,V_n] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 161.83/161.93 => 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 ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__add__diff,axiom,
% 161.83/161.93 ! [V_m,V_n,V_k] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 161.83/161.93 => 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))) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_le__diff__conv,axiom,
% 161.83/161.93 ! [V_i_2,V_k_2,V_j_2] :
% 161.83/161.93 ( 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))
% 161.83/161.93 <=> 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))) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_diff__diff__right,axiom,
% 161.83/161.93 ! [V_i,V_j,V_k] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 161.83/161.93 => 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) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_map__add__dom__app__simps_I1_J,axiom,
% 161.83/161.93 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2)))
% 161.83/161.93 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_map__add__dom__app__simps_I3_J,axiom,
% 161.83/161.93 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] :
% 161.83/161.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2)))
% 161.83/161.93 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l1_2,V_m_2) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_map__add__dom__app__simps_I2_J,axiom,
% 161.83/161.93 ! [V_l2_2,V_l1_2,T_b,V_m_2,T_a] :
% 161.83/161.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l1_2)))
% 161.83/161.93 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_map__add__SomeD,axiom,
% 161.83/161.93 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] :
% 161.83/161.93 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 161.83/161.93 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 161.83/161.93 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 161.83/161.93 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_map__add__Some__iff,axiom,
% 161.83/161.93 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] :
% 161.83/161.93 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 161.83/161.93 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 161.83/161.93 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 161.83/161.93 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_map__add__upd,axiom,
% 161.83/161.93 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_f_2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_g_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__add(T_a,T_b,V_f_2,V_g_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 161.83/161.93 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 161.83/161.93 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 161.83/161.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 161.83/161.93 => 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) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_less__add__iff2,axiom,
% 161.83/161.93 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 161.83/161.93 ( class_Rings_Oordered__ring(T_a)
% 161.83/161.93 => ( 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)))
% 161.83/161.93 <=> 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))) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_less__add__iff1,axiom,
% 161.83/161.93 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 161.83/161.93 ( class_Rings_Oordered__ring(T_a)
% 161.83/161.93 => ( 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)))
% 161.83/161.93 <=> 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)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_card__insert__le,axiom,
% 161.83/161.93 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)))) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_diff__Suc__diff__eq1,axiom,
% 161.83/161.93 ! [V_m,V_j,V_k] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 161.83/161.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(c_Nat_OSuc,V_j)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_diff__Suc__diff__eq2,axiom,
% 161.83/161.93 ! [V_m,V_j,V_k] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 161.83/161.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))),V_m) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_j)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_fold__graph__insert__swap,axiom,
% 161.83/161.93 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_a] :
% 161.83/161.93 ( class_Groups_Oab__semigroup__mult(T_a)
% 161.83/161.93 => ( 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))
% 161.83/161.93 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 161.83/161.93 => 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))) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 161.83/161.93 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
% 161.83/161.93 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 161.83/161.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.93 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 161.83/161.93 => 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) ) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_diff__single__insert,axiom,
% 161.83/161.93 ! [V_B_2,V_x_2,V_A_2,T_a] :
% 161.83/161.93 ( 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))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.93 => 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))) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_subset__insert__iff,axiom,
% 161.83/161.93 ! [V_B_2,V_x_2,V_A_2,T_a] :
% 161.83/161.93 ( 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)))
% 161.83/161.93 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.93 => 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)) )
% 161.83/161.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_card__Diff__subset,axiom,
% 161.83/161.93 ! [V_A_2,V_B_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 161.83/161.93 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_diff__card__le__card__Diff,axiom,
% 161.83/161.93 ! [V_A_2,V_B_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_card__psubset,axiom,
% 161.83/161.93 ! [V_A_2,V_B_2,T_a] :
% 161.83/161.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)))
% 161.83/161.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_nat__less__add__iff1,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_nat__less__add__iff2,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_nat__le__add__iff1,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 161.83/161.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 161.83/161.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_nat__diff__add__eq1,axiom,
% 161.83/161.93 ! [V_n,V_m,V_u,V_i,V_j] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 161.83/161.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_u)),V_m)),V_n) ) ).
% 161.83/161.93
% 161.83/161.93 fof(fact_nat__eq__add__iff1,axiom,
% 161.83/161.93 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 161.83/161.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 161.83/161.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
% 161.83/161.94 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2) = V_n_2 ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_nat__le__add__iff2,axiom,
% 161.83/161.94 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_nat__diff__add__eq2,axiom,
% 161.83/161.94 ! [V_n,V_m,V_u,V_j,V_i] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 161.83/161.94 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i)),V_u)),V_n)) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_nat__eq__add__iff2,axiom,
% 161.83/161.94 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 161.83/161.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
% 161.83/161.94 <=> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 161.83/161.94 ! [V_x,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__ring__1(T_a)
% 161.83/161.94 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_x) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 161.83/161.94 ! [V_y,V_x,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__ring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_nat__mult__assoc,axiom,
% 161.83/161.94 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_nat__mult__commute,axiom,
% 161.83/161.94 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 161.83/161.94 ! [V_d,V_c,V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 161.83/161.94 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 161.83/161.94 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 161.83/161.94 ! [V_d,V_c,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 161.83/161.94 ! [V_d,V_c,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 161.83/161.94 ! [V_c,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 161.83/161.94 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 161.83/161.94 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 161.83/161.94 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 161.83/161.94 ! [V_rx,V_ly,V_lx,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 161.83/161.94 ! [V_rx,V_ly,V_lx,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 161.83/161.94 ! [V_ry,V_rx,V_lx,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 161.83/161.94 ! [V_ry,V_rx,V_lx,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_left__add__mult__distrib,axiom,
% 161.83/161.94 ! [V_k,V_j,V_u,V_i] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_crossproduct__eq,axiom,
% 161.83/161.94 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
% 161.83/161.94 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 161.83/161.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))
% 161.83/161.94 <=> ( V_w_2 = V_x_2
% 161.83/161.94 | V_y_2 = V_z_2 ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 161.83/161.94 ! [V_b,V_m,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 161.83/161.94 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_crossproduct__noteq,axiom,
% 161.83/161.94 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 161.83/161.94 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 161.83/161.94 => ( ( V_a_2 != V_b_2
% 161.83/161.94 & V_ca_2 != V_d_2 )
% 161.83/161.94 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 161.83/161.94 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 161.83/161.94 ! [V_a,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 161.83/161.94 ! [V_a,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 161.83/161.94 ! [V_m,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 161.83/161.94 ! [V_a,V_m,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 161.83/161.94 ! [V_m,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_Plus__eq__empty__conv,axiom,
% 161.83/161.94 ! [V_B_2,V_A_2,T_b,T_a] :
% 161.83/161.94 ( 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))
% 161.83/161.94 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.94 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_card__Plus__conv__if,axiom,
% 161.83/161.94 ! [V_B_2,T_b,V_A_2,T_a] :
% 161.83/161.94 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.94 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) )
% 161.83/161.94 => 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)) )
% 161.83/161.94 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.94 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) )
% 161.83/161.94 => 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) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_finite__subset__induct,axiom,
% 161.83/161.94 ! [V_P_2,V_A_2,V_F_2,T_a] :
% 161.83/161.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_A_2))
% 161.83/161.94 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 161.83/161.94 => ( ! [B_a,B_F] :
% 161.83/161.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 161.83/161.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_F))
% 161.83/161.94 => ( hBOOL(hAPP(V_P_2,B_F))
% 161.83/161.94 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_F))) ) ) ) )
% 161.83/161.94 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_fold1__insert,axiom,
% 161.83/161.94 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.94 ( class_Groups_Oab__semigroup__mult(T_a)
% 161.83/161.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.94 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)) ) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_convex__bound__lt,axiom,
% 161.83/161.94 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 161.83/161.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 161.83/161.94 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.94 => ( 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)
% 161.83/161.94 => 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)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_fun__upd__image,axiom,
% 161.83/161.94 ! [V_y_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 161.83/161.94 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.94 => 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)))))) )
% 161.83/161.94 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.94 => 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) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__eq__if,axiom,
% 161.83/161.94 ! [V_n,V_m] :
% 161.83/161.94 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 161.83/161.94 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__eq__if,axiom,
% 161.83/161.94 ! [V_n,V_m] :
% 161.83/161.94 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 161.83/161.94 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_image__eqI,axiom,
% 161.83/161.94 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_b_2] :
% 161.83/161.94 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_finite__imageI,axiom,
% 161.83/161.94 ! [V_h_2,T_b,V_F_2,T_a] :
% 161.83/161.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 161.83/161.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_F_2))) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_less__zeroE,axiom,
% 161.83/161.94 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_le0,axiom,
% 161.83/161.94 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_zero__less__Suc,axiom,
% 161.83/161.94 ! [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))) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_zero__reorient,axiom,
% 161.83/161.94 ! [V_x_2,T_a] :
% 161.83/161.94 ( class_Groups_Ozero(T_a)
% 161.83/161.94 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 161.83/161.94 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_bot__nat__def,axiom,
% 161.83/161.94 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_rev__image__eqI,axiom,
% 161.83/161.94 ! [T_b,V_f_2,V_b_2,V_A_2,V_x_2,T_a] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.94 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_imageI,axiom,
% 161.83/161.94 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.94 => 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))) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_image__iff,axiom,
% 161.83/161.94 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
% 161.83/161.94 <=> ? [B_x] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 161.83/161.94 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_image__is__empty,axiom,
% 161.83/161.94 ! [V_A_2,V_f_2,T_a,T_b] :
% 161.83/161.94 ( 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))
% 161.83/161.94 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_image__empty,axiom,
% 161.83/161.94 ! [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)) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_empty__is__image,axiom,
% 161.83/161.94 ! [V_A_2,V_f_2,T_b,T_a] :
% 161.83/161.94 ( 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)
% 161.83/161.94 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_image__insert,axiom,
% 161.83/161.94 ! [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)) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_image__mono,axiom,
% 161.83/161.94 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_subset__image__iff,axiom,
% 161.83/161.94 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] :
% 161.83/161.94 ( 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)))
% 161.83/161.94 <=> ? [B_AA] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_AA),V_A_2))
% 161.83/161.94 & V_B_2 = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),B_AA) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 161.83/161.94 ! [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) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 161.83/161.94 ! [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) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__0__left,axiom,
% 161.83/161.94 ! [V_a,T_a] :
% 161.83/161.94 ( class_Groups_Omonoid__add(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__0,axiom,
% 161.83/161.94 ! [V_a,T_a] :
% 161.83/161.94 ( class_Groups_Ocomm__monoid__add(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_double__zero__sym,axiom,
% 161.83/161.94 ! [V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Olinordered__ab__group__add(T_a)
% 161.83/161.94 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)
% 161.83/161.94 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__0__right,axiom,
% 161.83/161.94 ! [V_a,T_a] :
% 161.83/161.94 ( class_Groups_Omonoid__add(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add_Ocomm__neutral,axiom,
% 161.83/161.94 ! [V_a,T_a] :
% 161.83/161.94 ( class_Groups_Ocomm__monoid__add(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 161.83/161.94 ! [V_a,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 161.83/161.94 ! [V_a,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__0__iff,axiom,
% 161.83/161.94 ! [V_a_2,V_b_2,T_a] :
% 161.83/161.94 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 161.83/161.94 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)
% 161.83/161.94 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_divisors__zero,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Ono__zero__divisors(T_a)
% 161.83/161.94 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.94 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.94 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_no__zero__divisors,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Ono__zero__divisors(T_a)
% 161.83/161.94 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.94 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__eq__0__iff,axiom,
% 161.83/161.94 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.94 ( class_Rings_Oring__no__zero__divisors(T_a)
% 161.83/161.94 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.94 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.94 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__zero__right,axiom,
% 161.83/161.94 ! [V_a,T_a] :
% 161.83/161.94 ( class_Rings_Omult__zero(T_a)
% 161.83/161.94 => 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) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__zero__left,axiom,
% 161.83/161.94 ! [V_a,T_a] :
% 161.83/161.94 ( class_Rings_Omult__zero(T_a)
% 161.83/161.94 => 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) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 161.83/161.94 ! [V_a,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => 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) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 161.83/161.94 ! [V_a,T_a] :
% 161.83/161.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.94 => 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) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_diff__0__right,axiom,
% 161.83/161.94 ! [V_a,T_a] :
% 161.83/161.94 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_diff__self,axiom,
% 161.83/161.94 ! [V_a,T_a] :
% 161.83/161.94 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.94 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_eq__iff__diff__eq__0,axiom,
% 161.83/161.94 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Oab__group__add(T_a)
% 161.83/161.94 => ( V_a_2 = V_b_2
% 161.83/161.94 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_right__minus__eq,axiom,
% 161.83/161.94 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.94 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.94 <=> V_a_2 = V_b_2 ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_one__neq__zero,axiom,
% 161.83/161.94 ! [T_a] :
% 161.83/161.94 ( class_Rings_Ozero__neq__one(T_a)
% 161.83/161.94 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_zero__neq__one,axiom,
% 161.83/161.94 ! [T_a] :
% 161.83/161.94 ( class_Rings_Ozero__neq__one(T_a)
% 161.83/161.94 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_neg__equal__zero,axiom,
% 161.83/161.94 ! [V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Olinordered__ab__group__add(T_a)
% 161.83/161.94 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_a_2
% 161.83/161.94 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_neg__equal__0__iff__equal,axiom,
% 161.83/161.94 ! [V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.94 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.94 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_equal__neg__zero,axiom,
% 161.83/161.94 ! [V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Olinordered__ab__group__add(T_a)
% 161.83/161.94 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)
% 161.83/161.94 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_neg__0__equal__iff__equal,axiom,
% 161.83/161.94 ! [V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.94 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)
% 161.83/161.94 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_minus__zero,axiom,
% 161.83/161.94 ! [T_a] :
% 161.83/161.94 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.94 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_Zero__not__Suc,axiom,
% 161.83/161.94 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_nat_Osimps_I2_J,axiom,
% 161.83/161.94 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_Suc__not__Zero,axiom,
% 161.83/161.94 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_nat_Osimps_I3_J,axiom,
% 161.83/161.94 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_Zero__neq__Suc,axiom,
% 161.83/161.94 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_Suc__neq__Zero,axiom,
% 161.83/161.94 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_not__less0,axiom,
% 161.83/161.94 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_neq0__conv,axiom,
% 161.83/161.94 ! [V_n_2] :
% 161.83/161.94 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_less__nat__zero__code,axiom,
% 161.83/161.94 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_gr__implies__not0,axiom,
% 161.83/161.94 ! [V_n,V_m] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 161.83/161.94 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_gr0I,axiom,
% 161.83/161.94 ! [V_n] :
% 161.83/161.94 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_plus__nat_Oadd__0,axiom,
% 161.83/161.94 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 161.83/161.94
% 161.83/161.94 fof(fact_Nat_Oadd__0__right,axiom,
% 161.83/161.94 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__is__0,axiom,
% 161.83/161.94 ! [V_n_2,V_m_2] :
% 161.83/161.94 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.94 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.94 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__eq__self__zero,axiom,
% 161.83/161.94 ! [V_n,V_m] :
% 161.83/161.94 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 161.83/161.94 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_le__0__eq,axiom,
% 161.83/161.94 ! [V_n_2] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 161.83/161.94 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 161.83/161.94 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_diff__0__eq__0,axiom,
% 161.83/161.94 ! [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) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_minus__nat_Odiff__0,axiom,
% 161.83/161.94 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 161.83/161.94
% 161.83/161.94 fof(fact_diff__self__eq__0,axiom,
% 161.83/161.94 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_diffs0__imp__equal,axiom,
% 161.83/161.94 ! [V_n,V_m] :
% 161.83/161.94 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.94 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.94 => V_m = V_n ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__0,axiom,
% 161.83/161.94 ! [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) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__0__right,axiom,
% 161.83/161.94 ! [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) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__is__0,axiom,
% 161.83/161.94 ! [V_n_2,V_m_2] :
% 161.83/161.94 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.94 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.94 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__cancel1,axiom,
% 161.83/161.94 ! [V_n_2,V_m_2,V_k_2] :
% 161.83/161.94 ( 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)
% 161.83/161.94 <=> ( V_m_2 = V_n_2
% 161.83/161.94 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__cancel2,axiom,
% 161.83/161.94 ! [V_n_2,V_k_2,V_m_2] :
% 161.83/161.94 ( 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)
% 161.83/161.94 <=> ( V_m_2 = V_n_2
% 161.83/161.94 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 161.83/161.94 ! [V_n_2,V_m_2,V_k_2] :
% 161.83/161.94 ( 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)
% 161.83/161.94 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.94 | V_m_2 = V_n_2 ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_insert__image,axiom,
% 161.83/161.94 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.94 => 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) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_finite__surj,axiom,
% 161.83/161.94 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] :
% 161.83/161.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.94 => ( 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)))
% 161.83/161.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_image__diff__subset,axiom,
% 161.83/161.94 ! [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)))) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__nonpos__nonpos,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => 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))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__increasing2,axiom,
% 161.83/161.94 ! [V_a,V_b,V_c,T_a] :
% 161.83/161.94 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 161.83/161.94 => 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))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__increasing,axiom,
% 161.83/161.94 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.94 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 161.83/161.94 => 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))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__nonneg__eq__0__iff,axiom,
% 161.83/161.94 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.94 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x_2))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y_2))
% 161.83/161.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.94 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.94 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__nonneg__nonneg,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 161.83/161.94 ! [V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Olinordered__ab__group__add(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 161.83/161.94 ! [V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Olinordered__ab__group__add(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)))
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_split__mult__neg__le,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Oordered__cancel__semiring(T_a)
% 161.83/161.94 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 161.83/161.94 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 161.83/161.94 => 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))) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_split__mult__pos__le,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Oordered__ring(T_a)
% 161.83/161.94 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 161.83/161.94 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 161.83/161.94 => 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))) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__mono,axiom,
% 161.83/161.94 ! [V_d,V_c,V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Oordered__semiring(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__mono_H,axiom,
% 161.83/161.94 ! [V_d,V_c,V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Oordered__semiring(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__left__mono__neg,axiom,
% 161.83/161.94 ! [V_c,V_a,V_b,T_a] :
% 161.83/161.94 ( class_Rings_Oordered__ring(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__right__mono__neg,axiom,
% 161.83/161.94 ! [V_c,V_a,V_b,T_a] :
% 161.83/161.94 ( class_Rings_Oordered__ring(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__mult__left__mono,axiom,
% 161.83/161.94 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Oordered__comm__semiring(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__left__mono,axiom,
% 161.83/161.94 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Oordered__semiring(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__right__mono,axiom,
% 161.83/161.94 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Oordered__semiring(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__nonpos__nonpos,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Oordered__ring(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => 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))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__nonpos__nonneg,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Oordered__cancel__semiring(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 161.83/161.94 => 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))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__nonneg__nonpos2,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Oordered__cancel__semiring(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => 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))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__nonneg__nonpos,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Oordered__cancel__semiring(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => 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))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__nonneg__nonneg,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Oordered__cancel__semiring(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 161.83/161.94 => 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))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__le__0__iff,axiom,
% 161.83/161.94 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__ring__strict(T_a)
% 161.83/161.94 => ( 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)))
% 161.83/161.94 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 161.83/161.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 161.83/161.94 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_zero__le__mult__iff,axiom,
% 161.83/161.94 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__ring__strict(T_a)
% 161.83/161.94 => ( 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)))
% 161.83/161.94 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 161.83/161.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 161.83/161.94 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_zero__le__square,axiom,
% 161.83/161.94 ! [V_a,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__ring(T_a)
% 161.83/161.94 => 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))) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__neg__neg,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_pos__add__strict,axiom,
% 161.83/161.94 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semidom(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__pos__pos,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 161.83/161.94 ! [V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Olinordered__ab__group__add(T_a)
% 161.83/161.94 => ( 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)))
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 161.83/161.94 ! [V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Olinordered__ab__group__add(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)))
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_not__square__less__zero,axiom,
% 161.83/161.94 ! [V_a,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__ring(T_a)
% 161.83/161.94 => ~ 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))) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__less__cancel__right__disj,axiom,
% 161.83/161.94 ! [V_b_2,V_ca_2,V_a_2,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__ring__strict(T_a)
% 161.83/161.94 => ( 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)))
% 161.83/161.94 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 161.83/161.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) )
% 161.83/161.94 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__less__cancel__left__disj,axiom,
% 161.83/161.94 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__ring__strict(T_a)
% 161.83/161.94 => ( 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)))
% 161.83/161.94 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 161.83/161.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) )
% 161.83/161.94 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__less__cancel__left__pos,axiom,
% 161.83/161.94 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__ring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 161.83/161.94 => ( 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)))
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__pos__pos,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semiring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 161.83/161.94 => 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))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__pos__neg,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semiring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => 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))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__pos__neg2,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semiring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => 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))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_zero__less__mult__pos,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semiring__strict(T_a)
% 161.83/161.94 => ( 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)))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_zero__less__mult__pos2,axiom,
% 161.83/161.94 ! [V_a,V_b,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semiring__strict(T_a)
% 161.83/161.94 => ( 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)))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__less__cancel__left__neg,axiom,
% 161.83/161.94 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__ring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => ( 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)))
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__neg__pos,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semiring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 161.83/161.94 => 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))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__neg__neg,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__ring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => 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))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__strict__right__mono,axiom,
% 161.83/161.94 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semiring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__strict__left__mono,axiom,
% 161.83/161.94 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semiring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_comm__mult__strict__left__mono,axiom,
% 161.83/161.94 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__strict__right__mono__neg,axiom,
% 161.83/161.94 ! [V_c,V_a,V_b,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__ring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__strict__left__mono__neg,axiom,
% 161.83/161.94 ! [V_c,V_a,V_b,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__ring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_le__iff__diff__le__0,axiom,
% 161.83/161.94 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Oordered__ab__group__add(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 161.83/161.94 <=> 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))) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_less__iff__diff__less__0,axiom,
% 161.83/161.94 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Oordered__ab__group__add(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 161.83/161.94 <=> 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))) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_sum__squares__eq__zero__iff,axiom,
% 161.83/161.94 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__ring__strict(T_a)
% 161.83/161.94 => ( 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)
% 161.83/161.94 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.94 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__scale__eq__noteq,axiom,
% 161.83/161.94 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 161.83/161.94 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 161.83/161.94 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.94 => ( ( V_a = V_b
% 161.83/161.94 & V_c != V_d )
% 161.83/161.94 => 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)) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_zero__le__one,axiom,
% 161.83/161.94 ! [T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semidom(T_a)
% 161.83/161.94 => 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))) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_not__one__le__zero,axiom,
% 161.83/161.94 ! [T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semidom(T_a)
% 161.83/161.94 => ~ 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))) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_not__one__less__zero,axiom,
% 161.83/161.94 ! [T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semidom(T_a)
% 161.83/161.94 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_zero__less__one,axiom,
% 161.83/161.94 ! [T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semidom(T_a)
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_minus__le__self__iff,axiom,
% 161.83/161.94 ! [V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Olinordered__ab__group__add(T_a)
% 161.83/161.94 => ( 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))
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_neg__le__0__iff__le,axiom,
% 161.83/161.94 ! [V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Oordered__ab__group__add(T_a)
% 161.83/161.94 => ( 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)))
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_le__minus__self__iff,axiom,
% 161.83/161.94 ! [V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Olinordered__ab__group__add(T_a)
% 161.83/161.94 => ( 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)))
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_neg__0__le__iff__le,axiom,
% 161.83/161.94 ! [V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Oordered__ab__group__add(T_a)
% 161.83/161.94 => ( 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)))
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_neg__less__nonneg,axiom,
% 161.83/161.94 ! [V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Olinordered__ab__group__add(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2))
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_neg__less__0__iff__less,axiom,
% 161.83/161.94 ! [V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Oordered__ab__group__add(T_a)
% 161.83/161.94 => ( 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)))
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_less__minus__self__iff,axiom,
% 161.83/161.94 ! [V_a_2,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__idom(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_neg__0__less__iff__less,axiom,
% 161.83/161.94 ! [V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Oordered__ab__group__add(T_a)
% 161.83/161.94 => ( 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)))
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_minus__unique,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.94 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_ab__left__minus,axiom,
% 161.83/161.94 ! [V_a,T_a] :
% 161.83/161.94 ( class_Groups_Oab__group__add(T_a)
% 161.83/161.94 => 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) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_left__minus,axiom,
% 161.83/161.94 ! [V_a,T_a] :
% 161.83/161.94 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.94 => 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) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 161.83/161.94 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.94 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.94 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
% 161.83/161.94 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_right__minus,axiom,
% 161.83/161.94 ! [V_a,T_a] :
% 161.83/161.94 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.94 => 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) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_diff__0,axiom,
% 161.83/161.94 ! [V_a,T_a] :
% 161.83/161.94 ( class_Groups_Ogroup__add(T_a)
% 161.83/161.94 => 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) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_less__Suc__eq__0__disj,axiom,
% 161.83/161.94 ! [V_n_2,V_m_2] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 161.83/161.94 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.94 | ? [B_j] :
% 161.83/161.94 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 161.83/161.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_less__Suc0,axiom,
% 161.83/161.94 ! [V_n_2] :
% 161.83/161.94 ( 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))))
% 161.83/161.94 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_gr0__conv__Suc,axiom,
% 161.83/161.94 ! [V_n_2] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 161.83/161.94 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__is__1,axiom,
% 161.83/161.94 ! [V_n_2,V_m_2] :
% 161.83/161.94 ( 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))
% 161.83/161.94 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 161.83/161.94 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 161.83/161.94 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.94 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_one__is__add,axiom,
% 161.83/161.94 ! [V_n_2,V_m_2] :
% 161.83/161.94 ( 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)
% 161.83/161.94 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 161.83/161.94 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 161.83/161.94 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.94 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__gr__0,axiom,
% 161.83/161.94 ! [V_n_2,V_m_2] :
% 161.83/161.94 ( 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)))
% 161.83/161.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 161.83/161.94 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_card_Oempty,axiom,
% 161.83/161.94 ! [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) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_card__infinite,axiom,
% 161.83/161.94 ! [V_A_2,T_a] :
% 161.83/161.94 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.94 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__eq__1__iff,axiom,
% 161.83/161.94 ! [V_n_2,V_m_2] :
% 161.83/161.94 ( 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))
% 161.83/161.94 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 161.83/161.94 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_zero__less__diff,axiom,
% 161.83/161.94 ! [V_m_2,V_n_2] :
% 161.83/161.94 ( 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)))
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_diff__less,axiom,
% 161.83/161.94 ! [V_m,V_n] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 161.83/161.94 => 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)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__less__mono2,axiom,
% 161.83/161.94 ! [V_k,V_j,V_i] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 161.83/161.94 => 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))) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__less__mono1,axiom,
% 161.83/161.94 ! [V_k,V_j,V_i] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 161.83/161.94 => 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))) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__less__cancel2,axiom,
% 161.83/161.94 ! [V_n_2,V_k_2,V_m_2] :
% 161.83/161.94 ( 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)))
% 161.83/161.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 161.83/161.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__less__cancel1,axiom,
% 161.83/161.94 ! [V_n_2,V_m_2,V_k_2] :
% 161.83/161.94 ( 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)))
% 161.83/161.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 161.83/161.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_nat__0__less__mult__iff,axiom,
% 161.83/161.94 ! [V_n_2,V_m_2] :
% 161.83/161.94 ( 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)))
% 161.83/161.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 161.83/161.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_nat__mult__less__cancel1,axiom,
% 161.83/161.94 ! [V_n_2,V_m_2,V_k_2] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 161.83/161.94 => ( 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)))
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_nat__mult__eq__cancel1,axiom,
% 161.83/161.94 ! [V_n_2,V_m_2,V_k_2] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 161.83/161.94 => ( 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)
% 161.83/161.94 <=> V_m_2 = V_n_2 ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_diff__add__0,axiom,
% 161.83/161.94 ! [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) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_fold1__singleton__def,axiom,
% 161.83/161.94 ! [V_a_2,V_f_2,T_a,V_g_2] :
% 161.83/161.94 ( V_g_2 = c_Finite__Set_Ofold1(T_a,V_f_2)
% 161.83/161.94 => hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_fold1__singleton,axiom,
% 161.83/161.94 ! [V_a_2,V_f_2,T_a] : hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ).
% 161.83/161.94
% 161.83/161.94 fof(fact_diff__is__0__eq_H,axiom,
% 161.83/161.94 ! [V_n,V_m] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 161.83/161.94 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_diff__is__0__eq,axiom,
% 161.83/161.94 ! [V_n_2,V_m_2] :
% 161.83/161.94 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_One__nat__def,axiom,
% 161.83/161.94 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__eq__self__implies__10,axiom,
% 161.83/161.94 ! [V_n,V_m] :
% 161.83/161.94 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 161.83/161.94 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 161.83/161.94 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_folding__one_Oeq__fold,axiom,
% 161.83/161.94 ! [V_A_2,V_F_2,V_f_2,T_a] :
% 161.83/161.94 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 161.83/161.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.94 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_card__image__le,axiom,
% 161.83/161.94 ! [V_f_2,T_b,V_A_2,T_a] :
% 161.83/161.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.94 => 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))) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_image__map__upd,axiom,
% 161.83/161.94 ! [V_y_2,V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 161.83/161.94 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.94 => 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) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__nonpos__neg,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__neg__nonpos,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__strict__increasing2,axiom,
% 161.83/161.94 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.94 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__strict__increasing,axiom,
% 161.83/161.94 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.94 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__nonneg__pos,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_add__pos__nonneg,axiom,
% 161.83/161.94 ! [V_b,V_a,T_a] :
% 161.83/161.94 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__left__le__imp__le,axiom,
% 161.83/161.94 ! [V_b,V_a,V_c,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semiring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__right__le__imp__le,axiom,
% 161.83/161.94 ! [V_b,V_c,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semiring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__less__imp__less__left,axiom,
% 161.83/161.94 ! [V_b,V_a,V_c,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semiring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__left__less__imp__less,axiom,
% 161.83/161.94 ! [V_b,V_a,V_c,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semiring(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__less__imp__less__right,axiom,
% 161.83/161.94 ! [V_b,V_c,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semiring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__right__less__imp__less,axiom,
% 161.83/161.94 ! [V_b,V_c,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semiring(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__le__less__imp__less,axiom,
% 161.83/161.94 ! [V_d,V_c,V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semiring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__less__le__imp__less,axiom,
% 161.83/161.94 ! [V_d,V_c,V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semiring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__strict__mono_H,axiom,
% 161.83/161.94 ! [V_d,V_c,V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semiring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__strict__mono,axiom,
% 161.83/161.94 ! [V_d,V_c,V_b,V_a,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semiring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__le__cancel__left__neg,axiom,
% 161.83/161.94 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__ring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.94 => ( 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)))
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__le__cancel__left__pos,axiom,
% 161.83/161.94 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__ring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 161.83/161.94 => ( 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)))
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_sum__squares__le__zero__iff,axiom,
% 161.83/161.94 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__ring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_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)))
% 161.83/161.94 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.94 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_sum__squares__ge__zero,axiom,
% 161.83/161.94 ! [V_y,V_x,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__ring(T_a)
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_not__sum__squares__lt__zero,axiom,
% 161.83/161.94 ! [V_y,V_x,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__ring(T_a)
% 161.83/161.94 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_sum__squares__gt__zero__iff,axiom,
% 161.83/161.94 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__ring__strict(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),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))))
% 161.83/161.94 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.94 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__right__le__one__le,axiom,
% 161.83/161.94 ! [V_y,V_x,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__idom(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)) ) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__left__le__one__le,axiom,
% 161.83/161.94 ! [V_y,V_x,T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__idom(T_a)
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)) ) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_zero__less__two,axiom,
% 161.83/161.94 ! [T_a] :
% 161.83/161.94 ( class_Rings_Olinordered__semidom(T_a)
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_card__eq__0__iff,axiom,
% 161.83/161.94 ! [V_A_2,T_a] :
% 161.83/161.94 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.94 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.94 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_card__ge__0__finite,axiom,
% 161.83/161.94 ! [V_A_2,T_a] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)))
% 161.83/161.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_Suc__pred,axiom,
% 161.83/161.94 ! [V_n] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 161.83/161.94 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_diff__Suc__less,axiom,
% 161.83/161.94 ! [V_i,V_n] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_i))),V_n)) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_one__less__mult,axiom,
% 161.83/161.94 ! [V_m,V_n] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_n__less__n__mult__m,axiom,
% 161.83/161.94 ! [V_m,V_n] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_n__less__m__mult__n,axiom,
% 161.83/161.94 ! [V_m,V_n] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_nat__diff__split__asm,axiom,
% 161.83/161.94 ! [V_b_2,V_a_2,V_P_2] :
% 161.83/161.94 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 161.83/161.94 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 161.83/161.94 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 161.83/161.94 | ? [B_d] :
% 161.83/161.94 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 161.83/161.94 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_nat__diff__split,axiom,
% 161.83/161.94 ! [V_b_2,V_a_2,V_P_2] :
% 161.83/161.94 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 161.83/161.94 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 161.83/161.94 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 161.83/161.94 & ! [B_d] :
% 161.83/161.94 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 161.83/161.94 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_one__le__mult__iff,axiom,
% 161.83/161.94 ! [V_n_2,V_m_2] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))
% 161.83/161.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2))
% 161.83/161.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__le__cancel2,axiom,
% 161.83/161.94 ! [V_n_2,V_k_2,V_m_2] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
% 161.83/161.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_mult__le__cancel1,axiom,
% 161.83/161.94 ! [V_n_2,V_m_2,V_k_2] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 161.83/161.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 161.83/161.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_nat__mult__le__cancel1,axiom,
% 161.83/161.94 ! [V_n_2,V_m_2,V_k_2] :
% 161.83/161.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 161.83/161.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 161.83/161.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_Body__triple__valid__0,axiom,
% 161.83/161.94 ! [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)) ).
% 161.83/161.94
% 161.83/161.94 fof(fact_convex__bound__le,axiom,
% 161.83/161.94 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 161.83/161.95 ( class_Rings_Olinordered__semiring__1(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 161.83/161.95 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_card__gt__0__iff,axiom,
% 161.83/161.95 ! [V_A_2,T_a] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)))
% 161.83/161.95 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.95 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_fold1__insert__idem,axiom,
% 161.83/161.95 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.95 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 161.83/161.95 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.95 => 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)) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Suc__diff__1,axiom,
% 161.83/161.95 ! [V_n] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 161.83/161.95 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Suc__pred_H,axiom,
% 161.83/161.95 ! [V_n] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 161.83/161.95 => V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_triple_Osize_I1_J,axiom,
% 161.83/161.95 ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_a] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_a,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_even__less__0__iff,axiom,
% 161.83/161.95 ! [V_a_2,T_a] :
% 161.83/161.95 ( class_Rings_Olinordered__idom(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_triple_Osize_I2_J,axiom,
% 161.83/161.95 ! [V_fun2_2,V_com_2,V_fun1_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_fold1__in,axiom,
% 161.83/161.95 ! [V_A_2,T_a] :
% 161.83/161.95 ( class_Groups_Oab__semigroup__mult(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.95 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.95 => ( ! [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))))))
% 161.83/161.95 => 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)) ) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_card__Suc__eq,axiom,
% 161.83/161.95 ! [V_k_2,V_A_2,T_a] :
% 161.83/161.95 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 161.83/161.95 <=> ? [B_b,B_B] :
% 161.83/161.95 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_b),B_B)
% 161.83/161.95 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_b),B_B))
% 161.83/161.95 & hAPP(c_Finite__Set_Ocard(T_a),B_B) = V_k_2
% 161.83/161.95 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.95 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_option_Osize_I2_J,axiom,
% 161.83/161.95 ! [V_a_2,V_fa_2,T_a] : c_Option_Ooption_Ooption__size(T_a,V_fa_2,hAPP(c_Option_Ooption_OSome(T_a),V_a_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 161.83/161.95 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a] :
% 161.83/161.95 ( 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))
% 161.83/161.95 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.95 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 161.83/161.95 | ? [B_x,B_y] :
% 161.83/161.95 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 161.83/161.95 & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a2_2))
% 161.83/161.95 & 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) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osize_I4_J,axiom,
% 161.83/161.95 ! [V_com2,V_com1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1)),c_Com_Ocom_Ocom__size(V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_double__eq__0__iff,axiom,
% 161.83/161.95 ! [V_a_2,T_a] :
% 161.83/161.95 ( class_Groups_Olinordered__ab__group__add(T_a)
% 161.83/161.95 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.95 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_option_Osize_I1_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osize_I7_J,axiom,
% 161.83/161.95 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osize_I8_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osize_I1_J,axiom,
% 161.83/161.95 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_nat_Osize_I2_J,axiom,
% 161.83/161.95 ! [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))) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_nat_Osize_I4_J,axiom,
% 161.83/161.95 ! [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))) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_option_Osize_I4_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_option_Osize_I3_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Ints__odd__less__0,axiom,
% 161.83/161.95 ! [V_a_2,T_a] :
% 161.83/161.95 ( class_Rings_Olinordered__idom(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 161.83/161.95 => ( 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)))
% 161.83/161.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osize_I12_J,axiom,
% 161.83/161.95 ! [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))) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_hom__fold1__commute,axiom,
% 161.83/161.95 ! [V_N_2,V_h_2,T_a] :
% 161.83/161.95 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 161.83/161.95 => ( ! [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))
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 161.83/161.95 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.95 => 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)) ) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_ex__least__nat__less,axiom,
% 161.83/161.95 ! [V_n_2,V_P_2] :
% 161.83/161.95 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 161.83/161.95 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 161.83/161.95 => ? [B_k] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 161.83/161.95 & ! [B_i] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 161.83/161.95 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 161.83/161.95 & 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)))) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_nat__size,axiom,
% 161.83/161.95 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Ints__0,axiom,
% 161.83/161.95 ! [T_a] :
% 161.83/161.95 ( class_Rings_Oring__1(T_a)
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Ints__add,axiom,
% 161.83/161.95 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.95 ( class_Rings_Oring__1(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
% 161.83/161.95 => 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))) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Ints__mult,axiom,
% 161.83/161.95 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.95 ( class_Rings_Oring__1(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
% 161.83/161.95 => 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))) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_nat_Osize_I3_J,axiom,
% 161.83/161.95 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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Ints__diff,axiom,
% 161.83/161.95 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.95 ( class_Rings_Oring__1(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
% 161.83/161.95 => 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))) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Ints__1,axiom,
% 161.83/161.95 ! [T_a] :
% 161.83/161.95 ( class_Rings_Oring__1(T_a)
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Ints__minus,axiom,
% 161.83/161.95 ! [V_a_2,T_a] :
% 161.83/161.95 ( class_Rings_Oring__1(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 161.83/161.95 => 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))) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osize_I15_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osize_I16_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osize_I9_J,axiom,
% 161.83/161.95 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_nat_Osize_I1_J,axiom,
% 161.83/161.95 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Ints__double__eq__0__iff,axiom,
% 161.83/161.95 ! [V_a_2,T_a] :
% 161.83/161.95 ( class_Int_Oring__char__0(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 161.83/161.95 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.95 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Ints__odd__nonzero,axiom,
% 161.83/161.95 ! [V_a_2,T_a] :
% 161.83/161.95 ( class_Int_Oring__char__0(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 161.83/161.95 => 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) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sgn__if,axiom,
% 161.83/161.95 ! [V_x,T_a] :
% 161.83/161.95 ( class_Groups_Osgn__if(T_a)
% 161.83/161.95 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.95 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 161.83/161.95 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 161.83/161.95 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 161.83/161.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 161.83/161.95 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sgn__1__neg,axiom,
% 161.83/161.95 ! [V_a_2,T_a] :
% 161.83/161.95 ( class_Rings_Olinordered__idom(T_a)
% 161.83/161.95 => ( 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))
% 161.83/161.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sgn__neg,axiom,
% 161.83/161.95 ! [V_a,T_a] :
% 161.83/161.95 ( class_Rings_Olinordered__idom(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 161.83/161.95 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 161.83/161.95 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_a] :
% 161.83/161.95 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 161.83/161.95 => ( ! [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))
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 161.83/161.95 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.95 => 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)) ) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osize_I13_J,axiom,
% 161.83/161.95 ! [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))) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osize_I5_J,axiom,
% 161.83/161.95 ! [V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1_2)),c_Com_Ocom_Ocom__size(V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_card_Oneutral,axiom,
% 161.83/161.95 ! [V_A_2,T_a] :
% 161.83/161.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.95 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 161.83/161.95 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 161.83/161.95 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_expand__Suc,axiom,
% 161.83/161.95 ! [V_v] :
% 161.83/161.95 ( 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)))
% 161.83/161.95 => 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))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_evaln_OIfFalse,axiom,
% 161.83/161.95 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] :
% 161.83/161.95 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_s1_2))
% 161.83/161.95 => 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)) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_evaln_OIfTrue,axiom,
% 161.83/161.95 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] :
% 161.83/161.95 ( hBOOL(hAPP(V_b_2,V_s_2))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0_2),V_s_2),V_n_2),V_s1_2))
% 161.83/161.95 => 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)) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_evaln__elim__cases_I5_J,axiom,
% 161.83/161.95 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 161.83/161.95 ( 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))
% 161.83/161.95 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 161.83/161.95 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_t_2)) )
% 161.83/161.95 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 161.83/161.95 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2_2),V_s_2),V_n_2),V_t_2)) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_evalc__elim__cases_I5_J,axiom,
% 161.83/161.95 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 161.83/161.95 ( 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))
% 161.83/161.95 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 161.83/161.95 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) )
% 161.83/161.95 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 161.83/161.95 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_evalc_OIfTrue,axiom,
% 161.83/161.95 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] :
% 161.83/161.95 ( hBOOL(hAPP(V_b_2,V_s_2))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2))
% 161.83/161.95 => 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)) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_evalc_OIfFalse,axiom,
% 161.83/161.95 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] :
% 161.83/161.95 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2))
% 161.83/161.95 => 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)) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_WTs__elim__cases_I5_J,axiom,
% 161.83/161.95 ! [V_c2_2,V_c1_2,V_b_2] :
% 161.83/161.95 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)))
% 161.83/161.95 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 161.83/161.95 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osimps_I4_J,axiom,
% 161.83/161.95 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
% 161.83/161.95 ( 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)
% 161.83/161.95 <=> ( V_fun_2 = V_fun_H_2
% 161.83/161.95 & V_com1_2 = V_com1_H_2
% 161.83/161.95 & V_com2_2 = V_com2_H_2 ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sgn__sgn,axiom,
% 161.83/161.95 ! [V_a,T_a] :
% 161.83/161.95 ( class_Rings_Olinordered__idom(T_a)
% 161.83/161.95 => 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) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_number__of__reorient,axiom,
% 161.83/161.95 ! [V_x_2,V_w_2,T_a] :
% 161.83/161.95 ( class_Int_Onumber(T_a)
% 161.83/161.95 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = V_x_2
% 161.83/161.95 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_eq__number__of,axiom,
% 161.83/161.95 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.95 ( ( class_Int_Onumber__ring(T_a)
% 161.83/161.95 & class_Int_Oring__char__0(T_a) )
% 161.83/161.95 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 161.83/161.95 <=> V_x_2 = V_y_2 ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_le__number__of,axiom,
% 161.83/161.95 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.95 ( ( class_Int_Onumber__ring(T_a)
% 161.83/161.95 & class_Rings_Olinordered__idom(T_a) )
% 161.83/161.95 => ( 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)))
% 161.83/161.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_less__number__of,axiom,
% 161.83/161.95 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.95 ( ( class_Int_Onumber__ring(T_a)
% 161.83/161.95 & class_Rings_Olinordered__idom(T_a) )
% 161.83/161.95 => ( 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)))
% 161.83/161.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_number__of__add,axiom,
% 161.83/161.95 ! [V_w,V_v,T_a] :
% 161.83/161.95 ( class_Int_Onumber__ring(T_a)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_add__number__of__eq,axiom,
% 161.83/161.95 ! [V_w,V_v,T_a] :
% 161.83/161.95 ( class_Int_Onumber__ring(T_a)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_add__number__of__left,axiom,
% 161.83/161.95 ! [V_z,V_w,V_v,T_a] :
% 161.83/161.95 ( class_Int_Onumber__ring(T_a)
% 161.83/161.95 => 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) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_number__of__mult,axiom,
% 161.83/161.95 ! [V_w,V_v,T_a] :
% 161.83/161.95 ( class_Int_Onumber__ring(T_a)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_arith__simps_I32_J,axiom,
% 161.83/161.95 ! [V_w,V_v,T_a] :
% 161.83/161.95 ( class_Int_Onumber__ring(T_a)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_mult__number__of__left,axiom,
% 161.83/161.95 ! [V_z,V_w,V_v,T_a] :
% 161.83/161.95 ( class_Int_Onumber__ring(T_a)
% 161.83/161.95 => 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) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_number__of__diff,axiom,
% 161.83/161.95 ! [V_w,V_v,T_a] :
% 161.83/161.95 ( class_Int_Onumber__ring(T_a)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_diff__number__of__eq,axiom,
% 161.83/161.95 ! [V_w,V_v,T_a] :
% 161.83/161.95 ( class_Int_Onumber__ring(T_a)
% 161.83/161.95 => 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))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_arith__simps_I30_J,axiom,
% 161.83/161.95 ! [V_w,T_a] :
% 161.83/161.95 ( class_Int_Onumber__ring(T_a)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_number__of__minus,axiom,
% 161.83/161.95 ! [V_w,T_a] :
% 161.83/161.95 ( class_Int_Onumber__ring(T_a)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_evaln_Oequations_I5_J,axiom,
% 161.83/161.95 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] :
% 161.83/161.95 ( 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))
% 161.83/161.95 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 161.83/161.95 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) )
% 161.83/161.95 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 161.83/161.95 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_evaln_Oequations_I6_J,axiom,
% 161.83/161.95 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] :
% 161.83/161.95 ( 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))
% 161.83/161.95 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 161.83/161.95 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) )
% 161.83/161.95 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 161.83/161.95 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_evalc_Oequations_I6_J,axiom,
% 161.83/161.95 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] :
% 161.83/161.95 ( 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))
% 161.83/161.95 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 161.83/161.95 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) )
% 161.83/161.95 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 161.83/161.95 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_evalc_Oequations_I5_J,axiom,
% 161.83/161.95 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] :
% 161.83/161.95 ( 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))
% 161.83/161.95 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 161.83/161.95 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) )
% 161.83/161.95 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 161.83/161.95 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osimps_I55_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osimps_I54_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_WT_Oequations_I5_J,axiom,
% 161.83/161.95 ! [V_a2_2,V_a1_2,V_a3_2] :
% 161.83/161.95 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2)))
% 161.83/161.95 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 161.83/161.95 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_WT_OIf,axiom,
% 161.83/161.95 ! [V_b_2,V_c1_2,V_c0_2] :
% 161.83/161.95 ( hBOOL(hAPP(c_Com_OWT,V_c0_2))
% 161.83/161.95 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 161.83/161.95 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osimps_I57_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osimps_I56_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osimps_I44_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osimps_I45_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osimps_I14_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osimps_I15_J,axiom,
% 161.83/161.95 ! [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 ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sgn0,axiom,
% 161.83/161.95 ! [T_a] :
% 161.83/161.95 ( class_Groups_Osgn__if(T_a)
% 161.83/161.95 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sgn__0__0,axiom,
% 161.83/161.95 ! [V_a_2,T_a] :
% 161.83/161.95 ( class_Rings_Olinordered__idom(T_a)
% 161.83/161.95 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.95 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sgn__times,axiom,
% 161.83/161.95 ! [V_b,V_a,T_a] :
% 161.83/161.95 ( class_Rings_Olinordered__idom(T_a)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_le__number__of__eq__not__less,axiom,
% 161.83/161.95 ! [V_w_2,V_v_2,T_a] :
% 161.83/161.95 ( ( class_Int_Onumber(T_a)
% 161.83/161.95 & class_Orderings_Olinorder(T_a) )
% 161.83/161.95 => ( 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)))
% 161.83/161.95 <=> ~ 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))) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_left__distrib__number__of,axiom,
% 161.83/161.95 ! [V_v,V_b,V_a,T_b] :
% 161.83/161.95 ( ( class_Int_Onumber(T_b)
% 161.83/161.95 & class_Rings_Osemiring(T_b) )
% 161.83/161.95 => 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))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_right__distrib__number__of,axiom,
% 161.83/161.95 ! [V_c,V_b,V_v,T_b] :
% 161.83/161.95 ( ( class_Int_Onumber(T_b)
% 161.83/161.95 & class_Rings_Osemiring(T_b) )
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_add__number__of__diff2,axiom,
% 161.83/161.95 ! [V_w,V_c,V_v,T_a] :
% 161.83/161.95 ( class_Int_Onumber__ring(T_a)
% 161.83/161.95 => 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) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_add__number__of__diff1,axiom,
% 161.83/161.95 ! [V_c,V_w,V_v,T_a] :
% 161.83/161.95 ( class_Int_Onumber__ring(T_a)
% 161.83/161.95 => 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) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_right__diff__distrib__number__of,axiom,
% 161.83/161.95 ! [V_c,V_b,V_v,T_b] :
% 161.83/161.95 ( ( class_Int_Onumber(T_b)
% 161.83/161.95 & class_Rings_Oring(T_b) )
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_left__diff__distrib__number__of,axiom,
% 161.83/161.95 ! [V_v,V_b,V_a,T_b] :
% 161.83/161.95 ( ( class_Int_Onumber(T_b)
% 161.83/161.95 & class_Rings_Oring(T_b) )
% 161.83/161.95 => 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))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_minus__number__of__mult,axiom,
% 161.83/161.95 ! [V_z,V_w,T_a] :
% 161.83/161.95 ( class_Int_Onumber__ring(T_a)
% 161.83/161.95 => 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) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Ints__number__of,axiom,
% 161.83/161.95 ! [V_w_2,T_a] :
% 161.83/161.95 ( class_Int_Onumber__ring(T_a)
% 161.83/161.95 => 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))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sgn__less,axiom,
% 161.83/161.95 ! [V_a_2,T_a] :
% 161.83/161.95 ( class_Rings_Olinordered__idom(T_a)
% 161.83/161.95 => ( 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)))
% 161.83/161.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sgn__greater,axiom,
% 161.83/161.95 ! [V_a_2,T_a] :
% 161.83/161.95 ( class_Rings_Olinordered__idom(T_a)
% 161.83/161.95 => ( 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)))
% 161.83/161.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sgn__pos,axiom,
% 161.83/161.95 ! [V_a,T_a] :
% 161.83/161.95 ( class_Rings_Olinordered__idom(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 161.83/161.95 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sgn__1__pos,axiom,
% 161.83/161.95 ! [V_a_2,T_a] :
% 161.83/161.95 ( class_Rings_Olinordered__idom(T_a)
% 161.83/161.95 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a)
% 161.83/161.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osize_I3_J,axiom,
% 161.83/161.95 ! [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))) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osize_I11_J,axiom,
% 161.83/161.95 ! [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))) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_number__of__pred,axiom,
% 161.83/161.95 ! [V_w,T_a] :
% 161.83/161.95 ( class_Int_Onumber__ring(T_a)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_fold1__eq__fold,axiom,
% 161.83/161.95 ! [V_a_2,V_A_2,T_a] :
% 161.83/161.95 ( class_Groups_Oab__semigroup__mult(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 161.83/161.95 => 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) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_MGF__lemma2__simult,axiom,
% 161.83/161.95 ! [V_F_2] :
% 161.83/161.95 ( c_Hoare__Mirabelle_Ostate__not__singleton
% 161.83/161.95 => ( c_Com_OWT__bodies
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),V_F_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))))
% 161.83/161.95 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)),V_F_2) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_bool_Osize_I2_J,axiom,
% 161.83/161.95 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_bool_Osize_I1_J,axiom,
% 161.83/161.95 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_number__of__succ,axiom,
% 161.83/161.95 ! [V_k,T_a] :
% 161.83/161.95 ( class_Int_Onumber__ring(T_a)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_WTs__elim__cases_I3_J,axiom,
% 161.83/161.95 ! [V_ca_2,V_a_2,V_Y_2] :
% 161.83/161.95 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2)))
% 161.83/161.95 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_minus__numeral__code_I6_J,axiom,
% 161.83/161.95 ! [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))) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_minus__numeral__code_I5_J,axiom,
% 161.83/161.95 ! [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)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_times__numeral__code_I5_J,axiom,
% 161.83/161.95 ! [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)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_less__eq__number__of__int__code,axiom,
% 161.83/161.95 ! [V_l_2,V_k_2] :
% 161.83/161.95 ( 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)))
% 161.83/161.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_less__number__of__int__code,axiom,
% 161.83/161.95 ! [V_l_2,V_k_2] :
% 161.83/161.95 ( 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)))
% 161.83/161.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_plus__numeral__code_I9_J,axiom,
% 161.83/161.95 ! [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)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zsgn__def,axiom,
% 161.83/161.95 ! [V_i] :
% 161.83/161.95 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.95 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 161.83/161.95 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 161.83/161.95 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 161.83/161.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 161.83/161.95 => 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)) ) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zmult__zless__mono2,axiom,
% 161.83/161.95 ! [V_k,V_j,V_i] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j))) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_pos__zmult__eq__1__iff,axiom,
% 161.83/161.95 ! [V_n_2,V_m_2] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 161.83/161.95 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 161.83/161.95 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 161.83/161.95 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_le__imp__0__less,axiom,
% 161.83/161.95 ! [V_z] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_int__one__le__iff__zero__less,axiom,
% 161.83/161.95 ! [V_z_2] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 161.83/161.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zadd__zminus__inverse2,axiom,
% 161.83/161.95 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zminus__0,axiom,
% 161.83/161.95 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_int__0__less__1,axiom,
% 161.83/161.95 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_odd__less__0,axiom,
% 161.83/161.95 ! [V_z_2] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_less__bin__lemma,axiom,
% 161.83/161.95 ! [V_l_2,V_k_2] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 161.83/161.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_odd__nonzero,axiom,
% 161.83/161.95 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zadd__0,axiom,
% 161.83/161.95 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zadd__0__right,axiom,
% 161.83/161.95 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 161.83/161.95
% 161.83/161.95 fof(fact_image__ident,axiom,
% 161.83/161.95 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ).
% 161.83/161.95
% 161.83/161.95 fof(fact_image__image,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_succ__pred,axiom,
% 161.83/161.95 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 161.83/161.95
% 161.83/161.95 fof(fact_pred__def,axiom,
% 161.83/161.95 ! [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)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zadd__assoc,axiom,
% 161.83/161.95 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zadd__left__commute,axiom,
% 161.83/161.95 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zadd__commute,axiom,
% 161.83/161.95 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_succ__def,axiom,
% 161.83/161.95 ! [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)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zadd__strict__right__mono,axiom,
% 161.83/161.95 ! [V_k,V_j,V_i] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zless__add1__eq,axiom,
% 161.83/161.95 ! [V_z_2,V_w_2] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
% 161.83/161.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 161.83/161.95 | V_w_2 = V_z_2 ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zless__linear,axiom,
% 161.83/161.95 ! [V_y,V_x] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 161.83/161.95 | V_x = V_y
% 161.83/161.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zle__antisym,axiom,
% 161.83/161.95 ! [V_w,V_z] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 161.83/161.95 => V_z = V_w ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zle__trans,axiom,
% 161.83/161.95 ! [V_k,V_j,V_i] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zmult__assoc,axiom,
% 161.83/161.95 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zmult__zminus,axiom,
% 161.83/161.95 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_w) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zle__linear,axiom,
% 161.83/161.95 ! [V_w,V_z] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 161.83/161.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zmult__commute,axiom,
% 161.83/161.95 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zminus__zminus,axiom,
% 161.83/161.95 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zle__refl,axiom,
% 161.83/161.95 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zdiff__zmult__distrib2,axiom,
% 161.83/161.95 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zdiff__zmult__distrib,axiom,
% 161.83/161.95 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zmult__1__right,axiom,
% 161.83/161.95 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zmult__1,axiom,
% 161.83/161.95 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zadd__left__mono,axiom,
% 161.83/161.95 ! [V_k,V_j,V_i] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zadd__zmult__distrib,axiom,
% 161.83/161.95 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zadd__zmult__distrib2,axiom,
% 161.83/161.95 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zminus__zadd__distrib,axiom,
% 161.83/161.95 ! [V_w,V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_le__iff__pred__less,axiom,
% 161.83/161.95 ! [V_l_2,V_k_2] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 161.83/161.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zless__le,axiom,
% 161.83/161.95 ! [V_w_2,V_z_2] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 161.83/161.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 161.83/161.95 & V_z_2 != V_w_2 ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zle__add1__eq__le,axiom,
% 161.83/161.95 ! [V_z_2,V_w_2] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
% 161.83/161.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_add1__zle__eq,axiom,
% 161.83/161.95 ! [V_z_2,V_w_2] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))
% 161.83/161.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zless__imp__add1__zle,axiom,
% 161.83/161.95 ! [V_z,V_w] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zadd__zless__mono,axiom,
% 161.83/161.95 ! [V_z,V_z_H,V_w,V_w_H] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z))) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_diff__int__def,axiom,
% 161.83/161.95 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_diff__int__def__symmetric,axiom,
% 161.83/161.95 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zle__diff1__eq,axiom,
% 161.83/161.95 ! [V_z_2,V_w_2] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
% 161.83/161.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_fun__upd__def,axiom,
% 161.83/161.95 ! [V_b_2,V_f_2,T_b,T_a,V_a_2,V_x_2] :
% 161.83/161.95 ( ( V_x_2 = V_a_2
% 161.83/161.95 => 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 )
% 161.83/161.95 & ( V_x_2 != V_a_2
% 161.83/161.95 => 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) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osimps_I2_J,axiom,
% 161.83/161.95 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
% 161.83/161.95 ( 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)
% 161.83/161.95 <=> ( V_loc_2 = V_loc_H_2
% 161.83/161.95 & V_fun_2 = V_fun_H_2
% 161.83/161.95 & V_com_2 = V_com_H_2 ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_bot__fun__def,axiom,
% 161.83/161.95 ! [V_x_2,T_b,T_a] :
% 161.83/161.95 ( class_Orderings_Obot(T_a)
% 161.83/161.95 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_fun__diff__def,axiom,
% 161.83/161.95 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 161.83/161.95 ( class_Groups_Ominus(T_a)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_fun__Compl__def,axiom,
% 161.83/161.95 ! [V_x_2,V_A_2,T_b,T_a] :
% 161.83/161.95 ( class_Groups_Ouminus(T_a)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_empty__upd__none,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_map__add__empty,axiom,
% 161.83/161.95 ! [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 ).
% 161.83/161.95
% 161.83/161.95 fof(fact_empty__map__add,axiom,
% 161.83/161.95 ! [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 ).
% 161.83/161.95
% 161.83/161.95 fof(fact_map__add__def,axiom,
% 161.83/161.95 ! [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)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_restrict__map__empty,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_fold__empty,axiom,
% 161.83/161.95 ! [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 ).
% 161.83/161.95
% 161.83/161.95 fof(fact_map__comp__empty_I2_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_map__comp__empty_I1_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_map__comp__def,axiom,
% 161.83/161.95 ! [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)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_minus__fold__remove,axiom,
% 161.83/161.95 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.95 => 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) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_image__constant__conv,axiom,
% 161.83/161.95 ! [V_ca_2,T_b,T_a,V_A_2] :
% 161.83/161.95 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.95 => 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)) )
% 161.83/161.95 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.95 => 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))) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_less__eq__Suc__le__raw,axiom,
% 161.83/161.95 ! [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)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_dom__empty,axiom,
% 161.83/161.95 ! [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)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_dom__eq__empty__conv,axiom,
% 161.83/161.95 ! [V_f_2,T_b,T_a] :
% 161.83/161.95 ( c_Map_Odom(T_a,T_b,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.95 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_restrict__map__def,axiom,
% 161.83/161.95 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 161.83/161.95 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.95 => 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) )
% 161.83/161.95 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.95 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_restrict__map__to__empty,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_map__upd__nonempty,axiom,
% 161.83/161.95 ! [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)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osimps_I40_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osimps_I41_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_WT_OLocal,axiom,
% 161.83/161.95 ! [V_a_2,V_Y_2,V_ca_2] :
% 161.83/161.95 ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
% 161.83/161.95 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_WT_Oequations_I3_J,axiom,
% 161.83/161.95 ! [V_a1_2,V_a3_2,V_a2_2] :
% 161.83/161.95 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2)))
% 161.83/161.95 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osimps_I36_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osimps_I37_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_ran__empty,axiom,
% 161.83/161.95 ! [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)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osimps_I34_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osimps_I35_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osimps_I42_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osimps_I43_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osimps_I11_J,axiom,
% 161.83/161.95 ! [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 ).
% 161.83/161.95
% 161.83/161.95 fof(fact_com_Osimps_I10_J,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_image__constant,axiom,
% 161.83/161.95 ! [V_ca_2,T_b,V_A_2,V_x_2,T_a] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.95 => 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))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_MGT__def,axiom,
% 161.83/161.95 ! [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)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_dom__eq__singleton__conv,axiom,
% 161.83/161.95 ! [V_x_2,V_f_2,T_b,T_a] :
% 161.83/161.95 ( 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)))
% 161.83/161.95 <=> ? [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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 161.83/161.95 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_a] :
% 161.83/161.95 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.95 => 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) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_fold1__eq__fold__idem,axiom,
% 161.83/161.95 ! [V_a_2,V_A_2,T_a] :
% 161.83/161.95 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.95 => 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) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_folding__one_Oeq__fold_H,axiom,
% 161.83/161.95 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 161.83/161.95 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.95 => 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) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_self__quotient__aux2,axiom,
% 161.83/161.95 ! [V_q,V_r,V_a] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 161.83/161.95 => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_self__quotient__aux1,axiom,
% 161.83/161.95 ! [V_q,V_r,V_a] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 161.83/161.95 => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_q__pos__lemma,axiom,
% 161.83/161.95 ! [V_r_H,V_q_H,V_b_H] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_q__neg__lemma,axiom,
% 161.83/161.95 ! [V_r_H,V_q_H,V_b_H] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_unique__quotient__lemma,axiom,
% 161.83/161.95 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zdiv__mono2__lemma,axiom,
% 161.83/161.95 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 161.83/161.95 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_unique__quotient__lemma__neg,axiom,
% 161.83/161.95 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 161.83/161.95 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 161.83/161.95 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_number__of__is__id,axiom,
% 161.83/161.95 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 161.83/161.95
% 161.83/161.95 fof(fact_int__0__neq__1,axiom,
% 161.83/161.95 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 161.83/161.95 ! [V_y,V_x] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 161.83/161.95 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 161.83/161.95 ! [V_y,V_x] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_MGT__alternD,axiom,
% 161.83/161.95 ! [V_ca_2,V_G_2] :
% 161.83/161.95 ( c_Hoare__Mirabelle_Ostate__not__singleton
% 161.83/161.95 => ( 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))))
% 161.83/161.95 => 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)))) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_MGT__Body,axiom,
% 161.83/161.95 ! [V_Procs_2,V_G_2] :
% 161.83/161.95 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),V_G_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Procs_2))
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),V_Procs_2))
% 161.83/161.95 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),V_Procs_2)) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Body1,axiom,
% 161.83/161.95 ! [V_pn_2,V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] :
% 161.83/161.95 ( 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))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procs_2))
% 161.83/161.95 => 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)))) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 161.83/161.95 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 161.83/161.95 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.95 => 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)))))) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_UnCI,axiom,
% 161.83/161.95 ! [V_A_2,V_B_2,V_ca_2,T_a] :
% 161.83/161.95 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) )
% 161.83/161.95 => 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))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_UnE,axiom,
% 161.83/161.95 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 161.83/161.95 ( 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)))
% 161.83/161.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 161.83/161.95 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_ball__Un,axiom,
% 161.83/161.95 ! [V_P_2,V_B_2,V_A_2,T_a] :
% 161.83/161.95 ( ! [B_x] :
% 161.83/161.95 ( 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)))
% 161.83/161.95 => hBOOL(hAPP(V_P_2,B_x)) )
% 161.83/161.95 <=> ( ! [B_x] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 161.83/161.95 => hBOOL(hAPP(V_P_2,B_x)) )
% 161.83/161.95 & ! [B_x] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2))
% 161.83/161.95 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_bex__Un,axiom,
% 161.83/161.95 ! [V_P_2,V_B_2,V_A_2,T_a] :
% 161.83/161.95 ( ? [B_x] :
% 161.83/161.95 ( 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)))
% 161.83/161.95 & hBOOL(hAPP(V_P_2,B_x)) )
% 161.83/161.95 <=> ( ? [B_x] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 161.83/161.95 & hBOOL(hAPP(V_P_2,B_x)) )
% 161.83/161.95 | ? [B_x] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2))
% 161.83/161.95 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Un__assoc,axiom,
% 161.83/161.95 ! [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)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Un__left__commute,axiom,
% 161.83/161.95 ! [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)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Un__left__absorb,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Un__commute,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Un__absorb,axiom,
% 161.83/161.95 ! [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 ).
% 161.83/161.95
% 161.83/161.95 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 161.83/161.95 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 161.83/161.95 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup__apply,axiom,
% 161.83/161.95 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 161.83/161.95 ( class_Lattices_Olattice(T_a)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup__assoc,axiom,
% 161.83/161.95 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_inf__sup__aci_I6_J,axiom,
% 161.83/161.95 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.95 ( class_Lattices_Olattice(T_a)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup_Oassoc,axiom,
% 161.83/161.95 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup__left__commute,axiom,
% 161.83/161.95 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_inf__sup__aci_I7_J,axiom,
% 161.83/161.95 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.95 ( class_Lattices_Olattice(T_a)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup_Oleft__commute,axiom,
% 161.83/161.95 ! [V_c,V_a,V_b,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup__left__idem,axiom,
% 161.83/161.95 ! [V_y,V_x,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => 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) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_inf__sup__aci_I8_J,axiom,
% 161.83/161.95 ! [V_y,V_x,T_a] :
% 161.83/161.95 ( class_Lattices_Olattice(T_a)
% 161.83/161.95 => 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) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup_Oleft__idem,axiom,
% 161.83/161.95 ! [V_b,V_a,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => 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) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup__commute,axiom,
% 161.83/161.95 ! [V_y,V_x,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => 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) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_inf__sup__aci_I5_J,axiom,
% 161.83/161.95 ! [V_y,V_x,T_a] :
% 161.83/161.95 ( class_Lattices_Olattice(T_a)
% 161.83/161.95 => 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) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup_Ocommute,axiom,
% 161.83/161.95 ! [V_b,V_a,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => 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) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup__idem,axiom,
% 161.83/161.95 ! [V_x,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup_Oidem,axiom,
% 161.83/161.95 ! [V_a,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup__fun__def,axiom,
% 161.83/161.95 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 161.83/161.95 ( class_Lattices_Olattice(T_a)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 161.83/161.95 ! [V_g_2,T_c,V_f_2,T_b,T_a] :
% 161.83/161.95 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 161.83/161.95 => 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_le__supE,axiom,
% 161.83/161.95 ! [V_x,V_b,V_a,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => ( 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))
% 161.83/161.95 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 161.83/161.95 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup__mono,axiom,
% 161.83/161.95 ! [V_d,V_b,V_c,V_a,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 161.83/161.95 => 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))) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup__least,axiom,
% 161.83/161.95 ! [V_z,V_x,V_y,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 161.83/161.95 => 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)) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_le__supI,axiom,
% 161.83/161.95 ! [V_b,V_x,V_a,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 161.83/161.95 => 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)) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup__absorb1,axiom,
% 161.83/161.95 ! [V_x,V_y,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 161.83/161.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup__absorb2,axiom,
% 161.83/161.95 ! [V_y,V_x,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 161.83/161.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_le__supI2,axiom,
% 161.83/161.95 ! [V_a,V_b,V_x,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 161.83/161.95 => 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))) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_le__supI1,axiom,
% 161.83/161.95 ! [V_b,V_a,V_x,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 161.83/161.95 => 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))) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_le__sup__iff,axiom,
% 161.83/161.95 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => ( 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))
% 161.83/161.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
% 161.83/161.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_le__iff__sup,axiom,
% 161.83/161.95 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 161.83/161.95 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = V_y_2 ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup__ge2,axiom,
% 161.83/161.95 ! [V_x,V_y,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => 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))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_inf__sup__ord_I4_J,axiom,
% 161.83/161.95 ! [V_x,V_y,T_a] :
% 161.83/161.95 ( class_Lattices_Olattice(T_a)
% 161.83/161.95 => 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))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup__ge1,axiom,
% 161.83/161.95 ! [V_y,V_x,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => 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))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_inf__sup__ord_I3_J,axiom,
% 161.83/161.95 ! [V_y,V_x,T_a] :
% 161.83/161.95 ( class_Lattices_Olattice(T_a)
% 161.83/161.95 => 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))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_less__supI2,axiom,
% 161.83/161.95 ! [V_a,V_b,V_x,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 161.83/161.95 => 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))) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_less__supI1,axiom,
% 161.83/161.95 ! [V_b,V_a,V_x,T_a] :
% 161.83/161.95 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 161.83/161.95 => 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))) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup__eq__bot__iff,axiom,
% 161.83/161.95 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.95 ( class_Lattices_Obounded__lattice__bot(T_a)
% 161.83/161.95 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_a)
% 161.83/161.95 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_a)
% 161.83/161.95 & V_y_2 = c_Orderings_Obot__class_Obot(T_a) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup__bot__right,axiom,
% 161.83/161.95 ! [V_x,T_a] :
% 161.83/161.95 ( class_Lattices_Obounded__lattice__bot(T_a)
% 161.83/161.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_sup__bot__left,axiom,
% 161.83/161.95 ! [V_x,T_a] :
% 161.83/161.95 ( class_Lattices_Obounded__lattice__bot(T_a)
% 161.83/161.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_UnI2,axiom,
% 161.83/161.95 ! [V_A_2,V_B_2,V_ca_2,T_a] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
% 161.83/161.95 => 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))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_UnI1,axiom,
% 161.83/161.95 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 161.83/161.95 => 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))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Un__iff,axiom,
% 161.83/161.95 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 161.83/161.95 ( 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)))
% 161.83/161.95 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 161.83/161.95 | hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Un__empty,axiom,
% 161.83/161.95 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.95 ( 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))
% 161.83/161.95 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.95 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Un__empty__right,axiom,
% 161.83/161.95 ! [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 ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Un__empty__left,axiom,
% 161.83/161.95 ! [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 ).
% 161.83/161.95
% 161.83/161.95 fof(fact_finite__Un,axiom,
% 161.83/161.95 ! [V_G_2,V_F_2,T_a] :
% 161.83/161.95 ( 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)))
% 161.83/161.95 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 161.83/161.95 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_finite__UnI,axiom,
% 161.83/161.95 ! [V_G_2,V_F_2,T_a] :
% 161.83/161.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2))
% 161.83/161.95 => 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))) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Un__insert__left,axiom,
% 161.83/161.95 ! [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)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Un__insert__right,axiom,
% 161.83/161.95 ! [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)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Un__mono,axiom,
% 161.83/161.95 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))
% 161.83/161.95 => 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))) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Un__least,axiom,
% 161.83/161.95 ! [V_B_2,V_C_2,V_A_2,T_a] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 161.83/161.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 161.83/161.95 => 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)) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Un__absorb2,axiom,
% 161.83/161.95 ! [V_A_2,V_B_2,T_a] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 161.83/161.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Un__absorb1,axiom,
% 161.83/161.95 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_subset__Un__eq,axiom,
% 161.83/161.95 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.95 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Un__upper2,axiom,
% 161.83/161.95 ! [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))) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Un__upper1,axiom,
% 161.83/161.95 ! [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))) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_image__Un,axiom,
% 161.83/161.95 ! [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)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Un__Diff,axiom,
% 161.83/161.95 ! [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)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Un__Diff__cancel2,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Un__Diff__cancel,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_triple__valid__def,axiom,
% 161.83/161.95 ! [V_t_2,V_n_2,T_a] :
% 161.83/161.95 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,V_t_2)
% 161.83/161.95 <=> 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)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_fun__left__comm,axiom,
% 161.83/161.95 ! [T_a] :
% 161.83/161.95 ( class_Groups_Oab__semigroup__mult(T_a)
% 161.83/161.95 => c_Finite__Set_Ofun__left__comm(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_insert__is__Un,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 161.83/161.95 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 161.83/161.95 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2))
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
% 161.83/161.95 => V_y_2 = V_x_2 ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Diff__partition,axiom,
% 161.83/161.95 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.95 => 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 ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Diff__subset__conv,axiom,
% 161.83/161.95 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 161.83/161.95 ( 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))
% 161.83/161.95 <=> 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))) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_Compl__Diff__eq,axiom,
% 161.83/161.95 ! [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) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_dom__map__add,axiom,
% 161.83/161.95 ! [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)) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 161.83/161.95 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 161.83/161.95 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 161.83/161.95 => 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)) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 161.83/161.95 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 161.83/161.95 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.95 => 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) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 161.83/161.95 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
% 161.83/161.95 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.95 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 161.83/161.95 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.95 => 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)) ) ) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 161.83/161.95 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 161.83/161.95 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
% 161.83/161.95 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_union__fold__insert,axiom,
% 161.83/161.95 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.95 => 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) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_fold1__Un2,axiom,
% 161.83/161.95 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.95 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.95 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 161.83/161.95 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.95 => 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)) ) ) ) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 161.83/161.95 ! [V_z_2,V_A_2,V_f_2,T_b,T_a] :
% 161.83/161.95 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 161.83/161.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.95 => 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))) ) ) ).
% 161.83/161.95
% 161.83/161.95 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 161.83/161.96 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 161.83/161.96 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.96 => 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) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 161.83/161.96 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 161.83/161.96 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.96 => 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)) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 161.83/161.96 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_hoare__derivs_OBody,axiom,
% 161.83/161.96 ! [V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] :
% 161.83/161.96 ( 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))
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Body__sound__lemma,axiom,
% 161.83/161.96 ! [V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] :
% 161.83/161.96 ( 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))
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 161.83/161.96 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] :
% 161.83/161.96 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => 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)))))) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_MGT__alternI,axiom,
% 161.83/161.96 ! [V_ca_2,V_G_2] :
% 161.83/161.96 ( 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))))
% 161.83/161.96 => 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)))) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_sup__le__fold__sup,axiom,
% 161.83/161.96 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 161.83/161.96 => 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))) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_fold__sup__insert,axiom,
% 161.83/161.96 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => 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)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_sup1E,axiom,
% 161.83/161.96 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 161.83/161.96 ( 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))
% 161.83/161.96 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 161.83/161.96 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_sup1CI,axiom,
% 161.83/161.96 ! [T_a,V_A_2,V_x_2,V_B_2] :
% 161.83/161.96 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 161.83/161.96 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_finite__pointwise,axiom,
% 161.83/161.96 ! [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] :
% 161.83/161.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_U_2))
% 161.83/161.96 => ( ! [B_p] :
% 161.83/161.96 ( 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))))
% 161.83/161.96 => 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)))) )
% 161.83/161.96 => ( 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))
% 161.83/161.96 => 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)) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_sup__Un__eq,axiom,
% 161.83/161.96 ! [V_x_2,V_S_2,V_R_2,T_a] :
% 161.83/161.96 ( 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))
% 161.83/161.96 <=> 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))) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_pred__subset__eq,axiom,
% 161.83/161.96 ! [V_S_2,V_R_2,T_a] :
% 161.83/161.96 ( 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)))
% 161.83/161.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_eq__mem,axiom,
% 161.83/161.96 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2)))
% 161.83/161.96 <=> V_x_2 = V_y_2 ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Sup__fin_Oidem,axiom,
% 161.83/161.96 ! [V_x,T_a] :
% 161.83/161.96 ( class_Lattices_Olattice(T_a)
% 161.83/161.96 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_predicate1D,axiom,
% 161.83/161.96 ! [V_x_2,V_Q_2,V_P_2,T_a] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2))
% 161.83/161.96 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 161.83/161.96 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_rev__predicate1D,axiom,
% 161.83/161.96 ! [V_Q_2,T_a,V_x_2,V_P_2] :
% 161.83/161.96 ( hBOOL(hAPP(V_P_2,V_x_2))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2))
% 161.83/161.96 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_sup1I2,axiom,
% 161.83/161.96 ! [V_A_2,T_a,V_x_2,V_B_2] :
% 161.83/161.96 ( hBOOL(hAPP(V_B_2,V_x_2))
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_sup1I1,axiom,
% 161.83/161.96 ! [V_B_2,T_a,V_x_2,V_A_2] :
% 161.83/161.96 ( hBOOL(hAPP(V_A_2,V_x_2))
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_pred__equals__eq,axiom,
% 161.83/161.96 ! [V_S_2,V_R_2,T_a] :
% 161.83/161.96 ( 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)
% 161.83/161.96 <=> V_R_2 = V_S_2 ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_bot__empty__eq,axiom,
% 161.83/161.96 ! [V_x_2,T_a] :
% 161.83/161.96 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2))
% 161.83/161.96 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_semilattice__big_OF__eq,axiom,
% 161.83/161.96 ! [V_A_2,V_F_2,V_f_2,T_a] :
% 161.83/161.96 ( c_Big__Operators_Osemilattice__big(T_a,V_f_2,V_F_2)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 161.83/161.96 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 161.83/161.96 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 161.83/161.96 => ? [B_y_H] :
% 161.83/161.96 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 161.83/161.96 & 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)) ) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Suc__nat__number__of__add,axiom,
% 161.83/161.96 ! [V_n,V_v] :
% 161.83/161.96 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 161.83/161.96 => 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) )
% 161.83/161.96 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 161.83/161.96 => 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) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_tsub__def,axiom,
% 161.83/161.96 ! [V_x,V_y] :
% 161.83/161.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 161.83/161.96 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 161.83/161.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 161.83/161.96 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Sup__fin_Oremove,axiom,
% 161.83/161.96 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Lattices_Olattice(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.96 => ( ( 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))
% 161.83/161.96 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = V_x_2 )
% 161.83/161.96 & ( 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))
% 161.83/161.96 => 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)))))) ) ) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_,axiom,
% 161.83/161.96 ! [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) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__number__of__diff__1,axiom,
% 161.83/161.96 ! [V_v] :
% 161.83/161.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 161.83/161.96 => 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) )
% 161.83/161.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 161.83/161.96 => 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)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_not__neg__number__of__Pls,axiom,
% 161.83/161.96 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Pls__def,axiom,
% 161.83/161.96 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_rel__simps_I19_J,axiom,
% 161.83/161.96 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_rel__simps_I2_J,axiom,
% 161.83/161.96 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_add__Pls__right,axiom,
% 161.83/161.96 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 161.83/161.96
% 161.83/161.96 fof(fact_add__Pls,axiom,
% 161.83/161.96 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 161.83/161.96
% 161.83/161.96 fof(fact_mult__Pls,axiom,
% 161.83/161.96 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 161.83/161.96
% 161.83/161.96 fof(fact_diff__bin__simps_I1_J,axiom,
% 161.83/161.96 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 161.83/161.96
% 161.83/161.96 fof(fact_minus__Pls,axiom,
% 161.83/161.96 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 161.83/161.96
% 161.83/161.96 fof(fact_not__neg__0,axiom,
% 161.83/161.96 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_not__neg__1,axiom,
% 161.83/161.96 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_number__of__Pls,axiom,
% 161.83/161.96 ! [T_a] :
% 161.83/161.96 ( class_Int_Onumber__ring(T_a)
% 161.83/161.96 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_semiring__norm_I112_J,axiom,
% 161.83/161.96 ! [T_a] :
% 161.83/161.96 ( class_Int_Onumber__ring(T_a)
% 161.83/161.96 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_add__numeral__0,axiom,
% 161.83/161.96 ! [V_a,T_a] :
% 161.83/161.96 ( class_Int_Onumber__ring(T_a)
% 161.83/161.96 => 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 ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_add__numeral__0__right,axiom,
% 161.83/161.96 ! [V_a,T_a] :
% 161.83/161.96 ( class_Int_Onumber__ring(T_a)
% 161.83/161.96 => 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 ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_bin__less__0__simps_I1_J,axiom,
% 161.83/161.96 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_semiring__norm_I113_J,axiom,
% 161.83/161.96 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__number__of__Pls,axiom,
% 161.83/161.96 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_zero__is__num__zero,axiom,
% 161.83/161.96 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Sup__fin_Osingleton,axiom,
% 161.83/161.96 ! [V_x_2,T_a] :
% 161.83/161.96 ( class_Lattices_Olattice(T_a)
% 161.83/161.96 => 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 ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_not__neg__eq__ge__0,axiom,
% 161.83/161.96 ! [V_x_2] :
% 161.83/161.96 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 161.83/161.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_neg__def,axiom,
% 161.83/161.96 ! [V_Z_2] :
% 161.83/161.96 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 161.83/161.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_eq__0__number__of,axiom,
% 161.83/161.96 ! [V_v_2] :
% 161.83/161.96 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 161.83/161.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_eq__number__of__0,axiom,
% 161.83/161.96 ! [V_v_2] :
% 161.83/161.96 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_less__nat__number__of,axiom,
% 161.83/161.96 ! [V_v_H_2,V_v_2] :
% 161.83/161.96 ( 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)))
% 161.83/161.96 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 161.83/161.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 161.83/161.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_le__nat__number__of,axiom,
% 161.83/161.96 ! [V_v_H_2,V_v_2] :
% 161.83/161.96 ( 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)))
% 161.83/161.96 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 161.83/161.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Sup__fin_Oin__idem,axiom,
% 161.83/161.96 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Lattices_Olattice(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.96 => 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) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_neg__imp__number__of__eq__0,axiom,
% 161.83/161.96 ! [V_v] :
% 161.83/161.96 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 161.83/161.96 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Sup__fin_OF__eq,axiom,
% 161.83/161.96 ! [V_A_2,T_a] :
% 161.83/161.96 ( class_Lattices_Olattice(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => 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) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_le__special_I1_J,axiom,
% 161.83/161.96 ! [V_y_2,T_a] :
% 161.83/161.96 ( ( class_Int_Onumber__ring(T_a)
% 161.83/161.96 & class_Rings_Olinordered__idom(T_a) )
% 161.83/161.96 => ( 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)))
% 161.83/161.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_le__special_I3_J,axiom,
% 161.83/161.96 ! [V_x_2,T_a] :
% 161.83/161.96 ( ( class_Int_Onumber__ring(T_a)
% 161.83/161.96 & class_Rings_Olinordered__idom(T_a) )
% 161.83/161.96 => ( 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)))
% 161.83/161.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_less__special_I1_J,axiom,
% 161.83/161.96 ! [V_y_2,T_a] :
% 161.83/161.96 ( ( class_Int_Onumber__ring(T_a)
% 161.83/161.96 & class_Rings_Olinordered__idom(T_a) )
% 161.83/161.96 => ( 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)))
% 161.83/161.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_less__special_I3_J,axiom,
% 161.83/161.96 ! [V_x_2,T_a] :
% 161.83/161.96 ( ( class_Int_Onumber__ring(T_a)
% 161.83/161.96 & class_Rings_Olinordered__idom(T_a) )
% 161.83/161.96 => ( 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)))
% 161.83/161.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_less__0__number__of,axiom,
% 161.83/161.96 ! [V_v_2] :
% 161.83/161.96 ( 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)))
% 161.83/161.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_add__nat__number__of,axiom,
% 161.83/161.96 ! [V_v_H,V_v] :
% 161.83/161.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 161.83/161.96 => 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) )
% 161.83/161.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 161.83/161.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 161.83/161.96 => 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) )
% 161.83/161.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 161.83/161.96 => 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)) ) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 161.83/161.96 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Lattices_Olattice(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.96 => 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)) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Sup__fin_Osubset__idem,axiom,
% 161.83/161.96 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Lattices_Olattice(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 161.83/161.96 => 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) ) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Sup__fin_Ounion__idem,axiom,
% 161.83/161.96 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Lattices_Olattice(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 161.83/161.96 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.96 => 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)) ) ) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_eq__nat__number__of,axiom,
% 161.83/161.96 ! [V_v_H_2,V_v_2] :
% 161.83/161.96 ( 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)
% 161.83/161.96 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 161.83/161.96 => 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))) )
% 161.83/161.96 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 161.83/161.96 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 161.83/161.96 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 161.83/161.96 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 161.83/161.96 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 161.83/161.96 ! [V_a_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Lattices_Olattice(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => 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) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__number__of__add__left,axiom,
% 161.83/161.96 ! [V_k,V_v_H,V_v] :
% 161.83/161.96 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 161.83/161.96 => 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) )
% 161.83/161.96 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 161.83/161.96 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 161.83/161.96 => 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) )
% 161.83/161.96 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 161.83/161.96 => 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) ) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 161.83/161.96 ! [V_y,V_x] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 161.83/161.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(V_x,V_y))) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_neg__number__of__pred__iff__0,axiom,
% 161.83/161.96 ! [V_v_2] :
% 161.83/161.96 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 161.83/161.96 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_tsub__eq,axiom,
% 161.83/161.96 ! [V_x,V_y] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 161.83/161.96 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_mult__nat__number__of,axiom,
% 161.83/161.96 ! [V_v_H,V_v] :
% 161.83/161.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 161.83/161.96 => 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) )
% 161.83/161.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 161.83/161.96 => 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)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__number__of__mult__left,axiom,
% 161.83/161.96 ! [V_k,V_v_H,V_v] :
% 161.83/161.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 161.83/161.96 => 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) )
% 161.83/161.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 161.83/161.96 => 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) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Suc__diff__number__of,axiom,
% 161.83/161.96 ! [V_m,V_v] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 161.83/161.96 => 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))) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__1__add__number__of,axiom,
% 161.83/161.96 ! [V_v] :
% 161.83/161.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 161.83/161.96 => 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) )
% 161.83/161.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 161.83/161.96 => 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)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__number__of__add__1,axiom,
% 161.83/161.96 ! [V_v] :
% 161.83/161.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 161.83/161.96 => 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) )
% 161.83/161.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 161.83/161.96 => 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)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Sup__fin_Oinsert,axiom,
% 161.83/161.96 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Lattices_Olattice(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.96 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.96 => 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)) ) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 161.83/161.96 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Lattices_Olattice(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => ( ( 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))
% 161.83/161.96 => 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 )
% 161.83/161.96 & ( 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))
% 161.83/161.96 => 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)))))) ) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 161.83/161.96 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Lattices_Olattice(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.96 => 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) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Suc__nat__number__of,axiom,
% 161.83/161.96 ! [V_v] :
% 161.83/161.96 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 161.83/161.96 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 161.83/161.96 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 161.83/161.96 => 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)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_number__of2,axiom,
% 161.83/161.96 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_diff__nat__number__of,axiom,
% 161.83/161.96 ! [V_v_2,V_v_H_2] :
% 161.83/161.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 161.83/161.96 => 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) )
% 161.83/161.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 161.83/161.96 => 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)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_eq__special_I1_J,axiom,
% 161.83/161.96 ! [V_y_2,T_a] :
% 161.83/161.96 ( class_Int_Onumber__ring(T_a)
% 161.83/161.96 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 161.83/161.96 <=> 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)))) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_eq__special_I3_J,axiom,
% 161.83/161.96 ! [V_x_2,T_a] :
% 161.83/161.96 ( class_Int_Onumber__ring(T_a)
% 161.83/161.96 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.96 <=> 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)))) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Sup__fin_Oclosed,axiom,
% 161.83/161.96 ! [V_A_2,T_a] :
% 161.83/161.96 ( class_Lattices_Olattice(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.96 => ( ! [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))))))
% 161.83/161.96 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_small_H_Osimps,axiom,
% 161.83/161.96 ! [V_f_2,V_i_2,V_d_2] :
% 161.83/161.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 161.83/161.96 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 161.83/161.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 161.83/161.96 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Nats__number__of,axiom,
% 161.83/161.96 ! [V_w_2,T_a] :
% 161.83/161.96 ( class_Int_Onumber__ring(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 161.83/161.96 => 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))) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 161.83/161.96 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))) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_iszero__def,axiom,
% 161.83/161.96 ! [V_z_2,T_a] :
% 161.83/161.96 ( class_Rings_Osemiring__1(T_a)
% 161.83/161.96 => ( c_Int_Oiszero(T_a,V_z_2)
% 161.83/161.96 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_iszero__0,axiom,
% 161.83/161.96 ! [T_a] :
% 161.83/161.96 ( class_Rings_Osemiring__1(T_a)
% 161.83/161.96 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__0,axiom,
% 161.83/161.96 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 161.83/161.96 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_not__iszero__1,axiom,
% 161.83/161.96 ! [T_a] :
% 161.83/161.96 ( class_Rings_Osemiring__1(T_a)
% 161.83/161.96 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_eq__nat__nat__iff,axiom,
% 161.83/161.96 ! [V_z_H_2,V_z_2] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 161.83/161.96 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 161.83/161.96 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 161.83/161.96 ! [V_y_2,V_x_2] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 161.83/161.96 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 161.83/161.96 <=> V_x_2 = V_y_2 ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_all__nat,axiom,
% 161.83/161.96 ! [V_P_2] :
% 161.83/161.96 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 161.83/161.96 <=> ! [B_x] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 161.83/161.96 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_ex__nat,axiom,
% 161.83/161.96 ! [V_P_2] :
% 161.83/161.96 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 161.83/161.96 <=> ? [B_x] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 161.83/161.96 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__number__of,axiom,
% 161.83/161.96 ! [V_w] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__number__of__def,axiom,
% 161.83/161.96 ! [V_v] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 161.83/161.96 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_neg__nat,axiom,
% 161.83/161.96 ! [V_z] :
% 161.83/161.96 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 161.83/161.96 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__0__iff,axiom,
% 161.83/161.96 ! [V_i_2] :
% 161.83/161.96 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__le__0,axiom,
% 161.83/161.96 ! [V_z] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.96 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_zless__nat__conj,axiom,
% 161.83/161.96 ! [V_z_2,V_w_2] :
% 161.83/161.96 ( 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)))
% 161.83/161.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 161.83/161.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__mono__iff,axiom,
% 161.83/161.96 ! [V_w_2,V_z_2] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 161.83/161.96 => ( 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)))
% 161.83/161.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 161.83/161.96 ! [V_y_2,V_x_2] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 161.83/161.96 => ( 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)))
% 161.83/161.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__1,axiom,
% 161.83/161.96 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_iszero__Numeral0,axiom,
% 161.83/161.96 ! [T_a] :
% 161.83/161.96 ( class_Int_Onumber__ring(T_a)
% 161.83/161.96 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Nats__0,axiom,
% 161.83/161.96 ! [T_a] :
% 161.83/161.96 ( class_Rings_Osemiring__1(T_a)
% 161.83/161.96 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Nats__add,axiom,
% 161.83/161.96 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.96 ( class_Rings_Osemiring__1(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 161.83/161.96 => 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))) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Nats__mult,axiom,
% 161.83/161.96 ! [V_b_2,V_a_2,T_a] :
% 161.83/161.96 ( class_Rings_Osemiring__1(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 161.83/161.96 => 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))) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Nats__1,axiom,
% 161.83/161.96 ! [T_a] :
% 161.83/161.96 ( class_Rings_Osemiring__1(T_a)
% 161.83/161.96 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_zero__less__nat__eq,axiom,
% 161.83/161.96 ! [V_z_2] :
% 161.83/161.96 ( 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)))
% 161.83/161.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__less__eq__zless,axiom,
% 161.83/161.96 ! [V_z_2,V_w_2] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 161.83/161.96 => ( 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)))
% 161.83/161.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 161.83/161.96 ! [V_y_2,V_x_2] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 161.83/161.96 => ( 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)))
% 161.83/161.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__le__eq__zle,axiom,
% 161.83/161.96 ! [V_z_2,V_w_2] :
% 161.83/161.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 161.83/161.96 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 161.83/161.96 => ( 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)))
% 161.83/161.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__add__distrib,axiom,
% 161.83/161.96 ! [V_z_H,V_z] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 161.83/161.96 => 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)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 161.83/161.96 ! [V_y,V_x] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 161.83/161.96 => 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)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__mult__distrib,axiom,
% 161.83/161.96 ! [V_z_H,V_z] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 161.83/161.96 ! [V_y,V_x] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 161.83/161.96 => 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)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__diff__distrib,axiom,
% 161.83/161.96 ! [V_z,V_z_H] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 161.83/161.96 => 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)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 161.83/161.96 ! [V_y,V_x] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 161.83/161.96 => 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)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_diff__nat__eq__if,axiom,
% 161.83/161.96 ! [V_z_2,V_z_H_2] :
% 161.83/161.96 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 161.83/161.96 => 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) )
% 161.83/161.96 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 161.83/161.96 => 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)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_one__less__nat__eq,axiom,
% 161.83/161.96 ! [V_z_2] :
% 161.83/161.96 ( 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)))
% 161.83/161.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 161.83/161.96 ! [V_z] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__mult__distrib__neg,axiom,
% 161.83/161.96 ! [V_z_H,V_z] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.96 => 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))) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_eq__number__of__eq,axiom,
% 161.83/161.96 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.96 ( class_Int_Onumber__ring(T_a)
% 161.83/161.96 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 161.83/161.96 <=> 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)))) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Suc__eq__number__of,axiom,
% 161.83/161.96 ! [V_v_2,V_n_2] :
% 161.83/161.96 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 161.83/161.96 <=> 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))))) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_eq__number__of__Suc,axiom,
% 161.83/161.96 ! [V_n_2,V_v_2] :
% 161.83/161.96 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 161.83/161.96 <=> 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))))) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_less__Suc__number__of,axiom,
% 161.83/161.96 ! [V_v_2,V_n_2] :
% 161.83/161.96 ( 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)))
% 161.83/161.96 <=> 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))))) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_less__number__of__Suc,axiom,
% 161.83/161.96 ! [V_n_2,V_v_2] :
% 161.83/161.96 ( 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)))
% 161.83/161.96 <=> 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)))) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_le__Suc__number__of,axiom,
% 161.83/161.96 ! [V_v_2,V_n_2] :
% 161.83/161.96 ( 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)))
% 161.83/161.96 <=> 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))))) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_le__number__of__Suc,axiom,
% 161.83/161.96 ! [V_n_2,V_v_2] :
% 161.83/161.96 ( 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)))
% 161.83/161.96 <=> 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)))) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__case__add__eq__if,axiom,
% 161.83/161.96 ! [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)))) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__aux__def,axiom,
% 161.83/161.96 ! [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) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__case__number__of,axiom,
% 161.83/161.96 ! [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))) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__rec__add__eq__if,axiom,
% 161.83/161.96 ! [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))))) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__rec__number__of,axiom,
% 161.83/161.96 ! [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)))) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_transfer__morphism__nat__int,axiom,
% 161.83/161.96 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))) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__Suc__number__of,axiom,
% 161.83/161.96 ! [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)))) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Min_Oidem,axiom,
% 161.83/161.96 ! [V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oinf__assoc,axiom,
% 161.83/161.96 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oinf_Oassoc,axiom,
% 161.83/161.96 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oinf__left__commute,axiom,
% 161.83/161.96 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 161.83/161.96 ! [V_c,V_a,V_b,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oinf__left__idem,axiom,
% 161.83/161.96 ! [V_y,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 161.83/161.96 ! [V_b,V_a,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oinf__commute,axiom,
% 161.83/161.96 ! [V_y,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oinf_Ocommute,axiom,
% 161.83/161.96 ! [V_b,V_a,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oinf_Oidem,axiom,
% 161.83/161.96 ! [V_a,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__le__iff__disj,axiom,
% 161.83/161.96 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( 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))
% 161.83/161.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
% 161.83/161.96 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Ole__infE,axiom,
% 161.83/161.96 ! [V_b,V_a,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( 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)))
% 161.83/161.96 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 161.83/161.96 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oinf__mono,axiom,
% 161.83/161.96 ! [V_d,V_b,V_c,V_a,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 161.83/161.96 => 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))) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oinf__greatest,axiom,
% 161.83/161.96 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 161.83/161.96 => 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))) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Ole__infI,axiom,
% 161.83/161.96 ! [V_b,V_a,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 161.83/161.96 => 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))) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oinf__absorb2,axiom,
% 161.83/161.96 ! [V_x,V_y,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 161.83/161.96 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oinf__absorb1,axiom,
% 161.83/161.96 ! [V_y,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 161.83/161.96 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Ole__infI2,axiom,
% 161.83/161.96 ! [V_a,V_x,V_b,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 161.83/161.96 => 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)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Ole__infI1,axiom,
% 161.83/161.96 ! [V_b,V_x,V_a,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 161.83/161.96 => 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)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Ole__inf__iff,axiom,
% 161.83/161.96 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( 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)))
% 161.83/161.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 161.83/161.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Ole__iff__inf,axiom,
% 161.83/161.96 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 161.83/161.96 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2) = V_x_2 ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oinf__le2,axiom,
% 161.83/161.96 ! [V_y,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oinf__le1,axiom,
% 161.83/161.96 ! [V_y,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__less__iff__disj,axiom,
% 161.83/161.96 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( 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))
% 161.83/161.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2))
% 161.83/161.96 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__less__iff__conj,axiom,
% 161.83/161.96 ! [V_y_2,V_x_2,V_z_2,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( 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)))
% 161.83/161.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2))
% 161.83/161.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oless__infI2,axiom,
% 161.83/161.96 ! [V_a,V_x,V_b,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 161.83/161.96 => 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)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oless__infI1,axiom,
% 161.83/161.96 ! [V_b,V_x,V_a,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 161.83/161.96 => 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)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__add__distrib__left,axiom,
% 161.83/161.96 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.96 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__diff__distrib__left,axiom,
% 161.83/161.96 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.96 ( class_Groups_Oordered__ab__group__add(T_a)
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__0R,axiom,
% 161.83/161.96 ! [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) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__0L,axiom,
% 161.83/161.96 ! [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) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__Suc__Suc,axiom,
% 161.83/161.96 ! [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)) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__diff,axiom,
% 161.83/161.96 ! [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) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__Suc1,axiom,
% 161.83/161.96 ! [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) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__Suc2,axiom,
% 161.83/161.96 ! [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) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__number__of,axiom,
% 161.83/161.96 ! [V_v,V_u,T_b] :
% 161.83/161.96 ( ( class_Int_Onumber(T_b)
% 161.83/161.96 & class_Orderings_Oord(T_b) )
% 161.83/161.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
% 161.83/161.96 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) )
% 161.83/161.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
% 161.83/161.96 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__rec__0,axiom,
% 161.83/161.96 ! [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 ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__rec__Suc,axiom,
% 161.83/161.96 ! [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)) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__case__0,axiom,
% 161.83/161.96 ! [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 ).
% 161.83/161.96
% 161.83/161.96 fof(fact_nat__case__Suc,axiom,
% 161.83/161.96 ! [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) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Ofold__inf__insert,axiom,
% 161.83/161.96 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => 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)) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 161.83/161.96 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 161.83/161.96 => 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))) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Ofold1__belowI,axiom,
% 161.83/161.96 ! [V_a_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 161.83/161.96 => 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)) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 161.83/161.96 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.96 => ( 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)))
% 161.83/161.96 <=> ! [B_x] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 161.83/161.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_fold1__below__iff,axiom,
% 161.83/161.96 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.96 => ( 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))
% 161.83/161.96 <=> ? [B_x] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 161.83/161.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_x_2)) ) ) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_strict__below__fold1__iff,axiom,
% 161.83/161.96 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.96 => ( 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)))
% 161.83/161.96 <=> ! [B_x] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 161.83/161.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),B_x)) ) ) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_fold1__strict__below__iff,axiom,
% 161.83/161.96 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.96 => ( 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))
% 161.83/161.96 <=> ? [B_x] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 161.83/161.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_x_2)) ) ) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_fold1__antimono,axiom,
% 161.83/161.96 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 161.83/161.96 => 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))) ) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 161.83/161.96 ! [V_n_2,V_m_2] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 161.83/161.96 <=> 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_diff__Suc,axiom,
% 161.83/161.96 ! [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)) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__number__of__Suc,axiom,
% 161.83/161.96 ! [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)))) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_dual__max,axiom,
% 161.83/161.96 ! [T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__ord__min,axiom,
% 161.83/161.96 ! [T_a] :
% 161.83/161.96 ( class_Orderings_Oord(T_a)
% 161.83/161.96 => c_Orderings_Oord__class_Omin(T_a) = c_Orderings_Oord_Omin(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Min_Oremove,axiom,
% 161.83/161.96 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.96 => ( ( 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))
% 161.83/161.96 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 )
% 161.83/161.96 & ( 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))
% 161.83/161.96 => 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)))))) ) ) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 161.83/161.96 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.96 => ( ( 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))
% 161.83/161.96 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = V_x_2 )
% 161.83/161.96 & ( 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))
% 161.83/161.96 => 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)))))) ) ) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_max__Suc__number__of,axiom,
% 161.83/161.96 ! [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)))) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_max__number__of__Suc,axiom,
% 161.83/161.96 ! [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)))) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_decr__mult__lemma,axiom,
% 161.83/161.96 ! [V_k_2,V_P_2,V_d_2] :
% 161.83/161.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 161.83/161.96 => ( ! [B_x] :
% 161.83/161.96 ( hBOOL(hAPP(V_P_2,B_x))
% 161.83/161.96 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 161.83/161.96 => ! [B_x] :
% 161.83/161.96 ( hBOOL(hAPP(V_P_2,B_x))
% 161.83/161.96 => 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)))) ) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Osup_Oidem,axiom,
% 161.83/161.96 ! [V_a,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Osup_Ocommute,axiom,
% 161.83/161.96 ! [V_b,V_a,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Osup__commute,axiom,
% 161.83/161.96 ! [V_y,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 161.83/161.96 ! [V_b,V_a,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Osup__left__idem,axiom,
% 161.83/161.96 ! [V_y,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 161.83/161.96 ! [V_c,V_a,V_b,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Osup__left__commute,axiom,
% 161.83/161.96 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Osup_Oassoc,axiom,
% 161.83/161.96 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Osup__assoc,axiom,
% 161.83/161.96 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_max__ord__max,axiom,
% 161.83/161.96 ! [T_a] :
% 161.83/161.96 ( class_Orderings_Oord(T_a)
% 161.83/161.96 => c_Orderings_Oord__class_Omax(T_a) = c_Orderings_Oord_Omax(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_Max_Oidem,axiom,
% 161.83/161.96 ! [V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_sup__nat__def,axiom,
% 161.83/161.96 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_le__maxI1,axiom,
% 161.83/161.96 ! [V_y,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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))) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_le__maxI2,axiom,
% 161.83/161.96 ! [V_x,V_y,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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))) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Ole__iff__sup,axiom,
% 161.83/161.96 ! [V_y_2,V_x_2,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 161.83/161.96 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2) = V_y_2 ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Ole__sup__iff,axiom,
% 161.83/161.96 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( 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))
% 161.83/161.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
% 161.83/161.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Ole__supI1,axiom,
% 161.83/161.96 ! [V_b,V_a,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 161.83/161.96 => 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))) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Ole__supI2,axiom,
% 161.83/161.96 ! [V_a,V_b,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 161.83/161.96 => 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))) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Osup__absorb2,axiom,
% 161.83/161.96 ! [V_y,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 161.83/161.96 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Osup__absorb1,axiom,
% 161.83/161.96 ! [V_x,V_y,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 161.83/161.96 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Ole__supI,axiom,
% 161.83/161.96 ! [V_b,V_x,V_a,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 161.83/161.96 => 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)) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Osup__least,axiom,
% 161.83/161.96 ! [V_z,V_x,V_y,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 161.83/161.96 => 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)) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Osup__mono,axiom,
% 161.83/161.96 ! [V_d,V_b,V_c,V_a,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 161.83/161.96 => 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))) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Ole__supE,axiom,
% 161.83/161.96 ! [V_x,V_b,V_a,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( 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))
% 161.83/161.96 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 161.83/161.96 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_le__max__iff__disj,axiom,
% 161.83/161.96 ! [V_y_2,V_x_2,V_z_2,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( 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)))
% 161.83/161.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_x_2))
% 161.83/161.96 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_y_2)) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oless__supI1,axiom,
% 161.83/161.96 ! [V_b,V_a,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 161.83/161.96 => 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))) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oless__supI2,axiom,
% 161.83/161.96 ! [V_a,V_b,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 161.83/161.96 => 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))) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_less__max__iff__disj,axiom,
% 161.83/161.96 ! [V_y_2,V_x_2,V_z_2,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( 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)))
% 161.83/161.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2))
% 161.83/161.96 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_max__less__iff__conj,axiom,
% 161.83/161.96 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => ( 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))
% 161.83/161.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2))
% 161.83/161.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_max__add__distrib__left,axiom,
% 161.83/161.96 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.96 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_dual__min,axiom,
% 161.83/161.96 ! [T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_max__diff__distrib__left,axiom,
% 161.83/161.96 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.96 ( class_Groups_Oordered__ab__group__add(T_a)
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_sup__max,axiom,
% 161.83/161.96 ! [T_a] :
% 161.83/161.96 ( ( class_Lattices_Osemilattice__sup(T_a)
% 161.83/161.96 & class_Orderings_Olinorder(T_a) )
% 161.83/161.96 => c_Lattices_Osemilattice__sup__class_Osup(T_a) = c_Orderings_Oord__class_Omax(T_a) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_max__0L,axiom,
% 161.83/161.96 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 161.83/161.96
% 161.83/161.96 fof(fact_max__0R,axiom,
% 161.83/161.96 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 161.83/161.96
% 161.83/161.96 fof(fact_max__Suc__Suc,axiom,
% 161.83/161.96 ! [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)) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Osup__inf__absorb,axiom,
% 161.83/161.96 ! [V_y,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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 ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 161.83/161.96 ! [V_y,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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 ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 161.83/161.96 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 161.83/161.96 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 161.83/161.96 ! [V_x,V_z,V_y,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 161.83/161.96 ! [V_x,V_z,V_y,T_a] :
% 161.83/161.96 ( class_Orderings_Olinorder(T_a)
% 161.83/161.96 => 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)) ) ).
% 161.83/161.96
% 161.83/161.96 fof(fact_max__Suc1,axiom,
% 161.83/161.97 ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),V_m_2) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_max__Suc2,axiom,
% 161.83/161.97 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),V_n_2)),V_m_2) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 161.83/161.97 ! [V_a_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 161.83/161.97 => 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 ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_max__number__of,axiom,
% 161.83/161.97 ! [V_v,V_u,T_b] :
% 161.83/161.97 ( ( class_Int_Onumber(T_b)
% 161.83/161.97 & class_Orderings_Oord(T_b) )
% 161.83/161.97 => ( ( 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)))
% 161.83/161.97 => 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) )
% 161.83/161.97 & ( ~ 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)))
% 161.83/161.97 => 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) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_Odistrib__inf__le,axiom,
% 161.83/161.97 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => 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)))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_Odistrib__sup__le,axiom,
% 161.83/161.97 ! [V_z,V_y,V_x,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => 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)))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_minus__min__eq__max,axiom,
% 161.83/161.97 ! [V_y,V_x,T_a] :
% 161.83/161.97 ( class_Groups_Olinordered__ab__group__add(T_a)
% 161.83/161.97 => 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)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_minus__max__eq__min,axiom,
% 161.83/161.97 ! [V_y,V_x,T_a] :
% 161.83/161.97 ( class_Groups_Olinordered__ab__group__add(T_a)
% 161.83/161.97 => 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)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_nat__minus__add__max,axiom,
% 161.83/161.97 ! [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) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Min_Osingleton,axiom,
% 161.83/161.97 ! [V_x_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => 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 ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_Ofold__sup__insert,axiom,
% 161.83/161.97 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => 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)) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.97 => 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) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Min__le,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.97 => 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)) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 161.83/161.97 ! [V_x_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => 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 ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Min__in,axiom,
% 161.83/161.97 ! [V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Min_Oin__idem,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.97 => 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) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 161.83/161.97 ! [V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => 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) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Min_OF__eq,axiom,
% 161.83/161.97 ! [V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => 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) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 161.83/161.97 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 161.83/161.97 => 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))) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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)) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 161.83/161.97 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 161.83/161.97 => 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) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 161.83/161.97 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 161.83/161.97 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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)) ) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Min__antimono,axiom,
% 161.83/161.97 ! [V_N_2,V_M_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2))
% 161.83/161.97 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 161.83/161.97 => 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))) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 161.83/161.97 ! [V_a_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => 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) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Min__insert,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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)) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Min_Osubset__idem,axiom,
% 161.83/161.97 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 161.83/161.97 => 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) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Min__Un,axiom,
% 161.83/161.97 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 161.83/161.97 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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)) ) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 161.83/161.97 ! [V_a_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => 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) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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)) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( ( 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))
% 161.83/161.97 => 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 )
% 161.83/161.97 & ( 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))
% 161.83/161.97 => 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)))))) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.97 => 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) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Min_Oinsert,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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)) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Min_Oinsert__remove,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( ( 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))
% 161.83/161.97 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 161.83/161.97 & ( 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))
% 161.83/161.97 => 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)))))) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Min_Oeq__fold_H,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.97 => 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) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 161.83/161.97 ! [V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => ( ! [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))))))
% 161.83/161.97 => 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)) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Min_Oclosed,axiom,
% 161.83/161.97 ! [V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => ( ! [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))))))
% 161.83/161.97 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Max_Oremove,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.97 => ( ( 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))
% 161.83/161.97 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 )
% 161.83/161.97 & ( 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))
% 161.83/161.97 => 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)))))) ) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OInf__le__Sup,axiom,
% 161.83/161.97 ! [V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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))) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.97 => ( ( 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))
% 161.83/161.97 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = V_x_2 )
% 161.83/161.97 & ( 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))
% 161.83/161.97 => 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)))))) ) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 161.83/161.97 ! [V_N_2,V_h_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( ! [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))
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 161.83/161.97 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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)) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Max_Osingleton,axiom,
% 161.83/161.97 ! [V_x_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => 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 ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.97 => 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) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Max__ge,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.97 => 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))) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 161.83/161.97 ! [V_x_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => 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 ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Max__in,axiom,
% 161.83/161.97 ! [V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Max_Oin__idem,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.97 => 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) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 161.83/161.97 ! [V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => 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) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Max_OF__eq,axiom,
% 161.83/161.97 ! [V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => 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) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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)) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 161.83/161.97 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 161.83/161.97 => 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) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 161.83/161.97 ! [V_a_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 161.83/161.97 => 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 ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 161.83/161.97 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 161.83/161.97 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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)) ) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Max__mono,axiom,
% 161.83/161.97 ! [V_N_2,V_M_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2))
% 161.83/161.97 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 161.83/161.97 => 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))) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 161.83/161.97 ! [V_a_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => 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) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Max__insert,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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)) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Max_Osubset__idem,axiom,
% 161.83/161.97 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 161.83/161.97 => 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) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Max__Un,axiom,
% 161.83/161.97 ! [V_B_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 161.83/161.97 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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)) ) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 161.83/161.97 ! [V_a_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => 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) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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)) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( ( 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))
% 161.83/161.97 => 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 )
% 161.83/161.97 & ( 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))
% 161.83/161.97 => 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)))))) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.97 => 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) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Max_Oinsert,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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)) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Max_Oinsert__remove,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( ( 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))
% 161.83/161.97 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 161.83/161.97 & ( 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))
% 161.83/161.97 => 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)))))) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Max_Oeq__fold_H,axiom,
% 161.83/161.97 ! [V_x_2,V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 161.83/161.97 => 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) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_minus__Min__eq__Max,axiom,
% 161.83/161.97 ! [V_S_2,T_a] :
% 161.83/161.97 ( class_Groups_Olinordered__ab__group__add(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 161.83/161.97 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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)) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_minus__Max__eq__Min,axiom,
% 161.83/161.97 ! [V_S_2,T_a] :
% 161.83/161.97 ( class_Groups_Olinordered__ab__group__add(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 161.83/161.97 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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)) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 161.83/161.97 ! [V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => ( ! [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))))))
% 161.83/161.97 => 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)) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Max_Oclosed,axiom,
% 161.83/161.97 ! [V_A_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => ( ! [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))))))
% 161.83/161.97 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 161.83/161.97 ! [V_N_2,V_h_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( ! [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))
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 161.83/161.97 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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)) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Max_Ohom__commute,axiom,
% 161.83/161.97 ! [V_N_2,V_h_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( ! [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))
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 161.83/161.97 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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)) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Min_Ohom__commute,axiom,
% 161.83/161.97 ! [V_N_2,V_h_2,T_a] :
% 161.83/161.97 ( class_Orderings_Olinorder(T_a)
% 161.83/161.97 => ( ! [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))
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 161.83/161.97 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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)) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Sup__fin_Ohom__commute,axiom,
% 161.83/161.97 ! [V_N_2,V_h_2,T_a] :
% 161.83/161.97 ( class_Lattices_Olattice(T_a)
% 161.83/161.97 => ( ! [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))
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 161.83/161.97 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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)) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_nat__number__of__Bit1,axiom,
% 161.83/161.97 ! [V_w_2] :
% 161.83/161.97 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 161.83/161.97 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 161.83/161.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 161.83/161.97 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_SUPR__fold__sup,axiom,
% 161.83/161.97 ! [V_f_2,V_A_2,T_a,T_b] :
% 161.83/161.97 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => 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) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_incr__mult__lemma,axiom,
% 161.83/161.97 ! [V_k_2,V_P_2,V_d_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 161.83/161.97 => ( ! [B_x] :
% 161.83/161.97 ( hBOOL(hAPP(V_P_2,B_x))
% 161.83/161.97 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 161.83/161.97 => ! [B_x] :
% 161.83/161.97 ( hBOOL(hAPP(V_P_2,B_x))
% 161.83/161.97 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_eq__special_I4_J,axiom,
% 161.83/161.97 ! [V_x_2,T_a] :
% 161.83/161.97 ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 161.83/161.97 <=> 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))))) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_eq__special_I2_J,axiom,
% 161.83/161.97 ! [V_y_2,T_a] :
% 161.83/161.97 ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 => ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 161.83/161.97 <=> 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)))) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_of__nat__number__of__lemma,axiom,
% 161.83/161.97 ! [V_v,T_a] :
% 161.83/161.97 ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 161.83/161.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) )
% 161.83/161.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 161.83/161.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_SUP1__I,axiom,
% 161.83/161.97 ! [T_b,V_b_2,V_B_2,V_A_2,V_a_2,T_a] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 161.83/161.97 => 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)) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_SUP2__I,axiom,
% 161.83/161.97 ! [T_c,T_b,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_a] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
% 161.83/161.97 => 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)) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_negative__zle,axiom,
% 161.83/161.97 ! [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))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_negative__zless,axiom,
% 161.83/161.97 ! [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))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I51_J,axiom,
% 161.83/161.97 ! [V_l_2,V_k_2] :
% 161.83/161.97 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 161.83/161.97 <=> V_k_2 = V_l_2 ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_of__nat__eq__iff,axiom,
% 161.83/161.97 ! [V_n_2,V_m_2,T_a] :
% 161.83/161.97 ( class_Nat_Osemiring__char__0(T_a)
% 161.83/161.97 => ( 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)
% 161.83/161.97 <=> V_m_2 = V_n_2 ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_finite__UN,axiom,
% 161.83/161.97 ! [V_B_2,T_b,V_A_2,T_a] :
% 161.83/161.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => ( 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)))
% 161.83/161.97 <=> ! [B_x] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 161.83/161.97 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_less__eq__int__code_I16_J,axiom,
% 161.83/161.97 ! [V_k2_2,V_k1_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I34_J,axiom,
% 161.83/161.97 ! [V_l_2,V_k_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_less__int__code_I16_J,axiom,
% 161.83/161.97 ! [V_k2_2,V_k1_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I17_J,axiom,
% 161.83/161.97 ! [V_l_2,V_k_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I46_J,axiom,
% 161.83/161.97 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I39_J,axiom,
% 161.83/161.97 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_nat__int,axiom,
% 161.83/161.97 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 161.83/161.97
% 161.83/161.97 fof(fact_not__neg__int,axiom,
% 161.83/161.97 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 161.83/161.97 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 161.83/161.97 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)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_int__eq__0__conv,axiom,
% 161.83/161.97 ! [V_n_2] :
% 161.83/161.97 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.97 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_int__0,axiom,
% 161.83/161.97 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) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 161.83/161.97 ! [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))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 161.83/161.97 ! [V_P_2] :
% 161.83/161.97 ( ? [B_x] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 161.83/161.97 & hBOOL(hAPP(V_P_2,B_x)) )
% 161.83/161.97 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 161.83/161.97 ! [V_P_2] :
% 161.83/161.97 ( ! [B_x] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 161.83/161.97 => hBOOL(hAPP(V_P_2,B_x)) )
% 161.83/161.97 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_zero__zle__int,axiom,
% 161.83/161.97 ! [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))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_int__less__0__conv,axiom,
% 161.83/161.97 ! [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))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 161.83/161.97 ! [V_y_2,V_x_2] :
% 161.83/161.97 ( 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)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_zless__int,axiom,
% 161.83/161.97 ! [V_n_2,V_m_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_bin__less__0__simps_I4_J,axiom,
% 161.83/161.97 ! [V_w_2] :
% 161.83/161.97 ( 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)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 161.83/161.97 ! [V_y_2,V_x_2] :
% 161.83/161.97 ( 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)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_zle__int,axiom,
% 161.83/161.97 ! [V_n_2,V_m_2] :
% 161.83/161.97 ( 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)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 161.83/161.97 ! [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)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_zadd__int,axiom,
% 161.83/161.97 ! [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)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_zadd__int__left,axiom,
% 161.83/161.97 ! [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) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_zle__iff__zadd,axiom,
% 161.83/161.97 ! [V_z_2,V_w_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 161.83/161.97 <=> ? [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)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I22_J,axiom,
% 161.83/161.97 ! [V_k_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I12_J,axiom,
% 161.83/161.97 ! [V_k_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_zero__le__imp__of__nat,axiom,
% 161.83/161.97 ! [V_m,T_a] :
% 161.83/161.97 ( class_Rings_Olinordered__semidom(T_a)
% 161.83/161.97 => 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))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_of__nat__0__le__iff,axiom,
% 161.83/161.97 ! [V_n,T_a] :
% 161.83/161.97 ( class_Rings_Olinordered__semidom(T_a)
% 161.83/161.97 => 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))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_negative__eq__positive,axiom,
% 161.83/161.97 ! [V_m_2,V_n_2] :
% 161.83/161.97 ( 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)
% 161.83/161.97 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.97 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_of__nat__less__0__iff,axiom,
% 161.83/161.97 ! [V_m,T_a] :
% 161.83/161.97 ( class_Rings_Olinordered__semidom(T_a)
% 161.83/161.97 => ~ 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))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Bit1__def,axiom,
% 161.83/161.97 ! [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) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_not__int__zless__negative,axiom,
% 161.83/161.97 ! [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)))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 161.83/161.97 ! [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)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_zmult__int,axiom,
% 161.83/161.97 ! [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)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_int__mult,axiom,
% 161.83/161.97 ! [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)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_of__nat__0,axiom,
% 161.83/161.97 ! [T_a] :
% 161.83/161.97 ( class_Rings_Osemiring__1(T_a)
% 161.83/161.97 => 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) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_of__nat__less__iff,axiom,
% 161.83/161.97 ! [V_n_2,V_m_2,T_a] :
% 161.83/161.97 ( class_Rings_Olinordered__semidom(T_a)
% 161.83/161.97 => ( 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)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_less__imp__of__nat__less,axiom,
% 161.83/161.97 ! [V_n,V_m,T_a] :
% 161.83/161.97 ( class_Rings_Olinordered__semidom(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 161.83/161.97 => 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))) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_of__nat__less__imp__less,axiom,
% 161.83/161.97 ! [V_n,V_m,T_a] :
% 161.83/161.97 ( class_Rings_Olinordered__semidom(T_a)
% 161.83/161.97 => ( 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)))
% 161.83/161.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 161.83/161.97 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)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_int__1,axiom,
% 161.83/161.97 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) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_of__nat__le__iff,axiom,
% 161.83/161.97 ! [V_n_2,V_m_2,T_a] :
% 161.83/161.97 ( class_Rings_Olinordered__semidom(T_a)
% 161.83/161.97 => ( 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)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_of__nat__add,axiom,
% 161.83/161.97 ! [V_n,V_m,T_a] :
% 161.83/161.97 ( class_Rings_Osemiring__1(T_a)
% 161.83/161.97 => 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)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_of__nat__mult,axiom,
% 161.83/161.97 ! [V_n,V_m,T_a] :
% 161.83/161.97 ( class_Rings_Osemiring__1(T_a)
% 161.83/161.97 => 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)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_neg__number__of__Bit1,axiom,
% 161.83/161.97 ! [V_w_2] :
% 161.83/161.97 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 161.83/161.97 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_not__neg__nat,axiom,
% 161.83/161.97 ! [V_z] :
% 161.83/161.97 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 161.83/161.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_of__nat__1,axiom,
% 161.83/161.97 ! [T_a] :
% 161.83/161.97 ( class_Rings_Osemiring__1(T_a)
% 161.83/161.97 => 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) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_minus__Bit1,axiom,
% 161.83/161.97 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 161.83/161.97 ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 161.83/161.97 ! [V_A_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) = V_A_2 ).
% 161.83/161.97
% 161.83/161.97 fof(fact_iszero__number__of__Bit1,axiom,
% 161.83/161.97 ! [V_w,T_a] :
% 161.83/161.97 ( ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 & class_Int_Oring__char__0(T_a) )
% 161.83/161.97 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Ints__of__nat,axiom,
% 161.83/161.97 ! [V_n_2,T_a] :
% 161.83/161.97 ( class_Rings_Oring__1(T_a)
% 161.83/161.97 => 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))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_succ__Pls,axiom,
% 161.83/161.97 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_of__nat__in__Nats,axiom,
% 161.83/161.97 ! [V_n_2,T_a] :
% 161.83/161.97 ( class_Rings_Osemiring__1(T_a)
% 161.83/161.97 => 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))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 161.83/161.97 ! [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)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 161.83/161.97 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))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_number__of__Bit1,axiom,
% 161.83/161.97 ! [V_w,T_a] :
% 161.83/161.97 ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 => 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)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_mult__numeral__1,axiom,
% 161.83/161.97 ! [V_a,T_a] :
% 161.83/161.97 ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))),V_a) = V_a ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_mult__numeral__1__right,axiom,
% 161.83/161.97 ! [V_a,T_a] :
% 161.83/161.97 ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_int__le__0__conv,axiom,
% 161.83/161.97 ! [V_n_2] :
% 161.83/161.97 ( 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)))
% 161.83/161.97 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_numeral__1__eq__1,axiom,
% 161.83/161.97 ! [T_a] :
% 161.83/161.97 ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_semiring__norm_I110_J,axiom,
% 161.83/161.97 ! [T_a] :
% 161.83/161.97 ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_int__Suc0__eq__1,axiom,
% 161.83/161.97 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) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_zless__iff__Suc__zadd,axiom,
% 161.83/161.97 ! [V_z_2,V_w_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 161.83/161.97 <=> ? [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))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_nat__0__le,axiom,
% 161.83/161.97 ! [V_z] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 161.83/161.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_int__eq__iff,axiom,
% 161.83/161.97 ! [V_z_2,V_m_2] :
% 161.83/161.97 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 161.83/161.97 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 161.83/161.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_int__nat__eq,axiom,
% 161.83/161.97 ! [V_z] :
% 161.83/161.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 161.83/161.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 161.83/161.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 161.83/161.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_zless__nat__eq__int__zless,axiom,
% 161.83/161.97 ! [V_z_2,V_m_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I5_J,axiom,
% 161.83/161.97 ! [V_k_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I29_J,axiom,
% 161.83/161.97 ! [V_k_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_int__zle__neg,axiom,
% 161.83/161.97 ! [V_m_2,V_n_2] :
% 161.83/161.97 ( 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))))
% 161.83/161.97 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.97 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_int__Suc,axiom,
% 161.83/161.97 ! [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)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_negative__zle__0,axiom,
% 161.83/161.97 ! [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))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_nat__zminus__int,axiom,
% 161.83/161.97 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_one__is__num__one,axiom,
% 161.83/161.97 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_zdiff__int,axiom,
% 161.83/161.97 ! [V_m,V_n] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 161.83/161.97 => 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)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_nat__numeral__1__eq__1,axiom,
% 161.83/161.97 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Numeral1__eq1__nat,axiom,
% 161.83/161.97 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_of__nat__Suc,axiom,
% 161.83/161.97 ! [V_m,T_a] :
% 161.83/161.97 ( class_Rings_Osemiring__1(T_a)
% 161.83/161.97 => 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)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_neg__zminus__int,axiom,
% 161.83/161.97 ! [V_n] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_of__nat__diff,axiom,
% 161.83/161.97 ! [V_m,V_n,T_a] :
% 161.83/161.97 ( class_Rings_Oring__1(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 161.83/161.97 => 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)) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_not__iszero__Numeral1,axiom,
% 161.83/161.97 ! [T_a] :
% 161.83/161.97 ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_zero__less__int__conv,axiom,
% 161.83/161.97 ! [V_n_2] :
% 161.83/161.97 ( 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)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_nat__eq__iff2,axiom,
% 161.83/161.97 ! [V_w_2,V_m_2] :
% 161.83/161.97 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 161.83/161.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 161.83/161.97 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 161.83/161.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 161.83/161.97 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_nat__eq__iff,axiom,
% 161.83/161.97 ! [V_m_2,V_w_2] :
% 161.83/161.97 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 161.83/161.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 161.83/161.97 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 161.83/161.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 161.83/161.97 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_split__nat,axiom,
% 161.83/161.97 ! [V_i_2,V_P_2] :
% 161.83/161.97 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
% 161.83/161.97 <=> ( ! [B_n] :
% 161.83/161.97 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 161.83/161.97 => hBOOL(hAPP(V_P_2,B_n)) )
% 161.83/161.97 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.97 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_zmult__zless__mono2__lemma,axiom,
% 161.83/161.97 ! [V_k,V_j,V_i] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 161.83/161.97 => 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))) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_numeral__3__eq__3,axiom,
% 161.83/161.97 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_numeral__1__eq__Suc__0,axiom,
% 161.83/161.97 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_not__zle__0__negative,axiom,
% 161.83/161.97 ! [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))))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_negative__zless__0,axiom,
% 161.83/161.97 ! [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))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 161.83/161.97 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Suc3__eq__add__3,axiom,
% 161.83/161.97 ! [V_n] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_int__eq__iff__number__of,axiom,
% 161.83/161.97 ! [V_v_2,V_m_2] :
% 161.83/161.97 ( 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)
% 161.83/161.97 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 161.83/161.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 161.83/161.97 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_of__nat__0__less__iff,axiom,
% 161.83/161.97 ! [V_n_2,T_a] :
% 161.83/161.97 ( class_Rings_Olinordered__semidom(T_a)
% 161.83/161.97 => ( 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)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_int__nat__number__of,axiom,
% 161.83/161.97 ! [V_v] :
% 161.83/161.97 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 161.83/161.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 161.83/161.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 161.83/161.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_le__special_I4_J,axiom,
% 161.83/161.97 ! [V_x_2,T_a] :
% 161.83/161.97 ( ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 & class_Rings_Olinordered__idom(T_a) )
% 161.83/161.97 => ( 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)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_le__special_I2_J,axiom,
% 161.83/161.97 ! [V_y_2,T_a] :
% 161.83/161.97 ( ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 & class_Rings_Olinordered__idom(T_a) )
% 161.83/161.97 => ( 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)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_less__special_I4_J,axiom,
% 161.83/161.97 ! [V_x_2,T_a] :
% 161.83/161.97 ( ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 & class_Rings_Olinordered__idom(T_a) )
% 161.83/161.97 => ( 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)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_less__special_I2_J,axiom,
% 161.83/161.97 ! [V_y_2,T_a] :
% 161.83/161.97 ( ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 & class_Rings_Olinordered__idom(T_a) )
% 161.83/161.97 => ( 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)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_add__special_I2_J,axiom,
% 161.83/161.97 ! [V_w,T_a] :
% 161.83/161.97 ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_add__special_I3_J,axiom,
% 161.83/161.97 ! [V_v,T_a] :
% 161.83/161.97 ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),c_Int_OBit1(c_Int_OPls))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_nat__less__iff,axiom,
% 161.83/161.97 ! [V_m_2,V_w_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 161.83/161.97 ! [V_m,V_n] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),V_n))
% 161.83/161.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_zdiff__int__split,axiom,
% 161.83/161.97 ! [V_y_2,V_x_2,V_P_2] :
% 161.83/161.97 ( 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))))
% 161.83/161.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 161.83/161.97 => 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)))) )
% 161.83/161.97 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 161.83/161.97 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_sup__SUPR__fold__sup,axiom,
% 161.83/161.97 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 161.83/161.97 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 161.83/161.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 161.83/161.97 => 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) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_of__nat__number__of__eq,axiom,
% 161.83/161.97 ! [V_v,T_a] :
% 161.83/161.97 ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 161.83/161.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) )
% 161.83/161.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 161.83/161.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_diff__special_I1_J,axiom,
% 161.83/161.97 ! [V_w,T_a] :
% 161.83/161.97 ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_diff__special_I2_J,axiom,
% 161.83/161.97 ! [V_v,T_a] :
% 161.83/161.97 ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_image__eq__UN,axiom,
% 161.83/161.97 ! [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)))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_UN__I,axiom,
% 161.83/161.97 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 161.83/161.97 => 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))) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_le__SUPI,axiom,
% 161.83/161.97 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] :
% 161.83/161.97 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2))
% 161.83/161.97 => 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))) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 161.83/161.97 ! [V_n_2,T_a] :
% 161.83/161.97 ( class_Rings_Osemiring__1(T_a)
% 161.83/161.97 => 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)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_SUP__subset,axiom,
% 161.83/161.97 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 161.83/161.97 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.97 => 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))) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_of__nat__double,axiom,
% 161.83/161.97 ! [V_x,T_a] :
% 161.83/161.97 ( class_Rings_Osemiring__1(T_a)
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 161.83/161.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_UN__extend__simps_I9_J,axiom,
% 161.83/161.97 ! [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) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_UN__simps_I9_J,axiom,
% 161.83/161.97 ! [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)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_UN__UN__flatten,axiom,
% 161.83/161.97 ! [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)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_SUP1__iff,axiom,
% 161.83/161.97 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 161.83/161.97 ( 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))
% 161.83/161.97 <=> ? [B_x] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 161.83/161.97 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_SUP2__iff,axiom,
% 161.83/161.97 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 161.83/161.97 ( 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))
% 161.83/161.97 <=> ? [B_x] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 161.83/161.97 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_int__int__eq,axiom,
% 161.83/161.97 ! [V_n_2,V_m_2] :
% 161.83/161.97 ( 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)
% 161.83/161.97 <=> V_m_2 = V_n_2 ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_ball__UN,axiom,
% 161.83/161.97 ! [V_P_2,V_B_2,V_A_2,T_b,T_a] :
% 161.83/161.97 ( ! [B_x] :
% 161.83/161.97 ( 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)))
% 161.83/161.97 => hBOOL(hAPP(V_P_2,B_x)) )
% 161.83/161.97 <=> ! [B_x] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 161.83/161.97 => ! [B_xa] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(V_B_2,B_x)))
% 161.83/161.97 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 161.83/161.97 ! [V_y_2,V_x_2] :
% 161.83/161.97 ( 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)
% 161.83/161.97 <=> V_x_2 = V_y_2 ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 161.83/161.97 ! [V_B_2,V_A_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.97 <=> 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))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 161.83/161.97 ! [V_A_2] :
% 161.83/161.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 161.83/161.97 <=> 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))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 161.83/161.97 ! [V_B_2,V_A_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.97 <=> 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))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 161.83/161.97 ! [V_A_2,V_x_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 161.83/161.97 <=> 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))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 161.83/161.97 ! [V_B_2,V_A_2] :
% 161.83/161.97 ( V_A_2 = V_B_2
% 161.83/161.97 <=> 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) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 161.83/161.97 ! [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)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I48_J,axiom,
% 161.83/161.97 ! [V_l_2,V_k_2] :
% 161.83/161.97 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 161.83/161.97 <=> V_k_2 = V_l_2 ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I31_J,axiom,
% 161.83/161.97 ! [V_l_2,V_k_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_less__eq__int__code_I13_J,axiom,
% 161.83/161.97 ! [V_k2_2,V_k1_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I14_J,axiom,
% 161.83/161.97 ! [V_l_2,V_k_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_less__int__code_I13_J,axiom,
% 161.83/161.97 ! [V_k2_2,V_k1_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Bit0__Pls,axiom,
% 161.83/161.97 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I38_J,axiom,
% 161.83/161.97 ! [V_l_2] :
% 161.83/161.97 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 161.83/161.97 <=> c_Int_OPls = V_l_2 ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I44_J,axiom,
% 161.83/161.97 ! [V_k_2] :
% 161.83/161.97 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 161.83/161.97 <=> V_k_2 = c_Int_OPls ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I49_J,axiom,
% 161.83/161.97 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I50_J,axiom,
% 161.83/161.97 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_Bit0__def,axiom,
% 161.83/161.97 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_add__Bit0__Bit0,axiom,
% 161.83/161.97 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_mult__Bit0,axiom,
% 161.83/161.97 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_diff__bin__simps_I7_J,axiom,
% 161.83/161.97 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_minus__Bit0,axiom,
% 161.83/161.97 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(V_k)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_bin__less__0__simps_I3_J,axiom,
% 161.83/161.97 ! [V_w_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I27_J,axiom,
% 161.83/161.97 ! [V_k_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I21_J,axiom,
% 161.83/161.97 ! [V_k_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_less__eq__int__code_I14_J,axiom,
% 161.83/161.97 ! [V_k2_2,V_k1_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I32_J,axiom,
% 161.83/161.97 ! [V_l_2,V_k_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I10_J,axiom,
% 161.83/161.97 ! [V_k_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I4_J,axiom,
% 161.83/161.97 ! [V_k_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_less__int__code_I15_J,axiom,
% 161.83/161.97 ! [V_k2_2,V_k1_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I16_J,axiom,
% 161.83/161.97 ! [V_l_2,V_k_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_add__Bit1__Bit0,axiom,
% 161.83/161.97 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_add__Bit0__Bit1,axiom,
% 161.83/161.97 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_diff__bin__simps_I3_J,axiom,
% 161.83/161.97 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),V_l)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_diff__bin__simps_I9_J,axiom,
% 161.83/161.97 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_diff__bin__simps_I10_J,axiom,
% 161.83/161.97 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_neg__number__of__Bit0,axiom,
% 161.83/161.97 ! [V_w_2] :
% 161.83/161.97 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 161.83/161.97 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_pred__Bit0,axiom,
% 161.83/161.97 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_pred__Bit1,axiom,
% 161.83/161.97 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_iszero__number__of__Bit0,axiom,
% 161.83/161.97 ! [V_w_2,T_a] :
% 161.83/161.97 ( ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 & class_Int_Oring__char__0(T_a) )
% 161.83/161.97 => ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w_2)))
% 161.83/161.97 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_succ__Bit1,axiom,
% 161.83/161.97 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_succ__Bit0,axiom,
% 161.83/161.97 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_nat__number__of__Bit0,axiom,
% 161.83/161.97 ! [V_w_2] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_number__of__Bit0,axiom,
% 161.83/161.97 ! [V_w,T_a] :
% 161.83/161.97 ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_less__eq__int__code_I15_J,axiom,
% 161.83/161.97 ! [V_k2_2,V_k1_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I33_J,axiom,
% 161.83/161.97 ! [V_l_2,V_k_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_less__int__code_I14_J,axiom,
% 161.83/161.97 ! [V_k2_2,V_k1_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_rel__simps_I15_J,axiom,
% 161.83/161.97 ! [V_l_2,V_k_2] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 161.83/161.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_mult__Bit1,axiom,
% 161.83/161.97 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(V_k)),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l))),V_l) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 161.83/161.97 ! [V_i_2,V_inc_2,T_a] :
% 161.83/161.97 ( class_Rings_Osemiring__1(T_a)
% 161.83/161.97 => 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 ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 161.83/161.97 ! [V_i_2,V_n_2,V_inc_2,T_a] :
% 161.83/161.97 ( class_Rings_Osemiring__1(T_a)
% 161.83/161.97 => 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)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_diff__bin__simps_I8_J,axiom,
% 161.83/161.97 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(V_k)),V_l)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_add__Bit1__Bit1,axiom,
% 161.83/161.97 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_Osucc(V_l))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_double__number__of__Bit0,axiom,
% 161.83/161.97 ! [V_w,T_a] :
% 161.83/161.97 ( class_Int_Onumber__ring(T_a)
% 161.83/161.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_number__of1,axiom,
% 161.83/161.97 ! [V_n] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
% 161.83/161.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_n))))
% 161.83/161.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_n)))) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 161.83/161.97 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_UN__iff,axiom,
% 161.83/161.97 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 161.83/161.97 ( 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)))
% 161.83/161.97 <=> ? [B_x] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 161.83/161.97 & hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_UNION__empty__conv_I1_J,axiom,
% 161.83/161.97 ! [V_B_2,V_A_2,T_b,T_a] :
% 161.83/161.97 ( 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)
% 161.83/161.97 <=> ! [B_x] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 161.83/161.97 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_UN__empty2,axiom,
% 161.83/161.97 ! [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)) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_UN__constant,axiom,
% 161.83/161.97 ! [V_ca_2,T_b,T_a,V_A_2] :
% 161.83/161.97 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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)) )
% 161.83/161.97 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.97 => 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 ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_UNION__empty__conv_I2_J,axiom,
% 161.83/161.97 ! [V_B_2,V_A_2,T_a,T_b] :
% 161.83/161.97 ( 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))
% 161.83/161.97 <=> ! [B_x] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 161.83/161.97 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_UN__subset__iff,axiom,
% 161.83/161.97 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] :
% 161.83/161.97 ( 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))
% 161.83/161.97 <=> ! [B_x] :
% 161.83/161.97 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 161.83/161.97 => 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)) ) ) ).
% 161.83/161.97
% 161.83/161.97 fof(fact_UN__simps_I10_J,axiom,
% 161.83/161.98 ! [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)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_image__UN,axiom,
% 161.83/161.98 ! [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)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_UN__extend__simps_I10_J,axiom,
% 161.83/161.98 ! [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) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_UN__Un__distrib,axiom,
% 161.83/161.98 ! [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)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_UN__Un,axiom,
% 161.83/161.98 ! [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)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mult__2__right,axiom,
% 161.83/161.98 ! [V_z,T_a] :
% 161.83/161.98 ( class_Int_Onumber__ring(T_a)
% 161.83/161.98 => 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) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mult__2,axiom,
% 161.83/161.98 ! [V_z,T_a] :
% 161.83/161.98 ( class_Int_Onumber__ring(T_a)
% 161.83/161.98 => 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) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_one__add__one__is__two,axiom,
% 161.83/161.98 ! [T_a] :
% 161.83/161.98 ( class_Int_Onumber__ring(T_a)
% 161.83/161.98 => 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))) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_SUPR__apply,axiom,
% 161.83/161.98 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] :
% 161.83/161.98 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 161.83/161.98 => 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)) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_SUP__commute,axiom,
% 161.83/161.98 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] :
% 161.83/161.98 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 161.83/161.98 => 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))) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_UN__extend__simps_I6_J,axiom,
% 161.83/161.98 ! [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)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_UN__simps_I6_J,axiom,
% 161.83/161.98 ! [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) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_semiring__norm_I115_J,axiom,
% 161.83/161.98 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))) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_numeral__2__eq__2,axiom,
% 161.83/161.98 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))) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 161.83/161.98 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))))) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_add__2__eq__Suc,axiom,
% 161.83/161.98 ! [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)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_add__2__eq__Suc_H,axiom,
% 161.83/161.98 ! [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)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_nat__mult__2__right,axiom,
% 161.83/161.98 ! [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) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_nat__mult__2,axiom,
% 161.83/161.98 ! [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) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 161.83/161.98 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)))) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_nat__1__add__1,axiom,
% 161.83/161.98 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))) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_less__2__cases,axiom,
% 161.83/161.98 ! [V_n] :
% 161.83/161.98 ( 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)))))
% 161.83/161.98 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.98 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_nat__2,axiom,
% 161.83/161.98 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))) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_UN__insert__distrib,axiom,
% 161.83/161.98 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2))
% 161.83/161.98 => 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)) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_UN__upper,axiom,
% 161.83/161.98 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 161.83/161.98 => 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))) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_UN__absorb,axiom,
% 161.83/161.98 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2))
% 161.83/161.98 => 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) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_UN__simps_I1_J,axiom,
% 161.83/161.98 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] :
% 161.83/161.98 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.98 => 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)) )
% 161.83/161.98 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.98 => 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)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_UN__singleton,axiom,
% 161.83/161.98 ! [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 ).
% 161.83/161.98
% 161.83/161.98 fof(fact_UN__extend__simps_I1_J,axiom,
% 161.83/161.98 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] :
% 161.83/161.98 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.98 => 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))) )
% 161.83/161.98 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.98 => 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)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_SUP__le__iff,axiom,
% 161.83/161.98 ! [V_u_2,V_M_2,V_A_2,T_b,T_a] :
% 161.83/161.98 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 161.83/161.98 => ( 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))
% 161.83/161.98 <=> ! [B_x] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 161.83/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_less__SUP__iff,axiom,
% 161.83/161.98 ! [V_f_2,V_A_2,T_b,V_a_2,T_a] :
% 161.83/161.98 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 161.83/161.98 & class_Orderings_Olinorder(T_a) )
% 161.83/161.98 => ( 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)))
% 161.83/161.98 <=> ? [B_x] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 161.83/161.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_UN__extend__simps_I2_J,axiom,
% 161.83/161.98 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 161.83/161.98 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.98 => 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 )
% 161.83/161.98 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.98 => 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)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_UN__extend__simps_I3_J,axiom,
% 161.83/161.98 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 161.83/161.98 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.98 => 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 )
% 161.83/161.98 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.98 => 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)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_UN__simps_I2_J,axiom,
% 161.83/161.98 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 161.83/161.98 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.98 => 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)) )
% 161.83/161.98 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.98 => 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) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_UN__simps_I3_J,axiom,
% 161.83/161.98 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 161.83/161.98 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.98 => 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)) )
% 161.83/161.98 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.98 => 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)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_UN__insert,axiom,
% 161.83/161.98 ! [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)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_SUP__const,axiom,
% 161.83/161.98 ! [V_M_2,T_a,V_A_2,T_b] :
% 161.83/161.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 161.83/161.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 161.83/161.98 => 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 ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 161.83/161.98 ! [V_B_2,V_A_2] :
% 161.83/161.98 ( c_Nat__Transfer_Onat__set(V_A_2)
% 161.83/161.98 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 161.83/161.98 => 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))) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__number__of__Bit1,axiom,
% 161.83/161.98 ! [V_v,V_w] :
% 161.83/161.98 ( ( 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)))
% 161.83/161.98 => 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)) )
% 161.83/161.98 & ( ~ 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)))
% 161.83/161.98 => 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)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_neg__zmod__mult__2,axiom,
% 161.83/161.98 ! [V_b,V_a] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 => 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)) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_pos__zmod__mult__2,axiom,
% 161.83/161.98 ! [V_b,V_a] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 161.83/161.98 => 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))) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_neg__zdiv__mult__2,axiom,
% 161.83/161.98 ! [V_b,V_a] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 => 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) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_pos__zdiv__mult__2,axiom,
% 161.83/161.98 ! [V_b,V_a] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 161.83/161.98 => 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) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__mod__equality,axiom,
% 161.83/161.98 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__mod__equality2,axiom,
% 161.83/161.98 ! [V_c,V_a,V_b,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__div__equality,axiom,
% 161.83/161.98 ! [V_b,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__div__equality2,axiom,
% 161.83/161.98 ! [V_a,V_b,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 161.83/161.98 ! [V_b,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)) = V_a ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__zdiv__equality,axiom,
% 161.83/161.98 ! [V_b,V_a] : V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiv__zmult1__eq,axiom,
% 161.83/161.98 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiv__zmod__equality,axiom,
% 161.83/161.98 ! [V_k,V_a,V_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiv__zmod__equality2,axiom,
% 161.83/161.98 ! [V_k,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmult__div__cancel,axiom,
% 161.83/161.98 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__zdiv__equality_H,axiom,
% 161.83/161.98 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)),V_n)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiv__zadd1__eq,axiom,
% 161.83/161.98 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_DIVISION__BY__ZERO,axiom,
% 161.83/161.98 ! [V_a] :
% 161.83/161.98 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__div__trivial,axiom,
% 161.83/161.98 ! [V_b,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__zdiv__trivial,axiom,
% 161.83/161.98 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__mod__trivial,axiom,
% 161.83/161.98 ! [V_b,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => 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) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__self,axiom,
% 161.83/161.98 ! [V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__by__0,axiom,
% 161.83/161.98 ! [V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__0,axiom,
% 161.83/161.98 ! [V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__add__self2,axiom,
% 161.83/161.98 ! [V_b,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__add__self1,axiom,
% 161.83/161.98 ! [V_a,V_b,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__add__right__eq,axiom,
% 161.83/161.98 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__add__left__eq,axiom,
% 161.83/161.98 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__add__eq,axiom,
% 161.83/161.98 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__simps_I2_J,axiom,
% 161.83/161.98 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__simps_I1_J,axiom,
% 161.83/161.98 ! [V_b,V_c,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__add__cong,axiom,
% 161.83/161.98 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 161.83/161.98 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__mult__right__eq,axiom,
% 161.83/161.98 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__mult__left__eq,axiom,
% 161.83/161.98 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__mult__eq,axiom,
% 161.83/161.98 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__mult__mult1,axiom,
% 161.83/161.98 ! [V_b,V_a,V_c,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => 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)) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__mult__mult2,axiom,
% 161.83/161.98 ! [V_b,V_c,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__simps_I4_J,axiom,
% 161.83/161.98 ! [V_b,V_c,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__mult__cong,axiom,
% 161.83/161.98 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 161.83/161.98 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__diff__right__eq,axiom,
% 161.83/161.98 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Oring__div(T_a)
% 161.83/161.98 => 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) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__diff__left__eq,axiom,
% 161.83/161.98 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Oring__div(T_a)
% 161.83/161.98 => 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) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__diff__eq,axiom,
% 161.83/161.98 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Oring__div(T_a)
% 161.83/161.98 => 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) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__diff__cong,axiom,
% 161.83/161.98 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Oring__div(T_a)
% 161.83/161.98 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 161.83/161.98 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 161.83/161.98 => 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) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__minus__eq,axiom,
% 161.83/161.98 ! [V_b,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Oring__div(T_a)
% 161.83/161.98 => 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) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__minus__cong,axiom,
% 161.83/161.98 ! [V_a_H,V_b,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Oring__div(T_a)
% 161.83/161.98 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 161.83/161.98 => 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) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiv__zero,axiom,
% 161.83/161.98 ! [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) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__self,axiom,
% 161.83/161.98 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__zero,axiom,
% 161.83/161.98 ! [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) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiv__zminus__zminus,axiom,
% 161.83/161.98 ! [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) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiv__zminus2,axiom,
% 161.83/161.98 ! [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) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__simps_I3_J,axiom,
% 161.83/161.98 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__zmult1__eq,axiom,
% 161.83/161.98 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiff__zmod__right,axiom,
% 161.83/161.98 ! [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) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiff__zmod__left,axiom,
% 161.83/161.98 ! [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) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zminus__zmod,axiom,
% 161.83/161.98 ! [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) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__zminus__zminus,axiom,
% 161.83/161.98 ! [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)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__zminus2,axiom,
% 161.83/161.98 ! [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)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__by__0,axiom,
% 161.83/161.98 ! [V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => 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) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__0,axiom,
% 161.83/161.98 ! [V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => 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) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__by__1,axiom,
% 161.83/161.98 ! [V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__mult__self2__is__0,axiom,
% 161.83/161.98 ! [V_b,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__mult__self1__is__0,axiom,
% 161.83/161.98 ! [V_a,V_b,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__zmult2__eq,axiom,
% 161.83/161.98 ! [V_b,V_a,V_c] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 161.83/161.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__mult__self2,axiom,
% 161.83/161.98 ! [V_c,V_b,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__mult__self1,axiom,
% 161.83/161.98 ! [V_b,V_c,V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__by__1,axiom,
% 161.83/161.98 ! [V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiv__zminus2__eq__if,axiom,
% 161.83/161.98 ! [V_a,V_b] :
% 161.83/161.98 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) )
% 161.83/161.98 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiv__zminus1__eq__if,axiom,
% 161.83/161.98 ! [V_a,V_b] :
% 161.83/161.98 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) )
% 161.83/161.98 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 161.83/161.98 ! [V_y,V_x] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 161.83/161.98 => 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))) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 161.83/161.98 ! [V_a_2,V_b_2] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 161.83/161.98 => ( 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)))
% 161.83/161.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 161.83/161.98 ! [V_a_2,V_b_2] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 => ( 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)))
% 161.83/161.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__neg__pos__less0,axiom,
% 161.83/161.98 ! [V_b,V_a] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 161.83/161.98 => 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))) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiv__self,axiom,
% 161.83/161.98 ! [V_a] :
% 161.83/161.98 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__le__nonneg__dividend,axiom,
% 161.83/161.98 ! [V_k,V_m] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 161.83/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k)),V_m)) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 161.83/161.98 ! [V_y,V_x] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 161.83/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_pos__mod__bound,axiom,
% 161.83/161.98 ! [V_a,V_b] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 161.83/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_neg__mod__bound,axiom,
% 161.83/161.98 ! [V_a,V_b] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiv__number__of__Bit0,axiom,
% 161.83/161.98 ! [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)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__eq__0__iff,axiom,
% 161.83/161.98 ! [V_d_2,V_m_2] :
% 161.83/161.98 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__zminus2__not__zero,axiom,
% 161.83/161.98 ! [V_l,V_k] :
% 161.83/161.98 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__zminus1__not__zero,axiom,
% 161.83/161.98 ! [V_l,V_k] :
% 161.83/161.98 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__mult__mult1__if,axiom,
% 161.83/161.98 ! [V_b,V_a,V_c,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.98 => 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) )
% 161.83/161.98 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.98 => 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) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__mult__self2__is__id,axiom,
% 161.83/161.98 ! [V_a,V_b,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.98 => 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 ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__mult__self1__is__id,axiom,
% 161.83/161.98 ! [V_a,V_b,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.98 => 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 ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__mult__mult2,axiom,
% 161.83/161.98 ! [V_b,V_a,V_c,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.98 => 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) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__mult__mult1,axiom,
% 161.83/161.98 ! [V_b,V_a,V_c,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.98 => 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) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__self,axiom,
% 161.83/161.98 ! [V_a,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.98 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 161.83/161.98 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_split__pos__lemma,axiom,
% 161.83/161.98 ! [V_n_2,V_P_2,V_k_2] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 161.83/161.98 <=> ! [B_i,B_j] :
% 161.83/161.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 161.83/161.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 161.83/161.98 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 161.83/161.98 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_split__neg__lemma,axiom,
% 161.83/161.98 ! [V_n_2,V_P_2,V_k_2] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 161.83/161.98 <=> ! [B_i,B_j] :
% 161.83/161.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 161.83/161.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 161.83/161.98 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 161.83/161.98 ! [V_B_2,V_A_2] :
% 161.83/161.98 ( c_Nat__Transfer_Onat__set(V_A_2)
% 161.83/161.98 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 161.83/161.98 => 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)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_nat__set__def,axiom,
% 161.83/161.98 ! [V_S_2] :
% 161.83/161.98 ( c_Nat__Transfer_Onat__set(V_S_2)
% 161.83/161.98 <=> ! [B_x] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 161.83/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 161.83/161.98 ! [V_x_2,V_A_2] :
% 161.83/161.98 ( c_Nat__Transfer_Onat__set(V_A_2)
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 161.83/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiv__eq__0__iff,axiom,
% 161.83/161.98 ! [V_k_2,V_i_2] :
% 161.83/161.98 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 161.83/161.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 161.83/161.98 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 161.83/161.98 ! [V_a_2,V_b_2] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 161.83/161.98 => ( 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)))
% 161.83/161.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 161.83/161.98 ! [V_i_2,V_k_2] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 161.83/161.98 => ( 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)))
% 161.83/161.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 161.83/161.98 ! [V_b_2,V_a_2] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 161.83/161.98 => ( 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)))
% 161.83/161.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 161.83/161.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiv__mono2,axiom,
% 161.83/161.98 ! [V_b,V_b_H,V_a] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 161.83/161.98 => 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))) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__nonneg__neg__le0,axiom,
% 161.83/161.98 ! [V_b,V_a] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 => 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))) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__pos__pos__trivial,axiom,
% 161.83/161.98 ! [V_b,V_a] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 161.83/161.98 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 161.83/161.98 ! [V_a_2,V_b_2] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 => ( 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)))
% 161.83/161.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__nonpos__pos__le0,axiom,
% 161.83/161.98 ! [V_b,V_a] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 161.83/161.98 => 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))) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiv__mono2__neg,axiom,
% 161.83/161.98 ! [V_b,V_b_H,V_a] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 161.83/161.98 => 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))) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__neg__neg__trivial,axiom,
% 161.83/161.98 ! [V_b,V_a] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 161.83/161.98 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiv__mono1,axiom,
% 161.83/161.98 ! [V_b,V_a_H,V_a] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 161.83/161.98 => 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))) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiv__mono1__neg,axiom,
% 161.83/161.98 ! [V_b,V_a_H,V_a] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 => 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))) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_int__div__less__self,axiom,
% 161.83/161.98 ! [V_k,V_x] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 161.83/161.98 => 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)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiv__zmult2__eq,axiom,
% 161.83/161.98 ! [V_b,V_a,V_c] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 161.83/161.98 => 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) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_pos__mod__sign,axiom,
% 161.83/161.98 ! [V_a,V_b] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 161.83/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_pos__mod__conj,axiom,
% 161.83/161.98 ! [V_a,V_b] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))
% 161.83/161.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__pos__pos__trivial,axiom,
% 161.83/161.98 ! [V_b,V_a] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 161.83/161.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_neg__mod__sign,axiom,
% 161.83/161.98 ! [V_a,V_b] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_neg__mod__conj,axiom,
% 161.83/161.98 ! [V_a,V_b] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__neg__neg__trivial,axiom,
% 161.83/161.98 ! [V_b,V_a] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 161.83/161.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 161.83/161.98 ! [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)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 161.83/161.98 ! [V_A_2] :
% 161.83/161.98 ( c_Nat__Transfer_Onat__set(V_A_2)
% 161.83/161.98 => 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)) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 161.83/161.98 ! [V_B_2,V_A_2] :
% 161.83/161.98 ( c_Nat__Transfer_Onat__set(V_A_2)
% 161.83/161.98 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 161.83/161.98 => ( V_A_2 = V_B_2
% 161.83/161.98 <=> 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) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 161.83/161.98 ! [V_B_2,V_A_2] :
% 161.83/161.98 ( c_Nat__Transfer_Onat__set(V_A_2)
% 161.83/161.98 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.98 <=> 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))) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 161.83/161.98 ! [V_A_2] :
% 161.83/161.98 ( c_Nat__Transfer_Onat__set(V_A_2)
% 161.83/161.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 161.83/161.98 <=> 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))) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 161.83/161.98 ! [V_B_2,V_A_2] :
% 161.83/161.98 ( c_Nat__Transfer_Onat__set(V_A_2)
% 161.83/161.98 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 161.83/161.98 <=> 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))) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__zminus2__eq__if,axiom,
% 161.83/161.98 ! [V_b,V_a] :
% 161.83/161.98 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 161.83/161.98 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__zminus1__eq__if,axiom,
% 161.83/161.98 ! [V_b,V_a] :
% 161.83/161.98 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 161.83/161.98 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__mult__self2,axiom,
% 161.83/161.98 ! [V_c,V_a,V_b,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.98 => 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)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__mult__self1,axiom,
% 161.83/161.98 ! [V_c,V_a,V_b,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.98 => 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)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__add__self1,axiom,
% 161.83/161.98 ! [V_a,V_b,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.98 => 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)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__add__self2,axiom,
% 161.83/161.98 ! [V_a,V_b,T_a] :
% 161.83/161.98 ( class_Divides_Osemiring__div(T_a)
% 161.83/161.98 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 161.83/161.98 => 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)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__pos__neg__trivial,axiom,
% 161.83/161.98 ! [V_b,V_a] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_split__zdiv,axiom,
% 161.83/161.98 ! [V_k_2,V_n_2,V_P_2] :
% 161.83/161.98 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 161.83/161.98 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 161.83/161.98 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 161.83/161.98 => ! [B_i] :
% 161.83/161.98 ( ? [B_j] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 161.83/161.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 161.83/161.98 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 161.83/161.98 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 161.83/161.98 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 => ! [B_i] :
% 161.83/161.98 ( ? [B_j] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 161.83/161.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 161.83/161.98 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_divmod__int__rel__div__eq,axiom,
% 161.83/161.98 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 161.83/161.98 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1)
% 161.83/161.98 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 161.83/161.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 161.83/161.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 161.83/161.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 161.83/161.98 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_split__zmod,axiom,
% 161.83/161.98 ! [V_k_2,V_n_2,V_P_2] :
% 161.83/161.98 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 161.83/161.98 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 161.83/161.98 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 161.83/161.98 => ! [B_i,B_j] :
% 161.83/161.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 161.83/161.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 161.83/161.98 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 161.83/161.98 => hBOOL(hAPP(V_P_2,B_j)) ) )
% 161.83/161.98 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 => ! [B_i,B_j] :
% 161.83/161.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 161.83/161.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 161.83/161.98 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmult2__lemma__aux3,axiom,
% 161.83/161.98 ! [V_q,V_b,V_r,V_c] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 161.83/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmult2__lemma__aux4,axiom,
% 161.83/161.98 ! [V_q,V_b,V_r,V_c] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 161.83/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmult2__lemma__aux1,axiom,
% 161.83/161.98 ! [V_q,V_r,V_b,V_c] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmult2__lemma__aux2,axiom,
% 161.83/161.98 ! [V_q,V_r,V_b,V_c] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 161.83/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_divmod__int__rel__mod__eq,axiom,
% 161.83/161.98 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 161.83/161.98 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_q_1)),V_y)
% 161.83/161.98 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 161.83/161.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 161.83/161.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 161.83/161.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 161.83/161.98 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 161.83/161.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__number__of__Bit0,axiom,
% 161.83/161.98 ! [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))) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 161.83/161.98 ! [V_A_2] :
% 161.83/161.98 ( c_Nat__Transfer_Onat__set(V_A_2)
% 161.83/161.98 => 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 ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiv__number__of__Bit1,axiom,
% 161.83/161.98 ! [V_v,V_w] :
% 161.83/161.98 ( ( 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)))
% 161.83/161.98 => 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)) )
% 161.83/161.98 & ( ~ 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)))
% 161.83/161.98 => 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)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_z3div__def,axiom,
% 161.83/161.98 ! [V_k,V_l] :
% 161.83/161.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 161.83/161.98 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 161.83/161.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 161.83/161.98 => 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))) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_z3mod__def,axiom,
% 161.83/161.98 ! [V_k,V_l] :
% 161.83/161.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 161.83/161.98 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 161.83/161.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 161.83/161.98 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 161.83/161.98 ! [V_N_2] :
% 161.83/161.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 161.83/161.98 <=> ? [B_m] :
% 161.83/161.98 ! [B_x] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 161.83/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_power__number__of__odd__number__of,axiom,
% 161.83/161.98 ! [V_v_2,V_w_2,T_a] :
% 161.83/161.98 ( class_Int_Onumber__ring(T_a)
% 161.83/161.98 => ( ( 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)))
% 161.83/161.98 => 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))) )
% 161.83/161.98 & ( ~ 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)))
% 161.83/161.98 => 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) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_finite__nat__set__iff__bounded,axiom,
% 161.83/161.98 ! [V_N_2] :
% 161.83/161.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 161.83/161.98 <=> ? [B_m] :
% 161.83/161.98 ! [B_x] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 161.83/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_one__mod__nat__number__of,axiom,
% 161.83/161.98 ! [V_v_H] :
% 161.83/161.98 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 161.83/161.98 => 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)) )
% 161.83/161.98 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 161.83/161.98 => 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))) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__mult2__eq,axiom,
% 161.83/161.98 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__mult1__eq,axiom,
% 161.83/161.98 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__add1__eq,axiom,
% 161.83/161.98 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__mod__equality_H,axiom,
% 161.83/161.98 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mult__div__cancel,axiom,
% 161.83/161.98 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_Divides_Omod__div__equality_H,axiom,
% 161.83/161.98 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 161.83/161.98 ! [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)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_int__power,axiom,
% 161.83/161.98 ! [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) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zpower__int,axiom,
% 161.83/161.98 ! [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)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 161.83/161.98 ! [V_q,V_y,V_x,T_a] :
% 161.83/161.98 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.98 => 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)) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__le__mono,axiom,
% 161.83/161.98 ! [V_k,V_n,V_m] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 161.83/161.98 => 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))) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__le__dividend,axiom,
% 161.83/161.98 ! [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)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 161.83/161.98 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__mult2__eq,axiom,
% 161.83/161.98 ! [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) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__less,axiom,
% 161.83/161.98 ! [V_n,V_m] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 161.83/161.98 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__less__eq__dividend,axiom,
% 161.83/161.98 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_m)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__mult__distrib2,axiom,
% 161.83/161.98 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__mult__distrib,axiom,
% 161.83/161.98 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_k) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 161.83/161.98 ! [V_q,V_p,V_x,T_a] :
% 161.83/161.98 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.98 => 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)) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zpower__zpower,axiom,
% 161.83/161.98 ! [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)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 161.83/161.98 ! [V_x,T_a] :
% 161.83/161.98 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.98 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zpower__zmod,axiom,
% 161.83/161.98 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 161.83/161.98 ! [V_n,V_x] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 161.83/161.98 => 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)) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_nat__power__eq,axiom,
% 161.83/161.98 ! [V_n,V_z] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 161.83/161.98 => 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) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__1,axiom,
% 161.83/161.98 ! [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 ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__less,axiom,
% 161.83/161.98 ! [V_n,V_m] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 161.83/161.98 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_nat__mult__div__cancel__disj,axiom,
% 161.83/161.98 ! [V_n,V_m,V_k] :
% 161.83/161.98 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.98 => 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) )
% 161.83/161.98 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.98 => 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) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 161.83/161.98 ! [V_q,V_x,T_a] :
% 161.83/161.98 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.98 => 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)) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 161.83/161.98 ! [V_q,V_x,T_a] :
% 161.83/161.98 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.98 => 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)) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 161.83/161.98 ! [V_q,V_x,T_a] :
% 161.83/161.98 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.98 => 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)) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__1,axiom,
% 161.83/161.98 ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__Suc,axiom,
% 161.83/161.98 ! [V_n,V_m] :
% 161.83/161.98 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 161.83/161.98 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 161.83/161.98 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 161.83/161.98 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__less__divisor,axiom,
% 161.83/161.98 ! [V_m,V_n] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 161.83/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 161.83/161.98 ! [V_x,T_a] :
% 161.83/161.98 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.98 => 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) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 161.83/161.98 ! [V_q,V_p,V_x,T_a] :
% 161.83/161.98 ( class_Rings_Ocomm__semiring__1(T_a)
% 161.83/161.98 => 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)) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__eq__0__iff,axiom,
% 161.83/161.98 ! [V_d_2,V_m_2] :
% 161.83/161.98 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.98 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 161.83/161.98 ! [V_n,V_x] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 161.83/161.98 => 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))) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__geq,axiom,
% 161.83/161.98 ! [V_n,V_m] :
% 161.83/161.98 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 161.83/161.98 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__if,axiom,
% 161.83/161.98 ! [V_n,V_m] :
% 161.83/161.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 161.83/161.98 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 161.83/161.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 161.83/161.98 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__mult__self3,axiom,
% 161.83/161.98 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_le__mod__geq,axiom,
% 161.83/161.98 ! [V_m,V_n] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 161.83/161.98 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zdiv__int,axiom,
% 161.83/161.98 ! [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)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 161.83/161.98 ! [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)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zpower__zadd__distrib,axiom,
% 161.83/161.98 ! [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)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zmod__int,axiom,
% 161.83/161.98 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 161.83/161.98 ! [V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_Ints__power,axiom,
% 161.83/161.98 ! [V_n_2,V_a_2,T_a] :
% 161.83/161.98 ( class_Rings_Oring__1(T_a)
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 161.83/161.98 => 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))) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_power__nat__number__of,axiom,
% 161.83/161.98 ! [V_n,V_v] :
% 161.83/161.98 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 161.83/161.98 => 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) )
% 161.83/161.98 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 161.83/161.98 => 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)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_power__nat__number__of__number__of,axiom,
% 161.83/161.98 ! [V_w,V_v] :
% 161.83/161.98 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 161.83/161.98 => 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)) )
% 161.83/161.98 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 161.83/161.98 => 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))) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__le__mono2,axiom,
% 161.83/161.98 ! [V_k,V_n,V_m] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 161.83/161.98 => 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))) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__mult__self1__is__m,axiom,
% 161.83/161.98 ! [V_m,V_n] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 161.83/161.98 => 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 ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__mult__self__is__m,axiom,
% 161.83/161.98 ! [V_m,V_n] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 161.83/161.98 => 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 ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_nat__mult__div__cancel1,axiom,
% 161.83/161.98 ! [V_n,V_m,V_k] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 161.83/161.98 => 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) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__less__dividend,axiom,
% 161.83/161.98 ! [V_m,V_n] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 161.83/161.98 => 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)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__le__divisor,axiom,
% 161.83/161.98 ! [V_m,V_n] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 161.83/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__mult__self4,axiom,
% 161.83/161.98 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m)),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_power__number__of__even,axiom,
% 161.83/161.98 ! [V_w_2,V_z_2,T_a] :
% 161.83/161.98 ( class_Int_Onumber__ring(T_a)
% 161.83/161.98 => 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))) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_zpower__number__of__even,axiom,
% 161.83/161.98 ! [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))) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__geq,axiom,
% 161.83/161.98 ! [V_m,V_n] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 161.83/161.98 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 161.83/161.98 => 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)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_div__if,axiom,
% 161.83/161.98 ! [V_m,V_n] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 161.83/161.98 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 161.83/161.98 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 161.83/161.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 161.83/161.98 => 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)) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_split__div,axiom,
% 161.83/161.98 ! [V_k_2,V_n_2,V_P_2] :
% 161.83/161.98 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 161.83/161.98 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.98 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 161.83/161.98 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.98 => ! [B_i,B_j] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 161.83/161.98 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
% 161.83/161.98 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_nat__div__distrib,axiom,
% 161.83/161.98 ! [V_y,V_x] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 161.83/161.98 => 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)) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 161.83/161.98 ! [V_y,V_x] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 161.83/161.98 => 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)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_split__mod,axiom,
% 161.83/161.98 ! [V_k_2,V_n_2,V_P_2] :
% 161.83/161.98 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 161.83/161.98 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.98 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 161.83/161.98 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.98 => ! [B_i,B_j] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 161.83/161.98 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
% 161.83/161.98 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_mod__lemma,axiom,
% 161.83/161.98 ! [V_q,V_b,V_r,V_c] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 161.83/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c))) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_power3__eq__cube,axiom,
% 161.83/161.98 ! [V_a,T_a] :
% 161.83/161.98 ( class_Groups_Omonoid__mult(T_a)
% 161.83/161.98 => 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) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_Suc__times__mod__eq,axiom,
% 161.83/161.98 ! [V_m,V_k] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 161.83/161.98 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_nat__mod__distrib,axiom,
% 161.83/161.98 ! [V_y,V_x] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 161.83/161.98 => hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 161.83/161.98 ! [V_y,V_x] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 161.83/161.98 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_power__eq__if,axiom,
% 161.83/161.98 ! [V_p,V_m] :
% 161.83/161.98 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.98 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 161.83/161.98 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 161.83/161.98 => 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)))) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_power__number__of__even__number__of,axiom,
% 161.83/161.98 ! [V_w_2,V_v_2,T_a] :
% 161.83/161.98 ( class_Int_Onumber__ring(T_a)
% 161.83/161.98 => 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))) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_le__div__geq,axiom,
% 161.83/161.98 ! [V_m,V_n] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 161.83/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 161.83/161.98 => 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)) ) ) ).
% 161.83/161.98
% 161.83/161.98 fof(fact_split__div__lemma,axiom,
% 161.83/161.98 ! [V_m_2,V_q_2,V_n_2] :
% 161.83/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 161.83/161.98 => ( ( 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))
% 161.83/161.98 & 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)))) )
% 162.14/161.98 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_split__div_H,axiom,
% 162.14/161.98 ! [V_n_2,V_m_2,V_P_2] :
% 162.14/161.98 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 162.14/161.98 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.14/161.98 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 162.14/161.98 | ? [B_q] :
% 162.14/161.98 ( 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))
% 162.14/161.98 & 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))))
% 162.14/161.98 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 162.14/161.98 ! [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)) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_Suc__div__eq__add3__div,axiom,
% 162.14/161.98 ! [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) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_div__Suc__eq__div__add3,axiom,
% 162.14/161.98 ! [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)) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_div2__Suc__Suc,axiom,
% 162.14/161.98 ! [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))))) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_add__self__div__2,axiom,
% 162.14/161.98 ! [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 ).
% 162.14/161.98
% 162.14/161.98 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 162.14/161.98 ! [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)) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 162.14/161.98 ! [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) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 162.14/161.98 ! [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)) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_zero__eq__power2,axiom,
% 162.14/161.98 ! [V_a_2,T_a] :
% 162.14/161.98 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 162.14/161.98 => ( 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)
% 162.14/161.98 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_zero__power2,axiom,
% 162.14/161.98 ! [T_a] :
% 162.14/161.98 ( class_Rings_Osemiring__1(T_a)
% 162.14/161.98 => 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) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_power2__eq__square,axiom,
% 162.14/161.98 ! [V_a,T_a] :
% 162.14/161.98 ( class_Groups_Omonoid__mult(T_a)
% 162.14/161.98 => 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) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 162.14/161.98 ! [V_x,T_a] :
% 162.14/161.98 ( class_Rings_Ocomm__semiring__1(T_a)
% 162.14/161.98 => 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)))) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_mod2__Suc__Suc,axiom,
% 162.14/161.98 ! [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)))) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_one__power2,axiom,
% 162.14/161.98 ! [T_a] :
% 162.14/161.98 ( class_Rings_Osemiring__1(T_a)
% 162.14/161.98 => 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) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_power2__minus,axiom,
% 162.14/161.98 ! [V_a,T_a] :
% 162.14/161.98 ( class_Rings_Oring__1(T_a)
% 162.14/161.98 => 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)))) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_power__even__eq,axiom,
% 162.14/161.98 ! [V_n,V_a,T_a] :
% 162.14/161.98 ( class_Groups_Omonoid__mult(T_a)
% 162.14/161.98 => 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)))) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_zero__le__power2,axiom,
% 162.14/161.98 ! [V_a,T_a] :
% 162.14/161.98 ( class_Rings_Olinordered__idom(T_a)
% 162.14/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_power2__le__imp__le,axiom,
% 162.14/161.98 ! [V_y,V_x,T_a] :
% 162.14/161.98 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.98 => ( 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))))))
% 162.14/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 162.14/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_power2__eq__imp__eq,axiom,
% 162.14/161.98 ! [V_y,V_x,T_a] :
% 162.14/161.98 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.98 => ( 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))))
% 162.14/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 162.14/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 162.14/161.98 => V_x = V_y ) ) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_power2__less__0,axiom,
% 162.14/161.98 ! [V_a,T_a] :
% 162.14/161.98 ( class_Rings_Olinordered__idom(T_a)
% 162.14/161.98 => ~ 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))) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_zero__less__power2,axiom,
% 162.14/161.98 ! [V_a_2,T_a] :
% 162.14/161.98 ( class_Rings_Olinordered__idom(T_a)
% 162.14/161.98 => ( 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))))))
% 162.14/161.98 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_sum__power2__eq__zero__iff,axiom,
% 162.14/161.98 ! [V_y_2,V_x_2,T_a] :
% 162.14/161.98 ( class_Rings_Olinordered__idom(T_a)
% 162.14/161.98 => ( 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)
% 162.14/161.98 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 162.14/161.98 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_power2__eq__square__number__of,axiom,
% 162.14/161.98 ! [V_w,T_b] :
% 162.14/161.98 ( ( class_Groups_Omonoid__mult(T_b)
% 162.14/161.98 & class_Int_Onumber(T_b) )
% 162.14/161.98 => 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)) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_power2__eq__1__iff,axiom,
% 162.14/161.98 ! [V_a_2,T_a] :
% 162.14/161.98 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 162.14/161.98 => ( 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)
% 162.14/161.98 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_a)
% 162.14/161.98 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_div__nat__number__of,axiom,
% 162.14/161.98 ! [V_v_H,V_v] :
% 162.14/161.98 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 162.14/161.98 => 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) )
% 162.14/161.98 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 162.14/161.98 => 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))) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 162.14/161.98 ! [V_n,V_x,T_a] :
% 162.14/161.98 ( class_Rings_Ocomm__semiring__1(T_a)
% 162.14/161.98 => 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)) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_power__minus__even,axiom,
% 162.14/161.98 ! [V_n,V_a,T_a] :
% 162.14/161.98 ( class_Rings_Oring__1(T_a)
% 162.14/161.98 => 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)) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_mod__nat__number__of,axiom,
% 162.14/161.98 ! [V_v_H,V_v] :
% 162.14/161.98 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 162.14/161.98 => 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) )
% 162.14/161.98 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 162.14/161.98 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 162.14/161.98 => 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) )
% 162.14/161.98 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 162.14/161.98 => 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))) ) ) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_div__2__gt__zero,axiom,
% 162.14/161.98 ! [V_n] :
% 162.14/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 162.14/161.98 => 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)))))) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_power2__less__imp__less,axiom,
% 162.14/161.98 ! [V_y,V_x,T_a] :
% 162.14/161.98 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.98 => ( 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))))))
% 162.14/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 162.14/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_one__div__nat__number__of,axiom,
% 162.14/161.98 ! [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))) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_sum__power2__le__zero__iff,axiom,
% 162.14/161.98 ! [V_y_2,V_x_2,T_a] :
% 162.14/161.98 ( class_Rings_Olinordered__idom(T_a)
% 162.14/161.98 => ( 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)))
% 162.14/161.98 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 162.14/161.98 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_sum__power2__ge__zero,axiom,
% 162.14/161.98 ! [V_y,V_x,T_a] :
% 162.14/161.98 ( class_Rings_Olinordered__idom(T_a)
% 162.14/161.98 => 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))))))) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_sum__power2__gt__zero__iff,axiom,
% 162.14/161.98 ! [V_y_2,V_x_2,T_a] :
% 162.14/161.98 ( class_Rings_Olinordered__idom(T_a)
% 162.14/161.98 => ( 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)))))))
% 162.14/161.98 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 162.14/161.98 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_not__sum__power2__lt__zero,axiom,
% 162.14/161.98 ! [V_y,V_x,T_a] :
% 162.14/161.98 ( class_Rings_Olinordered__idom(T_a)
% 162.14/161.98 => ~ 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))) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_power2__sum,axiom,
% 162.14/161.98 ! [V_y,V_x,T_a] :
% 162.14/161.98 ( class_Int_Onumber__ring(T_a)
% 162.14/161.98 => 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)) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_zero__le__even__power_H,axiom,
% 162.14/161.98 ! [V_n,V_a,T_a] :
% 162.14/161.98 ( class_Rings_Olinordered__idom(T_a)
% 162.14/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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)))) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_power__odd__eq,axiom,
% 162.14/161.98 ! [V_n,V_a,T_a] :
% 162.14/161.98 ( class_Groups_Omonoid__mult(T_a)
% 162.14/161.98 => 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))))) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 162.14/161.98 ! [V_n,V_x,T_a] :
% 162.14/161.98 ( class_Rings_Ocomm__semiring__1(T_a)
% 162.14/161.98 => 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))) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_mod2__gr__0,axiom,
% 162.14/161.98 ! [V_m_2] :
% 162.14/161.98 ( 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))))))
% 162.14/161.98 <=> 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) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_power__minus1__even,axiom,
% 162.14/161.98 ! [V_n,T_a] :
% 162.14/161.98 ( class_Rings_Oring__1(T_a)
% 162.14/161.98 => 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) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_int__power__div__base,axiom,
% 162.14/161.98 ! [V_k,V_m] :
% 162.14/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 162.14/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 162.14/161.98 => 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)))) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_power__number__of__odd,axiom,
% 162.14/161.98 ! [V_z_2,V_w_2,T_a] :
% 162.14/161.98 ( class_Int_Onumber__ring(T_a)
% 162.14/161.98 => ( ( 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)))
% 162.14/161.98 => 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))) )
% 162.14/161.98 & ( ~ 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)))
% 162.14/161.98 => 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) ) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_zpower__number__of__odd,axiom,
% 162.14/161.98 ! [V_z_2,V_w_2] :
% 162.14/161.98 ( ( 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)))
% 162.14/161.98 => 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))) )
% 162.14/161.98 & ( ~ 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)))
% 162.14/161.98 => 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) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 162.14/161.98 ! [V_n] :
% 162.14/161.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 162.14/161.98 => 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)))))) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_power2__diff,axiom,
% 162.14/161.98 ! [V_y,V_x,T_a] :
% 162.14/161.98 ( class_Int_Onumber__ring(T_a)
% 162.14/161.98 => 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)) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 162.14/161.98 ! [V_n,V_a,T_a] :
% 162.14/161.98 ( class_Rings_Olinordered__idom(T_a)
% 162.14/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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)))))
% 162.14/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_odd__power__less__zero,axiom,
% 162.14/161.98 ! [V_n,V_a,T_a] :
% 162.14/161.98 ( class_Rings_Olinordered__idom(T_a)
% 162.14/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 162.14/161.98 => 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))) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_power__minus1__odd,axiom,
% 162.14/161.98 ! [V_n,T_a] :
% 162.14/161.98 ( class_Rings_Oring__1(T_a)
% 162.14/161.98 => 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)) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_power__strict__mono,axiom,
% 162.14/161.98 ! [V_n,V_b,V_a,T_a] :
% 162.14/161.98 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 162.14/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 162.14/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 162.14/161.98 => 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))) ) ) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_one__less__power,axiom,
% 162.14/161.98 ! [V_n,V_a,T_a] :
% 162.14/161.98 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 162.14/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 162.14/161.98 => 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))) ) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_power__increasing__iff,axiom,
% 162.14/161.98 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 162.14/161.98 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2))
% 162.14/161.98 => ( 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)))
% 162.14/161.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_power__le__imp__le__exp,axiom,
% 162.14/161.98 ! [V_n,V_m,V_a,T_a] :
% 162.14/161.98 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 162.14/161.98 => ( 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)))
% 162.14/161.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 162.14/161.98
% 162.14/161.98 fof(fact_power__decreasing,axiom,
% 162.14/161.98 ! [V_a,V_N,V_n,T_a] :
% 162.14/161.98 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 162.14/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 162.14/161.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 162.14/161.98 => 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))) ) ) ) ) ).
% 162.14/161.98
% 162.14/161.99 fof(fact_field__power__not__zero,axiom,
% 162.14/161.99 ! [V_n,V_a,T_a] :
% 162.14/161.99 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 162.14/161.99 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 162.14/161.99 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 162.14/161.99 ! [V_m_2,V_x_2] :
% 162.14/161.99 ( 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))
% 162.14/161.99 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.14/161.99 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__Suc__0,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_nat__zero__less__power__iff,axiom,
% 162.14/161.99 ! [V_n_2,V_x_2] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 162.14/161.99 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_nat__power__less__imp__less,axiom,
% 162.14/161.99 ! [V_n,V_m,V_i] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 162.14/161.99 => ( 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)))
% 162.14/161.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__commutes,axiom,
% 162.14/161.99 ! [V_n,V_a,T_a] :
% 162.14/161.99 ( class_Groups_Omonoid__mult(T_a)
% 162.14/161.99 => 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__mult__distrib,axiom,
% 162.14/161.99 ! [V_n,V_b,V_a,T_a] :
% 162.14/161.99 ( class_Groups_Ocomm__monoid__mult(T_a)
% 162.14/161.99 => 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__one,axiom,
% 162.14/161.99 ! [V_n,T_a] :
% 162.14/161.99 ( class_Groups_Omonoid__mult(T_a)
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__nat__power,axiom,
% 162.14/161.99 ! [V_n,V_m,T_a] :
% 162.14/161.99 ( class_Rings_Osemiring__1(T_a)
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__mult,axiom,
% 162.14/161.99 ! [V_n,V_m,V_a,T_a] :
% 162.14/161.99 ( class_Groups_Omonoid__mult(T_a)
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__one__right,axiom,
% 162.14/161.99 ! [V_a,T_a] :
% 162.14/161.99 ( class_Groups_Omonoid__mult(T_a)
% 162.14/161.99 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_zero__le__power,axiom,
% 162.14/161.99 ! [V_n,V_a,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 162.14/161.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__mono,axiom,
% 162.14/161.99 ! [V_n,V_b,V_a,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 162.14/161.99 => 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))) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_zero__less__power,axiom,
% 162.14/161.99 ! [V_n,V_a,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 162.14/161.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__eq__0__iff,axiom,
% 162.14/161.99 ! [V_n_2,V_a_2,T_a] :
% 162.14/161.99 ( ( class_Power_Opower(T_a)
% 162.14/161.99 & class_Rings_Omult__zero(T_a)
% 162.14/161.99 & class_Rings_Ono__zero__divisors(T_a)
% 162.14/161.99 & class_Rings_Ozero__neq__one(T_a) )
% 162.14/161.99 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
% 162.14/161.99 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 162.14/161.99 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_one__le__power,axiom,
% 162.14/161.99 ! [V_n,V_a,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 162.14/161.99 => 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))) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__0__Suc,axiom,
% 162.14/161.99 ! [V_n,T_a] :
% 162.14/161.99 ( ( class_Power_Opower(T_a)
% 162.14/161.99 & class_Rings_Osemiring__0(T_a) )
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__inject__exp,axiom,
% 162.14/161.99 ! [V_n_2,V_m_2,V_a_2,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2))
% 162.14/161.99 => ( 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)
% 162.14/161.99 <=> V_m_2 = V_n_2 ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__Suc2,axiom,
% 162.14/161.99 ! [V_n,V_a,T_a] :
% 162.14/161.99 ( class_Groups_Omonoid__mult(T_a)
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__Suc,axiom,
% 162.14/161.99 ! [V_n,V_a,T_a] :
% 162.14/161.99 ( class_Power_Opower(T_a)
% 162.14/161.99 => 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_nat__one__le__power,axiom,
% 162.14/161.99 ! [V_n,V_i] :
% 162.14/161.99 ( 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))
% 162.14/161.99 => 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))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__0,axiom,
% 162.14/161.99 ! [V_a,T_a] :
% 162.14/161.99 ( class_Power_Opower(T_a)
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__add,axiom,
% 162.14/161.99 ! [V_n,V_m,V_a,T_a] :
% 162.14/161.99 ( class_Groups_Omonoid__mult(T_a)
% 162.14/161.99 => 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__less__imp__less__base,axiom,
% 162.14/161.99 ! [V_b,V_n,V_a,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.99 => ( 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)))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 162.14/161.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__inject__base,axiom,
% 162.14/161.99 ! [V_b,V_n,V_a,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.99 => ( 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))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 162.14/161.99 => V_a = V_b ) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__le__imp__le__base,axiom,
% 162.14/161.99 ! [V_b,V_n,V_a,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.99 => ( 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))))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 162.14/161.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__gt1__lemma,axiom,
% 162.14/161.99 ! [V_n,V_a,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 162.14/161.99 => 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)))) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__less__power__Suc,axiom,
% 162.14/161.99 ! [V_n,V_a,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 162.14/161.99 => 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)))) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__0__left,axiom,
% 162.14/161.99 ! [V_n,T_a] :
% 162.14/161.99 ( ( class_Power_Opower(T_a)
% 162.14/161.99 & class_Rings_Osemiring__0(T_a) )
% 162.14/161.99 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.14/161.99 => 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) )
% 162.14/161.99 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.14/161.99 => 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) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__gt1,axiom,
% 162.14/161.99 ! [V_n,V_a,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 162.14/161.99 => 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)))) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__strict__increasing__iff,axiom,
% 162.14/161.99 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2))
% 162.14/161.99 => ( 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)))
% 162.14/161.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__less__imp__less__exp,axiom,
% 162.14/161.99 ! [V_n,V_m,V_a,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 162.14/161.99 => ( 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)))
% 162.14/161.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__strict__increasing,axiom,
% 162.14/161.99 ! [V_a,V_N,V_n,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 162.14/161.99 => 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))) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__increasing,axiom,
% 162.14/161.99 ! [V_a,V_N,V_n,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 162.14/161.99 => 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))) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__minus,axiom,
% 162.14/161.99 ! [V_n,V_a,T_a] :
% 162.14/161.99 ( class_Rings_Oring__1(T_a)
% 162.14/161.99 => 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__Suc__less,axiom,
% 162.14/161.99 ! [V_n,V_a,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 162.14/161.99 => 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))) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__eq__imp__eq__base,axiom,
% 162.14/161.99 ! [V_b,V_n,V_a,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.99 => ( 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)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 162.14/161.99 => V_a = V_b ) ) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__Suc__less__one,axiom,
% 162.14/161.99 ! [V_n,V_a,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 162.14/161.99 => 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))) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__strict__decreasing,axiom,
% 162.14/161.99 ! [V_a,V_N,V_n,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__semidom(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 162.14/161.99 => 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))) ) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_int__of__code,axiom,
% 162.14/161.99 ! [V_k] :
% 162.14/161.99 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 162.14/161.99 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 162.14/161.99 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 162.14/161.99 => ( ( 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)
% 162.14/161.99 => 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)))))) )
% 162.14/161.99 & ( 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)
% 162.14/161.99 => 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)) ) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__power__power,axiom,
% 162.14/161.99 ! [T_a] :
% 162.14/161.99 ( class_Power_Opower(T_a)
% 162.14/161.99 => 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__m1__odd,axiom,
% 162.14/161.99 ! [V_n,T_a] :
% 162.14/161.99 ( class_Int_Onumber__ring(T_a)
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power__m1__even,axiom,
% 162.14/161.99 ! [V_n,T_a] :
% 162.14/161.99 ( class_Int_Onumber__ring(T_a)
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 162.14/161.99 ! [V_A_2,V_x_2] :
% 162.14/161.99 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 162.14/161.99 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 162.14/161.99 <=> 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))) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rel__simps_I24_J,axiom,
% 162.14/161.99 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rel__simps_I7_J,axiom,
% 162.14/161.99 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rel__simps_I37_J,axiom,
% 162.14/161.99 c_Int_OPls != c_Int_OMin ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rel__simps_I40_J,axiom,
% 162.14/161.99 c_Int_OMin != c_Int_OPls ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rel__simps_I47_J,axiom,
% 162.14/161.99 ! [V_k_2] :
% 162.14/161.99 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 162.14/161.99 <=> V_k_2 = c_Int_OMin ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rel__simps_I43_J,axiom,
% 162.14/161.99 ! [V_l_2] :
% 162.14/161.99 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 162.14/161.99 <=> c_Int_OMin = V_l_2 ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_Bit1__Min,axiom,
% 162.14/161.99 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rel__simps_I45_J,axiom,
% 162.14/161.99 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rel__simps_I42_J,axiom,
% 162.14/161.99 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_code__numeral__zero__minus__one,axiom,
% 162.14/161.99 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) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 162.14/161.99 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 162.14/161.99 ! [V_y,V_x] :
% 162.14/161.99 ( c_Nat__Transfer_Ois__nat(V_x)
% 162.14/161.99 => ( c_Nat__Transfer_Ois__nat(V_y)
% 162.14/161.99 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 162.14/161.99 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 162.14/161.99 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 162.14/161.99 ! [V_y,V_x] :
% 162.14/161.99 ( c_Nat__Transfer_Ois__nat(V_x)
% 162.14/161.99 => ( c_Nat__Transfer_Ois__nat(V_y)
% 162.14/161.99 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 162.14/161.99 ! [V_y,V_x] :
% 162.14/161.99 ( c_Nat__Transfer_Ois__nat(V_x)
% 162.14/161.99 => ( c_Nat__Transfer_Ois__nat(V_y)
% 162.14/161.99 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 162.14/161.99 ! [V_y,V_x] :
% 162.14/161.99 ( c_Nat__Transfer_Ois__nat(V_x)
% 162.14/161.99 => ( c_Nat__Transfer_Ois__nat(V_y)
% 162.14/161.99 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 162.14/161.99 ! [V_n,V_x] :
% 162.14/161.99 ( c_Nat__Transfer_Ois__nat(V_x)
% 162.14/161.99 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_bin__less__0__simps_I2_J,axiom,
% 162.14/161.99 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rel__simps_I20_J,axiom,
% 162.14/161.99 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rel__simps_I23_J,axiom,
% 162.14/161.99 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rel__simps_I30_J,axiom,
% 162.14/161.99 ! [V_k_2] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 162.14/161.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rel__simps_I26_J,axiom,
% 162.14/161.99 ! [V_k_2] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 162.14/161.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rel__simps_I3_J,axiom,
% 162.14/161.99 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rel__simps_I6_J,axiom,
% 162.14/161.99 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rel__simps_I13_J,axiom,
% 162.14/161.99 ! [V_k_2] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 162.14/161.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rel__simps_I9_J,axiom,
% 162.14/161.99 ! [V_k_2] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 162.14/161.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rel__simps_I28_J,axiom,
% 162.14/161.99 ! [V_k_2] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 162.14/161.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rel__simps_I8_J,axiom,
% 162.14/161.99 ! [V_k_2] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 162.14/161.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_eq__number__of__Pls__Min,axiom,
% 162.14/161.99 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) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_Int_OMin__def,axiom,
% 162.14/161.99 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_mult__Min,axiom,
% 162.14/161.99 ! [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) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 162.14/161.99 ! [V_y,V_x] :
% 162.14/161.99 ( c_Nat__Transfer_Ois__nat(V_x)
% 162.14/161.99 => ( c_Nat__Transfer_Ois__nat(V_y)
% 162.14/161.99 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_neg__number__of__Min,axiom,
% 162.14/161.99 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_pred__Pls,axiom,
% 162.14/161.99 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 162.14/161.99
% 162.14/161.99 fof(fact_add__Min,axiom,
% 162.14/161.99 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_add__Min__right,axiom,
% 162.14/161.99 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_pred__Min,axiom,
% 162.14/161.99 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_nonzero__number__of__Min,axiom,
% 162.14/161.99 ! [T_a] :
% 162.14/161.99 ( class_Int_Onumber__ring(T_a)
% 162.14/161.99 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_succ__Min,axiom,
% 162.14/161.99 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 162.14/161.99
% 162.14/161.99 fof(fact_diff__bin__simps_I2_J,axiom,
% 162.14/161.99 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_is__nat__def,axiom,
% 162.14/161.99 ! [V_x_2] :
% 162.14/161.99 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 162.14/161.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_mult__minus1,axiom,
% 162.14/161.99 ! [V_z,T_a] :
% 162.14/161.99 ( class_Int_Onumber__ring(T_a)
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_mult__minus1__right,axiom,
% 162.14/161.99 ! [V_z,T_a] :
% 162.14/161.99 ( class_Int_Onumber__ring(T_a)
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_number__of__Min,axiom,
% 162.14/161.99 ! [T_a] :
% 162.14/161.99 ( class_Int_Onumber__ring(T_a)
% 162.14/161.99 => 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_arith__simps_I31_J,axiom,
% 162.14/161.99 ! [T_a] :
% 162.14/161.99 ( class_Int_Onumber__ring(T_a)
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rel__simps_I11_J,axiom,
% 162.14/161.99 ! [V_k_2] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 162.14/161.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rel__simps_I25_J,axiom,
% 162.14/161.99 ! [V_k_2] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 162.14/161.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_zmod__minus1__right,axiom,
% 162.14/161.99 ! [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) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_diff__bin__simps_I4_J,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_minus__Min,axiom,
% 162.14/161.99 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 162.14/161.99 ! [V_n,V_m] :
% 162.14/161.99 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 162.14/161.99 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 162.14/161.99 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_zmult__eq__1__iff,axiom,
% 162.14/161.99 ! [V_n_2,V_m_2] :
% 162.14/161.99 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 162.14/161.99 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 162.14/161.99 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 162.14/161.99 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 162.14/161.99 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_diff__bin__simps_I5_J,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_diff__bin__simps_I6_J,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power_Opower_Opower__0,axiom,
% 162.14/161.99 ! [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 ).
% 162.14/161.99
% 162.14/161.99 fof(fact_power_Opower_Opower__Suc,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_zdiv__minus1__right,axiom,
% 162.14/161.99 ! [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) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 162.14/161.99 ! [V_x_2,V_A_2] :
% 162.14/161.99 ( c_Nat__Transfer_Onat__set(V_A_2)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 162.14/161.99 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_zero__code__numeral__code,axiom,
% 162.14/161.99 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) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_div__eq__minus1,axiom,
% 162.14/161.99 ! [V_b] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 162.14/161.99 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 162.14/161.99 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_div__pos__neg__trivial,axiom,
% 162.14/161.99 ! [V_b,V_a] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 162.14/161.99 => ( 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)))
% 162.14/161.99 => 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) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_zmod__minus1,axiom,
% 162.14/161.99 ! [V_b] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 162.14/161.99 => 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_one__code__numeral__code,axiom,
% 162.14/161.99 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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_small__int__def,axiom,
% 162.14/161.99 ! [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))) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_full__small__int__def,axiom,
% 162.14/161.99 ! [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))) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_code__numeral_Osize_I1_J,axiom,
% 162.14/161.99 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) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_card__greaterThanLessThan__int,axiom,
% 162.14/161.99 ! [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)))) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 162.14/161.99 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 162.14/161.99 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_finite__greaterThanLessThan__int,axiom,
% 162.14/161.99 ! [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))) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_greaterThanLessThan__empty,axiom,
% 162.14/161.99 ! [V_k_2,V_l_2,T_a] :
% 162.14/161.99 ( class_Orderings_Oorder(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2))
% 162.14/161.99 => 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)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 162.14/161.99 ! [V_y_2,V_x_2,T_a] :
% 162.14/161.99 ( class_Groups_Oordered__ab__group__add(T_a)
% 162.14/161.99 => 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_nat__of__aux__code,axiom,
% 162.14/161.99 ! [V_n,V_i] :
% 162.14/161.99 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 162.14/161.99 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 162.14/161.99 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 162.14/161.99 => 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)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_code__numeral_Osize_I2_J,axiom,
% 162.14/161.99 ! [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))) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_ord_OatMost__iff,axiom,
% 162.14/161.99 ! [V_k_2,V_less__eq_2,V_i_2,T_a] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2)))
% 162.14/161.99 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_ord_OatLeast__iff,axiom,
% 162.14/161.99 ! [V_k_2,V_less__eq_2,V_i_2,T_a] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2)))
% 162.14/161.99 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_ord_OlessThan__iff,axiom,
% 162.14/161.99 ! [V_k_2,V_less_2,V_i_2,T_a] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2)))
% 162.14/161.99 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_finite__greaterThanLessThan,axiom,
% 162.14/161.99 ! [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))) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_code__numeral_Oinject,axiom,
% 162.14/161.99 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 162.14/161.99 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 162.14/161.99 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 162.14/161.99 ! [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) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 162.14/161.99 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_Suc__code__numeral__minus__one,axiom,
% 162.14/161.99 ! [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 ).
% 162.14/161.99
% 162.14/161.99 fof(fact_card__greaterThanLessThan,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_code__numeral_Osize_I4_J,axiom,
% 162.14/161.99 ! [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))) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 162.14/161.99 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 162.14/161.99 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 162.14/161.99 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 162.14/161.99 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 162.14/161.99 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 162.14/161.99 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_ord_OgreaterThan__iff,axiom,
% 162.14/161.99 ! [V_k_2,V_less_2,V_i_2,T_a] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2)))
% 162.14/161.99 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_code__numeral_Osize_I3_J,axiom,
% 162.14/161.99 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) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_ivl__disj__un_I4_J,axiom,
% 162.14/161.99 ! [V_u_2,V_l_2,T_a] :
% 162.14/161.99 ( class_Orderings_Olinorder(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 162.14/161.99 => 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) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__of__nat,axiom,
% 162.14/161.99 ! [V_k,T_a] :
% 162.14/161.99 ( class_Rings_Oring__1(T_a)
% 162.14/161.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.14/161.99 => 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)))) )
% 162.14/161.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.14/161.99 => 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)) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_setprod__gen__delta,axiom,
% 162.14/161.99 ! [V_ca_2,V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 162.14/161.99 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.14/161.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 162.14/161.99 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 162.14/161.99 => 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)))) )
% 162.14/161.99 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 162.14/161.99 => 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)) ) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_adjust__eq,axiom,
% 162.14/161.99 ! [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))) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_negD,axiom,
% 162.14/161.99 ! [V_x] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.14/161.99 => ? [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))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_finite__greaterThanAtMost,axiom,
% 162.14/161.99 ! [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))) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_finite__greaterThanAtMost__int,axiom,
% 162.14/161.99 ! [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))) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_sup__Un__eq2,axiom,
% 162.14/161.99 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] :
% 162.14/161.99 ( 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))
% 162.14/161.99 <=> 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))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_pred__equals__eq2,axiom,
% 162.14/161.99 ! [V_S_2,V_R_2,T_b,T_a] :
% 162.14/161.99 ( 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)
% 162.14/161.99 <=> V_R_2 = V_S_2 ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_pred__subset__eq2,axiom,
% 162.14/161.99 ! [V_S_2,V_R_2,T_b,T_a] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 <=> 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_bot__empty__eq2,axiom,
% 162.14/161.99 ! [V_y_2,V_x_2,T_b,T_a] :
% 162.14/161.99 ( 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))
% 162.14/161.99 <=> 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)))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__eq__iff,axiom,
% 162.14/161.99 ! [V_z_2,V_w_2,T_a] :
% 162.14/161.99 ( class_Int_Oring__char__0(T_a)
% 162.14/161.99 => ( 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)
% 162.14/161.99 <=> V_w_2 = V_z_2 ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__setprod,axiom,
% 162.14/161.99 ! [V_A_2,V_f_2,T_b,T_a] :
% 162.14/161.99 ( ( class_Groups_Ocomm__monoid__mult(T_a)
% 162.14/161.99 & class_Rings_Oring__1(T_a) )
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__nat__setprod,axiom,
% 162.14/161.99 ! [V_A_2,V_f_2,T_b,T_a] :
% 162.14/161.99 ( ( class_Groups_Ocomm__monoid__mult(T_a)
% 162.14/161.99 & class_Rings_Osemiring__1(T_a) )
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_int__setprod,axiom,
% 162.14/161.99 ! [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) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_number__of__eq,axiom,
% 162.14/161.99 ! [V_k,T_a] :
% 162.14/161.99 ( class_Int_Onumber__ring(T_a)
% 162.14/161.99 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_setprod__timesf,axiom,
% 162.14/161.99 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
% 162.14/161.99 ( class_Groups_Ocomm__monoid__mult(T_a)
% 162.14/161.99 => 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_int__number__of__def,axiom,
% 162.14/161.99 ! [V_w] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),V_w) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__int__eq,axiom,
% 162.14/161.99 ! [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) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_setprod__1,axiom,
% 162.14/161.99 ! [V_A_2,T_b,T_a] :
% 162.14/161.99 ( class_Groups_Ocomm__monoid__mult(T_a)
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 162.14/161.99 ! [V_A_2,V_f_2,T_a] :
% 162.14/161.99 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 162.14/161.99 & class_Groups_Ocomm__monoid__mult(T_a) )
% 162.14/161.99 => 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_setprod__zero__iff,axiom,
% 162.14/161.99 ! [V_f_2,V_A_2,T_a,T_b] :
% 162.14/161.99 ( ( class_Rings_Ocomm__semiring__1(T_b)
% 162.14/161.99 & class_Rings_Ono__zero__divisors(T_b) )
% 162.14/161.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.14/161.99 => ( 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)
% 162.14/161.99 <=> ? [B_x] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.14/161.99 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_setprod__zero,axiom,
% 162.14/161.99 ! [V_f_2,V_A_2,T_a,T_b] :
% 162.14/161.99 ( class_Rings_Ocomm__semiring__1(T_b)
% 162.14/161.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.14/161.99 => ( ? [B_x] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.14/161.99 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 162.14/161.99 => 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) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_setprod__empty,axiom,
% 162.14/161.99 ! [V_f_2,T_b,T_a] :
% 162.14/161.99 ( class_Groups_Ocomm__monoid__mult(T_a)
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_setprod_Oempty,axiom,
% 162.14/161.99 ! [V_g_2,T_b,T_a] :
% 162.14/161.99 ( class_Groups_Ocomm__monoid__mult(T_a)
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_setprod_Oinfinite,axiom,
% 162.14/161.99 ! [V_g_2,V_A_2,T_a,T_b] :
% 162.14/161.99 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.14/161.99 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.14/161.99 => 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) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_setprod__infinite,axiom,
% 162.14/161.99 ! [V_f_2,V_A_2,T_a,T_b] :
% 162.14/161.99 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.14/161.99 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.14/161.99 => 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) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_setprod__eq__1__iff,axiom,
% 162.14/161.99 ! [V_f_2,V_F_2,T_a] :
% 162.14/161.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 162.14/161.99 => ( 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)
% 162.14/161.99 <=> ! [B_x] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2))
% 162.14/161.99 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 162.14/161.99 ! [V_f_2,V_A_2,T_a] :
% 162.14/161.99 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 162.14/161.99 & class_Groups_Ocomm__monoid__mult(T_a) )
% 162.14/161.99 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 162.14/161.99 => 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)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_small__prod__def,axiom,
% 162.14/161.99 ! [V_d_2,V_f_2,T_a,T_b] :
% 162.14/161.99 ( ( class_Smallcheck_Osmall(T_b)
% 162.14/161.99 & class_Smallcheck_Osmall(T_a) )
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_setprod_Odistrib,axiom,
% 162.14/161.99 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 162.14/161.99 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.14/161.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.14/161.99 => 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)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__eq__0__iff,axiom,
% 162.14/161.99 ! [V_z_2,T_a] :
% 162.14/161.99 ( class_Int_Oring__char__0(T_a)
% 162.14/161.99 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) = c_Groups_Ozero__class_Ozero(T_a)
% 162.14/161.99 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__0__eq__iff,axiom,
% 162.14/161.99 ! [V_z_2,T_a] :
% 162.14/161.99 ( class_Int_Oring__char__0(T_a)
% 162.14/161.99 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)
% 162.14/161.99 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__0,axiom,
% 162.14/161.99 ! [T_a] :
% 162.14/161.99 ( class_Rings_Oring__1(T_a)
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__le__iff,axiom,
% 162.14/161.99 ! [V_z_2,V_w_2,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__idom(T_a)
% 162.14/161.99 => ( 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)))
% 162.14/161.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__less__iff,axiom,
% 162.14/161.99 ! [V_z_2,V_w_2,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__idom(T_a)
% 162.14/161.99 => ( 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)))
% 162.14/161.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__add,axiom,
% 162.14/161.99 ! [V_z,V_w,T_a] :
% 162.14/161.99 ( class_Rings_Oring__1(T_a)
% 162.14/161.99 => 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__number__of__eq,axiom,
% 162.14/161.99 ! [V_v,T_a] :
% 162.14/161.99 ( class_Int_Onumber__ring(T_a)
% 162.14/161.99 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__mult,axiom,
% 162.14/161.99 ! [V_z,V_w,T_a] :
% 162.14/161.99 ( class_Rings_Oring__1(T_a)
% 162.14/161.99 => 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__1,axiom,
% 162.14/161.99 ! [T_a] :
% 162.14/161.99 ( class_Rings_Oring__1(T_a)
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__diff,axiom,
% 162.14/161.99 ! [V_z,V_w,T_a] :
% 162.14/161.99 ( class_Rings_Oring__1(T_a)
% 162.14/161.99 => 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__of__nat__eq,axiom,
% 162.14/161.99 ! [V_n,T_a] :
% 162.14/161.99 ( class_Rings_Oring__1(T_a)
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__minus,axiom,
% 162.14/161.99 ! [V_z,T_a] :
% 162.14/161.99 ( class_Rings_Oring__1(T_a)
% 162.14/161.99 => 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_Ints__of__int,axiom,
% 162.14/161.99 ! [V_z_2,T_a] :
% 162.14/161.99 ( class_Rings_Oring__1(T_a)
% 162.14/161.99 => 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))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__power,axiom,
% 162.14/161.99 ! [V_n,V_z,T_a] :
% 162.14/161.99 ( class_Rings_Oring__1(T_a)
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_setprod__pos__nat__iff,axiom,
% 162.14/161.99 ! [V_f_2,V_S_2,T_a] :
% 162.14/161.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 162.14/161.99 => ( 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)))
% 162.14/161.99 <=> ! [B_x] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 162.14/161.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_greaterThanAtMost__empty,axiom,
% 162.14/161.99 ! [V_k_2,V_l_2,T_a] :
% 162.14/161.99 ( class_Orderings_Oorder(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2))
% 162.14/161.99 => 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)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 162.14/161.99 ! [V_l_2,V_k_2,T_a] :
% 162.14/161.99 ( class_Orderings_Oorder(T_a)
% 162.14/161.99 => ( 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)
% 162.14/161.99 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 162.14/161.99 ! [V_l_2,V_k_2,T_a] :
% 162.14/161.99 ( class_Orderings_Oorder(T_a)
% 162.14/161.99 => ( 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))
% 162.14/161.99 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_ivl__disj__un_I20_J,axiom,
% 162.14/161.99 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 162.14/161.99 ( class_Orderings_Olinorder(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 162.14/161.99 => 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) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_setprod__delta,axiom,
% 162.14/161.99 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 162.14/161.99 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.14/161.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 162.14/161.99 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 162.14/161.99 => 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) )
% 162.14/161.99 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 162.14/161.99 => 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) ) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_setprod__delta_H,axiom,
% 162.14/161.99 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 162.14/161.99 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.14/161.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 162.14/161.99 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 162.14/161.99 => 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) )
% 162.14/161.99 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 162.14/161.99 => 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) ) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_card__greaterThanAtMost,axiom,
% 162.14/161.99 ! [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) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_setprod__constant,axiom,
% 162.14/161.99 ! [V_y_2,V_A_2,T_a,T_b] :
% 162.14/161.99 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.14/161.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.14/161.99 => 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)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_setprod_Oinsert,axiom,
% 162.14/161.99 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 162.14/161.99 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.14/161.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.14/161.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.14/161.99 => 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)) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_setprod__insert,axiom,
% 162.14/161.99 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 162.14/161.99 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.14/161.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.14/161.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.14/161.99 => 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)) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__m1,axiom,
% 162.14/161.99 ! [T_a] :
% 162.14/161.99 ( class_Int_Onumber__ring(T_a)
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_setprod_Oinsert__remove,axiom,
% 162.14/161.99 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] :
% 162.14/161.99 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.14/161.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.14/161.99 => 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)))))) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__le__0__iff,axiom,
% 162.14/161.99 ! [V_z_2,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__idom(T_a)
% 162.14/161.99 => ( 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)))
% 162.14/161.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__0__le__iff,axiom,
% 162.14/161.99 ! [V_z_2,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__idom(T_a)
% 162.14/161.99 => ( 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)))
% 162.14/161.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__less__0__iff,axiom,
% 162.14/161.99 ! [V_z_2,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__idom(T_a)
% 162.14/161.99 => ( 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)))
% 162.14/161.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__0__less__iff,axiom,
% 162.14/161.99 ! [V_z_2,T_a] :
% 162.14/161.99 ( class_Rings_Olinordered__idom(T_a)
% 162.14/161.99 => ( 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)))
% 162.14/161.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__nat__nat,axiom,
% 162.14/161.99 ! [V_z,T_a] :
% 162.14/161.99 ( class_Rings_Oring__1(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 162.14/161.99 => 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) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_card__greaterThanAtMost__int,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_setprod_Oremove,axiom,
% 162.14/161.99 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 162.14/161.99 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.14/161.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.14/161.99 => 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)))))) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_ivl__disj__un_I16_J,axiom,
% 162.14/161.99 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 162.14/161.99 ( class_Orderings_Olinorder(T_a)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2))
% 162.14/161.99 => 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) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 162.14/161.99 ! [V_w] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( ( 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))))
% 162.14/161.99 => 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))) )
% 162.14/161.99 & ( ~ 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))))
% 162.14/161.99 => 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)))) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_negDivAlg__eqn__number__of,axiom,
% 162.14/161.99 ! [V_w,V_v] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( ( 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))))
% 162.14/161.99 => 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))) )
% 162.14/161.99 & ( ~ 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))))
% 162.14/161.99 => 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)))) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_negDivAlg__eqn,axiom,
% 162.14/161.99 ! [V_a,V_b] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 162.14/161.99 => ( ( 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)))
% 162.14/161.99 => 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)) )
% 162.14/161.99 & ( ~ 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)))
% 162.14/161.99 => 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))) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_negDivAlg_Osimps,axiom,
% 162.14/161.99 ! [V_b,V_a] :
% 162.14/161.99 ( ( ( 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)))
% 162.14/161.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 162.14/161.99 => 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)) )
% 162.14/161.99 & ( ~ ( 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)))
% 162.14/161.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 162.14/161.99 => 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))) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 162.14/161.99 ! [V_w] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( ( 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)))
% 162.14/161.99 => 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)) )
% 162.14/161.99 & ( ~ 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)))
% 162.14/161.99 => 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)))) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_sup2E,axiom,
% 162.14/161.99 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 162.14/161.99 ( 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))
% 162.14/161.99 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 162.14/161.99 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_sup2CI,axiom,
% 162.14/161.99 ! [T_b,T_a,V_A_2,V_y_2,V_x_2,V_B_2] :
% 162.14/161.99 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 162.14/161.99 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 162.14/161.99 => 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_bot2E,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_sup2I1,axiom,
% 162.14/161.99 ! [V_B_2,T_b,T_a,V_y_2,V_x_2,V_A_2] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 162.14/161.99 => 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_sup2I2,axiom,
% 162.14/161.99 ! [V_A_2,T_b,T_a,V_y_2,V_x_2,V_B_2] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 162.14/161.99 => 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_less__by__empty,axiom,
% 162.14/161.99 ! [V_B_2,T_a,V_A_2] :
% 162.14/161.99 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 162.14/161.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_rev__predicate2D,axiom,
% 162.14/161.99 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_P_2] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 162.14/161.99 => ( 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))
% 162.14/161.99 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_predicate2D,axiom,
% 162.14/161.99 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_b,T_a] :
% 162.14/161.99 ( 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))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 162.14/161.99 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_posDivAlg__0,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_posDivAlg__div__mod,axiom,
% 162.14/161.99 ! [V_l,V_k] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 162.14/161.99 => 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)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_negDivAlg__div__mod,axiom,
% 162.14/161.99 ! [V_l,V_k] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 162.14/161.99 => 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)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_negDivAlg__minus1,axiom,
% 162.14/161.99 ! [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))) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_posDivAlg__eqn__number__of,axiom,
% 162.14/161.99 ! [V_w,V_v] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( ( 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)))
% 162.14/161.99 => 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)) )
% 162.14/161.99 & ( ~ 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)))
% 162.14/161.99 => 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)))) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_posDivAlg__eqn,axiom,
% 162.14/161.99 ! [V_a,V_b] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 162.14/161.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 162.14/161.99 => 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) )
% 162.14/161.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 162.14/161.99 => 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))) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_posDivAlg_Osimps,axiom,
% 162.14/161.99 ! [V_b,V_a] :
% 162.14/161.99 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 162.14/161.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 162.14/161.99 => 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) )
% 162.14/161.99 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 162.14/161.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 162.14/161.99 => 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))) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_in__rel__def,axiom,
% 162.14/161.99 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2))
% 162.14/161.99 <=> 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_div__mod__code__numeral__def,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_Nitpick_Orefl_H__def,axiom,
% 162.14/161.99 ! [V_r_2,T_a] :
% 162.14/161.99 ( c_Nitpick_Orefl_H(T_a,V_r_2)
% 162.14/161.99 <=> ! [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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_adjust__def,axiom,
% 162.14/161.99 ! [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))))))) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_pair__imageI,axiom,
% 162.14/161.99 ! [V_f_2,T_c,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 162.14/161.99 ( 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))
% 162.14/161.99 => 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))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_of__int__num,axiom,
% 162.14/161.99 ! [V_k_2,T_a] :
% 162.14/161.99 ( class_Rings_Oring__1(T_a)
% 162.14/161.99 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.14/161.99 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = c_Groups_Ozero__class_Ozero(T_a) )
% 162.14/161.99 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.14/161.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.14/161.99 => 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))) )
% 162.14/161.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.14/161.99 => 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))))) ) ) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__nat__step,axiom,
% 162.14/161.99 ! [V_m,V_n] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 162.14/161.99 => 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)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_negDivAlg_Opsimps,axiom,
% 162.14/161.99 ! [V_b_2,V_a_2] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( ( ( 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)))
% 162.14/161.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 162.14/161.99 => 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)) )
% 162.14/161.99 & ( ~ ( 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)))
% 162.14/161.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 162.14/161.99 => 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))) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_prod__caseI,axiom,
% 162.14/161.99 ! [T_b,T_a,V_b_2,V_a_2,V_f1_2] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 162.14/161.99 => 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))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_splitI,axiom,
% 162.14/161.99 ! [T_b,T_a,V_b_2,V_a_2,V_f_2] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 162.14/161.99 => 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))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_mem__splitI,axiom,
% 162.14/161.99 ! [T_c,T_b,V_b_2,V_a_2,V_ca_2,V_z_2,T_a] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2)))
% 162.14/161.99 => 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)))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_splitD_H,axiom,
% 162.14/161.99 ! [V_ca_2,V_b_2,V_a_2,V_R_2,T_c,T_b,T_a] :
% 162.14/161.99 ( 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))
% 162.14/161.99 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_splitD,axiom,
% 162.14/161.99 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_accp__downward,axiom,
% 162.14/161.99 ! [V_a_2,V_b_2,V_r_2,T_a] :
% 162.14/161.99 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_b_2))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 162.14/161.99 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_accp_Oequations,axiom,
% 162.14/161.99 ! [V_a_2,V_r_2,T_a] :
% 162.14/161.99 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2))
% 162.14/161.99 <=> ! [B_x] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 162.14/161.99 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_accp_Osimps,axiom,
% 162.14/161.99 ! [V_a_2,V_r_2,T_a] :
% 162.14/161.99 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2))
% 162.14/161.99 <=> ! [B_x] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 162.14/161.99 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__nat__zero,axiom,
% 162.14/161.99 ! [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) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__nat__if,axiom,
% 162.14/161.99 ! [V_m_2,V_n_2] :
% 162.14/161.99 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.14/161.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 162.14/161.99 => 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) )
% 162.14/161.99 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.14/161.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 162.14/161.99 => 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)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_accp__subset,axiom,
% 162.14/161.99 ! [V_R2_2,V_R1_2,T_a] :
% 162.14/161.99 ( 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))
% 162.14/161.99 => 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))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_split__paired__All,axiom,
% 162.14/161.99 ! [T_b,T_a,V_P_2] :
% 162.14/161.99 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 162.14/161.99 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_Pair__eq,axiom,
% 162.14/161.99 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] :
% 162.14/161.99 ( 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)
% 162.14/161.99 <=> ( V_a_2 = V_a_H_2
% 162.14/161.99 & V_b_2 = V_b_H_2 ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_Pair__inject,axiom,
% 162.14/161.99 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 162.14/161.99 ( 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)
% 162.14/161.99 => ~ ( V_a = V_a_H
% 162.14/161.99 => V_b != V_b_H ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_split__weak__cong,axiom,
% 162.14/161.99 ! [V_ca_2,T_c,T_b,T_a,V_q_2,V_p_2] :
% 162.14/161.99 ( V_p_2 = V_q_2
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__nat__base,axiom,
% 162.14/161.99 ! [V_n,V_m] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 162.14/161.99 => 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) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__nat__div__mod,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__int__mod__div,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_split__conv,axiom,
% 162.14/161.99 ! [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) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_prod_Osimps_I2_J,axiom,
% 162.14/161.99 ! [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) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_split__eta,axiom,
% 162.14/161.99 ! [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 ).
% 162.14/161.99
% 162.14/161.99 fof(fact_split__twice,axiom,
% 162.14/161.99 ! [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) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_posDivAlg_Opsimps,axiom,
% 162.14/161.99 ! [V_b_2,V_a_2] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 162.14/161.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 162.14/161.99 => 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) )
% 162.14/161.99 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 162.14/161.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 162.14/161.99 => 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))) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__int__def,axiom,
% 162.14/161.99 ! [V_b,V_a] :
% 162.14/161.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 162.14/161.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 162.14/161.99 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 162.14/161.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 162.14/161.99 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.14/161.99 => 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)) )
% 162.14/161.99 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.14/161.99 => 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))) ) ) ) ) )
% 162.14/161.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 162.14/161.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 162.14/161.99 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 162.14/161.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 162.14/161.99 => 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))) ) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_negDivAlg_Opinduct,axiom,
% 162.14/161.99 ! [V_P_2,V_a1_2,V_a0_2] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( ! [B_a,B_b] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( ( ~ ( 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)))
% 162.14/161.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 162.14/161.99 => 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))) )
% 162.14/161.99 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 162.14/161.99 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 162.14/161.99 ! [V_c,V_r,V_q,V_b,V_a] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 162.14/161.99 => 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)))) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__nat__rel__unique,axiom,
% 162.14/161.99 ! [V_qr_H,V_qr,V_n,V_m] :
% 162.14/161.99 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 162.14/161.99 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 162.14/161.99 => V_qr = V_qr_H ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 162.14/161.99 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__nat__eq,axiom,
% 162.14/161.99 ! [V_qr,V_n,V_m] :
% 162.14/161.99 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 162.14/161.99 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_mod__eq,axiom,
% 162.14/161.99 ! [V_r,V_q,V_n,V_m] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_div__eq,axiom,
% 162.14/161.99 ! [V_r,V_q,V_n,V_m] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_negateSnd__eq,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__nat__rel,axiom,
% 162.14/161.99 ! [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)))) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 162.14/161.99 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( 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)))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 162.14/161.99 => 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)))) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 162.14/161.99 ! [V_a,V_r,V_q,V_c,V_b] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 162.14/161.99 => 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)))) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_small_H_Opsimps,axiom,
% 162.14/161.99 ! [V_i_2,V_d_2,V_f_2] :
% 162.14/161.99 ( 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))))
% 162.14/161.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 162.14/161.99 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 162.14/161.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 162.14/161.99 => 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)) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_posDivAlg_Opinduct,axiom,
% 162.14/161.99 ! [V_P_2,V_a1_2,V_a0_2] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( ! [B_a,B_b] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 162.14/161.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 162.14/161.99 => 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))) )
% 162.14/161.99 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 162.14/161.99 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_zmult2__lemma,axiom,
% 162.14/161.99 ! [V_c,V_r,V_q,V_b,V_a] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 162.14/161.99 => 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)))) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 162.14/161.99 ! [V_f_2,V_A_2,T_a] :
% 162.14/161.99 ( ! [B_x] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.14/161.99 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 162.14/161.99 => 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)) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_unique__remainder,axiom,
% 162.14/161.99 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( 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)))
% 162.14/161.99 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.14/161.99 => V_r = V_r_H ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_unique__quotient,axiom,
% 162.14/161.99 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( 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)))
% 162.14/161.99 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.14/161.99 => V_q = V_q_H ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_self__remainder,axiom,
% 162.14/161.99 ! [V_r,V_q,V_a] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.14/161.99 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__int__rel__0,axiom,
% 162.14/161.99 ! [V_b] :
% 162.14/161.99 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.14/161.99 => 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)))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__int__rel__neg,axiom,
% 162.14/161.99 ! [V_qr,V_b,V_a] :
% 162.14/161.99 ( 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))
% 162.14/161.99 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__int__correct,axiom,
% 162.14/161.99 ! [V_a,V_b] :
% 162.14/161.99 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.14/161.99 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_self__quotient,axiom,
% 162.14/161.99 ! [V_r,V_q,V_a] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.14/161.99 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__int__rel__mod,axiom,
% 162.14/161.99 ! [V_r,V_q,V_b,V_a] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.14/161.99 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__int__rel__div,axiom,
% 162.14/161.99 ! [V_r,V_q,V_b,V_a] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.14/161.99 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_negDivAlg__correct,axiom,
% 162.14/161.99 ! [V_b,V_a] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 162.14/161.99 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__int__rel__div__mod,axiom,
% 162.14/161.99 ! [V_a,V_b] :
% 162.14/161.99 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.14/161.99 => 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)))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_posDivAlg__correct,axiom,
% 162.14/161.99 ! [V_b,V_a] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 162.14/161.99 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_zadd1__lemma,axiom,
% 162.14/161.99 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( 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)))
% 162.14/161.99 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.14/161.99 => 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)))) ) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_zminus1__lemma,axiom,
% 162.14/161.99 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => 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))))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__int__rel__def,axiom,
% 162.14/161.99 ! [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))))))) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_divmod__int__relI,axiom,
% 162.14/161.99 ! [V_r,V_q,V_b,V_a] :
% 162.14/161.99 ( 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)
% 162.14/161.99 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 162.14/161.99 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 162.14/161.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 162.14/161.99 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 162.14/161.99 => 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))) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_zmult1__lemma,axiom,
% 162.14/161.99 ! [V_a,V_r,V_q,V_c,V_b] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.14/161.99 => 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)))) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_small_H_Opinduct,axiom,
% 162.14/161.99 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] :
% 162.14/161.99 ( 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))))
% 162.14/161.99 => ( ! [B_f,B_d,B_i] :
% 162.14/161.99 ( 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))))
% 162.14/161.99 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 162.14/161.99 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
% 162.14/161.99 => 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)))) ) )
% 162.14/161.99 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) )
% 162.14/161.99 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_mod__pos__neg__1__number__of,axiom,
% 162.14/161.99 ! [V_w] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => 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))))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_in__measure,axiom,
% 162.14/161.99 ! [V_f_2,V_y_2,V_x_2,T_a] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 <=> 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))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_div__pos__neg__1__number__of,axiom,
% 162.14/161.99 ! [V_w] :
% 162.14/161.99 ( 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)))
% 162.14/161.99 => 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))))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_surjective__pairing,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_fst__conv,axiom,
% 162.14/161.99 ! [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 ).
% 162.14/161.99
% 162.14/161.99 fof(fact_snd__conv,axiom,
% 162.14/161.99 ! [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 ).
% 162.14/161.99
% 162.14/161.99 fof(fact_pair__collapse,axiom,
% 162.14/161.99 ! [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 ).
% 162.14/161.99
% 162.14/161.99 fof(fact_fst__eqD,axiom,
% 162.14/161.99 ! [V_a,V_y,V_x,T_b,T_a] :
% 162.14/161.99 ( 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
% 162.14/161.99 => V_x = V_a ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_snd__eqD,axiom,
% 162.14/161.99 ! [V_a,V_y,V_x,T_a,T_b] :
% 162.14/161.99 ( 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
% 162.14/161.99 => V_y = V_a ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_Pair__fst__snd__eq,axiom,
% 162.14/161.99 ! [T_b,T_a,V_t_2,V_s_2] :
% 162.14/161.99 ( V_s_2 = V_t_2
% 162.14/161.99 <=> ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_t_2)
% 162.14/161.99 & hAPP(c_Product__Type_Osnd(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_t_2) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_prod__eqI,axiom,
% 162.14/161.99 ! [V_q,V_p,T_b,T_a] :
% 162.14/161.99 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 162.14/161.99 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 162.14/161.99 => V_p = V_q ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_split__def,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_split__comp__eq,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_split__beta,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_prod__case__beta,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_fst__def,axiom,
% 162.14/161.99 ! [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) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_snd__def,axiom,
% 162.14/161.99 ! [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) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_div__int__def,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_mod__int__def,axiom,
% 162.14/161.99 ! [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)) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_div__neg__pos,axiom,
% 162.14/161.99 ! [V_b,V_a] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 162.14/161.99 => 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)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_mod__neg__pos,axiom,
% 162.14/161.99 ! [V_b,V_a] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 162.14/161.99 => 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)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_div__pos__pos,axiom,
% 162.14/161.99 ! [V_b,V_a] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 162.14/161.99 => 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)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_mod__pos__pos,axiom,
% 162.14/161.99 ! [V_b,V_a] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 162.14/161.99 => 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)) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_div__pos__pos__1__number__of,axiom,
% 162.14/161.99 ! [V_w] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 162.14/161.99 => 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))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_mod__pos__pos__1__number__of,axiom,
% 162.14/161.99 ! [V_w] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 162.14/161.99 => 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))) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_div__pos__neg,axiom,
% 162.14/161.99 ! [V_b,V_a] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.14/161.99 => 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)))) ) ) ).
% 162.14/161.99
% 162.14/161.99 fof(fact_mod__pos__neg,axiom,
% 162.14/161.99 ! [V_b,V_a] :
% 162.14/161.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 162.14/161.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.14/161.99 => 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)))) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_div__neg__neg,axiom,
% 162.14/162.00 ! [V_b,V_a] :
% 162.14/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.14/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.14/162.00 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_mod__neg__neg,axiom,
% 162.14/162.00 ! [V_b,V_a] :
% 162.14/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.14/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.14/162.00 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_prod__size__simp,axiom,
% 162.14/162.00 ! [V_p_2,V_g_2,V_f_2,T_b,T_a] : c_Product__Type_Oprod_Oprod__size(T_a,T_b,V_f_2,V_g_2,V_p_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_a,T_b),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_conjI__realizer,axiom,
% 162.14/162.00 ! [T_b,T_a,V_q_2,V_Q_2,V_p_2,V_P_2] :
% 162.14/162.00 ( hBOOL(hAPP(V_P_2,V_p_2))
% 162.14/162.00 => ( hBOOL(hAPP(V_Q_2,V_q_2))
% 162.14/162.00 => ( hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_p_2),V_q_2))))
% 162.14/162.00 & hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_p_2),V_q_2)))) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_exI__realizer,axiom,
% 162.14/162.00 ! [T_a,T_b,V_x_2,V_y_2,V_P_2] :
% 162.14/162.00 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
% 162.14/162.00 => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)))) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_Nitpick_OFrac__def,axiom,
% 162.14/162.00 c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_div__nat__def,axiom,
% 162.14/162.00 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_mod__nat__def,axiom,
% 162.14/162.00 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_divmod__nat__rel__def,axiom,
% 162.14/162.00 ! [V_qr_2,V_n_2,V_m_2] :
% 162.14/162.00 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 162.14/162.00 <=> ( V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))
% 162.14/162.00 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.14/162.00 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 162.14/162.00 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.14/162.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 162.14/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)))
% 162.14/162.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)) ) )
% 162.14/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 162.14/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)))
% 162.14/162.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_norm__frac_Osimps,axiom,
% 162.14/162.00 ! [V_a_2,V_b_2] :
% 162.14/162.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.14/162.00 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) )
% 162.14/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.14/162.00 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.14/162.00 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 162.14/162.00 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 162.14/162.00 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.14/162.00 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 162.14/162.00 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_norm__frac_Opsimps,axiom,
% 162.14/162.00 ! [V_b_2,V_a_2] :
% 162.14/162.00 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
% 162.14/162.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.14/162.00 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) )
% 162.14/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.14/162.00 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.14/162.00 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 162.14/162.00 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 162.14/162.00 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.14/162.00 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 162.14/162.00 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_mlex__leq,axiom,
% 162.14/162.00 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
% 162.14/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 162.14/162.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2))
% 162.14/162.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_mlex__less,axiom,
% 162.14/162.00 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
% 162.14/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 162.14/162.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_norm__frac_Opinduct,axiom,
% 162.14/162.00 ! [V_P_2,V_a1_2,V_a0_2] :
% 162.14/162.00 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 162.14/162.00 => ( ! [B_a,B_b] :
% 162.14/162.00 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
% 162.14/162.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.14/162.00 => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) )
% 162.14/162.00 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 162.14/162.00 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_prod_Orecs,axiom,
% 162.14/162.00 ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : c_Product__Type_Oprod_Oprod__rec(T_b,T_c,T_a,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_in__lex__prod,axiom,
% 162.14/162.00 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] :
% 162.14/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_a,T_b,V_r_2,V_s_2)))
% 162.14/162.00 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_H_2)),V_r_2))
% 162.14/162.00 | ( V_a_2 = V_a_H_2
% 162.14/162.00 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_b_H_2)),V_s_2)) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_in__finite__psubset,axiom,
% 162.14/162.00 ! [V_B_2,V_A_2,T_a] :
% 162.14/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_a)))
% 162.14/162.00 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 162.14/162.00 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_same__fstI,axiom,
% 162.14/162.00 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_P_2] :
% 162.14/162.00 ( hBOOL(hAPP(V_P_2,V_x_2))
% 162.14/162.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
% 162.14/162.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2))) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_setprod__diff1,axiom,
% 162.14/162.00 ! [V_a_2,V_f_2,V_A_2,T_a,T_b] :
% 162.14/162.00 ( class_Fields_Ofield(T_b)
% 162.14/162.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.14/162.00 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b)
% 162.14/162.00 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.14/162.00 => 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)) )
% 162.14/162.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.14/162.00 => 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) ) ) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_nat__def,axiom,
% 162.14/162.00 ! [V_z_2] : hAPP(c_Int_Onat,V_z_2) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_pair__lessI2,axiom,
% 162.14/162.00 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 162.14/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 162.14/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 162.14/162.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_diff__divide__distrib,axiom,
% 162.14/162.00 ! [V_c,V_b,V_a,T_a] :
% 162.14/162.00 ( class_Rings_Odivision__ring(T_a)
% 162.14/162.00 => 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)) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_divide__1,axiom,
% 162.14/162.00 ! [V_a,T_a] :
% 162.14/162.00 ( class_Rings_Odivision__ring(T_a)
% 162.14/162.00 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_power__divide,axiom,
% 162.14/162.00 ! [V_n,V_b,V_a,T_a] :
% 162.14/162.00 ( class_Fields_Ofield__inverse__zero(T_a)
% 162.14/162.00 => 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)) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_Rep__Integ__inject,axiom,
% 162.14/162.00 ! [V_y_2,V_x_2] :
% 162.14/162.00 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 162.14/162.00 <=> V_x_2 = V_y_2 ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_minus__divide__left,axiom,
% 162.14/162.00 ! [V_b,V_a,T_a] :
% 162.14/162.00 ( class_Rings_Odivision__ring(T_a)
% 162.14/162.00 => 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) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_times__divide__eq__right,axiom,
% 162.14/162.00 ! [V_c,V_b,V_a,T_a] :
% 162.14/162.00 ( class_Rings_Odivision__ring(T_a)
% 162.14/162.00 => 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) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_add__divide__distrib,axiom,
% 162.14/162.00 ! [V_c,V_b,V_a,T_a] :
% 162.14/162.00 ( class_Rings_Odivision__ring(T_a)
% 162.14/162.00 => 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)) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_divide__zero__left,axiom,
% 162.14/162.00 ! [V_a,T_a] :
% 162.14/162.00 ( class_Rings_Odivision__ring(T_a)
% 162.14/162.00 => 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) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_divide__zero,axiom,
% 162.14/162.00 ! [V_a,T_a] :
% 162.14/162.00 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 162.14/162.00 => 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) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_nonzero__eq__divide__eq,axiom,
% 162.14/162.00 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 162.14/162.00 ( class_Rings_Odivision__ring(T_a)
% 162.14/162.00 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 162.14/162.00 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)
% 162.14/162.00 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_nonzero__divide__eq__eq,axiom,
% 162.14/162.00 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 162.14/162.00 ( class_Rings_Odivision__ring(T_a)
% 162.14/162.00 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 162.14/162.00 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2
% 162.14/162.00 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_divide__eq__imp,axiom,
% 162.14/162.00 ! [V_a,V_b,V_c,T_a] :
% 162.14/162.00 ( class_Rings_Odivision__ring(T_a)
% 162.14/162.00 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 162.14/162.00 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 162.14/162.00 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_eq__divide__imp,axiom,
% 162.14/162.00 ! [V_b,V_a,V_c,T_a] :
% 162.14/162.00 ( class_Rings_Odivision__ring(T_a)
% 162.14/162.00 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 162.14/162.00 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 162.14/162.00 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_right__inverse__eq,axiom,
% 162.14/162.00 ! [V_a_2,V_b_2,T_a] :
% 162.14/162.00 ( class_Rings_Odivision__ring(T_a)
% 162.14/162.00 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
% 162.14/162.00 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a)
% 162.14/162.00 <=> V_a_2 = V_b_2 ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_divide__self,axiom,
% 162.14/162.00 ! [V_a,T_a] :
% 162.14/162.00 ( class_Rings_Odivision__ring(T_a)
% 162.14/162.00 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 162.14/162.00 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_divide__self__if,axiom,
% 162.14/162.00 ! [V_a,T_a] :
% 162.14/162.00 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 162.14/162.00 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 162.14/162.00 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 162.14/162.00 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 162.14/162.00 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_nonzero__minus__divide__divide,axiom,
% 162.14/162.00 ! [V_a,V_b,T_a] :
% 162.14/162.00 ( class_Rings_Odivision__ring(T_a)
% 162.14/162.00 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 162.14/162.00 => 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) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_nonzero__minus__divide__right,axiom,
% 162.14/162.00 ! [V_a,V_b,T_a] :
% 162.14/162.00 ( class_Rings_Odivision__ring(T_a)
% 162.14/162.00 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 162.14/162.00 => 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)) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_nonzero__power__divide,axiom,
% 162.14/162.00 ! [V_n,V_a,V_b,T_a] :
% 162.14/162.00 ( class_Fields_Ofield(T_a)
% 162.14/162.00 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 162.14/162.00 => 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)) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_power__one__over,axiom,
% 162.14/162.00 ! [V_n,V_a,T_a] :
% 162.14/162.00 ( class_Fields_Ofield__inverse__zero(T_a)
% 162.14/162.00 => 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) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_setprod__dividef,axiom,
% 162.14/162.00 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] :
% 162.14/162.00 ( class_Fields_Ofield__inverse__zero(T_b)
% 162.14/162.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.14/162.00 => 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)) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_divide__eq__eq__number__of1,axiom,
% 162.14/162.00 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 162.14/162.00 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 162.14/162.00 & class_Int_Onumber(T_a) )
% 162.14/162.00 => ( 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
% 162.14/162.00 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
% 162.14/162.00 => 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)) )
% 162.14/162.00 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
% 162.14/162.00 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_divide__eq__eq__number__of,axiom,
% 162.14/162.00 ! [V_w_2,V_ca_2,V_b_2,T_a] :
% 162.14/162.00 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 162.14/162.00 & class_Int_Onumber(T_a) )
% 162.14/162.00 => ( 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)
% 162.14/162.00 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 162.14/162.00 => 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) )
% 162.14/162.00 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 162.14/162.00 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_eq__divide__eq__number__of,axiom,
% 162.14/162.00 ! [V_ca_2,V_b_2,V_w_2,T_a] :
% 162.14/162.00 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 162.14/162.00 & class_Int_Onumber(T_a) )
% 162.14/162.00 => ( 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)
% 162.14/162.00 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 162.14/162.00 => 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 )
% 162.14/162.00 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 162.14/162.00 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_eq__divide__eq__number__of1,axiom,
% 162.14/162.00 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 162.14/162.00 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 162.14/162.00 & class_Int_Onumber(T_a) )
% 162.14/162.00 => ( 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))
% 162.14/162.00 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
% 162.14/162.00 => 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 )
% 162.14/162.00 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
% 162.14/162.00 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_divide__Numeral0,axiom,
% 162.14/162.00 ! [V_x,T_a] :
% 162.14/162.00 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 162.14/162.00 & class_Int_Onumber__ring(T_a) )
% 162.14/162.00 => 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) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_divide__numeral__1,axiom,
% 162.14/162.00 ! [V_a,T_a] :
% 162.14/162.00 ( ( class_Fields_Ofield(T_a)
% 162.14/162.00 & class_Int_Onumber__ring(T_a) )
% 162.14/162.00 => 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 ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_divide__Numeral1,axiom,
% 162.14/162.00 ! [V_x,T_a] :
% 162.14/162.00 ( ( class_Fields_Ofield(T_a)
% 162.14/162.00 & class_Int_Onumber__ring(T_a) )
% 162.14/162.00 => 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 ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_divide__minus1,axiom,
% 162.14/162.00 ! [V_x,T_a] :
% 162.14/162.00 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 162.14/162.00 & class_Int_Onumber__ring(T_a) )
% 162.14/162.00 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_less__divide__eq__number__of1,axiom,
% 162.14/162.00 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 162.14/162.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.14/162.00 & class_Int_Onumber(T_a) )
% 162.14/162.00 => ( 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))))
% 162.14/162.00 <=> ( ( 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)))
% 162.14/162.00 => 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)) )
% 162.14/162.00 & ( ~ 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)))
% 162.14/162.00 => ( ( 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)))
% 162.14/162.00 => 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)))) )
% 162.14/162.00 & ( ~ 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)))
% 162.14/162.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_less__divide__eq__number__of,axiom,
% 162.14/162.00 ! [V_ca_2,V_b_2,V_w_2,T_a] :
% 162.14/162.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.14/162.00 & class_Int_Onumber(T_a) )
% 162.14/162.00 => ( 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)))
% 162.14/162.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 162.14/162.00 => 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)) )
% 162.14/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 162.14/162.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.14/162.00 => 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))) )
% 162.14/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.14/162.00 => 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))) ) ) ) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_divide__less__eq__number__of,axiom,
% 162.14/162.00 ! [V_w_2,V_ca_2,V_b_2,T_a] :
% 162.14/162.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.14/162.00 & class_Int_Onumber(T_a) )
% 162.14/162.00 => ( 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)))
% 162.14/162.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 162.14/162.00 => 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))) )
% 162.14/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 162.14/162.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.14/162.00 => 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)) )
% 162.14/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.14/162.00 => 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))) ) ) ) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_divide__less__eq__number__of1,axiom,
% 162.14/162.00 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 162.14/162.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.14/162.00 & class_Int_Onumber(T_a) )
% 162.14/162.00 => ( 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))
% 162.14/162.00 <=> ( ( 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)))
% 162.14/162.00 => 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)))) )
% 162.14/162.00 & ( ~ 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)))
% 162.14/162.00 => ( ( 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)))
% 162.14/162.00 => 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)) )
% 162.14/162.00 & ( ~ 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)))
% 162.14/162.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_power__diff,axiom,
% 162.14/162.00 ! [V_m,V_n,V_a,T_a] :
% 162.14/162.00 ( class_Fields_Ofield(T_a)
% 162.14/162.00 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 162.14/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 162.14/162.00 => 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)) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_minus1__divide,axiom,
% 162.14/162.00 ! [V_x,T_a] :
% 162.14/162.00 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 162.14/162.00 & class_Int_Onumber__ring(T_a) )
% 162.14/162.00 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_x)) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_pair__lessI1,axiom,
% 162.14/162.00 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 162.14/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 162.14/162.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_le__divide__eq__number__of1,axiom,
% 162.14/162.00 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 162.14/162.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.14/162.00 & class_Int_Onumber(T_a) )
% 162.14/162.00 => ( 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))))
% 162.14/162.00 <=> ( ( 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)))
% 162.14/162.00 => 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)) )
% 162.14/162.00 & ( ~ 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)))
% 162.14/162.00 => ( ( 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)))
% 162.14/162.00 => 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)))) )
% 162.14/162.00 & ( ~ 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)))
% 162.14/162.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_le__divide__eq__number__of,axiom,
% 162.14/162.00 ! [V_ca_2,V_b_2,V_w_2,T_a] :
% 162.14/162.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.14/162.00 & class_Int_Onumber(T_a) )
% 162.14/162.00 => ( 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)))
% 162.14/162.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 162.14/162.00 => 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)) )
% 162.14/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 162.14/162.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.14/162.00 => 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))) )
% 162.14/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.14/162.00 => 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))) ) ) ) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_divide__le__eq__number__of,axiom,
% 162.14/162.00 ! [V_w_2,V_ca_2,V_b_2,T_a] :
% 162.14/162.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.14/162.00 & class_Int_Onumber(T_a) )
% 162.14/162.00 => ( 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)))
% 162.14/162.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 162.14/162.00 => 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))) )
% 162.14/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 162.14/162.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.14/162.00 => 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)) )
% 162.14/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.14/162.00 => 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))) ) ) ) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_divide__le__eq__number__of1,axiom,
% 162.14/162.00 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 162.14/162.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.14/162.00 & class_Int_Onumber(T_a) )
% 162.14/162.00 => ( 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))
% 162.14/162.00 <=> ( ( 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)))
% 162.14/162.00 => 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)))) )
% 162.14/162.00 & ( ~ 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)))
% 162.14/162.00 => ( ( 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)))
% 162.14/162.00 => 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)) )
% 162.14/162.00 & ( ~ 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)))
% 162.14/162.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_half__gt__zero__iff,axiom,
% 162.14/162.00 ! [V_r_2,T_a] :
% 162.14/162.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.14/162.00 & class_Int_Onumber__ring(T_a) )
% 162.14/162.00 => ( 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))))))
% 162.14/162.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r_2)) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_half__gt__zero,axiom,
% 162.14/162.00 ! [V_r,T_a] :
% 162.14/162.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.14/162.00 & class_Int_Onumber__ring(T_a) )
% 162.14/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 162.14/162.00 => 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)))))) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_le__divide__eq,axiom,
% 162.14/162.00 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 162.14/162.00 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.14/162.00 => ( 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)))
% 162.14/162.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 162.14/162.00 => 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)) )
% 162.14/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 162.14/162.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.14/162.00 => 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))) )
% 162.14/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.14/162.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_divide__le__eq,axiom,
% 162.14/162.00 ! [V_a_2,V_ca_2,V_b_2,T_a] :
% 162.14/162.00 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.14/162.00 => ( 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))
% 162.14/162.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 162.14/162.00 => 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))) )
% 162.14/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 162.14/162.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.14/162.00 => 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)) )
% 162.14/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.14/162.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_pos__le__divide__eq,axiom,
% 162.14/162.00 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 162.14/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.14/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 162.14/162.00 => ( 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)))
% 162.14/162.00 <=> 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)) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_pos__divide__le__eq,axiom,
% 162.14/162.00 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 162.14/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.14/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 162.14/162.00 => ( 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))
% 162.14/162.00 <=> 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))) ) ) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_times__divide__times__eq,axiom,
% 162.14/162.00 ! [V_w,V_z,V_y,V_x,T_a] :
% 162.14/162.00 ( class_Fields_Ofield__inverse__zero(T_a)
% 162.14/162.00 => 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)) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_minus__divide__right,axiom,
% 162.14/162.00 ! [V_b,V_a,T_a] :
% 162.14/162.00 ( class_Fields_Ofield__inverse__zero(T_a)
% 162.14/162.00 => 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)) ) ).
% 162.14/162.00
% 162.14/162.00 fof(fact_minus__divide__divide,axiom,
% 162.14/162.00 ! [V_b,V_a,T_a] :
% 162.14/162.00 ( class_Fields_Ofield__inverse__zero(T_a)
% 162.14/162.00 => 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) ) ).
% 162.14/162.00
% 162.20/162.00 fof(fact_zero__le__divide__iff,axiom,
% 162.20/162.00 ! [V_b_2,V_a_2,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.20/162.00 => ( 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)))
% 162.20/162.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 162.20/162.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 162.20/162.00 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__le__0__iff,axiom,
% 162.20/162.00 ! [V_b_2,V_a_2,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.20/162.00 => ( 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)))
% 162.20/162.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 162.20/162.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 162.20/162.00 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__right__mono,axiom,
% 162.20/162.00 ! [V_c,V_b,V_a,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 162.20/162.00 => 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))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__right__mono__neg,axiom,
% 162.20/162.00 ! [V_c,V_b,V_a,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 => 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))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__strict__right__mono__neg,axiom,
% 162.20/162.00 ! [V_c,V_a,V_b,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 => 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))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__strict__right__mono,axiom,
% 162.20/162.00 ! [V_c,V_b,V_a,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 162.20/162.00 => 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))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__neg__neg,axiom,
% 162.20/162.00 ! [V_y,V_x,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 => 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))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__neg__pos,axiom,
% 162.20/162.00 ! [V_y,V_x,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 162.20/162.00 => 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))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__pos__neg,axiom,
% 162.20/162.00 ! [V_y,V_x,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 => 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))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__pos__pos,axiom,
% 162.20/162.00 ! [V_y,V_x,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 162.20/162.00 => 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))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__less__0__iff,axiom,
% 162.20/162.00 ! [V_b_2,V_a_2,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.20/162.00 => ( 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)))
% 162.20/162.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 162.20/162.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 162.20/162.00 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_zero__less__divide__iff,axiom,
% 162.20/162.00 ! [V_b_2,V_a_2,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.20/162.00 => ( 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)))
% 162.20/162.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 162.20/162.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 162.20/162.00 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_frac__eq__eq,axiom,
% 162.20/162.00 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] :
% 162.20/162.00 ( class_Fields_Ofield(T_a)
% 162.20/162.00 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
% 162.20/162.00 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_a)
% 162.20/162.00 => ( 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)
% 162.20/162.00 <=> 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) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_mult__divide__mult__cancel__left,axiom,
% 162.20/162.00 ! [V_b,V_a,V_c,T_a] :
% 162.20/162.00 ( class_Fields_Ofield__inverse__zero(T_a)
% 162.20/162.00 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 162.20/162.00 => 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) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_mult__divide__mult__cancel__right,axiom,
% 162.20/162.00 ! [V_b,V_a,V_c,T_a] :
% 162.20/162.00 ( class_Fields_Ofield__inverse__zero(T_a)
% 162.20/162.00 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 162.20/162.00 => 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) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__eq__eq,axiom,
% 162.20/162.00 ! [V_a_2,V_ca_2,V_b_2,T_a] :
% 162.20/162.00 ( class_Fields_Ofield__inverse__zero(T_a)
% 162.20/162.00 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2
% 162.20/162.00 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 162.20/162.00 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) )
% 162.20/162.00 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 162.20/162.00 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_eq__divide__eq,axiom,
% 162.20/162.00 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 162.20/162.00 ( class_Fields_Ofield__inverse__zero(T_a)
% 162.20/162.00 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)
% 162.20/162.00 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 162.20/162.00 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 )
% 162.20/162.00 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 162.20/162.00 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__nonpos__neg,axiom,
% 162.20/162.00 ! [V_y,V_x,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 => 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))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__nonpos__pos,axiom,
% 162.20/162.00 ! [V_y,V_x,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 162.20/162.00 => 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))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_frac__le,axiom,
% 162.20/162.00 ! [V_z,V_w,V_y,V_x,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 162.20/162.00 => 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))) ) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_frac__less,axiom,
% 162.20/162.00 ! [V_z,V_w,V_y,V_x,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 162.20/162.00 => 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))) ) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_frac__less2,axiom,
% 162.20/162.00 ! [V_z,V_w,V_y,V_x,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 162.20/162.00 => 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))) ) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__nonneg__neg,axiom,
% 162.20/162.00 ! [V_y,V_x,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 => 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))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__nonneg__pos,axiom,
% 162.20/162.00 ! [V_y,V_x,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 162.20/162.00 => 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))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__strict__left__mono__neg,axiom,
% 162.20/162.00 ! [V_c,V_b,V_a,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 => ( 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)))
% 162.20/162.00 => 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))) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__strict__left__mono,axiom,
% 162.20/162.00 ! [V_c,V_a,V_b,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 162.20/162.00 => ( 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)))
% 162.20/162.00 => 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))) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_neg__divide__less__eq,axiom,
% 162.20/162.00 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 => ( 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))
% 162.20/162.00 <=> 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)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_neg__less__divide__eq,axiom,
% 162.20/162.00 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 => ( 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)))
% 162.20/162.00 <=> 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))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_mult__imp__less__div__pos,axiom,
% 162.20/162.00 ! [V_x,V_z,V_y,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 162.20/162.00 => ( 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))
% 162.20/162.00 => 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))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_mult__imp__div__pos__less,axiom,
% 162.20/162.00 ! [V_z,V_x,V_y,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 162.20/162.00 => ( 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)))
% 162.20/162.00 => 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)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_pos__divide__less__eq,axiom,
% 162.20/162.00 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 162.20/162.00 => ( 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))
% 162.20/162.00 <=> 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))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_pos__less__divide__eq,axiom,
% 162.20/162.00 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 162.20/162.00 => ( 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)))
% 162.20/162.00 <=> 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)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__less__eq,axiom,
% 162.20/162.00 ! [V_a_2,V_ca_2,V_b_2,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.20/162.00 => ( 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))
% 162.20/162.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 162.20/162.00 => 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))) )
% 162.20/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 162.20/162.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 => 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)) )
% 162.20/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_less__divide__eq,axiom,
% 162.20/162.00 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.20/162.00 => ( 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)))
% 162.20/162.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 162.20/162.00 => 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)) )
% 162.20/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 162.20/162.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 => 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))) )
% 162.20/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_add__num__frac,axiom,
% 162.20/162.00 ! [V_x,V_z,V_y,T_a] :
% 162.20/162.00 ( class_Fields_Ofield__inverse__zero(T_a)
% 162.20/162.00 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 162.20/162.00 => 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) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_add__divide__eq__iff,axiom,
% 162.20/162.00 ! [V_y,V_x,V_z,T_a] :
% 162.20/162.00 ( class_Fields_Ofield(T_a)
% 162.20/162.00 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 162.20/162.00 => 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) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_add__frac__num,axiom,
% 162.20/162.00 ! [V_z,V_x,V_y,T_a] :
% 162.20/162.00 ( class_Fields_Ofield__inverse__zero(T_a)
% 162.20/162.00 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 162.20/162.00 => 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) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__add__eq__iff,axiom,
% 162.20/162.00 ! [V_y,V_x,V_z,T_a] :
% 162.20/162.00 ( class_Fields_Ofield(T_a)
% 162.20/162.00 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 162.20/162.00 => 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) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_add__frac__eq,axiom,
% 162.20/162.00 ! [V_w,V_x,V_z,V_y,T_a] :
% 162.20/162.00 ( class_Fields_Ofield(T_a)
% 162.20/162.00 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 162.20/162.00 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 162.20/162.00 => 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)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_diff__frac__eq,axiom,
% 162.20/162.00 ! [V_w,V_x,V_z,V_y,T_a] :
% 162.20/162.00 ( class_Fields_Ofield(T_a)
% 162.20/162.00 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 162.20/162.00 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 162.20/162.00 => 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)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__diff__eq__iff,axiom,
% 162.20/162.00 ! [V_y,V_x,V_z,T_a] :
% 162.20/162.00 ( class_Fields_Ofield(T_a)
% 162.20/162.00 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 162.20/162.00 => 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) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_diff__divide__eq__iff,axiom,
% 162.20/162.00 ! [V_y,V_x,V_z,T_a] :
% 162.20/162.00 ( class_Fields_Ofield(T_a)
% 162.20/162.00 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 162.20/162.00 => 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) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_less__half__sum,axiom,
% 162.20/162.00 ! [V_b,V_a,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 162.20/162.00 => 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))))) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_gt__half__sum,axiom,
% 162.20/162.00 ! [V_b,V_a,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 162.20/162.00 => 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)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__left__mono__neg,axiom,
% 162.20/162.00 ! [V_c,V_b,V_a,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 => ( 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)))
% 162.20/162.00 => 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))) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_divide__left__mono,axiom,
% 162.20/162.00 ! [V_c,V_a,V_b,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 162.20/162.00 => ( 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)))
% 162.20/162.00 => 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))) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_neg__divide__le__eq,axiom,
% 162.20/162.00 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 => ( 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))
% 162.20/162.00 <=> 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)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_neg__le__divide__eq,axiom,
% 162.20/162.00 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 162.20/162.00 => ( 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)))
% 162.20/162.00 <=> 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))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_mult__imp__le__div__pos,axiom,
% 162.20/162.00 ! [V_x,V_z,V_y,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 162.20/162.00 => ( 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))
% 162.20/162.00 => 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))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_mult__imp__div__pos__le,axiom,
% 162.20/162.00 ! [V_z,V_x,V_y,T_a] :
% 162.20/162.00 ( class_Fields_Olinordered__field(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 162.20/162.00 => ( 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)))
% 162.20/162.00 => 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)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_pair__leqI2,axiom,
% 162.20/162.00 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 162.20/162.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_smax__insertI,axiom,
% 162.20/162.00 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),V_Y_2)),c_FunDef_Omax__strict))
% 162.20/162.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_X_2)),V_Y_2)),c_FunDef_Omax__strict)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_smin__insertI,axiom,
% 162.20/162.00 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__strict))
% 162.20/162.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__strict)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_pair__leqI1,axiom,
% 162.20/162.00 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 162.20/162.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_smin__emptyI,axiom,
% 162.20/162.00 ! [V_X_2] :
% 162.20/162.00 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 162.20/162.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_smax__emptyI,axiom,
% 162.20/162.00 ! [V_Y_2] :
% 162.20/162.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 162.20/162.00 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 162.20/162.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_Y_2)),c_FunDef_Omax__strict)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_wmin__insertI,axiom,
% 162.20/162.00 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__weak))
% 162.20/162.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__weak)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_wmax__insertI,axiom,
% 162.20/162.00 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omax__weak))
% 162.20/162.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)),V_YS_2)),c_FunDef_Omax__weak)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_wmin__emptyI,axiom,
% 162.20/162.00 ! [V_X_2] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_wmax__emptyI,axiom,
% 162.20/162.00 ! [V_X_2] :
% 162.20/162.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 162.20/162.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_X_2)),c_FunDef_Omax__weak)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_min__weak__def,axiom,
% 162.20/162.00 c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_max__weak__def,axiom,
% 162.20/162.00 c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_max__rpair__set,axiom,
% 162.20/162.00 c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_min__rpair__set,axiom,
% 162.20/162.00 c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_max__strict__def,axiom,
% 162.20/162.00 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_max__ext__additive,axiom,
% 162.20/162.00 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_a] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_a,V_R_2)))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_a,V_R_2)))
% 162.20/162.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_min__strict__def,axiom,
% 162.20/162.00 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_max__extp__max__ext__eq,axiom,
% 162.20/162.00 ! [V_xa_2,V_x_2,V_R_2,T_a] :
% 162.20/162.00 ( c_Wellfounded_Omax__extp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_R_2),V_x_2,V_xa_2)
% 162.20/162.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_less__than__iff,axiom,
% 162.20/162.00 ! [V_y_2,V_x_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than))
% 162.20/162.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_intrel__iff,axiom,
% 162.20/162.00 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2))),c_Int_Ointrel))
% 162.20/162.00 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_rp__inv__image__rp,axiom,
% 162.20/162.00 ! [V_f_2,T_b,V_P_2,T_a] :
% 162.20/162.00 ( c_FunDef_Oreduction__pair(T_a,V_P_2)
% 162.20/162.00 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_P_2),V_f_2)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_pair__less__def,axiom,
% 162.20/162.00 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_mlex__prod__def,axiom,
% 162.20/162.00 ! [V_R_2,V_f_2,T_a] : c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_a),T_a),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_a,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(tc_Nat_Onat,T_a)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,tc_prod(tc_Nat_Onat,T_a)),T_a),c_Product__Type_OPair(tc_Nat_Onat,T_a)),V_f_2)),c_COMBI(T_a))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_rp__inv__image__def,axiom,
% 162.20/162.00 ! [T_b,T_a] : c_FunDef_Orp__inv__image(T_a,T_b) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))))),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_COMBS(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(T_b,T_a)),c_Product__Type_OPair(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),c_Relation_Oinv__image(T_a,T_b))))),c_Relation_Oinv__image(T_a,T_b))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setprod__mono__one__left,axiom,
% 162.20/162.00 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.20/162.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 162.20/162.00 => ( ! [B_x] :
% 162.20/162.00 ( 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)))
% 162.20/162.00 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 162.20/162.00 => 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) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setprod__mono__one__right,axiom,
% 162.20/162.00 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.20/162.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 162.20/162.00 => ( ! [B_x] :
% 162.20/162.00 ( 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)))
% 162.20/162.00 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 162.20/162.00 => 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) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_measure__def,axiom,
% 162.20/162.00 ! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_in__inv__image,axiom,
% 162.20/162.00 ! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_r_2),V_f_2)))
% 162.20/162.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_zero__less__imp__eq__int,axiom,
% 162.20/162.00 ! [V_k] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 162.20/162.00 => ? [B_n] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 162.20/162.00 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_card__Pow,axiom,
% 162.20/162.00 ! [V_A_2,T_a] :
% 162.20/162.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.00 => 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)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_ivl__disj__un_I19_J,axiom,
% 162.20/162.00 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 162.20/162.00 => 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) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_finite__atLeastAtMost,axiom,
% 162.20/162.00 ! [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))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_finite__atLeastAtMost__int,axiom,
% 162.20/162.00 ! [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))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_PowI,axiom,
% 162.20/162.00 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 162.20/162.00 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Pow__empty,axiom,
% 162.20/162.00 ! [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))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Pow__bottom,axiom,
% 162.20/162.00 ! [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))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Pow__not__empty,axiom,
% 162.20/162.00 ! [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)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Un__Pow__subset,axiom,
% 162.20/162.00 ! [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)))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Pow__insert,axiom,
% 162.20/162.00 ! [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))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Pow__iff,axiom,
% 162.20/162.00 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2)))
% 162.20/162.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_PowD,axiom,
% 162.20/162.00 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2)))
% 162.20/162.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Pow__top,axiom,
% 162.20/162.00 ! [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))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_image__Suc__atLeastAtMost,axiom,
% 162.20/162.00 ! [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)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Cantors__paradox,axiom,
% 162.20/162.00 ! [V_A_2,T_a] :
% 162.20/162.00 ~ ? [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) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_image__Pow__surj,axiom,
% 162.20/162.00 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] :
% 162.20/162.00 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_B_2
% 162.20/162.00 => 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) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Pow__mono,axiom,
% 162.20/162.00 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 162.20/162.00 => 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))) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_finite__Pow__iff,axiom,
% 162.20/162.00 ! [V_A_2,T_a] :
% 162.20/162.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)))
% 162.20/162.00 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_image__add__atLeastAtMost,axiom,
% 162.20/162.00 ! [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)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 162.20/162.00 ! [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))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_UN__Pow__subset,axiom,
% 162.20/162.00 ! [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)))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 162.20/162.00 ! [V_n_2,V_m_2] :
% 162.20/162.00 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 162.20/162.00 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 162.20/162.00 => 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))) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 162.20/162.00 ! [V_y_2,V_x_2] :
% 162.20/162.00 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 162.20/162.00 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastatMost__empty__iff,axiom,
% 162.20/162.00 ! [V_b_2,V_a_2,T_a] :
% 162.20/162.00 ( class_Orderings_Oorder(T_a)
% 162.20/162.00 => ( 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))
% 162.20/162.00 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastatMost__empty__iff2,axiom,
% 162.20/162.00 ! [V_b_2,V_a_2,T_a] :
% 162.20/162.00 ( class_Orderings_Oorder(T_a)
% 162.20/162.00 => ( 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)
% 162.20/162.00 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastatMost__empty,axiom,
% 162.20/162.00 ! [V_a_2,V_b_2,T_a] :
% 162.20/162.00 ( class_Orderings_Oorder(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2))
% 162.20/162.00 => 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)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastatMost__subset__iff,axiom,
% 162.20/162.00 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 162.20/162.00 ( class_Orderings_Oorder(T_a)
% 162.20/162.00 => ( 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)))
% 162.20/162.00 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 162.20/162.00 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2))
% 162.20/162.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastAtMost__singleton_H,axiom,
% 162.20/162.00 ! [V_b_2,V_a_2,T_a] :
% 162.20/162.00 ( class_Orderings_Oorder(T_a)
% 162.20/162.00 => ( V_a_2 = V_b_2
% 162.20/162.00 => 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))) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 162.20/162.00 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 162.20/162.00 ( class_Orderings_Oorder(T_a)
% 162.20/162.00 => ( 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)))
% 162.20/162.00 <=> ( V_a_2 = V_b_2
% 162.20/162.00 & V_b_2 = V_ca_2 ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastAtMost__singleton,axiom,
% 162.20/162.00 ! [V_a_2,T_a] :
% 162.20/162.00 ( class_Orderings_Oorder(T_a)
% 162.20/162.00 => 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))) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_image__uminus__atLeastAtMost,axiom,
% 162.20/162.00 ! [V_y_2,V_x_2,T_a] :
% 162.20/162.00 ( class_Groups_Oordered__ab__group__add(T_a)
% 162.20/162.00 => 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)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_image__Pow__mono,axiom,
% 162.20/162.00 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 162.20/162.00 ( 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))
% 162.20/162.00 => 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))) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 162.20/162.00 ! [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) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 162.20/162.00 ! [V_y_2,V_x_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 162.20/162.00 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_card__atLeastAtMost,axiom,
% 162.20/162.00 ! [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) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastAtMostSuc__conv,axiom,
% 162.20/162.00 ! [V_n_2,V_m_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 162.20/162.00 => 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)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 162.20/162.00 ! [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) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastatMost__psubset__iff,axiom,
% 162.20/162.00 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 162.20/162.00 ( class_Orderings_Oorder(T_a)
% 162.20/162.00 => ( 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)))
% 162.20/162.00 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 162.20/162.00 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2))
% 162.20/162.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2))
% 162.20/162.00 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_a_2))
% 162.20/162.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_d_2)) ) ) )
% 162.20/162.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_ivl__disj__un_I22_J,axiom,
% 162.20/162.00 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 162.20/162.00 => 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) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_simp__from__to,axiom,
% 162.20/162.00 ! [V_i_2,V_j_2] :
% 162.20/162.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 162.20/162.00 => 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)) )
% 162.20/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 162.20/162.00 => 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)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_card__atLeastAtMost__int,axiom,
% 162.20/162.00 ! [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))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_ivl__disj__un_I5_J,axiom,
% 162.20/162.00 ! [V_u_2,V_l_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 162.20/162.00 => 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) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_bset_I8_J,axiom,
% 162.20/162.00 ! [V_B_2,V_t_2,V_D_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 162.20/162.00 => ( 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))
% 162.20/162.00 => ! [B_x] :
% 162.20/162.00 ( ! [B_xa] :
% 162.20/162.00 ( 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)))
% 162.20/162.00 => ! [B_xb] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 162.20/162.00 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 162.20/162.00 => 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))) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_aset_I6_J,axiom,
% 162.20/162.00 ! [V_A_2,V_t_2,V_D_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 162.20/162.00 => ( 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))
% 162.20/162.00 => ! [B_x] :
% 162.20/162.00 ( ! [B_xa] :
% 162.20/162.00 ( 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)))
% 162.20/162.00 => ! [B_xb] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 162.20/162.00 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 162.20/162.00 => 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)) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_irrefl__def,axiom,
% 162.20/162.00 ! [V_r_2,T_a] :
% 162.20/162.00 ( c_Relation_Oirrefl(T_a,V_r_2)
% 162.20/162.00 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_bset_I3_J,axiom,
% 162.20/162.00 ! [V_B_2,V_t_2,V_D_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 162.20/162.00 => ( 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))
% 162.20/162.00 => ( ! [B_x] :
% 162.20/162.00 ( 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)))
% 162.20/162.00 => ! [B_xa] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 162.20/162.00 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 162.20/162.00 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_ex__nat__less,axiom,
% 162.20/162.00 ! [V_P_2,V_n_2] :
% 162.20/162.00 ( ? [B_m] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 162.20/162.00 & hBOOL(hAPP(V_P_2,B_m)) )
% 162.20/162.00 <=> ? [B_x] :
% 162.20/162.00 ( 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)))
% 162.20/162.00 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_all__nat__less,axiom,
% 162.20/162.00 ! [V_P_2,V_n_2] :
% 162.20/162.00 ( ! [B_m] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 162.20/162.00 => hBOOL(hAPP(V_P_2,B_m)) )
% 162.20/162.00 <=> ! [B_x] :
% 162.20/162.00 ( 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)))
% 162.20/162.00 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Powp__Pow__eq,axiom,
% 162.20/162.00 ! [V_x_2,V_A_2,T_a] :
% 162.20/162.00 ( 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))
% 162.20/162.00 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_a),V_A_2))) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_aset_I4_J,axiom,
% 162.20/162.00 ! [V_A_2,V_t_2,V_D_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 162.20/162.00 => ! [B_x] :
% 162.20/162.00 ( ! [B_xa] :
% 162.20/162.00 ( 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)))
% 162.20/162.00 => ! [B_xb] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 162.20/162.00 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 162.20/162.00 => ( B_x != V_t_2
% 162.20/162.00 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Powp__mono,axiom,
% 162.20/162.00 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 162.20/162.00 => 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))) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_aset_I3_J,axiom,
% 162.20/162.00 ! [V_A_2,V_t_2,V_D_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 162.20/162.00 => ( 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))
% 162.20/162.00 => ( ! [B_x] :
% 162.20/162.00 ( 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)))
% 162.20/162.00 => ! [B_xa] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 162.20/162.00 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 162.20/162.00 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_aset_I5_J,axiom,
% 162.20/162.00 ! [V_A_2,V_t_2,V_D_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 162.20/162.00 => ! [B_x] :
% 162.20/162.00 ( ! [B_xa] :
% 162.20/162.00 ( 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)))
% 162.20/162.00 => ! [B_xb] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 162.20/162.00 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 162.20/162.00 => 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)) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_bset_I7_J,axiom,
% 162.20/162.00 ! [V_B_2,V_t_2,V_D_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 162.20/162.00 => ! [B_x] :
% 162.20/162.00 ( ! [B_xa] :
% 162.20/162.00 ( 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)))
% 162.20/162.00 => ! [B_xb] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 162.20/162.00 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 162.20/162.00 => 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))) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_bset_I4_J,axiom,
% 162.20/162.00 ! [V_B_2,V_t_2,V_D_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 162.20/162.00 => ! [B_x] :
% 162.20/162.00 ( ! [B_xa] :
% 162.20/162.00 ( 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)))
% 162.20/162.00 => ! [B_xb] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 162.20/162.00 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 162.20/162.00 => ( B_x != V_t_2
% 162.20/162.00 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_bset_I6_J,axiom,
% 162.20/162.00 ! [V_t_2,V_B_2,V_D_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 162.20/162.00 => ! [B_x] :
% 162.20/162.00 ( ! [B_xa] :
% 162.20/162.00 ( 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)))
% 162.20/162.00 => ! [B_xb] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 162.20/162.00 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 162.20/162.00 => 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)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_aset_I8_J,axiom,
% 162.20/162.00 ! [V_t_2,V_A_2,V_D_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 162.20/162.00 => ! [B_x] :
% 162.20/162.00 ( ! [B_xa] :
% 162.20/162.00 ( 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)))
% 162.20/162.00 => ! [B_xb] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 162.20/162.00 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 162.20/162.00 => 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))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Field__insert,axiom,
% 162.20/162.00 ! [V_r_2,V_b_2,V_a_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_a),V_r_2)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_periodic__finite__ex,axiom,
% 162.20/162.00 ! [V_P_2,V_d_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 162.20/162.00 => ( ! [B_x,B_k] :
% 162.20/162.00 ( hBOOL(hAPP(V_P_2,B_x))
% 162.20/162.00 <=> 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)))) )
% 162.20/162.00 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 162.20/162.00 <=> ? [B_x] :
% 162.20/162.00 ( 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)))
% 162.20/162.00 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Field__empty,axiom,
% 162.20/162.00 ! [T_a] : hAPP(c_Relation_OField(T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_mono__Field,axiom,
% 162.20/162.00 ! [V_s_2,V_r_2,T_a] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
% 162.20/162.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_Relation_OField(T_a),V_s_2))) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Field__Un,axiom,
% 162.20/162.00 ! [V_s_2,V_r_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_Relation_OField(T_a),V_s_2)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_finite__Field,axiom,
% 162.20/162.00 ! [V_r_2,T_a] :
% 162.20/162.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 162.20/162.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_OField(T_a),V_r_2))) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_bset_I5_J,axiom,
% 162.20/162.00 ! [V_t_2,V_B_2,V_D_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 162.20/162.00 => ! [B_x] :
% 162.20/162.00 ( ! [B_xa] :
% 162.20/162.00 ( 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)))
% 162.20/162.00 => ! [B_xb] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 162.20/162.00 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 162.20/162.00 => 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)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_aset_I7_J,axiom,
% 162.20/162.00 ! [V_t_2,V_A_2,V_D_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 162.20/162.00 => ! [B_x] :
% 162.20/162.00 ( ! [B_xa] :
% 162.20/162.00 ( 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)))
% 162.20/162.00 => ! [B_xb] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 162.20/162.00 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 162.20/162.00 => 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))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 162.20/162.00 ! [V_x_2,V_y_2,V_ca_2] :
% 162.20/162.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 162.20/162.00 => 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)) )
% 162.20/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 162.20/162.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 162.20/162.00 => 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))) )
% 162.20/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 162.20/162.00 => 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)) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 162.20/162.00 ! [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))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_finite__atLeastLessThan,axiom,
% 162.20/162.00 ! [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))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_finite__atMost,axiom,
% 162.20/162.00 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 162.20/162.00 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( 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)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2))
% 162.20/162.00 => V_b_2 = V_d_2 ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 162.20/162.00 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( 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)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2))
% 162.20/162.00 => V_a_2 = V_ca_2 ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastLessThan__eq__iff,axiom,
% 162.20/162.00 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2))
% 162.20/162.00 => ( 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)
% 162.20/162.00 <=> ( V_a_2 = V_ca_2
% 162.20/162.00 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atMost__eq__iff,axiom,
% 162.20/162.00 ! [V_y_2,V_x_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2)
% 162.20/162.00 <=> V_x_2 = V_y_2 ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_ex__nat__less__eq,axiom,
% 162.20/162.00 ! [V_P_2,V_n_2] :
% 162.20/162.00 ( ? [B_m] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 162.20/162.00 & hBOOL(hAPP(V_P_2,B_m)) )
% 162.20/162.00 <=> ? [B_x] :
% 162.20/162.00 ( 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)))
% 162.20/162.00 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_all__nat__less__eq,axiom,
% 162.20/162.00 ! [V_P_2,V_n_2] :
% 162.20/162.00 ( ! [B_m] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 162.20/162.00 => hBOOL(hAPP(V_P_2,B_m)) )
% 162.20/162.00 <=> ! [B_x] :
% 162.20/162.00 ( 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)))
% 162.20/162.00 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 162.20/162.00 ! [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) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastLessThan0,axiom,
% 162.20/162.00 ! [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)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_card__atLeastLessThan,axiom,
% 162.20/162.00 ! [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) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_image__Suc__atLeastLessThan,axiom,
% 162.20/162.00 ! [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)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastLessThan__empty,axiom,
% 162.20/162.00 ! [V_a_2,V_b_2,T_a] :
% 162.20/162.00 ( class_Orderings_Oorder(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2))
% 162.20/162.00 => 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)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 162.20/162.00 ! [V_b_2,V_a_2,T_a] :
% 162.20/162.00 ( class_Orderings_Oorder(T_a)
% 162.20/162.00 => ( 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)
% 162.20/162.00 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastLessThan__empty__iff,axiom,
% 162.20/162.00 ! [V_b_2,V_a_2,T_a] :
% 162.20/162.00 ( class_Orderings_Oorder(T_a)
% 162.20/162.00 => ( 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))
% 162.20/162.00 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastLessThan__subset__iff,axiom,
% 162.20/162.00 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( 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)))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2))
% 162.20/162.00 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2))
% 162.20/162.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_ivl__disj__un_I17_J,axiom,
% 162.20/162.00 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 162.20/162.00 => 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) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_ivl__diff,axiom,
% 162.20/162.00 ! [V_m_2,V_n_2,V_i_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_n_2))
% 162.20/162.00 => 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) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 162.20/162.00 ! [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) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeast0AtMost,axiom,
% 162.20/162.00 ! [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) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_image__add__atLeastLessThan,axiom,
% 162.20/162.00 ! [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)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_card__atMost,axiom,
% 162.20/162.00 ! [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) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atMost__Suc,axiom,
% 162.20/162.00 ! [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)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atMost__iff,axiom,
% 162.20/162.00 ! [V_k_2,V_i_2,T_a] :
% 162.20/162.00 ( class_Orderings_Oord(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2)))
% 162.20/162.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_k_2)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atMost__subset__iff,axiom,
% 162.20/162.00 ! [V_y_2,V_x_2,T_a] :
% 162.20/162.00 ( class_Orderings_Oorder(T_a)
% 162.20/162.00 => ( 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)))
% 162.20/162.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_UN__le__add__shift,axiom,
% 162.20/162.00 ! [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) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastLessThan__singleton,axiom,
% 162.20/162.00 ! [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))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_ivl__disj__un_I21_J,axiom,
% 162.20/162.00 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 162.20/162.00 => 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) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastLessThan__add__Un,axiom,
% 162.20/162.00 ! [V_k_2,V_j_2,V_i_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 162.20/162.00 => 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))) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_subset__card__intvl__is__intvl,axiom,
% 162.20/162.00 ! [V_k_2,V_A_2] :
% 162.20/162.00 ( 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)))))
% 162.20/162.00 => 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))) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_image__uminus__atLeastLessThan,axiom,
% 162.20/162.00 ! [V_y_2,V_x_2,T_a] :
% 162.20/162.00 ( class_Groups_Oordered__ab__group__add(T_a)
% 162.20/162.00 => 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)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 162.20/162.00 ! [V_y_2,V_x_2,T_a] :
% 162.20/162.00 ( class_Groups_Oordered__ab__group__add(T_a)
% 162.20/162.00 => 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)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastLessThanSuc,axiom,
% 162.20/162.00 ! [V_n_2,V_m_2] :
% 162.20/162.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 162.20/162.00 => 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)) )
% 162.20/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 162.20/162.00 => 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)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atMost__0,axiom,
% 162.20/162.00 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))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_ivl__disj__un_I9_J,axiom,
% 162.20/162.00 ! [V_u_2,V_l_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 162.20/162.00 => 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) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_ivl__disj__un_I15_J,axiom,
% 162.20/162.00 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 162.20/162.00 => 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) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_UN__le__eq__Un0,axiom,
% 162.20/162.00 ! [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))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_ivl__disj__un_I6_J,axiom,
% 162.20/162.00 ! [V_u_2,V_l_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 162.20/162.00 => 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) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_ivl__disj__un_I3_J,axiom,
% 162.20/162.00 ! [V_u_2,V_l_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 162.20/162.00 => 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) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_ivl__disj__un_I18_J,axiom,
% 162.20/162.00 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2))
% 162.20/162.00 => 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) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_ivl__disj__un_I7_J,axiom,
% 162.20/162.00 ! [V_u_2,V_l_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 162.20/162.00 => 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) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_ivl__disj__un_I10_J,axiom,
% 162.20/162.00 ! [V_u_2,V_l_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 162.20/162.00 => 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) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_equiv__intrel__iff,axiom,
% 162.20/162.00 ! [V_y_2,V_x_2] :
% 162.20/162.00 ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
% 162.20/162.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_Int_Ointrel)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_ivl__disj__un_I2_J,axiom,
% 162.20/162.00 ! [V_u_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => 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) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_finite__lessThan,axiom,
% 162.20/162.00 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_finite__atLeastLessThan__int,axiom,
% 162.20/162.00 ! [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))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Image__empty,axiom,
% 162.20/162.00 ! [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)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Image__Un,axiom,
% 162.20/162.00 ! [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)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_lessThan__eq__iff,axiom,
% 162.20/162.00 ! [V_y_2,V_x_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2)
% 162.20/162.00 <=> V_x_2 = V_y_2 ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Image__UN,axiom,
% 162.20/162.00 ! [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)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_card__lessThan,axiom,
% 162.20/162.00 ! [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 ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Image__mono,axiom,
% 162.20/162.00 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_b,T_a] :
% 162.20/162.00 ( 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))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 162.20/162.00 => 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))) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Un__Image,axiom,
% 162.20/162.00 ! [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)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeast0LessThan,axiom,
% 162.20/162.00 ! [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) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_lessThan__0,axiom,
% 162.20/162.00 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)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_lessThan__Suc,axiom,
% 162.20/162.00 ! [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)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_lessThan__Suc__atMost,axiom,
% 162.20/162.00 ! [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) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 162.20/162.00 ! [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))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 162.20/162.00 ! [V_u_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 162.20/162.00 => 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))) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_lessThan__iff,axiom,
% 162.20/162.00 ! [V_k_2,V_i_2,T_a] :
% 162.20/162.00 ( class_Orderings_Oord(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)))
% 162.20/162.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_i_2),V_k_2)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_lessThan__subset__iff,axiom,
% 162.20/162.00 ! [V_y_2,V_x_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( 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)))
% 162.20/162.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_rev__ImageI,axiom,
% 162.20/162.00 ! [V_r_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2))
% 162.20/162.00 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Image__iff,axiom,
% 162.20/162.00 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)))
% 162.20/162.00 <=> ? [B_x] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 162.20/162.00 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_lessThan__strict__subset__iff,axiom,
% 162.20/162.00 ! [V_n_2,V_m_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( 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)))
% 162.20/162.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_n_2)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Image__eq__UN,axiom,
% 162.20/162.00 ! [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))))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 162.20/162.00 ! [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) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_image__add__int__atLeastLessThan,axiom,
% 162.20/162.00 ! [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) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 162.20/162.00 ! [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) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_card__atLeastLessThan__int,axiom,
% 162.20/162.00 ! [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)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 162.20/162.00 ! [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) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_single__Diff__lessThan,axiom,
% 162.20/162.00 ! [V_k_2,T_a] :
% 162.20/162.00 ( class_Orderings_Oorder(T_a)
% 162.20/162.00 => 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))) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_ivl__disj__un_I8_J,axiom,
% 162.20/162.00 ! [V_u_2,V_l_2,T_a] :
% 162.20/162.00 ( class_Orderings_Olinorder(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 162.20/162.00 => 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) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Image__singleton__iff,axiom,
% 162.20/162.00 ! [V_a_2,V_r_2,T_b,V_b_2,T_a] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 162.20/162.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2),V_b_2)),V_r_2)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 162.20/162.00 ! [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))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_of__int,axiom,
% 162.20/162.00 ! [V_j_2,V_i_2,T_a] :
% 162.20/162.00 ( class_Rings_Oring__1(T_a)
% 162.20/162.00 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_i_2),V_j_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_j_2)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_One__int__def,axiom,
% 162.20/162.00 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_mult,axiom,
% 162.20/162.00 ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_v_2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_u_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_le,axiom,
% 162.20/162.00 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
% 162.20/162.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Rep__Integ__inverse,axiom,
% 162.20/162.00 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 162.20/162.00
% 162.20/162.00 fof(fact_minus,axiom,
% 162.20/162.00 ! [V_y_2,V_x_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_y_2),V_x_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_Zero__int__def,axiom,
% 162.20/162.00 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_int__def,axiom,
% 162.20/162.00 ! [V_m_2] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_add,axiom,
% 162.20/162.00 ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),V_v_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_nat,axiom,
% 162.20/162.00 ! [V_y_2,V_x_2] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_minus__int__def,axiom,
% 162.20/162.00 ! [V_z_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_2) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_less,axiom,
% 162.20/162.00 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
% 162.20/162.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_arith__series__int,axiom,
% 162.20/162.00 ! [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)))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_eq__Abs__Integ,axiom,
% 162.20/162.00 ! [V_z_2] :
% 162.20/162.00 ~ ! [B_x,B_y] : V_z_2 != hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_arith__series__nat,axiom,
% 162.20/162.00 ! [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)))) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_arith__series__general,axiom,
% 162.20/162.00 ! [V_n_2,V_d_2,V_a_2,T_a] :
% 162.20/162.00 ( class_Rings_Ocomm__semiring__1(T_a)
% 162.20/162.00 => 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)))) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__divide__distrib,axiom,
% 162.20/162.00 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] :
% 162.20/162.00 ( class_Fields_Ofield(T_a)
% 162.20/162.00 => 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) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__subtractf,axiom,
% 162.20/162.00 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
% 162.20/162.00 ( class_Groups_Oab__group__add(T_a)
% 162.20/162.00 => 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)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__0,axiom,
% 162.20/162.00 ! [V_A_2,T_b,T_a] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.00 => 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) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 162.20/162.00 ! [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)) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_int__setsum,axiom,
% 162.20/162.00 ! [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) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_of__nat__setsum,axiom,
% 162.20/162.00 ! [V_A_2,V_f_2,T_b,T_a] :
% 162.20/162.00 ( class_Rings_Osemiring__1(T_a)
% 162.20/162.00 => 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) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__commute,axiom,
% 162.20/162.00 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.00 => 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) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_of__int__setsum,axiom,
% 162.20/162.00 ! [V_A_2,V_f_2,T_b,T_a] :
% 162.20/162.00 ( class_Rings_Oring__1(T_a)
% 162.20/162.00 => 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) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__product,axiom,
% 162.20/162.00 ! [V_B_2,V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] :
% 162.20/162.00 ( class_Rings_Osemiring__0(T_a)
% 162.20/162.00 => 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) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__left__distrib,axiom,
% 162.20/162.00 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] :
% 162.20/162.00 ( class_Rings_Osemiring__0(T_a)
% 162.20/162.00 => 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) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__right__distrib,axiom,
% 162.20/162.00 ! [V_A_2,V_f_2,T_b,V_r_2,T_a] :
% 162.20/162.00 ( class_Rings_Osemiring__0(T_a)
% 162.20/162.00 => 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) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__addf,axiom,
% 162.20/162.00 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.00 => 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)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__negf,axiom,
% 162.20/162.00 ! [V_A_2,V_f_2,T_b,T_a] :
% 162.20/162.00 ( class_Groups_Oab__group__add(T_a)
% 162.20/162.00 => 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)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum_Oempty,axiom,
% 162.20/162.00 ! [V_g_2,T_b,T_a] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.00 => 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) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__empty,axiom,
% 162.20/162.00 ! [V_f_2,T_b,T_a] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.00 => 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) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum_Oinfinite,axiom,
% 162.20/162.00 ! [V_g_2,V_A_2,T_a,T_b] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.20/162.00 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.00 => 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) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__infinite,axiom,
% 162.20/162.00 ! [V_f_2,V_A_2,T_a,T_b] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.20/162.00 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.00 => 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) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__eq__0__iff,axiom,
% 162.20/162.00 ! [V_f_2,V_F_2,T_a] :
% 162.20/162.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 162.20/162.00 => ( 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)
% 162.20/162.00 <=> ! [B_x] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2))
% 162.20/162.00 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum_Odistrib,axiom,
% 162.20/162.00 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.20/162.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.00 => 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)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_card__eq__setsum,axiom,
% 162.20/162.00 ! [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) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 162.20/162.00 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.00 => 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)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 162.20/162.00 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.00 => 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)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 162.20/162.00 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.00 => 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)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 162.20/162.00 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.00 => 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)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__eq__Suc0__iff,axiom,
% 162.20/162.00 ! [V_f_2,V_A_2,T_a] :
% 162.20/162.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.00 => ( 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))
% 162.20/162.00 <=> ? [B_x] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.20/162.00 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 162.20/162.00 & ! [B_xa] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 162.20/162.00 => ( B_x != B_xa
% 162.20/162.00 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__eq__1__iff,axiom,
% 162.20/162.00 ! [V_f_2,V_A_2,T_a] :
% 162.20/162.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.00 => ( 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)
% 162.20/162.00 <=> ? [B_x] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.20/162.00 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 162.20/162.00 & ! [B_xa] :
% 162.20/162.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 162.20/162.00 => ( B_x != B_xa
% 162.20/162.00 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__add__nat__ivl,axiom,
% 162.20/162.00 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 162.20/162.00 => 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)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__diff__nat__ivl,axiom,
% 162.20/162.00 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] :
% 162.20/162.00 ( class_Groups_Oab__group__add(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 162.20/162.00 => 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)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 162.20/162.00 ! [V_k_2,V_f_2] :
% 162.20/162.00 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.20/162.00 => 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)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__delta,axiom,
% 162.20/162.00 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.20/162.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 162.20/162.00 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 162.20/162.00 => 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) )
% 162.20/162.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 162.20/162.00 => 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) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__delta_H,axiom,
% 162.20/162.00 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.20/162.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 162.20/162.00 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 162.20/162.00 => 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) )
% 162.20/162.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 162.20/162.00 => 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) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__constant,axiom,
% 162.20/162.00 ! [V_A_2,V_y_2,T_b,T_a] :
% 162.20/162.00 ( class_Rings_Osemiring__1(T_a)
% 162.20/162.00 => 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) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__lessThan__Suc,axiom,
% 162.20/162.00 ! [V_n_2,V_f_2,T_a] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.00 => 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)) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__atMost__Suc,axiom,
% 162.20/162.00 ! [V_n_2,V_f_2,T_a] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.00 => 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))) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum_Oinsert,axiom,
% 162.20/162.00 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.20/162.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.00 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.20/162.00 => 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)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__insert,axiom,
% 162.20/162.00 ! [V_f_2,V_a_2,V_F_2,T_a,T_b] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.20/162.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 162.20/162.00 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_F_2))
% 162.20/162.00 => 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)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__diff,axiom,
% 162.20/162.00 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 162.20/162.00 ( class_Groups_Oab__group__add(T_b)
% 162.20/162.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 162.20/162.00 => 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)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__diff__nat,axiom,
% 162.20/162.00 ! [V_f_2,V_A_2,V_B_2,T_a] :
% 162.20/162.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 162.20/162.00 => 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)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 162.20/162.00 ! [V_k_2,V_f_2,T_a] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.00 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a)
% 162.20/162.00 => 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)) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__head__upt__Suc,axiom,
% 162.20/162.00 ! [V_f_2,V_n_2,V_m_2,T_a] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 162.20/162.00 => 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))) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__head__Suc,axiom,
% 162.20/162.00 ! [V_f_2,V_n_2,V_m_2,T_a] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 162.20/162.00 => 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))) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum_Oinsert__remove,axiom,
% 162.20/162.00 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.20/162.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.00 => 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)))))) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__diff1__nat,axiom,
% 162.20/162.00 ! [V_f_2,V_A_2,V_a_2,T_a] :
% 162.20/162.00 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.20/162.00 => 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)) )
% 162.20/162.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.20/162.00 => 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) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__op__ivl__Suc,axiom,
% 162.20/162.00 ! [V_f_2,V_m_2,V_n_2,T_a] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 162.20/162.00 => 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) )
% 162.20/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 162.20/162.00 => 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)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__cl__ivl__Suc,axiom,
% 162.20/162.00 ! [V_f_2,V_m_2,V_n_2,T_a] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 162.20/162.00 => 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) )
% 162.20/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 162.20/162.00 => 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))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__head,axiom,
% 162.20/162.00 ! [V_P_2,V_n_2,V_m_2,T_a] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 162.20/162.00 => 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))) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__ub__add__nat,axiom,
% 162.20/162.00 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_a] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.00 => ( 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))))
% 162.20/162.00 => 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)))) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum_Oremove,axiom,
% 162.20/162.00 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.20/162.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.20/162.00 => 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)))))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__diff1_H,axiom,
% 162.20/162.00 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 162.20/162.00 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.20/162.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.20/162.00 => 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)))))) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__diff1__ring,axiom,
% 162.20/162.00 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 162.20/162.00 ( class_Rings_Oring(T_b)
% 162.20/162.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.20/162.00 => 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)) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__diff1,axiom,
% 162.20/162.00 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 162.20/162.00 ( class_Groups_Oab__group__add(T_b)
% 162.20/162.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.00 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.20/162.00 => 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)) )
% 162.20/162.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.20/162.00 => 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) ) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_geometric__sum,axiom,
% 162.20/162.00 ! [V_n_2,V_x_2,T_a] :
% 162.20/162.00 ( class_Fields_Ofield(T_a)
% 162.20/162.00 => ( V_x_2 != c_Groups_Oone__class_Oone(T_a)
% 162.20/162.00 => 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))) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_gauss__sum,axiom,
% 162.20/162.00 ! [V_n_2,T_a] :
% 162.20/162.00 ( class_Rings_Ocomm__semiring__1(T_a)
% 162.20/162.00 => 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))) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_setsum__natinterval__difff,axiom,
% 162.20/162.00 ! [V_f_2,V_n_2,V_m_2,T_a] :
% 162.20/162.00 ( class_Groups_Oab__group__add(T_a)
% 162.20/162.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 162.20/162.00 => 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)))) )
% 162.20/162.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 162.20/162.00 => 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) ) ) ) ).
% 162.20/162.00
% 162.20/162.00 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 162.20/162.01 ! [V_f_2,V_A_2,T_a] :
% 162.20/162.01 ( ! [B_x] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.20/162.01 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_setsum__mono2,axiom,
% 162.20/162.01 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] :
% 162.20/162.01 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 162.20/162.01 => ( ! [B_b] :
% 162.20/162.01 ( 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)))
% 162.20/162.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_b))) )
% 162.20/162.01 => 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))) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_setsum__bounded,axiom,
% 162.20/162.01 ! [V_K_2,V_f_2,V_A_2,T_a,T_b] :
% 162.20/162.01 ( ( class_Groups_Oordered__ab__semigroup__add(T_b)
% 162.20/162.01 & class_Rings_Osemiring__1(T_b) )
% 162.20/162.01 => ( ! [B_i] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_A_2))
% 162.20/162.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_i)),V_K_2)) )
% 162.20/162.01 => 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))) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_setsum__mono3,axiom,
% 162.20/162.01 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] :
% 162.20/162.01 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 162.20/162.01 & class_Groups_Oordered__ab__semigroup__add(T_b) )
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 162.20/162.01 => ( ! [B_x] :
% 162.20/162.01 ( 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)))
% 162.20/162.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) )
% 162.20/162.01 => 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))) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 162.20/162.01 ! [V_A_2,V_f_2,T_a] :
% 162.20/162.01 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.01 & class_Groups_Ocomm__monoid__mult(T_a) )
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 162.20/162.01 ! [V_f_2,V_A_2,T_a] :
% 162.20/162.01 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 162.20/162.01 & class_Groups_Ocomm__monoid__mult(T_a) )
% 162.20/162.01 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 162.20/162.01 => 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)) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Id__on__def,axiom,
% 162.20/162.01 ! [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)))) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_quotient__def,axiom,
% 162.20/162.01 ! [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)))) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_setsum__nonneg__leq__bound,axiom,
% 162.20/162.01 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_a,T_b] :
% 162.20/162.01 ( class_Groups_Oordered__ab__group__add(T_b)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
% 162.20/162.01 => ( ! [B_i] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2))
% 162.20/162.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) )
% 162.20/162.01 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = V_B_2
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2))
% 162.20/162.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_setsum__nonneg__0,axiom,
% 162.20/162.01 ! [V_i_2,V_f_2,V_s_2,T_a,T_b] :
% 162.20/162.01 ( class_Groups_Oordered__ab__group__add(T_b)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
% 162.20/162.01 => ( ! [B_i] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2))
% 162.20/162.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) )
% 162.20/162.01 => ( 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)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2))
% 162.20/162.01 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_quotient__empty,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_quotient__is__empty2,axiom,
% 162.20/162.01 ! [V_r_2,V_A_2,T_a] :
% 162.20/162.01 ( 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)
% 162.20/162.01 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_quotient__is__empty,axiom,
% 162.20/162.01 ! [V_r_2,V_A_2,T_a] :
% 162.20/162.01 ( 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))
% 162.20/162.01 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Id__on__def_H,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Id__on__empty,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_quotientI,axiom,
% 162.20/162.01 ! [V_r_2,V_A_2,V_x_2,T_a] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.20/162.01 => 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))) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Id__on__eqI,axiom,
% 162.20/162.01 ! [V_A_2,T_a,V_b_2,V_a_2] :
% 162.20/162.01 ( V_a_2 = V_b_2
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.20/162.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Relation_OId__on(T_a,V_A_2))) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Id__on__iff,axiom,
% 162.20/162.01 ! [V_A_2,V_y_2,V_x_2,T_a] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Relation_OId__on(T_a,V_A_2)))
% 162.20/162.01 <=> ( V_x_2 = V_y_2
% 162.20/162.01 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_singleton__quotient,axiom,
% 162.20/162.01 ! [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))) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_subset__equiv__class,axiom,
% 162.20/162.01 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_a] :
% 162.20/162.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 162.20/162.01 => ( 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))))))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 162.20/162.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_quotientE,axiom,
% 162.20/162.01 ! [V_r_2,V_A_2,V_X_2,T_a] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 162.20/162.01 => ~ ! [B_x] :
% 162.20/162.01 ( 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))))
% 162.20/162.01 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_eq__equiv__class__iff2,axiom,
% 162.20/162.01 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 162.20/162.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 162.20/162.01 => ( 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)
% 162.20/162.01 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_equiv__class__subset,axiom,
% 162.20/162.01 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] :
% 162.20/162.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 162.20/162.01 => 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)))))) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_equiv__class__self,axiom,
% 162.20/162.01 ! [V_a_2,V_r_2,V_A_2,T_a] :
% 162.20/162.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.20/162.01 => 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)))))) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_equiv__class__eq,axiom,
% 162.20/162.01 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] :
% 162.20/162.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 162.20/162.01 => 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)))) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_quotient__eq__iff,axiom,
% 162.20/162.01 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
% 162.20/162.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 162.20/162.01 => ( 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)))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2))
% 162.20/162.01 => ( V_X_2 = V_Y_2
% 162.20/162.01 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_quotient__eqI,axiom,
% 162.20/162.01 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
% 162.20/162.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 162.20/162.01 => ( 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)))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 162.20/162.01 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_equiv__class__eq__iff,axiom,
% 162.20/162.01 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 162.20/162.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 162.20/162.01 <=> ( 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))))
% 162.20/162.01 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.20/162.01 & hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_eq__equiv__class__iff,axiom,
% 162.20/162.01 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 162.20/162.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 162.20/162.01 => ( 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))))
% 162.20/162.01 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_eq__equiv__class,axiom,
% 162.20/162.01 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_a] :
% 162.20/162.01 ( 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))))
% 162.20/162.01 => ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 162.20/162.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_UN__equiv__class,axiom,
% 162.20/162.01 ! [V_a_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
% 162.20/162.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 162.20/162.01 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.20/162.01 => 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) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_UN__equiv__class2,axiom,
% 162.20/162.01 ! [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] :
% 162.20/162.01 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
% 162.20/162.01 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
% 162.20/162.01 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a1_2),V_A1_2))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a2_2),V_A2_2))
% 162.20/162.01 => 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) ) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_equiv__class__nondisjoint,axiom,
% 162.20/162.01 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_a] :
% 162.20/162.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 162.20/162.01 => ( 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)))))))
% 162.20/162.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Id__onE,axiom,
% 162.20/162.01 ! [V_A_2,V_ca_2,T_a] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_ca_2),c_Relation_OId__on(T_a,V_A_2)))
% 162.20/162.01 => ~ ! [B_x] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.20/162.01 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf1E,axiom,
% 162.20/162.01 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( 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))
% 162.20/162.01 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 162.20/162.01 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf1I,axiom,
% 162.20/162.01 ! [T_a,V_B_2,V_x_2,V_A_2] :
% 162.20/162.01 ( hBOOL(hAPP(V_A_2,V_x_2))
% 162.20/162.01 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 162.20/162.01 => 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)) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_IntI,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
% 162.20/162.01 => 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))) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_IntE,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 162.20/162.01 ( 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)))
% 162.20/162.01 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 162.20/162.01 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_finite__Int,axiom,
% 162.20/162.01 ! [V_G_2,V_F_2,T_a] :
% 162.20/162.01 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 162.20/162.01 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) )
% 162.20/162.01 => 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))) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__sup__ord_I1_J,axiom,
% 162.20/162.01 ! [V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__le1,axiom,
% 162.20/162.01 ! [V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__sup__ord_I2_J,axiom,
% 162.20/162.01 ! [V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__le2,axiom,
% 162.20/162.01 ! [V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_le__iff__inf,axiom,
% 162.20/162.01 ! [V_y_2,V_x_2,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 162.20/162.01 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = V_x_2 ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_le__inf__iff,axiom,
% 162.20/162.01 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => ( 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)))
% 162.20/162.01 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 162.20/162.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_le__infI1,axiom,
% 162.20/162.01 ! [V_b,V_x,V_a,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 162.20/162.01 => 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)) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_le__infI2,axiom,
% 162.20/162.01 ! [V_a,V_x,V_b,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 162.20/162.01 => 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)) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__absorb1,axiom,
% 162.20/162.01 ! [V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 162.20/162.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__absorb2,axiom,
% 162.20/162.01 ! [V_x,V_y,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 162.20/162.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_le__infI,axiom,
% 162.20/162.01 ! [V_b,V_a,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 162.20/162.01 => 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))) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__greatest,axiom,
% 162.20/162.01 ! [V_z,V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 162.20/162.01 => 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))) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__mono,axiom,
% 162.20/162.01 ! [V_d,V_b,V_c,V_a,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 162.20/162.01 => 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))) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_le__infE,axiom,
% 162.20/162.01 ! [V_b,V_a,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => ( 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)))
% 162.20/162.01 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 162.20/162.01 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__lower1,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__lower2,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__absorb2,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 162.20/162.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__absorb1,axiom,
% 162.20/162.01 ! [V_A_2,V_B_2,T_a] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 162.20/162.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__greatest,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,V_C_2,T_a] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2))
% 162.20/162.01 => 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))) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__mono,axiom,
% 162.20/162.01 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))
% 162.20/162.01 => 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))) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_IntD2,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 162.20/162.01 ( 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)))
% 162.20/162.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_IntD1,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 162.20/162.01 ( 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)))
% 162.20/162.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__iff,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 162.20/162.01 ( 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)))
% 162.20/162.01 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 162.20/162.01 & hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Un__Int__crazy,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Un__Int__distrib2,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__Un__distrib2,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Un__Int__distrib,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__Un__distrib,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_sup__inf__distrib2,axiom,
% 162.20/162.01 ! [V_x,V_z,V_y,T_a] :
% 162.20/162.01 ( class_Lattices_Odistrib__lattice(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__sup__distrib2,axiom,
% 162.20/162.01 ! [V_x,V_z,V_y,T_a] :
% 162.20/162.01 ( class_Lattices_Odistrib__lattice(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_sup__inf__distrib1,axiom,
% 162.20/162.01 ! [V_z,V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Odistrib__lattice(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__sup__distrib1,axiom,
% 162.20/162.01 ! [V_z,V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Odistrib__lattice(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_sup__inf__absorb,axiom,
% 162.20/162.01 ! [V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => 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 ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__sup__absorb,axiom,
% 162.20/162.01 ! [V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => 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 ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__bot__left,axiom,
% 162.20/162.01 ! [V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Obounded__lattice__bot(T_a)
% 162.20/162.01 => 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) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__bot__right,axiom,
% 162.20/162.01 ! [V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Obounded__lattice__bot(T_a)
% 162.20/162.01 => 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) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__empty__left,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__empty__right,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_disjoint__iff__not__equal,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( 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))
% 162.20/162.01 <=> ! [B_x] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.20/162.01 => ! [B_xa] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_B_2))
% 162.20/162.01 => B_x != B_xa ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__Int__eq,axiom,
% 162.20/162.01 ! [V_x_2,V_S_2,V_R_2,T_a] :
% 162.20/162.01 ( 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))
% 162.20/162.01 <=> 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))) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_restrict__restrict,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__min,axiom,
% 162.20/162.01 ! [T_a] :
% 162.20/162.01 ( ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 & class_Orderings_Olinorder(T_a) )
% 162.20/162.01 => c_Lattices_Osemilattice__inf__class_Oinf(T_a) = c_Orderings_Oord__class_Omin(T_a) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__fun__def,axiom,
% 162.20/162.01 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf1D2,axiom,
% 162.20/162.01 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( 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))
% 162.20/162.01 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf1D1,axiom,
% 162.20/162.01 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( 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))
% 162.20/162.01 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Inf__fin_Oidem,axiom,
% 162.20/162.01 ! [V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__assoc,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__left__commute,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__left__absorb,axiom,
% 162.20/162.01 ! [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) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__commute,axiom,
% 162.20/162.01 ! [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) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__absorb,axiom,
% 162.20/162.01 ! [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 ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__apply,axiom,
% 162.20/162.01 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__assoc,axiom,
% 162.20/162.01 ! [V_z,V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__sup__aci_I2_J,axiom,
% 162.20/162.01 ! [V_z,V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf_Oassoc,axiom,
% 162.20/162.01 ! [V_c,V_b,V_a,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__left__commute,axiom,
% 162.20/162.01 ! [V_z,V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__sup__aci_I3_J,axiom,
% 162.20/162.01 ! [V_z,V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf_Oleft__commute,axiom,
% 162.20/162.01 ! [V_c,V_a,V_b,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__left__idem,axiom,
% 162.20/162.01 ! [V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => 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) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__sup__aci_I4_J,axiom,
% 162.20/162.01 ! [V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => 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) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf_Oleft__idem,axiom,
% 162.20/162.01 ! [V_b,V_a,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => 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) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__commute,axiom,
% 162.20/162.01 ! [V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => 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) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__sup__aci_I1_J,axiom,
% 162.20/162.01 ! [V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => 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) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf_Ocommute,axiom,
% 162.20/162.01 ! [V_b,V_a,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => 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) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__idem,axiom,
% 162.20/162.01 ! [V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf_Oidem,axiom,
% 162.20/162.01 ! [V_a,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_less__infI1,axiom,
% 162.20/162.01 ! [V_b,V_x,V_a,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 162.20/162.01 => 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)) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_less__infI2,axiom,
% 162.20/162.01 ! [V_a,V_x,V_b,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 162.20/162.01 => 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)) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Diff__Int2,axiom,
% 162.20/162.01 ! [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) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Diff__Int__distrib2,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__Diff,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Diff__Int__distrib,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2] :
% 162.20/162.01 ( c_Nat__Transfer_Onat__set(V_A_2)
% 162.20/162.01 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 162.20/162.01 => 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)) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Pow__Int__eq,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_insert__inter__insert,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__UN__distrib2,axiom,
% 162.20/162.01 ! [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))) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_UN__extend__simps_I4_J,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__UN__distrib,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_UN__extend__simps_I5_J,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_UN__simps_I4_J,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_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) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_UN__simps_I5_J,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_distrib__sup__le,axiom,
% 162.20/162.01 ! [V_z,V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => 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)))) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_distrib__inf__le,axiom,
% 162.20/162.01 ! [V_z,V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => 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)))) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__compl__bot,axiom,
% 162.20/162.01 ! [V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Oboolean__algebra(T_a)
% 162.20/162.01 => 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) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_compl__inf__bot,axiom,
% 162.20/162.01 ! [V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Oboolean__algebra(T_a)
% 162.20/162.01 => 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) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_diff__eq,axiom,
% 162.20/162.01 ! [V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Oboolean__algebra(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_compl__inf,axiom,
% 162.20/162.01 ! [V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Oboolean__algebra(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_compl__sup,axiom,
% 162.20/162.01 ! [V_y,V_x,T_a] :
% 162.20/162.01 ( class_Lattices_Oboolean__algebra(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__insert__right,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,V_a_2,T_a] :
% 162.20/162.01 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.20/162.01 => 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)) )
% 162.20/162.01 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.20/162.01 => 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) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__insert__left,axiom,
% 162.20/162.01 ! [V_B_2,V_C_2,V_a_2,T_a] :
% 162.20/162.01 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 162.20/162.01 => 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)) )
% 162.20/162.01 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 162.20/162.01 => 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) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__insert__right__if0,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,V_a_2,T_a] :
% 162.20/162.01 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.20/162.01 => 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) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__insert__left__if0,axiom,
% 162.20/162.01 ! [V_B_2,V_C_2,V_a_2,T_a] :
% 162.20/162.01 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 162.20/162.01 => 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) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__insert__right__if1,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,V_a_2,T_a] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__insert__left__if1,axiom,
% 162.20/162.01 ! [V_B_2,V_C_2,V_a_2,T_a] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_image__Int__subset,axiom,
% 162.20/162.01 ! [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)))) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Diff__disjoint,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Diff__triv,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( 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))
% 162.20/162.01 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Un__Int__assoc__eq,axiom,
% 162.20/162.01 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( 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))
% 162.20/162.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Un__Diff__Int,axiom,
% 162.20/162.01 ! [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 ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Diff__Un,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Diff__Int,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_ivl__disj__int_I11_J,axiom,
% 162.20/162.01 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 162.20/162.01 ( class_Orderings_Oorder(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 162.20/162.01 ! [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))) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Compl__disjoint2,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Compl__disjoint,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Image__Int__subset,axiom,
% 162.20/162.01 ! [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)))) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Compl__Un,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Compl__Int,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Diff__Compl,axiom,
% 162.20/162.01 ! [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) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Diff__eq,axiom,
% 162.20/162.01 ! [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)) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_ivl__disj__int_I14_J,axiom,
% 162.20/162.01 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 162.20/162.01 ( class_Orderings_Oorder(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_dom__restrict,axiom,
% 162.20/162.01 ! [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) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Image__Id__on,axiom,
% 162.20/162.01 ! [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) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2] :
% 162.20/162.01 ( c_Nat__Transfer_Onat__set(V_A_2)
% 162.20/162.01 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 162.20/162.01 => 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))) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_congruent2__implies__congruent,axiom,
% 162.20/162.01 ! [V_a_2,V_f_2,V_r2_2,T_c,T_b,V_r1_2,V_A_2,T_a] :
% 162.20/162.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r1_2)
% 162.20/162.01 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.20/162.01 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_fold__inf__insert,axiom,
% 162.20/162.01 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => 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)) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__Sup__absorb,axiom,
% 162.20/162.01 ! [V_a_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.20/162.01 => 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 ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_disjoint__eq__subset__Compl,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( 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))
% 162.20/162.01 <=> 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))) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_ivl__disj__int_I15_J,axiom,
% 162.20/162.01 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 162.20/162.01 ( class_Orderings_Oorder(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__atLeastAtMost,axiom,
% 162.20/162.01 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 162.20/162.01 ( class_Orderings_Olinorder(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__atLeastLessThan,axiom,
% 162.20/162.01 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 162.20/162.01 ( class_Orderings_Olinorder(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_ivl__disj__int_I4_J,axiom,
% 162.20/162.01 ! [V_u_2,V_l_2,T_a] :
% 162.20/162.01 ( class_Orderings_Oorder(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_ivl__disj__int_I2_J,axiom,
% 162.20/162.01 ! [V_u_2,V_l_2,T_a] :
% 162.20/162.01 ( class_Orderings_Oorder(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_ivl__disj__int_I16_J,axiom,
% 162.20/162.01 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 162.20/162.01 ( class_Orderings_Oorder(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_ivl__disj__int_I13_J,axiom,
% 162.20/162.01 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 162.20/162.01 ( class_Orderings_Oorder(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_ivl__disj__int_I12_J,axiom,
% 162.20/162.01 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 162.20/162.01 ( class_Orderings_Oorder(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__greaterThanAtMost,axiom,
% 162.20/162.01 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 162.20/162.01 ( class_Orderings_Olinorder(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_ivl__disj__int_I9_J,axiom,
% 162.20/162.01 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 162.20/162.01 ( class_Orderings_Oorder(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__greaterThanLessThan,axiom,
% 162.20/162.01 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 162.20/162.01 ( class_Orderings_Olinorder(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__atLeastAtMostL1,axiom,
% 162.20/162.01 ! [V_d_2,V_b_2,V_a_2,T_a] :
% 162.20/162.01 ( class_Orderings_Olinorder(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Int__atLeastAtMostR1,axiom,
% 162.20/162.01 ! [V_d_2,V_ca_2,V_b_2,T_a] :
% 162.20/162.01 ( class_Orderings_Olinorder(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_map__add__comm,axiom,
% 162.20/162.01 ! [V_m2_2,V_m1_2,T_b,T_a] :
% 162.20/162.01 ( 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))
% 162.20/162.01 => 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) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_ivl__disj__int_I3_J,axiom,
% 162.20/162.01 ! [V_u_2,V_l_2,T_a] :
% 162.20/162.01 ( class_Orderings_Oorder(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_ivl__disj__int_I10_J,axiom,
% 162.20/162.01 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 162.20/162.01 ( class_Orderings_Oorder(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_ivl__disj__int_I1_J,axiom,
% 162.20/162.01 ! [V_u_2,V_l_2,T_a] :
% 162.20/162.01 ( class_Orderings_Oorder(T_a)
% 162.20/162.01 => 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)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 162.20/162.01 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 162.20/162.01 => 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)) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_fold__inf__le__inf,axiom,
% 162.20/162.01 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.20/162.01 => 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))) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_fold1__belowI,axiom,
% 162.20/162.01 ! [V_a_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.20/162.01 => 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)) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_below__fold1__iff,axiom,
% 162.20/162.01 ! [V_x_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Osemilattice__inf(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => ( 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)))
% 162.20/162.01 <=> ! [B_x] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.20/162.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_setsum__Un__Int,axiom,
% 162.20/162.01 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 162.20/162.01 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => 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)) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_setprod_Ounion__inter,axiom,
% 162.20/162.01 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 162.20/162.01 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => 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)) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_setprod__Un__Int,axiom,
% 162.20/162.01 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 162.20/162.01 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => 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)) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_card__Un__Int,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => 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))) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_card_Ounion__inter,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => 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)) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_card__Diff__subset__Int,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( 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)))
% 162.20/162.01 => 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))) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_setsum__restrict__set,axiom,
% 162.20/162.01 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] :
% 162.20/162.01 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => 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) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_quotient__disj,axiom,
% 162.20/162.01 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
% 162.20/162.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 162.20/162.01 => ( 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)))
% 162.20/162.01 => ( V_X_2 = V_Y_2
% 162.20/162.01 | 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)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 162.20/162.01 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => 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)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_folding__one_Ounion__disjoint,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
% 162.20/162.01 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => 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)) ) ) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_folding__one_Ounion__inter,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
% 162.20/162.01 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => 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)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_setsum__Un__disjoint,axiom,
% 162.20/162.01 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 162.20/162.01 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => 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)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_setsum__Un,axiom,
% 162.20/162.01 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 162.20/162.01 ( class_Groups_Oab__group__add(T_b)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => 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))) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_setprod_Ounion__disjoint,axiom,
% 162.20/162.01 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 162.20/162.01 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => 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)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_setprod__Un__disjoint,axiom,
% 162.20/162.01 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 162.20/162.01 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => 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)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_card__Un__disjoint,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => 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)) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_fold1__Un,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Groups_Oab__semigroup__mult(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => 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)) ) ) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Sup__fin_Ounion__inter,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => 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)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => 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)) ) ) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Min_Ounion__disjoint,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Orderings_Olinorder(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => 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)) ) ) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Min_Ounion__inter,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Orderings_Olinorder(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => 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)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Max_Ounion__disjoint,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Orderings_Olinorder(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => 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)) ) ) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Max_Ounion__inter,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Orderings_Olinorder(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => 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)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Orderings_Olinorder(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => 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)) ) ) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Orderings_Olinorder(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => 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)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Orderings_Olinorder(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => 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)) ) ) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Orderings_Olinorder(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => 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)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_congruent2D,axiom,
% 162.20/162.01 ! [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] :
% 162.20/162.01 ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2)
% 162.20/162.01 => ( 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))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_setsum__Un__nat,axiom,
% 162.20/162.01 ! [V_f_2,V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => 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))) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_congruentD,axiom,
% 162.20/162.01 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_b,T_a] :
% 162.20/162.01 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),V_r_2))
% 162.20/162.01 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_congruent2__implies__congruent__UN,axiom,
% 162.20/162.01 ! [V_a_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] :
% 162.20/162.01 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
% 162.20/162.01 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
% 162.20/162.01 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A2_2))
% 162.20/162.01 => 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)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_UN__equiv__class__inject,axiom,
% 162.20/162.01 ! [V_Y_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
% 162.20/162.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 162.20/162.01 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
% 162.20/162.01 => ( 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)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 162.20/162.01 => ( 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)))
% 162.20/162.01 => ( ! [B_x] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.20/162.01 => ! [B_y] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2))
% 162.20/162.01 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 162.20/162.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2)) ) ) )
% 162.20/162.01 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_UN__equiv__class__type2,axiom,
% 162.20/162.01 ! [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] :
% 162.20/162.01 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
% 162.20/162.01 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
% 162.20/162.01 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 162.20/162.01 => ( 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)))
% 162.20/162.01 => ( 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)))
% 162.20/162.01 => ( ! [B_x1] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x1),V_A1_2))
% 162.20/162.01 => ! [B_x2] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x2),V_A2_2))
% 162.20/162.01 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 162.20/162.01 => 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)) ) ) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_UN__equiv__class__type,axiom,
% 162.20/162.01 ! [V_B_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
% 162.20/162.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 162.20/162.01 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 162.20/162.01 => ( ! [B_x] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.20/162.01 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 162.20/162.01 => 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)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_card_Ounion__inter__neutral,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( ( ? [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)))
% 162.20/162.01 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 162.20/162.01 => 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)) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__nat__def,axiom,
% 162.20/162.01 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf__Int__eq2,axiom,
% 162.20/162.01 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] :
% 162.20/162.01 ( 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))
% 162.20/162.01 <=> 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))) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_setprod__Un,axiom,
% 162.20/162.01 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 162.20/162.01 ( class_Fields_Ofield(T_b)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( ! [B_x] :
% 162.20/162.01 ( 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)))
% 162.20/162.01 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b) )
% 162.20/162.01 => 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))) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_setprod__Un__one,axiom,
% 162.20/162.01 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
% 162.20/162.01 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 162.20/162.01 => ( ! [B_x] :
% 162.20/162.01 ( 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)))
% 162.20/162.01 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 162.20/162.01 => 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)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 162.20/162.01 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 162.20/162.01 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( ! [B_x] :
% 162.20/162.01 ( 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)))
% 162.20/162.01 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 162.20/162.01 => 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)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf2E,axiom,
% 162.20/162.01 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 162.20/162.01 ( 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))
% 162.20/162.01 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 162.20/162.01 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf2I,axiom,
% 162.20/162.01 ! [T_b,T_a,V_B_2,V_y_2,V_x_2,V_A_2] :
% 162.20/162.01 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 162.20/162.01 => 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)) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf2D2,axiom,
% 162.20/162.01 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 162.20/162.01 ( 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))
% 162.20/162.01 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_inf2D1,axiom,
% 162.20/162.01 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 162.20/162.01 ( 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))
% 162.20/162.01 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 162.20/162.01 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 162.20/162.01 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( ! [B_x] :
% 162.20/162.01 ( 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)))
% 162.20/162.01 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 162.20/162.01 => 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)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_setsum__Un__zero,axiom,
% 162.20/162.01 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
% 162.20/162.01 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 162.20/162.01 => ( ! [B_x] :
% 162.20/162.01 ( 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)))
% 162.20/162.01 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 162.20/162.01 => 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)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Inf__fin_Oremove,axiom,
% 162.20/162.01 ! [V_x_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.20/162.01 => ( ( 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))
% 162.20/162.01 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = V_x_2 )
% 162.20/162.01 & ( 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))
% 162.20/162.01 => 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)))))) ) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Inf__fin_Osingleton,axiom,
% 162.20/162.01 ! [V_x_2,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => 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 ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_sup__Inf__absorb,axiom,
% 162.20/162.01 ! [V_a_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.20/162.01 => 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 ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Inf__fin_Oin__idem,axiom,
% 162.20/162.01 ! [V_x_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.20/162.01 => 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) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Inf__fin_OF__eq,axiom,
% 162.20/162.01 ! [V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => 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) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 162.20/162.01 ! [V_x_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => 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)) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Inf__fin_Osubset__idem,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 162.20/162.01 => 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) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Inf__fin_Ounion__idem,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => 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)) ) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Inf__le__Sup,axiom,
% 162.20/162.01 ! [V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => 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))) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 162.20/162.01 ! [V_a_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => 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) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Inf__fin_Oinsert,axiom,
% 162.20/162.01 ! [V_x_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.20/162.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => 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)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 162.20/162.01 ! [V_x_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( ( 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))
% 162.20/162.01 => 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 )
% 162.20/162.01 & ( 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))
% 162.20/162.01 => 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)))))) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Inf__fin_Ounion__inter,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => 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)) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 162.20/162.01 ! [V_B_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.20/162.01 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.20/162.01 => ( 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))
% 162.20/162.01 => 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)) ) ) ) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 162.20/162.01 ! [V_x_2,V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.20/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.20/162.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.20/162.01 => 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) ) ) ) ).
% 162.20/162.01
% 162.20/162.01 fof(fact_Inf__fin_Oclosed,axiom,
% 162.20/162.01 ! [V_A_2,T_a] :
% 162.20/162.01 ( class_Lattices_Olattice(T_a)
% 162.26/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.01 => ( ! [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))))))
% 162.26/162.01 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_card__quotient__disjoint,axiom,
% 162.26/162.01 ! [V_r_2,V_A_2,T_a] :
% 162.26/162.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => ( 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)
% 162.26/162.01 => 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) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_fold__Un__disjoint,axiom,
% 162.26/162.01 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 162.26/162.01 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.26/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.26/162.01 => ( 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))
% 162.26/162.01 => 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)) ) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__on__empty,axiom,
% 162.26/162.01 ! [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))) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__uminus,axiom,
% 162.26/162.01 ! [V_A_2,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add(T_a)
% 162.26/162.01 => c_Fun_Oinj__on(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a),V_A_2) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_subset__inj__on,axiom,
% 162.26/162.01 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 162.26/162.01 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__onD,axiom,
% 162.26/162.01 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.01 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 162.26/162.01 => V_x_2 = V_y_2 ) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__on__iff,axiom,
% 162.26/162.01 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 162.26/162.01 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 162.26/162.01 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__on__contraD,axiom,
% 162.26/162.01 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.01 => ( V_x_2 != V_y_2
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 162.26/162.01 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_fold__image__empty,axiom,
% 162.26/162.01 ! [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 ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__on__id2,axiom,
% 162.26/162.01 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__on__def,axiom,
% 162.26/162.01 ! [V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.01 <=> ! [B_x] :
% 162.26/162.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.01 => ! [B_xa] :
% 162.26/162.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 162.26/162.01 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 162.26/162.01 => B_x = B_xa ) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__on__diff,axiom,
% 162.26/162.01 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.01 => 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__on__Int,axiom,
% 162.26/162.01 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.01 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 162.26/162.01 => 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)) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_fold__image__def,axiom,
% 162.26/162.01 ! [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)) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_finite__imageD,axiom,
% 162.26/162.01 ! [V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
% 162.26/162.01 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2)
% 162.26/162.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 162.26/162.01 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( 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))
% 162.26/162.01 => ( 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)
% 162.26/162.01 <=> V_A_2 = V_B_2 ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_card__image,axiom,
% 162.26/162.01 ! [V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.01 => 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) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__on__strict__subset,axiom,
% 162.26/162.01 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 162.26/162.01 => 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))) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 162.26/162.01 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 162.26/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 162.26/162.01 => 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) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_finite__surj__inj,axiom,
% 162.26/162.01 ! [V_f_2,V_A_2,T_a] :
% 162.26/162.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => ( 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)))
% 162.26/162.01 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_endo__inj__surj,axiom,
% 162.26/162.01 ! [V_f_2,V_A_2,T_a] :
% 162.26/162.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => ( 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))
% 162.26/162.01 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2)
% 162.26/162.01 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__on__image__Int,axiom,
% 162.26/162.01 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 162.26/162.01 => 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)) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__on__iff__eq__card,axiom,
% 162.26/162.01 ! [V_f_2,T_b,V_A_2,T_a] :
% 162.26/162.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.01 <=> 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) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_eq__card__imp__inj__on,axiom,
% 162.26/162.01 ! [V_f_2,T_b,V_A_2,T_a] :
% 162.26/162.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => ( 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)
% 162.26/162.01 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__on__image__set__diff,axiom,
% 162.26/162.01 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 162.26/162.01 => 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)) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_pigeonhole,axiom,
% 162.26/162.01 ! [V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( 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)))
% 162.26/162.01 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__on__fun__updI,axiom,
% 162.26/162.01 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 162.26/162.01 => 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) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_card__bij__eq,axiom,
% 162.26/162.01 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.01 => ( 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))
% 162.26/162.01 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2)
% 162.26/162.01 => ( 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))
% 162.26/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 162.26/162.01 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),V_B_2) ) ) ) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_fold__image__distrib,axiom,
% 162.26/162.01 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 162.26/162.01 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.26/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => 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)) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_fold__image__insert,axiom,
% 162.26/162.01 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_a,T_b] :
% 162.26/162.01 ( class_Groups_Oab__semigroup__mult(T_b)
% 162.26/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.26/162.01 => 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)) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_setsum_Oeq__fold,axiom,
% 162.26/162.01 ! [V_g_2,V_A_2,T_a,T_b] :
% 162.26/162.01 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.26/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => 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) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_setsum_OF__eq,axiom,
% 162.26/162.01 ! [V_g_2,V_A_2,T_a,T_b] :
% 162.26/162.01 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.26/162.01 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => 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) )
% 162.26/162.01 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => 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) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_setprod_OF__eq,axiom,
% 162.26/162.01 ! [V_g_2,V_A_2,T_a,T_b] :
% 162.26/162.01 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.26/162.01 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => 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) )
% 162.26/162.01 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => 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) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_setprod_Oeq__fold,axiom,
% 162.26/162.01 ! [V_g_2,V_A_2,T_a,T_b] :
% 162.26/162.01 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.26/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => 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) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__on__insert,axiom,
% 162.26/162.01 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))
% 162.26/162.01 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.01 & ~ 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))))))) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__on__Un,axiom,
% 162.26/162.01 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( 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))
% 162.26/162.01 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.01 & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 162.26/162.01 & 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)) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_card__inj__on__le,axiom,
% 162.26/162.01 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.01 => ( 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))
% 162.26/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 162.26/162.01 => 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))) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__on__iff__card__le,axiom,
% 162.26/162.01 ! [V_B_2,T_b,V_A_2,T_a] :
% 162.26/162.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 162.26/162.01 => ( ? [B_f] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2)
% 162.26/162.01 & 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)) )
% 162.26/162.01 <=> 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))) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_quotient__diff1,axiom,
% 162.26/162.01 ! [V_a_2,V_A_2,V_r_2,T_a] :
% 162.26/162.01 ( 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)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.26/162.01 => 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)) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_fold__image__Un__Int,axiom,
% 162.26/162.01 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 162.26/162.01 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.26/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.26/162.01 => 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))) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_image__eq__fold__image,axiom,
% 162.26/162.01 ! [V_f_2,T_b,V_A_2,T_a] :
% 162.26/162.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => 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) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_card_Oeq__fold__g,axiom,
% 162.26/162.01 ! [V_A_2,T_a] :
% 162.26/162.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => 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) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_card__def,axiom,
% 162.26/162.01 ! [V_A_2,T_a] :
% 162.26/162.01 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => 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) )
% 162.26/162.01 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__on__iff__surj,axiom,
% 162.26/162.01 ! [V_A_H_2,T_b,T_a,V_A_2] :
% 162.26/162.01 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.01 => ( ? [B_f] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2)
% 162.26/162.01 & 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)) )
% 162.26/162.01 <=> ? [B_g] : hAPP(c_Set_Oimage(T_b,T_a,B_g),V_A_H_2) = V_A_2 ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_comm__monoid__big_OF__eq,axiom,
% 162.26/162.01 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 162.26/162.01 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 162.26/162.01 => 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) )
% 162.26/162.01 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 162.26/162.01 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_fold__image__Un__one,axiom,
% 162.26/162.01 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
% 162.26/162.01 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.26/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 162.26/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 162.26/162.01 => ( ! [B_x] :
% 162.26/162.01 ( 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)))
% 162.26/162.01 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 162.26/162.01 => 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)) ) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__Some,axiom,
% 162.26/162.01 ! [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) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__Suc,axiom,
% 162.26/162.01 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__on__add__nat,axiom,
% 162.26/162.01 ! [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) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__on__map__add__dom,axiom,
% 162.26/162.01 ! [V_m_H_2,V_m_2,T_b,T_a] :
% 162.26/162.01 ( 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))
% 162.26/162.01 <=> 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_swap__inj__on,axiom,
% 162.26/162.01 ! [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) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 162.26/162.01 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 162.26/162.01 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 162.26/162.01 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_the__inv__into__into,axiom,
% 162.26/162.01 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 162.26/162.01 => 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)) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_sum__diff__distrib,axiom,
% 162.26/162.01 ! [V_n_2,V_P_2,V_Q_2] :
% 162.26/162.01 ( ! [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)))
% 162.26/162.01 => 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_Inf__fin_Ohom__commute,axiom,
% 162.26/162.01 ! [V_N_2,V_h_2,T_a] :
% 162.26/162.01 ( class_Lattices_Olattice(T_a)
% 162.26/162.01 => ( ! [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))
% 162.26/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 162.26/162.01 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.01 => 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)) ) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_the__inv__into__f__eq,axiom,
% 162.26/162.01 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.01 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.26/162.01 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_the__inv__into__f__f,axiom,
% 162.26/162.01 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.26/162.01 => 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 ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_the__inv__into__onto,axiom,
% 162.26/162.01 ! [V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.01 => 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 ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_inj__on__the__inv__into,axiom,
% 162.26/162.01 ! [V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.01 => 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_f__the__inv__into__f,axiom,
% 162.26/162.01 ! [V_y_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 162.26/162.01 => 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 ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_ImageE,axiom,
% 162.26/162.01 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] :
% 162.26/162.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)))
% 162.26/162.01 => ~ ! [B_x] :
% 162.26/162.01 ( 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))
% 162.26/162.01 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_setsum__mono__zero__right,axiom,
% 162.26/162.01 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 162.26/162.01 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.26/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 162.26/162.01 => ( ! [B_x] :
% 162.26/162.01 ( 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)))
% 162.26/162.01 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 162.26/162.01 => 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) ) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_setsum__mono__zero__left,axiom,
% 162.26/162.01 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 162.26/162.01 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.26/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 162.26/162.01 => ( ! [B_x] :
% 162.26/162.01 ( 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)))
% 162.26/162.01 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 162.26/162.01 => 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) ) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_setsum__strict__mono,axiom,
% 162.26/162.01 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] :
% 162.26/162.01 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 162.26/162.01 & class_Groups_Oordered__cancel__ab__semigroup__add(T_b) )
% 162.26/162.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.01 => ( ! [B_x] :
% 162.26/162.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 162.26/162.01 => 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))) ) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_atMost__Int__atLeast,axiom,
% 162.26/162.01 ! [V_n_2,T_a] :
% 162.26/162.01 ( class_Orderings_Oorder(T_a)
% 162.26/162.01 => 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))) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_escape,axiom,
% 162.26/162.01 ! [V_Q_2,V_ca_2,V_G_2,T_a,V_P_2] :
% 162.26/162.01 ( ! [B_Z,B_s] :
% 162.26/162.01 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 162.26/162.01 => 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)))) )
% 162.26/162.01 => 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)))) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_atLeast__eq__iff,axiom,
% 162.26/162.01 ! [V_y_2,V_x_2,T_a] :
% 162.26/162.01 ( class_Orderings_Olinorder(T_a)
% 162.26/162.01 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2)
% 162.26/162.01 <=> V_x_2 = V_y_2 ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_atLeast__iff,axiom,
% 162.26/162.01 ! [V_k_2,V_i_2,T_a] :
% 162.26/162.01 ( class_Orderings_Oord(T_a)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2)))
% 162.26/162.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_k_2),V_i_2)) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_atLeast__subset__iff,axiom,
% 162.26/162.01 ! [V_y_2,V_x_2,T_a] :
% 162.26/162.01 ( class_Orderings_Oorder(T_a)
% 162.26/162.01 => ( 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)))
% 162.26/162.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_Compl__atLeast,axiom,
% 162.26/162.01 ! [V_k_2,T_a] :
% 162.26/162.01 ( class_Orderings_Olinorder(T_a)
% 162.26/162.01 => 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) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_Compl__lessThan,axiom,
% 162.26/162.01 ! [V_k_2,T_a] :
% 162.26/162.01 ( class_Orderings_Olinorder(T_a)
% 162.26/162.01 => 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) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_ivl__disj__un_I14_J,axiom,
% 162.26/162.01 ! [V_u_2,V_l_2,T_a] :
% 162.26/162.01 ( class_Orderings_Olinorder(T_a)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 162.26/162.01 => 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) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_ivl__disj__int_I8_J,axiom,
% 162.26/162.01 ! [V_u_2,V_l_2,T_a] :
% 162.26/162.01 ( class_Orderings_Oorder(T_a)
% 162.26/162.01 => 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_Int__atLeastAtMostL2,axiom,
% 162.26/162.01 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 162.26/162.01 ( class_Orderings_Olinorder(T_a)
% 162.26/162.01 => 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) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_Int__atLeastAtMostR2,axiom,
% 162.26/162.01 ! [V_d_2,V_ca_2,V_a_2,T_a] :
% 162.26/162.01 ( class_Orderings_Olinorder(T_a)
% 162.26/162.01 => 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) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_ivl__disj__int_I6_J,axiom,
% 162.26/162.01 ! [V_u_2,V_l_2,T_a] :
% 162.26/162.01 ( class_Orderings_Oorder(T_a)
% 162.26/162.01 => 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_image__uminus__atMost,axiom,
% 162.26/162.01 ! [V_x_2,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add(T_a)
% 162.26/162.01 => 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_image__uminus__atLeast,axiom,
% 162.26/162.01 ! [V_x_2,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add(T_a)
% 162.26/162.01 => 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_atLeast__Suc,axiom,
% 162.26/162.01 ! [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)))) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_ivl__disj__un_I12_J,axiom,
% 162.26/162.01 ! [V_u_2,V_l_2,T_a] :
% 162.26/162.01 ( class_Orderings_Olinorder(T_a)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 162.26/162.01 => 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) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_ivl__disj__un_I13_J,axiom,
% 162.26/162.01 ! [V_u_2,V_l_2,T_a] :
% 162.26/162.01 ( class_Orderings_Olinorder(T_a)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 162.26/162.01 => 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) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_ivl__disj__un_I1_J,axiom,
% 162.26/162.01 ! [V_l_2,T_a] :
% 162.26/162.01 ( class_Orderings_Olinorder(T_a)
% 162.26/162.01 => 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) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_atLeast__Suc__greaterThan,axiom,
% 162.26/162.01 ! [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) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_greaterThan__eq__iff,axiom,
% 162.26/162.01 ! [V_y_2,V_x_2,T_a] :
% 162.26/162.01 ( class_Orderings_Olinorder(T_a)
% 162.26/162.01 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2)
% 162.26/162.01 <=> V_x_2 = V_y_2 ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_greaterThan__iff,axiom,
% 162.26/162.01 ! [V_k_2,V_i_2,T_a] :
% 162.26/162.01 ( class_Orderings_Oord(T_a)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2)))
% 162.26/162.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_i_2)) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_greaterThan__subset__iff,axiom,
% 162.26/162.01 ! [V_y_2,V_x_2,T_a] :
% 162.26/162.01 ( class_Orderings_Olinorder(T_a)
% 162.26/162.01 => ( 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)))
% 162.26/162.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_Compl__greaterThan,axiom,
% 162.26/162.01 ! [V_k_2,T_a] :
% 162.26/162.01 ( class_Orderings_Olinorder(T_a)
% 162.26/162.01 => 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) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_Compl__atMost,axiom,
% 162.26/162.01 ! [V_k_2,T_a] :
% 162.26/162.01 ( class_Orderings_Olinorder(T_a)
% 162.26/162.01 => 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) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_ivl__disj__int_I7_J,axiom,
% 162.26/162.01 ! [V_u_2,V_l_2,T_a] :
% 162.26/162.01 ( class_Orderings_Oorder(T_a)
% 162.26/162.01 => 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_ivl__disj__un_I11_J,axiom,
% 162.26/162.01 ! [V_u_2,V_l_2,T_a] :
% 162.26/162.01 ( class_Orderings_Olinorder(T_a)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 162.26/162.01 => 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) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_image__uminus__lessThan,axiom,
% 162.26/162.01 ! [V_x_2,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add(T_a)
% 162.26/162.01 => 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_image__uminus__greaterThan,axiom,
% 162.26/162.01 ! [V_x_2,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add(T_a)
% 162.26/162.01 => 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_ivl__disj__int_I5_J,axiom,
% 162.26/162.01 ! [V_u_2,V_l_2,T_a] :
% 162.26/162.01 ( class_Orderings_Oorder(T_a)
% 162.26/162.01 => 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_greaterThan__Suc,axiom,
% 162.26/162.01 ! [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)))) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_field__le__mult__one__interval,axiom,
% 162.26/162.01 ! [V_y,V_x,T_a] :
% 162.26/162.01 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.26/162.01 => ( ! [B_z] :
% 162.26/162.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 162.26/162.01 => 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)) ) )
% 162.26/162.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 162.26/162.01 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] :
% 162.26/162.01 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 162.26/162.01 & class_Groups_Ocomm__monoid__mult(T_a) )
% 162.26/162.01 => ( V_A_2 = V_B_2
% 162.26/162.01 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 162.26/162.01 => ( ! [B_x] :
% 162.26/162.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 162.26/162.01 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 162.26/162.01 => 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) ) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 162.26/162.01 ! [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) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 162.26/162.01 ! [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 ).
% 162.26/162.01
% 162.26/162.01 fof(fact_divmod__int__pdivmod,axiom,
% 162.26/162.01 ! [V_l_2,V_k_2] :
% 162.26/162.01 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.26/162.01 => 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)) )
% 162.26/162.01 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.26/162.01 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.26/162.01 => 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) )
% 162.26/162.01 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.26/162.01 => 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)))) ) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_incr__lemma,axiom,
% 162.26/162.01 ! [V_x,V_z,V_d] :
% 162.26/162.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 162.26/162.01 => 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)))) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_decr__lemma,axiom,
% 162.26/162.01 ! [V_z,V_x,V_d] :
% 162.26/162.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 162.26/162.01 => 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_setsum__abs,axiom,
% 162.26/162.01 ! [V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => 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))) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_setsum__abs__ge__zero,axiom,
% 162.26/162.01 ! [V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => 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))) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_apsnd__conv,axiom,
% 162.26/162.01 ! [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)) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__setsum__abs,axiom,
% 162.26/162.01 ! [V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => 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) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__setprod,axiom,
% 162.26/162.01 ! [V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.01 ( class_Fields_Olinordered__field(T_a)
% 162.26/162.01 => 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) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__divide,axiom,
% 162.26/162.01 ! [V_b,V_a,T_a] :
% 162.26/162.01 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.26/162.01 => 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__one,axiom,
% 162.26/162.01 ! [T_a] :
% 162.26/162.01 ( class_Rings_Olinordered__idom(T_a)
% 162.26/162.01 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_power__abs,axiom,
% 162.26/162.01 ! [V_n,V_a,T_a] :
% 162.26/162.01 ( class_Rings_Olinordered__idom(T_a)
% 162.26/162.01 => 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) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__add__abs,axiom,
% 162.26/162.01 ! [V_b,V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__mult__self,axiom,
% 162.26/162.01 ! [V_a,T_a] :
% 162.26/162.01 ( class_Rings_Olinordered__idom(T_a)
% 162.26/162.01 => 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) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__mult,axiom,
% 162.26/162.01 ! [V_b,V_a,T_a] :
% 162.26/162.01 ( class_Rings_Olinordered__idom(T_a)
% 162.26/162.01 => 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__idempotent,axiom,
% 162.26/162.01 ! [V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => 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) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__int__eq,axiom,
% 162.26/162.01 ! [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) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__of__nat,axiom,
% 162.26/162.01 ! [V_n,T_a] :
% 162.26/162.01 ( class_Rings_Olinordered__idom(T_a)
% 162.26/162.01 => 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) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__minus__cancel,axiom,
% 162.26/162.01 ! [V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => 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) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__zero,axiom,
% 162.26/162.01 ! [T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__eq__0,axiom,
% 162.26/162.01 ! [V_a_2,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 162.26/162.01 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__le__D1,axiom,
% 162.26/162.01 ! [V_b,V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 162.26/162.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__ge__self,axiom,
% 162.26/162.01 ! [V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__minus__commute,axiom,
% 162.26/162.01 ! [V_b,V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__ge__zero,axiom,
% 162.26/162.01 ! [V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => 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))) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__le__zero__iff,axiom,
% 162.26/162.01 ! [V_a_2,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => ( 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)))
% 162.26/162.01 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__of__nonneg,axiom,
% 162.26/162.01 ! [V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 162.26/162.01 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__of__pos,axiom,
% 162.26/162.01 ! [V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 162.26/162.01 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_zero__less__abs__iff,axiom,
% 162.26/162.01 ! [V_a_2,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => ( 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)))
% 162.26/162.01 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__not__less__zero,axiom,
% 162.26/162.01 ! [V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => ~ 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))) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__triangle__ineq,axiom,
% 162.26/162.01 ! [V_b,V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => 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)))) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__mult__less,axiom,
% 162.26/162.01 ! [V_d,V_b,V_c,V_a,T_a] :
% 162.26/162.01 ( class_Rings_Olinordered__idom(T_a)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 162.26/162.01 => 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))) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_fst__apsnd,axiom,
% 162.26/162.01 ! [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) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__triangle__ineq2__sym,axiom,
% 162.26/162.01 ! [V_b,V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => 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)))) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__triangle__ineq2,axiom,
% 162.26/162.01 ! [V_b,V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => 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)))) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__triangle__ineq3,axiom,
% 162.26/162.01 ! [V_b,V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => 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)))) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__ge__minus__self,axiom,
% 162.26/162.01 ! [V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => 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))) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__le__iff,axiom,
% 162.26/162.01 ! [V_b_2,V_a_2,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => ( 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))
% 162.26/162.01 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 162.26/162.01 & 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)) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__leI,axiom,
% 162.26/162.01 ! [V_b,V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 162.26/162.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__le__D2,axiom,
% 162.26/162.01 ! [V_b,V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 162.26/162.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_snd__apsnd,axiom,
% 162.26/162.01 ! [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)) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_apsnd__eq__conv,axiom,
% 162.26/162.01 ! [V_g_2,V_x_2,V_f_2,T_a,T_b,T_c] :
% 162.26/162.01 ( 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)
% 162.26/162.01 <=> 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__less__iff,axiom,
% 162.26/162.01 ! [V_b_2,V_a_2,T_a] :
% 162.26/162.01 ( class_Rings_Olinordered__idom(T_a)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2))
% 162.26/162.01 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 162.26/162.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_nonzero__abs__divide,axiom,
% 162.26/162.01 ! [V_a,V_b,T_a] :
% 162.26/162.01 ( class_Fields_Olinordered__field(T_a)
% 162.26/162.01 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 162.26/162.01 => 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)) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__power__minus,axiom,
% 162.26/162.01 ! [V_n,V_a,T_a] :
% 162.26/162.01 ( class_Rings_Olinordered__idom(T_a)
% 162.26/162.01 => 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__zmult__eq__1,axiom,
% 162.26/162.01 ! [V_n,V_m] :
% 162.26/162.01 ( 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)
% 162.26/162.01 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_pdivmod__def,axiom,
% 162.26/162.01 ! [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))) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_mult__sgn__abs,axiom,
% 162.26/162.01 ! [V_x,T_a] :
% 162.26/162.01 ( class_Rings_Olinordered__idom(T_a)
% 162.26/162.01 => 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 ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__sgn,axiom,
% 162.26/162.01 ! [V_k,T_a] :
% 162.26/162.01 ( class_Rings_Olinordered__idom(T_a)
% 162.26/162.01 => 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_pdivmod__posDivAlg,axiom,
% 162.26/162.01 ! [V_k,V_l] :
% 162.26/162.01 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.26/162.01 => 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)) )
% 162.26/162.01 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.26/162.01 => 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)) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__mult__pos,axiom,
% 162.26/162.01 ! [V_y,V_x,T_a] :
% 162.26/162.01 ( class_Rings_Olinordered__idom(T_a)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 162.26/162.01 => 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)) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__eq__mult,axiom,
% 162.26/162.01 ! [V_b,V_a,T_a] :
% 162.26/162.01 ( class_Rings_Oordered__ring__abs(T_a)
% 162.26/162.01 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 162.26/162.01 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 162.26/162.01 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 162.26/162.01 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 162.26/162.01 => 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)) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__triangle__ineq4,axiom,
% 162.26/162.01 ! [V_b,V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => 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)))) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__diff__triangle__ineq,axiom,
% 162.26/162.01 ! [V_d,V_c,V_b,V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => 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))))) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__minus__le__zero,axiom,
% 162.26/162.01 ! [V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => 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))) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__of__nonpos,axiom,
% 162.26/162.01 ! [V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 162.26/162.01 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__if,axiom,
% 162.26/162.01 ! [V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oabs__if(T_a)
% 162.26/162.01 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 162.26/162.01 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 162.26/162.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 162.26/162.01 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__of__neg,axiom,
% 162.26/162.01 ! [V_a,T_a] :
% 162.26/162.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 162.26/162.01 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_zero__le__power__abs,axiom,
% 162.26/162.01 ! [V_n,V_a,T_a] :
% 162.26/162.01 ( class_Rings_Olinordered__idom(T_a)
% 162.26/162.01 => 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))) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__div__pos,axiom,
% 162.26/162.01 ! [V_x,V_y,T_a] :
% 162.26/162.01 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 162.26/162.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 162.26/162.01 => 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)) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__minus__one,axiom,
% 162.26/162.01 ! [T_a] :
% 162.26/162.01 ( ( class_Int_Onumber__ring(T_a)
% 162.26/162.01 & class_Rings_Olinordered__idom(T_a) )
% 162.26/162.01 => 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) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_zabs__less__one__iff,axiom,
% 162.26/162.01 ! [V_z_2] :
% 162.26/162.01 ( 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)))
% 162.26/162.01 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_zabs__def,axiom,
% 162.26/162.01 ! [V_i] :
% 162.26/162.01 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.26/162.01 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 162.26/162.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 162.26/162.01 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_nat__abs__mult__distrib,axiom,
% 162.26/162.01 ! [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))) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_zero__le__zpower__abs,axiom,
% 162.26/162.01 ! [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))) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_negateSnd__def,axiom,
% 162.26/162.01 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__number__of,axiom,
% 162.26/162.01 ! [V_x,T_a] :
% 162.26/162.01 ( ( class_Int_Onumber__ring(T_a)
% 162.26/162.01 & class_Rings_Olinordered__idom(T_a) )
% 162.26/162.01 => ( ( 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)))
% 162.26/162.01 => 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)) )
% 162.26/162.01 & ( ~ 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)))
% 162.26/162.01 => 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) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__power__minus__one,axiom,
% 162.26/162.01 ! [V_n,T_a] :
% 162.26/162.01 ( ( class_Int_Onumber__ring(T_a)
% 162.26/162.01 & class_Rings_Olinordered__idom(T_a) )
% 162.26/162.01 => 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) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_zero__less__zpower__abs__iff,axiom,
% 162.26/162.01 ! [V_n_2,V_x_2] :
% 162.26/162.01 ( 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)))
% 162.26/162.01 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.26/162.01 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_power2__abs,axiom,
% 162.26/162.01 ! [V_a,T_a] :
% 162.26/162.01 ( class_Rings_Olinordered__idom(T_a)
% 162.26/162.01 => 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)))) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_abs__power2,axiom,
% 162.26/162.01 ! [V_a,T_a] :
% 162.26/162.01 ( class_Rings_Olinordered__idom(T_a)
% 162.26/162.01 => 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)))) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_divmod__int__code,axiom,
% 162.26/162.01 ! [V_l_2,V_k_2] :
% 162.26/162.01 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.26/162.01 => 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)) )
% 162.26/162.01 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.26/162.01 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.26/162.01 => 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) )
% 162.26/162.01 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 162.26/162.01 => 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)))) ) ) ) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 162.26/162.01 ! [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)))) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 162.26/162.01 ! [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)))) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_apfst__apsnd,axiom,
% 162.26/162.01 ! [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))) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_apfst__conv,axiom,
% 162.26/162.01 ! [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) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_apfst__eq__conv,axiom,
% 162.26/162.01 ! [V_g_2,V_x_2,V_f_2,T_b,T_a,T_c] :
% 162.26/162.01 ( 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)
% 162.26/162.01 <=> 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)) ) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_fst__apfst,axiom,
% 162.26/162.01 ! [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)) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_snd__apfst,axiom,
% 162.26/162.01 ! [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) ).
% 162.26/162.01
% 162.26/162.01 fof(fact_apsnd__apfst__commute,axiom,
% 162.26/162.01 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_nat__gcd_Osimps,axiom,
% 162.26/162.02 ! [V_x,V_y] :
% 162.26/162.02 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.02 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 162.26/162.02 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.02 => 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_apsnd__apfst,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_nat__gcd_Opsimps,axiom,
% 162.26/162.02 ! [V_y_2,V_x_2] :
% 162.26/162.02 ( 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)))
% 162.26/162.02 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.02 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 162.26/162.02 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.02 => 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)) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_compl__unique,axiom,
% 162.26/162.02 ! [V_y,V_x,T_a] :
% 162.26/162.02 ( class_Lattices_Oboolean__algebra(T_a)
% 162.26/162.02 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 162.26/162.02 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 162.26/162.02 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 162.26/162.02 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] :
% 162.26/162.02 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 162.26/162.02 & class_Groups_Ocomm__monoid__mult(T_a) )
% 162.26/162.02 => ( V_A_2 = V_B_2
% 162.26/162.02 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 162.26/162.02 => ( ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 162.26/162.02 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 162.26/162.02 => 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) ) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_UNIV__I,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_UN__lessThan__UNIV,axiom,
% 162.26/162.02 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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_UNIV__option__conv,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inj__int,axiom,
% 162.26/162.02 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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_injD,axiom,
% 162.26/162.02 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.02 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 162.26/162.02 => V_x_2 = V_y_2 ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inj__eq,axiom,
% 162.26/162.02 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.02 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 162.26/162.02 <=> V_x_2 = V_y_2 ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Int__UNIV__right,axiom,
% 162.26/162.02 ! [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 ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Int__UNIV__left,axiom,
% 162.26/162.02 ! [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 ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inf__top__left,axiom,
% 162.26/162.02 ! [V_x,T_a] :
% 162.26/162.02 ( class_Lattices_Obounded__lattice__top(T_a)
% 162.26/162.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inf__top__right,axiom,
% 162.26/162.02 ! [V_x,T_a] :
% 162.26/162.02 ( class_Lattices_Obounded__lattice__top(T_a)
% 162.26/162.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inf__eq__top__iff,axiom,
% 162.26/162.02 ! [V_y_2,V_x_2,T_a] :
% 162.26/162.02 ( class_Lattices_Obounded__lattice__top(T_a)
% 162.26/162.02 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_a)
% 162.26/162.02 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_a)
% 162.26/162.02 & V_y_2 = c_Orderings_Otop__class_Otop(T_a) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Pow__UNIV,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_card__UNIV__unit,axiom,
% 162.26/162.02 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) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_top__apply,axiom,
% 162.26/162.02 ! [V_x_2,T_b,T_a] :
% 162.26/162.02 ( class_Orderings_Otop(T_a)
% 162.26/162.02 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_UNIV__Plus__UNIV,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_UNIV__not__empty,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Un__UNIV__left,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Un__UNIV__right,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_subset__UNIV,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_infinite__UNIV__nat,axiom,
% 162.26/162.02 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__Prod__UNIV,axiom,
% 162.26/162.02 ! [T_b,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 162.26/162.02 => 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)))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__option__UNIV,axiom,
% 162.26/162.02 ! [T_a] :
% 162.26/162.02 ( 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))))
% 162.26/162.02 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__fun__UNIVD2,axiom,
% 162.26/162.02 ! [T_b,T_a] :
% 162.26/162.02 ( 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))))
% 162.26/162.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__UNIV,axiom,
% 162.26/162.02 ! [T_a] :
% 162.26/162.02 ( class_Finite__Set_Ofinite(T_a)
% 162.26/162.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__Plus__UNIV__iff,axiom,
% 162.26/162.02 ! [T_b,T_a] :
% 162.26/162.02 ( 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))))
% 162.26/162.02 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 162.26/162.02 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_range__composition,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_equiv__intrel,axiom,
% 162.26/162.02 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) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_sup__top__right,axiom,
% 162.26/162.02 ! [V_x,T_a] :
% 162.26/162.02 ( class_Lattices_Obounded__lattice__top(T_a)
% 162.26/162.02 => 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) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_sup__top__left,axiom,
% 162.26/162.02 ! [V_x,T_a] :
% 162.26/162.02 ( class_Lattices_Obounded__lattice__top(T_a)
% 162.26/162.02 => 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) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_top__greatest,axiom,
% 162.26/162.02 ! [V_x,T_a] :
% 162.26/162.02 ( class_Orderings_Otop(T_a)
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_infinite__UNIV__int,axiom,
% 162.26/162.02 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_UN__atMost__UNIV,axiom,
% 162.26/162.02 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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_range__eqI,axiom,
% 162.26/162.02 ! [T_b,T_a,V_x_2,V_f_2,V_b_2] :
% 162.26/162.02 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 162.26/162.02 => 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))))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_rangeI,axiom,
% 162.26/162.02 ! [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))))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_UN__atLeast__UNIV,axiom,
% 162.26/162.02 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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Diff__UNIV,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 162.26/162.02 ! [V_A_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 162.26/162.02 => ( 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)))
% 162.26/162.02 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inj__image__eq__iff,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.02 => ( 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)
% 162.26/162.02 <=> V_A_2 = V_B_2 ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Compl__UNIV__eq,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Compl__empty__eq,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__compl,axiom,
% 162.26/162.02 ! [V_A_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
% 162.26/162.02 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Compl__partition,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Compl__partition2,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 162.26/162.02 ! [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) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_SUP__UN__eq,axiom,
% 162.26/162.02 ! [V_x_2,V_r_2,T_b,T_a] :
% 162.26/162.02 ( 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))
% 162.26/162.02 <=> 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))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__range__imageI,axiom,
% 162.26/162.02 ! [V_f_2,T_c,V_g_2,T_b,T_a] :
% 162.26/162.02 ( 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)))))
% 162.26/162.02 => 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))))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_the__inv__f__f,axiom,
% 162.26/162.02 ! [V_x_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.02 => 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 ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__fun__UNIVD1,axiom,
% 162.26/162.02 ! [T_b,T_a] :
% 162.26/162.02 ( 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))))
% 162.26/162.02 => ( 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))
% 162.26/162.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inj__of__nat,axiom,
% 162.26/162.02 ! [T_a] :
% 162.26/162.02 ( class_Nat_Osemiring__char__0(T_a)
% 162.26/162.02 => 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))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_dom__const,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_atLeast__0,axiom,
% 162.26/162.02 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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inj__fun,axiom,
% 162.26/162.02 ! [T_c,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.02 => 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))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_compl__bot__eq,axiom,
% 162.26/162.02 ! [T_a] :
% 162.26/162.02 ( class_Lattices_Oboolean__algebra(T_a)
% 162.26/162.02 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_compl__top__eq,axiom,
% 162.26/162.02 ! [T_a] :
% 162.26/162.02 ( class_Lattices_Oboolean__algebra(T_a)
% 162.26/162.02 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_sup__compl__top,axiom,
% 162.26/162.02 ! [V_x,T_a] :
% 162.26/162.02 ( class_Lattices_Oboolean__algebra(T_a)
% 162.26/162.02 => 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) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_compl__sup__top,axiom,
% 162.26/162.02 ! [V_x,T_a] :
% 162.26/162.02 ( class_Lattices_Oboolean__algebra(T_a)
% 162.26/162.02 => 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) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inj__image__mem__iff,axiom,
% 162.26/162.02 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.02 => ( 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)))
% 162.26/162.02 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_range__ex1__eq,axiom,
% 162.26/162.02 ! [V_b_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.02 => ( 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)))))
% 162.26/162.02 <=> ? [B_x] :
% 162.26/162.02 ( V_b_2 = hAPP(V_f_2,B_x)
% 162.26/162.02 & ! [B_y] :
% 162.26/162.02 ( V_b_2 = hAPP(V_f_2,B_y)
% 162.26/162.02 => B_y = B_x ) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__UNIV__inj__surj,axiom,
% 162.26/162.02 ! [V_f_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 162.26/162.02 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.02 => 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__UNIV__surj__inj,axiom,
% 162.26/162.02 ! [V_f_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 162.26/162.02 => ( 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))
% 162.26/162.02 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inj__image__subset__iff,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.02 => ( 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)))
% 162.26/162.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_image__Int,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.02 => 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)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_image__set__diff,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.02 => 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)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_surj__Compl__image__subset,axiom,
% 162.26/162.02 ! [V_A_2,V_f_2,T_a,T_b] :
% 162.26/162.02 ( 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))
% 162.26/162.02 => 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)))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__range__updI,axiom,
% 162.26/162.02 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( 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)))))
% 162.26/162.02 => 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))))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_UN__UN__finite__eq,axiom,
% 162.26/162.02 ! [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) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inj__singleton,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__UNIV__card__ge__0,axiom,
% 162.26/162.02 ! [T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 162.26/162.02 => 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))))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_card__UNIV__bool,axiom,
% 162.26/162.02 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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inj__image__Compl__subset,axiom,
% 162.26/162.02 ! [V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.02 => 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)))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_greaterThan__0,axiom,
% 162.26/162.02 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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_SUP__UN__eq2,axiom,
% 162.26/162.02 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] :
% 162.26/162.02 ( 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))
% 162.26/162.02 <=> 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))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_nat__gcd_Opinduct,axiom,
% 162.26/162.02 ! [V_P_2,V_a1_2,V_a0_2] :
% 162.26/162.02 ( 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)))
% 162.26/162.02 => ( ! [B_x,B_y] :
% 162.26/162.02 ( 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)))
% 162.26/162.02 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.02 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 162.26/162.02 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
% 162.26/162.02 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_UN__finite2__subset,axiom,
% 162.26/162.02 ! [V_B_2,V_k_2,V_A_2,T_a] :
% 162.26/162.02 ( ! [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)))
% 162.26/162.02 => 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))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INFI__fold__inf,axiom,
% 162.26/162.02 ! [V_f_2,V_A_2,T_a,T_b] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => 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) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_top1I,axiom,
% 162.26/162.02 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__E,axiom,
% 162.26/162.02 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 162.26/162.02 ( 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)))
% 162.26/162.02 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2)))
% 162.26/162.02 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__D,axiom,
% 162.26/162.02 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 162.26/162.02 ( 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)))
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INF1__D,axiom,
% 162.26/162.02 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 162.26/162.02 ( 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))
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INF1__E,axiom,
% 162.26/162.02 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 162.26/162.02 ( 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))
% 162.26/162.02 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 162.26/162.02 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INF2__E,axiom,
% 162.26/162.02 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 162.26/162.02 ( 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))
% 162.26/162.02 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
% 162.26/162.02 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INF2__D,axiom,
% 162.26/162.02 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 162.26/162.02 ( 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))
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__INT,axiom,
% 162.26/162.02 ! [V_A_2,T_b,V_I_2,T_a] :
% 162.26/162.02 ( ? [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_I_2))
% 162.26/162.02 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_A_2,B_x))) )
% 162.26/162.02 => 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))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_b,T_a] :
% 162.26/162.02 ( 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)
% 162.26/162.02 <=> ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 162.26/162.02 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a,T_b] :
% 162.26/162.02 ( 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))
% 162.26/162.02 <=> ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 162.26/162.02 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INF__INT__eq2,axiom,
% 162.26/162.02 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] :
% 162.26/162.02 ( 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))
% 162.26/162.02 <=> 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))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__empty,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__constant,axiom,
% 162.26/162.02 ! [V_ca_2,T_b,T_a,V_A_2] :
% 162.26/162.02 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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)) )
% 162.26/162.02 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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 ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INF__INT__eq,axiom,
% 162.26/162.02 ! [V_x_2,V_r_2,T_b,T_a] :
% 162.26/162.02 ( 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))
% 162.26/162.02 <=> 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))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__simps_I10_J,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__extend__simps_I10_J,axiom,
% 162.26/162.02 ! [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) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__subset__iff,axiom,
% 162.26/162.02 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] :
% 162.26/162.02 ( 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)))
% 162.26/162.02 <=> ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 162.26/162.02 => 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))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__iff,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 162.26/162.02 ( 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)))
% 162.26/162.02 <=> ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__simps_I7_J,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__simps_I6_J,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_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) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__extend__simps_I7_J,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Un__INT__distrib,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__extend__simps_I6_J,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Un__INT__distrib2,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INFI__apply,axiom,
% 162.26/162.02 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => 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)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INF__commute,axiom,
% 162.26/162.02 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => 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))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Pow__INT__eq,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__simps_I5_J,axiom,
% 162.26/162.02 ! [V_B_2,V_a_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__extend__simps_I5_J,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__simps_I9_J,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__extend__simps_I9_J,axiom,
% 162.26/162.02 ! [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) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__Int__distrib,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_le__INF__iff,axiom,
% 162.26/162.02 ! [V_M_2,V_A_2,T_b,V_u_2,T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => ( 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)))
% 162.26/162.02 <=> ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INF__less__iff,axiom,
% 162.26/162.02 ! [V_a_2,V_f_2,V_A_2,T_b,T_a] :
% 162.26/162.02 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 & class_Orderings_Olinorder(T_a) )
% 162.26/162.02 => ( 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))
% 162.26/162.02 <=> ? [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 162.26/162.02 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__insert__distrib,axiom,
% 162.26/162.02 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2))
% 162.26/162.02 => 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)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__lower,axiom,
% 162.26/162.02 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.26/162.02 => 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))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__absorb,axiom,
% 162.26/162.02 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2))
% 162.26/162.02 => 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) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INF__const,axiom,
% 162.26/162.02 ! [V_M_2,T_a,V_A_2,T_b] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 162.26/162.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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 ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__extend__simps_I1_J,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 162.26/162.02 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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 )
% 162.26/162.02 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__extend__simps_I2_J,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 162.26/162.02 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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 )
% 162.26/162.02 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__simps_I2_J,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 162.26/162.02 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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)) )
% 162.26/162.02 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__simps_I1_J,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 162.26/162.02 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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)) )
% 162.26/162.02 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__insert,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__simps_I3_J,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 162.26/162.02 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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)) )
% 162.26/162.02 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__extend__simps_I3_J,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 162.26/162.02 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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) )
% 162.26/162.02 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__Un,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_UN__simps_I7_J,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_UN__extend__simps_I7_J,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Image__INT__subset,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Compl__UN,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Compl__INT,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__greaterThan__UNIV,axiom,
% 162.26/162.02 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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INF__subset,axiom,
% 162.26/162.02 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 162.26/162.02 => 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))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__extend__simps_I4_J,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 162.26/162.02 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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 )
% 162.26/162.02 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__simps_I4_J,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 162.26/162.02 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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)) )
% 162.26/162.02 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INF__leI,axiom,
% 162.26/162.02 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2))
% 162.26/162.02 => 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))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inf__INFI__fold__inf,axiom,
% 162.26/162.02 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => 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) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Integ__def,axiom,
% 162.26/162.02 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) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_UN__finite2__eq,axiom,
% 162.26/162.02 ! [V_B_2,V_k_2,V_A_2,T_a] :
% 162.26/162.02 ( ! [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)
% 162.26/162.02 => 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) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_UN__finite__subset,axiom,
% 162.26/162.02 ! [V_C_2,V_A_2,T_a] :
% 162.26/162.02 ( ! [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))
% 162.26/162.02 => 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)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INF1__iff,axiom,
% 162.26/162.02 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 162.26/162.02 ( 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))
% 162.26/162.02 <=> ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INF2__iff,axiom,
% 162.26/162.02 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 162.26/162.02 ( 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))
% 162.26/162.02 <=> ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Rep__Integ,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_iso__tuple__UNIV__I,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_image__INT,axiom,
% 162.26/162.02 ! [V_j_2,V_B_2,V_A_2,T_c,V_C_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
% 162.26/162.02 => ( ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) )
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_j_2),V_A_2))
% 162.26/162.02 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Oimage(T_a,T_b,V_f_2)),V_B_2)) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_equivp__equiv,axiom,
% 162.26/162.02 ! [V_A_2,T_a] :
% 162.26/162.02 ( c_Equiv__Relations_Oequiv(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_A_2)
% 162.26/162.02 <=> 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)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_equivp__transp,axiom,
% 162.26/162.02 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_a] :
% 162.26/162.02 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_equivp__symp,axiom,
% 162.26/162.02 ! [V_y_2,V_x_2,V_R_2,T_a] :
% 162.26/162.02 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_equivp__reflp,axiom,
% 162.26/162.02 ! [V_x_2,V_R_2,T_a] :
% 162.26/162.02 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 162.26/162.02 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_equivp__def,axiom,
% 162.26/162.02 ! [V_R_2,T_a] :
% 162.26/162.02 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 162.26/162.02 <=> ! [B_x,B_y] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 162.26/162.02 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_identity__equivp,axiom,
% 162.26/162.02 ! [T_a] : c_Equiv__Relations_Oequivp(T_a,c_fequal) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_type__definition__Integ,axiom,
% 162.26/162.02 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) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Inf__fold__inf,axiom,
% 162.26/162.02 ! [V_A_2,T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => 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) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_accp__acc__eq,axiom,
% 162.26/162.02 ! [V_x_2,V_r_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),V_x_2))
% 162.26/162.02 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__Inter,axiom,
% 162.26/162.02 ! [V_M_2,T_a] :
% 162.26/162.02 ( ? [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_M_2))
% 162.26/162.02 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_x)) )
% 162.26/162.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_M_2))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_InterE,axiom,
% 162.26/162.02 ! [V_X_2,V_C_2,V_A_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2)))
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_InterD,axiom,
% 162.26/162.02 ! [V_X_2,V_C_2,V_A_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2)))
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Inf__less__iff,axiom,
% 162.26/162.02 ! [V_a_2,V_S_2,T_a] :
% 162.26/162.02 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 & class_Orderings_Olinorder(T_a) )
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2)),V_a_2))
% 162.26/162.02 <=> ? [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 162.26/162.02 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_a_2)) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_le__Inf__iff,axiom,
% 162.26/162.02 ! [V_A_2,V_b_2,T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)))
% 162.26/162.02 <=> ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Un__Inter,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Inter__lower,axiom,
% 162.26/162.02 ! [V_A_2,V_B_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),V_B_2)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Inter__anti__mono,axiom,
% 162.26/162.02 ! [V_A_2,V_B_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Inter__empty,axiom,
% 162.26/162.02 ! [T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Inter__insert,axiom,
% 162.26/162.02 ! [V_B_2,V_a_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Inter__UNIV,axiom,
% 162.26/162.02 ! [T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Inf__lower,axiom,
% 162.26/162.02 ! [V_A_2,V_x_2,T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)),V_x_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_acc__subset,axiom,
% 162.26/162.02 ! [V_R2_2,V_R1_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R1_2),V_R2_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Oacc(T_a,V_R2_2)),c_Wellfounded_Oacc(T_a,V_R1_2))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Inter__Un__distrib,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Inf__singleton,axiom,
% 162.26/162.02 ! [V_a_2,T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Inf__empty,axiom,
% 162.26/162.02 ! [T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Inf__UNIV,axiom,
% 162.26/162.02 ! [T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Inf__insert,axiom,
% 162.26/162.02 ! [V_A_2,V_a_2,T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INTER__eq__Inter__image,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Inter__image__eq,axiom,
% 162.26/162.02 ! [V_A_2,V_B_2,T_b,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_acc__downward,axiom,
% 162.26/162.02 ! [V_a_2,V_r_2,V_b_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_acc_Osimps,axiom,
% 162.26/162.02 ! [V_r_2,V_a_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 162.26/162.02 <=> ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_a_2)),V_r_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Int__eq__Inter,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Int__Inter__image,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Inter__Un__subset,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Inf__binary,axiom,
% 162.26/162.02 ! [V_b_2,V_a_2,T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),V_b_2) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inf__Inf__fold__inf,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => 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) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Inf__fin__Inf,axiom,
% 162.26/162.02 ! [V_A_2,T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_type__definition_ORep__range,axiom,
% 162.26/162.02 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 162.26/162.02 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 162.26/162.02 => 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 ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_type__definition_OAbs__image,axiom,
% 162.26/162.02 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 162.26/162.02 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 162.26/162.02 => 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)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_type__definition_OAbs__inject,axiom,
% 162.26/162.02 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 162.26/162.02 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 162.26/162.02 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 162.26/162.02 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Inter__def,axiom,
% 162.26/162.02 ! [V_S_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_a,tc_HOL_Obool))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_type__definition_ORep__inverse,axiom,
% 162.26/162.02 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 162.26/162.02 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 162.26/162.02 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_type__definition_ORep__inject,axiom,
% 162.26/162.02 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 162.26/162.02 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 162.26/162.02 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 162.26/162.02 <=> V_x_2 = V_y_2 ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_type__definition_ORep,axiom,
% 162.26/162.02 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 162.26/162.02 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_type__definition_OAbs__inverse,axiom,
% 162.26/162.02 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 162.26/162.02 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 162.26/162.02 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_max__extp_Oequations,axiom,
% 162.26/162.02 ! [V_a2_2,V_a1_2,V_R_2,T_a] :
% 162.26/162.02 ( c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2)
% 162.26/162.02 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2))
% 162.26/162.02 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2))
% 162.26/162.02 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 & ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2))
% 162.26/162.02 => ? [B_xa] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2))
% 162.26/162.02 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Sup__fold__sup,axiom,
% 162.26/162.02 ! [V_A_2,T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => 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) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_max__ext_Ointros,axiom,
% 162.26/162.02 ! [V_R_2,V_Y_2,V_X_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2))
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Y_2))
% 162.26/162.02 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => ( ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2))
% 162.26/162.02 => ? [B_xa] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2))
% 162.26/162.02 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_R_2)) ) )
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_UnionI,axiom,
% 162.26/162.02 ! [V_A_2,V_C_2,V_X_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_image__Union,axiom,
% 162.26/162.02 ! [V_S_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_b,T_a,V_f_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_UN__extend__simps_I8_J,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_UN__simps_I8_J,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Int__Union2,axiom,
% 162.26/162.02 ! [V_A_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Int__Union,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_less__Sup__iff,axiom,
% 162.26/162.02 ! [V_S_2,V_a_2,T_a] :
% 162.26/162.02 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 & class_Orderings_Olinorder(T_a) )
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2)))
% 162.26/162.02 <=> ? [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 162.26/162.02 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),B_x)) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Union__Pow__eq,axiom,
% 162.26/162.02 ! [V_A_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_OPow(T_a),V_A_2)) = V_A_2 ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Field__Union,axiom,
% 162.26/162.02 ! [V_R_2,T_a] : hAPP(c_Relation_OField(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Relation_OField(T_a)),V_R_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Sup__le__iff,axiom,
% 162.26/162.02 ! [V_b_2,V_A_2,T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)),V_b_2))
% 162.26/162.02 <=> ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Union__disjoint,axiom,
% 162.26/162.02 ! [V_A_2,V_C_2,T_a] :
% 162.26/162.02 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 <=> ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_C_2))
% 162.26/162.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Union__upper,axiom,
% 162.26/162.02 ! [V_A_2,V_B_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Union__empty,axiom,
% 162.26/162.02 ! [T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Union__mono,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Union__insert,axiom,
% 162.26/162.02 ! [V_B_2,V_a_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Union__quotient,axiom,
% 162.26/162.02 ! [V_r_2,V_A_2,T_a] :
% 162.26/162.02 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 162.26/162.02 => c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)) = V_A_2 ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__UnionD,axiom,
% 162.26/162.02 ! [V_A_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)))
% 162.26/162.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_subset__Pow__Union,axiom,
% 162.26/162.02 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Union__UNIV,axiom,
% 162.26/162.02 ! [T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Union__Un__distrib,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Union__image__eq,axiom,
% 162.26/162.02 ! [V_A_2,V_B_2,T_b,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_UNION__eq__Union__image,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Sup__upper,axiom,
% 162.26/162.02 ! [V_A_2,V_x_2,T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Sup__empty,axiom,
% 162.26/162.02 ! [T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Sup__singleton,axiom,
% 162.26/162.02 ! [V_a_2,T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Sup__insert,axiom,
% 162.26/162.02 ! [V_A_2,V_a_2,T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Sup__UNIV,axiom,
% 162.26/162.02 ! [T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__extend__simps_I8_J,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_INT__simps_I8_J,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Un__eq__Union,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Un__Union__image,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Union__Int__subset,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Sup__binary,axiom,
% 162.26/162.02 ! [V_b_2,V_a_2,T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),V_b_2) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_sup__Sup__fold__sup,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => 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) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Sup__fin__Sup,axiom,
% 162.26/162.02 ! [V_A_2,T_a] :
% 162.26/162.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 162.26/162.02 ! [T_a] : c_Nitpick_Ozero__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inj__on__Inter,axiom,
% 162.26/162.02 ! [V_f_2,T_b,T_a,V_S_2] :
% 162.26/162.02 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))
% 162.26/162.02 => ( ! [B_A] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_A),V_S_2))
% 162.26/162.02 => c_Fun_Oinj__on(T_a,T_b,V_f_2,B_A) )
% 162.26/162.02 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_S_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Inter__subset,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a] :
% 162.26/162.02 ( ! [B_X] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_X),V_B_2)) )
% 162.26/162.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),V_B_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Union__def,axiom,
% 162.26/162.02 ! [V_S_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_a,tc_HOL_Obool))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Nitpick_Oone__frac__def,axiom,
% 162.26/162.02 ! [T_a] : c_Nitpick_Oone__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 162.26/162.02 ! [V_n,T_a] : c_Nitpick_Onumber__of__frac(T_a,V_n) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_n),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Nitpick_Ofrac__def,axiom,
% 162.26/162.02 ! [V_b,V_a,T_a] : hAPP(hAPP(c_Nitpick_Ofrac(T_a),V_a),V_b) = c_Nitpick_OAbs__Frac(T_a,c_Nitpick_Onorm__frac(V_a,V_b)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__Union,axiom,
% 162.26/162.02 ! [V_A_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2))
% 162.26/162.02 => ( ! [B_M] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_M),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_M)) )
% 162.26/162.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_insert__partition,axiom,
% 162.26/162.02 ! [V_F_2,V_x_2,T_a] :
% 162.26/162.02 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2))
% 162.26/162.02 => ( ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2)))
% 162.26/162.02 => ! [B_xa] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2)))
% 162.26/162.02 => ( B_x != B_xa
% 162.26/162.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) )
% 162.26/162.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_card__partition,axiom,
% 162.26/162.02 ! [V_k_2,V_C_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_C_2))
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)))
% 162.26/162.02 => ( ! [B_c] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c),V_C_2))
% 162.26/162.02 => hAPP(c_Finite__Set_Ocard(T_a),B_c) = V_k_2 )
% 162.26/162.02 => ( ! [B_c1] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c1),V_C_2))
% 162.26/162.02 => ! [B_c2] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c2),V_C_2))
% 162.26/162.02 => ( B_c1 != B_c2
% 162.26/162.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) )
% 162.26/162.02 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)) ) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_the__elem__def,axiom,
% 162.26/162.02 ! [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))))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_nat0__intermed__int__val,axiom,
% 162.26/162.02 ! [V_k_2,V_f_2,V_n_2] :
% 162.26/162.02 ( ! [B_i] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 162.26/162.02 => 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))) )
% 162.26/162.02 => ( 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))
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 162.26/162.02 => ? [B_i] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 162.26/162.02 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_int__val__lemma,axiom,
% 162.26/162.02 ! [V_k_2,V_f_2,V_n_2] :
% 162.26/162.02 ( ! [B_i] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 162.26/162.02 => 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))) )
% 162.26/162.02 => ( 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))
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 162.26/162.02 => ? [B_i] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 162.26/162.02 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_split__paired__The,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_The__split__eq,axiom,
% 162.26/162.02 ! [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) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_the__inv__into__def,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_fold__def,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_divmod__nat__def,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_fold1__def,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_The__split,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_flat__lub__def,axiom,
% 162.26/162.02 ! [V_b_2,V_A_2,T_a] :
% 162.26/162.02 ( ( 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)))))
% 162.26/162.02 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = V_b_2 )
% 162.26/162.02 & ( ~ 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)))))
% 162.26/162.02 => 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)))))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inj__vimage__singleton,axiom,
% 162.26/162.02 ! [V_a_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.02 => 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))))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Option_Omap__def,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimageI,axiom,
% 162.26/162.02 ! [T_b,V_B_2,T_a,V_b_2,V_a_2,V_f_2] :
% 162.26/162.02 ( hAPP(V_f_2,V_a_2) = V_b_2
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_B_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__Diff,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_option__map__None,axiom,
% 162.26/162.02 ! [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) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_option__map__is__None,axiom,
% 162.26/162.02 ! [V_opt_2,V_f_2,T_a,T_b] :
% 162.26/162.02 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_a)
% 162.26/162.02 <=> V_opt_2 = c_Option_Ooption_ONone(T_b) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_option__map__Some,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_option__map__eq__Some,axiom,
% 162.26/162.02 ! [V_y_2,V_xo_2,V_f_2,T_a,T_b] :
% 162.26/162.02 ( 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)
% 162.26/162.02 <=> ? [B_z] :
% 162.26/162.02 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),B_z)
% 162.26/162.02 & hAPP(V_f_2,B_z) = V_y_2 ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__mono,axiom,
% 162.26/162.02 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 162.26/162.02 => 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))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__Un,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__empty,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__ident,axiom,
% 162.26/162.02 ! [V_Y_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__code,axiom,
% 162.26/162.02 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2),V_x_2))
% 162.26/162.02 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__Compl,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__Int,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__UNIV,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__eq,axiom,
% 162.26/162.02 ! [V_B_2,V_f_2,T_b,V_a_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)))
% 162.26/162.02 <=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimageD,axiom,
% 162.26/162.02 ! [V_A_2,V_f_2,T_b,V_a_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimageI2,axiom,
% 162.26/162.02 ! [T_b,V_A_2,V_a_2,V_f_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_a_2)),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__INT,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__UN,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_dom__option__map,axiom,
% 162.26/162.02 ! [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) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_image__vimage__subset,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_surj__image__vimage__eq,axiom,
% 162.26/162.02 ! [V_A_2,V_f_2,T_a,T_b] :
% 162.26/162.02 ( 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))
% 162.26/162.02 => 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 ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__Union,axiom,
% 162.26/162.02 ! [V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_a,T_b,V_f_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__singleton__eq,axiom,
% 162.26/162.02 ! [V_b_2,V_f_2,T_b,V_a_2,T_a] :
% 162.26/162.02 ( 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))))))
% 162.26/162.02 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__insert,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__vimageD,axiom,
% 162.26/162.02 ! [V_F_2,V_h_2,T_b,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Ovimage(T_a,T_b,V_h_2),V_F_2)))
% 162.26/162.02 => ( 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))
% 162.26/162.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__subsetD,axiom,
% 162.26/162.02 ! [V_A_2,V_B_2,V_f_2,T_a,T_b] :
% 162.26/162.02 ( 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))
% 162.26/162.02 => ( 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))
% 162.26/162.02 => 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))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_image__vimage__eq,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__vimageI,axiom,
% 162.26/162.02 ! [V_h_2,T_b,V_F_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 162.26/162.02 => ( c_Fun_Oinj__on(T_b,T_a,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 162.26/162.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_a,V_h_2),V_F_2))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inj__vimage__image__eq,axiom,
% 162.26/162.02 ! [V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.02 => 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 ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__const,axiom,
% 162.26/162.02 ! [T_b,V_A_2,V_ca_2,T_a] :
% 162.26/162.02 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 162.26/162.02 => 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)) )
% 162.26/162.02 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 162.26/162.02 => 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__eq__UN,axiom,
% 162.26/162.02 ! [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))))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__subsetI,axiom,
% 162.26/162.02 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.02 => ( 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)))
% 162.26/162.02 => 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__if,axiom,
% 162.26/162.02 ! [V_B_2,T_b,V_d_2,V_A_2,V_ca_2,T_a] :
% 162.26/162.02 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 162.26/162.02 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 162.26/162.02 => 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)) )
% 162.26/162.02 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 162.26/162.02 => 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 ) ) )
% 162.26/162.02 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 162.26/162.02 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 162.26/162.02 => 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) )
% 162.26/162.02 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 162.26/162.02 => 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)) ) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_image__split__eq__Sigma,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_setprod__pos__nat,axiom,
% 162.26/162.02 ! [V_f_2,V_S_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 162.26/162.02 => ( ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 162.26/162.02 => 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))) )
% 162.26/162.02 => 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))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Rep__Integ__cases,axiom,
% 162.26/162.02 ! [V_y_2] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 162.26/162.02 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_SigmaI,axiom,
% 162.26/162.02 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Sigma__Union,axiom,
% 162.26/162.02 ! [V_B_2,V_X_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),c_Product__Type_OSigma(T_a,T_b)),V_B_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Times__eq__cancel2,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2))
% 162.26/162.02 => ( 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))
% 162.26/162.02 <=> V_A_2 = V_B_2 ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Sigma__Diff__distrib1,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Times__Diff__distrib1,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Sigma__Diff__distrib2,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Sigma__empty1,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_card__cartesian__product,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_setsum__cartesian__product,axiom,
% 162.26/162.02 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
% 162.26/162.02 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.26/162.02 => 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))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Times__empty,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_b,T_a] :
% 162.26/162.02 ( 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))
% 162.26/162.02 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Sigma__empty2,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Compl__Times__UNIV2,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Compl__Times__UNIV1,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_setprod__cartesian__product,axiom,
% 162.26/162.02 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
% 162.26/162.02 ( class_Groups_Ocomm__monoid__mult(T_a)
% 162.26/162.02 => 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))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Sigma__Un__distrib1,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Times__Un__distrib1,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Sigma__Un__distrib2,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_swap__product,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__cartesian__product,axiom,
% 162.26/162.02 ! [V_B_2,T_b,V_A_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 162.26/162.02 => 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)))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_equiv__type,axiom,
% 162.26/162.02 ! [V_r_2,V_A_2,T_a] :
% 162.26/162.02 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Sigma__Int__distrib2,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Times__Int__distrib1,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Sigma__Int__distrib1,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Id__on__subset__Times,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_UNIV__Times__UNIV,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_SigmaE2,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
% 162.26/162.02 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.26/162.02 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_SigmaD2,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_SigmaD1,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_mem__Sigma__iff,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
% 162.26/162.02 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.26/162.02 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_card__cartesian__product__singleton,axiom,
% 162.26/162.02 ! [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) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Times__subset__cancel2,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2))
% 162.26/162.02 => ( 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))))
% 162.26/162.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Image__subset,axiom,
% 162.26/162.02 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_b,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
% 162.26/162.02 => 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)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__cartesian__productD2,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_b,T_a] :
% 162.26/162.02 ( 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))))
% 162.26/162.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__cartesian__productD1,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_b,T_a] :
% 162.26/162.02 ( 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))))
% 162.26/162.02 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 162.26/162.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_fst__image__times,axiom,
% 162.26/162.02 ! [V_A_2,T_b,T_a,V_B_2] :
% 162.26/162.02 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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)) )
% 162.26/162.02 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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 ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_snd__image__times,axiom,
% 162.26/162.02 ! [V_B_2,T_b,T_a,V_A_2] :
% 162.26/162.02 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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)) )
% 162.26/162.02 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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 ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_insert__times__insert,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__equiv__class,axiom,
% 162.26/162.02 ! [V_X_2,V_r_2,V_A_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
% 162.26/162.02 => ( 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)))
% 162.26/162.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_UN__Times__distrib,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Sigma__def,axiom,
% 162.26/162.02 ! [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))))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__quotient,axiom,
% 162.26/162.02 ! [V_r_2,V_A_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
% 162.26/162.02 => 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))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 162.26/162.02 ! [V_A_2,V_I_2,T_b,T_a] :
% 162.26/162.02 ? [B_f] :
% 162.26/162.02 ( 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))
% 162.26/162.02 & 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))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_fold__image__Sigma,axiom,
% 162.26/162.02 ! [V_g_2,V_B_2,T_b,V_A_2,T_a,T_c] :
% 162.26/162.02 ( class_Groups_Ocomm__monoid__mult(T_c)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => ( ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 162.26/162.02 => 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)) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__SigmaI,axiom,
% 162.26/162.02 ! [V_B_2,T_b,V_A_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => ( ! [B_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) )
% 162.26/162.02 => 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))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_setprod__Sigma,axiom,
% 162.26/162.02 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] :
% 162.26/162.02 ( class_Groups_Ocomm__monoid__mult(T_c)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => ( ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 162.26/162.02 => 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)) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_setsum__Sigma,axiom,
% 162.26/162.02 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] :
% 162.26/162.02 ( class_Groups_Ocomm__monoid__add(T_c)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => ( ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 162.26/162.02 => 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)) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_card__SigmaI,axiom,
% 162.26/162.02 ! [V_B_2,T_b,V_A_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => ( ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 162.26/162.02 => 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) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_SigmaE,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,V_ca_2,T_b,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_ca_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
% 162.26/162.02 => ~ ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.02 => ! [B_y] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(V_B_2,B_x)))
% 162.26/162.02 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_map__pair__surj,axiom,
% 162.26/162.02 ! [V_g_2,T_c,T_d,V_f_2,T_a,T_b] :
% 162.26/162.02 ( 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))
% 162.26/162.02 => ( 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))
% 162.26/162.02 => 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_map__pair__inj__on,axiom,
% 162.26/162.02 ! [V_B_2,V_g_2,T_d,T_c,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.02 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,V_B_2)
% 162.26/162.02 => 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))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_map__pair__imageI,axiom,
% 162.26/162.02 ! [V_g_2,V_f_2,T_d,T_c,V_R_2,V_b_2,V_a_2,T_b,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_R_2))
% 162.26/162.02 => 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))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_fst__map__pair,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_snd__prod__fun,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_map__pair__simp,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_map__pair__ident,axiom,
% 162.26/162.02 ! [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 ).
% 162.26/162.02
% 162.26/162.02 fof(fact_map__pair__def,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_map__pair__surj__on,axiom,
% 162.26/162.02 ! [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] :
% 162.26/162.02 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_A_H_2
% 162.26/162.02 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2) = V_B_H_2
% 162.26/162.02 => 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_prod__fun__imageE,axiom,
% 162.26/162.02 ! [V_R_2,V_g_2,V_f_2,T_d,T_c,V_ca_2,T_b,T_a] :
% 162.26/162.02 ( 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)))
% 162.26/162.02 => ~ ! [B_x,B_y] :
% 162.26/162.02 ( 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))
% 162.26/162.02 => ~ 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_refl__on__def,axiom,
% 162.26/162.02 ! [V_r_2,V_A_2,T_a] :
% 162.26/162.02 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 162.26/162.02 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
% 162.26/162.02 & ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Rep__Integ__induct,axiom,
% 162.26/162.02 ! [V_P_2,V_y_2] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 162.26/162.02 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
% 162.26/162.02 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_refl__on__Id__on,axiom,
% 162.26/162.02 ! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_refl__on__empty,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_refl__on__Un,axiom,
% 162.26/162.02 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] :
% 162.26/162.02 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 162.26/162.02 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2)
% 162.26/162.02 => 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_refl__on__Int,axiom,
% 162.26/162.02 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] :
% 162.26/162.02 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 162.26/162.02 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2)
% 162.26/162.02 => 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_refl__onD,axiom,
% 162.26/162.02 ! [V_a_2,V_r_2,V_A_2,T_a] :
% 162.26/162.02 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_refl__onD1,axiom,
% 162.26/162.02 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 162.26/162.02 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_refl__onD2,axiom,
% 162.26/162.02 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 162.26/162.02 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_refl__onI,axiom,
% 162.26/162.02 ! [V_A_2,V_r_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
% 162.26/162.02 => ( ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) )
% 162.26/162.02 => c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 162.26/162.02 => ( ! [B_x] :
% 162.26/162.02 ( 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)))
% 162.26/162.02 => hAPP(V_g_2,B_x) = V_z_2 )
% 162.26/162.02 => 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)) ) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inj__on__INTER,axiom,
% 162.26/162.02 ! [V_A_2,V_f_2,T_c,T_b,T_a,V_I_2] :
% 162.26/162.02 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => ( ! [B_i] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_I_2))
% 162.26/162.02 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(V_A_2,B_i)) )
% 162.26/162.02 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_fun__left__comm__idem__remove,axiom,
% 162.26/162.02 ! [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))))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 162.26/162.02 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 162.26/162.02 => ( 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))
% 162.26/162.02 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.26/162.02 => ~ ! [B_y] :
% 162.26/162.02 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 162.26/162.02 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_card__less__Suc2,axiom,
% 162.26/162.02 ! [V_i_2,V_M_2] :
% 162.26/162.02 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 162.26/162.02 => 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))))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_CollectI,axiom,
% 162.26/162.02 ! [T_a,V_a_2,V_P_2] :
% 162.26/162.02 ( hBOOL(hAPP(V_P_2,V_a_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__Collect__conjI,axiom,
% 162.26/162.02 ! [V_Q_2,V_P_2,T_a] :
% 162.26/162.02 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 162.26/162.02 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) )
% 162.26/162.02 => 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)))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__Collect__less__nat,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__Collect__le__nat,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Collect__split,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_SetCompr__Sigma__eq,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Collect__neg__eq,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 162.26/162.02 ! [T_a] :
% 162.26/162.02 ( class_Orderings_Olinorder(T_a)
% 162.26/162.02 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 162.26/162.02 ! [T_a] :
% 162.26/162.02 ( class_Orderings_Olinorder(T_a)
% 162.26/162.02 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__Collect__eq,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_fun__left__comm__idem__sup,axiom,
% 162.26/162.02 ! [T_a] :
% 162.26/162.02 ( class_Lattices_Osemilattice__sup(T_a)
% 162.26/162.02 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_fun__left__comm__idem__inf,axiom,
% 162.26/162.02 ! [T_a] :
% 162.26/162.02 ( class_Lattices_Osemilattice__inf(T_a)
% 162.26/162.02 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_fun__left__comm__idem,axiom,
% 162.26/162.02 ! [T_a] :
% 162.26/162.02 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 162.26/162.02 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_CollectE,axiom,
% 162.26/162.02 ! [V_P_2,V_a_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 162.26/162.02 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_CollectD,axiom,
% 162.26/162.02 ! [V_P_2,V_a_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 162.26/162.02 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_mem__Collect__eq,axiom,
% 162.26/162.02 ! [V_P_2,V_a_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 162.26/162.02 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Collect__mem__eq,axiom,
% 162.26/162.02 ! [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 ).
% 162.26/162.02
% 162.26/162.02 fof(fact_UNIV__def,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__Collect__disjI,axiom,
% 162.26/162.02 ! [V_Q_2,V_P_2,T_a] :
% 162.26/162.02 ( 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))))
% 162.26/162.02 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 162.26/162.02 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_insert__Collect,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_fun__left__comm__idem__insert,axiom,
% 162.26/162.02 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Collect__conj__eq,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 162.26/162.02 ! [V_g_2,T_c,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 162.26/162.02 => 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)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 162.26/162.02 ! [V_z_2,V_x_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 162.26/162.02 => 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) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Collect__def,axiom,
% 162.26/162.02 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),V_P_2) = V_P_2 ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Collect__empty__eq,axiom,
% 162.26/162.02 ! [V_P_2,T_a] :
% 162.26/162.02 ( hAPP(c_Set_OCollect(T_a),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_empty__Collect__eq,axiom,
% 162.26/162.02 ! [V_P_2,T_a] :
% 162.26/162.02 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),V_P_2)
% 162.26/162.02 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_empty__def,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Collect__disj__eq,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_insert__compr__raw,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_insert__compr,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Un__def,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = 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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Int__def,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = 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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Int__Collect,axiom,
% 162.26/162.02 ! [V_P_2,V_A_2,V_x_2,T_a] :
% 162.26/162.02 ( 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))))
% 162.26/162.02 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.26/162.02 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_singleton__conv2,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_singleton__conv,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Collect__conv__if2,axiom,
% 162.26/162.02 ! [T_a,V_a_2,V_P_2] :
% 162.26/162.02 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 162.26/162.02 => 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))) )
% 162.26/162.02 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 162.26/162.02 => 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Collect__conv__if,axiom,
% 162.26/162.02 ! [T_a,V_a_2,V_P_2] :
% 162.26/162.02 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 162.26/162.02 => 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))) )
% 162.26/162.02 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 162.26/162.02 => 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_set__diff__eq,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__Collect__not,axiom,
% 162.26/162.02 ! [V_P_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 162.26/162.02 => ( 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))))
% 162.26/162.02 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_insert__def,axiom,
% 162.26/162.02 ! [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) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Compl__eq,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__def,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Collect__imp__eq,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_dom__def,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__M__bounded__by__nat,axiom,
% 162.26/162.02 ! [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))))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_setsum__setsum__restrict,axiom,
% 162.26/162.02 ! [V_R_2,V_f_2,V_T_2,T_b,V_S_2,T_a,T_c] :
% 162.26/162.02 ( class_Groups_Ocomm__monoid__add(T_c)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 162.26/162.02 => 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) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_if__image__distrib,axiom,
% 162.26/162.02 ! [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))))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Collect__all__eq,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_dom__if,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_nat__seg__image__imp__finite,axiom,
% 162.26/162.02 ! [V_n_2,V_f_2,T_a,V_A_2] :
% 162.26/162.02 ( 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)))
% 162.26/162.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_setsum__restrict__set_H,axiom,
% 162.26/162.02 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] :
% 162.26/162.02 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => 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) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_setsum__image__gen,axiom,
% 162.26/162.02 ! [V_f_2,T_c,V_g_2,V_S_2,T_a,T_b] :
% 162.26/162.02 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 162.26/162.02 => 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Image__singleton,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_setsum__cases,axiom,
% 162.26/162.02 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_a,T_b] :
% 162.26/162.02 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => 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))))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 162.26/162.02 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 162.26/162.02 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.02 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => 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) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_card__less__Suc,axiom,
% 162.26/162.02 ! [V_i_2,V_M_2] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 162.26/162.02 => 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))))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_card__less,axiom,
% 162.26/162.02 ! [V_i_2,V_M_2] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 162.26/162.02 => 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) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_dom__override__on,axiom,
% 162.26/162.02 ! [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))))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_setsum__multicount,axiom,
% 162.26/162.02 ! [V_k_2,V_R_2,V_T_2,T_b,V_S_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 162.26/162.02 => ( ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_T_2))
% 162.26/162.02 => 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 )
% 162.26/162.02 => 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)) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a] :
% 162.26/162.02 ( class_Orderings_Olinorder(T_a)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.26/162.02 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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))))))) ) ) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__Collect__subsets,axiom,
% 162.26/162.02 ! [V_A_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => 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)))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Pow__Compl,axiom,
% 162.26/162.02 ! [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))))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Pow__def,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__image__set,axiom,
% 162.26/162.02 ! [V_f_2,T_b,V_P_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 162.26/162.02 => 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))))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__Collect__bounded__ex,axiom,
% 162.26/162.02 ! [V_Q_2,T_b,V_P_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 162.26/162.02 => ( 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)))))
% 162.26/162.02 <=> ! [B_y] :
% 162.26/162.02 ( hBOOL(hAPP(V_P_2,B_y))
% 162.26/162.02 => 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)))) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_override__on__apply__notin,axiom,
% 162.26/162.02 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
% 162.26/162.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.26/162.02 => 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) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_override__on__apply__in,axiom,
% 162.26/162.02 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.26/162.02 => 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) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_override__on__emptyset,axiom,
% 162.26/162.02 ! [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 ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inj__graph,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_override__on__def,axiom,
% 162.26/162.02 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
% 162.26/162.02 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.26/162.02 => 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) )
% 162.26/162.02 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 162.26/162.02 => 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) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__psubset__def,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_ran__def,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inv__image__def,axiom,
% 162.26/162.02 ! [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))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_add__Max__commute,axiom,
% 162.26/162.02 ! [V_k_2,V_N_2,T_a] :
% 162.26/162.02 ( class_Groups_Olinordered__ab__semigroup__add(T_a)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 162.26/162.02 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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))))) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_add__Min__commute,axiom,
% 162.26/162.02 ! [V_k_2,V_N_2,T_a] :
% 162.26/162.02 ( class_Groups_Olinordered__ab__semigroup__add(T_a)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 162.26/162.02 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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))))) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_sup__Inf1__distrib,axiom,
% 162.26/162.02 ! [V_x_2,V_A_2,T_a] :
% 162.26/162.02 ( class_Lattices_Odistrib__lattice(T_a)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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))))) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_sup__Inf2__distrib,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a] :
% 162.26/162.02 ( class_Lattices_Odistrib__lattice(T_a)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.26/162.02 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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))))))) ) ) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inf__Sup1__distrib,axiom,
% 162.26/162.02 ! [V_x_2,V_A_2,T_a] :
% 162.26/162.02 ( class_Lattices_Odistrib__lattice(T_a)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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))))) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inf__Sup2__distrib,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a] :
% 162.26/162.02 ( class_Lattices_Odistrib__lattice(T_a)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.26/162.02 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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))))))) ) ) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 162.26/162.02 ! [V_x_2,V_A_2,T_a] :
% 162.26/162.02 ( class_Orderings_Olinorder(T_a)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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))))) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a] :
% 162.26/162.02 ( class_Orderings_Olinorder(T_a)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.26/162.02 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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))))))) ) ) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 162.26/162.02 ! [V_x_2,V_A_2,T_a] :
% 162.26/162.02 ( class_Orderings_Olinorder(T_a)
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 => 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))))) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Nitpick_Oprod__def,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_int__ge__less__than__def,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_int__ge__less__than2__def,axiom,
% 162.26/162.02 ! [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)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_reflp__def,axiom,
% 162.26/162.02 ! [V_r_2,T_a] :
% 162.26/162.02 ( c_Predicate_Oreflp(T_a,V_r_2)
% 162.26/162.02 <=> 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))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] :
% 162.26/162.02 ( class_Rings_Osemiring__0(T_c)
% 162.26/162.02 => ( 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)))
% 162.26/162.02 => 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))))))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_setsum__multicount__gen,axiom,
% 162.26/162.02 ! [V_k_2,V_R_2,V_t_2,T_b,V_s_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
% 162.26/162.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_t_2))
% 162.26/162.02 => ( ! [B_x] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_t_2))
% 162.26/162.02 => 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) )
% 162.26/162.02 => 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) ) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_inj__on__id,axiom,
% 162.26/162.02 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_Fun_Oid(T_a),V_A_2) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_id__def,axiom,
% 162.26/162.02 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 162.26/162.02
% 162.26/162.02 fof(fact_reflpE,axiom,
% 162.26/162.02 ! [V_x_2,V_r_2,T_a] :
% 162.26/162.02 ( c_Predicate_Oreflp(T_a,V_r_2)
% 162.26/162.02 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_id__apply,axiom,
% 162.26/162.02 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 162.26/162.02
% 162.26/162.02 fof(fact_apfst__id,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_apsnd__id,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Option_Omap_Oid,axiom,
% 162.26/162.02 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_vimage__id,axiom,
% 162.26/162.02 ! [V_A_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_Fun_Oid(T_a)),V_A_2) = V_A_2 ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Option_Omap_Oidentity,axiom,
% 162.26/162.02 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_of__int__eq__id,axiom,
% 162.26/162.02 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_map__pair_Oidentity,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_map__pair_Oid,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_image__id,axiom,
% 162.26/162.02 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),V_Y_2) = V_Y_2 ).
% 162.26/162.02
% 162.26/162.02 fof(fact_surj__id,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_apfst__def,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_apsnd__def,axiom,
% 162.26/162.02 ! [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) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_split__Pair,axiom,
% 162.26/162.02 ! [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)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_setsum__reindex__id,axiom,
% 162.26/162.02 ! [V_B_2,V_f_2,T_a,T_b] :
% 162.26/162.02 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.26/162.02 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 162.26/162.02 => 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_setprod__reindex__id,axiom,
% 162.26/162.02 ! [V_B_2,V_f_2,T_a,T_b] :
% 162.26/162.02 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.26/162.02 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 162.26/162.02 => 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)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__conv__nat__seg__image,axiom,
% 162.26/162.02 ! [V_A_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.02 <=> ? [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))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_rel__comp__def,axiom,
% 162.26/162.02 ! [V_s_2,V_r_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBC(T_c,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_a,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_c),tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_a,T_c)))),c_Product__Type_OPair(T_a,T_c)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_b)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_c,T_b)))),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))))),V_s_2))))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Range__Collect__split,axiom,
% 162.26/162.02 ! [V_P_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(c_Set_OCollect(tc_prod(T_b,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),V_P_2))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_rel__compI,axiom,
% 162.26/162.02 ! [V_s_2,V_ca_2,T_c,V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2))
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_b_2),V_ca_2)),V_s_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_a_2),V_ca_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_RangeI,axiom,
% 162.26/162.02 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_rel__comp__UNION__distrib,axiom,
% 162.26/162.02 ! [V_r_2,V_I_2,T_d,V_s_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_d),hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_s_2)),V_r_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_rel__comp__UNION__distrib2,axiom,
% 162.26/162.02 ! [V_s_2,V_r_2,V_I_2,T_d,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_d),c_Relation_Orel__comp(T_a,T_c,T_b)),V_r_2)),V_s_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Range__Id__on,axiom,
% 162.26/162.02 ! [V_A_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = V_A_2 ).
% 162.26/162.02
% 162.26/162.02 fof(fact_O__assoc,axiom,
% 162.26/162.02 ! [V_T_2,V_S_2,V_R_2,T_d,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_d,T_c),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_d,T_b),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_d,T_c,T_b),V_S_2),V_T_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_rel__comp__mono,axiom,
% 162.26/162.02 ! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2))
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_s_H_2),V_s_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_rel__comp__distrib2,axiom,
% 162.26/162.02 ! [V_R_2,V_T_2,V_S_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),V_S_2),V_T_2)),V_R_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_T_2),V_R_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_rel__comp__distrib,axiom,
% 162.26/162.02 ! [V_T_2,V_S_2,V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),V_T_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_rel__comp__empty1,axiom,
% 162.26/162.02 ! [V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_rel__comp__empty2,axiom,
% 162.26/162.02 ! [V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_union__comp__emptyR,axiom,
% 162.26/162.02 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 162.26/162.02 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 162.26/162.02 => ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 162.26/162.02 => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_union__comp__emptyL,axiom,
% 162.26/162.02 ! [V_B_2,V_C_2,V_A_2,T_a] :
% 162.26/162.02 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 162.26/162.02 => ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 162.26/162.02 => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Range__Union,axiom,
% 162.26/162.02 ! [V_S_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_b,T_a)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Range__empty,axiom,
% 162.26/162.02 ! [T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Range__empty__iff,axiom,
% 162.26/162.02 ! [V_r_2,T_a,T_b] :
% 162.26/162.02 ( hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.02 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_rel__comp__subset__Sigma,axiom,
% 162.26/162.02 ! [V_C_2,V_s_2,T_c,V_B_2,V_A_2,V_r_2,T_b,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_C_2)))) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Range__Un__eq,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_finite__Range,axiom,
% 162.26/162.02 ! [V_r_2,T_b,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2))
% 162.26/162.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_snd__eq__Range,axiom,
% 162.26/162.02 ! [V_R_2,T_a,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_a,c_Product__Type_Osnd(T_b,T_a)),V_R_2) = hAPP(c_Relation_ORange(T_b,T_a),V_R_2) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Range__iff,axiom,
% 162.26/162.02 ! [V_r_2,T_b,V_a_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)))
% 162.26/162.02 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_y),V_a_2)),V_r_2)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Range__insert,axiom,
% 162.26/162.02 ! [V_r_2,V_b_2,V_a_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Range__Int__subset,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Range__Diff__subset,axiom,
% 162.26/162.02 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2))),hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_max__ext__compat,axiom,
% 162.26/162.02 ! [V_S_2,V_R_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_a,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_a,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_min__ext__compat,axiom,
% 162.26/162.02 ! [V_S_2,V_R_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_a,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_a,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_a,V_R_2))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_RangeP__Range__eq,axiom,
% 162.26/162.02 ! [V_x_2,V_r_2,T_b,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2))
% 162.26/162.02 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_RangeE,axiom,
% 162.26/162.02 ! [V_r_2,T_b,V_b_2,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)))
% 162.26/162.02 => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_pred__comp__rel__comp__eq,axiom,
% 162.26/162.02 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_c,T_b,T_a] :
% 162.26/162.02 ( 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)
% 162.26/162.02 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_pred__comp_Ointros,axiom,
% 162.26/162.02 ! [T_c,T_b,T_a,V_ca_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2))
% 162.26/162.02 => c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2,V_a_2,V_ca_2) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_RangeP_Ointros,axiom,
% 162.26/162.02 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 162.26/162.02 => hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_b_2)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_pred__comp_Oequations,axiom,
% 162.26/162.02 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_c,T_b,T_a] :
% 162.26/162.02 ( c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2,V_a1_2,V_a3_2)
% 162.26/162.02 <=> ? [B_b] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 162.26/162.02 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_RangeP_Oequations,axiom,
% 162.26/162.02 ! [V_a2_2,V_r_2,T_b,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_a2_2))
% 162.26/162.02 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_reduction__pairI,axiom,
% 162.26/162.02 ! [V_S_2,V_R_2,T_a] :
% 162.26/162.02 ( c_Wellfounded_Owf(T_a,V_R_2)
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2))
% 162.26/162.02 => c_FunDef_Oreduction__pair(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_Domain__Collect__split,axiom,
% 162.26/162.02 ! [V_P_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),V_P_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_the__sym__eq__trivial,axiom,
% 162.26/162.02 ! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 162.26/162.02
% 162.26/162.02 fof(fact_wf__less__than,axiom,
% 162.26/162.02 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_wf__empty,axiom,
% 162.26/162.02 ! [T_a] : c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_wf__inv__image,axiom,
% 162.26/162.02 ! [V_f_2,T_b,V_r_2,T_a] :
% 162.26/162.02 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.02 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_wf__lex__prod,axiom,
% 162.26/162.02 ! [V_rb_2,T_b,V_ra_2,T_a] :
% 162.26/162.02 ( c_Wellfounded_Owf(T_a,V_ra_2)
% 162.26/162.02 => ( c_Wellfounded_Owf(T_b,V_rb_2)
% 162.26/162.02 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2)) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_wf__measure,axiom,
% 162.26/162.02 ! [V_f_2,T_a] : c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_DomainI,axiom,
% 162.26/162.02 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 162.26/162.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2))
% 162.26/162.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_wf__comp__self,axiom,
% 162.26/162.02 ! [V_R_2,T_a] :
% 162.26/162.02 ( c_Wellfounded_Owf(T_a,V_R_2)
% 162.26/162.02 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_wf__subset,axiom,
% 162.26/162.02 ! [V_p_2,V_r_2,T_a] :
% 162.26/162.02 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_p_2),V_r_2))
% 162.26/162.02 => c_Wellfounded_Owf(T_a,V_p_2) ) ) ).
% 162.26/162.02
% 162.26/162.02 fof(fact_min__ext__wf,axiom,
% 162.26/162.03 ! [V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.03 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__int__ge__less__than2,axiom,
% 162.26/162.03 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__int__ge__less__than,axiom,
% 162.26/162.03 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__irrefl,axiom,
% 162.26/162.03 ! [V_a_2,V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.03 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__asym,axiom,
% 162.26/162.03 ! [V_x_2,V_a_2,V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.03 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_x_2)),V_r_2))
% 162.26/162.03 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_a_2)),V_r_2)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__not__sym,axiom,
% 162.26/162.03 ! [V_x_2,V_a_2,V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.03 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_x_2)),V_r_2))
% 162.26/162.03 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_a_2)),V_r_2)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__not__refl,axiom,
% 162.26/162.03 ! [V_a_2,V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.03 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__mlex,axiom,
% 162.26/162.03 ! [V_f_2,V_R_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_R_2)
% 162.26/162.03 => c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__Int2,axiom,
% 162.26/162.03 ! [V_r_H_2,V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__Int1,axiom,
% 162.26/162.03 ! [V_r_H_2,V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_max__ext__wf,axiom,
% 162.26/162.03 ! [V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.03 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__pair__less,axiom,
% 162.26/162.03 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Domain__Id__on,axiom,
% 162.26/162.03 ! [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 ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__finite__psubset,axiom,
% 162.26/162.03 ! [T_a] : c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__less,axiom,
% 162.26/162.03 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)))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__Un,axiom,
% 162.26/162.03 ! [V_s_2,V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.03 => ( c_Wellfounded_Owf(T_a,V_s_2)
% 162.26/162.03 => ( 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))
% 162.26/162.03 => 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)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_acc__wfD,axiom,
% 162.26/162.03 ! [V_x_2,V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.03 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__acc__iff,axiom,
% 162.26/162.03 ! [V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.03 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__no__loop,axiom,
% 162.26/162.03 ! [V_R_2,T_a] :
% 162.26/162.03 ( 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))
% 162.26/162.03 => c_Wellfounded_Owf(T_a,V_R_2) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__union__merge,axiom,
% 162.26/162.03 ! [V_S_2,V_R_2,T_a] :
% 162.26/162.03 ( 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))
% 162.26/162.03 <=> 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Domain__empty,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Domain__empty__iff,axiom,
% 162.26/162.03 ! [V_r_2,T_b,T_a] :
% 162.26/162.03 ( hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.03 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Domain__mono,axiom,
% 162.26/162.03 ! [V_s_2,V_r_2,T_b,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Domain__Un__eq,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_finite__Domain,axiom,
% 162.26/162.03 ! [V_r_2,T_b,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2))
% 162.26/162.03 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_fst__eq__Domain,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 162.26/162.03 ! [V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.03 <=> ~ ? [B_f] :
% 162.26/162.03 ! [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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wfE__pf,axiom,
% 162.26/162.03 ! [V_A_2,V_R_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_R_2)
% 162.26/162.03 => ( 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)))
% 162.26/162.03 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__union__compatible,axiom,
% 162.26/162.03 ! [V_S_2,V_R_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_R_2)
% 162.26/162.03 => ( c_Wellfounded_Owf(T_a,V_S_2)
% 162.26/162.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2))
% 162.26/162.03 => 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)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Domain__iff,axiom,
% 162.26/162.03 ! [V_r_2,T_b,V_a_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)))
% 162.26/162.03 <=> ? [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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf,axiom,
% 162.26/162.03 ! [T_a] :
% 162.26/162.03 ( class_Orderings_Owellorder(T_a)
% 162.26/162.03 => 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)))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Domain__insert,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_reduction__pair__def,axiom,
% 162.26/162.03 ! [V_P_2,T_a] :
% 162.26/162.03 ( c_FunDef_Oreduction__pair(T_a,V_P_2)
% 162.26/162.03 <=> ( 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))
% 162.26/162.03 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(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))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_reduction__pair__lemma,axiom,
% 162.26/162.03 ! [V_S_2,V_R_2,V_P_2,T_a] :
% 162.26/162.03 ( c_FunDef_Oreduction__pair(T_a,V_P_2)
% 162.26/162.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),hAPP(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)))
% 162.26/162.03 => ( 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)))
% 162.26/162.03 => ( c_Wellfounded_Owf(T_a,V_S_2)
% 162.26/162.03 => 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)) ) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Domain__Int__subset,axiom,
% 162.26/162.03 ! [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)))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Domain__Diff__subset,axiom,
% 162.26/162.03 ! [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)))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Field__def,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__map__pair__image,axiom,
% 162.26/162.03 ! [V_f_2,T_b,V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.03 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Domain__Union,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_the__eq__trivial,axiom,
% 162.26/162.03 ! [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 ).
% 162.26/162.03
% 162.26/162.03 fof(fact_DomainP__Domain__eq,axiom,
% 162.26/162.03 ! [V_x_2,V_r_2,T_b,T_a] :
% 162.26/162.03 ( 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))
% 162.26/162.03 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__lenlex,axiom,
% 162.26/162.03 ! [V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.03 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olenlex(T_a,V_r_2)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_DomainE,axiom,
% 162.26/162.03 ! [V_r_2,T_b,V_a_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)))
% 162.26/162.03 => ~ ! [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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_DomainP_Ointros,axiom,
% 162.26/162.03 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 162.26/162.03 => hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a_2)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_DomainP_Oequations,axiom,
% 162.26/162.03 ! [V_a1_2,V_r_2,T_b,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a1_2))
% 162.26/162.03 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_pred__nat__def,axiom,
% 162.26/162.03 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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__lex,axiom,
% 162.26/162.03 ! [V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.03 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olex(T_a,V_r_2)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__pred__nat,axiom,
% 162.26/162.03 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lex__def,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__lexn,axiom,
% 162.26/162.03 ! [V_n_2,V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.03 => c_Wellfounded_Owf(tc_List_Olist(T_a),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lexn_Osimps_I1_J,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__same__fst,axiom,
% 162.26/162.03 ! [T_a,V_R_2,T_b,V_P_2] :
% 162.26/162.03 ( ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(V_P_2,B_x))
% 162.26/162.03 => c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)) )
% 162.26/162.03 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__if__measure,axiom,
% 162.26/162.03 ! [T_a,V_g_2,V_f_2,V_P_2] :
% 162.26/162.03 ( ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(V_P_2,B_x))
% 162.26/162.03 => 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))) )
% 162.26/162.03 => 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))))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wfP__def,axiom,
% 162.26/162.03 ! [V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 162.26/162.03 <=> 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_pigeonhole__infinite,axiom,
% 162.26/162.03 ! [V_f_2,T_b,V_A_2,T_a] :
% 162.26/162.03 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 162.26/162.03 => ? [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.03 & ~ 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)))))) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wfP__empty,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wfP__accp__iff,axiom,
% 162.26/162.03 ! [V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 162.26/162.03 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_accp__wfPD,axiom,
% 162.26/162.03 ! [V_x_2,V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 162.26/162.03 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wfP__subset,axiom,
% 162.26/162.03 ! [V_p_2,V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 162.26/162.03 => ( 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))
% 162.26/162.03 => c_Wellfounded_OwfP(T_a,V_p_2) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__in__rel,axiom,
% 162.26/162.03 ! [V_R_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_R_2)
% 162.26/162.03 => c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wfP__wf__eq,axiom,
% 162.26/162.03 ! [V_r_2,T_a] :
% 162.26/162.03 ( 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))
% 162.26/162.03 <=> c_Wellfounded_Owf(T_a,V_r_2) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wfP__acyclicP,axiom,
% 162.26/162.03 ! [V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 162.26/162.03 => c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_refl__on__def_H,axiom,
% 162.26/162.03 ! [V_r_2,V_A_2,T_a] :
% 162.26/162.03 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 162.26/162.03 <=> ( ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2))
% 162.26/162.03 => 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)) )
% 162.26/162.03 & ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.03 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__acyclic,axiom,
% 162.26/162.03 ! [V_r_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.03 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_acyclic__subset,axiom,
% 162.26/162.03 ! [V_r_2,V_s_2,T_a] :
% 162.26/162.03 ( c_Wellfounded_Oacyclic(T_a,V_s_2)
% 162.26/162.03 => ( 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))
% 162.26/162.03 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Powp__def,axiom,
% 162.26/162.03 ! [V_B_2,V_A_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,V_A_2),V_B_2))
% 162.26/162.03 <=> ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2))
% 162.26/162.03 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_INFI__bool__eq,axiom,
% 162.26/162.03 ! [T_a] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_HOL_Obool) = c_Set_OBall(T_a) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_ball__UNIV,axiom,
% 162.26/162.03 ! [V_P_2,T_a] :
% 162.26/162.03 ( ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 162.26/162.03 => hBOOL(hAPP(V_P_2,B_x)) )
% 162.26/162.03 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_ball__empty,axiom,
% 162.26/162.03 ! [V_P_2,T_a,B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 162.26/162.03 => hBOOL(hAPP(V_P_2,B_x)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Collect__ball__eq,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_congruent__def,axiom,
% 162.26/162.03 ! [V_f_2,V_r_2,T_b,T_a] :
% 162.26/162.03 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2)
% 162.26/162.03 <=> ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2))
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_INTER__def,axiom,
% 162.26/162.03 ! [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)))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 162.26/162.03 ! [V_r_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 162.26/162.03 => ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.03 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_finite__acyclic__wf,axiom,
% 162.26/162.03 ! [V_r_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 162.26/162.03 => ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 162.26/162.03 => c_Wellfounded_Owf(T_a,V_r_2) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Sup__Inf,axiom,
% 162.26/162.03 ! [V_A_2,T_a] :
% 162.26/162.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.03 => 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)))))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Inf__Sup,axiom,
% 162.26/162.03 ! [V_A_2,T_a] :
% 162.26/162.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.03 => 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))))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Nitpick_Owf_H__def,axiom,
% 162.26/162.03 ! [V_r_2,T_a] :
% 162.26/162.03 ( c_Nitpick_Owf_H(T_a,V_r_2)
% 162.26/162.03 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 162.26/162.03 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 162.26/162.03 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_LoopF,axiom,
% 162.26/162.03 ! [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)))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_evaln_OWhileFalse,axiom,
% 162.26/162.03 ! [V_n_2,V_ca_2,V_s_2,V_b_2] :
% 162.26/162.03 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_evaln_OWhileTrue,axiom,
% 162.26/162.03 ! [V_s2_2,V_s1_2,V_n_2,V_ca_2,V_s0_2,V_b_2] :
% 162.26/162.03 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 162.26/162.03 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s0_2),V_n_2),V_s1_2))
% 162.26/162.03 => ( 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))
% 162.26/162.03 => 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)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_evalc_OWhileTrue,axiom,
% 162.26/162.03 ! [V_s2_2,V_s1_2,V_ca_2,V_s0_2,V_b_2] :
% 162.26/162.03 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 162.26/162.03 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s0_2),V_s1_2))
% 162.26/162.03 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s1_2),V_s2_2))
% 162.26/162.03 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s0_2),V_s2_2)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_evalc_OWhileFalse,axiom,
% 162.26/162.03 ! [V_ca_2,V_s_2,V_b_2] :
% 162.26/162.03 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 162.26/162.03 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_s_2)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_WTs__elim__cases_I6_J,axiom,
% 162.26/162.03 ! [V_ca_2,V_b_2] :
% 162.26/162.03 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_ca_2)))
% 162.26/162.03 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_com_Osimps_I60_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_com_Osimps_I61_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_com_Osimps_I46_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_com_Osimps_I47_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_com_Osimps_I39_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_com_Osimps_I38_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_com_Osimps_I53_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_com_Osimps_I52_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_evaln_Oequations_I7_J,axiom,
% 162.26/162.03 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 162.26/162.03 ( 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))
% 162.26/162.03 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 162.26/162.03 => ? [B_s1] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1))
% 162.26/162.03 & 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)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_evaln_Oequations_I8_J,axiom,
% 162.26/162.03 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 162.26/162.03 ( 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))
% 162.26/162.03 <=> ( ( V_a6_2 = V_a2_2
% 162.26/162.03 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 162.26/162.03 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 162.26/162.03 & ? [B_s1] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1))
% 162.26/162.03 & 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)) ) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_evalc_Oequations_I8_J,axiom,
% 162.26/162.03 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2))
% 162.26/162.03 <=> ( ( V_a5_2 = V_a2_2
% 162.26/162.03 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 162.26/162.03 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 162.26/162.03 & ? [B_s1] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 162.26/162.03 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_evalc_Oequations_I7_J,axiom,
% 162.26/162.03 ! [V_a2_2,V_a3_2,V_a1_2] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2))
% 162.26/162.03 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 162.26/162.03 => ? [B_s1] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 162.26/162.03 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_com_Osimps_I59_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_com_Osimps_I58_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_WT_Oequations_I6_J,axiom,
% 162.26/162.03 ! [V_a1_2,V_a2_2] :
% 162.26/162.03 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2)))
% 162.26/162.03 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_While,axiom,
% 162.26/162.03 ! [V_b_2,V_ca_2] :
% 162.26/162.03 ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
% 162.26/162.03 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_ca_2))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_com_Osimps_I5_J,axiom,
% 162.26/162.03 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
% 162.26/162.03 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
% 162.26/162.03 <=> ( V_fun_2 = V_fun_H_2
% 162.26/162.03 & V_com_2 = V_com_H_2 ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_com_Osimps_I16_J,axiom,
% 162.26/162.03 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_com_Osimps_I17_J,axiom,
% 162.26/162.03 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 162.26/162.03
% 162.26/162.03 fof(fact_triples__valid__Suc,axiom,
% 162.26/162.03 ! [V_n_2,V_ts_2,T_a] :
% 162.26/162.03 ( ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
% 162.26/162.03 => c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),B_x) )
% 162.26/162.03 => ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
% 162.26/162.03 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,B_x) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_hoare__valids__def,axiom,
% 162.26/162.03 ! [V_ts_2,V_G_2,T_a] :
% 162.26/162.03 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,V_ts_2)
% 162.26/162.03 <=> ! [B_n] :
% 162.26/162.03 ( ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_G_2))
% 162.26/162.03 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) )
% 162.26/162.03 => ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
% 162.26/162.03 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Inter__eq,axiom,
% 162.26/162.03 ! [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)))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_com_Osize_I14_J,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_com_Osize_I6_J,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Abs__Integ__cases,axiom,
% 162.26/162.03 ! [V_x_2] :
% 162.26/162.03 ~ ! [B_y] :
% 162.26/162.03 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 162.26/162.03 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Abs__Integ__induct,axiom,
% 162.26/162.03 ! [V_x_2,V_P_2] :
% 162.26/162.03 ( ! [B_y] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 162.26/162.03 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 162.26/162.03 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_finite__range__map__of__map__add,axiom,
% 162.26/162.03 ! [V_l_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( 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)))))
% 162.26/162.03 => 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))))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_finite__UN__I,axiom,
% 162.26/162.03 ! [V_B_2,T_b,V_A_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => ( ! [B_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 162.26/162.03 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) )
% 162.26/162.03 => 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))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_finite__dom__map__of,axiom,
% 162.26/162.03 ! [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)))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_finite__range__map__of,axiom,
% 162.26/162.03 ! [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))))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__add__map__of__foldr,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of__mapk__SomeI,axiom,
% 162.26/162.03 ! [V_x_2,V_k_2,V_t_2,T_c,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.03 => ( 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)
% 162.26/162.03 => 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) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_inj__mapI,axiom,
% 162.26/162.03 ! [V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_inj__map,axiom,
% 162.26/162.03 ! [V_f_2,T_b,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 <=> c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_inj__map__eq__map,axiom,
% 162.26/162.03 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.03 => ( 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)
% 162.26/162.03 <=> V_xs_2 = V_ys_2 ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_inj__mapD,axiom,
% 162.26/162.03 ! [V_f_2,T_b,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__injective,axiom,
% 162.26/162.03 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 162.26/162.03 => V_xs_2 = V_ys_2 ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__ident,axiom,
% 162.26/162.03 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)),V_xs_2) = V_xs_2 ).
% 162.26/162.03
% 162.26/162.03 fof(fact_List_Omap_Oidentity,axiom,
% 162.26/162.03 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_List_Omap_Oid,axiom,
% 162.26/162.03 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_body__def,axiom,
% 162.26/162.03 c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of__map__keys,axiom,
% 162.26/162.03 ! [V_m_2,T_b,V_xs_2,T_a] :
% 162.26/162.03 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Map_Odom(T_a,T_b,V_m_2)
% 162.26/162.03 => 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 ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_finite__set,axiom,
% 162.26/162.03 ! [V_xs_2,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_List_Oset(T_a),V_xs_2))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__map,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__eq__conv,axiom,
% 162.26/162.03 ! [V_g_2,V_xs_2,V_f_2,T_a,T_b] :
% 162.26/162.03 ( 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)
% 162.26/162.03 <=> ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 162.26/162.03 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_infinite__UNIV__listI,axiom,
% 162.26/162.03 ! [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)))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_WT__bodies__def,axiom,
% 162.26/162.03 ( c_Com_OWT__bodies
% 162.26/162.03 <=> ! [B_x] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_inj__on__map__eq__map,axiom,
% 162.26/162.03 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => ( 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)
% 162.26/162.03 <=> V_xs_2 = V_ys_2 ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__inj__on,axiom,
% 162.26/162.03 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => ( 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)))
% 162.26/162.03 => V_xs_2 = V_ys_2 ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__fun__upd,axiom,
% 162.26/162.03 ! [V_v_2,V_f_2,T_b,V_xs_2,V_y_2,T_a] :
% 162.26/162.03 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_inj__on__mapI,axiom,
% 162.26/162.03 ! [V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of__eq__dom,axiom,
% 162.26/162.03 ! [V_ys_2,V_xs_2,T_b,T_a] :
% 162.26/162.03 ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2)
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of__is__SomeD,axiom,
% 162.26/162.03 ! [V_y_2,V_x_2,V_xys_2,T_a,T_b] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xys_2))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of__SomeD,axiom,
% 162.26/162.03 ! [V_y_2,V_k_2,V_xs_2,T_a,T_b] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_dom__map__of__conv__image__fst,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of__eq__None__iff,axiom,
% 162.26/162.03 ! [V_x_2,V_xys_2,T_a,T_b] :
% 162.26/162.03 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_a)
% 162.26/162.03 <=> ~ 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)))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_ran__distinct,axiom,
% 162.26/162.03 ! [V_al_2,T_b,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__map__of__compr,axiom,
% 162.26/162.03 ! [V_xs_2,T_b,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => 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)))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_distinct__map,axiom,
% 162.26/162.03 ! [V_xs_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)))
% 162.26/162.03 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 162.26/162.03 & c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of__inject__set,axiom,
% 162.26/162.03 ! [V_ys_2,V_xs_2,T_b,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => ( 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)))
% 162.26/162.03 => ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2)
% 162.26/162.03 <=> 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) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Some__eq__map__of__iff,axiom,
% 162.26/162.03 ! [V_x_2,V_y_2,V_xys_2,T_b,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => ( 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)
% 162.26/162.03 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of__eq__Some__iff,axiom,
% 162.26/162.03 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => ( 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)
% 162.26/162.03 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of__is__SomeI,axiom,
% 162.26/162.03 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2)))
% 162.26/162.03 => 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) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_greaterThanLessThan__upto,axiom,
% 162.26/162.03 ! [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)))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_weak__map__of__SomeI,axiom,
% 162.26/162.03 ! [V_l_2,V_x_2,V_k_2,T_b,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => ? [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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_atLeastAtMost__upto,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__upto,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_distinct__upto,axiom,
% 162.26/162.03 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_atLeastLessThan__upto,axiom,
% 162.26/162.03 ! [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)))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_greaterThanAtMost__upto,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_nat__list__def,axiom,
% 162.26/162.03 ! [V_l_2] :
% 162.26/162.03 ( c_List_Onat__list(V_l_2)
% 162.26/162.03 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of__map__restrict,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_o__id,axiom,
% 162.26/162.03 ! [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 ).
% 162.26/162.03
% 162.26/162.03 fof(fact_id__o,axiom,
% 162.26/162.03 ! [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 ).
% 162.26/162.03
% 162.26/162.03 fof(fact_o__eq__id__dest,axiom,
% 162.26/162.03 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_inj__comp,axiom,
% 162.26/162.03 ! [V_g_2,T_c,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.03 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 162.26/162.03 => 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))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_inj__on__imageI2,axiom,
% 162.26/162.03 ! [V_A_2,V_f_2,V_f_H_2,T_c,T_b,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => c_Fun_Oinj__on(T_a,T_c,V_f_2,V_A_2) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 162.26/162.03 ! [V_x_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__pair_Ocompositionality,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__pair__compose,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__pair_Ocomp,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_vimage__compose,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Option_Omap_Ocomp,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Option_Omap_Ocompositionality,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_option__map__comp,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_K__record__comp,axiom,
% 162.26/162.03 ! [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 ).
% 162.26/162.03
% 162.26/162.03 fof(fact_o__eq__dest__lhs,axiom,
% 162.26/162.03 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] :
% 162.26/162.03 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = V_ca_2
% 162.26/162.03 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_apsnd__compose,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_apfst__compose,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 162.26/162.03 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 162.26/162.03 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_fun__upd__comp,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_o__assoc,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_o__apply,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_o__eq__dest,axiom,
% 162.26/162.03 ! [V_v_2,V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_o__eq__elim,axiom,
% 162.26/162.03 ! [V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_comp__cong,axiom,
% 162.26/162.03 ! [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] :
% 162.26/162.03 ( 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))
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_o__def,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_image__compose,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_inj__on__imageI,axiom,
% 162.26/162.03 ! [V_A_2,V_f_2,V_g_2,T_c,T_b,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_comp__inj__on,axiom,
% 162.26/162.03 ! [V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.03 => ( 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))
% 162.26/162.03 => 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) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_comp__inj__on__iff,axiom,
% 162.26/162.03 ! [V_f_H_2,T_c,V_A_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.03 => ( 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))
% 162.26/162.03 <=> 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) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_comp__surj,axiom,
% 162.26/162.03 ! [V_g_2,T_c,V_f_2,T_a,T_b] :
% 162.26/162.03 ( 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))
% 162.26/162.03 => ( 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))
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_List_Omap_Ocomp,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__comp__map,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_List_Omap_Ocompositionality,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__map,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_option__map__o__empty,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_setsum__reindex,axiom,
% 162.26/162.03 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] :
% 162.26/162.03 ( class_Groups_Ocomm__monoid__add(T_c)
% 162.26/162.03 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 162.26/162.03 => 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) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_setprod__reindex__cong,axiom,
% 162.26/162.03 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
% 162.26/162.03 ( class_Groups_Ocomm__monoid__mult(T_c)
% 162.26/162.03 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.03 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
% 162.26/162.03 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)
% 162.26/162.03 => 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) ) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_setprod__reindex,axiom,
% 162.26/162.03 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] :
% 162.26/162.03 ( class_Groups_Ocomm__monoid__mult(T_c)
% 162.26/162.03 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 162.26/162.03 => 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) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_option__map__o__map__upd,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_setsum_Oreindex,axiom,
% 162.26/162.03 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] :
% 162.26/162.03 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2)
% 162.26/162.03 => 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) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_setprod_Oreindex,axiom,
% 162.26/162.03 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] :
% 162.26/162.03 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2)
% 162.26/162.03 => 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) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_the__inv__into__comp,axiom,
% 162.26/162.03 ! [V_x_2,V_A_2,V_g_2,T_c,V_f_2,T_b,T_a] :
% 162.26/162.03 ( 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))
% 162.26/162.03 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,V_A_2)
% 162.26/162.03 => ( 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))))
% 162.26/162.03 => 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) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_fold__image__reindex,axiom,
% 162.26/162.03 ! [V_z_2,V_g_2,V_h_2,T_b,V_A_2,T_a,T_c] :
% 162.26/162.03 ( class_Groups_Oab__semigroup__mult(T_c)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => ( c_Fun_Oinj__on(T_a,T_b,V_h_2,V_A_2)
% 162.26/162.03 => 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) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of__map,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding_Oremove,axiom,
% 162.26/162.03 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.26/162.03 => 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)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding__image_Oreindex,axiom,
% 162.26/162.03 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 162.26/162.03 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 162.26/162.03 => 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) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_snd__comp__map__pair,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_fst__comp__map__pair,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 162.26/162.03 ! [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] :
% 162.26/162.03 ( c_Finite__Set_Ofolding(T_a,T_b,V_fa_2,V_F_2)
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding_Ocommute__comp,axiom,
% 162.26/162.03 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding_Ocommute__left__comp,axiom,
% 162.26/162.03 ! [V_g_2,V_x_2,V_y_2,T_c,V_F_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_UN__o,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_foldr__map,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding__image_Odistrib,axiom,
% 162.26/162.03 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_split__comp,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding_Ocommute__comp_H,axiom,
% 162.26/162.03 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 162.26/162.03 ! [V_g_2,V_x_2,T_c,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 162.26/162.03 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.26/162.03 => 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)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 162.26/162.03 ! [V_g_2,T_c,V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.26/162.03 => 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)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding_Oempty,axiom,
% 162.26/162.03 ! [V_F_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 162.26/162.03 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Fun_Oid(T_b) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding_Oeq__fold,axiom,
% 162.26/162.03 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_s_2),V_A_2) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding__image_Oeq__fold,axiom,
% 162.26/162.03 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 162.26/162.03 => 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) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_vimage__Times,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding_Oinsert,axiom,
% 162.26/162.03 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.26/162.03 => 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)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding_Ounion__inter,axiom,
% 162.26/162.03 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.26/162.03 => 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)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding_Oinsert__remove,axiom,
% 162.26/162.03 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding_Ounion,axiom,
% 162.26/162.03 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.26/162.03 => ( 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))
% 162.26/162.03 => 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)) ) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Loop__sound__lemma,axiom,
% 162.26/162.03 ! [V_ca_2,V_b_2,V_P_2,V_G_2,T_a] :
% 162.26/162.03 ( 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))))
% 162.26/162.03 => 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)))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_hoare__derivs_OIf,axiom,
% 162.26/162.03 ! [V_d_2,V_Q_2,V_ca_2,V_b_2,V_P_2,V_G_2,T_a] :
% 162.26/162.03 ( 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))))
% 162.26/162.03 => ( 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))))
% 162.26/162.03 => 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)))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_peek__and__def,axiom,
% 162.26/162.03 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_p_2),V_Z_2),V_s_2))
% 162.26/162.03 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2))
% 162.26/162.03 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Loop,axiom,
% 162.26/162.03 ! [V_ca_2,V_b_2,V_P_2,V_G_2,T_a] :
% 162.26/162.03 ( 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))))
% 162.26/162.03 => 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)))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_setsum__reindex__nonzero,axiom,
% 162.26/162.03 ! [T_b,V_h_2,V_f_2,V_S_2,T_a,T_c] :
% 162.26/162.03 ( class_Groups_Ocomm__monoid__add(T_c)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 162.26/162.03 => ( ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 162.26/162.03 => ! [B_y] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_S_2))
% 162.26/162.03 => ( B_x != B_y
% 162.26/162.03 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 162.26/162.03 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) )
% 162.26/162.03 => 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) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding__idem_Ounion__idem,axiom,
% 162.26/162.03 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 162.26/162.03 => 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)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 162.26/162.03 ! [V_g_2,V_x_2,T_c,V_F_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding__idem_Oidem__comp,axiom,
% 162.26/162.03 ! [V_x_2,V_F_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 162.26/162.03 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.26/162.03 => 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) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding__idem_Oinsert__idem,axiom,
% 162.26/162.03 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 162.26/162.03 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 162.26/162.03 => 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) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__remove1__eq,axiom,
% 162.26/162.03 ! [V_x_2,V_xs_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 162.26/162.03 => 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)))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of__zip__map,axiom,
% 162.26/162.03 ! [V_f_2,T_b,V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => 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)) )
% 162.26/162.03 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => 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) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_remove1__commute,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_distinct__zipI1,axiom,
% 162.26/162.03 ! [V_ys,T_b,V_xs,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 162.26/162.03 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_distinct__remove1,axiom,
% 162.26/162.03 ! [V_x,V_xs,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 162.26/162.03 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_distinct__zipI2,axiom,
% 162.26/162.03 ! [V_xs,T_b,V_ys,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 162.26/162.03 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_remove1__idem,axiom,
% 162.26/162.03 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => c_List_Oremove1(T_a,V_x_2,V_xs_2) = V_xs_2 ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_notin__set__remove1,axiom,
% 162.26/162.03 ! [V_y_2,V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => ~ 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)))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_in__set__remove1,axiom,
% 162.26/162.03 ! [V_xs_2,T_a,V_b_2,V_a_2] :
% 162.26/162.03 ( V_a_2 != V_b_2
% 162.26/162.03 => ( 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))))
% 162.26/162.03 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_zip__same__conv__map,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__remove1__subset,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_zip__map__fst__snd,axiom,
% 162.26/162.03 ! [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 ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__zip__map2,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__zip__map,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_in__set__zipE,axiom,
% 162.26/162.03 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),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))))
% 162.26/162.03 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__zip__rightD,axiom,
% 162.26/162.03 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),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))))
% 162.26/162.03 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__zip__leftD,axiom,
% 162.26/162.03 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),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))))
% 162.26/162.03 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_zip__same,axiom,
% 162.26/162.03 ! [V_xs_2,V_b_2,V_a_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),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))))
% 162.26/162.03 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 & V_a_2 = V_b_2 ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_zip__map2,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_zip__map1,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_zip__map__map,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_sorted__list__of__set__remove,axiom,
% 162.26/162.03 ! [V_x_2,V_A_2,T_a] :
% 162.26/162.03 ( class_Orderings_Olinorder(T_a)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_strong__setprod__reindex__cong,axiom,
% 162.26/162.03 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
% 162.26/162.03 ( class_Groups_Ocomm__monoid__mult(T_c)
% 162.26/162.03 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.03 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
% 162.26/162.03 => ( ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.03 => 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) )
% 162.26/162.03 => 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) ) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_sorted__list__of__set__insert,axiom,
% 162.26/162.03 ! [V_x_2,V_A_2,T_a] :
% 162.26/162.03 ( class_Orderings_Olinorder(T_a)
% 162.26/162.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => 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)))))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of__zip__upd,axiom,
% 162.26/162.03 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_b,V_ys_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => ( 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)
% 162.26/162.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 162.26/162.03 => ( 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))
% 162.26/162.03 => 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)) ) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lexn__length,axiom,
% 162.26/162.03 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = V_n_2
% 162.26/162.03 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_fun__left__comm__insort,axiom,
% 162.26/162.03 ! [T_a] :
% 162.26/162.03 ( class_Orderings_Olinorder(T_a)
% 162.26/162.03 => c_Finite__Set_Ofun__left__comm(T_a,tc_List_Olist(T_a),c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_insort__left__comm,axiom,
% 162.26/162.03 ! [V_xs_2,V_y_2,V_x_2,T_a] :
% 162.26/162.03 ( class_Orderings_Olinorder(T_a)
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_insort__key__left__comm,axiom,
% 162.26/162.03 ! [V_xs_2,T_b,V_y_2,V_x_2,V_f_2,T_a] :
% 162.26/162.03 ( class_Orderings_Olinorder(T_a)
% 162.26/162.03 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_neq__if__length__neq,axiom,
% 162.26/162.03 ! [V_ys,V_xs,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => V_xs != V_ys ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_length__insort,axiom,
% 162.26/162.03 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 162.26/162.03 ( class_Orderings_Olinorder(T_b)
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_length__map,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__eq__imp__length__eq,axiom,
% 162.26/162.03 ! [V_ys_2,V_g_2,T_c,V_xs_2,V_f_2,T_a,T_b] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_length__zip,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_remove1__insort,axiom,
% 162.26/162.03 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( class_Orderings_Olinorder(T_a)
% 162.26/162.03 => 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 ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__insort,axiom,
% 162.26/162.03 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 162.26/162.03 ( class_Orderings_Olinorder(T_b)
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_card__length,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_distinct__card,axiom,
% 162.26/162.03 ! [V_xs_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_card__distinct,axiom,
% 162.26/162.03 ! [V_xs_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of__zip__inject,axiom,
% 162.26/162.03 ! [V_zs_2,V_xs_2,T_b,V_ys_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => ( 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)
% 162.26/162.03 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 162.26/162.03 => ( 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))
% 162.26/162.03 => V_ys_2 = V_zs_2 ) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__fst__zip,axiom,
% 162.26/162.03 ! [V_ys_2,T_b,V_xs_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => 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 ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__snd__zip,axiom,
% 162.26/162.03 ! [V_ys_2,T_b,V_xs_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => 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 ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_distinct__insort,axiom,
% 162.26/162.03 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 162.26/162.03 ( class_Orderings_Olinorder(T_b)
% 162.26/162.03 => ( 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)))
% 162.26/162.03 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_length__pos__if__in__set,axiom,
% 162.26/162.03 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_zip__eq__conv,axiom,
% 162.26/162.03 ! [V_zs_2,V_ys_2,T_b,V_xs_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => ( hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2) = V_zs_2
% 162.26/162.03 <=> ( 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
% 162.26/162.03 & 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 ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lenlex__conv,axiom,
% 162.26/162.03 ! [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)))))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lenlex__def,axiom,
% 162.26/162.03 ! [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)))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_finite__lists__length__eq,axiom,
% 162.26/162.03 ! [V_n_2,V_A_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => 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))))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__eq__iff__zip__eq,axiom,
% 162.26/162.03 ! [T_a,V_ys_2,V_xs_2] :
% 162.26/162.03 ( V_xs_2 = V_ys_2
% 162.26/162.03 <=> ( 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)
% 162.26/162.03 & ! [B_x] :
% 162.26/162.03 ( 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))))
% 162.26/162.03 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of__zip__is__None,axiom,
% 162.26/162.03 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => ( 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)
% 162.26/162.03 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of__zip__is__Some,axiom,
% 162.26/162.03 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 <=> ? [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) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_length__remove1,axiom,
% 162.26/162.03 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => 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)) )
% 162.26/162.03 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => 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) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_dom__map__of__zip,axiom,
% 162.26/162.03 ! [V_ys_2,T_b,V_xs_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 162.26/162.03 => 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) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_finite__lists__length__le,axiom,
% 162.26/162.03 ! [V_n_2,V_A_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => 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))))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel__iff__zip,axiom,
% 162.26/162.03 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 <=> ( 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)
% 162.26/162.03 & ! [B_x] :
% 162.26/162.03 ( 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))))
% 162.26/162.03 => 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)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_length__sublist,axiom,
% 162.26/162.03 ! [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)))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel__eq__len,axiom,
% 162.26/162.03 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel__mono,axiom,
% 162.26/162.03 ! [V_s_2,V_r_2,T_a] :
% 162.26/162.03 ( 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))
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_distinct__sublistI,axiom,
% 162.26/162.03 ! [V_I_2,V_xs_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 162.26/162.03 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_notin__set__sublistI,axiom,
% 162.26/162.03 ! [V_I_2,V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => ~ 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)))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_in__set__sublistD,axiom,
% 162.26/162.03 ! [V_I_2,V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( 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))))
% 162.26/162.03 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__sublist__subset,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrelp__listrel__eq,axiom,
% 162.26/162.03 ! [V_xa_2,V_x_2,V_r_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 <=> 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lexn_Osimps_I2_J,axiom,
% 162.26/162.03 ! [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)))))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_impossible__Cons,axiom,
% 162.26/162.03 ! [V_x,V_ys,V_xs,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_zip__Cons__Cons,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__ConsD,axiom,
% 162.26/162.03 ! [V_xs_2,V_x_2,V_y_2,T_a] :
% 162.26/162.03 ( 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))))
% 162.26/162.03 => ( V_y_2 = V_x_2
% 162.26/162.03 | hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__subset__Cons,axiom,
% 162.26/162.03 ! [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)))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_not__Cons__self,axiom,
% 162.26/162.03 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_not__Cons__self2,axiom,
% 162.26/162.03 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list_Oinject,axiom,
% 162.26/162.03 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 <=> ( V_a_2 = V_a_H_2
% 162.26/162.03 & V_list_2 = V_list_H_2 ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrelp_Oequations_I2_J,axiom,
% 162.26/162.03 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_a] :
% 162.26/162.03 ( 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))
% 162.26/162.03 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 162.26/162.03 & c_List_Olistrelp(T_a,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrelp_OCons,axiom,
% 162.26/162.03 ! [V_ys_2,V_xs_2,T_a,V_y_2,V_x_2,V_r_2] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 162.26/162.03 => ( c_List_Olistrelp(T_a,V_r_2,V_xs_2,V_ys_2)
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map_Osimps_I2_J,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_foldr_Osimps_I2_J,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_remove1_Osimps_I2_J,axiom,
% 162.26/162.03 ! [V_xs,T_a,V_y,V_x] :
% 162.26/162.03 ( ( V_x = V_y
% 162.26/162.03 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 162.26/162.03 & ( V_x != V_y
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_insort__key_Osimps_I2_J,axiom,
% 162.26/162.03 ! [V_ys_2,T_b,V_y_2,V_x_2,V_f_2,T_a] :
% 162.26/162.03 ( class_Orderings_Olinorder(T_a)
% 162.26/162.03 => ( ( 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)))
% 162.26/162.03 => 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)) )
% 162.26/162.03 & ( ~ 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)))
% 162.26/162.03 => 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)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_distinct_Osimps_I2_J,axiom,
% 162.26/162.03 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))
% 162.26/162.03 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of__Cons__code_I2_J,axiom,
% 162.26/162.03 ! [V_ps,V_v,T_c,T_b,V_k,V_l] :
% 162.26/162.03 ( ( V_l = V_k
% 162.26/162.03 => 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) )
% 162.26/162.03 & ( V_l != V_k
% 162.26/162.03 => 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) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list_Osize_I4_J,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel_OCons,axiom,
% 162.26/162.03 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 162.26/162.03 => ( 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)))
% 162.26/162.03 => 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))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of_Osimps_I2_J,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Cons__in__lex,axiom,
% 162.26/162.03 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 162.26/162.03 & 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) )
% 162.26/162.03 | ( V_x_2 = V_y_2
% 162.26/162.03 & 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))) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel__Cons,axiom,
% 162.26/162.03 ! [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))))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__Cons__def,axiom,
% 162.26/162.03 ! [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)))))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel__Cons2,axiom,
% 162.26/162.03 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => ~ ! [B_x,B_xs] :
% 162.26/162.03 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs)
% 162.26/162.03 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_y_2)),V_r_2))
% 162.26/162.03 => ~ 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))) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel__Cons1,axiom,
% 162.26/162.03 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => ~ ! [B_y,B_ys] :
% 162.26/162.03 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys)
% 162.26/162.03 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),B_y)),V_r_2))
% 162.26/162.03 => ~ 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))) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_insort__insert__insort__key,axiom,
% 162.26/162.03 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] :
% 162.26/162.03 ( class_Orderings_Olinorder(T_a)
% 162.26/162.03 => ( ~ 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))))
% 162.26/162.03 => 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) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lexord__cons__cons,axiom,
% 162.26/162.03 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 162.26/162.03 | ( V_a_2 = V_b_2
% 162.26/162.03 & 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))) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_distinct__insort__insert,axiom,
% 162.26/162.03 ! [V_x_2,V_f_2,V_xs_2,T_a,T_b] :
% 162.26/162.03 ( class_Orderings_Olinorder(T_b)
% 162.26/162.03 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 162.26/162.03 => 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))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_insort__insert__triv,axiom,
% 162.26/162.03 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( class_Orderings_Olinorder(T_a)
% 162.26/162.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__insort__insert,axiom,
% 162.26/162.03 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( class_Orderings_Olinorder(T_a)
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_insort__insert__key__triv,axiom,
% 162.26/162.03 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] :
% 162.26/162.03 ( class_Orderings_Olinorder(T_a)
% 162.26/162.03 => ( 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))))
% 162.26/162.03 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lexord__lex,axiom,
% 162.26/162.03 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 <=> ( 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)))
% 162.26/162.03 & 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) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_insort__insert__insort,axiom,
% 162.26/162.03 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( class_Orderings_Olinorder(T_a)
% 162.26/162.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => 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) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__zip,axiom,
% 162.26/162.03 ! [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)))))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list_Osize_I2_J,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_nth__Cons__0,axiom,
% 162.26/162.03 ! [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 ).
% 162.26/162.03
% 162.26/162.03 fof(fact_nth__Cons__Suc,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__eq__iff__nth__eq,axiom,
% 162.26/162.03 ! [T_a,V_ys_2,V_xs_2] :
% 162.26/162.03 ( V_xs_2 = V_ys_2
% 162.26/162.03 <=> ( 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)
% 162.26/162.03 & ! [B_i] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_i) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_nth__zip,axiom,
% 162.26/162.03 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => ( 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)))
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__size__map,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_nth_Osimps,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_all__set__conv__all__nth,axiom,
% 162.26/162.03 ! [V_P_2,V_xs_2,T_a] :
% 162.26/162.03 ( ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => hBOOL(hAPP(V_P_2,B_x)) )
% 162.26/162.03 <=> ! [B_i] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_nth__map,axiom,
% 162.26/162.03 ! [V_f_2,T_b,V_xs_2,T_a,V_n_2] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_distinct__conv__nth,axiom,
% 162.26/162.03 ! [V_xs_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 162.26/162.03 <=> ! [B_i] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => ! [B_j] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => ( B_i != B_j
% 162.26/162.03 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j) ) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_nth__eq__iff__index__eq,axiom,
% 162.26/162.03 ! [V_j_2,V_i_2,V_xs_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 162.26/162.03 => ( 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)))
% 162.26/162.03 => ( 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)))
% 162.26/162.03 => ( 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)
% 162.26/162.03 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_in__set__conv__nth,axiom,
% 162.26/162.03 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 <=> ? [B_i] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 & hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = V_x_2 ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_nth__mem,axiom,
% 162.26/162.03 ! [V_xs_2,T_a,V_n_2] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_nth__Cons_H,axiom,
% 162.26/162.03 ! [V_xs,V_x,T_a,V_n] :
% 162.26/162.03 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.03 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 162.26/162.03 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.03 => 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))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__conv__nth,axiom,
% 162.26/162.03 ! [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))))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_nth__Cons__number__of,axiom,
% 162.26/162.03 ! [V_xs,V_x,T_a,V_v] :
% 162.26/162.03 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.03 => 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 )
% 162.26/162.03 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.03 => 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))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__size__estimation,axiom,
% 162.26/162.03 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 162.26/162.03 => 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))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__size__estimation_H,axiom,
% 162.26/162.03 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 162.26/162.03 => 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))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__sublist,axiom,
% 162.26/162.03 ! [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))))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel__iff__nth,axiom,
% 162.26/162.03 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 <=> ( 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)
% 162.26/162.03 & ! [B_n] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 162.26/162.03 => 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)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lexord__take__index__conv,axiom,
% 162.26/162.03 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 <=> ( ( 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)))
% 162.26/162.03 & 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 )
% 162.26/162.03 | ? [B_i] :
% 162.26/162.03 ( 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))))
% 162.26/162.03 & hAPP(hAPP(c_List_Otake(T_a),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_a),B_i),V_y_2)
% 162.26/162.03 & 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)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_distinct__list__update,axiom,
% 162.26/162.03 ! [V_i_2,V_a_2,V_xs_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 162.26/162.03 => ( ~ 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))))))
% 162.26/162.03 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__update__id,axiom,
% 162.26/162.03 ! [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 ).
% 162.26/162.03
% 162.26/162.03 fof(fact_nth__list__update__neq,axiom,
% 162.26/162.03 ! [V_x,V_xs,T_a,V_j,V_i] :
% 162.26/162.03 ( V_i != V_j
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_nth__take,axiom,
% 162.26/162.03 ! [V_xs,T_a,V_n,V_i] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_take__all,axiom,
% 162.26/162.03 ! [V_n,V_xs,T_a] :
% 162.26/162.03 ( 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))
% 162.26/162.03 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__update__beyond,axiom,
% 162.26/162.03 ! [V_x,V_i,V_xs,T_a] :
% 162.26/162.03 ( 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))
% 162.26/162.03 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__take__subset,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_update__zip,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_take__zip,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_take__map,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__update,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__update__swap,axiom,
% 162.26/162.03 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 162.26/162.03 ( V_i != V_i_H
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__update__overwrite,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_take__take,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_distinct__take,axiom,
% 162.26/162.03 ! [V_i,V_xs,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 162.26/162.03 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_zip__update,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_length__take,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_length__list__update,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_sublist__upt__eq__take,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_in__set__takeD,axiom,
% 162.26/162.03 ! [V_xs_2,V_n_2,V_x_2,T_a] :
% 162.26/162.03 ( 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))))
% 162.26/162.03 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_take__Suc__Cons,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__update__code_I3_J,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__update_Osimps_I2_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__update__code_I2_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__take__subset__set__take,axiom,
% 162.26/162.03 ! [V_xs_2,T_a,V_n_2,V_m_2] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 162.26/162.03 => 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)))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__update__subsetI,axiom,
% 162.26/162.03 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_a] :
% 162.26/162.03 ( 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))
% 162.26/162.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__update__subset__insert,axiom,
% 162.26/162.03 ! [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)))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_nth__list__update__eq,axiom,
% 162.26/162.03 ! [V_x,V_xs,T_a,V_i] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => 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 ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__update__same__conv,axiom,
% 162.26/162.03 ! [V_x_2,V_xs_2,T_a,V_i_2] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 162.26/162.03 <=> hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_nth__list__update,axiom,
% 162.26/162.03 ! [V_x,V_j,V_xs,T_a,V_i] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => ( ( V_i = V_j
% 162.26/162.03 => 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 )
% 162.26/162.03 & ( V_i != V_j
% 162.26/162.03 => 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) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__update__memI,axiom,
% 162.26/162.03 ! [V_x_2,V_xs_2,T_a,V_n_2] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => 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)))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__upd__upds__conv__if,axiom,
% 162.26/162.03 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_b,V_x_2,T_a] :
% 162.26/162.03 ( ( 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))))
% 162.26/162.03 => 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) )
% 162.26/162.03 & ( ~ 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))))
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel__subset,axiom,
% 162.26/162.03 ! [V_A_2,V_r_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_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))))
% 162.26/162.03 => 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))))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__add__upds,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lists__mono,axiom,
% 162.26/162.03 ! [V_B_2,V_A_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__upds__apply__nontin,axiom,
% 162.26/162.03 ! [V_ys_2,V_f_2,T_b,V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lists__UNIV,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_equiv__listrel,axiom,
% 162.26/162.03 ! [V_r_2,V_A_2,T_a] :
% 162.26/162.03 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel__refl__on,axiom,
% 162.26/162.03 ! [V_r_2,V_A_2,T_a] :
% 162.26/162.03 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__upds__Cons,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Cons__in__lists__iff,axiom,
% 162.26/162.03 ! [V_A_2,V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.26/162.03 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_in__lists__conv__set,axiom,
% 162.26/162.03 ! [V_A_2,V_xs_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2)))
% 162.26/162.03 <=> ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__upds__list__update2__drop,axiom,
% 162.26/162.03 ! [V_y_2,V_m_2,V_ys_2,T_b,V_i_2,V_xs_2,T_a] :
% 162.26/162.03 ( 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))
% 162.26/162.03 => ( 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)))
% 162.26/162.03 => 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) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__upds__twist,axiom,
% 162.26/162.03 ! [V_bs_2,V_b_2,V_m_2,T_b,V_as_2,V_a_2,T_a] :
% 162.26/162.03 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_as_2)))
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lists__eq__set,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_restrict__map__upds,axiom,
% 162.26/162.03 ! [V_m_2,V_D_2,V_ys_2,T_b,V_xs_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => ( 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))
% 162.26/162.03 => 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) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_dom__map__upds,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel1__subset__listrel,axiom,
% 162.26/162.03 ! [V_r_H_2,V_r_2,T_a] :
% 162.26/162.03 ( 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))
% 162.26/162.03 => ( c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_r_H_2)
% 162.26/162.03 => 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))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lexord__irreflexive,axiom,
% 162.26/162.03 ! [V_y_2,V_r_2,T_a] :
% 162.26/162.03 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2))
% 162.26/162.03 => ~ 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Cons__acc__listrel1I,axiom,
% 162.26/162.03 ! [V_xs_2,V_r_2,V_x_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 162.26/162.03 => ( 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))))
% 162.26/162.03 => 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)))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel1__mono,axiom,
% 162.26/162.03 ! [V_s_2,V_r_2,T_a] :
% 162.26/162.03 ( 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))
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel1I2,axiom,
% 162.26/162.03 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel1__eq__len,axiom,
% 162.26/162.03 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lists__accI,axiom,
% 162.26/162.03 ! [V_r_2,V_xs_2,T_a] :
% 162.26/162.03 ( 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))))
% 162.26/162.03 => 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)))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lists__accD,axiom,
% 162.26/162.03 ! [V_r_2,V_xs_2,T_a] :
% 162.26/162.03 ( 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))))
% 162.26/162.03 => 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)))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel1I1,axiom,
% 162.26/162.03 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Cons__listrel1__Cons,axiom,
% 162.26/162.03 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 162.26/162.03 & V_xs_2 = V_ys_2 )
% 162.26/162.03 | ( V_x_2 = V_y_2
% 162.26/162.03 & 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))) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel1__iff__update,axiom,
% 162.26/162.03 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 <=> ? [B_y,B_n] :
% 162.26/162.03 ( 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))
% 162.26/162.03 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 162.26/162.03 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),B_n),B_y) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lexord__linear,axiom,
% 162.26/162.03 ! [V_y_2,V_x_2,V_r_2,T_a] :
% 162.26/162.03 ( ! [B_a,B_b] :
% 162.26/162.03 ( 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))
% 162.26/162.03 | B_a = B_b
% 162.26/162.03 | 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)) )
% 162.26/162.03 => ( 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)))
% 162.26/162.03 | V_x_2 = V_y_2
% 162.26/162.03 | 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))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listsum__setsum__nth,axiom,
% 162.26/162.03 ! [V_xs_2,T_a] :
% 162.26/162.03 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__size__pointwise,axiom,
% 162.26/162.03 ! [V_g_2,V_f_2,V_xs_2,T_a] :
% 162.26/162.03 ( ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 162.26/162.03 ! [V_ns_2] :
% 162.26/162.03 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.03 <=> ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 162.26/162.03 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listsum__simps_I2_J,axiom,
% 162.26/162.03 ! [V_xs,V_x,T_a] :
% 162.26/162.03 ( class_Groups_Omonoid__add(T_a)
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_elem__le__listsum__nat,axiom,
% 162.26/162.03 ! [V_ns,V_k] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listsum__0,axiom,
% 162.26/162.03 ! [V_xs_2,T_b,T_a] :
% 162.26/162.03 ( class_Groups_Omonoid__add(T_a)
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listsum__addf,axiom,
% 162.26/162.03 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listsum__mult__const,axiom,
% 162.26/162.03 ! [V_xs_2,V_ca_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( class_Rings_Osemiring__0(T_a)
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listsum__const__mult,axiom,
% 162.26/162.03 ! [V_xs_2,V_f_2,V_ca_2,T_b,T_a] :
% 162.26/162.03 ( class_Rings_Osemiring__0(T_a)
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listsum__subtractf,axiom,
% 162.26/162.03 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( class_Groups_Oab__group__add(T_a)
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listsum__update__nat,axiom,
% 162.26/162.03 ! [V_n,V_ns,V_k] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listsum__abs,axiom,
% 162.26/162.03 ! [V_xs_2,T_a] :
% 162.26/162.03 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 162.26/162.03 => 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)))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_uminus__listsum__map,axiom,
% 162.26/162.03 ! [V_xs_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( class_Groups_Oab__group__add(T_a)
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__size__conv__listsum,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 162.26/162.03 ! [V_xs_2,T_a] :
% 162.26/162.03 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.26/162.03 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 162.26/162.03 ! [V_f_2,V_xs_2,T_a,T_b] :
% 162.26/162.03 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.26/162.03 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 162.26/162.03 ! [V_l_2,V_k_2,V_f_2,T_a] :
% 162.26/162.03 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 162.26/162.03 ! [V_j_2,V_i_2,V_f_2,T_a] :
% 162.26/162.03 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listsum__triv,axiom,
% 162.26/162.03 ! [V_xs_2,V_r_2,T_b,T_a] :
% 162.26/162.03 ( class_Rings_Osemiring__1(T_a)
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listsum__map__remove1,axiom,
% 162.26/162.03 ! [V_f_2,V_xs_2,V_x_2,T_a,T_b] :
% 162.26/162.03 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.26/162.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => 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)))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 162.26/162.03 ! [V_f_2,V_A_2,T_a,T_b] :
% 162.26/162.03 ( class_Groups_Ocomm__monoid__add(T_b)
% 162.26/162.03 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => 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))))) )
% 162.26/162.03 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listsum__mono,axiom,
% 162.26/162.03 ! [V_g_2,V_f_2,V_xs_2,T_a,T_b] :
% 162.26/162.03 ( ( class_Groups_Omonoid__add(T_b)
% 162.26/162.03 & class_Groups_Oordered__ab__semigroup__add(T_b) )
% 162.26/162.03 => ( ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 162.26/162.03 => 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)))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_some__sym__eq__trivial,axiom,
% 162.26/162.03 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 162.26/162.03
% 162.26/162.03 fof(fact_some__eq__trivial,axiom,
% 162.26/162.03 ! [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 ).
% 162.26/162.03
% 162.26/162.03 fof(fact_some__eq__ex,axiom,
% 162.26/162.03 ! [T_a,V_P_2] :
% 162.26/162.03 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2)))
% 162.26/162.03 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_someI__ex,axiom,
% 162.26/162.03 ! [T_a,V_P_2] :
% 162.26/162.03 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 162.26/162.03 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_tfl__some,axiom,
% 162.26/162.03 ! [T_a,B_P] :
% 162.26/162.03 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 162.26/162.03 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_a,B_P))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_someI,axiom,
% 162.26/162.03 ! [T_a,V_x_2,V_P_2] :
% 162.26/162.03 ( hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.03 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_exE__some,axiom,
% 162.26/162.03 ! [T_a,V_ca_2,V_P_2] :
% 162.26/162.03 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 162.26/162.03 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_a,V_P_2)
% 162.26/162.03 => hBOOL(hAPP(V_P_2,V_ca_2)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Nitpick_Ocard_H__def,axiom,
% 162.26/162.03 ! [V_A_2,T_a] :
% 162.26/162.03 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => 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)))) )
% 162.26/162.03 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.03 => c_Nitpick_Ocard_H(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_LeastM__def,axiom,
% 162.26/162.03 ! [V_P_2,V_m_2,T_a,T_b] :
% 162.26/162.03 ( class_Orderings_Oord(T_b)
% 162.26/162.03 => 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))))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_LeastM__nat__lemma,axiom,
% 162.26/162.03 ! [V_m_2,T_a,V_k_2,V_P_2] :
% 162.26/162.03 ( hBOOL(hAPP(V_P_2,V_k_2))
% 162.26/162.03 => ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2)))
% 162.26/162.03 & ! [B_y] :
% 162.26/162.03 ( hBOOL(hAPP(V_P_2,B_y))
% 162.26/162.03 => 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))) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_LeastM__nat__le,axiom,
% 162.26/162.03 ! [T_a,V_m_2,V_x_2,V_P_2] :
% 162.26/162.03 ( hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_split__paired__Eps,axiom,
% 162.26/162.03 ! [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)))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Eps__split__eq,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Eps__split,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_GreatestM__def,axiom,
% 162.26/162.03 ! [V_P_2,V_m_2,T_a,T_b] :
% 162.26/162.03 ( class_Orderings_Oord(T_b)
% 162.26/162.03 => 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))))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_butlast__take,axiom,
% 162.26/162.03 ! [V_xs,T_a,V_n] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_LeastM__natI,axiom,
% 162.26/162.03 ! [V_m_2,T_a,V_k_2,V_P_2] :
% 162.26/162.03 ( hBOOL(hAPP(V_P_2,V_k_2))
% 162.26/162.03 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__butlast,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_in__set__butlastD,axiom,
% 162.26/162.03 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2))))
% 162.26/162.03 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_take__butlast,axiom,
% 162.26/162.03 ! [V_xs,T_a,V_n] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_length__butlast,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_butlast__conv__take,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_butlast__list__update,axiom,
% 162.26/162.03 ! [V_x,V_xs,T_a,V_k] :
% 162.26/162.03 ( ( 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))
% 162.26/162.03 => 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) )
% 162.26/162.03 & ( 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))
% 162.26/162.03 => 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) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Greatest__def,axiom,
% 162.26/162.03 ! [T_a] :
% 162.26/162.03 ( class_Orderings_Oord(T_a)
% 162.26/162.03 => c_Hilbert__Choice_OGreatest(T_a) = c_Hilbert__Choice_OGreatestM(T_a,T_a,c_COMBI(T_a)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_nth__take__lemma,axiom,
% 162.26/162.03 ! [V_ys,V_xs,T_a,V_k] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => ( 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)))
% 162.26/162.03 => ( ! [B_i] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 162.26/162.03 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 162.26/162.03 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_take__Cons__number__of,axiom,
% 162.26/162.03 ! [V_xs,V_x,T_a,V_v] :
% 162.26/162.03 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.03 => 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) )
% 162.26/162.03 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_partition__set,axiom,
% 162.26/162.03 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lists_ONil,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel__Nil2,axiom,
% 162.26/162.03 ! [V_r_2,V_xs_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel__Nil1,axiom,
% 162.26/162.03 ! [V_r_2,V_xs_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_sorted__list__of__set__empty,axiom,
% 162.26/162.03 ! [T_a] :
% 162.26/162.03 ( class_Orderings_Olinorder(T_a)
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list_Osimps_I2_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list_Osimps_I3_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_insort__key_Osimps_I1_J,axiom,
% 162.26/162.03 ! [V_x_2,V_f_2,T_a,T_b] :
% 162.26/162.03 ( class_Orderings_Olinorder(T_b)
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_sublist__nil,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_partition_Osimps_I1_J,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_distinct_Osimps_I1_J,axiom,
% 162.26/162.03 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of__Cons__code_I1_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_foldr_Osimps_I1_J,axiom,
% 162.26/162.03 ! [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 ).
% 162.26/162.03
% 162.26/162.03 fof(fact_upto__empty,axiom,
% 162.26/162.03 ! [V_i,V_j] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 162.26/162.03 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_remove1_Osimps_I1_J,axiom,
% 162.26/162.03 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_zip_Osimps_I1_J,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_zip__Nil,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_insort__not__Nil,axiom,
% 162.26/162.03 ! [V_xs_2,V_a_2,V_f_2,T_a,T_b] :
% 162.26/162.03 ( class_Orderings_Olinorder(T_b)
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrelp_ONil,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrelp_Oequations_I1_J,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list_Osize_I1_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__upds__Nil2,axiom,
% 162.26/162.03 ! [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 ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__upds__Nil1,axiom,
% 162.26/162.03 ! [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 ).
% 162.26/162.03
% 162.26/162.03 fof(fact_take__eq__Nil,axiom,
% 162.26/162.03 ! [V_xs_2,V_n_2,T_a] :
% 162.26/162.03 ( hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 162.26/162.03 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.03 | V_xs_2 = c_List_Olist_ONil(T_a) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_take__0,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_take__Nil,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__update__code_I1_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__update_Osimps_I1_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__update__nonempty,axiom,
% 162.26/162.03 ! [V_x_2,V_k_2,V_xs_2,T_a] :
% 162.26/162.03 ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_a)
% 162.26/162.03 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Nil__is__map__conv,axiom,
% 162.26/162.03 ! [V_xs_2,V_f_2,T_b,T_a] :
% 162.26/162.03 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)
% 162.26/162.03 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map_Osimps_I1_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__is__Nil__conv,axiom,
% 162.26/162.03 ! [V_xs_2,V_f_2,T_a,T_b] :
% 162.26/162.03 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 162.26/162.03 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_length__0__conv,axiom,
% 162.26/162.03 ! [V_xs_2,T_a] :
% 162.26/162.03 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.03 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list_Osize_I3_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__empty,axiom,
% 162.26/162.03 ! [V_xs_2,T_a] :
% 162.26/162.03 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.03 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__empty2,axiom,
% 162.26/162.03 ! [V_xs_2,T_a] :
% 162.26/162.03 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),V_xs_2)
% 162.26/162.03 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listsum__simps_I1_J,axiom,
% 162.26/162.03 ! [T_a] :
% 162.26/162.03 ( class_Groups_Omonoid__add(T_a)
% 162.26/162.03 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_butlast_Osimps_I1_J,axiom,
% 162.26/162.03 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_distinct__butlast,axiom,
% 162.26/162.03 ! [T_a,V_xs] :
% 162.26/162.03 ( V_xs != c_List_Olist_ONil(T_a)
% 162.26/162.03 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 162.26/162.03 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_butlast_Osimps_I2_J,axiom,
% 162.26/162.03 ! [V_x,T_a,V_xs] :
% 162.26/162.03 ( ( V_xs = c_List_Olist_ONil(T_a)
% 162.26/162.03 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 162.26/162.03 & ( V_xs != c_List_Olist_ONil(T_a)
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_sublist__empty,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of_Osimps_I1_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_length__greater__0__conv,axiom,
% 162.26/162.03 ! [V_xs_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 <=> V_xs_2 != c_List_Olist_ONil(T_a) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_take__1__Cons,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_not__listrel1__Nil,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_not__Nil__listrel1,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel_ONil,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lexord__Nil__right,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Nil__notin__lex,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Nil2__notin__lex,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_partition__P,axiom,
% 162.26/162.03 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => ( ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_yes_2)))
% 162.26/162.03 => hBOOL(hAPP(V_P_2,B_x)) )
% 162.26/162.03 & ! [B_x] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_no_2)))
% 162.26/162.03 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_take__Cons,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_upto_Osimps,axiom,
% 162.26/162.03 ! [V_j,V_i] :
% 162.26/162.03 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 162.26/162.03 => 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)) )
% 162.26/162.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 162.26/162.03 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_sublist__singleton,axiom,
% 162.26/162.03 ! [V_x_2,T_a,V_A_2] :
% 162.26/162.03 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 162.26/162.03 => 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)) )
% 162.26/162.03 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 162.26/162.03 => 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) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_partition_Osimps_I2_J,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lists__empty,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_take__Cons_H,axiom,
% 162.26/162.03 ! [V_xs,V_x,T_a,V_n] :
% 162.26/162.03 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.03 => 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) )
% 162.26/162.03 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_upto__rec__number__of,axiom,
% 162.26/162.03 ! [V_n,V_m] :
% 162.26/162.03 ( ( 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)))
% 162.26/162.03 => 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))) )
% 162.26/162.03 & ( ~ 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)))
% 162.26/162.03 => 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) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel__Nil,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__Cons__sing__Nil,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_upto_Opsimps,axiom,
% 162.26/162.03 ! [V_j_2,V_i_2] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 162.26/162.03 => 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)) )
% 162.26/162.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 162.26/162.03 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_anamorph_Osimps,axiom,
% 162.26/162.03 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] :
% 162.26/162.03 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 162.26/162.03 => 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) )
% 162.26/162.03 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listset_Osimps_I1_J,axiom,
% 162.26/162.03 ! [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))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_zip__Cons,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list_Osimps_I5_J,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list_Osimps_I4_J,axiom,
% 162.26/162.03 ! [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 ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listset_Osimps_I2_J,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_zip__Cons1,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_upto_Opinduct,axiom,
% 162.26/162.03 ! [V_P_2,V_a1_2,V_a0_2] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => ( ! [B_i,B_j] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 162.26/162.03 => 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)) )
% 162.26/162.03 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) )
% 162.26/162.03 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__upds__append1,axiom,
% 162.26/162.03 ! [V_x_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => 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)))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_append__eq__Cons__conv,axiom,
% 162.26/162.03 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a)
% 162.26/162.03 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) )
% 162.26/162.03 | ? [B_ys_H] :
% 162.26/162.03 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H)
% 162.26/162.03 & hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Cons__eq__append__conv,axiom,
% 162.26/162.03 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a)
% 162.26/162.03 & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2 )
% 162.26/162.03 | ? [B_ys_H] :
% 162.26/162.03 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2
% 162.26/162.03 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_append1__eq__conv,axiom,
% 162.26/162.03 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 <=> ( V_xs_2 = V_ys_2
% 162.26/162.03 & V_x_2 = V_y_2 ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_append__Nil,axiom,
% 162.26/162.03 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Nil__is__append__conv,axiom,
% 162.26/162.03 ! [V_ys_2,V_xs_2,T_a] :
% 162.26/162.03 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
% 162.26/162.03 <=> ( V_xs_2 = c_List_Olist_ONil(T_a)
% 162.26/162.03 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_append__Nil2,axiom,
% 162.26/162.03 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 162.26/162.03
% 162.26/162.03 fof(fact_self__append__conv,axiom,
% 162.26/162.03 ! [V_ys_2,T_a,V_xs_2] :
% 162.26/162.03 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
% 162.26/162.03 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_self__append__conv2,axiom,
% 162.26/162.03 ! [V_xs_2,T_a,V_ys_2] :
% 162.26/162.03 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
% 162.26/162.03 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_append__is__Nil__conv,axiom,
% 162.26/162.03 ! [V_ys_2,V_xs_2,T_a] :
% 162.26/162.03 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_a)
% 162.26/162.03 <=> ( V_xs_2 = c_List_Olist_ONil(T_a)
% 162.26/162.03 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_append__self__conv,axiom,
% 162.26/162.03 ! [V_ys_2,V_xs_2,T_a] :
% 162.26/162.03 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_xs_2
% 162.26/162.03 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_append__self__conv2,axiom,
% 162.26/162.03 ! [V_ys_2,V_xs_2,T_a] :
% 162.26/162.03 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_ys_2
% 162.26/162.03 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_eq__Nil__appendI,axiom,
% 162.26/162.03 ! [T_a,V_ys,V_xs] :
% 162.26/162.03 ( V_xs = V_ys
% 162.26/162.03 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_butlast__append,axiom,
% 162.26/162.03 ! [V_xs,T_a,V_ys] :
% 162.26/162.03 ( ( V_ys = c_List_Olist_ONil(T_a)
% 162.26/162.03 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 162.26/162.03 & ( V_ys != c_List_Olist_ONil(T_a)
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listsum__append,axiom,
% 162.26/162.03 ! [V_ys,V_xs,T_a] :
% 162.26/162.03 ( class_Groups_Omonoid__add(T_a)
% 162.26/162.03 => 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)) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_length__append,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_zip__append,axiom,
% 162.26/162.03 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => ( 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)
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_set__append,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__append,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_fun__upds__append2__drop,axiom,
% 162.26/162.03 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_fun__upds__append__drop,axiom,
% 162.26/162.03 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_append__in__lists__conv,axiom,
% 162.26/162.03 ! [V_A_2,V_ys_2,V_xs_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2)))
% 162.26/162.03 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_foldr__append,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_append__eq__appendI,axiom,
% 162.26/162.03 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 162.26/162.03 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 162.26/162.03 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 162.26/162.03 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_append__same__eq,axiom,
% 162.26/162.03 ! [V_zs_2,V_xs_2,V_ys_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 <=> V_ys_2 = V_zs_2 ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_same__append__eq,axiom,
% 162.26/162.03 ! [V_zs_2,V_ys_2,V_xs_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 <=> V_ys_2 = V_zs_2 ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_append__eq__append__conv2,axiom,
% 162.26/162.03 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a] :
% 162.26/162.03 ( 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)
% 162.26/162.03 <=> ? [B_us] :
% 162.26/162.03 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us)
% 162.26/162.03 & hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) = V_ts_2 )
% 162.26/162.03 | ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us) = V_zs_2
% 162.26/162.03 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_append__assoc,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_map__of__append,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_append__Cons,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_Cons__eq__appendI,axiom,
% 162.26/162.03 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 162.26/162.03 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 162.26/162.03 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 162.26/162.03 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_nth__append__length,axiom,
% 162.26/162.03 ! [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 ).
% 162.26/162.03
% 162.26/162.03 fof(fact_nth__append__length__plus,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_take__append,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__update__append1,axiom,
% 162.26/162.03 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => 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) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__update__length,axiom,
% 162.26/162.03 ! [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)) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_remove1__append,axiom,
% 162.26/162.03 ! [V_ys_2,V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => 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) )
% 162.26/162.03 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_in__set__butlast__appendI,axiom,
% 162.26/162.03 ! [V_ys_2,V_xs_2,V_x_2,T_a] :
% 162.26/162.03 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2))))
% 162.26/162.03 | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_ys_2)))) )
% 162.26/162.03 => 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))))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_butlast__snoc,axiom,
% 162.26/162.03 ! [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 ).
% 162.26/162.03
% 162.26/162.03 fof(fact_append__listrel1I,axiom,
% 162.26/162.03 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 162.26/162.03 ( ( ( 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)))
% 162.26/162.03 & V_us_2 = V_vs_2 )
% 162.26/162.03 | ( V_xs_2 = V_ys_2
% 162.26/162.03 & 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))) ) )
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lexord__append__leftI,axiom,
% 162.26/162.03 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_distinct__append,axiom,
% 162.26/162.03 ! [V_ys_2,V_xs_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)))
% 162.26/162.03 <=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 162.26/162.03 & hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2))
% 162.26/162.03 & 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_nth__append,axiom,
% 162.26/162.03 ! [V_ys,V_xs,T_a,V_n] :
% 162.26/162.03 ( ( 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)))
% 162.26/162.03 => 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) )
% 162.26/162.03 & ( ~ 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)))
% 162.26/162.03 => 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))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_list__update__append,axiom,
% 162.26/162.03 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 162.26/162.03 ( ( 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)))
% 162.26/162.03 => 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) )
% 162.26/162.03 & ( ~ 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)))
% 162.26/162.03 => 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)) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_sublist__append,axiom,
% 162.26/162.03 ! [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)))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel1I,axiom,
% 162.26/162.03 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 162.26/162.03 => ( 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))
% 162.26/162.03 => ( 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))
% 162.26/162.03 => 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))) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lexord__append__left__rightI,axiom,
% 162.26/162.03 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_a] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_take__Suc__conv__app__nth,axiom,
% 162.26/162.03 ! [V_xs,T_a,V_i] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => 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))) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 162.26/162.03 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 <=> ( ( 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)))
% 162.26/162.03 & V_x_2 = V_y_2 )
% 162.26/162.03 | ( V_xs_2 = V_ys_2
% 162.26/162.03 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_sublist__Cons,axiom,
% 162.26/162.03 ! [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)))) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_listrel1E,axiom,
% 162.26/162.03 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => ~ ! [B_x,B_y] :
% 162.26/162.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2))
% 162.26/162.03 => ! [B_us,B_vs] :
% 162.26/162.03 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_vs))
% 162.26/162.03 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_vs)) ) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_lexord__append__leftD,axiom,
% 162.26/162.03 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_a] :
% 162.26/162.03 ( 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)))
% 162.26/162.03 => ( ! [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))
% 162.26/162.03 => 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))) ) ) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_rotate1__def,axiom,
% 162.26/162.03 ! [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) ).
% 162.26/162.03
% 162.26/162.03 fof(fact_upd__conv__take__nth__drop,axiom,
% 162.26/162.03 ! [V_a,V_xs,T_a,V_i] :
% 162.26/162.03 ( 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)))
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_append__take__drop__id,axiom,
% 162.26/162.04 ! [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 ).
% 162.26/162.04
% 162.26/162.04 fof(fact_drop__Nil,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rotate1__is__Nil__conv,axiom,
% 162.26/162.04 ! [V_xs_2,T_a] :
% 162.26/162.04 ( hAPP(c_List_Orotate1(T_a),V_xs_2) = c_List_Olist_ONil(T_a)
% 162.26/162.04 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_butlast__drop,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_drop__butlast,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_set__drop__subset,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_in__set__dropD,axiom,
% 162.26/162.04 ! [V_xs_2,V_n_2,V_x_2,T_a] :
% 162.26/162.04 ( 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))))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__drop,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__rotate1,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_set__rotate1,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_drop__map,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_take__drop,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_drop__take,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_drop__zip,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_drop__drop,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_drop__0,axiom,
% 162.26/162.04 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 162.26/162.04
% 162.26/162.04 fof(fact_distinct1__rotate,axiom,
% 162.26/162.04 ! [V_xs_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2)))
% 162.26/162.04 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_distinct__drop,axiom,
% 162.26/162.04 ! [V_i,V_xs,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 162.26/162.04 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_nth__via__drop,axiom,
% 162.26/162.04 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 162.26/162.04 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 162.26/162.04 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_drop__1__Cons,axiom,
% 162.26/162.04 ! [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 ).
% 162.26/162.04
% 162.26/162.04 fof(fact_drop__Suc__Cons,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_set__drop__subset__set__drop,axiom,
% 162.26/162.04 ! [V_xs_2,T_a,V_m_2,V_n_2] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 162.26/162.04 => 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)))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_drop__eq__Nil,axiom,
% 162.26/162.04 ! [V_xs_2,V_n_2,T_a] :
% 162.26/162.04 ( hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 162.26/162.04 <=> 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_drop__all,axiom,
% 162.26/162.04 ! [V_n,V_xs,T_a] :
% 162.26/162.04 ( 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))
% 162.26/162.04 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_drop__append,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_append__eq__conv__conj,axiom,
% 162.26/162.04 ! [V_zs_2,V_ys_2,V_xs_2,T_a] :
% 162.26/162.04 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_zs_2
% 162.26/162.04 <=> ( 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)
% 162.26/162.04 & 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) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_drop__Cons,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_drop__Cons_H,axiom,
% 162.26/162.04 ! [V_xs,V_x,T_a,V_n] :
% 162.26/162.04 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.04 => 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) )
% 162.26/162.04 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.04 => 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) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_nth__drop,axiom,
% 162.26/162.04 ! [V_xs,T_a,V_i,V_n] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_append__eq__append__conv__if,axiom,
% 162.26/162.04 ! [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] :
% 162.26/162.04 ( 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)
% 162.26/162.04 <=> ( ( 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)))
% 162.26/162.04 => ( 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)
% 162.26/162.04 & 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) ) )
% 162.26/162.04 & ( ~ 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)))
% 162.26/162.04 => ( 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
% 162.26/162.04 & 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 ) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_nth__drop_H,axiom,
% 162.26/162.04 ! [V_xs,T_a,V_i] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rotate__simps,axiom,
% 162.26/162.04 ! [V_xs,V_x,T_b,T_a] :
% 162.26/162.04 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 162.26/162.04 & 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_drop__Cons__number__of,axiom,
% 162.26/162.04 ! [V_xs,V_x,T_a,V_v] :
% 162.26/162.04 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.04 => 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) )
% 162.26/162.04 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.04 => 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) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_take__add,axiom,
% 162.26/162.04 ! [V_xs,T_a,V_j,V_i] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rotate1__length01,axiom,
% 162.26/162.04 ! [V_xs,T_a] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_zip__append2,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_zip__append1,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_id__take__nth__drop,axiom,
% 162.26/162.04 ! [V_xs,T_a,V_i] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_take__hd__drop,axiom,
% 162.26/162.04 ! [V_xs,T_a,V_n] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_hd__drop__conv__nth,axiom,
% 162.26/162.04 ! [V_n,T_a,V_xs] :
% 162.26/162.04 ( V_xs != c_List_Olist_ONil(T_a)
% 162.26/162.04 => ( 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)))
% 162.26/162.04 => 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) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_hd_Osimps,axiom,
% 162.26/162.04 ! [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 ).
% 162.26/162.04
% 162.26/162.04 fof(fact_hd__map,axiom,
% 162.26/162.04 ! [V_f_2,T_b,T_a,V_xs_2] :
% 162.26/162.04 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_hd__append2,axiom,
% 162.26/162.04 ! [V_ys,T_a,V_xs] :
% 162.26/162.04 ( V_xs != c_List_Olist_ONil(T_a)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_hd__append,axiom,
% 162.26/162.04 ! [V_ys,T_a,V_xs] :
% 162.26/162.04 ( ( V_xs = c_List_Olist_ONil(T_a)
% 162.26/162.04 => 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) )
% 162.26/162.04 & ( V_xs != c_List_Olist_ONil(T_a)
% 162.26/162.04 => 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) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_hd__in__set,axiom,
% 162.26/162.04 ! [T_a,V_xs_2] :
% 162.26/162.04 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_hd__conv__nth,axiom,
% 162.26/162.04 ! [T_a,V_xs] :
% 162.26/162.04 ( V_xs != c_List_Olist_ONil(T_a)
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rotate1__hd__tl,axiom,
% 162.26/162.04 ! [T_a,V_xs] :
% 162.26/162.04 ( V_xs != c_List_Olist_ONil(T_a)
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_hd__rotate__conv__nth,axiom,
% 162.26/162.04 ! [V_n,T_a,V_xs] :
% 162.26/162.04 ( V_xs != c_List_Olist_ONil(T_a)
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_drop__tl,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_tl__drop,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_tl_Osimps_I1_J,axiom,
% 162.26/162.04 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rotate__is__Nil__conv,axiom,
% 162.26/162.04 ! [V_xs_2,V_n_2,T_a] :
% 162.26/162.04 ( hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 162.26/162.04 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__rotate,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_set__rotate,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rotate__map,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_map__tl,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rotate__rotate,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_distinct__rotate,axiom,
% 162.26/162.04 ! [V_xs_2,V_n_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2)))
% 162.26/162.04 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_distinct__tl,axiom,
% 162.26/162.04 ! [V_xs,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 162.26/162.04 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_tl_Osimps_I2_J,axiom,
% 162.26/162.04 ! [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 ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rotate1__rotate__swap,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_tl__append2,axiom,
% 162.26/162.04 ! [V_ys,T_a,V_xs] :
% 162.26/162.04 ( V_xs != c_List_Olist_ONil(T_a)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_take__tl,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rotate__conv__mod,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_drop__Suc,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rotate__Suc,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_tl__append,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rotate0,axiom,
% 162.26/162.04 ! [T_a] : c_List_Orotate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_a)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rotate__add,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rotate__id,axiom,
% 162.26/162.04 ! [V_xs,T_a,V_n] :
% 162.26/162.04 ( 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)
% 162.26/162.04 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rotate__length01,axiom,
% 162.26/162.04 ! [V_n,V_xs,T_a] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__tl,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_tl__take,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_take__Suc,axiom,
% 162.26/162.04 ! [V_n,T_a,V_xs] :
% 162.26/162.04 ( V_xs != c_List_Olist_ONil(T_a)
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rotate__drop__take,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_fold1__set,axiom,
% 162.26/162.04 ! [V_xs_2,T_a] :
% 162.26/162.04 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 162.26/162.04 => ( V_xs_2 != c_List_Olist_ONil(T_a)
% 162.26/162.04 => 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)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_lexord__append__rightI,axiom,
% 162.26/162.04 ! [V_r_2,V_x_2,T_a,V_y_2] :
% 162.26/162.04 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_b),B_z)
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_foldl__Cons,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_start__le__sum,axiom,
% 162.26/162.04 ! [V_ns_2,V_n_2,V_m_2] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_foldl__absorb0,axiom,
% 162.26/162.04 ! [V_zs_2,V_x_2,T_a] :
% 162.26/162.04 ( class_Groups_Omonoid__add(T_a)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_foldl__assoc,axiom,
% 162.26/162.04 ! [V_zs_2,V_y_2,V_x_2,T_a] :
% 162.26/162.04 ( class_Groups_Osemigroup__add(T_a)
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_foldr__conv__foldl,axiom,
% 162.26/162.04 ! [V_a_2,V_xs_2,T_a] :
% 162.26/162.04 ( class_Groups_Oab__semigroup__add(T_a)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_foldl__map,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_foldl__Nil,axiom,
% 162.26/162.04 ! [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 ).
% 162.26/162.04
% 162.26/162.04 fof(fact_foldl__append,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_listsum__foldl,axiom,
% 162.26/162.04 ! [T_a] :
% 162.26/162.04 ( class_Groups_Omonoid__add(T_a)
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_foldl__foldr1,axiom,
% 162.26/162.04 ! [V_xs_2,T_a] :
% 162.26/162.04 ( class_Groups_Omonoid__add(T_a)
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_foldl__foldr1__lemma,axiom,
% 162.26/162.04 ! [V_xs_2,V_a_2,T_a] :
% 162.26/162.04 ( class_Groups_Omonoid__add(T_a)
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sum__eq__0__conv,axiom,
% 162.26/162.04 ! [V_ns_2,V_m_2] :
% 162.26/162.04 ( 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)
% 162.26/162.04 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.04 & ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 162.26/162.04 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 162.26/162.04 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] :
% 162.26/162.04 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_Sup__set__fold,axiom,
% 162.26/162.04 ! [V_xs_2,T_a] :
% 162.26/162.04 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_Inf__set__fold,axiom,
% 162.26/162.04 ! [V_xs_2,T_a] :
% 162.26/162.04 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_Sup__fin__set__fold,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.04 ( class_Lattices_Olattice(T_a)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_Inf__fin__set__fold,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.04 ( class_Lattices_Olattice(T_a)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_Min__fin__set__fold,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_Max__fin__set__fold,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_SUPR__set__fold,axiom,
% 162.26/162.04 ! [V_f_2,V_xs_2,T_b,T_a] :
% 162.26/162.04 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_INFI__set__fold,axiom,
% 162.26/162.04 ! [V_f_2,V_xs_2,T_b,T_a] :
% 162.26/162.04 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_map__upds__fold__map__upd,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_elem__le__sum,axiom,
% 162.26/162.04 ! [V_ns_2,V_n_2] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_lexord__Nil__left,axiom,
% 162.26/162.04 ! [V_r_2,V_y_2,T_a] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_last__list__update,axiom,
% 162.26/162.04 ! [V_x,V_k,T_a,V_xs] :
% 162.26/162.04 ( V_xs != c_List_Olist_ONil(T_a)
% 162.26/162.04 => ( ( 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))
% 162.26/162.04 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 162.26/162.04 & ( 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))
% 162.26/162.04 => 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) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_last__appendL,axiom,
% 162.26/162.04 ! [V_xs,T_a,V_ys] :
% 162.26/162.04 ( V_ys = c_List_Olist_ONil(T_a)
% 162.26/162.04 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_last__appendR,axiom,
% 162.26/162.04 ! [V_xs,T_a,V_ys] :
% 162.26/162.04 ( V_ys != c_List_Olist_ONil(T_a)
% 162.26/162.04 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_last__append,axiom,
% 162.26/162.04 ! [V_xs,T_a,V_ys] :
% 162.26/162.04 ( ( V_ys = c_List_Olist_ONil(T_a)
% 162.26/162.04 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 162.26/162.04 & ( V_ys != c_List_Olist_ONil(T_a)
% 162.26/162.04 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_last_Osimps,axiom,
% 162.26/162.04 ! [V_x,T_a,V_xs] :
% 162.26/162.04 ( ( V_xs = c_List_Olist_ONil(T_a)
% 162.26/162.04 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 162.26/162.04 & ( V_xs != c_List_Olist_ONil(T_a)
% 162.26/162.04 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_last__ConsR,axiom,
% 162.26/162.04 ! [V_x,T_a,V_xs] :
% 162.26/162.04 ( V_xs != c_List_Olist_ONil(T_a)
% 162.26/162.04 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_last__ConsL,axiom,
% 162.26/162.04 ! [V_x,T_a,V_xs] :
% 162.26/162.04 ( V_xs = c_List_Olist_ONil(T_a)
% 162.26/162.04 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_last__map,axiom,
% 162.26/162.04 ! [V_f_2,T_b,T_a,V_xs_2] :
% 162.26/162.04 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_last__in__set,axiom,
% 162.26/162.04 ! [T_a,V_as_2] :
% 162.26/162.04 ( V_as_2 != c_List_Olist_ONil(T_a)
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_member(T_a),c_List_Olast(T_a,V_as_2)),hAPP(c_List_Oset(T_a),V_as_2))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_last__snoc,axiom,
% 162.26/162.04 ! [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 ).
% 162.26/162.04
% 162.26/162.04 fof(fact_last__drop,axiom,
% 162.26/162.04 ! [V_xs,T_a,V_n] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_append__butlast__last__id,axiom,
% 162.26/162.04 ! [T_a,V_xs] :
% 162.26/162.04 ( V_xs != c_List_Olist_ONil(T_a)
% 162.26/162.04 => 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 ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_snoc__eq__iff__butlast,axiom,
% 162.26/162.04 ! [V_ys_2,V_x_2,V_xs_2,T_a] :
% 162.26/162.04 ( 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
% 162.26/162.04 <=> ( V_ys_2 != c_List_Olist_ONil(T_a)
% 162.26/162.04 & c_List_Obutlast(T_a,V_ys_2) = V_xs_2
% 162.26/162.04 & c_List_Olast(T_a,V_ys_2) = V_x_2 ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_last__conv__nth,axiom,
% 162.26/162.04 ! [T_a,V_xs] :
% 162.26/162.04 ( V_xs != c_List_Olist_ONil(T_a)
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_lists_Osimps,axiom,
% 162.26/162.04 ! [V_A_2,V_a_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_a_2),c_List_Olists(T_a,V_A_2)))
% 162.26/162.04 <=> ( V_a_2 = c_List_Olist_ONil(T_a)
% 162.26/162.04 | ? [B_a,B_l] :
% 162.26/162.04 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l)
% 162.26/162.04 & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 162.26/162.04 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2))) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_transpose__aux__max,axiom,
% 162.26/162.04 ! [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)))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_filter_Osimps_I2_J,axiom,
% 162.26/162.04 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 162.26/162.04 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.04 => 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)) )
% 162.26/162.04 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.04 => 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) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_distinct__filter,axiom,
% 162.26/162.04 ! [V_P_2,V_xs_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 162.26/162.04 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_filter__filter,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_remove1__filter__not,axiom,
% 162.26/162.04 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 162.26/162.04 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_filter__remove1,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_filter__insort__triv,axiom,
% 162.26/162.04 ! [V_xs_2,V_f_2,T_a,V_x_2,V_P_2,T_b] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_b)
% 162.26/162.04 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.04 => 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) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_filter__id__conv,axiom,
% 162.26/162.04 ! [V_xs_2,V_P_2,T_a] :
% 162.26/162.04 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = V_xs_2
% 162.26/162.04 <=> ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sum__length__filter__compl,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_filter__map,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_filter__is__subset,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__filter__le,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_partition__filter1,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_filter__empty__conv,axiom,
% 162.26/162.04 ! [V_xs_2,V_P_2,T_a] :
% 162.26/162.04 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 162.26/162.04 <=> ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_filter_Osimps_I1_J,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_filter__append,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_partition__filter2,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_set__filter,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__filter__map,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__filter__less,axiom,
% 162.26/162.04 ! [V_P_2,V_xs_2,V_x_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.04 => 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_partition__filter__conv,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_set__minus__filter__out,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_filter__in__sublist,axiom,
% 162.26/162.04 ! [V_s_2,V_xs_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__filter__conv__card,axiom,
% 162.26/162.04 ! [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))))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_map__filter__def,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_transpose__max__length,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_transpose_Osimps_I1_J,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_map__filter__simps_I2_J,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_transpose__empty,axiom,
% 162.26/162.04 ! [V_xs_2,T_a] :
% 162.26/162.04 ( c_List_Otranspose(T_a,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_a))
% 162.26/162.04 <=> ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 162.26/162.04 => B_x = c_List_Olist_ONil(T_a) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_transpose__map__map,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_transpose_Osimps_I2_J,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_map__of__filter__in,axiom,
% 162.26/162.04 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_a,T_b] :
% 162.26/162.04 ( 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)
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2))
% 162.26/162.04 => 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) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_map__filter__simps_I1_J,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sublist__shift__lemma__Suc,axiom,
% 162.26/162.04 ! [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)))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_nth__transpose,axiom,
% 162.26/162.04 ! [V_xs_2,T_a,V_i_2] :
% 162.26/162.04 ( 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))))
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__transpose,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_map__filter__map__filter,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_insort__key__remove1,axiom,
% 162.26/162.04 ! [V_f_2,V_xs_2,V_a_2,T_a,T_b] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_b)
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))
% 162.26/162.04 => ( 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
% 162.26/162.04 => 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 ) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sublist__def,axiom,
% 162.26/162.04 ! [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))))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted_ONil,axiom,
% 162.26/162.04 ! [T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__single,axiom,
% 162.26/162.04 ! [V_x,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__same,axiom,
% 162.26/162.04 ! [V_xs_2,V_g_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__map__same,axiom,
% 162.26/162.04 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__filter,axiom,
% 162.26/162.04 ! [V_P_2,V_xs_2,V_f_2,T_b,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 162.26/162.04 => 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__tl,axiom,
% 162.26/162.04 ! [V_xs,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 162.26/162.04 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_upt__rec,axiom,
% 162.26/162.04 ! [V_j,V_i] :
% 162.26/162.04 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 162.26/162.04 => 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)) )
% 162.26/162.04 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 162.26/162.04 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__many__eq,axiom,
% 162.26/162.04 ! [V_zs_2,V_y_2,V_x_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( 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)))
% 162.26/162.04 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 162.26/162.04 & c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__many,axiom,
% 162.26/162.04 ! [V_zs,V_y,V_x,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 162.26/162.04 => 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))) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_upt__conv__Cons,axiom,
% 162.26/162.04 ! [V_j,V_i] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_take__upt,axiom,
% 162.26/162.04 ! [V_n,V_m,V_i] :
% 162.26/162.04 ( 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))
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__insort__insert,axiom,
% 162.26/162.04 ! [V_x_2,V_xs_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 162.26/162.04 => 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)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_distinct__upt,axiom,
% 162.26/162.04 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__list__of__set__range,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__upto,axiom,
% 162.26/162.04 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__upt,axiom,
% 162.26/162.04 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__remove1,axiom,
% 162.26/162.04 ! [V_a,V_xs,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 162.26/162.04 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__insort,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( 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))
% 162.26/162.04 <=> c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__take,axiom,
% 162.26/162.04 ! [V_n,V_xs,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 162.26/162.04 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__insort__key,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( 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)))
% 162.26/162.04 <=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__map__remove1,axiom,
% 162.26/162.04 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 162.26/162.04 => 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_map__Suc__upt,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__distinct__set__unique,axiom,
% 162.26/162.04 ! [V_ys_2,V_xs_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 162.26/162.04 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,V_ys_2)
% 162.26/162.04 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2))
% 162.26/162.04 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2)
% 162.26/162.04 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__butlast,axiom,
% 162.26/162.04 ! [V_xs,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( V_xs != c_List_Olist_ONil(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 162.26/162.04 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted_Oequations_I1_J,axiom,
% 162.26/162.04 ! [T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_upt__0,axiom,
% 162.26/162.04 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_upt__eq__Nil__conv,axiom,
% 162.26/162.04 ! [V_j_2,V_i_2] :
% 162.26/162.04 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 162.26/162.04 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.04 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_upt__conv__Nil,axiom,
% 162.26/162.04 ! [V_i,V_j] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 162.26/162.04 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__insort__insert__key,axiom,
% 162.26/162.04 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 162.26/162.04 => 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_upt__add__eq__append,axiom,
% 162.26/162.04 ! [V_k,V_j,V_i] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_upt__Suc,axiom,
% 162.26/162.04 ! [V_j,V_i] :
% 162.26/162.04 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 162.26/162.04 => 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))) )
% 162.26/162.04 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 162.26/162.04 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_upt__Suc__append,axiom,
% 162.26/162.04 ! [V_j,V_i] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_atLeastLessThan__upt,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_set__upt,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_hd__upt,axiom,
% 162.26/162.04 ! [V_j,V_i] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 162.26/162.04 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__drop,axiom,
% 162.26/162.04 ! [V_n,V_xs,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 162.26/162.04 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_drop__upt,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__upt,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__Cons,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
% 162.26/162.04 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 162.26/162.04 & ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__append,axiom,
% 162.26/162.04 ! [V_ys_2,V_xs_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
% 162.26/162.04 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 162.26/162.04 & c_List_Olinorder__class_Osorted(T_a,V_ys_2)
% 162.26/162.04 & ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => ! [B_xa] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),V_ys_2)))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) ) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_upt__rec__number__of,axiom,
% 162.26/162.04 ! [V_n,V_m] :
% 162.26/162.04 ( ( 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)))
% 162.26/162.04 => 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))) )
% 162.26/162.04 & ( ~ 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)))
% 162.26/162.04 => 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) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_upt__eq__Cons__conv,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 162.26/162.04 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 162.26/162.04 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 162.26/162.04 & V_i_2 = V_x_2
% 162.26/162.04 & 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 ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_last__upt,axiom,
% 162.26/162.04 ! [V_j,V_i] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_filter__insort,axiom,
% 162.26/162.04 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_b,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 162.26/162.04 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.04 => 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)) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_map__nth,axiom,
% 162.26/162.04 ! [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 ).
% 162.26/162.04
% 162.26/162.04 fof(fact_atLeastAtMost__upt,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_atLeast__upt,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 162.26/162.04 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 162.26/162.04 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 162.26/162.04 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 162.26/162.04 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_nth__upt,axiom,
% 162.26/162.04 ! [V_j,V_k,V_i] :
% 162.26/162.04 ( 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))
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_greaterThanAtMost__upt,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted_Oequations_I2_J,axiom,
% 162.26/162.04 ! [V_a1_2,V_a2_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a1_2))
% 162.26/162.04 <=> ( ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_a1_2)))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a2_2),B_x)) )
% 162.26/162.04 & c_List_Olinorder__class_Osorted(T_a,V_a1_2) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_greaterThanLessThan__upt,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_nth__map__upt,axiom,
% 162.26/162.04 ! [V_f_2,T_a,V_m_2,V_n_2,V_i_2] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__list__of__set,axiom,
% 162.26/162.04 ! [V_A_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.04 => ( hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) = V_A_2
% 162.26/162.04 & c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))
% 162.26/162.04 & hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_atMost__upto,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_insort__remove1,axiom,
% 162.26/162.04 ! [V_xs_2,V_a_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 162.26/162.04 => 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 ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__equals__nth__mono,axiom,
% 162.26/162.04 ! [V_xs_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 162.26/162.04 <=> ! [B_j] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => ! [B_i] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 162.26/162.04 => 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))) ) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__nth__mono,axiom,
% 162.26/162.04 ! [V_j,V_i,V_xs,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 162.26/162.04 => ( 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)))
% 162.26/162.04 => 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))) ) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_map__sorted__distinct__set__unique,axiom,
% 162.26/162.04 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_b)
% 162.26/162.04 => ( 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)))
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))
% 162.26/162.04 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)))
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2))
% 162.26/162.04 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)))
% 162.26/162.04 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2)
% 162.26/162.04 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sublist__shift__lemma,axiom,
% 162.26/162.04 ! [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))))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_transpose__rectangle,axiom,
% 162.26/162.04 ! [V_n_2,T_a,V_xs_2] :
% 162.26/162.04 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a))
% 162.26/162.04 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 162.26/162.04 => ( ! [B_i] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => 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 )
% 162.26/162.04 => 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)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_transpose_Opsimps_I2_J,axiom,
% 162.26/162.04 ! [V_xss_2,T_a] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_transpose_Opsimps_I1_J,axiom,
% 162.26/162.04 ! [T_a] :
% 162.26/162.04 ( 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))))
% 162.26/162.04 => c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_transpose__column,axiom,
% 162.26/162.04 ! [V_i_2,V_xs_2,T_a] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => ( 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)))
% 162.26/162.04 => 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) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_transpose__aux__filter__head,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_inj__on__rev,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rev__foldl__cons,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_concat__conv__foldl,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rev__singleton__conv,axiom,
% 162.26/162.04 ! [V_x_2,V_xs_2,T_a] :
% 162.26/162.04 ( 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))
% 162.26/162.04 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_singleton__rev__conv,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.04 ( 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)
% 162.26/162.04 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rev__concat,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rev__map,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rev__is__Nil__conv,axiom,
% 162.26/162.04 ! [V_xs_2,T_a] :
% 162.26/162.04 ( hAPP(c_List_Orev(T_a),V_xs_2) = c_List_Olist_ONil(T_a)
% 162.26/162.04 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_Nil__is__rev__conv,axiom,
% 162.26/162.04 ! [V_xs_2,T_a] :
% 162.26/162.04 ( c_List_Olist_ONil(T_a) = hAPP(c_List_Orev(T_a),V_xs_2)
% 162.26/162.04 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rev_Osimps_I1_J,axiom,
% 162.26/162.04 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_concat__append,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rev__append,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_distinct__rev,axiom,
% 162.26/162.04 ! [V_xs_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orev(T_a),V_xs_2)))
% 162.26/162.04 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_foldl__conv__concat,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_foldl__foldr,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_foldr__foldl,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_concat_Osimps_I1_J,axiom,
% 162.26/162.04 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__rev,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rev__rev__ident,axiom,
% 162.26/162.04 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rev__swap,axiom,
% 162.26/162.04 ! [V_ys_2,V_xs_2,T_a] :
% 162.26/162.04 ( hAPP(c_List_Orev(T_a),V_xs_2) = V_ys_2
% 162.26/162.04 <=> V_xs_2 = hAPP(c_List_Orev(T_a),V_ys_2) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rev__is__rev__conv,axiom,
% 162.26/162.04 ! [V_ys_2,V_xs_2,T_a] :
% 162.26/162.04 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Orev(T_a),V_ys_2)
% 162.26/162.04 <=> V_xs_2 = V_ys_2 ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_listsum__rev,axiom,
% 162.26/162.04 ! [V_xs,T_a] :
% 162.26/162.04 ( class_Groups_Ocomm__monoid__add(T_a)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_set__rev,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_zip__rev,axiom,
% 162.26/162.04 ! [V_ys,T_b,V_xs,T_a] :
% 162.26/162.04 ( 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)
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rev__filter,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_concat_Osimps_I2_J,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_concat__eq__Nil__conv,axiom,
% 162.26/162.04 ! [V_xss_2,T_a] :
% 162.26/162.04 ( c_List_Oconcat(T_a,V_xss_2) = c_List_Olist_ONil(T_a)
% 162.26/162.04 <=> ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)))
% 162.26/162.04 => B_x = c_List_Olist_ONil(T_a) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_Nil__eq__concat__conv,axiom,
% 162.26/162.04 ! [V_xss_2,T_a] :
% 162.26/162.04 ( c_List_Olist_ONil(T_a) = c_List_Oconcat(T_a,V_xss_2)
% 162.26/162.04 <=> ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)))
% 162.26/162.04 => B_x = c_List_Olist_ONil(T_a) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_map__concat,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_filter__concat,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rev__eq__Cons__iff,axiom,
% 162.26/162.04 ! [V_ys_2,V_y_2,V_xs_2,T_a] :
% 162.26/162.04 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)
% 162.26/162.04 <=> 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rev_Osimps_I2_J,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__concat,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_set__concat,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_hd__rev,axiom,
% 162.26/162.04 ! [T_a,V_xs] :
% 162.26/162.04 ( V_xs != c_List_Olist_ONil(T_a)
% 162.26/162.04 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_last__rev,axiom,
% 162.26/162.04 ! [T_a,V_xs] :
% 162.26/162.04 ( V_xs != c_List_Olist_ONil(T_a)
% 162.26/162.04 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__transpose,axiom,
% 162.26/162.04 ! [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)))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rev__drop,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rev__take,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rotate__rev,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_transpose_Osimps_I3_J,axiom,
% 162.26/162.04 ! [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))))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rev__nth,axiom,
% 162.26/162.04 ! [V_xs,T_a,V_n] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_concat__injective,axiom,
% 162.26/162.04 ! [V_ys_2,V_xs_2,T_a] :
% 162.26/162.04 ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2)
% 162.26/162.04 => ( 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)
% 162.26/162.04 => ( ! [B_x] :
% 162.26/162.04 ( 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))))
% 162.26/162.04 => 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)) )
% 162.26/162.04 => V_xs_2 = V_ys_2 ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_concat__eq__concat__iff,axiom,
% 162.26/162.04 ! [V_ys_2,V_xs_2,T_a] :
% 162.26/162.04 ( ! [B_x] :
% 162.26/162.04 ( 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))))
% 162.26/162.04 => 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)) )
% 162.26/162.04 => ( 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)
% 162.26/162.04 => ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2)
% 162.26/162.04 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rev__update,axiom,
% 162.26/162.04 ! [V_y,V_xs,T_a,V_k] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_concat__map__singleton,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__rev__nth__mono,axiom,
% 162.26/162.04 ! [V_j,V_i,V_xs,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 162.26/162.04 => ( 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)))
% 162.26/162.04 => 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))) ) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_foldr__max__sorted,axiom,
% 162.26/162.04 ! [V_y_2,V_xs_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs_2))
% 162.26/162.04 => ( ( V_xs_2 = c_List_Olist_ONil(T_a)
% 162.26/162.04 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = V_y_2 )
% 162.26/162.04 & ( V_xs_2 != c_List_Olist_ONil(T_a)
% 162.26/162.04 => 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) ) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_transpose_Opsimps_I3_J,axiom,
% 162.26/162.04 ! [V_xss_2,V_xs_2,V_x_2,T_a] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => 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))))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__transpose__sorted,axiom,
% 162.26/162.04 ! [V_xs_2,T_a] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a))
% 162.26/162.04 => 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) )
% 162.26/162.04 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_a))
% 162.26/162.04 => 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))) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_transpose__column__length,axiom,
% 162.26/162.04 ! [V_i_2,V_xs_2,T_a] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => ( 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)))
% 162.26/162.04 => 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)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_transpose__aux__filter__tail,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_nth__nth__transpose__sorted,axiom,
% 162.26/162.04 ! [V_j_2,V_i_2,V_xs_2,T_a] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => ( 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))))
% 162.26/162.04 => ( 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))))
% 162.26/162.04 => 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) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_transpose__transpose,axiom,
% 162.26/162.04 ! [V_xs_2,T_a] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 162.26/162.04 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_takeWhile__map,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_zip__takeWhile__snd,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_zip__takeWhile__fst,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_takeWhile__eq__all__conv,axiom,
% 162.26/162.04 ! [V_xs_2,V_P_2,T_a] :
% 162.26/162.04 ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = V_xs_2
% 162.26/162.04 <=> ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_set__takeWhileD,axiom,
% 162.26/162.04 ! [V_xs_2,V_P_2,V_x_2,T_a] :
% 162.26/162.04 ( 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))))
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__takeWhile__le,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_takeWhile__eq__take,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_distinct__takeWhile,axiom,
% 162.26/162.04 ! [V_P_2,V_xs_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 162.26/162.04 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_takeWhile__tail,axiom,
% 162.26/162.04 ! [V_l_2,V_xs_2,T_a,V_x_2,V_P_2] :
% 162.26/162.04 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__takeWhile,axiom,
% 162.26/162.04 ! [V_P_2,V_xs_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 162.26/162.04 => c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 162.26/162.04 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 162.26/162.04 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.04 => 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)) )
% 162.26/162.04 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.04 => 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) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_return__list__def,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_takeWhile__append1,axiom,
% 162.26/162.04 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.04 => 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) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_takeWhile__nth,axiom,
% 162.26/162.04 ! [V_xs_2,V_P_2,T_a,V_j_2] :
% 162.26/162.04 ( 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))))
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_nth__length__takeWhile,axiom,
% 162.26/162.04 ! [V_xs_2,V_P_2,T_a] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => ~ 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))))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_map__upds__def,axiom,
% 162.26/162.04 ! [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)))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_takeWhile__not__last,axiom,
% 162.26/162.04 ! [T_a,V_xs_2] :
% 162.26/162.04 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 162.26/162.04 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 162.26/162.04 => 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) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 162.26/162.04 ! [V_t_2,V_xs_2,V_f_2,T_b,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( 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)))
% 162.26/162.04 => 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) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 162.26/162.04 ! [V_l] :
% 162.26/162.04 ( c_List_Onat__list(V_l)
% 162.26/162.04 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__remdups__concat,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_distinct__remdups,axiom,
% 162.26/162.04 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__remdups__leq,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_remdups__map__remdups,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_set__remdups,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_remove1__remdups,axiom,
% 162.26/162.04 ! [V_x,V_xs,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__remdups,axiom,
% 162.26/162.04 ! [V_l,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 162.26/162.04 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_remdups__eq__nil__iff,axiom,
% 162.26/162.04 ! [V_x_2,T_a] :
% 162.26/162.04 ( c_List_Oremdups(T_a,V_x_2) = c_List_Olist_ONil(T_a)
% 162.26/162.04 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_remdups__eq__nil__right__iff,axiom,
% 162.26/162.04 ! [V_x_2,T_a] :
% 162.26/162.04 ( c_List_Olist_ONil(T_a) = c_List_Oremdups(T_a,V_x_2)
% 162.26/162.04 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_remdups_Osimps_I1_J,axiom,
% 162.26/162.04 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_remdups__id__iff__distinct,axiom,
% 162.26/162.04 ! [V_xs_2,T_a] :
% 162.26/162.04 ( c_List_Oremdups(T_a,V_xs_2) = V_xs_2
% 162.26/162.04 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_distinct__remdups__id,axiom,
% 162.26/162.04 ! [V_xs,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 162.26/162.04 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__remdups__eq,axiom,
% 162.26/162.04 ! [V_xs_2,T_a] :
% 162.26/162.04 ( 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)
% 162.26/162.04 <=> c_List_Oremdups(T_a,V_xs_2) = V_xs_2 ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_remdups__remdups,axiom,
% 162.26/162.04 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_remdups__filter,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_embed__list__def,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_remdups_Osimps_I2_J,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.04 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => 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) )
% 162.26/162.04 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => 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)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__remdups__card__conv,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
% 162.26/162.04 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] :
% 162.26/162.04 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_takeWhile__neq__rev,axiom,
% 162.26/162.04 ! [V_x_2,V_xs_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_dropWhile__neq__rev,axiom,
% 162.26/162.04 ! [V_x_2,V_xs_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__dropWhile__le,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_distinct__dropWhile,axiom,
% 162.26/162.04 ! [V_P_2,V_xs_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 162.26/162.04 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__dropWhile,axiom,
% 162.26/162.04 ! [V_P_2,V_xs_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 162.26/162.04 => c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 162.26/162.04 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 162.26/162.04 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.04 => 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) )
% 162.26/162.04 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.04 => 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) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_dropWhile__eq__Nil__conv,axiom,
% 162.26/162.04 ! [V_xs_2,V_P_2,T_a] :
% 162.26/162.04 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = c_List_Olist_ONil(T_a)
% 162.26/162.04 <=> ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_takeWhile__dropWhile__id,axiom,
% 162.26/162.04 ! [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 ).
% 162.26/162.04
% 162.26/162.04 fof(fact_hd__dropWhile,axiom,
% 162.26/162.04 ! [V_xs_2,V_P_2,T_a] :
% 162.26/162.04 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) != c_List_Olist_ONil(T_a)
% 162.26/162.04 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_dropWhile__map,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_dropWhile__append1,axiom,
% 162.26/162.04 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.04 => 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) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_dropWhile__eq__Cons__conv,axiom,
% 162.26/162.04 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_a] :
% 162.26/162.04 ( 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)
% 162.26/162.04 <=> ( 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))
% 162.26/162.04 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_dropWhile__eq__drop,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_dropWhile__nth,axiom,
% 162.26/162.04 ! [V_xs_2,V_P_2,T_a,V_j_2] :
% 162.26/162.04 ( 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))))
% 162.26/162.04 => 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)))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_listsum__map__filter,axiom,
% 162.26/162.04 ! [V_f_2,V_P_2,V_xs_2,T_a,T_b] :
% 162.26/162.04 ( class_Groups_Omonoid__add(T_b)
% 162.26/162.04 => ( ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => ( ~ hBOOL(hAPP(V_P_2,B_x))
% 162.26/162.04 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) )
% 162.26/162.04 => 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)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__nth__monoI,axiom,
% 162.26/162.04 ! [V_xs,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( ! [B_i,B_j] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 162.26/162.04 => ( 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)))
% 162.26/162.04 => 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))) ) )
% 162.26/162.04 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_n__lists_Osimps_I2_J,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sublists__powset,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_distinct__n__lists,axiom,
% 162.26/162.04 ! [V_n,V_xs,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 162.26/162.04 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_distinct__set__sublists,axiom,
% 162.26/162.04 ! [V_xs_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 162.26/162.04 => 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)))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__n__lists,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__n__lists__elem,axiom,
% 162.26/162.04 ! [V_xs_2,V_n_2,V_ys_2,T_a] :
% 162.26/162.04 ( 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))))
% 162.26/162.04 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sublists_Osimps_I1_J,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_n__lists__Nil,axiom,
% 162.26/162.04 ! [T_a,V_n] :
% 162.26/162.04 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.04 => 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))) )
% 162.26/162.04 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.04 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_n__lists_Osimps_I1_J,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sublists_Osimps_I2_J,axiom,
% 162.26/162.04 ! [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))))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_set__n__lists,axiom,
% 162.26/162.04 ! [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)))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__sublists,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_product_Osimps_I2_J,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_enum__the__def,axiom,
% 162.26/162.04 ! [V_P_2,T_a] : c_Enum_Oenum__the(T_a,V_P_2) = c_HOL_OThe(T_a,V_P_2) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_product_Osimps_I1_J,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_distinct__product,axiom,
% 162.26/162.04 ! [V_ys,T_b,V_xs,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 162.26/162.04 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
% 162.26/162.04 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_product__list__set,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_map__of__zip__enum__inject,axiom,
% 162.26/162.04 ! [V_ys_2,V_xs_2,T_a,T_b] :
% 162.26/162.04 ( ( class_Enum_Oenum(T_b)
% 162.26/162.04 & class_Enum_Oenum(T_a) )
% 162.26/162.04 => ( 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))
% 162.26/162.04 => ( 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))
% 162.26/162.04 => ( 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)))
% 162.26/162.04 => V_xs_2 = V_ys_2 ) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sort__foldl__insort,axiom,
% 162.26/162.04 ! [V_xs_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_enum__prod__def,axiom,
% 162.26/162.04 ! [T_b,T_a] :
% 162.26/162.04 ( ( class_Enum_Oenum(T_a)
% 162.26/162.04 & class_Enum_Oenum(T_b) )
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_enum__distinct,axiom,
% 162.26/162.04 ! [T_a] :
% 162.26/162.04 ( class_Enum_Oenum(T_a)
% 162.26/162.04 => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_enum__option__def,axiom,
% 162.26/162.04 ! [T_a] :
% 162.26/162.04 ( class_Enum_Oenum(T_a)
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_distinct__sort,axiom,
% 162.26/162.04 ! [V_xs_2,V_f_2,T_a,T_b] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_b)
% 162.26/162.04 => ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)))
% 162.26/162.04 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_filter__sort,axiom,
% 162.26/162.04 ! [V_xs_2,V_f_2,V_P_2,T_a,T_b] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_b)
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__sort,axiom,
% 162.26/162.04 ! [V_xs_2,V_f_2,T_a,T_b] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_b)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sort__key__simps_I1_J,axiom,
% 162.26/162.04 ! [V_f_2,T_a,T_b] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_b)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__sort,axiom,
% 162.26/162.04 ! [V_xs_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_set__sort,axiom,
% 162.26/162.04 ! [V_xs_2,V_f_2,T_a,T_b] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_b)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_enum__UNIV,axiom,
% 162.26/162.04 ! [T_a] :
% 162.26/162.04 ( class_Enum_Oenum(T_a)
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_UNIV__enum,axiom,
% 162.26/162.04 ! [T_a] :
% 162.26/162.04 ( class_Enum_Oenum(T_a)
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_in__enum,axiom,
% 162.26/162.04 ! [V_x_2,T_a] :
% 162.26/162.04 ( class_Enum_Oenum(T_a)
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__sort__key,axiom,
% 162.26/162.04 ! [V_xs_2,V_f_2,T_b,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sort__key__simps_I2_J,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_b)
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_enum__fun__code,axiom,
% 162.26/162.04 ! [T_b,T_a] :
% 162.26/162.04 ( ( class_Enum_Oenum(T_a)
% 162.26/162.04 & class_HOL_Oequal(T_a)
% 162.26/162.04 & class_Enum_Oenum(T_b) )
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_enum__fun__def,axiom,
% 162.26/162.04 ! [T_b,T_a] :
% 162.26/162.04 ( ( class_Enum_Oenum(T_a)
% 162.26/162.04 & class_Enum_Oenum(T_b) )
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted__list__of__set__sort__remdups,axiom,
% 162.26/162.04 ! [V_xs_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_all__n__lists__def,axiom,
% 162.26/162.04 ! [V_n_2,V_P_2,T_a] :
% 162.26/162.04 ( class_Enum_Oenum(T_a)
% 162.26/162.04 => ( c_Enum_Oall__n__lists(T_a,V_P_2,V_n_2)
% 162.26/162.04 <=> ! [B_x] :
% 162.26/162.04 ( 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)))))
% 162.26/162.04 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_ex__n__lists__def,axiom,
% 162.26/162.04 ! [V_n_2,V_P_2,T_a] :
% 162.26/162.04 ( class_Enum_Oenum(T_a)
% 162.26/162.04 => ( c_Enum_Oex__n__lists(T_a,V_P_2,V_n_2)
% 162.26/162.04 <=> ? [B_x] :
% 162.26/162.04 ( 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)))))
% 162.26/162.04 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_enum__all__fun__def,axiom,
% 162.26/162.04 ! [V_P_2,T_a,T_b] :
% 162.26/162.04 ( ( class_Enum_Oenum(T_b)
% 162.26/162.04 & class_Enum_Oenum(T_a) )
% 162.26/162.04 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2))
% 162.26/162.04 <=> 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_enum__ex__fun__def,axiom,
% 162.26/162.04 ! [V_P_2,T_a,T_b] :
% 162.26/162.04 ( ( class_Enum_Oenum(T_b)
% 162.26/162.04 & class_Enum_Oenum(T_a) )
% 162.26/162.04 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2))
% 162.26/162.04 <=> 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_enum__all__prod__def,axiom,
% 162.26/162.04 ! [V_P_2,T_a,T_b] :
% 162.26/162.04 ( ( class_Enum_Oenum(T_b)
% 162.26/162.04 & class_Enum_Oenum(T_a) )
% 162.26/162.04 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_a,T_b)),V_P_2))
% 162.26/162.04 <=> 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))))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_enum__ex__prod__def,axiom,
% 162.26/162.04 ! [V_P_2,T_a,T_b] :
% 162.26/162.04 ( ( class_Enum_Oenum(T_b)
% 162.26/162.04 & class_Enum_Oenum(T_a) )
% 162.26/162.04 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_a,T_b)),V_P_2))
% 162.26/162.04 <=> 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))))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_enum__ex__option__def,axiom,
% 162.26/162.04 ! [V_P_2,T_a] :
% 162.26/162.04 ( class_Enum_Oenum(T_a)
% 162.26/162.04 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_a)),V_P_2))
% 162.26/162.04 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a)))
% 162.26/162.04 | 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)))) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_enum__all__option__def,axiom,
% 162.26/162.04 ! [V_P_2,T_a] :
% 162.26/162.04 ( class_Enum_Oenum(T_a)
% 162.26/162.04 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_a)),V_P_2))
% 162.26/162.04 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a)))
% 162.26/162.04 & 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)))) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_all__code,axiom,
% 162.26/162.04 ! [V_P_2,T_a] :
% 162.26/162.04 ( class_Enum_Oenum(T_a)
% 162.26/162.04 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 162.26/162.04 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_exists__code,axiom,
% 162.26/162.04 ! [V_P_2,T_a] :
% 162.26/162.04 ( class_Enum_Oenum(T_a)
% 162.26/162.04 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 162.26/162.04 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_enum__all,axiom,
% 162.26/162.04 ! [V_P_2,T_a] :
% 162.26/162.04 ( class_Enum_Oenum(T_a)
% 162.26/162.04 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2))
% 162.26/162.04 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_enum__ex,axiom,
% 162.26/162.04 ! [V_P_2,T_a] :
% 162.26/162.04 ( class_Enum_Oenum(T_a)
% 162.26/162.04 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2))
% 162.26/162.04 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_order__fun_I1_J,axiom,
% 162.26/162.04 ! [V_g_2,V_f_2,T_a,T_b] :
% 162.26/162.04 ( ( class_Orderings_Oorder(T_b)
% 162.26/162.04 & class_Enum_Oenum(T_a) )
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 162.26/162.04 <=> 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_order__fun_I2_J,axiom,
% 162.26/162.04 ! [V_g_2,V_f_2,T_a,T_b] :
% 162.26/162.04 ( ( class_Orderings_Oorder(T_b)
% 162.26/162.04 & class_Enum_Oenum(T_a) )
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 162.26/162.04 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 162.26/162.04 & 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)))) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_enum__ex__fun__code,axiom,
% 162.26/162.04 ! [V_P_2,T_a,T_b] :
% 162.26/162.04 ( ( class_Enum_Oenum(T_b)
% 162.26/162.04 & class_Enum_Oenum(T_a)
% 162.26/162.04 & class_HOL_Oequal(T_a) )
% 162.26/162.04 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2))
% 162.26/162.04 <=> 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_enum__all__fun__code,axiom,
% 162.26/162.04 ! [V_P_2,T_a,T_b] :
% 162.26/162.04 ( ( class_Enum_Oenum(T_b)
% 162.26/162.04 & class_Enum_Oenum(T_a)
% 162.26/162.04 & class_HOL_Oequal(T_a) )
% 162.26/162.04 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2))
% 162.26/162.04 <=> 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_map__of__zip__enum__is__Some,axiom,
% 162.26/162.04 ! [V_x,V_ys,T_b,T_a] :
% 162.26/162.04 ( class_Enum_Oenum(T_a)
% 162.26/162.04 => ( 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))
% 162.26/162.04 => ? [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) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_takeWhile__eq__filter,axiom,
% 162.26/162.04 ! [V_xs_2,V_P_2,T_a] :
% 162.26/162.04 ( ! [B_x] :
% 162.26/162.04 ( 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))))
% 162.26/162.04 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 162.26/162.04 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_takeWhile__eq__take__P__nth,axiom,
% 162.26/162.04 ! [V_P_2,V_xs_2,T_a,V_n_2] :
% 162.26/162.04 ( ! [B_i] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 162.26/162.04 => ( 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)))
% 162.26/162.04 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) )
% 162.26/162.04 => ( ( 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)))
% 162.26/162.04 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) )
% 162.26/162.04 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_length__takeWhile__less__P__nth,axiom,
% 162.26/162.04 ! [V_xs_2,T_a,V_P_2,V_j_2] :
% 162.26/162.04 ( ! [B_i] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
% 162.26/162.04 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) )
% 162.26/162.04 => ( 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)))
% 162.26/162.04 => 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)))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_lists__Int__eq,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_lists__IntI,axiom,
% 162.26/162.04 ! [V_B_2,V_A_2,V_l_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_A_2)))
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_B_2)))
% 162.26/162.04 => 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)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_listsp_ONil,axiom,
% 162.26/162.04 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_append__in__listsp__conv,axiom,
% 162.26/162.04 ! [V_ys_2,V_xs_2,V_A_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)))
% 162.26/162.04 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2))
% 162.26/162.04 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_in__listsp__conv__set,axiom,
% 162.26/162.04 ! [V_xs_2,V_A_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2))
% 162.26/162.04 <=> ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_listsp_Oequations_I1_J,axiom,
% 162.26/162.04 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_listsp__conj__eq,axiom,
% 162.26/162.04 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 162.26/162.04 ( 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))
% 162.26/162.04 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2))
% 162.26/162.04 & hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_listsp__inf__eq,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_listsp__infI,axiom,
% 162.26/162.04 ! [V_B_2,V_l_2,V_A_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_l_2))
% 162.26/162.04 => ( hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_l_2))
% 162.26/162.04 => 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)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_listsp_Oequations_I2_J,axiom,
% 162.26/162.04 ! [V_a2_2,V_a1_2,V_A_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2)))
% 162.26/162.04 <=> ( hBOOL(hAPP(V_A_2,V_a1_2))
% 162.26/162.04 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_listsp__mono,axiom,
% 162.26/162.04 ! [V_B_2,V_A_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_listsp__lists__eq,axiom,
% 162.26/162.04 ! [V_x_2,V_A_2,T_a] :
% 162.26/162.04 ( 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))
% 162.26/162.04 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2__def,axiom,
% 162.26/162.04 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 162.26/162.04 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 162.26/162.04 <=> ( 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)
% 162.26/162.04 & ! [B_x] :
% 162.26/162.04 ( 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))))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted_Osimps,axiom,
% 162.26/162.04 ! [V_a_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,V_a_2)
% 162.26/162.04 <=> ( V_a_2 = c_List_Olist_ONil(T_a)
% 162.26/162.04 | ? [B_xs,B_x] :
% 162.26/162.04 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs)
% 162.26/162.04 & ! [B_xa] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),B_xs)))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) )
% 162.26/162.04 & c_List_Olinorder__class_Osorted(T_a,B_xs) ) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2__Cons,axiom,
% 162.26/162.04 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_b,T_a] :
% 162.26/162.04 ( 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))
% 162.26/162.04 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 162.26/162.04 & c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2__map1,axiom,
% 162.26/162.04 ! [V_bs_2,V_as_2,V_f_2,T_c,V_P_2,T_b,T_a] :
% 162.26/162.04 ( 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)
% 162.26/162.04 <=> 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2__map2,axiom,
% 162.26/162.04 ! [V_bs_2,V_f_2,T_c,V_as_2,V_P_2,T_b,T_a] :
% 162.26/162.04 ( 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))
% 162.26/162.04 <=> 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2__eq,axiom,
% 162.26/162.04 ! [T_a,V_ys_2,V_xs_2] :
% 162.26/162.04 ( V_xs_2 = V_ys_2
% 162.26/162.04 <=> c_List_Olist__all2(T_a,T_a,c_fequal,V_xs_2,V_ys_2) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2__lengthD,axiom,
% 162.26/162.04 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 162.26/162.04 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2__takeI,axiom,
% 162.26/162.04 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 162.26/162.04 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2__dropI,axiom,
% 162.26/162.04 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_b,T_a] :
% 162.26/162.04 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,V_bs_2)
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2__Nil,axiom,
% 162.26/162.04 ! [V_ys_2,V_P_2,T_b,T_a] :
% 162.26/162.04 ( c_List_Olist__all2(T_a,T_b,V_P_2,c_List_Olist_ONil(T_a),V_ys_2)
% 162.26/162.04 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2__Nil2,axiom,
% 162.26/162.04 ! [V_xs_2,V_P_2,T_b,T_a] :
% 162.26/162.04 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,c_List_Olist_ONil(T_b))
% 162.26/162.04 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2__rev,axiom,
% 162.26/162.04 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 162.26/162.04 ( 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))
% 162.26/162.04 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2__rev1,axiom,
% 162.26/162.04 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 162.26/162.04 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),V_ys_2)
% 162.26/162.04 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,hAPP(c_List_Orev(T_b),V_ys_2)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2__append,axiom,
% 162.26/162.04 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_b,V_xs_2,T_a] :
% 162.26/162.04 ( 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)
% 162.26/162.04 => ( 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))
% 162.26/162.04 <=> ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 162.26/162.04 & c_List_Olist__all2(T_a,T_b,V_P_2,V_us_2,V_vs_2) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2__appendI,axiom,
% 162.26/162.04 ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_P_2,T_b,T_a] :
% 162.26/162.04 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2)
% 162.26/162.04 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_ca_2,V_d_2)
% 162.26/162.04 => 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)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2__conv__all__nth,axiom,
% 162.26/162.04 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 162.26/162.04 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 162.26/162.04 <=> ( 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)
% 162.26/162.04 & ! [B_i] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => 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))) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2__nthD,axiom,
% 162.26/162.04 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 162.26/162.04 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 162.26/162.04 => ( 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)))
% 162.26/162.04 => 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2__nthD2,axiom,
% 162.26/162.04 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 162.26/162.04 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 162.26/162.04 => ( 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)))
% 162.26/162.04 => 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2__update__cong,axiom,
% 162.26/162.04 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_b,V_xs_2,T_a,V_i_2] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 162.26/162.04 => 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)) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2__update__cong2,axiom,
% 162.26/162.04 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 162.26/162.04 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 162.26/162.04 => ( 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)))
% 162.26/162.04 => 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)) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2I,axiom,
% 162.26/162.04 ! [V_P_2,V_b_2,V_a_2,T_b,T_a] :
% 162.26/162.04 ( ! [B_x] :
% 162.26/162.04 ( 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))))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) )
% 162.26/162.04 => ( 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)
% 162.26/162.04 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_all__nth__imp__all__set,axiom,
% 162.26/162.04 ! [V_x_2,V_P_2,V_xs_2,T_a] :
% 162.26/162.04 ( ! [B_i] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) )
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_map__removeAll__inj__on,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_not__in__set__insert,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.04 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_removeAll_Osimps_I2_J,axiom,
% 162.26/162.04 ! [V_xs,T_a,V_y,V_x] :
% 162.26/162.04 ( ( V_x = V_y
% 162.26/162.04 => 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) )
% 162.26/162.04 & ( V_x != V_y
% 162.26/162.04 => 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)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_distinct__insert,axiom,
% 162.26/162.04 ! [V_x,V_xs,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 162.26/162.04 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_distinct__removeAll,axiom,
% 162.26/162.04 ! [V_x,V_xs,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 162.26/162.04 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_insert__remdups,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_removeAll__filter__not__eq,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_removeAll__filter__not,axiom,
% 162.26/162.04 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 162.26/162.04 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_removeAll_Osimps_I1_J,axiom,
% 162.26/162.04 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_removeAll__append,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_removeAll__id,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.04 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2) = V_xs_2 ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_distinct__remove1__removeAll,axiom,
% 162.26/162.04 ! [V_x,V_xs,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 162.26/162.04 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_in__set__insert,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_List_Oset__insert,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_insert__Nil,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_map__removeAll__inj,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
% 162.26/162.04 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_set__removeAll,axiom,
% 162.26/162.04 ! [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)))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_List_Oinsert__def,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.04 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 )
% 162.26/162.04 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => 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) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_maps__def,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_concat__map__maps,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_maps__simps_I2_J,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_maps__simps_I1_J,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_distinct__concat,axiom,
% 162.26/162.04 ! [V_xs_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),V_xs_2))
% 162.26/162.04 => ( ! [B_ys] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 162.26/162.04 => hBOOL(hAPP(c_List_Odistinct(T_a),B_ys)) )
% 162.26/162.04 => ( ! [B_ys] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 162.26/162.04 => ! [B_zs] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 162.26/162.04 => ( B_ys != B_zs
% 162.26/162.04 => 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)) ) ) )
% 162.26/162.04 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oconcat(T_a,V_xs_2))) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_measures__lesseq,axiom,
% 162.26/162.04 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => ( 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)))
% 162.26/162.04 => 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)))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_wf__measures,axiom,
% 162.26/162.04 ! [V_fs_2,T_a] : c_Wellfounded_Owf(T_a,c_List_Omeasures(T_a,V_fs_2)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_in__measures_I1_J,axiom,
% 162.26/162.04 ! [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))))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_measures__def,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_measures__less,axiom,
% 162.26/162.04 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => 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)))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_in__measures_I2_J,axiom,
% 162.26/162.04 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_a] :
% 162.26/162.04 ( 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))))
% 162.26/162.04 <=> ( 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)))
% 162.26/162.04 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 162.26/162.04 & 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))) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_foldl__apply,axiom,
% 162.26/162.04 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_b,T_c,V_xs_2,T_a] :
% 162.26/162.04 ( ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => 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)) )
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_zip__obtain__same__length,axiom,
% 162.26/162.04 ! [V_P_2,V_ys_2,T_b,V_xs_2,T_a] :
% 162.26/162.04 ( ( 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))
% 162.26/162.04 => 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)))) )
% 162.26/162.04 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_map__of__eqI,axiom,
% 162.26/162.04 ! [V_ys_2,V_xs_2,T_b,T_a] :
% 162.26/162.04 ( 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))
% 162.26/162.04 => ( ! [B_x] :
% 162.26/162.04 ( 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))))
% 162.26/162.04 => 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) )
% 162.26/162.04 => hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_inj__on__diff__nat,axiom,
% 162.26/162.04 ! [V_k_2,V_N_2] :
% 162.26/162.04 ( ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_wfP__SUP,axiom,
% 162.26/162.04 ! [T_a,V_r_2,T_b] :
% 162.26/162.04 ( ! [B_i] : c_Wellfounded_OwfP(T_b,hAPP(V_r_2,B_i))
% 162.26/162.04 => ( ! [B_i,B_j] :
% 162.26/162.04 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 162.26/162.04 => 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)) )
% 162.26/162.04 => 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)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_dropWhile__append2,axiom,
% 162.26/162.04 ! [V_ys_2,V_P_2,V_xs_2,T_a] :
% 162.26/162.04 ( ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => hBOOL(hAPP(V_P_2,B_x)) )
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__all2__all__nthI,axiom,
% 162.26/162.04 ! [V_P_2,V_b_2,T_b,V_a_2,T_a] :
% 162.26/162.04 ( 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)
% 162.26/162.04 => ( ! [B_n] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => 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))) )
% 162.26/162.04 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_finite__map__freshness,axiom,
% 162.26/162.04 ! [V_f_2,T_b,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,V_f_2)))
% 162.26/162.04 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 162.26/162.04 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_b) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_mem__splitI2,axiom,
% 162.26/162.04 ! [V_ca_2,V_z_2,T_c,T_b,T_a,V_p_2] :
% 162.26/162.04 ( ! [B_a,B_b] :
% 162.26/162.04 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) )
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_mem__splitE,axiom,
% 162.26/162.04 ! [V_p_2,V_ca_2,T_c,T_b,V_z_2,T_a] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => ~ ! [B_x,B_y] :
% 162.26/162.04 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)
% 162.26/162.04 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_finite__sorted__distinct__unique,axiom,
% 162.26/162.04 ! [V_A_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.04 => ? [B_x] :
% 162.26/162.04 ( hAPP(c_List_Oset(T_a),B_x) = V_A_2
% 162.26/162.04 & c_List_Olinorder__class_Osorted(T_a,B_x)
% 162.26/162.04 & hBOOL(hAPP(c_List_Odistinct(T_a),B_x))
% 162.26/162.04 & ! [B_y] :
% 162.26/162.04 ( ( hAPP(c_List_Oset(T_a),B_y) = V_A_2
% 162.26/162.04 & c_List_Olinorder__class_Osorted(T_a,B_y)
% 162.26/162.04 & hBOOL(hAPP(c_List_Odistinct(T_a),B_y)) )
% 162.26/162.04 => B_y = B_x ) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_setsum__SucD,axiom,
% 162.26/162.04 ! [V_n_2,V_A_2,V_f_2,T_a] :
% 162.26/162.04 ( 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)
% 162.26/162.04 => ? [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.04 & 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_nat__mod__eq__lemma,axiom,
% 162.26/162.04 ! [V_y,V_n,V_x] :
% 162.26/162.04 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 162.26/162.04 => ? [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)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_takeWhile__append2,axiom,
% 162.26/162.04 ! [V_ys_2,V_P_2,V_xs_2,T_a] :
% 162.26/162.04 ( ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => hBOOL(hAPP(V_P_2,B_x)) )
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_insort__is__Cons,axiom,
% 162.26/162.04 ! [V_a_2,V_f_2,V_xs_2,T_a,T_b] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_b)
% 162.26/162.04 => ( ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
% 162.26/162.04 => 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) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_wfI__pf,axiom,
% 162.26/162.04 ! [V_R_2,T_a] :
% 162.26/162.04 ( ! [B_A] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
% 162.26/162.04 => c_Wellfounded_Owf(T_a,V_R_2) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_filter__eq__Cons__iff,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_a] :
% 162.26/162.04 ( 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)
% 162.26/162.04 <=> ? [B_us,B_vs] :
% 162.26/162.04 ( 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))
% 162.26/162.04 & ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us)))
% 162.26/162.04 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 162.26/162.04 & hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.04 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_Cons__eq__filter__iff,axiom,
% 162.26/162.04 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
% 162.26/162.04 ( 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)
% 162.26/162.04 <=> ? [B_us,B_vs] :
% 162.26/162.04 ( 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))
% 162.26/162.04 & ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us)))
% 162.26/162.04 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 162.26/162.04 & hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.04 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_Sigma__mono,axiom,
% 162.26/162.04 ! [V_D_2,V_B_2,T_b,V_C_2,V_A_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 162.26/162.04 => ( ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.04 => 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))) )
% 162.26/162.04 => 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_acc_OaccI,axiom,
% 162.26/162.04 ! [V_r_2,V_x_2,T_a] :
% 162.26/162.04 ( ! [B_y] :
% 162.26/162.04 ( 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))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))) )
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_not__acc__down,axiom,
% 162.26/162.04 ! [V_R_2,V_x_2,T_a] :
% 162.26/162.04 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2)))
% 162.26/162.04 => ~ ! [B_z] :
% 162.26/162.04 ( 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))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_fold__image__1,axiom,
% 162.26/162.04 ! [V_f_2,V_S_2,T_a,T_b] :
% 162.26/162.04 ( class_Groups_Ocomm__monoid__mult(T_b)
% 162.26/162.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 162.26/162.04 => ( ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 162.26/162.04 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 162.26/162.04 => 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) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__ball__nth,axiom,
% 162.26/162.04 ! [V_P_2,V_xs_2,T_a,V_n_2] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => ( ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => hBOOL(hAPP(V_P_2,B_x)) )
% 162.26/162.04 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_max__ext_Osimps,axiom,
% 162.26/162.04 ! [V_R_2,V_a2_2,V_a1_2,T_a] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2))
% 162.26/162.04 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2))
% 162.26/162.04 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 162.26/162.04 & ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2))
% 162.26/162.04 => ? [B_xa] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2))
% 162.26/162.04 & 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)) ) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 162.26/162.04 ! [V_ca_2,V_b_2,V_A_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.04 => ( ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) )
% 162.26/162.04 => 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))) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 162.26/162.04 ! [V_ca_2,V_b_2,V_A_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.04 => ( ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) )
% 162.26/162.04 => 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))) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_mod__induct__0,axiom,
% 162.26/162.04 ! [V_i_2,V_P_2,V_p_2] :
% 162.26/162.04 ( ! [B_i] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 162.26/162.04 => ( hBOOL(hAPP(V_P_2,B_i))
% 162.26/162.04 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 162.26/162.04 => ( hBOOL(hAPP(V_P_2,V_i_2))
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 162.26/162.04 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_sorted_OCons,axiom,
% 162.26/162.04 ! [V_x_2,V_xs_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) )
% 162.26/162.04 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 162.26/162.04 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_InterI,axiom,
% 162.26/162.04 ! [V_A_2,V_C_2,T_a] :
% 162.26/162.04 ( ! [B_X] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) )
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_fold__image__cong,axiom,
% 162.26/162.04 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 162.26/162.04 ( class_Groups_Oab__semigroup__mult(T_b)
% 162.26/162.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.04 => ( ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.04 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 162.26/162.04 => 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) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_Min__eqI,axiom,
% 162.26/162.04 ! [V_x_2,V_A_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.04 => ( ! [B_y] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_y)) )
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.26/162.04 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_Max__eqI,axiom,
% 162.26/162.04 ! [V_x_2,V_A_2,T_a] :
% 162.26/162.04 ( class_Orderings_Olinorder(T_a)
% 162.26/162.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.04 => ( ! [B_y] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_y),V_x_2)) )
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 162.26/162.04 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_inf__le__fold__inf,axiom,
% 162.26/162.04 ! [V_ca_2,V_b_2,V_A_2,T_a] :
% 162.26/162.04 ( class_Lattices_Osemilattice__inf(T_a)
% 162.26/162.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.04 => ( ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) )
% 162.26/162.04 => 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))) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_fold__sup__le__sup,axiom,
% 162.26/162.04 ! [V_ca_2,V_b_2,V_A_2,T_a] :
% 162.26/162.04 ( class_Lattices_Osemilattice__sup(T_a)
% 162.26/162.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 162.26/162.04 => ( ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) )
% 162.26/162.04 => 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))) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_wf__no__infinite__down__chainE,axiom,
% 162.26/162.04 ! [V_f_2,V_r_2,T_a] :
% 162.26/162.04 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.04 => ~ ! [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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__ex__length,axiom,
% 162.26/162.04 ! [V_xs_2,V_P_2,T_a] :
% 162.26/162.04 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
% 162.26/162.04 <=> ? [B_n] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__ex__simps_I2_J,axiom,
% 162.26/162.04 ! [V_P_2,T_a] : ~ c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__ex__iff,axiom,
% 162.26/162.04 ! [V_xs_2,V_P_2,T_a] :
% 162.26/162.04 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
% 162.26/162.04 <=> ? [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.04 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__ex__rev,axiom,
% 162.26/162.04 ! [V_xs_2,V_P_2,T_a] :
% 162.26/162.04 ( c_List_Olist__ex(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2))
% 162.26/162.04 <=> c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__ex__append,axiom,
% 162.26/162.04 ! [V_ys_2,V_xs_2,V_P_2,T_a] :
% 162.26/162.04 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
% 162.26/162.04 <=> ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
% 162.26/162.04 | c_List_Olist__ex(T_a,V_P_2,V_ys_2) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_list__ex__simps_I1_J,axiom,
% 162.26/162.04 ! [V_xs_2,V_x_2,V_P_2,T_a] :
% 162.26/162.04 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
% 162.26/162.04 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.04 | c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_setsum__reindex__cong,axiom,
% 162.26/162.04 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
% 162.26/162.04 ( class_Groups_Ocomm__monoid__add(T_c)
% 162.26/162.04 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 162.26/162.04 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
% 162.26/162.04 => ( ! [B_a] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 162.26/162.04 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 162.26/162.04 => 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) ) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_scomp__unfold,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_scomp__def,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_scomp__apply,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_scomp__Pair,axiom,
% 162.26/162.04 ! [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 ).
% 162.26/162.04
% 162.26/162.04 fof(fact_Pair__scomp,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_scomp__scomp,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_iterate_Osimps,axiom,
% 162.26/162.04 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] :
% 162.26/162.04 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 162.26/162.04 => 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) )
% 162.26/162.04 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 162.26/162.04 => 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)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_setsum__ivl__cong,axiom,
% 162.26/162.04 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_a,T_b] :
% 162.26/162.04 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 162.26/162.04 & class_Orderings_Oord(T_a) )
% 162.26/162.04 => ( V_a_2 = V_ca_2
% 162.26/162.04 => ( V_b_2 = V_d_2
% 162.26/162.04 => ( ! [B_x] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),B_x))
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_d_2))
% 162.26/162.04 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 162.26/162.04 => 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)) ) ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_log_Osimps,axiom,
% 162.26/162.04 ! [V_i,V_b] :
% 162.26/162.04 ( ( ( 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)))
% 162.26/162.04 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 162.26/162.04 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 162.26/162.04 & ( ~ ( 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)))
% 162.26/162.04 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 162.26/162.04 => 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_minus__shift__def,axiom,
% 162.26/162.04 ! [V_r,V_l,V_k] :
% 162.26/162.04 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 162.26/162.04 => 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) )
% 162.26/162.04 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 162.26/162.04 => 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) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_inc__shift__def,axiom,
% 162.26/162.04 ! [V_k,V_v] :
% 162.26/162.04 ( ( V_v = V_k
% 162.26/162.04 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 162.26/162.04 & ( V_v != V_k
% 162.26/162.04 => 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)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_select,axiom,
% 162.26/162.04 ! [V_s_2,T_a,V_xs_2] :
% 162.26/162.04 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_select__weight__member,axiom,
% 162.26/162.04 ! [V_s_2,V_xs_2,T_a] :
% 162.26/162.04 ( 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))))
% 162.26/162.04 => 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)))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_select__weigth__select,axiom,
% 162.26/162.04 ! [T_a,V_xs_2] :
% 162.26/162.04 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_select__weight__cons__zero,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_select__weigth__drop__zero,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_pick__member,axiom,
% 162.26/162.04 ! [V_xs_2,T_a,V_i_2] :
% 162.26/162.04 ( 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))))
% 162.26/162.04 => 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)))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_pick_Osimps,axiom,
% 162.26/162.04 ! [V_xs,V_x,T_a,V_i] :
% 162.26/162.04 ( ( 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)))
% 162.26/162.04 => 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) )
% 162.26/162.04 & ( ~ 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)))
% 162.26/162.04 => 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_pick__drop__zero,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_select__weight__def,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_pick__same,axiom,
% 162.26/162.04 ! [V_xs_2,T_a,V_l_2] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => 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) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 162.26/162.04 ! [V_y_2,V_x_2] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 162.26/162.04 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 162.26/162.04 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 162.26/162.04 <=> V_x_2 = V_y_2 ) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_one__code__numeral__def,axiom,
% 162.26/162.04 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_zero__code__numeral__def,axiom,
% 162.26/162.04 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_times__code__numeral__code,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 162.26/162.04 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 162.26/162.04 ! [V_m_2,V_n_2] :
% 162.26/162.04 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 162.26/162.04 <=> V_n_2 = V_m_2 ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_number__of__code__numeral__def,axiom,
% 162.26/162.04 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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_plus__code__numeral__code,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_less__code__numeral__code,axiom,
% 162.26/162.04 ! [V_m_2,V_n_2] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_less__eq__code__numeral__code,axiom,
% 162.26/162.04 ! [V_m_2,V_n_2] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_code__numeral__not__eq__zero,axiom,
% 162.26/162.04 ! [V_i_2] :
% 162.26/162.04 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 162.26/162.04 <=> 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_range,axiom,
% 162.26/162.04 ! [V_s,V_k] :
% 162.26/162.04 ( 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))
% 162.26/162.04 => 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)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_select__def,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_subtract__code__numeral__code,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_type__definition__code__numeral,axiom,
% 162.26/162.04 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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_nat__of__of__nat,axiom,
% 162.26/162.04 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 162.26/162.04
% 162.26/162.04 fof(fact_of__nat__nat__of,axiom,
% 162.26/162.04 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 162.26/162.04
% 162.26/162.04 fof(fact_nat__of__inverse,axiom,
% 162.26/162.04 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 162.26/162.04
% 162.26/162.04 fof(fact_times__code__numeral__def,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_less__code__numeral__def,axiom,
% 162.26/162.04 ! [V_m_2,V_n_2] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 162.26/162.04 <=> 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_int__of__def,axiom,
% 162.26/162.04 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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_nat__of__number,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_code__numeral_Onat__of__inject,axiom,
% 162.26/162.04 ! [V_y_2,V_x_2] :
% 162.26/162.04 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 162.26/162.04 <=> V_x_2 = V_y_2 ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 162.26/162.04 ! [V_l_2,V_k_2] :
% 162.26/162.04 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 162.26/162.04 <=> V_k_2 = V_l_2 ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_nat__of,axiom,
% 162.26/162.04 ! [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)))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_less__eq__code__numeral__def,axiom,
% 162.26/162.04 ! [V_m_2,V_n_2] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 162.26/162.04 <=> 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_nat__of__code,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_nat__of__aux__def,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_Suc__code__numeral__def,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_minus__code__numeral__def,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_of__nat__inverse,axiom,
% 162.26/162.04 ! [V_y_2] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 162.26/162.04 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_plus__code__numeral__def,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_div__code__numeral__def,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_minus__code__numeral__code,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_subtract__code__numeral__def,axiom,
% 162.26/162.04 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_mod__code__numeral__def,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_code__numeral__decr,axiom,
% 162.26/162.04 ! [V_k] :
% 162.26/162.04 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_less__eq,axiom,
% 162.26/162.04 ! [V_n_2,V_m_2] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_less__than__def,axiom,
% 162.26/162.04 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_wf__trancl,axiom,
% 162.26/162.04 ! [V_r_2,T_a] :
% 162.26/162.04 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.04 => c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_acyclic__def,axiom,
% 162.26/162.04 ! [V_r_2,T_a] :
% 162.26/162.04 ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 162.26/162.04 <=> ! [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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_trancl_Or__into__trancl,axiom,
% 162.26/162.04 ! [V_r_2,V_b_2,V_a_2,T_a] :
% 162.26/162.04 ( 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))
% 162.26/162.04 => 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))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_trancl__subset__Field2,axiom,
% 162.26/162.04 ! [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))))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_r__into__trancl_H,axiom,
% 162.26/162.04 ! [V_r_2,V_p_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_trancl__empty,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_trancl__domain,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_trancl__range,axiom,
% 162.26/162.04 ! [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) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_finite__trancl,axiom,
% 162.26/162.04 ! [V_r_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 162.26/162.04 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_r__r__into__trancl,axiom,
% 162.26/162.04 ! [V_ca_2,V_R_2,V_b_2,V_a_2,T_a] :
% 162.26/162.04 ( 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))
% 162.26/162.04 => ( 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))
% 162.26/162.04 => 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_trancl__into__trancl2,axiom,
% 162.26/162.04 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 162.26/162.04 ( 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))
% 162.26/162.04 => ( 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)))
% 162.26/162.04 => 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 162.26/162.04 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => ( 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))
% 162.26/162.04 => 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_trancl__trans,axiom,
% 162.26/162.04 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => ( 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)))
% 162.26/162.04 => 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))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_trancl__mono,axiom,
% 162.26/162.04 ! [V_s_2,V_r_2,V_p_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 162.26/162.04 => ( 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))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2))) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_trancl__unfold,axiom,
% 162.26/162.04 ! [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)) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_trancl__subset__Sigma,axiom,
% 162.26/162.04 ! [V_A_2,V_r_2,T_a] :
% 162.26/162.04 ( 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))))
% 162.26/162.04 => 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)))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_trancl__Int__subset,axiom,
% 162.26/162.04 ! [V_s_2,V_r_2,T_a] :
% 162.26/162.04 ( 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))
% 162.26/162.04 => ( 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))
% 162.26/162.04 => 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)) ) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_trancl__insert,axiom,
% 162.26/162.04 ! [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)))))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_reflcl__set__eq,axiom,
% 162.26/162.04 ! [V_y_2,V_x_2,V_r_2,T_a] :
% 162.26/162.04 ( 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))
% 162.26/162.04 <=> 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)))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_r__into__rtrancl,axiom,
% 162.26/162.04 ! [V_r_2,V_p_2,T_a] :
% 162.26/162.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2))
% 162.26/162.04 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_IdI,axiom,
% 162.26/162.04 ! [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))) ).
% 162.26/162.04
% 162.26/162.04 fof(fact_trancl__into__rtrancl,axiom,
% 162.26/162.04 ! [V_r_2,V_b_2,V_a_2,T_a] :
% 162.26/162.04 ( 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)))
% 162.26/162.04 => 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))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_listrel__rtrancl__refl,axiom,
% 162.26/162.05 ! [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)))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_trancl__unfold__right,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_trancl__unfold__left,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_reflcl__trancl,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_trancl__reflcl,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_trancl__rtrancl__absorb,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__trancl__absorb,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__trancl__trancl,axiom,
% 162.26/162.05 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ( 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)))
% 162.26/162.05 => 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))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_trancl__rtrancl__trancl,axiom,
% 162.26/162.05 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ( 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)))
% 162.26/162.05 => 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))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__into__trancl1,axiom,
% 162.26/162.05 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ( 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))
% 162.26/162.05 => 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))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtranclD,axiom,
% 162.26/162.05 ! [V_R_2,V_b_2,V_a_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ( V_a_2 = V_b_2
% 162.26/162.05 | ( V_a_2 != V_b_2
% 162.26/162.05 & 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))) ) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__into__trancl2,axiom,
% 162.26/162.05 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 162.26/162.05 ( 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))
% 162.26/162.05 => ( 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)))
% 162.26/162.05 => 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))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__eq__or__trancl,axiom,
% 162.26/162.05 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 <=> ( V_x_2 = V_y_2
% 162.26/162.05 | ( V_x_2 != V_y_2
% 162.26/162.05 & 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))) ) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 162.26/162.05 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 162.26/162.05 ( 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))
% 162.26/162.05 => ( 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)))
% 162.26/162.05 => 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))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 162.26/162.05 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ( 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))
% 162.26/162.05 => 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))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__trans,axiom,
% 162.26/162.05 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ( 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)))
% 162.26/162.05 => 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))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__mono,axiom,
% 162.26/162.05 ! [V_s_2,V_r_2,T_a] :
% 162.26/162.05 ( 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))
% 162.26/162.05 => 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))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__subset,axiom,
% 162.26/162.05 ! [V_S_2,V_R_2,T_a] :
% 162.26/162.05 ( 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))
% 162.26/162.05 => ( 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)))
% 162.26/162.05 => c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__subset__rtrancl,axiom,
% 162.26/162.05 ! [V_s_2,V_r_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => 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))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__Un__subset,axiom,
% 162.26/162.05 ! [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)))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Image__closed__trancl,axiom,
% 162.26/162.05 ! [V_X_2,V_r_2,T_a] :
% 162.26/162.05 ( 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))
% 162.26/162.05 => hAPP(c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_X_2) = V_X_2 ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__Int__subset,axiom,
% 162.26/162.05 ! [V_r_2,V_s_2,T_a] :
% 162.26/162.05 ( 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))
% 162.26/162.05 => ( 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))
% 162.26/162.05 => 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)) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__idemp,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__r__diff__Id,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__reflcl,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__Un__rtrancl,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__reflcl__absorb,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__unfold,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_r__comp__rtrancl__eq,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__idemp__self__comp,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Range__rtrancl,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Domain__rtrancl,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_in__rtrancl__UnI,axiom,
% 162.26/162.05 ! [V_S_2,V_R_2,V_x_2,T_a] :
% 162.26/162.05 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 162.26/162.05 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) )
% 162.26/162.05 => 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)))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__empty,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_refl__rtrancl,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Range__Id,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_refl__Id,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Domain__Id,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Image__Id,axiom,
% 162.26/162.05 ! [V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a)),V_A_2) = V_A_2 ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Id__O__R,axiom,
% 162.26/162.05 ! [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 ).
% 162.26/162.05
% 162.26/162.05 fof(fact_R__O__Id,axiom,
% 162.26/162.05 ! [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 ).
% 162.26/162.05
% 162.26/162.05 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 162.26/162.05 ! [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)))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_pair__in__Id__conv,axiom,
% 162.26/162.05 ! [V_b_2,V_a_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 <=> V_a_2 = V_b_2 ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_listrel__rtrancl__trans,axiom,
% 162.26/162.05 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 162.26/162.05 ( 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))))
% 162.26/162.05 => ( 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))))
% 162.26/162.05 => 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)))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 162.26/162.05 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ( 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))))
% 162.26/162.05 => 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)))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 162.26/162.05 ! [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)))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_pair__leq__def,axiom,
% 162.26/162.05 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))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Not__Domain__rtrancl,axiom,
% 162.26/162.05 ! [V_y_2,V_R_2,V_x_2,T_a] :
% 162.26/162.05 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_a),V_R_2)))
% 162.26/162.05 => ( 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)))
% 162.26/162.05 <=> V_x_2 = V_y_2 ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_acc__downwards,axiom,
% 162.26/162.05 ! [V_b_2,V_r_2,V_a_2,T_a] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 162.26/162.05 => ( 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)))
% 162.26/162.05 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_acc__downwards__aux,axiom,
% 162.26/162.05 ! [V_r_2,V_a_2,V_b_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 162.26/162.05 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_wf__insert,axiom,
% 162.26/162.05 ! [V_r_2,V_x_2,V_y_2,T_a] :
% 162.26/162.05 ( 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))
% 162.26/162.05 <=> ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.05 & ~ 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))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 162.26/162.05 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 162.26/162.05 ( 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))))
% 162.26/162.05 => 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)))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 162.26/162.05 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 162.26/162.05 ( 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))))
% 162.26/162.05 => 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) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_acyclic__insert,axiom,
% 162.26/162.05 ! [V_r_2,V_x_2,V_y_2,T_a] :
% 162.26/162.05 ( 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))
% 162.26/162.05 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 162.26/162.05 & ~ 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))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 162.26/162.05 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => 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)))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 162.26/162.05 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => 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)))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_refl__reflcl,axiom,
% 162.26/162.05 ! [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))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Id__def,axiom,
% 162.26/162.05 ! [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))))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_irrefl__diff__Id,axiom,
% 162.26/162.05 ! [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))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_pred__nat__trancl__eq__le,axiom,
% 162.26/162.05 ! [V_n_2,V_m_2] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_trancl__subset__Sigma__aux,axiom,
% 162.26/162.05 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ( 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))))
% 162.26/162.05 => ( V_a_2 = V_b_2
% 162.26/162.05 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_irrefl__tranclI,axiom,
% 162.26/162.05 ! [V_x_2,V_r_2,T_a] :
% 162.26/162.05 ( 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))
% 162.26/162.05 => ~ 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))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_sequence__trans,axiom,
% 162.26/162.05 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_a] :
% 162.26/162.05 ( ! [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)))
% 162.26/162.05 => 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))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__converseI,axiom,
% 162.26/162.05 ! [V_r_2,V_x_2,V_y_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => 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)))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__converseD,axiom,
% 162.26/162.05 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 162.26/162.05 ( 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))))
% 162.26/162.05 => 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))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__converse,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_converse__Id,axiom,
% 162.26/162.05 ! [T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId(T_a)) = c_Relation_OId(T_a) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_in__listrel1__converse,axiom,
% 162.26/162.05 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 162.26/162.05 ( 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))))
% 162.26/162.05 <=> 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)))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_converse__iff,axiom,
% 162.26/162.05 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 <=> 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)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_converseI,axiom,
% 162.26/162.05 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 162.26/162.05 ( 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))
% 162.26/162.05 => 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))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_converseD,axiom,
% 162.26/162.05 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => 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)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_converse__inv__image,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_converse__Int,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_finite__converse,axiom,
% 162.26/162.05 ! [V_r_2,T_b,T_a] :
% 162.26/162.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)))
% 162.26/162.05 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_a)),V_r_2)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_acyclic__converse,axiom,
% 162.26/162.05 ! [V_r_2,T_a] :
% 162.26/162.05 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 162.26/162.05 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_converse__converse,axiom,
% 162.26/162.05 ! [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 ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Field__converse,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_converse__Id__on,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_converse__Un,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_converse__rel__comp,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_converse__INTER,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Range__def,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Domain__converse,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Range__converse,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_equiv__comp__eq,axiom,
% 162.26/162.05 ! [V_r_2,V_A_2,T_a] :
% 162.26/162.05 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 162.26/162.05 => 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 ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_listrel1__converse,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_refl__on__converse,axiom,
% 162.26/162.05 ! [V_r_2,V_A_2,T_a] :
% 162.26/162.05 ( c_Relation_Orefl__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 162.26/162.05 <=> c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_converse__UNION,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_trancl__converseI,axiom,
% 162.26/162.05 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 162.26/162.05 ( 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))))
% 162.26/162.05 => 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)))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_trancl__converseD,axiom,
% 162.26/162.05 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 162.26/162.05 ( 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))))
% 162.26/162.05 => 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)))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_trancl__converse,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_wf__converse__trancl,axiom,
% 162.26/162.05 ! [V_r_2,T_a] :
% 162.26/162.05 ( c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 162.26/162.05 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Image__subset__eq,axiom,
% 162.26/162.05 ! [V_B_2,V_A_2,V_r_2,T_b,T_a] :
% 162.26/162.05 ( 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))
% 162.26/162.05 <=> 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))))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_refl__on__comp__subset,axiom,
% 162.26/162.05 ! [V_r_2,V_A_2,T_a] :
% 162.26/162.05 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 162.26/162.05 => 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))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_comp__equivI,axiom,
% 162.26/162.05 ! [V_A_2,V_r_2,T_a] :
% 162.26/162.05 ( 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
% 162.26/162.05 => ( hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) = V_A_2
% 162.26/162.05 => c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_finite__acyclic__wf__converse,axiom,
% 162.26/162.05 ! [V_r_2,T_a] :
% 162.26/162.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 162.26/162.05 => ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 162.26/162.05 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_converse__def,axiom,
% 162.26/162.05 ! [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))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Image__INT__eq,axiom,
% 162.26/162.05 ! [V_B_2,T_c,V_A_2,V_r_2,T_b,T_a] :
% 162.26/162.05 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))
% 162.26/162.05 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 162.26/162.05 => 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)) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_total__on__diff__Id,axiom,
% 162.26/162.05 ! [V_r_2,V_A_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_single__valued__Id,axiom,
% 162.26/162.05 ! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_total__on__converse,axiom,
% 162.26/162.05 ! [V_r_2,V_A_2,T_a] :
% 162.26/162.05 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 162.26/162.05 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_total__on__empty,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_single__valued__Id__on,axiom,
% 162.26/162.05 ! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_single__valued__rel__comp,axiom,
% 162.26/162.05 ! [V_s_2,T_c,V_r_2,T_b,T_a] :
% 162.26/162.05 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
% 162.26/162.05 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 162.26/162.05 => 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)) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_single__valued__subset,axiom,
% 162.26/162.05 ! [V_s_2,V_r_2,T_b,T_a] :
% 162.26/162.05 ( 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))
% 162.26/162.05 => ( c_Relation_Osingle__valued(T_a,T_b,V_s_2)
% 162.26/162.05 => c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_single__valuedD,axiom,
% 162.26/162.05 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] :
% 162.26/162.05 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
% 162.26/162.05 => ( 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))
% 162.26/162.05 => ( 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))
% 162.26/162.05 => V_y_2 = V_z_2 ) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_single__valued__def,axiom,
% 162.26/162.05 ! [V_r_2,T_b,T_a] :
% 162.26/162.05 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
% 162.26/162.05 <=> ! [B_x,B_y] :
% 162.26/162.05 ( 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))
% 162.26/162.05 => ! [B_z] :
% 162.26/162.05 ( 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))
% 162.26/162.05 => B_y = B_z ) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_total__on__def,axiom,
% 162.26/162.05 ! [V_r_2,V_A_2,T_a] :
% 162.26/162.05 ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2)
% 162.26/162.05 <=> ! [B_x] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.05 => ! [B_xa] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 162.26/162.05 => ( B_x != B_xa
% 162.26/162.05 => ( 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))
% 162.26/162.05 | 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)) ) ) ) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_single__valued__confluent,axiom,
% 162.26/162.05 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] :
% 162.26/162.05 ( c_Relation_Osingle__valued(T_a,T_a,V_r_2)
% 162.26/162.05 => ( 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)))
% 162.26/162.05 => ( 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)))
% 162.26/162.05 => ( 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)))
% 162.26/162.05 | 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))) ) ) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Image__Int__eq,axiom,
% 162.26/162.05 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] :
% 162.26/162.05 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_R_2))
% 162.26/162.05 => 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)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 162.26/162.05 ! [V_R_2,V_p_2,T_a] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 162.26/162.05 => 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)))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_acyclicI,axiom,
% 162.26/162.05 ! [V_r_2,T_a] :
% 162.26/162.05 ( ! [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)))
% 162.26/162.05 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_single__valued__rel__pow,axiom,
% 162.26/162.05 ! [V_n_2,V_R_2,T_a] :
% 162.26/162.05 ( c_Relation_Osingle__valued(T_a,T_a,V_R_2)
% 162.26/162.05 => 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)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rel__pow__0__E,axiom,
% 162.26/162.05 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => V_x_2 = V_y_2 ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rel__pow__0__I,axiom,
% 162.26/162.05 ! [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))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_comp__funpow,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_funpow__swap1,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_wf__exp,axiom,
% 162.26/162.05 ! [V_R_2,V_n_2,T_a] :
% 162.26/162.05 ( 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))
% 162.26/162.05 => c_Wellfounded_Owf(T_a,V_R_2) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_funpow__mult,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rel__pow__commute,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_relpow_Osimps_I2_J,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rel__pow__1,axiom,
% 162.26/162.05 ! [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 ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rel__pow__add,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_funpow__add,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_funpow_Osimps_I2_J,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rel__pow__Suc__I2,axiom,
% 162.26/162.05 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_a] :
% 162.26/162.05 ( 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))
% 162.26/162.05 => ( 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)))
% 162.26/162.05 => 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))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rel__pow__Suc__I,axiom,
% 162.26/162.05 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ( 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))
% 162.26/162.05 => 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))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__power,axiom,
% 162.26/162.05 ! [V_R_2,V_p_2,T_a] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 162.26/162.05 <=> ? [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))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rel__pow__imp__rtrancl,axiom,
% 162.26/162.05 ! [V_R_2,V_n_2,V_p_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_relpow_Osimps_I1_J,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_funpow_Osimps_I1_J,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_trancl__power,axiom,
% 162.26/162.05 ! [V_R_2,V_p_2,T_a] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
% 162.26/162.05 <=> ? [B_n] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 162.26/162.05 & 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))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_funpow__code__def,axiom,
% 162.26/162.05 ! [T_a] : c_Nat_Ofunpow(T_a) = c_Nat_Ocompow(T_a,T_a) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rel__pow__E,axiom,
% 162.26/162.05 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.05 => V_x_2 != V_z_2 )
% 162.26/162.05 => ~ ! [B_y,B_m] :
% 162.26/162.05 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 162.26/162.05 => ( 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)))
% 162.26/162.05 => ~ 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)) ) ) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rotate__def,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rel__pow__E2,axiom,
% 162.26/162.05 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 162.26/162.05 => V_x_2 != V_z_2 )
% 162.26/162.05 => ~ ! [B_y,B_m] :
% 162.26/162.05 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 162.26/162.05 => ( 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))
% 162.26/162.05 => ~ 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))) ) ) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_pos__not__random__dseq__def,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 162.26/162.05 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] :
% 162.26/162.05 ( 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))))
% 162.26/162.05 => ( ! [B_x] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ! [B_y] :
% 162.26/162.05 ( 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))
% 162.26/162.05 => B_y = B_x ) )
% 162.26/162.05 => 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))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rtrancl__Un__separatorE,axiom,
% 162.26/162.05 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] :
% 162.26/162.05 ( 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))))
% 162.26/162.05 => ( ! [B_x] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ! [B_y] :
% 162.26/162.05 ( 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))
% 162.26/162.05 => B_x = B_y ) )
% 162.26/162.05 => 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))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rel__pow__Suc__D2,axiom,
% 162.26/162.05 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ? [B_y] :
% 162.26/162.05 ( 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))
% 162.26/162.05 & 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))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rel__pow__Suc__E2,axiom,
% 162.26/162.05 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ~ ! [B_y] :
% 162.26/162.05 ( 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))
% 162.26/162.05 => ~ 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))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rel__pow__Suc__E,axiom,
% 162.26/162.05 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ~ ! [B_y] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ~ 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)) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_tranclD,axiom,
% 162.26/162.05 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ? [B_z] :
% 162.26/162.05 ( 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))
% 162.26/162.05 & 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))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_tranclD2,axiom,
% 162.26/162.05 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ? [B_z] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 & 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)) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_IdE,axiom,
% 162.26/162.05 ! [V_p_2,T_a] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a)))
% 162.26/162.05 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_nat__intermed__int__val,axiom,
% 162.26/162.05 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 162.26/162.05 ( ! [B_i] :
% 162.26/162.05 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 162.26/162.05 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 162.26/162.05 => 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))) )
% 162.26/162.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 162.26/162.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 162.26/162.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 162.26/162.05 => ? [B_i] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 162.26/162.05 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 162.26/162.05 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_in__set__conv__decomp,axiom,
% 162.26/162.05 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.05 <=> ? [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)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_in__set__conv__decomp__first,axiom,
% 162.26/162.05 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.05 <=> ? [B_ys] :
% 162.26/162.05 ( ? [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))
% 162.26/162.05 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_ys))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_in__set__conv__decomp__last,axiom,
% 162.26/162.05 ! [V_xs_2,V_x_2,T_a] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.05 <=> ? [B_ys,B_zs] :
% 162.26/162.05 ( 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))
% 162.26/162.05 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_zs))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_mod__div__decomp,axiom,
% 162.26/162.05 ! [V_b,V_a,T_a] :
% 162.26/162.05 ( class_Divides_Osemiring__div(T_a)
% 162.26/162.05 => 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)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_wf__eq__minimal,axiom,
% 162.26/162.05 ! [V_r_2,T_a] :
% 162.26/162.05 ( c_Wellfounded_Owf(T_a,V_r_2)
% 162.26/162.05 <=> ! [B_Q] :
% 162.26/162.05 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q))
% 162.26/162.05 => ? [B_x] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q))
% 162.26/162.05 & ! [B_y] :
% 162.26/162.05 ( 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))
% 162.26/162.05 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),B_Q)) ) ) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_transfer__nat__int__set__cong,axiom,
% 162.26/162.05 ! [V_P_H_2,V_P_2] :
% 162.26/162.05 ( ! [B_x] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 162.26/162.05 => ( hBOOL(hAPP(V_P_2,B_x))
% 162.26/162.05 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 162.26/162.05 => 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)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Int__Collect__mono,axiom,
% 162.26/162.05 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_a] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 162.26/162.05 => ( ! [B_x] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.05 => ( hBOOL(hAPP(V_P_2,B_x))
% 162.26/162.05 => hBOOL(hAPP(V_Q_2,B_x)) ) )
% 162.26/162.05 => 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)))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_UnionE,axiom,
% 162.26/162.05 ! [V_C_2,V_A_2,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ~ ! [B_X] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X))
% 162.26/162.05 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_converseE,axiom,
% 162.26/162.05 ! [V_r_2,V_yx_2,T_b,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ~ ! [B_x,B_y] :
% 162.26/162.05 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_y),B_x)
% 162.26/162.05 => ~ 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)) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_rel__compE,axiom,
% 162.26/162.05 ! [V_s_2,V_r_2,T_c,V_xz_2,T_b,T_a] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => ~ ! [B_x,B_y,B_z] :
% 162.26/162.05 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)
% 162.26/162.05 => ( 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))
% 162.26/162.05 => ~ 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)) ) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 162.26/162.05 ! [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))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 162.26/162.05 ! [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))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Nitpick_Oof__frac__def,axiom,
% 162.26/162.05 ! [V_q,T_a,T_b] :
% 162.26/162.05 ( ( class_Rings_Oinverse(T_b)
% 162.26/162.05 & class_Rings_Oring__1(T_b) )
% 162.26/162.05 => 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))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 162.26/162.05 ! [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))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Nitpick_Oless__frac__def,axiom,
% 162.26/162.05 ! [V_r_2,V_q_2,T_a] :
% 162.26/162.05 ( c_Nitpick_Oless__frac(T_a,V_q_2,V_r_2)
% 162.26/162.05 <=> 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))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 162.26/162.05 ! [V_r_2,V_q_2,T_a] :
% 162.26/162.05 ( c_Nitpick_Oless__eq__frac(T_a,V_q_2,V_r_2)
% 162.26/162.05 <=> 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))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Nitpick_Odenom__def,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Nitpick_Onum__def,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_setprod__pos,axiom,
% 162.26/162.05 ! [V_f_2,V_A_2,T_a,T_b] :
% 162.26/162.05 ( class_Rings_Olinordered__semidom(T_b)
% 162.26/162.05 => ( ! [B_x] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) )
% 162.26/162.05 => 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))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_list__all__length,axiom,
% 162.26/162.05 ! [V_xs_2,V_P_2,T_a] :
% 162.26/162.05 ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
% 162.26/162.05 <=> ! [B_n] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_Ball__set__list__all,axiom,
% 162.26/162.05 ! [V_P_2,V_xs_2,T_a] :
% 162.26/162.05 ( ! [B_x] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.05 => hBOOL(hAPP(V_P_2,B_x)) )
% 162.26/162.05 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_list__all__simps_I1_J,axiom,
% 162.26/162.05 ! [V_xs_2,V_x_2,V_P_2,T_a] :
% 162.26/162.05 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
% 162.26/162.05 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.05 & c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_list__all__append,axiom,
% 162.26/162.05 ! [V_ys_2,V_xs_2,V_P_2,T_a] :
% 162.26/162.05 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
% 162.26/162.05 <=> ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
% 162.26/162.05 & c_List_Olist__all(T_a,V_P_2,V_ys_2) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_list__all__rev,axiom,
% 162.26/162.05 ! [V_xs_2,V_P_2,T_a] :
% 162.26/162.05 ( c_List_Olist__all(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2))
% 162.26/162.05 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_list__all__iff,axiom,
% 162.26/162.05 ! [V_xs_2,V_P_2,T_a] :
% 162.26/162.05 ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
% 162.26/162.05 <=> ! [B_x] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.05 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_list__all__simps_I2_J,axiom,
% 162.26/162.05 ! [V_P_2,T_a] : c_List_Olist__all(T_a,V_P_2,c_List_Olist_ONil(T_a)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_list__all__iff__raw,axiom,
% 162.26/162.05 ! [V_xs_2,V_P_2,T_a] :
% 162.26/162.05 ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
% 162.26/162.05 <=> ! [B_x] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.05 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_list__ex1__simps_I2_J,axiom,
% 162.26/162.05 ! [V_xs_2,V_x_2,V_P_2,T_a] :
% 162.26/162.05 ( c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
% 162.26/162.05 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.05 => 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) )
% 162.26/162.05 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 162.26/162.05 => c_List_Olist__ex1(T_a,V_P_2,V_xs_2) ) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_internal__split__def,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_list__ex1__simps_I1_J,axiom,
% 162.26/162.05 ! [V_P_2,T_a] : ~ c_List_Olist__ex1(T_a,V_P_2,c_List_Olist_ONil(T_a)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_exists1__code,axiom,
% 162.26/162.05 ! [V_P_2,T_a] :
% 162.26/162.05 ( class_Enum_Oenum(T_a)
% 162.26/162.05 => ( ? [B_x] :
% 162.26/162.05 ( hBOOL(hAPP(V_P_2,B_x))
% 162.26/162.05 & ! [B_y] :
% 162.26/162.05 ( hBOOL(hAPP(V_P_2,B_y))
% 162.26/162.05 => B_y = B_x ) )
% 162.26/162.05 <=> c_List_Olist__ex1(T_a,V_P_2,c_Enum_Oenum__class_Oenum(T_a)) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_internal__split__conv,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_list__ex1__iff,axiom,
% 162.26/162.05 ! [V_xs_2,V_P_2,T_a] :
% 162.26/162.05 ( c_List_Olist__ex1(T_a,V_P_2,V_xs_2)
% 162.26/162.05 <=> ? [B_x] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.05 & hBOOL(hAPP(V_P_2,B_x))
% 162.26/162.05 & ! [B_y] :
% 162.26/162.05 ( ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),hAPP(c_List_Oset(T_a),V_xs_2)))
% 162.26/162.05 & hBOOL(hAPP(V_P_2,B_y)) )
% 162.26/162.05 => B_y = B_x ) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_setprod__nonneg,axiom,
% 162.26/162.05 ! [V_f_2,V_A_2,T_a,T_b] :
% 162.26/162.05 ( class_Rings_Olinordered__semidom(T_b)
% 162.26/162.05 => ( ! [B_x] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 162.26/162.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) )
% 162.26/162.05 => 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))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_finite__less__ub,axiom,
% 162.26/162.05 ! [V_u_2,V_f_2] :
% 162.26/162.05 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
% 162.26/162.05 => 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)))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_measure__function__int,axiom,
% 162.26/162.05 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))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_equal__fun__def,axiom,
% 162.26/162.05 ! [V_g_2,V_f_2,T_a,T_b] :
% 162.26/162.05 ( ( class_HOL_Oequal(T_b)
% 162.26/162.05 & class_Enum_Oenum(T_a) )
% 162.26/162.05 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 162.26/162.05 <=> ! [B_x] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a))))
% 162.26/162.05 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_measure__snd,axiom,
% 162.26/162.05 ! [T_b,V_f_2,T_a] :
% 162.26/162.05 ( c_FunDef_Ois__measure(T_a,V_f_2)
% 162.26/162.05 => 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))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_eq__equal,axiom,
% 162.26/162.05 ! [T_a] :
% 162.26/162.05 ( class_HOL_Oequal(T_a)
% 162.26/162.05 => c_fequal = c_HOL_Oequal__class_Oequal(T_a) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_equal__eq,axiom,
% 162.26/162.05 ! [V_y_2,V_x_2,T_a] :
% 162.26/162.05 ( class_HOL_Oequal(T_a)
% 162.26/162.05 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x_2),V_y_2))
% 162.26/162.05 <=> V_x_2 = V_y_2 ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_equal__refl,axiom,
% 162.26/162.05 ! [V_x,T_a] :
% 162.26/162.05 ( class_HOL_Oequal(T_a)
% 162.26/162.05 => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_equal,axiom,
% 162.26/162.05 ! [T_a] :
% 162.26/162.05 ( class_HOL_Oequal(T_a)
% 162.26/162.05 => c_HOL_Oequal__class_Oequal(T_a) = c_fequal ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_is__measure_Osimps,axiom,
% 162.26/162.05 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_is__measure_Oequations,axiom,
% 162.26/162.05 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_is__measure_Ointros,axiom,
% 162.26/162.05 ! [V_f_2,T_a] : c_FunDef_Ois__measure(T_a,V_f_2) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_measure__size,axiom,
% 162.26/162.05 ! [T_a] :
% 162.26/162.05 ( class_Nat_Osize(T_a)
% 162.26/162.05 => c_FunDef_Ois__measure(T_a,c_Nat_Osize__class_Osize(T_a)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_measure__fst,axiom,
% 162.26/162.05 ! [T_b,V_f_2,T_a] :
% 162.26/162.05 ( c_FunDef_Ois__measure(T_a,V_f_2)
% 162.26/162.05 => 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))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_transfer__morphism__int__nat,axiom,
% 162.26/162.05 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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 162.26/162.05 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] :
% 162.26/162.05 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 162.26/162.05 => 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) )
% 162.26/162.05 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 162.26/162.05 => 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)) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_eq__int__code_I2_J,axiom,
% 162.26/162.05 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_eq__int__code_I5_J,axiom,
% 162.26/162.05 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_eq__int__code_I12_J,axiom,
% 162.26/162.05 ! [V_k1_2] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin))
% 162.26/162.05 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_eq__int__code_I8_J,axiom,
% 162.26/162.05 ! [V_k2_2] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2)))
% 162.26/162.05 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_eq__int__code_I11_J,axiom,
% 162.26/162.05 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_eq__int__code_I7_J,axiom,
% 162.26/162.05 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_eq__int__code_I9_J,axiom,
% 162.26/162.05 ! [V_k1_2] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls))
% 162.26/162.05 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_eq__int__code_I3_J,axiom,
% 162.26/162.05 ! [V_k2_2] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2)))
% 162.26/162.05 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_eq__int__code_I15_J,axiom,
% 162.26/162.05 ! [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))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_eq__int__code_I14_J,axiom,
% 162.26/162.05 ! [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))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_equal__int__def,axiom,
% 162.26/162.05 ! [V_l_2,V_k_2] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2))
% 162.26/162.05 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_eq__int__code_I6_J,axiom,
% 162.26/162.05 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_eq__int__code_I1_J,axiom,
% 162.26/162.05 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_eq__int__code_I16_J,axiom,
% 162.26/162.05 ! [V_k2_2,V_k1_2] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 162.26/162.05 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_eq__int__code_I13_J,axiom,
% 162.26/162.05 ! [V_k2_2,V_k1_2] :
% 162.26/162.05 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 162.26/162.05 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_eq__number__of__int__code,axiom,
% 162.26/162.05 ! [V_l_2,V_k_2] :
% 162.26/162.05 ( 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)))
% 162.26/162.05 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_eq__int__code_I10_J,axiom,
% 162.26/162.05 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_eq__int__code_I4_J,axiom,
% 162.26/162.05 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_bool_Osize_I4_J,axiom,
% 162.26/162.05 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_bool_Osize_I3_J,axiom,
% 162.26/162.05 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 162.26/162.05 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_eq__int__refl,axiom,
% 162.26/162.05 ! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_pos__empty__def,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_pos__bind__def,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_size__code,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_lazy__sequence__size__code,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_seq__case,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_yieldn__def,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_lazy__sequence_Osize_I2_J,axiom,
% 162.26/162.05 ! [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))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_lazy__sequence_Osimps_I5_J,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_lazy__sequence_Oinject,axiom,
% 162.26/162.05 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_a] :
% 162.26/162.05 ( 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)
% 162.26/162.05 <=> ( V_a_2 = V_a_H_2
% 162.26/162.05 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact__01,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_lazy__sequence_Osize_I4_J,axiom,
% 162.26/162.05 ! [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))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_pos__map__def,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 162.26/162.05 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] :
% 162.26/162.05 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 162.26/162.05 => 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) )
% 162.26/162.05 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 162.26/162.05 => 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)) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_pos__single__def,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_New__DSequence_Opos__single__def,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_neg__bind__def,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact__02,axiom,
% 162.26/162.05 ! [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)))) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_neg__map__def,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_small__lazy__list_Osimps,axiom,
% 162.26/162.05 ! [V_d_2,T_a] :
% 162.26/162.05 ( class_Lazy__Sequence_Osmall__lazy(T_a)
% 162.26/162.05 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_a),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_a),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),c_Lazy__Sequence_Oproduct(T_a,tc_List_Olist(T_a),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a))),T_a),hAPP(c_COMBB(tc_List_Olist(T_a),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a)),tc_List_Olist(T_a)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_a)))),c_List_Olist_OCons(T_a))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_a)))) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_small__lazy__prod__def,axiom,
% 162.26/162.05 ! [V_d,T_b,T_a] :
% 162.26/162.05 ( ( class_Lazy__Sequence_Osmall__lazy(T_a)
% 162.26/162.05 & class_Lazy__Sequence_Osmall__lazy(T_b) )
% 162.26/162.05 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(T_a,T_b),V_d) = c_Lazy__Sequence_Oproduct(T_a,T_b,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,V_d),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,V_d)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact__03,axiom,
% 162.26/162.05 ! [V_yq,V_xq,V_x,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq),V_yq) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,c_Lazy__Sequence_Oappend(T_a,V_xq,V_yq)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_neg__single__def,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_New__DSequence_Opos__union__def,axiom,
% 162.26/162.05 ! [V_i_2,V_yq_2,V_xq_2,T_a] : hAPP(c_New__DSequence_Opos__union(T_a,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_a,hAPP(V_xq_2,V_i_2),hAPP(V_yq_2,V_i_2)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_pos__union__def,axiom,
% 162.26/162.05 ! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_a] : c_New__Random__Sequence_Opos__union(T_a,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_a,hAPP(hAPP(hAPP(V_R1_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(hAPP(V_R2_2,V_nrandom_2),V_size_2),V_seed_2)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_small__lazy_H_Osimps,axiom,
% 162.26/162.05 ! [V_i,V_d] :
% 162.26/162.05 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 162.26/162.05 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 162.26/162.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 162.26/162.05 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i),c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_small__lazy_H_Opsimps,axiom,
% 162.26/162.05 ! [V_i_2,V_d_2] :
% 162.26/162.05 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2)))
% 162.26/162.05 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 162.26/162.05 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 162.26/162.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 162.26/162.05 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i_2),c_Lazy__Sequence_Osmall__lazy_H(V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_small__lazy__int__def,axiom,
% 162.26/162.05 ! [V_d] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,V_d) = c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d)) ).
% 162.26/162.05
% 162.26/162.05 fof(fact_small__lazy_H_Opinduct,axiom,
% 162.26/162.05 ! [V_P_2,V_a1_2,V_a0_2] :
% 162.26/162.05 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 162.26/162.05 => ( ! [B_d,B_i] :
% 162.26/162.05 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i)))
% 162.26/162.05 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 162.26/162.05 => hBOOL(hAPP(hAPP(V_P_2,B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
% 162.26/162.05 => hBOOL(hAPP(hAPP(V_P_2,B_d),B_i)) ) )
% 162.26/162.05 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 162.26/162.05
% 162.26/162.05 %----Arity declarations (237)
% 162.26/162.05 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 162.26/162.05 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 162.26/162.05 ! [T_2,T_1] :
% 162.26/162.05 ( class_Lattices_Obounded__lattice(T_1)
% 162.26/162.05 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 162.26/162.05 ! [T_2,T_1] :
% 162.26/162.05 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 162.26/162.05 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 162.26/162.05 ! [T_2,T_1] :
% 162.26/162.05 ( class_Lattices_Obounded__lattice(T_1)
% 162.26/162.05 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 162.26/162.05 ! [T_2,T_1] :
% 162.26/162.05 ( class_Lattices_Obounded__lattice(T_1)
% 162.26/162.05 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 162.26/162.05 ! [T_2,T_1] :
% 162.26/162.05 ( class_Lattices_Olattice(T_1)
% 162.26/162.05 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 162.26/162.05 ! [T_2,T_1] :
% 162.26/162.05 ( class_Lattices_Olattice(T_1)
% 162.26/162.05 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 162.26/162.05 ! [T_2,T_1] :
% 162.26/162.05 ( class_Lattices_Odistrib__lattice(T_1)
% 162.26/162.05 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 162.26/162.05 ! [T_2,T_1] :
% 162.26/162.05 ( class_Lattices_Oboolean__algebra(T_1)
% 162.26/162.05 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_fun__Orderings_Opreorder,axiom,
% 162.26/162.05 ! [T_2,T_1] :
% 162.26/162.05 ( class_Orderings_Opreorder(T_1)
% 162.26/162.05 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 162.26/162.05 ! [T_1,T_2] :
% 162.26/162.05 ( ( class_Finite__Set_Ofinite(T_2)
% 162.26/162.05 & class_Finite__Set_Ofinite(T_1) )
% 162.26/162.05 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_fun__Lattices_Olattice,axiom,
% 162.26/162.05 ! [T_2,T_1] :
% 162.26/162.05 ( class_Lattices_Olattice(T_1)
% 162.26/162.05 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_fun__Orderings_Oorder,axiom,
% 162.26/162.05 ! [T_2,T_1] :
% 162.26/162.05 ( class_Orderings_Oorder(T_1)
% 162.26/162.05 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_fun__Orderings_Otop,axiom,
% 162.26/162.05 ! [T_2,T_1] :
% 162.26/162.05 ( class_Orderings_Otop(T_1)
% 162.26/162.05 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_fun__Orderings_Oord,axiom,
% 162.26/162.05 ! [T_2,T_1] :
% 162.26/162.05 ( class_Orderings_Oord(T_1)
% 162.26/162.05 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_fun__Orderings_Obot,axiom,
% 162.26/162.05 ! [T_2,T_1] :
% 162.26/162.05 ( class_Orderings_Obot(T_1)
% 162.26/162.05 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_fun__Groups_Ouminus,axiom,
% 162.26/162.05 ! [T_2,T_1] :
% 162.26/162.05 ( class_Groups_Ouminus(T_1)
% 162.26/162.05 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_fun__Groups_Ominus,axiom,
% 162.26/162.05 ! [T_2,T_1] :
% 162.26/162.05 ( class_Groups_Ominus(T_1)
% 162.26/162.05 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_fun__HOL_Oequal,axiom,
% 162.26/162.05 ! [T_1,T_2] :
% 162.26/162.05 ( ( class_Enum_Oenum(T_2)
% 162.26/162.05 & class_HOL_Oequal(T_1) )
% 162.26/162.05 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_fun__Enum_Oenum,axiom,
% 162.26/162.05 ! [T_1,T_2] :
% 162.26/162.05 ( ( class_Enum_Oenum(T_2)
% 162.26/162.05 & class_Enum_Oenum(T_1) )
% 162.26/162.05 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Com__Ocom__HOL_Oequal,axiom,
% 162.26/162.05 class_HOL_Oequal(tc_Com_Ocom) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Com__Ocom__Nat_Osize,axiom,
% 162.26/162.05 class_Nat_Osize(tc_Com_Ocom) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 162.26/162.05 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 162.26/162.05 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 162.26/162.05 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 162.26/162.05 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 162.26/162.05 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 162.26/162.05 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 162.26/162.05 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 162.26/162.05 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 162.26/162.05 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 162.26/162.05 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 162.26/162.05 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 162.26/162.05 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 162.26/162.05 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 162.26/162.05 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 162.26/162.05 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 162.26/162.05 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 162.26/162.05 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 162.26/162.05 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 162.26/162.05 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 162.26/162.05 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 162.26/162.05 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 162.26/162.05 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom,
% 162.26/162.05 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 162.26/162.05 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 162.26/162.05 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 162.26/162.05 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 162.26/162.05 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 162.26/162.05 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 162.26/162.05 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 162.26/162.05 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 162.26/162.05 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 162.26/162.05 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 162.26/162.05 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 162.26/162.05 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 162.26/162.05 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 162.26/162.05 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 162.26/162.05 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 162.26/162.05 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 162.26/162.05 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 162.26/162.05 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 162.26/162.05 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 162.26/162.05 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 162.26/162.05 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 162.26/162.05 class_Orderings_Opreorder(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 162.26/162.05 class_Orderings_Olinorder(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 162.26/162.05 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 162.26/162.05 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 162.26/162.05 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Smallcheck_Osmall,axiom,
% 162.26/162.05 class_Smallcheck_Osmall(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 162.26/162.05 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 162.26/162.05 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 162.26/162.05 class_Lattices_Olattice(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 162.26/162.05 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 162.26/162.05 class_Divides_Oring__div(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 162.26/162.05 class_Rings_Omult__zero(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 162.26/162.05 class_Orderings_Oorder(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 162.26/162.05 class_Int_Oring__char__0(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 162.26/162.05 class_Int_Onumber__ring(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 162.26/162.05 class_Rings_Osemiring(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 162.26/162.05 class_Orderings_Oord(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 162.26/162.05 class_Groups_Ouminus(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 162.26/162.05 class_Groups_Osgn__if(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 162.26/162.05 class_Groups_Oabs__if(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 162.26/162.05 class_Rings_Oring__1(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 162.26/162.05 class_Groups_Ominus(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Power_Opower,axiom,
% 162.26/162.05 class_Power_Opower(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 162.26/162.05 class_Groups_Ozero(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Oring,axiom,
% 162.26/162.05 class_Rings_Oring(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 162.26/162.05 class_Rings_Oidom(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Int_Onumber,axiom,
% 162.26/162.05 class_Int_Onumber(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__Groups_Oone,axiom,
% 162.26/162.05 class_Groups_Oone(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Int__Oint__HOL_Oequal,axiom,
% 162.26/162.05 class_HOL_Oequal(tc_Int_Oint) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 162.26/162.05 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 162.26/162.05 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 162.26/162.05 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 162.26/162.05 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 162.26/162.05 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 162.26/162.05 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 162.26/162.05 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 162.26/162.05 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 162.26/162.05 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 162.26/162.05 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 162.26/162.05 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 162.26/162.05 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 162.26/162.05 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 162.26/162.05 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 162.26/162.05 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 162.26/162.05 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 162.26/162.05 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 162.26/162.05 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 162.26/162.05 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 162.26/162.05 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 162.26/162.05 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 162.26/162.05 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 162.26/162.05 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 162.26/162.05 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 162.26/162.05 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 162.26/162.05 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 162.26/162.05 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 162.26/162.05 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 162.26/162.05 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 162.26/162.05 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 162.26/162.05 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 162.26/162.05 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 162.26/162.05 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 162.26/162.05 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 162.26/162.05 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 162.26/162.05 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 162.26/162.05 class_Lattices_Olattice(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 162.26/162.05 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 162.26/162.05 class_Orderings_Oorder(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 162.26/162.05 class_Rings_Osemiring(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 162.26/162.05 class_Orderings_Oord(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 162.26/162.05 class_Orderings_Obot(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 162.26/162.05 class_Groups_Ominus(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Power_Opower,axiom,
% 162.26/162.05 class_Power_Opower(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 162.26/162.05 class_Groups_Ozero(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 162.26/162.05 class_Int_Onumber(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 162.26/162.05 class_Groups_Oone(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__HOL_Oequal,axiom,
% 162.26/162.05 class_HOL_Oequal(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Nat__Onat__Nat_Osize,axiom,
% 162.26/162.05 class_Nat_Osize(tc_Nat_Onat) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 162.26/162.05 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 162.26/162.05 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 162.26/162.05 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 162.26/162.05 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 162.26/162.05 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 162.26/162.05 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 162.26/162.05 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 162.26/162.05 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 162.26/162.05 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 162.26/162.05 class_Lattices_Olattice(tc_HOL_Obool) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 162.26/162.05 class_Orderings_Oorder(tc_HOL_Obool) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 162.26/162.05 class_Orderings_Otop(tc_HOL_Obool) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 162.26/162.05 class_Orderings_Oord(tc_HOL_Obool) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 162.26/162.05 class_Orderings_Obot(tc_HOL_Obool) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 162.26/162.05 class_Groups_Ouminus(tc_HOL_Obool) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 162.26/162.05 class_Groups_Ominus(tc_HOL_Obool) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_HOL__Obool__HOL_Oequal,axiom,
% 162.26/162.05 class_HOL_Oequal(tc_HOL_Obool) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_HOL__Obool__Enum_Oenum,axiom,
% 162.26/162.05 class_Enum_Oenum(tc_HOL_Obool) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_HOL__Obool__Nat_Osize,axiom,
% 162.26/162.05 class_Nat_Osize(tc_HOL_Obool) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Com__Ostate__HOL_Oequal,axiom,
% 162.26/162.05 class_HOL_Oequal(tc_Com_Ostate) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Com__Ostate__Nat_Osize,axiom,
% 162.26/162.05 class_Nat_Osize(tc_Com_Ostate) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Com__Ovname__HOL_Oequal,axiom,
% 162.26/162.05 class_HOL_Oequal(tc_Com_Ovname) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Com__Ovname__Nat_Osize,axiom,
% 162.26/162.05 class_Nat_Osize(tc_Com_Ovname) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom,
% 162.26/162.05 ! [T_1] :
% 162.26/162.05 ( class_Lazy__Sequence_Osmall__lazy(T_1)
% 162.26/162.05 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_List__Olist__HOL_Oequal,axiom,
% 162.26/162.05 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_List__Olist__Nat_Osize,axiom,
% 162.26/162.05 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 162.26/162.05 ! [T_1,T_2] :
% 162.26/162.05 ( ( class_Finite__Set_Ofinite(T_2)
% 162.26/162.05 & class_Finite__Set_Ofinite(T_1) )
% 162.26/162.05 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_sum__HOL_Oequal,axiom,
% 162.26/162.05 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_sum__Enum_Oenum,axiom,
% 162.26/162.05 ! [T_1,T_2] :
% 162.26/162.05 ( ( class_Enum_Oenum(T_2)
% 162.26/162.05 & class_Enum_Oenum(T_1) )
% 162.26/162.05 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_sum__Nat_Osize,axiom,
% 162.26/162.05 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 162.26/162.05 ! [T_1] :
% 162.26/162.05 ( class_Finite__Set_Ofinite(T_1)
% 162.26/162.05 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Option__Ooption__HOL_Oequal,axiom,
% 162.26/162.05 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Option__Ooption__Enum_Oenum,axiom,
% 162.26/162.05 ! [T_1] :
% 162.26/162.05 ( class_Enum_Oenum(T_1)
% 162.26/162.05 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Option__Ooption__Nat_Osize,axiom,
% 162.26/162.05 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom,
% 162.26/162.05 ! [T_1,T_2] :
% 162.26/162.05 ( ( class_Lazy__Sequence_Osmall__lazy(T_2)
% 162.26/162.05 & class_Lazy__Sequence_Osmall__lazy(T_1) )
% 162.26/162.05 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 162.26/162.05 ! [T_1,T_2] :
% 162.26/162.05 ( ( class_Finite__Set_Ofinite(T_2)
% 162.26/162.05 & class_Finite__Set_Ofinite(T_1) )
% 162.26/162.05 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_prod__Smallcheck_Osmall,axiom,
% 162.26/162.05 ! [T_1,T_2] :
% 162.26/162.05 ( ( class_Smallcheck_Osmall(T_2)
% 162.26/162.05 & class_Smallcheck_Osmall(T_1) )
% 162.26/162.05 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_prod__HOL_Oequal,axiom,
% 162.26/162.05 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_prod__Enum_Oenum,axiom,
% 162.26/162.05 ! [T_1,T_2] :
% 162.26/162.05 ( ( class_Enum_Oenum(T_2)
% 162.26/162.05 & class_Enum_Oenum(T_1) )
% 162.26/162.05 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_prod__Nat_Osize,axiom,
% 162.26/162.05 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom,
% 162.26/162.05 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 162.26/162.05 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom,
% 162.26/162.05 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom,
% 162.26/162.05 class_HOL_Oequal(tc_Product__Type_Ounit) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
% 162.26/162.05 class_Enum_Oenum(tc_Product__Type_Ounit) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
% 162.26/162.05 class_Nat_Osize(tc_Product__Type_Ounit) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom,
% 162.26/162.05 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
% 162.26/162.05 class_Nat_Osize(tc_Code__Evaluation_Oterm) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom,
% 162.26/162.05 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
% 162.26/162.05 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 162.26/162.05 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 162.26/162.05 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 162.26/162.05 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 162.26/162.05 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 162.26/162.05 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 162.26/162.05 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 162.26/162.05 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 162.26/162.05 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 162.26/162.05 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 162.26/162.05 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 162.26/162.05 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 162.26/162.05 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 162.26/162.05 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 162.26/162.05 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 162.26/162.05 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 162.26/162.05 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 162.26/162.05 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 162.26/162.05 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 162.26/162.05 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 162.26/162.05 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 162.26/162.05 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 162.26/162.05 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 162.26/162.05 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 162.26/162.05 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 162.26/162.05 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 162.26/162.05 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 162.26/162.05 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 162.26/162.05 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 162.26/162.05 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 162.26/162.05 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 162.26/162.05 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 162.26/162.05 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 162.26/162.05 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 162.26/162.05 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 162.26/162.05 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 162.26/162.05 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 162.26/162.05 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 162.26/162.05 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 162.26/162.05 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 162.26/162.05 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom,
% 162.26/162.05 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
% 162.26/162.05 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom,
% 162.26/162.05 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 162.26/162.05
% 162.26/162.05 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
% 162.26/162.05 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 162.26/162.05
% 162.26/162.05 %----Helper facts (20)
% 162.26/162.05 fof(help_c__COMBI__1,axiom,
% 162.26/162.05 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 162.26/162.05
% 162.26/162.05 fof(help_c__COMBK__1,axiom,
% 162.26/162.05 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 162.26/162.05
% 162.26/162.05 fof(help_c__COMBB__1,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(help_c__COMBC__1,axiom,
% 162.26/162.05 ! [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) ).
% 162.26/162.05
% 162.26/162.05 fof(help_c__COMBS__1,axiom,
% 162.26/162.05 ! [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)) ).
% 162.26/162.05
% 162.26/162.05 fof(help_c__fequal__1,axiom,
% 162.26/162.05 ! [V_y_2,V_x_2] :
% 162.26/162.05 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 162.26/162.05 | V_x_2 = V_y_2 ) ).
% 162.26/162.05
% 162.26/162.05 fof(help_c__fequal__2,axiom,
% 162.26/162.05 ! [V_y_2,V_x_2] :
% 162.26/162.05 ( V_x_2 != V_y_2
% 162.26/162.05 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(help_c__fFalse__1,axiom,
% 162.26/162.05 ~ hBOOL(c_fFalse) ).
% 162.26/162.05
% 162.26/162.05 fof(help_c__fTrue__1,axiom,
% 162.26/162.05 hBOOL(c_fTrue) ).
% 162.26/162.05
% 162.26/162.05 fof(help_c__fNot__1,axiom,
% 162.26/162.05 ! [V_P_2] :
% 162.26/162.05 ( ~ hBOOL(hAPP(c_fNot,V_P_2))
% 162.26/162.05 | ~ hBOOL(V_P_2) ) ).
% 162.26/162.05
% 162.26/162.05 fof(help_c__fNot__2,axiom,
% 162.26/162.05 ! [V_P_2] :
% 162.26/162.05 ( ~ ~ hBOOL(V_P_2)
% 162.26/162.05 | hBOOL(hAPP(c_fNot,V_P_2)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(help_c__fconj__1,axiom,
% 162.26/162.05 ! [V_Q_2,V_P_2] :
% 162.26/162.05 ( ~ hBOOL(V_P_2)
% 162.26/162.05 | ~ hBOOL(V_Q_2)
% 162.26/162.05 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(help_c__fconj__2,axiom,
% 162.26/162.05 ! [V_Q_2,V_P_2] :
% 162.26/162.05 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 162.26/162.05 | hBOOL(V_P_2) ) ).
% 162.26/162.05
% 162.26/162.05 fof(help_c__fconj__3,axiom,
% 162.26/162.05 ! [V_Q_2,V_P_2] :
% 162.26/162.05 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 162.26/162.05 | hBOOL(V_Q_2) ) ).
% 162.26/162.05
% 162.26/162.05 fof(help_c__fdisj__1,axiom,
% 162.26/162.05 ! [V_Q_2,V_P_2] :
% 162.26/162.05 ( ~ hBOOL(V_P_2)
% 162.26/162.05 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(help_c__fdisj__2,axiom,
% 162.26/162.05 ! [V_P_2,V_Q_2] :
% 162.26/162.05 ( ~ hBOOL(V_Q_2)
% 162.26/162.05 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(help_c__fdisj__3,axiom,
% 162.26/162.05 ! [V_Q_2,V_P_2] :
% 162.26/162.05 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
% 162.26/162.05 | hBOOL(V_P_2)
% 162.26/162.05 | hBOOL(V_Q_2) ) ).
% 162.26/162.05
% 162.26/162.05 fof(help_c__fimplies__1,axiom,
% 162.26/162.05 ! [V_Q_2,V_P_2] :
% 162.26/162.05 ( hBOOL(V_P_2)
% 162.26/162.05 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(help_c__fimplies__2,axiom,
% 162.26/162.05 ! [V_P_2,V_Q_2] :
% 162.26/162.05 ( ~ hBOOL(V_Q_2)
% 162.26/162.05 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 162.26/162.05
% 162.26/162.05 fof(help_c__fimplies__3,axiom,
% 162.26/162.05 ! [V_Q_2,V_P_2] :
% 162.26/162.05 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
% 162.26/162.05 | ~ hBOOL(V_P_2)
% 162.26/162.05 | hBOOL(V_Q_2) ) ).
% 162.26/162.05
% 162.26/162.05 %----Conjectures (5)
% 162.26/162.05 fof(conj_0,hypothesis,
% 162.26/162.05 c_Hoare__Mirabelle_Ostate__not__singleton ).
% 162.26/162.05
% 162.26/162.05 fof(conj_1,hypothesis,
% 162.26/162.05 c_Com_OWT__bodies ).
% 162.26/162.05
% 162.26/162.05 fof(conj_2,hypothesis,
% 162.26/162.05 hBOOL(hAPP(c_Com_OWT,v_c)) ).
% 162.26/162.05
% 162.26/162.05 fof(conj_3,hypothesis,
% 162.26/162.05 hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) ).
% 162.26/162.05
% 162.26/162.05 fof(conj_4,conjecture,
% 162.26/162.05 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,hAPP(c_Com_Ocom_OBODY,v_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ).
% 162.26/162.05
% 162.26/162.05 %------------------------------------------------------------------------------
% 162.26/162.05 %-------------------------------------------
% 162.26/162.05 % Proof found
% 162.26/162.05 % SZS status Theorem for theBenchmark
% 162.26/162.05 % SZS output start Proof
% 162.26/162.05 %ClaNum:10239(EqnAxiom:2898)
% 162.26/162.05 %VarNum:70068(SingletonVarNum:20445)
% 162.26/162.05 %MaxLitNum:8
% 162.26/162.05 %MaxfuncDepth:15
% 162.26/162.05 %SharedTerms:1126
% 162.26/162.05 %goalClause: 4582
% 162.26/162.05 %singleGoalClaCount:1
% 162.26/162.05 [2899]P1(a5000)
% 162.26/162.05 [2900]P2(a5000)
% 162.26/162.05 [2904]P24(a195)
% 162.26/162.05 [2905]P25(a877)
% 162.26/162.05 [2906]P25(a883)
% 162.26/162.05 [2907]P26(a877)
% 162.26/162.05 [2908]P26(a886)
% 162.26/162.05 [2909]P65(a877)
% 162.26/162.05 [2910]P65(a883)
% 162.26/162.05 [2911]P65(a1)
% 162.26/162.05 [2912]P65(a105)
% 162.26/162.05 [2913]P106(a877)
% 162.26/162.05 [2914]P106(a883)
% 162.26/162.05 [2915]P106(a1)
% 162.26/162.05 [2916]P106(a105)
% 162.26/162.05 [2917]P107(a883)
% 162.26/162.05 [2918]P107(a1)
% 162.26/162.05 [2919]P107(a105)
% 162.26/162.05 [2920]P108(a877)
% 162.26/162.05 [2921]P108(a883)
% 162.26/162.05 [2922]P108(a1)
% 162.26/162.05 [2923]P108(a105)
% 162.26/162.05 [2924]P109(a877)
% 162.26/162.05 [2925]P109(a883)
% 162.26/162.05 [2926]P109(a1)
% 162.26/162.05 [2927]P109(a105)
% 162.26/162.05 [2928]P110(a883)
% 162.26/162.05 [2929]P110(a1)
% 162.26/162.05 [2930]P110(a105)
% 162.26/162.05 [2931]P66(a1)
% 162.26/162.05 [2932]P77(a1)
% 162.26/162.05 [2933]P81(a883)
% 162.26/162.05 [2934]P81(a1)
% 162.26/162.05 [2935]P81(a105)
% 162.26/162.05 [2936]P84(a883)
% 162.26/162.05 [2937]P84(a1)
% 162.26/162.05 [2938]P84(a105)
% 162.26/162.05 [2939]P111(a1)
% 162.26/162.05 [2940]P67(a883)
% 162.26/162.05 [2941]P67(a1)
% 162.26/162.05 [2942]P67(a105)
% 162.26/162.05 [2943]P68(a883)
% 162.26/162.05 [2944]P68(a1)
% 162.26/162.05 [2945]P68(a105)
% 162.26/162.05 [2946]P69(a883)
% 162.26/162.05 [2947]P69(a1)
% 162.26/162.05 [2948]P69(a105)
% 162.26/162.05 [2949]P70(a1)
% 162.26/162.05 [2950]P78(a883)
% 162.26/162.05 [2951]P78(a1)
% 162.26/162.05 [2952]P78(a105)
% 162.26/162.05 [2953]P71(a883)
% 162.26/162.05 [2954]P71(a1)
% 162.26/162.05 [2955]P71(a105)
% 162.26/162.05 [2956]P112(a1)
% 162.26/162.05 [2957]P125(a1)
% 162.26/162.05 [2958]P137(a1)
% 162.26/162.05 [2959]P85(a877)
% 162.26/162.05 [2960]P86(a877)
% 162.26/162.05 [2961]P86(a1)
% 162.26/162.05 [2962]P126(a1)
% 162.26/162.05 [2963]P113(a883)
% 162.26/162.05 [2964]P113(a1)
% 162.26/162.05 [2965]P113(a105)
% 162.26/162.05 [2966]P139(a883)
% 162.26/162.05 [2967]P139(a1)
% 162.26/162.05 [2968]P139(a105)
% 162.26/162.05 [2969]P82(a883)
% 162.26/162.05 [2970]P82(a1)
% 162.26/162.05 [2971]P82(a105)
% 162.26/162.05 [2972]P79(a883)
% 162.26/162.05 [2973]P79(a1)
% 162.26/162.05 [2974]P79(a105)
% 162.26/162.05 [2975]P73(a883)
% 162.26/162.05 [2976]P73(a1)
% 162.26/162.05 [2977]P73(a105)
% 162.26/162.05 [2978]P114(a1)
% 162.26/162.05 [2979]P118(a883)
% 162.26/162.05 [2980]P118(a1)
% 162.26/162.05 [2981]P118(a105)
% 162.26/162.05 [2982]P141(a883)
% 162.26/162.05 [2983]P141(a1)
% 162.26/162.05 [2984]P127(a1)
% 162.26/162.05 [2985]P90(a883)
% 162.26/162.05 [2986]P90(a1)
% 162.26/162.05 [2987]P90(a105)
% 162.26/162.05 [2988]P80(a883)
% 162.26/162.05 [2989]P80(a1)
% 162.26/162.05 [2990]P80(a105)
% 162.26/162.05 [2991]P74(a883)
% 162.26/162.05 [2992]P74(a1)
% 162.26/162.05 [2993]P74(a105)
% 162.26/162.05 [2994]P75(a1)
% 162.26/162.05 [2995]P130(a883)
% 162.26/162.05 [2996]P130(a1)
% 162.26/162.05 [2997]P130(a105)
% 162.26/162.05 [2998]P140(a1)
% 162.26/162.05 [2999]P131(a883)
% 162.26/162.05 [3000]P131(a1)
% 162.26/162.05 [3001]P131(a105)
% 162.26/162.05 [3002]P142(a883)
% 162.26/162.05 [3003]P142(a1)
% 162.26/162.05 [3004]P142(a105)
% 162.26/162.05 [3005]P87(a883)
% 162.26/162.05 [3006]P87(a1)
% 162.26/162.05 [3007]P87(a105)
% 162.26/162.05 [3008]P133(a883)
% 162.26/162.05 [3009]P133(a1)
% 162.26/162.05 [3010]P133(a105)
% 162.26/162.05 [3011]P135(a883)
% 162.26/162.05 [3012]P135(a1)
% 162.26/162.05 [3013]P135(a105)
% 162.26/162.05 [3014]P134(a883)
% 162.26/162.05 [3015]P134(a1)
% 162.26/162.05 [3016]P134(a105)
% 162.26/162.05 [3017]P123(a1)
% 162.26/162.05 [3018]P124(a1)
% 162.26/162.05 [3019]P132(a883)
% 162.26/162.05 [3020]P132(a1)
% 162.26/162.05 [3021]P132(a105)
% 162.26/162.05 [3022]P121(a883)
% 162.26/162.05 [3023]P121(a1)
% 162.26/162.05 [3024]P121(a105)
% 162.26/162.05 [3025]P128(a883)
% 162.26/162.05 [3026]P128(a1)
% 162.26/162.05 [3027]P128(a105)
% 162.26/162.05 [3028]P129(a1)
% 162.26/162.05 [3029]P138(a1)
% 162.26/162.05 [3030]P91(a1)
% 162.26/162.05 [3031]P88(a1)
% 162.26/162.05 [3032]P92(a883)
% 162.26/162.05 [3033]P92(a1)
% 162.26/162.05 [3034]P92(a105)
% 162.26/162.05 [3035]P94(a1)
% 162.26/162.05 [3036]P96(a877)
% 162.26/162.05 [3037]P96(a883)
% 162.26/162.05 [3038]P96(a1)
% 162.26/162.05 [3039]P101(a877)
% 162.26/162.05 [3040]P101(a883)
% 162.26/162.05 [3041]P101(a1)
% 162.26/162.05 [3042]P97(a877)
% 162.26/162.05 [3043]P143(a883)
% 162.26/162.05 [3044]P143(a1)
% 162.26/162.05 [3045]P143(a105)
% 162.26/162.05 [3046]P27(a877)
% 162.26/162.05 [3047]P103(a883)
% 162.26/162.05 [3048]P103(a1)
% 162.26/162.05 [3049]P103(a105)
% 162.26/162.05 [3050]P58(a883)
% 162.26/162.05 [3051]P58(a1)
% 162.26/162.05 [3052]P58(a105)
% 162.26/162.05 [3053]P59(a1)
% 162.26/162.05 [3054]P115(a883)
% 162.26/162.05 [3055]P115(a1)
% 162.26/162.05 [3056]P115(a105)
% 162.26/162.05 [3057]P144(a883)
% 162.26/162.05 [3058]P144(a1)
% 162.26/162.05 [3059]P144(a105)
% 162.26/162.05 [3060]P145(a1)
% 162.26/162.05 [3061]P145(a886)
% 162.26/162.05 [3062]P102(a877)
% 162.26/162.05 [3063]P102(a883)
% 162.26/162.05 [3064]P102(a1)
% 162.26/162.05 [3065]P99(a877)
% 162.26/162.05 [3066]P99(a883)
% 162.26/162.05 [3067]P99(a1)
% 162.26/162.05 [3068]P83(a1)
% 162.26/162.05 [3069]P136(a1)
% 162.26/162.05 [3070]P72(a1)
% 162.26/162.05 [3071]P100(a877)
% 162.26/162.05 [3072]P116(a877)
% 162.26/162.05 [3073]P76(a883)
% 162.26/162.05 [3074]P76(a1)
% 162.26/162.05 [3075]P76(a105)
% 162.26/162.05 [3076]P117(a883)
% 162.26/162.05 [3077]P89(a883)
% 162.26/162.05 [3078]P89(a1)
% 162.26/162.05 [3079]P89(a105)
% 162.26/162.05 [3080]P60(a877)
% 162.26/162.05 [3081]P60(a886)
% 162.26/162.05 [3082]P93(a877)
% 162.26/162.05 [3083]P93(a878)
% 162.26/162.05 [3084]P93(a879)
% 162.26/162.05 [3085]P93(a883)
% 162.26/162.05 [3086]P93(a1)
% 162.26/162.05 [3087]P93(a327)
% 162.26/162.05 [3088]P93(a105)
% 162.26/162.05 [3089]P93(a886)
% 162.26/162.05 [3090]P93(a881)
% 162.26/162.05 [3091]P105(a877)
% 162.26/162.05 [3092]P105(a878)
% 162.26/162.05 [3093]P105(a879)
% 162.26/162.05 [3094]P105(a883)
% 162.26/162.05 [3095]P105(a327)
% 162.26/162.05 [3096]P105(a105)
% 162.26/162.05 [3097]P105(a886)
% 162.26/162.05 [3098]P105(a881)
% 162.26/162.05 [3099]P104(a1)
% 162.26/162.05 [3100]P104(a886)
% 162.26/162.05 [3101]P98(a877)
% 162.26/162.05 [3121]P38(a883,a252)
% 162.26/162.05 [3122]P38(a883,a321)
% 162.26/162.05 [4479]~E(a103,a84)
% 162.26/162.05 [4480]~P24(a245)
% 162.26/162.05 [2901]E(f2(a1),a84)
% 162.26/162.05 [2902]E(f106(a105),a3)
% 162.26/162.05 [2903]E(f22(a105),a23)
% 162.26/162.05 [3102]E(f196(a883),f2(a883))
% 162.26/162.05 [3103]E(f32(a24),f2(a883))
% 162.26/162.05 [3104]E(f85(a245),f2(a883))
% 162.26/162.05 [3105]E(f85(a195),f2(a883))
% 162.26/162.05 [3106]E(f107(a883),f246(a883))
% 162.26/162.05 [3107]E(f251(a883),f108(a883))
% 162.26/162.05 [3108]E(f109(a1),f35(a1))
% 162.26/162.05 [3109]P28(f79(a1))
% 162.26/162.05 [3110]P28(f2(a1))
% 162.26/162.05 [3160]P24(f331(a25,a24))
% 162.26/162.05 [3161]P24(f331(a25,a888))
% 162.26/162.05 [3175]P38(f890(a883,a883),a36)
% 162.26/162.05 [3522]E(f323(a883,a883,a252,a252),a36)
% 162.26/162.05 [4481]~E(f79(a1),f2(a1))
% 162.26/162.05 [3111]E(f117(f2(a883)),f2(a883))
% 162.26/162.05 [3112]E(f4(f2(a105)),f2(a883))
% 162.26/162.05 [3124]E(f331(f80(a1),a84),a84)
% 162.26/162.05 [3127]E(f331(a118,f2(a883)),f79(a883))
% 162.26/162.05 [3128]E(f331(a111,f79(a1)),f79(a883))
% 162.26/162.05 [3129]E(f331(a3,f79(a883)),f79(a105))
% 162.26/162.05 [3131]E(f331(a3,f2(a883)),f2(a105))
% 162.26/162.05 [3133]E(f331(f110(a1),a84),f2(a1))
% 162.26/162.05 [3134]E(f331(f110(a105),a84),f2(a105))
% 162.26/162.05 [3135]E(f331(a111,f2(a1)),f2(a883))
% 162.26/162.05 [3136]E(f331(f197(a877),a245),f2(a883))
% 162.26/162.05 [3137]E(f331(f197(a877),a195),f2(a883))
% 162.26/162.05 [3138]E(f331(f197(a879),a24),f2(a883))
% 162.26/162.05 [3139]E(f331(f110(a883),a84),f2(a883))
% 162.26/162.05 [3144]E(f331(f80(a1),f79(a1)),a103)
% 162.26/162.05 [3151]E(f331(f80(a1),f2(a1)),f2(a1))
% 162.26/162.05 [3153]E(f331(f197(a105),f2(a105)),f2(a883))
% 162.26/162.05 [3154]E(f331(f106(a1),f79(a883)),f79(a1))
% 162.26/162.05 [3155]E(f331(f106(a1),f2(a883)),f2(a1))
% 162.26/162.05 [3162]E(f331(f239(a879),a892),f331(a26,a893))
% 162.26/162.05 [3171]E(f331(a111,f79(a1)),f331(a118,f2(a883)))
% 162.26/162.05 [3172]E(f331(f180(a880,a879),a27),a26)
% 162.26/162.05 [3173]E(f322(f890(a883,a883),a36),a37)
% 162.26/162.05 [3174]E(f324(f890(a883,a883),a36),a69)
% 162.26/162.05 [3195]E(f331(f254(a883),f2(a883)),f196(f891(a883,a877)))
% 162.26/162.05 [3196]E(f331(f255(a883),f2(a883)),f256(f891(a883,a877)))
% 162.26/162.05 [3204]P40(f196(f891(a1,a877)))
% 162.26/162.05 [3239]E(f331(f331(f22(a105),f2(a105)),f79(a105)),f2(a105))
% 162.26/162.05 [3317]P24(f331(f331(f248(a1),a103),f2(a1)))
% 162.26/162.05 [3342]P24(f331(f331(f248(a1),f2(a1)),f79(a1)))
% 162.26/162.05 [3343]P24(f331(f331(f247(a1),f2(a1)),f79(a1)))
% 162.26/162.05 [3515]P24(f331(f62(a880),f186(a880,a879,a26)))
% 162.26/162.05 [3551]E(f331(f331(f288(a883,a883,a883),a321),f307(a883,a321)),a252)
% 162.26/162.05 [3590]P41(a1,a883,a111,f331(f247(a1),f2(a1)))
% 162.26/162.05 [3594]E(f331(f331(f42(a883,f891(a883,a877)),f256(f891(a883,a877))),f300(a883)),f256(f891(a883,a877)))
% 162.26/162.05 [3595]E(f331(f331(f42(a883,f891(a883,a877)),f256(f891(a883,a877))),f254(a883)),f256(f891(a883,a877)))
% 162.26/162.05 [3596]E(f331(f331(f42(a883,f891(a883,a877)),f256(f891(a883,a877))),f255(a883)),f256(f891(a883,a877)))
% 162.26/162.05 [3597]E(f331(f331(f43(a883,f891(a883,a877)),f256(f891(a883,a877))),f303(a883)),f196(f891(a883,a877)))
% 162.26/162.05 [3614]P21(a883,a1,f106(a1),f256(f891(a883,a877)))
% 162.26/162.05 [3625]P41(a883,a1,f106(a1),f331(f16(a877,a883),a195))
% 162.26/162.05 [3753]E(f331(f74(a883,a105,a1,a3),a111),f110(a105))
% 162.26/162.05 [3974]P54(a105,a883,a19,a3,f256(f891(a883,a877)))
% 162.26/162.05 [3982]P54(a1,f891(f890(a883,a883),a877),a113,a90,a104)
% 162.26/162.05 [4240]E(f271(a1,a1,a1,a1,f35(a1),f80(a1)),a51)
% 162.26/162.05 [4504]~E(f331(f110(a1),a103),f331(f110(a1),a84))
% 162.26/162.05 [4505]~P24(f331(a202,f79(a1)))
% 162.26/162.05 [4506]~P24(f331(a202,f2(a1)))
% 162.26/162.05 [4554]~P24(f331(f331(f248(a1),a84),f2(a1)))
% 162.26/162.05 [3188]E(f331(f331(f22(a1),a103),a103),a84)
% 162.26/162.05 [3202]E(f331(f106(a1),f331(a118,f2(a883))),f79(a1))
% 162.26/162.05 [3266]E(f331(f38(a886),f256(f891(a886,a877))),f79(a883))
% 162.26/162.05 [3287]P24(f331(a202,f331(f110(a1),a103)))
% 162.26/162.05 [3288]P24(f331(f331(f248(a1),a103),a84))
% 162.26/162.05 [3290]P24(f331(f331(f247(a1),a103),a84))
% 162.26/162.05 [3355]E(f331(f331(f309(a883),f2(a883)),f196(f891(a883,a877))),f331(f300(a883),f2(a883)))
% 162.26/162.05 [3410]P24(f331(f331(f247(a1),f2(a1)),f331(f110(a1),a84)))
% 162.26/162.05 [3422]E(f331(f310(a883,a883,a118),f256(f891(a883,a877))),f331(f303(a883),f2(a883)))
% 162.26/162.05 [3461]P6(f890(a883,a883),f256(f891(f890(a883,a883),a877)),a115)
% 162.26/162.05 [3761]E(f331(f74(a883,a1,a105,f106(a1)),a19),a20)
% 162.26/162.05 [3824]P38(a883,f331(f253(f890(a883,a883)),f331(f270(a883,a883,a877),f248(a883))))
% 162.26/162.05 [4543]~P24(f331(a202,f331(f110(a1),a84)))
% 162.26/162.05 [4544]~P24(f331(f331(f248(a1),a84),a84))
% 162.26/162.05 [4545]~P24(f331(f331(f248(a1),a84),a103))
% 162.26/162.05 [4546]~P24(f331(f331(f248(a1),a103),a103))
% 162.26/162.05 [4547]~P24(f331(f331(f247(a1),a84),a103))
% 162.26/162.05 [4548]~P24(f331(f331(f92(a1),a84),a103))
% 162.26/162.05 [4549]~P24(f331(f331(f92(a1),a103),a84))
% 162.26/162.05 [4564]~P24(f331(f62(a883),f256(f891(a883,a877))))
% 162.26/162.05 [4565]~P24(f331(f62(a1),f256(f891(a1,a877))))
% 162.26/162.05 [4420]E(f331(f270(a1,a1,a877),f331(f331(f8(f891(a1,a877),f891(a1,a877),a1),f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f248(a1),f2(a1))))),f331(f331(f7(a1,a1,f891(a1,a877)),f331(f331(f8(f891(a1,f891(a1,a877)),f891(a1,f891(a1,a877)),a1),f7(a1,a1,a877)),f331(f331(f8(f891(a1,a1),f891(a1,f891(a1,a877)),a1),f331(f8(a1,f891(a1,a877),a1),a328)),a229))),f79(a1)))),a225)
% 162.26/162.05 [4582]~P20(a878,f196(f891(f882(a878),a877)),f331(f331(f309(f882(a878)),f331(a94,f331(a28,a893))),f196(f891(f882(a878),a877))))
% 162.26/162.05 [3524]E(f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a103)),a103),a103)
% 162.26/162.05 [3561]E(f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84),f331(f80(a1),a103))
% 162.26/162.05 [3599]E(f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84),f331(f331(f22(a1),a84),a103))
% 162.26/162.05 [3694]E(f331(f331(f61(f890(a883,a883)),f256(f891(f890(a883,a883),a877))),a115),a104)
% 162.26/162.05 [3763]E(f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)),f79(a1))
% 162.26/162.05 [3764]E(f331(f110(a105),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)),f79(a105))
% 162.26/162.05 [3765]E(f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)),f79(a883))
% 162.26/162.05 [3773]E(f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)),f331(a118,f2(a883)))
% 162.26/162.05 [4101]E(f331(f331(f107(f891(f890(f890(a883,a883),f890(a883,a883)),a877)),a36),f307(f890(a883,a883),f196(f891(f890(f890(a883,a883),f890(a883,a883)),a877)))),a71)
% 162.26/162.05 [4166]E(f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),f79(a883)),f2(a883))),f196(f891(f890(a883,a883),a877))))),f79(a1))
% 162.26/162.05 [4167]E(f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),f2(a883)),f2(a883))),f196(f891(f890(a883,a883),a877))))),f2(a1))
% 162.26/162.05 [4182]E(f331(f253(f890(a883,a883)),f331(f270(a883,a883,a877),f331(f331(f8(a883,f891(a883,a877),a883),f331(f7(a883,a883,a877),a328)),a118))),a321)
% 162.26/162.05 [3924]E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)),a103),a84)
% 162.26/162.05 [4232]E(f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(a118,f331(a118,f331(a118,f2(a883)))))
% 162.26/162.05 [4300]P22(f891(f890(a883,a883),a877),f331(f331(f261(f891(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),a877),f891(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),a877)),a37),a70))
% 162.26/162.05 [4301]P22(f891(f890(a883,a883),a877),f331(f331(f261(f891(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),a877),f891(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),a877)),a69),a72))
% 162.26/162.05 [4312]P28(f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))))
% 162.26/162.05 [4338]E(f331(f331(f107(f891(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),a877)),f324(f890(a883,a883),a71)),f331(f331(f309(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877))),f331(f331(f261(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),f196(f891(f890(a883,a883),a877))),f196(f891(f890(a883,a883),a877)))),f196(f891(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),a877)))),a72)
% 162.26/162.05 [4339]E(f331(f331(f107(f891(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),a877)),f322(f890(a883,a883),a71)),f331(f331(f309(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877))),f331(f331(f261(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),f196(f891(f890(a883,a883),a877))),f196(f891(f890(a883,a883),a877)))),f196(f891(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),a877)))),a70)
% 162.26/162.05 [4344]E(f331(f106(a1),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)))),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))))
% 162.26/162.05 [4358]P24(f331(f331(f247(a1),f2(a1)),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)))))
% 162.26/162.05 [4355]E(f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)),f331(a118,f331(a118,f2(a883))))
% 162.26/162.05 [4356]E(f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)),f331(f331(f81(a883),f79(a883)),f79(a883)))
% 162.26/162.05 [4357]E(f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)),f331(f38(a877),f256(f891(a877,a877))))
% 162.26/162.05 [4400]P28(f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))
% 162.26/162.05 [4401]E(f331(a111,f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f331(a118,f331(a118,f2(a883))))
% 162.26/162.05 [4422]E(f331(f106(a1),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))
% 162.26/162.05 [4434]P24(f331(f331(f247(a1),f2(a1)),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))
% 162.26/162.05 [3123]P5(x31231,a328)
% 162.26/162.05 [3523]P21(a883,a883,a118,x35231)
% 162.26/162.05 [3113]P93(f882(x31131))
% 162.26/162.05 [3114]P93(f887(x31141))
% 162.26/162.05 [3115]P93(f884(x31151))
% 162.26/162.05 [3116]P93(f885(x31161))
% 162.26/162.05 [3117]P105(f882(x31171))
% 162.26/162.05 [3118]P105(f887(x31181))
% 162.26/162.05 [3119]P105(f884(x31191))
% 162.26/162.05 [3120]P105(f885(x31201))
% 162.26/162.05 [3140]P38(a1,f112(x31401))
% 162.26/162.05 [3141]P38(a1,f114(x31411))
% 162.26/162.05 [3143]P39(x31431,f199(x31431))
% 162.26/162.05 [3192]P38(f891(x31921,a877),f306(x31921))
% 162.26/162.05 [3230]E(f45(a1,x32301,x32301),f2(a1))
% 162.26/162.06 [3284]P11(x32841,f891(x32841,a877),f309(x32841))
% 162.26/162.06 [4483]~E(f331(a28,x44831),a24)
% 162.26/162.06 [4485]~E(f331(a118,x44851),x44851)
% 162.26/162.06 [4495]~E(f331(a118,x44951),f2(a883))
% 162.26/162.06 [3125]E(f331(f197(a883),x31251),x31251)
% 162.26/162.06 [3126]E(f331(f110(a1),x31261),x31261)
% 162.26/162.06 [3142]E(f331(a90,f332(x31421)),x31421)
% 162.26/162.06 [3156]E(f120(x31561,f119(x31561)),f119(x31561))
% 162.26/162.06 [3157]E(f155(x31571,f119(x31571)),f119(x31571))
% 162.26/162.06 [3163]E(f32(f331(a28,x31631)),f2(a883))
% 162.26/162.06 [3168]E(f331(f171(x31681),f119(x31681)),f119(x31681))
% 162.26/162.06 [3169]E(f331(f174(x31691),f119(x31691)),f119(x31691))
% 162.26/162.06 [3170]E(f331(f172(x31701),f119(x31701)),f119(x31701))
% 162.26/162.06 [3176]E(f331(f110(a1),x31761),f331(f109(a1),x31761))
% 162.26/162.06 [3177]E(f331(a90,f331(a113,x31771)),x31771)
% 162.26/162.06 [3179]E(f331(a3,f331(a19,x31791)),x31791)
% 162.26/162.06 [3180]E(f331(a19,f331(a3,x31801)),x31801)
% 162.26/162.06 [3181]P28(f331(f106(a1),x31811))
% 162.26/162.06 [3186]E(f331(f197(f887(x31861)),f199(x31861)),f2(a883))
% 162.26/162.06 [3187]E(f331(f197(f884(x31871)),f119(x31871)),f2(a883))
% 162.26/162.06 [3191]E(f331(f197(a879),f331(a28,x31911)),f2(a883))
% 162.26/162.06 [3200]E(f240(x32001,f199(x32001)),f196(f891(x32001,a877)))
% 162.26/162.06 [3207]E(f331(f331(f22(a883),x32071),f2(a883)),x32071)
% 162.26/162.06 [3208]E(f331(f331(f81(a883),x32081),f2(a883)),x32081)
% 162.26/162.06 [3209]E(f331(f331(f81(a1),x32091),f2(a1)),x32091)
% 162.26/162.06 [3210]E(f331(f331(f82(a883),x32101),f79(a883)),x32101)
% 162.26/162.06 [3211]E(f331(f331(f82(a1),x32111),f79(a1)),x32111)
% 162.26/162.06 [3212]E(f331(f331(f246(a883),x32121),f2(a883)),x32121)
% 162.26/162.06 [3213]E(f331(f331(f82(a883),x32131),f2(a883)),f2(a883))
% 162.26/162.06 [3214]E(f331(f331(f251(a883),x32141),f2(a883)),f2(a883))
% 162.26/162.06 [3215]E(f331(f331(f39(a1),x32151),f2(a1)),f2(a1))
% 162.26/162.06 [3221]E(f331(f175(x32211),f119(x32211)),f196(f891(x32211,a877)))
% 162.26/162.06 [3225]P24(f331(f140(x32251),f119(x32251)))
% 162.26/162.06 [3231]E(f331(f210(x32311,x32311),f5(x32311)),f35(f887(x32311)))
% 162.26/162.06 [3232]E(f331(f210(x32321,x32321),f35(x32321)),f35(f887(x32321)))
% 162.26/162.06 [3233]E(f331(f157(x32331,x32331),f5(x32331)),f35(f884(x32331)))
% 162.26/162.06 [3234]E(f331(f157(x32341,x32341),f35(x32341)),f35(f884(x32341)))
% 162.26/162.06 [3235]E(f45(a1,x32351,f2(a1)),x32351)
% 162.26/162.06 [3236]E(f331(f247(a883),f331(a118,x32361)),f331(f248(a883),x32361))
% 162.26/162.06 [3237]E(f331(f254(a883),f331(a118,x32371)),f331(f300(a883),x32371))
% 162.26/162.06 [3238]E(f331(f255(a883),f331(a118,x32381)),f331(f303(a883),x32381))
% 162.26/162.06 [3240]E(f45(a1,f2(a1),x32401),f2(a1))
% 162.26/162.06 [3250]E(f331(f331(f81(a883),x32501),f79(a883)),f331(a118,x32501))
% 162.26/162.06 [3260]E(f331(f301(a883,x32601),f2(a883)),f196(f891(a883,a877)))
% 162.26/162.06 [3272]E(f302(a883,f2(a883),x32721),f331(f300(a883),x32721))
% 162.26/162.06 [3320]E(f331(f331(f22(a883),f331(a118,x33201)),f79(a883)),x33201)
% 162.26/162.06 [3333]E(f47(f2(a1),x33331),f331(f331(f261(a1,a1),f2(a1)),f2(a1)))
% 162.26/162.06 [3350]E(f331(f331(f331(f93(a878),a328),x33501),f203(x33501)),f331(a94,x33501))
% 162.26/162.06 [3385]P24(f331(f331(f248(a883),x33851),f331(a118,x33851)))
% 162.26/162.06 [3397]P24(f331(f331(f248(a883),f2(a883)),f331(a118,x33971)))
% 162.26/162.06 [3681]E(f331(f331(f22(a105),f331(a3,f331(a118,f331(a19,x36811)))),f79(a105)),x36811)
% 162.26/162.06 [3745]P24(f331(f331(f247(a1),f331(f80(a1),f331(f106(a1),x37451))),f2(a1)))
% 162.26/162.06 [3889]P24(f331(f331(f248(a1),f331(f80(a1),f331(f106(a1),f331(a118,x38891)))),f2(a1)))
% 162.26/162.06 [4510]~E(f256(f891(x45101,a877)),f196(f891(x45101,a877)))
% 162.26/162.06 [4557]~P24(f331(f331(f248(a883),x45571),f2(a883)))
% 162.26/162.06 [4571]~P24(f331(f331(f248(a1),f331(f106(a1),x45711)),f2(a1)))
% 162.26/162.06 [3190]E(f182(x31901,f119(f884(x31901))),f119(f884(x31901)))
% 162.26/162.06 [3193]E(f331(f331(f82(a1),a84),x31931),a84)
% 162.26/162.06 [3194]E(f331(f331(f81(a1),a84),x31941),x31941)
% 162.26/162.06 [3197]E(f331(a111,f331(f106(a1),x31971)),x31971)
% 162.26/162.06 [3198]E(f331(f331(f22(a1),x31981),a84),x31981)
% 162.26/162.06 [3199]E(f331(f331(f81(a1),x31991),a84),x31991)
% 162.26/162.06 [3201]E(f331(f331(f22(a883),x32011),x32011),f2(a883))
% 162.26/162.06 [3205]E(f331(f38(a883),f331(f254(a883),x32051)),x32051)
% 162.26/162.06 [3206]E(f331(f80(a1),f331(f80(a1),x32061)),x32061)
% 162.26/162.06 [3216]E(f331(f331(f81(a883),f2(a883)),x32161),x32161)
% 162.26/162.06 [3217]E(f331(f331(f81(a1),f2(a1)),x32171),x32171)
% 162.26/162.06 [3218]E(f331(f331(f82(a883),f79(a883)),x32181),x32181)
% 162.26/162.06 [3219]E(f331(f331(f82(a1),f79(a1)),x32191),x32191)
% 162.26/162.06 [3220]E(f331(f331(f246(a883),f2(a883)),x32201),x32201)
% 162.26/162.06 [3226]E(f331(f331(f22(a883),f2(a883)),x32261),f2(a883))
% 162.26/162.06 [3227]E(f331(f331(f82(a883),f2(a883)),x32271),f2(a883))
% 162.26/162.06 [3228]E(f331(f331(f251(a883),f2(a883)),x32281),f2(a883))
% 162.26/162.06 [3229]E(f331(f331(f39(a1),f2(a1)),x32291),f2(a1))
% 162.26/162.06 [3241]E(f128(x32411,f331(f80(a1),x32411)),f135(a1,x32411))
% 162.26/162.06 [3247]E(f331(f301(a883,f2(a883)),x32471),f331(f254(a883),x32471))
% 162.26/162.06 [3248]E(f331(f331(f82(a1),a103),x32481),f331(f80(a1),x32481))
% 162.26/162.06 [3252]E(f331(a111,f331(f110(a1),x32521)),f331(f110(a883),x32521))
% 162.26/162.06 [3253]E(f331(a19,f331(f110(a105),x32531)),f331(f110(a883),x32531))
% 162.26/162.06 [3254]E(f331(f38(a883),f331(f300(a883),x32541)),f331(a118,x32541))
% 162.26/162.06 [3264]E(f331(f331(f81(a883),f79(a883)),x32641),f331(a118,x32641))
% 162.26/162.06 [3268]E(f331(f109(a1),f331(f106(a1),x32681)),f331(f106(a1),x32681))
% 162.26/162.06 [3269]E(f331(f76(a1),f331(f106(a1),x32691)),f331(f106(a1),x32691))
% 162.26/162.06 [3274]E(f331(f38(x32741),f196(f891(x32741,a877))),f2(a883))
% 162.26/162.06 [3276]E(f331(f331(f39(a883),x32761),f331(a118,f2(a883))),x32761)
% 162.26/162.06 [3285]E(f45(a883,x32851,f331(a118,f2(a883))),f2(a883))
% 162.26/162.06 [3286]E(f45(a1,x32861,f331(f110(a1),a103)),f2(a1))
% 162.26/162.06 [3302]E(f331(f331(f39(a1),x33021),f331(f110(a1),a103)),f331(f80(a1),x33021))
% 162.26/162.06 [3306]E(f142(a883,f331(f301(a883,x33061),f2(a883))),f119(a883))
% 162.26/162.06 [3307]E(f331(f331(f81(a1),x33071),f79(a1)),f331(f331(f22(a1),x33071),a103))
% 162.26/162.06 [3308]E(f331(f331(f22(a1),x33081),f79(a1)),f331(f331(f81(a1),x33081),a103))
% 162.26/162.06 [3313]P24(f331(f331(f203(a24),x33131),x33131))
% 162.26/162.06 [3314]P24(f331(f331(f247(a883),x33141),x33141))
% 162.26/162.06 [3315]P24(f331(f331(f247(a1),x33151),x33151))
% 162.26/162.06 [3316]P24(f331(f331(f92(a1),x33161),x33161))
% 162.26/162.06 [3321]E(f331(f80(a1),f331(f110(a1),x33211)),f331(f110(a1),f331(f80(a1),x33211)))
% 162.26/162.06 [3322]P24(f331(f62(a883),f331(f300(a883),x33221)))
% 162.26/162.06 [3323]P24(f331(f62(a883),f331(f254(a883),x33231)))
% 162.26/162.06 [3331]E(f164(x33311,f256(f891(x33311,a877))),f256(f891(f884(x33311),a877)))
% 162.26/162.06 [3336]P24(f331(f331(f247(a883),f2(a883)),x33361))
% 162.26/162.06 [3347]E(f331(f331(f81(a883),f117(x33471)),f331(a118,f2(a883))),f117(f331(a118,x33471)))
% 162.26/162.06 [3348]E(f331(f253(x33481),f331(f16(a877,x33481),a245)),f196(f891(x33481,a877)))
% 162.26/162.06 [3349]E(f331(f253(x33491),f331(f16(a877,x33491),a195)),f256(f891(x33491,a877)))
% 162.26/162.06 [3354]E(f331(f331(f309(a883),x33541),f331(f254(a883),x33541)),f331(f254(a883),f331(a118,x33541)))
% 162.26/162.06 [3366]E(f331(f331(f81(a1),f79(a1)),f331(f106(a1),x33661)),f331(f106(a1),f331(a118,x33661)))
% 162.26/162.06 [3369]E(f331(f331(f154(f884(x33691)),f119(x33691)),f119(f884(x33691))),f54(x33691,f119(x33691)))
% 162.26/162.06 [3388]E(f196(f891(f890(x33881,x33881),a877)),f258(x33881,f196(f891(x33881,a877))))
% 162.26/162.06 [3389]E(f331(f308(x33891),f256(f891(x33891,a877))),f256(f891(f891(x33891,a877),a877)))
% 162.26/162.06 [3390]E(f331(f80(f891(x33901,a877)),f196(f891(x33901,a877))),f256(f891(x33901,a877)))
% 162.26/162.06 [3391]E(f331(f80(f891(x33911,a877)),f256(f891(x33911,a877))),f196(f891(x33911,a877)))
% 162.26/162.06 [3393]P24(f331(f62(x33931),f196(f891(x33931,a877))))
% 162.26/162.06 [3395]E(f331(f301(a883,x33951),f331(a118,x33951)),f331(f331(f309(a883),x33951),f196(f891(a883,a877))))
% 162.26/162.06 [3396]E(f86(f890(a883,a883),f48(x33961,f2(a883))),f331(f331(f261(a883,a883),f2(a883)),x33961))
% 162.26/162.06 [3409]E(f331(f331(f309(a883),f331(a118,x34091)),f331(f300(a883),x34091)),f331(f300(a883),f331(a118,x34091)))
% 162.26/162.06 [3413]P38(x34131,f196(f891(f890(x34131,x34131),a877)))
% 162.26/162.06 [3416]P24(f331(f331(f247(a1),f2(a1)),f331(f106(a1),x34161)))
% 162.26/162.06 [3424]E(f331(f331(f81(a883),f331(f197(a883),x34241)),f331(a118,f2(a883))),f331(f197(a883),f331(a118,x34241)))
% 162.26/162.06 [3531]P40(f331(f310(a883,a1,f106(a1)),x35311))
% 162.26/162.06 [3568]P48(x35681,f196(f891(x35681,a877)),f196(f891(f890(x35681,x35681),a877)))
% 162.26/162.06 [3587]E(f331(f331(f261(a1,a1),f331(f110(a1),a103)),f331(f331(f22(a1),x35871),f79(a1))),f50(f331(f110(a1),a103),x35871))
% 162.26/162.06 [3637]P57(x36371,f331(f16(f891(x36371,a877),x36371),f331(f16(a877,x36371),a245)))
% 162.26/162.06 [3835]P24(f331(f331(f333(f891(f890(a883,a883),a877)),f332(x38351)),a104))
% 162.26/162.06 [3858]P24(f331(f331(f333(f891(f890(a883,a883),a877)),f331(a113,x38581)),a104))
% 162.26/162.06 [3991]P21(x39911,f891(x39911,a877),f331(f331(f7(x39911,f891(x39911,a877),f891(x39911,a877)),f309(x39911)),f196(f891(x39911,a877))),f256(f891(x39911,a877)))
% 162.26/162.06 [4542]~E(f331(a3,f331(a118,f331(a19,x45421))),f2(a105))
% 162.26/162.06 [4550]~P24(f331(a202,f331(f106(a1),x45501)))
% 162.26/162.06 [4553]~P24(f331(f331(f248(a883),x45531),x45531))
% 162.26/162.06 [4566]~P24(f331(f331(f247(a883),f331(a118,x45661)),x45661))
% 162.26/162.06 [3338]E(f331(a111,f331(f80(a1),f331(f106(a1),x33381))),f2(a883))
% 162.26/162.06 [3341]E(f331(f331(f81(a1),f331(f80(a1),x33411)),x33411),f2(a1))
% 162.26/162.06 [3346]E(f331(f38(a1),f331(f301(a1,f2(a1)),x33461)),f331(a111,x33461))
% 162.26/162.06 [3359]E(f331(f331(f262(a883),f331(a118,f2(a883))),x33591),f331(a118,f2(a883)))
% 162.26/162.06 [3458]E(f331(f284(x34581),f196(f891(f890(x34581,x34581),a877))),f196(f891(x34581,a877)))
% 162.26/162.06 [3465]E(f41(f891(x34651,a877),f196(f891(f891(x34651,a877),a877))),f256(f891(x34651,a877)))
% 162.26/162.06 [3466]E(f41(f891(x34661,a877),f256(f891(f891(x34661,a877),a877))),f196(f891(x34661,a877)))
% 162.26/162.06 [3467]E(f40(f891(x34671,a877),f196(f891(f891(x34671,a877),a877))),f196(f891(x34671,a877)))
% 162.26/162.06 [3468]E(f40(f891(x34681,a877),f256(f891(f891(x34681,a877),a877))),f256(f891(x34681,a877)))
% 162.26/162.06 [3513]E(f331(f331(f309(f884(x35131)),f119(x35131)),f196(f891(f884(x35131),a877))),f164(x35131,f196(f891(x35131,a877))))
% 162.26/162.06 [3514]E(f331(f331(f309(f884(x35141)),f119(x35141)),f196(f891(f884(x35141),a877))),f165(x35141,f119(f891(x35141,a877))))
% 162.26/162.06 [3550]E(f331(f331(f81(a883),f4(x35501)),f331(a118,f2(a883))),f4(f331(a3,f331(a118,f331(a19,x35501)))))
% 162.26/162.06 [3579]E(f331(f38(a1),f331(f310(a883,a1,f106(a1)),x35791)),f331(f38(a883),x35791))
% 162.26/162.06 [3582]P24(f331(f331(f247(a883),x35821),f331(f331(f82(a883),x35821),x35821)))
% 162.26/162.06 [3618]E(f331(f310(a1,a883,a111),f302(a1,f2(a1),f331(f106(a1),x36181))),f331(f300(a883),x36181))
% 162.26/162.06 [3632]E(f331(f331(f39(a883),f331(a118,f2(a883))),f331(f110(a883),x36321)),f331(a111,f331(f331(f39(a1),f79(a1)),f331(f110(a1),x36321))))
% 162.26/162.06 [3634]E(f331(f175(a883),f142(a883,f331(f301(a883,f2(a883)),f331(a118,x36341)))),f331(f300(a883),x36341))
% 162.26/162.06 [3635]E(f331(f331(f81(a883),f331(f197(a105),x36351)),f331(a118,f2(a883))),f331(f197(a105),f331(a3,f331(a118,f331(a19,x36351)))))
% 162.26/162.06 [3655]E(f331(f310(a1,a883,a111),f331(f310(a883,a1,f106(a1)),x36551)),x36551)
% 162.26/162.06 [3686]E(f331(f331(f309(a883),f2(a883)),f331(f310(a883,a883,a118),f331(f254(a883),x36861))),f331(f254(a883),f331(a118,x36861)))
% 162.26/162.06 [3693]P52(x36931,x36931,f307(x36931,f196(f891(f890(x36931,x36931),a877))))
% 162.26/162.06 [3699]P24(f331(a202,f331(f80(a1),f331(f106(a1),f331(a118,x36991)))))
% 162.26/162.06 [3710]E(f331(f331(f22(f891(a883,a877)),f331(f255(a883),x37101)),f331(f331(f309(a883),x37101),f196(f891(a883,a877)))),f331(f255(a883),f331(a118,x37101)))
% 162.26/162.06 [3736]E(f331(f331(f309(f891(x37361,a877)),f196(f891(x37361,a877))),f196(f891(f891(x37361,a877),a877))),f331(f308(x37361),f196(f891(x37361,a877))))
% 162.26/162.06 [3766]E(f331(f331(f22(f891(a883,a877)),f331(f303(a883),x37661)),f331(f331(f309(a883),f331(a118,x37661)),f196(f891(a883,a877)))),f331(f303(a883),f331(a118,x37661)))
% 162.26/162.06 [3775]E(f331(f331(f309(f887(x37751)),f199(x37751)),f331(f310(x37751,f887(x37751),f239(x37751)),f256(f891(x37751,a877)))),f256(f891(f887(x37751),a877)))
% 162.26/162.06 [4248]P11(x42481,f891(x42481,a877),f331(f331(f8(f891(x42481,a877),f891(f891(x42481,a877),f891(x42481,a877)),x42481),f331(f7(f891(x42481,a877),f891(x42481,a877),f891(x42481,a877)),f22(f891(x42481,a877)))),f331(f331(f7(x42481,f891(x42481,a877),f891(x42481,a877)),f309(x42481)),f196(f891(x42481,a877)))))
% 162.26/162.06 [4337]E(f331(f253(f890(a1,a1)),f331(f270(a1,a1,a877),f331(f331(f8(f891(a1,a877),f891(a1,a877),a1),f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f247(a1),x43371)))),f248(a1)))),f114(x43371))
% 162.26/162.06 [4376]E(f331(f253(f890(a1,a1)),f331(f270(a1,a1,a877),f331(f331(f18(a1,f891(a1,a877),f891(a1,a877)),f331(f331(f8(f891(a877,a877),f891(f891(a1,a877),f891(a1,a877)),a1),f8(a877,a877,a1)),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f247(a1),x43761)))),f248(a1)))),f112(x43761))
% 162.26/162.06 [4441]E(f331(f253(f890(f891(x44411,a877),f891(x44411,a877))),f331(f270(f891(x44411,a877),f891(x44411,a877),a877),f331(f331(f7(f891(x44411,a877),f891(f891(x44411,a877),a877),f891(f891(x44411,a877),a877)),f331(f331(f8(f891(f891(x44411,a877),f891(a877,a877)),f891(f891(f891(x44411,a877),a877),f891(f891(x44411,a877),a877)),f891(x44411,a877)),f18(f891(x44411,a877),a877,a877)),f331(f331(f8(f891(f891(x44411,a877),a877),f891(f891(x44411,a877),f891(a877,a877)),f891(x44411,a877)),f331(f8(a877,f891(a877,a877),f891(x44411,a877)),a329)),f248(f891(x44411,a877))))),f62(x44411)))),f306(x44411))
% 162.26/162.06 [4570]~P24(f331(f62(f884(x45701)),f256(f891(f884(x45701),a877))))
% 162.26/162.06 [4581]~P24(f331(f331(f247(a1),f2(a1)),f331(f80(a1),f331(f106(a1),f331(a118,x45811)))))
% 162.26/162.06 [3491]E(f331(f331(f22(a1),f331(f331(f81(a1),x34911),a103)),a103),x34911)
% 162.26/162.06 [3506]E(f331(f175(a883),f142(a883,f331(f301(a883,f2(a883)),x35061))),f331(f254(a883),x35061))
% 162.26/162.06 [3791]E(f331(f286(x37911,x37911),f307(x37911,f196(f891(f890(x37911,x37911),a877)))),f307(x37911,f196(f891(f890(x37911,x37911),a877))))
% 162.26/162.06 [3836]P24(f331(f331(f247(a883),x38361),f331(f331(f82(a883),x38361),f331(f331(f82(a883),x38361),x38361))))
% 162.26/162.06 [4105]P24(f331(f62(a883),f331(f253(a883),f331(f331(f7(a883,a883,a877),f248(a883)),x41051))))
% 162.26/162.06 [4106]P24(f331(f62(a883),f331(f253(a883),f331(f331(f7(a883,a883,a877),f247(a883)),x41061))))
% 162.26/162.06 [4394]E(f331(f253(f890(x43941,x43941)),f331(f331(f8(f891(x43941,a877),a877,f890(x43941,x43941)),f87(x43941)),f331(f331(f7(f890(x43941,x43941),f891(x43941,f890(x43941,x43941)),f891(x43941,a877)),f331(f331(f8(f891(f890(x43941,x43941),a877),f891(f891(x43941,f890(x43941,x43941)),f891(x43941,a877)),f890(x43941,x43941)),f8(f890(x43941,x43941),a877,x43941)),a328)),f331(f331(f18(x43941,x43941,f890(x43941,x43941)),f261(x43941,x43941)),f5(x43941))))),f307(x43941,f196(f891(f890(x43941,x43941),a877))))
% 162.26/162.06 [4573]~E(f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x45731)),x45731),a84)
% 162.26/162.06 [4574]~E(f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x45741)),x45741),f2(a1))
% 162.26/162.06 [3969]E(f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f22(a1),a103),x39691))),f331(f331(f22(a1),a103),x39691)),f331(f331(f22(a1),a84),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x39691)),x39691)))
% 162.26/162.06 [4085]E(f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f80(a1),x40851)),a103))),f331(f331(f81(a1),f331(f80(a1),x40851)),a103)),f331(f80(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x40851)),x40851)))
% 162.26/162.06 [4161]E(f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),x41611),f2(a883))),f196(f891(f890(a883,a883),a877))))),f331(f106(a1),x41611))
% 162.26/162.06 [4172]E(f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),f336(x41721)),f444(x41721))),f196(f891(f890(a883,a883),a877))))),x41721)
% 162.26/162.06 [4180]E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f22(a1),a103),x41801))),f331(f331(f22(a1),a103),x41801))),a103),f331(f331(f22(a1),a103),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x41801)),x41801)))
% 162.26/162.06 [4210]E(f331(f253(a1),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f247(a1),f2(a1)))),x42101)),f331(f310(a883,a1,f106(a1)),f331(f253(a883),f331(f331(f8(a1,a877,a883),x42101),f106(a1)))))
% 162.26/162.06 [4256]P40(f331(f253(a1),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f247(a1),f2(a1)))),x42561)))
% 162.26/162.06 [4278]P24(f331(f331(f333(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877))),f331(f331(f261(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),x42781),f196(f891(f890(a883,a883),a877)))),a72))
% 162.26/162.06 [4284]E(f331(f310(a1,a883,a111),f331(f253(a1),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f247(a1),f2(a1)))),f331(f331(f8(a883,a877,a1),x42841),a111)))),f331(f253(a883),x42841))
% 162.26/162.06 [4454]E(f312(a883,f331(f331(f42(f890(a883,a883),f891(a883,a877)),f331(a113,x44541)),f331(f270(a883,a883,f891(a883,a877)),f331(f331(f7(a883,f891(a883,a877),f891(a883,f891(a883,a877))),f331(f331(f8(f891(a883,f891(f891(a883,a877),f891(a883,a877))),f891(f891(a883,a877),f891(a883,f891(a883,a877))),a883),f7(a883,f891(a883,a877),f891(a883,a877))),f331(f331(f8(f891(a883,a883),f891(a883,f891(f891(a883,a877),f891(a883,a877))),a883),f331(f8(a883,f891(f891(a883,a877),f891(a883,a877)),a883),f309(a883))),f22(a883)))),f196(f891(a883,a877)))))),f331(a111,x44541))
% 162.26/162.06 [4586]~P24(f331(f331(f92(a1),a84),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x45861)),x45861)))
% 162.26/162.06 [3940]E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x39401)),x39401)),a103),f331(f331(f81(a1),x39401),x39401))
% 162.26/162.06 [4195]E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f22(a1),x41951),a103))),f331(f331(f22(a1),x41951),a103))),a103),f331(f331(f22(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x41951)),x41951)),a103))
% 162.26/162.06 [4585]~E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x45851)),x45851)),a103),a103)
% 162.26/162.06 [4595]~P24(f331(f331(f92(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x45951)),x45951)),a84))
% 162.26/162.06 [4157]E(f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x41571)),x41571)),a103)),f331(f331(f89(a883,a883),f331(f110(a883),x41571)),f331(f331(f18(a883,a883,a883),f81(a883)),f5(a883))))
% 162.26/162.06 [4163]E(f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f22(a1),a103),x41631))),f331(f331(f22(a1),a103),x41631)),f331(f331(f22(a1),a103),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x41631)),x41631)),a103)))
% 162.26/162.06 [4194]E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f80(a1),x41941))),f331(f80(a1),x41941))),a103),f331(f80(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x41941)),x41941)),a103)))
% 162.26/162.06 [4218]E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f22(a1),a84),x42181))),f331(f331(f22(a1),a84),x42181))),a103),f331(f331(f22(a1),a84),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x42181)),x42181)),a103)))
% 162.26/162.06 [4469]E(f331(a90,f331(f331(f42(f890(a883,a883),f891(f890(a883,a883),a877)),f331(a113,x44691)),f331(f270(a883,a883,f891(f890(a883,a883),a877)),f331(f331(f8(f891(a883,f891(f890(a883,a883),a877)),f891(a883,f891(f890(a883,a883),a877)),a883),f331(f8(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877),a883),f285(f890(a883,a883),f890(a883,a883),a115))),f331(f331(f7(a883,f891(f890(a883,a883),a877),f891(a883,f891(f890(a883,a883),a877))),f331(f331(f8(f891(a883,f891(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877))),f891(f891(f890(a883,a883),a877),f891(a883,f891(f890(a883,a883),a877))),a883),f7(a883,f891(f890(a883,a883),a877),f891(f890(a883,a883),a877))),f331(f331(f8(f891(a883,f890(a883,a883)),f891(a883,f891(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877))),a883),f331(f8(f890(a883,a883),f891(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),a883),f309(f890(a883,a883)))),f331(f7(a883,a883,f890(a883,a883)),f261(a883,a883))))),f196(f891(f890(a883,a883),a877))))))),f331(f80(a1),x44691))
% 162.26/162.06 [4596]~P24(f331(f331(f92(a1),a103),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x45961)),x45961)),a103)))
% 162.26/162.06 [4221]E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x42211)),x42211)),a103)),a103),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),x42211),a103))),f331(f331(f81(a1),x42211),a103)))
% 162.26/162.06 [4359]E(f331(f331(f81(a883),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)))),x43591),f331(a118,f331(a118,f331(a118,x43591))))
% 162.26/162.06 [4598]~P24(f331(f331(f92(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x45981)),x45981)),a103)),a103))
% 162.26/162.06 [4402]E(f331(f331(f81(a883),x44021),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f331(a118,f331(a118,x44021)))
% 162.26/162.06 [4403]E(f331(f331(f82(a883),x44031),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f331(f331(f81(a883),x44031),x44031))
% 162.26/162.06 [4404]E(f331(f331(f39(a883),f331(f331(f81(a883),x44041),x44041)),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x44041)
% 162.26/162.06 [4435]E(f45(a883,f331(a118,f331(a118,x44351)),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f45(a883,x44351,f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))
% 162.26/162.06 [4432]E(f331(f331(f81(a883),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x44321),f331(a118,f331(a118,x44321)))
% 162.26/162.06 [4433]E(f331(f331(f82(a883),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x44331),f331(f331(f81(a883),x44331),x44331))
% 162.26/162.06 [4445]E(f331(f331(f39(a883),f331(a118,f331(a118,x44451))),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f331(a118,f331(f331(f39(a883),x44451),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))))
% 162.26/162.06 [4477]E(f331(f270(a1,a1,f890(a1,a1)),f331(f331(f18(a1,f891(a1,f890(a1,a1)),f891(a1,f890(a1,a1))),f331(f331(f8(f891(a1,f891(f890(a1,a1),f890(a1,a1))),f891(f891(a1,f890(a1,a1)),f891(a1,f890(a1,a1))),a1),f18(a1,f890(a1,a1),f890(a1,a1))),f331(f331(f8(f891(a1,f890(a1,a1)),f891(a1,f891(f890(a1,a1),f890(a1,a1))),a1),f331(f18(a1,f890(a1,a1),f891(f890(a1,a1),f890(a1,a1))),f331(f331(f8(a877,f891(f890(a1,a1),f891(f890(a1,a1),f890(a1,a1))),a1),f102(f890(a1,a1))),f331(f331(f8(a1,a877,a1),f331(f247(a1),f2(a1))),f331(f331(f7(a1,a1,a1),f22(a1)),x44771))))),f331(f331(f7(a1,f891(a1,a1),f891(a1,f890(a1,a1))),f331(f331(f8(f891(a1,f890(a1,a1)),f891(f891(a1,a1),f891(a1,f890(a1,a1))),a1),f8(a1,f890(a1,a1),a1)),f331(f331(f8(a1,f891(a1,f890(a1,a1)),a1),f261(a1,a1)),f331(f331(f7(a1,a1,a1),f331(f331(f8(a1,f891(a1,a1),a1),f81(a1)),f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))),f79(a1))))),f331(f331(f7(a1,a1,a1),f22(a1)),x44771))))),f331(f331(f8(a1,f891(a1,f890(a1,a1)),a1),f261(a1,a1)),f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))))),f44(x44771))
% 162.26/162.06 [3164]P93(f889(x31641,x31642))
% 162.26/162.06 [3165]P93(f890(x31651,x31652))
% 162.26/162.06 [3166]P105(f889(x31661,x31662))
% 162.26/162.06 [3167]P105(f890(x31671,x31672))
% 162.26/162.06 [3184]P29(a1,f181(x31841,x31842))
% 162.26/162.06 [3185]P38(x31851,f156(x31851,x31852))
% 162.26/162.06 [3249]P32(x32491,x32492,f119(x32491))
% 162.26/162.06 [3280]P48(x32801,x32802,f258(x32801,x32802))
% 162.26/162.06 [3281]P52(x32811,x32811,f258(x32811,x32812))
% 162.26/162.06 [3553]P21(x35531,x35531,f5(x35531),x35532)
% 162.26/162.06 [3554]P21(x35541,x35541,f35(x35541),x35542)
% 162.26/162.06 [3563]P33(x35631,x35632,f119(x35631),f119(x35631))
% 162.26/162.06 [3564]P21(x35641,f887(x35641),f239(x35641),x35642)
% 162.26/162.06 [3573]P21(f884(x35731),f884(x35731),f172(x35731),x35732)
% 162.26/162.06 [4488]~E(f34(x44881,x44882),a24)
% 162.26/162.06 [4489]~E(f33(x44891,x44892),a24)
% 162.26/162.06 [4519]~P34(x45191,x45192,f119(x45191))
% 162.26/162.06 [4520]~P36(x45201,x45202,f119(x45201))
% 162.26/162.06 [3145]E(f331(f5(x31451),x31452),x31452)
% 162.26/162.06 [3146]E(f331(f253(x31461),x31462),x31462)
% 162.26/162.06 [3148]E(f331(f35(x31481),x31482),x31482)
% 162.26/162.06 [3158]E(f331(f200(x31581),x31582),f121(x31581))
% 162.26/162.06 [3182]E(f86(x31821,f331(a328,x31822)),x31822)
% 162.26/162.06 [3183]E(f91(x31831,f331(a328,x31832)),x31832)
% 162.26/162.06 [3203]E(f331(f139(x32031,x32032),f119(x32031)),f119(x32031))
% 162.26/162.06 [3222]E(f155(x32221,f155(x32221,x32222)),f155(x32221,x32222))
% 162.26/162.06 [3223]E(f307(x32231,f307(x32231,x32232)),f307(x32231,x32232))
% 162.26/162.06 [3244]E(f331(f331(f137(x32441),x32442),f119(x32441)),x32442)
% 162.26/162.06 [3255]E(f331(f331(f176(x32551),x32552),f119(x32551)),f119(x32551))
% 162.26/162.06 [3256]E(f331(f331(f141(x32561),x32562),f119(x32561)),f119(x32561))
% 162.26/162.06 [3258]E(f241(x32581,x32582,f199(x32581)),f2(a883))
% 162.26/162.06 [3259]E(f158(x32591,x32592,f119(x32591)),f2(a883))
% 162.26/162.06 [3261]E(f173(x32611,x32612,f119(x32611)),f119(x32611))
% 162.26/162.06 [3262]E(f179(x32621,x32622,f119(x32621)),f119(x32621))
% 162.26/162.06 [3263]E(f177(x32631,f119(x32631),x32632),f119(x32631))
% 162.26/162.06 [3267]E(f331(f175(x32671),f155(x32671,x32672)),f331(f175(x32671),x32672))
% 162.26/162.06 [3270]E(f331(f257(x32701,x32701),f258(x32701,x32702)),x32702)
% 162.26/162.06 [3271]E(f331(f259(x32711,x32711),f258(x32711,x32712)),x32712)
% 162.26/162.06 [3279]E(f331(f286(x32791,x32791),f258(x32791,x32792)),f258(x32791,x32792))
% 162.26/162.06 [3294]E(f307(f884(x32941),f160(x32941,x32942)),f161(x32941,f307(x32941,x32942)))
% 162.26/162.06 [3296]P24(f331(f140(a1),f181(x32961,x32962)))
% 162.26/162.06 [3304]E(f331(f257(x33041,x33041),f307(x33041,x33042)),f256(f891(x33041,a877)))
% 162.26/162.06 [3305]E(f331(f259(x33051,x33051),f307(x33051,x33052)),f256(f891(x33051,a877)))
% 162.26/162.06 [3309]P24(f331(f140(x33091),f155(x33091,x33092)))
% 162.26/162.06 [3311]P24(f331(f163(x33111,x33112),f119(x33111)))
% 162.26/162.06 [3319]E(f331(f175(a1),f181(x33191,x33192)),f302(a1,x33191,x33192))
% 162.26/162.06 [3334]P53(x33341,f196(f891(x33341,a877)),x33342)
% 162.26/162.06 [3339]E(f331(f269(a1,a1),f46(x33391,x33392)),f45(a1,x33391,x33392))
% 162.26/162.06 [3340]E(f331(f301(a883,x33401),f331(a118,x33402)),f302(a883,x33401,x33402))
% 162.26/162.06 [3358]E(f331(f331(f154(x33581),x33582),f119(x33581)),f143(x33581,x33582,f119(x33581)))
% 162.26/162.06 [3371]E(f302(a883,f331(a118,x33711),x33712),f304(a883,x33711,x33712))
% 162.26/162.06 [3374]P48(x33741,f256(f891(x33741,a877)),f307(x33741,x33742))
% 162.26/162.06 [3435]E(f331(f331(f22(a883),x34351),f331(a118,x34352)),f331(f38(a883),f305(a883,x34352,x34351)))
% 162.26/162.06 [3492]E(f170(x34921,x34922,f119(x34921)),f331(f331(f261(f884(x34921),f884(x34921)),f119(x34921)),f119(x34921)))
% 162.26/162.06 [3511]E(f331(f270(x35111,x35112,f890(x35111,x35112)),f261(x35111,x35112)),f35(f890(x35111,x35112)))
% 162.26/162.06 [3516]P24(f331(f331(f333(f884(x35161)),f119(x35161)),f164(x35161,x35162)))
% 162.26/162.06 [3517]E(f331(f197(f884(x35171)),f120(x35171,x35172)),f331(f331(f22(a883),f331(f197(f884(x35171)),x35172)),f79(a883)))
% 162.26/162.06 [3525]P24(f331(f62(a883),f305(a883,x35251,x35252)))
% 162.26/162.06 [3526]P24(f331(f62(a883),f304(a883,x35261,x35262)))
% 162.26/162.06 [3527]P24(f331(f62(a883),f302(a883,x35271,x35272)))
% 162.26/162.06 [3528]P24(f331(f62(a1),f305(a1,x35281,x35282)))
% 162.26/162.06 [3529]P24(f331(f62(a1),f304(a1,x35291,x35292)))
% 162.26/162.06 [3530]P24(f331(f62(a1),f302(a1,x35301,x35302)))
% 162.26/162.06 [3631]E(f331(f310(a883,a883,a118),f302(a883,x36311,x36312)),f302(a883,f331(a118,x36311),f331(a118,x36312)))
% 162.26/162.06 [3652]E(f331(f331(f288(x36521,x36521,x36521),f307(x36521,x36522)),f307(x36521,x36522)),f307(x36521,x36522))
% 162.26/162.06 [3684]E(f331(f331(f261(a105,a105),f331(f331(f39(a105),x36841),x36842)),f45(a105,x36841,x36842)),f21(x36841,x36842))
% 162.26/162.06 [3685]E(f331(f331(f261(a1,a1),f331(f331(f39(a1),x36851),x36852)),f45(a1,x36851,x36852)),f46(x36851,x36852))
% 162.26/162.06 [3714]E(f331(f331(f261(a883,a883),f331(f331(f39(a883),x37141),x37142)),f45(a883,x37141,x37142)),f86(f890(a883,a883),f48(x37141,x37142)))
% 162.26/162.06 [3758]P24(f331(f331(f248(a883),f331(f331(f22(a883),x37581),x37582)),f331(a118,x37581)))
% 162.26/162.06 [3857]E(f331(f331(f81(a1),f331(f331(f82(a1),x38571),f331(f331(f39(a1),x38572),x38571))),f45(a1,x38572,x38571)),x38572)
% 162.26/162.06 [3861]E(f331(f331(f42(a883,f891(f890(f884(x38611),f884(x38611)),a877)),f256(f891(a883,a877))),f146(x38611,x38612)),f148(x38611,x38612))
% 162.26/162.06 [4080]P24(f331(f331(f333(f890(f884(x40801),f884(x40801))),f331(f331(f261(f884(x40801),f884(x40801)),f119(x40801)),f119(x40801))),f161(x40801,x40802)))
% 162.26/162.06 [4242]E(f271(x42421,x42421,x42422,x42422,f5(x42421),f5(x42422)),f35(f890(x42421,x42422)))
% 162.26/162.06 [4244]E(f271(x42441,x42441,x42442,x42442,f35(x42441),f35(x42442)),f35(f890(x42441,x42442)))
% 162.26/162.06 [4497]~E(f331(f239(x44971),x44972),f199(x44971))
% 162.26/162.06 [4507]~P39(x45071,f331(f239(x45071),x45072))
% 162.26/162.06 [3242]E(f331(f244(x32421),f331(f239(x32421),x32422)),x32422)
% 162.26/162.06 [3243]E(f331(f172(x32431),f331(f172(x32431),x32432)),x32432)
% 162.26/162.06 [3245]E(f331(f331(f141(x32451),f2(a883)),x32452),x32452)
% 162.26/162.06 [3257]E(f331(f331(f176(x32571),f2(a883)),x32572),f119(x32571))
% 162.26/162.06 [3265]E(f331(f331(f137(x32651),f119(x32651)),x32652),x32652)
% 162.26/162.06 [3273]E(f331(f197(f887(x32731)),f331(f239(x32731),x32732)),f2(a883))
% 162.26/162.06 [3275]E(f40(f891(x32751,a877),f331(f308(x32751),x32752)),x32752)
% 162.26/162.06 [3277]E(f331(f175(x32771),f331(f171(x32771),x32772)),f331(f175(x32771),x32772))
% 162.26/162.06 [3278]E(f331(f175(x32781),f331(f172(x32781),x32782)),f331(f175(x32781),x32782))
% 162.26/162.06 [3283]E(f331(f331(f22(a105),x32831),x32832),f331(f331(a23,x32831),x32832))
% 162.26/162.06 [3298]E(f331(f331(f81(a883),x32981),x32982),f331(f331(f81(a883),x32982),x32981))
% 162.26/162.06 [3299]E(f331(f331(f81(a1),x32991),x32992),f331(f331(f81(a1),x32992),x32991))
% 162.26/162.06 [3300]E(f331(f331(f82(a883),x33001),x33002),f331(f331(f82(a883),x33002),x33001))
% 162.26/162.06 [3301]E(f331(f331(f82(a1),x33011),x33012),f331(f331(f82(a1),x33012),x33011))
% 162.26/162.06 [3326]E(f331(f331(f191(x33261,x33261),f2(a883)),x33262),f35(x33261))
% 162.26/162.06 [3327]E(f331(f197(f884(x33271)),f331(f171(x33271),x33272)),f331(f197(f884(x33271)),x33272))
% 162.26/162.06 [3328]E(f331(f197(f884(x33281)),f331(f172(x33281),x33282)),f331(f197(f884(x33281)),x33282))
% 162.26/162.06 [3329]E(f177(x33291,x33292,f196(f891(a883,a877))),f119(x33291))
% 162.26/162.06 [3330]E(f331(f331(f157(x33301,x33301),f5(x33301)),x33302),x33302)
% 162.26/162.06 [3332]E(f331(f260(a1,a1),f46(x33321,x33322)),f331(f331(f39(a1),x33321),x33322))
% 162.26/162.06 [3351]E(f331(f197(f884(x33511)),f155(x33511,x33512)),f331(f38(x33511),f331(f175(x33511),x33512)))
% 162.26/162.06 [3352]E(f32(f33(x33521,x33522)),f331(f331(f81(a883),f32(x33522)),f331(a118,f2(a883))))
% 162.26/162.06 [3353]E(f331(f284(x33531),f331(f286(x33531,x33531),x33532)),f331(f284(x33531),x33532))
% 162.26/162.06 [3357]P24(f331(f62(x33571),f331(f175(x33571),x33572)))
% 162.26/162.06 [3365]E(f331(f331(f81(a1),x33651),f331(f80(a1),x33652)),f331(f331(f22(a1),x33651),x33652))
% 162.26/162.06 [3373]P20(x33731,x33732,f196(f891(f882(x33731),a877)))
% 162.26/162.06 [3375]E(f331(f310(x33751,x33751,f5(x33751)),x33752),x33752)
% 162.26/162.06 [3376]E(f331(f310(x33761,x33761,f35(x33761)),x33762),x33762)
% 162.26/162.06 [3377]E(f331(f311(x33771,x33771,f5(x33771)),x33772),x33772)
% 162.26/162.06 [3378]E(f331(f311(x33781,x33781,f35(x33781)),x33782),x33782)
% 162.26/162.06 [3379]P24(f331(f256(f891(x33791,a877)),x33792))
% 162.26/162.06 [3381]E(f331(f38(a883),f331(f301(a883,x33811),x33812)),f331(f331(f22(a883),x33812),x33811))
% 162.26/162.06 [3382]E(f331(f301(a883,f331(a118,x33821)),x33822),f305(a883,x33821,x33822))
% 162.26/162.06 [3394]E(f331(f331(f309(x33941),x33942),f196(f891(x33941,a877))),f331(f253(x33941),f331(a328,x33942)))
% 162.26/162.06 [3398]E(f331(f331(f309(x33981),x33982),f196(f891(x33981,a877))),f240(x33981,f331(f239(x33981),x33982)))
% 162.26/162.06 [3401]E(f307(x34011,f331(f286(x34011,x34011),x34012)),f331(f286(x34011,x34011),f307(x34011,x34012)))
% 162.26/162.06 [3405]E(f331(f331(f81(a883),f331(a118,x34051)),x34052),f331(f331(f81(a883),x34051),f331(a118,x34052)))
% 162.26/162.06 [3406]E(f331(f331(f22(a883),f331(a118,x34061)),f331(a118,x34062)),f331(f331(f22(a883),x34061),x34062))
% 162.26/162.06 [3411]E(f55(x34111,f2(a883),x34112),f331(f331(f154(f884(x34111)),f119(x34111)),f119(f884(x34111))))
% 162.26/162.06 [3412]E(f331(f38(a883),f304(a883,x34121,x34122)),f331(f331(f22(a883),x34122),x34121))
% 162.26/162.06 [3421]P38(x34211,f331(f331(f287(a883,x34211),a252),x34212))
% 162.26/162.06 [3423]P29(a883,f142(a883,f331(f301(a883,x34231),x34232)))
% 162.26/162.06 [3425]P24(f331(f62(a883),f331(f301(a883,x34251),x34252)))
% 162.26/162.06 [3426]P24(f331(f62(a1),f331(f301(a1,x34261),x34262)))
% 162.26/162.06 [3428]E(f331(f286(f884(x34281),f884(x34281)),f160(x34281,x34282)),f160(x34281,f331(f286(x34281,x34281),x34282)))
% 162.26/162.06 [3429]E(f331(f197(a879),f33(x34291,x34292)),f331(f331(f81(a883),f331(f197(a879),x34292)),f331(a118,f2(a883))))
% 162.26/162.06 [3431]E(f331(f301(a1,x34311),f331(f331(f81(a1),x34312),f79(a1))),f302(a1,x34311,x34312))
% 162.26/162.06 [3434]E(f331(f331(f39(a1),f331(f80(a1),x34341)),f331(f80(a1),x34342)),f331(f331(f39(a1),x34341),x34342))
% 162.26/162.06 [3442]E(f186(x34421,x34422,f331(f16(f887(x34422),x34421),f199(x34422))),f196(f891(x34421,a877)))
% 162.26/162.06 [3443]E(f188(x34431,x34432,f331(f16(f887(x34432),x34431),f199(x34432))),f196(f891(x34432,a877)))
% 162.26/162.06 [3444]E(f331(f331(f191(f890(x34441,x34441),a877),f79(a883)),x34442),x34442)
% 162.26/162.06 [3446]E(f331(f331(f22(f891(x34461,a877)),x34462),f196(f891(x34461,a877))),x34462)
% 162.26/162.06 [3447]E(f331(f331(f107(f891(x34471,a877)),x34472),f196(f891(x34471,a877))),x34472)
% 162.26/162.06 [3448]E(f331(f331(f108(f891(x34481,a877)),x34482),f256(f891(x34481,a877))),x34482)
% 162.26/162.06 [3449]E(f331(f260(a883,a883),f86(f890(a883,a883),f48(x34491,x34492))),f331(f331(f39(a883),x34491),x34492))
% 162.26/162.06 [3456]E(f313(x34561,f331(a20,x34562),f331(f80(a1),f331(a20,x34562))),f331(f331(f316(a1),x34561),x34562))
% 162.26/162.06 [3457]E(f302(a1,f331(f331(f81(a1),x34571),f79(a1)),x34572),f304(a1,x34571,x34572))
% 162.26/162.06 [3462]E(f331(f269(a883,a883),f86(f890(a883,a883),f48(x34621,x34622))),f45(a883,x34621,x34622))
% 162.26/162.06 [3469]E(f314(x34691,f331(a20,x34692),f331(f80(a1),f331(a20,x34692))),f315(a1,x34691,x34692))
% 162.26/162.06 [3472]P24(f331(f331(f333(x34721),x34722),f256(f891(x34721,a877))))
% 162.26/162.06 [3477]E(f331(f331(f22(a883),f331(a118,x34771)),x34772),f331(f38(a883),f302(a883,x34772,x34771)))
% 162.26/162.06 [3502]E(f331(f331(f22(f891(x35021,a877)),x35022),f256(f891(x35021,a877))),f196(f891(x35021,a877)))
% 162.26/162.06 [3503]E(f331(f331(f107(f891(x35031,a877)),x35032),f256(f891(x35031,a877))),f256(f891(x35031,a877)))
% 162.26/162.06 [3504]E(f331(f331(f108(f891(x35041,a877)),x35042),f196(f891(x35041,a877))),f196(f891(x35041,a877)))
% 162.26/162.06 [3519]E(f45(a1,f331(f80(a1),x35191),f331(f80(a1),x35192)),f331(f80(a1),f45(a1,x35191,x35192)))
% 162.26/162.06 [3520]E(f45(a1,f331(f106(a1),x35201),f331(f106(a1),x35202)),f331(f106(a1),f45(a883,x35201,x35202)))
% 162.26/162.06 [3532]E(f331(f197(f884(x35321)),f331(f174(x35321),x35322)),f331(f331(f22(a883),f331(f197(f884(x35321)),x35322)),f79(a883)))
% 162.26/162.06 [3555]E(f331(f331(f39(a1),f45(a1,x35551,x35552)),x35552),f2(a1))
% 162.26/162.06 [3566]E(f331(a3,f45(a883,f331(a19,x35661),f331(a19,x35662))),f45(a105,x35661,x35662))
% 162.26/162.06 [3600]E(f331(a3,f331(f331(f22(a883),f331(a19,x36001)),f331(a19,x36002))),f331(f331(f22(a105),x36001),x36002))
% 162.26/162.06 [3601]E(f331(a3,f331(f331(f81(a883),f331(a19,x36011)),f331(a19,x36012))),f331(f331(f81(a105),x36011),x36012))
% 162.26/162.06 [3602]E(f331(a3,f331(f331(f82(a883),f331(a19,x36021)),f331(a19,x36022))),f331(f331(f82(a105),x36021),x36022))
% 162.26/162.06 [3603]E(f331(a3,f331(f331(f39(a883),f331(a19,x36031)),f331(a19,x36032))),f331(f331(f39(a105),x36031),x36032))
% 162.26/162.06 [3612]E(f331(f310(a883,a883,a118),f331(f301(a883,x36121),x36122)),f331(f301(a883,f331(a118,x36121)),f331(a118,x36122)))
% 162.26/162.06 [3636]P24(f331(f48(x36361,x36362),f86(f890(a883,a883),f48(x36361,x36362))))
% 162.26/162.06 [3658]E(f331(f331(f81(a883),f331(f331(f81(a883),f32(x36581)),f32(x36582))),f331(a118,f2(a883))),f32(f34(x36581,x36582)))
% 162.26/162.06 [3659]E(f45(a883,f331(a118,f45(a883,x36591,x36592)),x36592),f45(a883,f331(a118,x36591),x36592))
% 162.26/162.06 [3673]E(f331(f331(f43(f891(x36731,a877),f891(x36731,a877)),x36732),f5(f891(x36731,a877))),f41(f891(x36731,a877),x36732))
% 162.26/162.06 [3674]E(f331(f331(f42(f891(x36741,a877),f891(x36741,a877)),x36742),f5(f891(x36741,a877))),f40(f891(x36741,a877),x36742))
% 162.26/162.06 [3675]E(f331(f310(f884(x36751),f891(x36751,a877),f175(x36751)),f331(f175(f884(x36751)),f54(x36751,x36752))),f331(f308(x36751),f331(f175(x36751),x36752)))
% 162.26/162.06 [3678]P24(f331(f331(f333(f891(x36781,a877)),x36782),f331(f308(x36781),x36782)))
% 162.26/162.06 [3683]E(f45(a1,f331(f80(a1),f45(a1,x36831,x36832)),x36832),f45(a1,f331(f80(a1),x36831),x36832))
% 162.26/162.06 [3695]P24(f331(f331(f247(f891(x36951,a877)),x36952),f256(f891(x36951,a877))))
% 162.26/162.06 [3697]E(f331(f331(f288(x36971,x36971,x36971),f307(x36971,x36972)),f307(x36971,f307(x36971,x36972))),f307(x36971,x36972))
% 162.26/162.06 [3698]E(f331(f331(f107(f891(x36981,a877)),f331(f259(x36981,x36981),x36982)),f331(f257(x36981,x36981),x36982)),f331(f284(x36981),x36982))
% 162.26/162.06 [3719]E(f318(x37191,x37192,f256(f891(x37191,a877)),f256(f891(x37192,a877))),f256(f891(f889(x37191,x37192),a877)))
% 162.26/162.06 [3767]P24(f331(f331(f247(a883),f45(a883,x37671,x37672)),x37671))
% 162.26/162.06 [3789]P24(f331(f331(f247(a1),f331(f80(a1),f331(f106(a1),x37891))),f331(f106(a1),x37892)))
% 162.26/162.06 [3815]P24(f331(f331(f333(f891(x38151,a877)),f196(f891(x38151,a877))),f331(f308(x38151),x38152)))
% 162.26/162.06 [3820]E(f307(x38201,f331(f331(f288(x38201,x38201,x38201),x38202),f307(x38201,x38202))),f307(x38201,x38202))
% 162.26/162.06 [3823]E(f331(f331(f288(x38231,x38231,x38231),f307(x38231,x38232)),x38232),f331(f331(f288(x38231,x38231,x38231),x38232),f307(x38231,x38232)))
% 162.26/162.06 [3825]E(f331(a111,f331(f331(f81(a1),f331(f331(f22(a1),x38251),x38252)),f79(a1))),f331(f38(a1),f302(a1,x38252,x38251)))
% 162.26/162.06 [3837]E(f331(f257(x38371,x38371),f331(f331(f288(x38371,x38371,x38371),x38372),f307(x38371,x38372))),f331(f257(x38371,x38371),x38372))
% 162.26/162.06 [3838]E(f331(f259(x38381,x38381),f331(f331(f288(x38381,x38381,x38381),x38382),f307(x38381,x38382))),f331(f259(x38381,x38381),x38382))
% 162.26/162.06 [3854]E(f331(f331(f81(a883),f331(f331(f81(a883),f331(f197(a879),x38541)),f331(f197(a879),x38542))),f331(a118,f2(a883))),f331(f197(a879),f34(x38541,x38542)))
% 162.26/162.06 [3865]P21(a883,a883,f331(f331(f7(a883,a883,a883),f81(a883)),x38651),x38652)
% 162.26/162.06 [3867]P29(a883,f331(f172(a883),f331(f331(f157(f884(x38671),a883),f197(f884(x38671))),f182(x38671,x38672))))
% 162.26/162.06 [3909]P24(f331(f331(f248(a1),f331(f80(a1),f331(f106(a1),f331(a118,x39091)))),f331(f106(a1),x39092)))
% 162.26/162.06 [3955]E(f331(f145(f884(x39551),x39551,f331(f7(x39551,f884(x39551),f884(x39551)),f154(x39551)),f119(x39551)),x39552),f331(f172(x39551),x39552))
% 162.26/162.06 [4006]P24(f331(f331(f247(f891(f890(f884(x40061),f884(x40061)),a877)),f161(x40061,x40062)),f307(f884(x40061),f160(x40061,x40062))))
% 162.26/162.06 [4035]P24(f331(f48(x40351,x40352),f331(f331(f261(a883,a883),f331(f331(f39(a883),x40351),x40352)),f45(a883,x40351,x40352))))
% 162.26/162.06 [4046]P24(f331(f331(f247(f891(f890(f884(x40461),f884(x40461)),a877)),f160(x40461,f307(x40461,x40462))),f307(f884(x40461),f160(x40461,x40462))))
% 162.26/162.06 [4269]E(f331(f331(f272(f890(a105,a105),a105,f890(a105,a105),f890(x42691,f890(a105,a105))),f276(f331(f169(a105),f331(f331(f157(f890(a105,x42691),a105),f260(a105,x42691)),x42692)))),f331(f331(f8(x42691,f891(f890(a105,a105),f890(x42691,f890(a105,a105))),a105),f261(x42691,f890(a105,a105))),f277(x42691,x42692))),f275(x42691,x42692))
% 162.26/162.06 [4384]E(f331(f242(a883,f890(x43841,f885(x43841)),f2(a883),f331(f270(x43841,f885(x43841),a883),f331(f16(f891(f885(x43841),a883),x43841),f331(f331(f7(f885(x43841),a883,a883),f331(f331(f8(a883,f891(a883,a883),f885(x43841)),f81(a883)),f197(f885(x43841)))),f79(a883))))),f331(f138(x43841),x43842)),f331(f197(f885(x43841)),x43842))
% 162.26/162.06 [4468]E(f331(f270(f891(f890(x44681,x44681),a877),f891(f890(x44681,x44681),a877),f891(f891(x44682,x44681),f890(f891(f890(x44682,x44682),a877),f891(f890(x44682,x44682),a877)))),f331(f331(f7(f891(f890(x44681,x44681),a877),f891(f891(f890(x44681,x44681),a877),f891(f891(x44682,x44681),f891(f890(x44682,x44682),a877))),f891(f891(f890(x44681,x44681),a877),f891(f891(x44682,x44681),f890(f891(f890(x44682,x44682),a877),f891(f890(x44682,x44682),a877))))),f331(f331(f8(f891(f891(f891(x44682,x44681),f891(f890(x44682,x44682),a877)),f891(f891(x44682,x44681),f890(f891(f890(x44682,x44682),a877),f891(f890(x44682,x44682),a877)))),f891(f891(f891(f890(x44681,x44681),a877),f891(f891(x44682,x44681),f891(f890(x44682,x44682),a877))),f891(f891(f890(x44681,x44681),a877),f891(f891(x44682,x44681),f890(f891(f890(x44682,x44682),a877),f891(f890(x44682,x44682),a877))))),f891(f890(x44681,x44681),a877)),f8(f891(f891(x44682,x44681),f891(f890(x44682,x44682),a877)),f891(f891(x44682,x44681),f890(f891(f890(x44682,x44682),a877),f891(f890(x44682,x44682),a877))),f891(f890(x44681,x44681),a877))),f331(f331(f8(f891(f891(x44682,x44681),f891(f891(f890(x44682,x44682),a877),f890(f891(f890(x44682,x44682),a877),f891(f890(x44682,x44682),a877)))),f891(f891(f891(x44682,x44681),f891(f890(x44682,x44682),a877)),f891(f891(x44682,x44681),f890(f891(f890(x44682,x44682),a877),f891(f890(x44682,x44682),a877)))),f891(f890(x44681,x44681),a877)),f18(f891(x44682,x44681),f891(f890(x44682,x44682),a877),f890(f891(f890(x44682,x44682),a877),f891(f890(x44682,x44682),a877)))),f331(f331(f8(f891(f891(x44682,x44681),f891(f890(x44682,x44682),a877)),f891(f891(x44682,x44681),f891(f891(f890(x44682,x44682),a877),f890(f891(f890(x44682,x44682),a877),f891(f890(x44682,x44682),a877)))),f891(f890(x44681,x44681),a877)),f331(f8(f891(f890(x44682,x44682),a877),f891(f891(f890(x44682,x44682),a877),f890(f891(f890(x44682,x44682),a877),f891(f890(x44682,x44682),a877))),f891(x44682,x44681)),f261(f891(f890(x44682,x44682),a877),f891(f890(x44682,x44682),a877)))),f287(x44681,x44682))))),f287(x44681,x44682))),f75(x44681,x44682))
% 162.26/162.06 [4551]~E(f331(f308(x45511),x45512),f196(f891(f891(x45511,a877),a877)))
% 162.26/162.06 [4569]~P24(f331(f331(f333(x45691),x45692),f196(f891(x45691,a877))))
% 162.26/162.06 [4576]~P24(f331(f331(f248(f891(x45761,a877)),x45762),f196(f891(x45761,a877))))
% 162.26/162.06 [3384]E(f331(f331(f22(a883),x33841),f331(f331(f81(a883),x33841),x33842)),f2(a883))
% 162.26/162.06 [3386]E(f331(f331(f107(f891(x33861,a877)),x33862),x33862),x33862)
% 162.26/162.06 [3387]E(f331(f331(f108(f891(x33871,a877)),x33872),x33872),x33872)
% 162.26/162.06 [3414]E(f331(f331(f22(f891(x34141,a877)),x34142),x34142),f196(f891(x34141,a877)))
% 162.26/162.06 [3417]E(f331(f146(x34171,x34172),f2(a883)),f196(f891(f890(f884(x34171),f884(x34171)),a877)))
% 162.26/162.06 [3418]E(f331(f331(f81(a883),x34181),f331(a118,x34182)),f331(a118,f331(f331(f81(a883),x34181),x34182)))
% 162.26/162.06 [3430]E(f204(f331(f106(a1),x34301),f331(f106(a1),x34302)),f331(f106(a1),f331(f331(f22(a883),x34301),x34302)))
% 162.26/162.06 [3433]E(f331(f331(f39(a1),f331(f80(a1),x34331)),x34332),f331(f331(f39(a1),x34331),f331(f80(a1),x34332)))
% 162.26/162.06 [3437]E(f331(f38(a1),f331(f301(a1,x34371),x34372)),f331(a111,f331(f331(f22(a1),x34372),x34371)))
% 162.26/162.06 [3440]E(f331(f331(f81(a883),f331(a118,x34401)),x34402),f331(a118,f331(f331(f81(a883),x34401),x34402)))
% 162.26/162.06 [3445]E(f331(f80(f891(x34451,a877)),f331(f80(f891(x34451,a877)),x34452)),x34452)
% 162.26/162.06 [3459]E(f182(x34591,f331(f331(f154(f884(x34591)),f119(x34591)),x34592)),f182(x34591,x34592))
% 162.26/162.06 [3463]E(f331(f331(f81(a883),x34631),f331(f331(f82(a883),x34631),x34632)),f331(f331(f82(a883),x34631),f331(a118,x34632)))
% 162.26/162.06 [3470]E(f331(f331(a23,f331(a3,x34701)),f331(a3,x34702)),f331(a3,f331(f331(f22(a883),x34701),x34702)))
% 162.26/162.06 [3483]E(f331(f331(f82(a1),f331(f80(a1),x34831)),x34832),f331(f80(a1),f331(f331(f82(a1),x34831),x34832)))
% 162.26/162.06 [3485]E(f331(f331(f262(a1),f331(f106(a1),x34851)),x34852),f331(f106(a1),f331(f331(f262(a883),x34851),x34852)))
% 162.26/162.06 [3486]E(f331(f331(f81(a105),f331(a3,x34861)),f331(a3,x34862)),f331(a3,f331(f331(f81(a883),x34861),x34862)))
% 162.26/162.06 [3487]E(f331(f331(f82(a105),f331(a3,x34871)),f331(a3,x34872)),f331(a3,f331(f331(f82(a883),x34871),x34872)))
% 162.26/162.06 [3488]E(f331(f331(f251(a883),f331(a118,x34881)),f331(a118,x34882)),f331(a118,f331(f331(f251(a883),x34881),x34882)))
% 162.26/162.06 [3489]E(f331(f331(f246(a883),f331(a118,x34891)),f331(a118,x34892)),f331(a118,f331(f331(f246(a883),x34891),x34892)))
% 162.26/162.06 [3495]E(f331(f175(a883),f142(a883,f331(f301(a883,x34951),x34952))),f331(f301(a883,x34951),x34952))
% 162.26/162.06 [3496]E(f312(x34961,f331(f331(f309(x34961),x34962),f196(f891(x34961,a877)))),x34962)
% 162.26/162.06 [3500]E(f331(f257(x35001,x35002),f196(f891(f890(x35001,x35002),a877))),f196(f891(x35002,a877)))
% 162.26/162.06 [3501]E(f331(f259(x35011,x35012),f196(f891(f890(x35011,x35012),a877))),f196(f891(x35011,a877)))
% 162.26/162.06 [3505]E(f331(a111,f331(f331(f22(a1),x35051),x35052)),f331(f38(a1),f304(a1,x35052,x35051)))
% 162.26/162.06 [3510]E(f331(f331(f81(a883),x35101),f331(f331(f82(a883),x35102),x35101)),f331(f331(f82(a883),f331(a118,x35102)),x35101))
% 162.26/162.06 [3512]E(f331(f331(f61(x35121),f196(f891(x35121,a877))),x35122),f196(f891(f891(x35121,a877),a877)))
% 162.26/162.06 [3521]E(f331(f197(f884(a883)),f142(a883,f331(f301(a883,x35211),x35212))),f331(f331(f22(a883),x35212),x35211))
% 162.26/162.06 [3536]E(f331(f331(f107(f891(x35361,a877)),f196(f891(x35361,a877))),x35362),x35362)
% 162.26/162.06 [3537]E(f331(f331(f108(f891(x35371,a877)),f256(f891(x35371,a877))),x35372),x35372)
% 162.26/162.06 [3538]E(f331(f331(f81(a1),f331(f80(a1),x35381)),f331(f80(a1),x35382)),f331(f80(a1),f331(f331(f81(a1),x35381),x35382)))
% 162.26/162.06 [3541]E(f331(f331(f81(a1),f331(f110(a1),x35411)),f331(f110(a1),x35412)),f331(f110(a1),f331(f331(f81(a1),x35411),x35412)))
% 162.26/162.06 [3543]E(f331(f331(f81(a1),f331(f106(a1),x35431)),f331(f106(a1),x35432)),f331(f106(a1),f331(f331(f81(a883),x35431),x35432)))
% 162.26/162.06 [3544]E(f331(f331(f82(a1),f331(f110(a1),x35441)),f331(f110(a1),x35442)),f331(f110(a1),f331(f331(f82(a1),x35441),x35442)))
% 162.26/162.06 [3546]E(f331(f331(f82(a1),f331(f106(a1),x35461)),f331(f106(a1),x35462)),f331(f106(a1),f331(f331(f82(a883),x35461),x35462)))
% 162.26/162.06 [3547]E(f331(f331(f39(a1),f331(f106(a1),x35471)),f331(f106(a1),x35472)),f331(f106(a1),f331(f331(f39(a883),x35471),x35472)))
% 162.26/162.06 [3567]E(f331(f331(f6(x35671,a883),f331(f16(a883,x35671),f79(a883))),x35672),f331(f38(x35671),x35672))
% 162.26/162.06 [3574]E(f331(f80(a1),f45(a1,f331(f80(a1),x35741),x35742)),f45(a1,x35741,f331(f80(a1),x35742)))
% 162.26/162.06 [3576]E(f331(f175(a1),f181(x35761,f331(f331(f22(a1),x35762),f79(a1)))),f331(f301(a1,x35761),x35762))
% 162.26/162.06 [3580]P24(f331(f331(f247(a883),x35801),f331(f331(f81(a883),x35802),x35801)))
% 162.26/162.06 [3581]P24(f331(f331(f247(a883),x35811),f331(f331(f81(a883),x35811),x35812)))
% 162.26/162.06 [3584]E(f331(f331(f22(f891(x35841,a877)),f196(f891(x35841,a877))),x35842),f196(f891(x35841,a877)))
% 162.26/162.06 [3585]E(f331(f331(f107(f891(x35851,a877)),f256(f891(x35851,a877))),x35852),f256(f891(x35851,a877)))
% 162.26/162.06 [3586]E(f331(f331(f108(f891(x35861,a877)),f196(f891(x35861,a877))),x35862),f196(f891(x35861,a877)))
% 162.26/162.06 [3591]E(f331(f331(f261(a1,a1),x35911),f331(f80(a1),x35912)),f331(a51,f331(f331(f261(a1,a1),x35911),x35912)))
% 162.26/162.06 [3592]E(f331(f301(a1,f331(f331(f81(a1),x35921),f79(a1))),x35922),f305(a1,x35921,x35922))
% 162.26/162.06 [3604]E(f331(f331(f82(a883),x36041),f331(f331(f39(a883),x36042),x36041)),f331(f331(f22(a883),x36042),f45(a883,x36042,x36041)))
% 162.26/162.06 [3605]E(f331(f331(f82(a1),x36051),f331(f331(f39(a1),x36052),x36051)),f331(f331(f22(a1),x36052),f45(a1,x36052,x36051)))
% 162.26/162.06 [3609]E(f331(f175(a1),f181(f331(f331(f81(a1),x36091),f79(a1)),x36092)),f304(a1,x36091,x36092))
% 162.26/162.06 [3613]P24(f331(f331(f247(f891(x36131,a877)),x36132),x36132))
% 162.26/162.06 [3616]E(f331(f331(f107(f891(x36161,a877)),x36162),f331(f80(f891(x36161,a877)),x36162)),f256(f891(x36161,a877)))
% 162.26/162.06 [3617]E(f331(f331(f108(f891(x36171,a877)),x36172),f331(f80(f891(x36171,a877)),x36172)),f196(f891(x36171,a877)))
% 162.26/162.06 [3623]E(f331(f331(f22(a883),f331(f331(f22(a883),x36231),f79(a883))),x36232),f331(f331(f22(a883),x36231),f331(a118,x36232)))
% 162.26/162.06 [3628]E(f331(f331(f22(f891(x36281,a877)),f256(f891(x36281,a877))),x36282),f331(f80(f891(x36281,a877)),x36282))
% 162.26/162.06 [3629]E(f331(f331(f22(a1),f331(f110(a1),x36291)),f331(f110(a1),x36292)),f331(f110(a1),f331(f331(f81(a1),x36291),f331(f80(a1),x36292))))
% 162.26/162.06 [3642]E(f331(f175(a883),f142(a883,f331(f301(a883,x36421),f331(a118,x36422)))),f302(a883,x36421,x36422))
% 162.26/162.06 [3650]P24(f331(f331(f331(f331(a205,a24),x36501),x36502),x36501))
% 162.26/162.06 [3656]E(f331(f197(f884(f884(x36561))),f54(x36561,x36562)),f331(f331(f262(a883),f331(a118,f331(a118,f2(a883)))),f331(f197(f884(x36561)),x36562)))
% 162.26/162.06 [3676]E(f331(f331(f191(f890(x36761,x36761),a877),f2(a883)),x36762),f307(x36761,f196(f891(f890(x36761,x36761),a877))))
% 162.26/162.06 [3680]P24(f331(f140(a883),f142(a883,f331(f301(a883,x36801),x36802))))
% 162.26/162.06 [3696]E(f331(f310(a1,a883,a111),f302(a1,f331(f106(a1),x36961),f331(f106(a1),x36962))),f302(a883,x36961,x36962))
% 162.26/162.06 [3706]E(f193(a883,f2(a883),f5(a883),f331(f331(f22(a883),x37061),x37062)),f331(f331(f22(a883),x37061),f331(a118,x37062)))
% 162.26/162.06 [3707]E(f331(a111,f331(f331(f22(a1),x37071),f331(f331(f81(a1),x37072),f79(a1)))),f331(f38(a1),f305(a1,x37072,x37071)))
% 162.26/162.06 [3737]E(f331(f331(f157(a883,a883),a118),f142(a883,f331(f301(a883,x37371),x37372))),f142(a883,f331(f301(a883,f331(a118,x37371)),f331(a118,x37372))))
% 162.26/162.06 [3743]E(f331(f175(a1),f181(f331(f331(f81(a1),x37431),f79(a1)),f331(f331(f22(a1),x37432),f79(a1)))),f305(a1,x37431,x37432))
% 162.26/162.06 [3754]P24(f331(f331(f247(f891(x37541,a877)),f196(f891(x37541,a877))),x37542))
% 162.26/162.06 [3759]E(f86(x37591,f331(f331(f7(x37591,x37591,a877),a328),x37592)),x37592)
% 162.26/162.06 [3760]E(f91(x37601,f331(f331(f7(x37601,x37601,a877),a328),x37602)),x37602)
% 162.26/162.06 [3768]E(f331(f175(a883),f142(a883,f331(f301(a883,f331(a118,x37681)),f331(a118,x37682)))),f304(a883,x37681,x37682))
% 162.26/162.06 [3792]E(f331(f331(f268(x37921,x37922),f256(f891(x37921,a877))),f331(f16(f891(x37922,a877),x37921),f256(f891(x37922,a877)))),f256(f891(f890(x37921,x37922),a877)))
% 162.26/162.06 [3827]E(f331(f253(x38271),f331(f331(f8(a877,a877,x38271),a326),x38272)),f331(f80(f891(x38271,a877)),f331(f253(x38271),x38272)))
% 162.26/162.06 [3830]E(f331(f253(x38301),f331(f331(f7(x38301,x38301,a877),a328),x38302)),f331(f331(f309(x38301),x38302),f196(f891(x38301,a877))))
% 162.26/162.06 [3851]P24(f331(f331(f247(a883),f331(f38(x38511),f331(f175(x38511),x38512))),f331(f197(f884(x38511)),x38512)))
% 162.26/162.06 [3852]P24(f331(f331(f247(a883),f331(f197(f884(x38521)),f155(x38521,x38522))),f331(f197(f884(x38521)),x38522)))
% 162.26/162.06 [3862]E(f331(f253(x38621),f331(f331(f7(x38621,f891(x38621,a877),a877),f333(x38621)),x38622)),x38622)
% 162.26/162.06 [3876]E(f331(f331(f176(x38761),f331(f331(f22(a883),f331(f197(f884(x38761)),x38762)),f79(a883))),x38762),f120(x38761,x38762))
% 162.26/162.06 [3896]E(f193(a883,f2(a883),f331(f331(f8(a883,a883,a883),a118),f331(f251(a883),x38961)),x38962),f331(f331(f251(a883),f331(a118,x38961)),x38962))
% 162.26/162.06 [3900]E(f40(f891(x39001,a877),f331(f310(f891(f890(x39001,x39001),a877),f891(x39001,a877),f284(x39001)),x39002)),f331(f284(x39001),f40(f891(f890(x39001,x39001),a877),x39002)))
% 162.26/162.06 [3901]E(f193(a883,f331(a118,x39011),f331(f331(f8(a883,a883,a883),a118),f331(f246(a883),x39011)),x39012),f331(f331(f246(a883),f331(a118,x39011)),x39012))
% 162.26/162.06 [3903]E(f331(f331(f261(a1,a1),f331(f331(f39(a1),f331(f76(a1),x39031)),f331(f76(a1),x39032))),f45(a1,f331(f76(a1),x39031),f331(f76(a1),x39032))),f53(x39031,x39032))
% 162.26/162.06 [3925]P24(f331(f331(f247(f891(f891(x39251,a877),a877)),x39252),f331(f308(x39251),f40(f891(x39251,a877),x39252))))
% 162.26/162.06 [3960]E(f331(f331(f42(x39601,f891(x39601,a877)),x39602),f331(f331(f7(x39601,f891(x39601,a877),f891(x39601,a877)),f309(x39601)),f196(f891(x39601,a877)))),x39602)
% 162.26/162.06 [3961]E(f331(f331(f288(x39611,x39611,x39611),f331(f286(x39611,x39611),x39612)),f307(x39611,f331(f286(x39611,x39611),x39612))),f331(f286(x39611,x39611),f331(f331(f288(x39611,x39611,x39611),x39612),f307(x39611,x39612))))
% 162.26/162.06 [4027]E(f331(f175(x40271),f331(f145(f884(x40271),f884(x40271),f137(x40271),f119(x40271)),x40272)),f331(f331(f42(f884(x40271),f891(x40271,a877)),f331(f175(f884(x40271)),x40272)),f175(x40271)))
% 162.26/162.06 [4058]E(f331(f331(f107(f891(f890(x40581,x40581),a877)),f307(x40581,f196(f891(f890(x40581,x40581),a877)))),f331(f331(f288(x40581,x40581,x40581),f307(x40581,x40582)),x40582)),f307(x40581,x40582))
% 162.26/162.06 [4091]E(f331(f331(f184(x40911,x40911),x40912),x40912),f331(f331(f157(x40911,f890(x40911,x40911)),f331(f331(f18(x40911,x40911,f890(x40911,x40911)),f261(x40911,x40911)),f5(x40911))),x40912))
% 162.26/162.06 [4203]E(f331(f145(a883,f884(x42031),f331(f7(f884(x42031),a883,a883),f331(f331(f8(a883,f891(a883,a883),f884(x42031)),f246(a883)),f197(f884(x42031)))),f2(a883)),f331(f172(f884(x42031)),x42032)),f331(f197(f884(f884(x42031))),f182(x42031,x42032)))
% 162.26/162.06 [4283]E(f331(f331(f287(f890(a883,f884(x42831)),f884(x42831)),f323(a883,f884(x42831),a252,f148(x42831,x42832))),f331(f331(f18(f884(x42831),f884(x42831),f890(a883,f884(x42831))),f331(f331(f8(a883,f891(f884(x42831),f890(a883,f884(x42831))),f884(x42831)),f261(a883,f884(x42831))),f197(f884(x42831)))),f5(f884(x42831)))),f149(x42831,x42832))
% 162.26/162.06 [4424]E(f331(f253(x44241),f331(f331(f8(f891(f891(x44241,a877),a877),a877,x44241),f88(f891(x44241,a877))),f331(f331(f8(f891(f891(x44241,a877),a877),f891(f891(x44241,a877),a877),x44241),f331(f18(f891(x44241,a877),a877,a877),f331(f331(f8(a877,f891(a877,a877),f891(x44241,a877)),a334),f331(f331(f7(f891(x44241,a877),f891(f891(x44241,a877),a877),a877),f333(f891(x44241,a877))),x44242)))),f333(x44241)))),f41(f891(x44241,a877),x44242))
% 162.26/162.06 [4577]~P24(f331(f331(f248(a1),f331(f106(a1),x45771)),f331(f80(a1),f331(f106(a1),x45772))))
% 162.26/162.06 [3508]E(f331(f331(f22(a883),f331(f331(f81(a883),x35081),x35082)),x35082),x35081)
% 162.26/162.06 [3509]E(f331(f331(f22(a883),f331(f331(f81(a883),x35091),x35092)),x35091),x35092)
% 162.26/162.06 [3575]E(f331(f331(f81(a883),f331(f331(f22(a883),x35751),x35752)),x35752),f331(f331(f246(a883),x35751),x35752))
% 162.26/162.06 [3682]E(f331(f331(f82(a883),f331(f331(f39(a883),x36821),x36822)),x36822),f331(f331(f22(a883),x36821),f45(a883,x36821,x36822)))
% 162.26/162.06 [3711]E(f331(f175(a883),f142(a883,f331(f301(a883,f331(a118,x37111)),x37112))),f305(a883,x37111,x37112))
% 162.26/162.06 [3718]E(f331(f106(a1),f228(f331(a111,f331(f76(a1),x37181)),f331(a111,f331(f76(a1),x37182)))),f331(f331(a229,x37181),x37182))
% 162.26/162.06 [3720]E(f331(f331(f107(f891(x37201,a877)),f331(f80(f891(x37201,a877)),x37202)),x37202),f256(f891(x37201,a877)))
% 162.26/162.06 [3721]E(f331(f331(f108(f891(x37211,a877)),f331(f80(f891(x37211,a877)),x37212)),x37212),f196(f891(x37211,a877)))
% 162.26/162.06 [3733]P24(f331(f331(f247(a883),f331(f331(f22(a883),x37331),x37332)),x37331))
% 162.26/162.06 [3734]P24(f331(f331(f247(a883),f331(f331(f39(a883),x37341),x37342)),x37341))
% 162.26/162.06 [3756]P24(f331(f331(f248(a883),x37561),f331(a118,f331(f331(f81(a883),x37562),x37561))))
% 162.26/162.06 [3757]P24(f331(f331(f248(a883),x37571),f331(a118,f331(f331(f81(a883),x37571),x37572))))
% 162.26/162.06 [3779]E(f331(f331(f82(a883),f331(a111,f331(f76(a1),x37791))),f331(a111,f331(f76(a1),x37792))),f331(a111,f331(f76(a1),f331(f331(f82(a1),x37791),x37792))))
% 162.26/162.06 [3788]P24(f331(f331(f247(a1),f2(a1)),f331(f331(f262(a1),f331(f76(a1),x37881)),x37882)))
% 162.26/162.06 [3856]E(f331(f285(f884(x38561),f884(x38561),f161(x38561,x38562)),f331(f331(f309(f884(x38561)),f119(x38561)),f196(f891(f884(x38561),a877)))),f331(f331(f309(f884(x38561)),f119(x38561)),f196(f891(f884(x38561),a877))))
% 162.26/162.06 [3874]E(f331(f331(f107(f891(f890(x38741,x38741),a877)),f307(x38741,x38742)),f307(x38741,f196(f891(f890(x38741,x38741),a877)))),f307(x38741,x38742))
% 162.26/162.06 [3956]E(f331(f253(f891(x39561,a877)),f331(f331(f7(f891(x39561,a877),f891(x39561,a877),a877),f247(f891(x39561,a877))),x39562)),f331(f308(x39561),x39562))
% 162.26/162.06 [3972]E(f331(f331(f157(a1,a883),a111),f331(f331(f137(a1),f331(f331(f157(a883,a1),f106(a1)),x39721)),f331(f331(f157(a883,a1),f106(a1)),x39722))),f331(f331(f137(a883),x39721),x39722))
% 162.26/162.06 [4005]E(f331(f310(a1,a1,f331(f331(f7(a1,a1,a1),f81(a1)),x40051)),f331(f301(a1,f2(a1)),f331(f331(f22(a1),x40052),x40051))),f331(f301(a1,x40051),x40052))
% 162.26/162.06 [4007]P49(x40071,f331(f331(f22(f891(f890(x40071,x40071),a877)),x40072),f307(x40071,f196(f891(f890(x40071,x40071),a877)))))
% 162.26/162.06 [4025]E(f331(f197(f884(x40251)),f331(f145(f884(x40251),f884(x40251),f137(x40251),f119(x40251)),x40252)),f331(f169(a883),f331(f331(f157(f884(x40251),a883),f197(f884(x40251))),x40252)))
% 162.26/162.06 [4030]P48(x40301,f256(f891(x40301,a877)),f331(f331(f107(f891(f890(x40301,x40301),a877)),x40302),f307(x40301,f196(f891(f890(x40301,x40301),a877)))))
% 162.26/162.06 [4070]E(f193(a883,f2(a883),f331(f331(f8(a883,a883,a883),a118),f331(f331(f7(a883,a883,a883),f251(a883)),x40701)),x40702),f331(f331(f251(a883),x40702),f331(a118,x40701)))
% 162.26/162.06 [4073]E(f193(a883,f331(a118,x40731),f331(f331(f8(a883,a883,a883),a118),f331(f331(f7(a883,a883,a883),f246(a883)),x40731)),x40732),f331(f331(f246(a883),x40732),f331(a118,x40731)))
% 162.26/162.06 [4076]E(f331(f310(x40761,f884(x40761),f331(f331(f7(x40761,f884(x40761),f884(x40761)),f154(x40761)),f119(x40761))),x40762),f178(x40761,x40762,f331(f331(f309(f884(x40761)),f119(x40761)),f196(f891(f884(x40761),a877)))))
% 162.26/162.06 [4077]E(f331(f331(f107(f891(f890(x40771,x40771),a877)),f331(f331(f288(x40771,x40771,x40771),x40772),f307(x40771,x40772))),f307(x40771,f196(f891(f890(x40771,x40771),a877)))),f307(x40771,x40772))
% 162.26/162.06 [4086]P24(f331(f331(f247(f891(f890(x40861,x40861),a877)),f258(x40861,x40862)),f331(f331(f268(x40861,x40861),x40862),f331(f16(f891(x40861,a877),x40861),x40862))))
% 162.26/162.06 [4089]E(f331(f310(a1,a883,a111),f331(f331(f107(f891(a1,a877)),f331(f310(a883,a1,f106(a1)),x40891)),f331(f310(a883,a1,f106(a1)),x40892))),f331(f331(f107(f891(a883,a877)),x40891),x40892))
% 162.26/162.06 [4090]E(f331(f310(a1,a883,a111),f331(f331(f108(f891(a1,a877)),f331(f310(a883,a1,f106(a1)),x40901)),f331(f310(a883,a1,f106(a1)),x40902))),f331(f331(f108(f891(a883,a877)),x40901),x40902))
% 162.26/162.06 [4094]E(f331(f253(x40941),f331(f331(f8(a877,a877,x40941),a326),f331(f331(f7(x40941,f891(x40941,a877),a877),f333(x40941)),x40942))),f331(f80(f891(x40941,a877)),x40942))
% 162.26/162.06 [4120]E(f331(f145(f884(x41201),f884(x41201),f137(x41201),f119(x41201)),f331(f331(f157(f884(x41201),f884(x41201)),f172(x41201)),f331(f172(f884(x41201)),x41202))),f331(f172(x41201),f331(f145(f884(x41201),f884(x41201),f137(x41201),f119(x41201)),x41202)))
% 162.26/162.06 [4145]E(f331(f331(f42(a883,f891(f890(x41451,x41451),a877)),f256(f891(a883,a877))),f331(f331(f7(a883,f891(f890(x41451,x41451),a877),f891(f890(x41451,x41451),a877)),f191(f890(x41451,x41451),a877)),x41452)),f307(x41451,x41452))
% 162.26/162.06 [4162]E(f86(x41621,f331(f331(f8(f891(x41621,a877),a877,x41621),f331(a328,x41622)),f331(f331(f7(x41621,f891(x41621,a877),f891(x41621,a877)),f309(x41621)),f196(f891(x41621,a877))))),f312(x41621,x41622))
% 162.26/162.06 [4171]E(f331(f197(f884(x41711)),f155(x41711,f331(f145(f884(x41711),f884(x41711),f137(x41711),f119(x41711)),x41712))),f331(f38(x41711),f331(f331(f42(f884(x41711),f891(x41711,a877)),f331(f175(f884(x41711)),x41712)),f175(x41711))))
% 162.26/162.06 [4187]E(f331(f331(f107(f891(f890(x41871,x41871),a877)),x41872),f331(f331(f288(x41871,x41871,x41871),f331(f331(f288(x41871,x41871,x41871),x41872),f307(x41871,x41872))),x41872)),f331(f331(f288(x41871,x41871,x41871),x41872),f307(x41871,x41872)))
% 162.26/162.06 [4215]P24(f331(f331(f247(f891(f890(x42151,x42151),a877)),f331(f331(f288(x42151,x42151,x42151),x42152),f307(x42151,x42152))),f331(f331(f268(x42151,x42151),f331(f284(x42151),x42152)),f331(f16(f891(x42151,a877),x42151),f331(f284(x42151),x42152)))))
% 162.26/162.06 [4257]E(f331(f253(f884(x42571)),f331(f331(f7(f884(x42571),f891(x42571,a877),a877),f331(f331(f8(f891(x42571,a877),f891(f891(x42571,a877),a877),f884(x42571)),f247(f891(x42571,a877))),f175(x42571))),x42572)),f164(x42571,x42572))
% 162.26/162.06 [4271]E(f331(f159(f884(x42711),x42711,f119(x42711),f331(f331(f8(f884(x42711),f891(f884(x42711),f884(x42711)),x42711),f331(f7(f884(x42711),f884(x42711),f884(x42711)),f137(x42711))),f331(f331(f7(x42711,f884(x42711),f884(x42711)),f154(x42711)),f119(x42711)))),x42712),f331(f171(x42711),x42712))
% 162.26/162.06 [4310]P21(f891(x43101,x43102),f891(f890(x43101,x43102),a877),f331(f331(f8(f891(f890(x43101,x43102),a877),f891(f890(x43101,x43102),a877),f891(x43101,x43102)),f253(f890(x43101,x43102))),f331(f331(f8(f891(x43101,f891(x43102,a877)),f891(f890(x43101,x43102),a877),f891(x43101,x43102)),f270(x43101,x43102,a877)),f331(f8(x43102,f891(x43102,a877),x43101),f331(f7(x43102,x43102,a877),a328)))),f256(f891(f891(x43101,x43102),a877)))
% 162.26/162.06 [4365]E(f331(f331(f42(x43651,f891(f890(x43651,x43651),a877)),x43652),f331(f331(f7(x43651,f891(f890(x43651,x43651),a877),f891(f890(x43651,x43651),a877)),f331(f331(f8(f890(x43651,x43651),f891(f891(f890(x43651,x43651),a877),f891(f890(x43651,x43651),a877)),x43651),f309(f890(x43651,x43651))),f331(f331(f18(x43651,x43651,f890(x43651,x43651)),f261(x43651,x43651)),f5(x43651)))),f196(f891(f890(x43651,x43651),a877)))),f258(x43651,x43652))
% 162.26/162.06 [4373]E(f214(x43731,f331(f331(f261(a1,a1),f331(f80(a1),f331(f331(f74(f890(a1,a1),a1,x43731,f260(a1,a1)),f224(x43731)),x43732))),f331(f331(f74(f890(a1,a1),a1,x43731,f269(a1,a1)),f224(x43731)),x43732))),f232(x43731,x43732))
% 162.26/162.06 [4463]E(f331(f253(f891(x44631,a877)),f331(f331(f8(f891(f891(x44631,a877),a877),a877,f891(x44631,a877)),f87(f891(x44631,a877))),f331(f331(f7(f891(x44631,a877),f891(f891(x44631,a877),a877),f891(f891(x44631,a877),a877)),f331(f331(f8(f891(f891(x44631,a877),f891(a877,a877)),f891(f891(f891(x44631,a877),a877),f891(f891(x44631,a877),a877)),f891(x44631,a877)),f18(f891(x44631,a877),a877,a877)),f331(f331(f8(f891(f891(x44631,a877),a877),f891(f891(x44631,a877),f891(a877,a877)),f891(x44631,a877)),f331(f8(a877,f891(a877,a877),f891(x44631,a877)),a329)),f331(f331(f7(f891(x44631,a877),f891(f891(x44631,a877),f891(x44631,a877)),f891(f891(x44631,a877),a877)),f331(f331(f8(f891(f891(x44631,a877),a877),f891(f891(f891(x44631,a877),f891(x44631,a877)),f891(f891(x44631,a877),a877)),f891(x44631,a877)),f8(f891(x44631,a877),a877,f891(x44631,a877))),a328)),f80(f891(x44631,a877)))))),f331(f331(f8(f891(f891(x44631,a877),a877),a877,f891(x44631,a877)),f331(f333(f891(x44631,a877)),x44632)),f308(x44631))))),f331(f308(x44631),f331(f80(f891(x44631,a877)),x44632)))
% 162.26/162.06 [4579]~P24(f331(f331(f248(a883),f331(f331(f81(a883),x45791),x45792)),x45792))
% 162.26/162.06 [4580]~P24(f331(f331(f248(a883),f331(f331(f81(a883),x45801),x45802)),x45801))
% 162.26/162.06 [3793]E(f331(f331(f22(a883),x37931),f331(f331(f82(a883),f331(f331(f39(a883),x37931),x37932)),x37932)),f45(a883,x37931,x37932))
% 162.26/162.06 [3794]E(f331(f331(f22(a1),x37941),f331(f331(f82(a1),f331(f331(f39(a1),x37941),x37942)),x37942)),f45(a1,x37941,x37942))
% 162.26/162.06 [3828]E(f331(f331(f157(a883,x38281),f331(f168(x38281),x38282)),f142(a883,f331(f301(a883,f2(a883)),f331(f197(f884(x38281)),x38282)))),x38282)
% 162.26/162.06 [3883]E(f331(f285(x38831,x38831,f307(x38831,f196(f891(f890(x38831,x38831),a877)))),x38832),x38832)
% 162.26/162.06 [4008]E(f307(x40081,f331(f331(f22(f891(f890(x40081,x40081),a877)),x40082),f307(x40081,f196(f891(f890(x40081,x40081),a877))))),f307(x40081,x40082))
% 162.26/162.06 [4009]E(f307(x40091,f331(f331(f107(f891(f890(x40091,x40091),a877)),x40092),f307(x40091,f196(f891(f890(x40091,x40091),a877))))),f307(x40091,x40092))
% 162.26/162.06 [4184]E(f331(f106(a1),f331(f331(f39(a883),f331(f331(f82(a883),f331(a111,f331(f76(a1),x41841))),f331(a111,f331(f76(a1),x41842)))),f228(f331(a111,f331(f76(a1),x41841)),f331(a111,f331(f76(a1),x41842))))),f230(x41841,x41842))
% 162.26/162.06 [4207]E(f331(f331(f22(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x42071)),x42071)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x42072)),x42072)),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f22(a1),x42071),x42072))),f331(f331(f22(a1),x42071),x42072))),a103))
% 162.26/162.06 [4231]E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x42311)),x42311)),a103)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x42312)),x42312)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),x42311),x42312))),f331(f331(f81(a1),x42311),x42312)))
% 162.26/162.06 [4235]E(f331(f331(f272(f890(a105,a105),a105,f890(a105,a105),f890(x42351,f890(a105,a105))),f276(f331(a3,f331(f197(f884(x42351)),x42352)))),f331(f331(f8(x42351,f891(f890(a105,a105),f890(x42351,f890(a105,a105))),a105),f261(x42351,f890(a105,a105))),f331(f331(f8(a883,x42351,a105),f331(f168(x42351),x42352)),a19))),f282(x42351,x42352))
% 162.26/162.06 [4264]E(f331(f331(f22(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x42641)),x42641)),a103)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x42642)),x42642)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f22(a1),f331(f331(f81(a1),x42641),a103)),x42642))),f331(f331(f22(a1),f331(f331(f81(a1),x42641),a103)),x42642)))
% 162.26/162.06 [4315]E(f331(f145(a883,f884(x43151),f331(f7(f884(x43151),a883,a883),f331(f331(f8(a883,f891(a883,a883),f884(x43151)),f246(a883)),f197(f884(x43151)))),f2(a883)),f331(f172(f884(x43151)),f182(x43151,x43152))),f331(f197(f884(f884(x43151))),f331(f139(f884(x43151),f331(f331(f8(a877,a877,f884(x43151)),a326),f331(f331(f7(f884(x43151),f884(x43151),a877),a328),f119(x43151)))),x43152)))
% 162.26/162.06 [4321]E(f331(f331(f42(a883,f891(x43211,a877)),f256(f891(a883,a877))),f331(f331(f7(a883,f891(a883,f891(x43211,a877)),f891(x43211,a877)),f331(f331(f8(f891(a883,a877),f891(f891(a883,f891(x43211,a877)),f891(x43211,a877)),a883),f42(a883,f891(x43211,a877))),f301(a883,f2(a883)))),x43212)),f331(f331(f42(a883,f891(x43211,a877)),f256(f891(a883,a877))),x43212))
% 162.26/162.06 [4342]P24(f331(f62(a883),f331(f253(a883),f331(f331(f18(a883,a877,a877),f331(f331(f8(a877,f891(a877,a877),a883),a329),x43421)),f331(f331(f7(a883,a883,a877),f248(a883)),x43422)))))
% 162.26/162.06 [4473]E(f331(f253(f890(f884(x44731),f884(x44731))),f331(f270(f884(x44731),f884(x44731),a877),f331(f331(f18(f884(x44731),f891(f884(x44731),a877),f891(f884(x44731),a877)),f331(f331(f8(f891(f884(x44731),f891(a877,a877)),f891(f891(f884(x44731),a877),f891(f884(x44731),a877)),f884(x44731)),f18(f884(x44731),a877,a877)),f331(f331(f8(f891(f884(x44731),a877),f891(f884(x44731),f891(a877,a877)),f884(x44731)),f331(f8(a877,f891(a877,a877),f884(x44731)),a330)),f331(f331(f7(f884(x44731),f891(f884(x44731),a883),f891(f884(x44731),a877)),f331(f331(f8(f891(a883,a877),f891(f891(f884(x44731),a883),f891(f884(x44731),a877)),f884(x44731)),f8(a883,a877,f884(x44731))),f331(f331(f8(a883,f891(a883,a877),f884(x44731)),f248(a883)),f197(f884(x44731))))),f197(f884(x44731)))))),f331(f331(f18(f884(x44731),f891(f884(x44731),a877),f891(f884(x44731),a877)),f331(f331(f8(f891(f884(x44731),f891(a877,a877)),f891(f891(f884(x44731),a877),f891(f884(x44731),a877)),f884(x44731)),f18(f884(x44731),a877,a877)),f331(f331(f8(f891(f884(x44731),a877),f891(f884(x44731),f891(a877,a877)),f884(x44731)),f331(f8(a877,f891(a877,a877),f884(x44731)),a329)),f331(f331(f7(f884(x44731),f891(f884(x44731),a883),f891(f884(x44731),a877)),f331(f331(f8(f891(a883,a877),f891(f891(f884(x44731),a883),f891(f884(x44731),a877)),f884(x44731)),f8(a883,a877,f884(x44731))),f331(f331(f8(a883,f891(a883,a877),f884(x44731)),a328),f197(f884(x44731))))),f197(f884(x44731)))))),f331(f331(f7(f884(x44731),f891(f890(f884(x44731),f884(x44731)),a877),f891(f884(x44731),a877)),f331(f331(f8(f891(f884(x44731),f891(f891(f890(f884(x44731),f884(x44731)),a877),a877)),f891(f891(f890(f884(x44731),f884(x44731)),a877),f891(f884(x44731),a877)),f884(x44731)),f7(f884(x44731),f891(f890(f884(x44731),f884(x44731)),a877),a877)),f331(f331(f8(f891(f884(x44731),f890(f884(x44731),f884(x44731))),f891(f884(x44731),f891(f891(f890(f884(x44731),f884(x44731)),a877),a877)),f884(x44731)),f331(f8(f890(f884(x44731),f884(x44731)),f891(f891(f890(f884(x44731),f884(x44731)),a877),a877),f884(x44731)),f333(f890(f884(x44731),f884(x44731))))),f261(f884(x44731),f884(x44731))))),f148(x44731,x44732)))))),f149(x44731,x44732))
% 162.26/162.06 [4599]~P24(f331(f331(f92(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x45991)),x45991)),a103)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x45992)),x45992)))
% 162.26/162.06 [4233]E(f331(a111,f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),x42331),x42332)),f196(f891(f890(a883,a883),a877)))))),f331(f331(f22(a883),x42331),x42332))
% 162.26/162.06 [4238]E(f331(f331(f288(x42381,x42381,x42381),f331(f331(f107(f891(f890(x42381,x42381),a877)),x42382),f307(x42381,f196(f891(f890(x42381,x42381),a877))))),f307(x42381,f331(f331(f107(f891(f890(x42381,x42381),a877)),x42382),f307(x42381,f196(f891(f890(x42381,x42381),a877)))))),f307(x42381,x42382))
% 162.26/162.06 [4275]E(f275(x42751,f331(f139(f890(a105,x42751),f331(f270(a105,x42751,a877),f331(f331(f8(a877,f891(x42751,a877),a105),f16(a877,x42751)),f331(f248(a105),f2(a105))))),x42752)),f275(x42751,x42752))
% 162.26/162.06 [4276]E(f277(x42761,f331(f139(f890(a105,x42761),f331(f270(a105,x42761,a877),f331(f331(f8(a877,f891(x42761,a877),a105),f16(a877,x42761)),f331(f248(a105),f2(a105))))),x42762)),f277(x42761,x42762))
% 162.26/162.06 [4277]E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),x42771),f331(f331(f22(a1),x42772),a103)))),f331(f331(f81(a1),x42771),f331(f331(f22(a1),x42772),a103)))),a103),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x42771)),x42771)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x42772)),x42772)))
% 162.26/162.06 [4279]E(f331(f80(a1),f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),x42791),x42792)),f196(f891(f890(a883,a883),a877)))))),f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),x42792),x42791)),f196(f891(f890(a883,a883),a877))))))
% 162.26/162.06 [4335]E(f331(f331(f287(f884(a883),x43351),f148(a883,a252)),f331(f331(f7(x43351,f884(f891(x43351,a883)),f884(a883)),f331(f331(f8(f891(f891(x43351,a883),a883),f891(f884(f891(x43351,a883)),f884(a883)),x43351),f157(f891(x43351,a883),a883)),f331(f7(f891(x43351,a883),x43351,a883),f5(f891(x43351,a883))))),x43352)),f156(x43351,x43352))
% 162.26/162.06 [4362]E(f331(f331(f89(a1,a883),f331(f110(a1),f331(f331(f81(a1),x43621),a103))),f331(f331(f18(a1,a883,a883),f331(f331(f7(a1,a883,f891(a883,a883)),f331(f331(f8(a877,f891(a883,f891(a883,a883)),a1),f102(a883)),a202)),f2(a883))),f331(f331(f8(a883,a883,a1),a118),f331(f331(f8(a883,a883,a1),f331(f251(a883),x43622)),a111)))),f331(f331(f251(a883),f331(a118,x43622)),f331(f110(a883),x43621)))
% 162.26/162.06 [4363]E(f331(f331(f89(a1,a883),f331(f110(a1),f331(f331(f81(a1),x43631),a103))),f331(f331(f18(a1,a883,a883),f331(f331(f7(a1,a883,f891(a883,a883)),f331(f331(f8(a877,f891(a883,f891(a883,a883)),a1),f102(a883)),a202)),f331(a118,x43632))),f331(f331(f8(a883,a883,a1),a118),f331(f331(f8(a883,a883,a1),f331(f246(a883),x43632)),a111)))),f331(f331(f246(a883),f331(a118,x43632)),f331(f110(a883),x43631)))
% 162.26/162.06 [4383]E(f331(f145(f884(x43831),f884(x43831),f137(x43831),f119(x43831)),f331(f331(f157(f884(x43831),f884(x43831)),f159(f884(x43831),x43831,f119(x43831),f331(f331(f8(f884(x43831),f891(f884(x43831),f884(x43831)),x43831),f16(f884(x43831),f884(x43831))),f331(f331(f7(x43831,f884(x43831),f884(x43831)),f154(x43831)),f119(x43831))))),x43832)),f331(f331(f157(f884(x43831),x43831),f144(x43831)),f331(f139(f884(x43831),f331(f331(f8(a877,a877,f884(x43831)),a326),f331(f331(f7(f884(x43831),f884(x43831),a877),a328),f119(x43831)))),x43832)))
% 162.26/162.06 [4455]E(f331(f270(a1,a1,a877),f331(f331(f7(a1,f891(a1,a877),f891(a1,a877)),f331(f331(f8(f891(a1,f891(a877,a877)),f891(f891(a1,a877),f891(a1,a877)),a1),f18(a1,a877,a877)),f331(f331(f8(f891(a1,a877),f891(a1,f891(a877,a877)),a1),f331(f8(a877,f891(a877,a877),a1),a329)),f331(f331(f8(f891(a1,a1),f891(a1,a877),a1),f331(f8(a1,a877,a1),f331(a328,x44551))),f331(f331(f8(a1,f891(a1,a1),a1),f81(a1)),f331(f82(a1),x44552)))))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f331(f8(a877,a877,a1),f331(a334,f331(f331(f248(a1),f2(a1)),x44552))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f247(a1),f2(a1)))),f331(f331(f7(a1,a1,a877),f248(a1)),x44552))))),f331(f331(f8(a877,a877,a1),f331(a334,f331(a326,f331(f331(f248(a1),f2(a1)),x44552)))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f248(a1),x44552))),f331(f331(f7(a1,a1,a877),f247(a1)),f2(a1))))))),f49(x44551,x44552))
% 162.26/162.06 [4457]E(f331(f253(x44571),f331(f331(f8(f891(a883,a877),a877,x44571),f87(a883)),f331(f331(f7(x44571,f891(a883,a877),f891(a883,a877)),f331(f331(f8(f891(a883,f891(a877,a877)),f891(f891(a883,a877),f891(a883,a877)),x44571),f18(a883,a877,a877)),f331(f331(f8(f891(a883,a877),f891(a883,f891(a877,a877)),x44571),f331(f8(a877,f891(a877,a877),a883),a329)),f331(f331(f7(x44571,f891(a883,x44571),f891(a883,a877)),f331(f331(f8(f891(x44571,a877),f891(f891(a883,x44571),f891(a883,a877)),x44571),f8(x44571,a877,a883)),a328)),f331(f168(x44571),x44572))))),f331(f331(f7(a883,a883,a877),f248(a883)),f331(f197(f884(x44571)),x44572))))),f331(f175(x44571),x44572))
% 162.26/162.06 [4588]~E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x45881)),x45881)),a103),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x45882)),x45882))
% 162.26/162.06 [4196]E(f331(f331(f22(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x41961)),x41961)),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x41962)),x41962)),a103)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f22(a1),x41961),x41962))),f331(f331(f22(a1),x41961),x41962)))
% 162.26/162.06 [4197]E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x41971)),x41971)),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x41972)),x41972)),a103)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),x41971),x41972))),f331(f331(f81(a1),x41971),x41972)))
% 162.26/162.06 [4288]E(f331(f331(f22(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x42881)),x42881)),a103)),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x42882)),x42882)),a103)),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f22(a1),x42881),x42882))),f331(f331(f22(a1),x42881),x42882))),a103))
% 162.26/162.06 [4289]E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x42891)),x42891)),a103)),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x42892)),x42892)),a103)),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),x42891),x42892))),f331(f331(f81(a1),x42891),x42892))),a103))
% 162.26/162.06 [4322]E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f82(a1),x43221),x43222))),f331(f331(f82(a1),x43221),x43222))),a103)),x43222),f331(f331(f82(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x43221)),x43221)),x43222))
% 162.26/162.06 [4378]E(f331(f145(f884(f884(x43781)),f884(f884(x43781)),f137(f884(x43781)),f119(f884(x43781))),f331(f331(f157(f884(x43781),f884(f884(x43781))),f159(f884(f884(x43781)),x43781,f119(f884(x43781)),f331(f16(f891(f884(x43781),f884(f884(x43781))),x43781),f331(f331(f7(f884(x43781),f884(f884(x43781)),f884(f884(x43781))),f154(f884(x43781))),f119(f884(x43781)))))),x43782)),f331(f331(f157(f884(x43781),f884(x43781)),f174(x43781)),f331(f139(f884(x43781),f331(f331(f8(a877,a877,f884(x43781)),a326),f331(f331(f7(f884(x43781),f884(x43781),a877),a328),f119(x43781)))),x43782)))
% 162.26/162.06 [4387]E(f331(f331(f89(a1,a883),f331(f110(a1),f331(f331(f81(a1),x43871),a103))),f331(f331(f18(a1,a883,a883),f331(f331(f7(a1,a883,f891(a883,a883)),f331(f331(f8(a877,f891(a883,f891(a883,a883)),a1),f102(a883)),a202)),f2(a883))),f331(f331(f8(a883,a883,a1),a118),f331(f331(f7(a1,a883,a883),f331(f331(f8(a883,f891(a883,a883),a1),f251(a883)),a111)),x43872)))),f331(f331(f251(a883),f331(f110(a883),x43871)),f331(a118,x43872)))
% 162.26/162.06 [4388]E(f331(f331(f89(a1,a883),f331(f110(a1),f331(f331(f81(a1),x43881),a103))),f331(f331(f18(a1,a883,a883),f331(f331(f7(a1,a883,f891(a883,a883)),f331(f331(f8(a877,f891(a883,f891(a883,a883)),a1),f102(a883)),a202)),f331(a118,x43882))),f331(f331(f8(a883,a883,a1),a118),f331(f331(f7(a1,a883,a883),f331(f331(f8(a883,f891(a883,a883),a1),f246(a883)),a111)),x43882)))),f331(f331(f246(a883),f331(f110(a883),x43881)),f331(a118,x43882)))
% 162.26/162.06 [4597]~P24(f331(f331(f92(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x45971)),x45971)),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x45972)),x45972)),a103)))
% 162.26/162.06 [4226]E(f331(f331(f262(a1),x42261),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x42262)),x42262)),a103))),f331(f331(f89(a1,a1),f331(f331(f262(a1),x42261),f331(f110(a883),x42262))),f331(f331(f18(a1,a1,a1),f82(a1)),f5(a1))))
% 162.26/162.06 [4262]E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f82(a1),x42621),x42622))),f331(f331(f82(a1),x42621),x42622))),a103),f331(f331(f82(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x42621)),x42621)),a103)),x42622))
% 162.26/162.06 [4324]E(f331(f331(f39(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x43241)),x43241)),a103))),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x43242)),x43242)),a103))),f331(f331(f39(a1),f331(f110(a1),x43241)),f331(f110(a1),x43242)))
% 162.26/162.06 [4377]E(f331(f270(x43771,x43771,a877),f331(f331(f18(x43771,a877,f891(x43771,a877)),f331(f331(f8(f891(x43771,f891(a877,a877)),f891(a877,f891(x43771,a877)),x43771),f7(x43771,a877,a877)),f331(f331(f8(f891(x43771,a877),f891(x43771,f891(a877,a877)),x43771),f331(f8(a877,f891(a877,a877),x43771),a329)),a328))),x43772)),f258(x43771,x43772))
% 162.26/162.06 [4438]E(f45(a1,f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x44381)),x44381)),a103)),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x44382)),x44382)),a103))),f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f45(a1,f331(f110(a1),x44381),f331(f110(a1),x44382))))
% 162.26/162.06 [4405]E(f331(f331(f39(a883),x44051),f331(f331(f81(a883),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)))),x44052)),f331(f331(f39(a883),x44051),f331(a118,f331(a118,f331(a118,x44052)))))
% 162.26/162.06 [4406]E(f45(a883,x44061,f331(f331(f81(a883),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)))),x44062)),f45(a883,x44061,f331(a118,f331(a118,f331(a118,x44062)))))
% 162.26/162.06 [4407]E(f45(a883,f331(f331(f81(a883),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)))),x44071),x44072),f45(a883,f331(a118,f331(a118,f331(a118,x44071))),x44072))
% 162.26/162.06 [4431]E(f127(f331(x44311,f331(f331(f82(a105),f331(f110(a105),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)))),x44312))),f331(f212(x44311),x44312))
% 162.26/162.06 [4436]E(f331(f331(f39(a883),f331(f331(f81(a883),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)))),x44361)),x44362),f331(f331(f39(a883),f331(a118,f331(a118,f331(a118,x44361)))),x44362))
% 162.26/162.06 [4498]~E(f34(x44981,x44982),f331(a28,x44983))
% 162.26/162.06 [4499]~E(f33(x44991,x44992),f331(a28,x44993))
% 162.26/162.06 [4500]~E(f331(a28,x45001),f34(x45002,x45003))
% 162.26/162.06 [4501]~E(f331(a28,x45011),f33(x45012,x45013))
% 162.26/162.06 [4514]~E(f29(x45141,x45142,x45143),a24)
% 162.26/162.06 [4515]~E(f31(x45151,x45152,x45153),a24)
% 162.26/162.06 [4516]~E(f30(x45161,x45162,x45163),a24)
% 162.26/162.06 [3224]E(f331(f201(x32241,x32242),x32243),f125(x32241,x32242))
% 162.26/162.06 [3246]E(f331(f211(x32461,x32462),x32463),f331(f129(x32461),x32462))
% 162.26/162.06 [3324]E(f331(f331(f210(x33241,x33242),x33243),f199(x33241)),f199(x33242))
% 162.26/162.06 [3325]E(f331(f331(f157(x33251,x33252),x33253),f119(x33251)),f119(x33252))
% 162.26/162.06 [3345]E(f32(f29(x33451,x33452,x33453)),f2(a883))
% 162.26/162.06 [3367]E(f331(f192(x33671,x33672,x33673),f2(a883)),x33672)
% 162.26/162.06 [3368]E(f331(f197(a879),f29(x33681,x33682,x33683)),f2(a883))
% 162.26/162.06 [3370]E(f331(f331(f184(x33701,x33702),x33703),f119(x33702)),f119(f890(x33701,x33702)))
% 162.26/162.06 [3404]E(f86(x34041,f63(x34041,x34042,x34043)),f331(f64(x34041,x34042),x34043))
% 162.26/162.06 [3455]E(f143(x34551,x34552,f155(x34551,x34553)),f155(x34551,f143(x34551,x34552,x34553)))
% 162.26/162.06 [3473]E(f331(f260(f884(x34731),f884(x34731)),f170(x34731,x34732,x34733)),f331(f139(x34731,x34732),x34733))
% 162.26/162.06 [3548]E(f193(x35481,x35482,x35483,f2(a883)),x35482)
% 162.26/162.06 [3549]E(f17(x35491,x35492,x35493,f2(a105)),x35492)
% 162.26/162.06 [3556]E(f166(x35561,x35562,x35563,f119(x35561)),f119(x35562))
% 162.26/162.06 [3557]E(f167(x35571,x35572,x35573,f119(x35571)),f119(x35572))
% 162.26/162.06 [3565]E(f331(f331(f168(x35651),f331(f331(f154(x35651),x35652),x35653)),f2(a883)),x35652)
% 162.26/162.06 [3593]E(f60(x35931,x35932,f119(x35931),x35933),f119(f890(x35931,x35932)))
% 162.26/162.06 [3615]P21(x36151,x36152,x36153,f196(f891(x36151,a877)))
% 162.26/162.06 [3770]E(f331(f74(x37701,x37702,x37701,x37703),f35(x37701)),x37703)
% 162.26/162.06 [3942]P24(f331(f331(f333(f890(x39421,x39421)),f331(f331(f261(x39421,x39421),x39422),x39422)),f307(x39421,x39423)))
% 162.26/162.06 [4590]~P24(f331(f331(f333(f890(f884(x45901),f884(x45901))),f331(f331(f261(f884(x45901),f884(x45901)),x45902),f119(x45901))),f148(x45901,x45903)))
% 162.26/162.06 [4591]~P24(f331(f331(f333(f890(f884(x45911),f884(x45911))),f331(f331(f261(f884(x45911),f884(x45911)),x45912),f119(x45911))),f150(x45911,x45913)))
% 162.26/162.06 [4592]~P24(f331(f331(f333(f890(f884(x45921),f884(x45921))),f331(f331(f261(f884(x45921),f884(x45921)),x45922),f119(x45921))),f160(x45921,x45923)))
% 162.26/162.06 [4593]~P24(f331(f331(f333(f890(f884(x45931),f884(x45931))),f331(f331(f261(f884(x45931),f884(x45931)),f119(x45931)),x45932)),f148(x45931,x45933)))
% 162.26/162.06 [4594]~P24(f331(f331(f333(f890(f884(x45941),f884(x45941))),f331(f331(f261(f884(x45941),f884(x45941)),f119(x45941)),x45942)),f160(x45941,x45943)))
% 162.26/162.06 [3297]E(f331(f331(f213(x32971),x32972),x32973),f214(x32971,f227(x32972,x32973)))
% 162.26/162.06 [3356]E(f331(f286(x33561,x33562),f331(f286(x33562,x33561),x33563)),x33563)
% 162.26/162.06 [3380]E(f331(f331(f184(x33801,x33802),f119(x33801)),x33803),f119(f890(x33801,x33802)))
% 162.26/162.06 [3383]E(f177(x33831,x33832,f331(f254(a883),x33833)),f331(f331(f176(x33831),x33833),x33832))
% 162.26/162.06 [3400]E(f155(x34001,f331(f139(x34001,x34002),x34003)),f331(f139(x34001,x34002),f155(x34001,x34003)))
% 162.26/162.06 [3402]E(f331(f257(x34021,x34022),f331(f286(x34022,x34021),x34023)),f331(f259(x34022,x34021),x34023))
% 162.26/162.06 [3403]E(f331(f259(x34031,x34032),f331(f286(x34032,x34031),x34033)),f331(f257(x34032,x34031),x34033))
% 162.26/162.06 [3419]E(f331(f139(x34191,x34192),f331(f172(x34191),x34193)),f331(f172(x34191),f331(f139(x34191,x34192),x34193)))
% 162.26/162.06 [3432]E(f331(f331(f141(x34321),x34322),f331(f174(x34321),x34323)),f331(f331(f141(x34321),f331(a118,x34322)),x34323))
% 162.26/162.06 [3450]E(f32(f30(x34501,x34502,x34503)),f331(f331(f81(a883),f32(x34503)),f331(a118,f2(a883))))
% 162.26/162.06 [3451]E(f331(f310(x34511,x34512,x34513),f196(f891(x34511,a877))),f196(f891(x34512,a877)))
% 162.26/162.06 [3452]E(f331(f285(x34521,x34522,x34523),f196(f891(x34521,a877))),f196(f891(x34522,a877)))
% 162.26/162.06 [3453]E(f331(f311(x34531,x34532,x34533),f196(f891(x34532,a877))),f196(f891(x34531,a877)))
% 162.26/162.06 [3454]E(f331(f311(x34541,x34542,x34543),f256(f891(x34542,a877))),f256(f891(x34541,a877)))
% 162.26/162.06 [3481]E(f331(f331(f309(x34811),x34812),f331(f175(x34811),x34813)),f331(f175(x34811),f143(x34811,x34812,x34813)))
% 162.26/162.06 [3493]E(f241(x34931,x34932,f331(f239(x34931),x34933)),f331(f331(f81(a883),f331(x34932,x34933)),f331(a118,f2(a883))))
% 162.26/162.06 [3569]E(f331(f197(a879),f30(x35691,x35692,x35693)),f331(f331(f81(a883),f331(f197(a879),x35693)),f331(a118,f2(a883))))
% 162.26/162.06 [3570]E(f331(f310(f890(x35701,x35702),x35702,f269(x35701,x35702)),x35703),f331(f257(x35701,x35702),x35703))
% 162.26/162.06 [3571]E(f331(f310(f890(x35711,x35712),x35711,f260(x35711,x35712)),x35713),f331(f259(x35711,x35712),x35713))
% 162.26/162.06 [3641]E(f331(f331(f261(x36411,x36412),f331(f260(x36411,x36412),x36413)),f331(f269(x36411,x36412),x36413)),x36413)
% 162.26/162.06 [3648]E(f331(f197(f885(x36481)),f130(x36481,x36482,x36483)),f331(f331(f81(a883),f331(f197(f885(x36481)),x36483)),f331(a118,f2(a883))))
% 162.26/162.06 [3651]E(f331(f331(f270(x36511,x36512,x36511),f16(x36511,x36512)),x36513),f331(f260(x36511,x36512),x36513))
% 162.26/162.06 [3671]E(f187(x36711,x36712,x36713,f331(f16(f887(x36712),x36711),f199(x36712))),x36713)
% 162.26/162.06 [3672]E(f187(x36721,x36722,f331(f16(f887(x36722),x36721),f199(x36722)),x36723),x36723)
% 162.26/162.06 [3722]E(f32(f31(x37221,x37222,x37223)),f331(f331(f81(a883),f331(f331(f81(a883),f32(x37222)),f32(x37223))),f331(a118,f2(a883))))
% 162.26/162.06 [3774]E(f331(f74(x37741,x37741,x37742,f35(x37741)),x37743),x37743)
% 162.26/162.06 [3877]E(f331(f197(a879),f31(x38771,x38772,x38773)),f331(f331(f81(a883),f331(f331(f81(a883),f331(f197(a879),x38772)),f331(f197(a879),x38773))),f331(a118,f2(a883))))
% 162.26/162.06 [3951]P24(f331(f331(f247(f891(x39511,a877)),f331(f175(x39511),f331(f139(x39511,x39512),x39513))),f331(f175(x39511),x39513)))
% 162.26/162.06 [3996]P24(f331(f331(f247(f891(x39961,a877)),f331(f175(x39961),f331(f331(f176(x39961),x39962),x39963))),f331(f175(x39961),x39963)))
% 162.26/162.06 [3997]P24(f331(f331(f247(f891(x39971,a877)),f331(f175(x39971),f331(f331(f141(x39971),x39972),x39973))),f331(f175(x39971),x39973)))
% 162.26/162.06 [4001]P24(f331(f331(f247(f891(x40011,a877)),f331(f175(x40011),f173(x40011,x40012,x40013))),f331(f175(x40011),x40013)))
% 162.26/162.06 [4002]P24(f331(f331(f247(f891(x40021,a877)),f331(f175(x40021),f177(x40021,x40022,x40023))),f331(f175(x40021),x40022)))
% 162.26/162.06 [4023]P21(f890(x40231,x40232),f890(x40232,x40231),f331(f270(x40231,x40232,f890(x40232,x40231)),f331(f7(x40232,x40231,f890(x40232,x40231)),f261(x40232,x40231))),x40233)
% 162.26/162.06 [4034]E(f331(f331(f331(f191(f884(x40341),f884(x40341)),f45(a883,x40342,f331(f197(f884(x40341)),x40343))),f171(x40341)),x40343),f331(f331(f331(f191(f884(x40341),f884(x40341)),x40342),f171(x40341)),x40343))
% 162.26/162.06 [4074]P24(f331(f331(f333(f890(f884(x40741),f884(x40741))),f331(f331(f261(f884(x40741),f884(x40741)),x40742),x40742)),f161(x40741,f307(x40741,x40743))))
% 162.26/162.06 [4219]E(f86(f890(x42191,x42192),f331(f331(f18(f890(x42191,x42192),x42192,a877),f331(f331(f8(x42191,f891(x42192,a877),f890(x42191,x42192)),x42193),f260(x42191,x42192))),f269(x42191,x42192))),f86(f890(x42191,x42192),f331(f270(x42191,x42192,a877),x42193)))
% 162.26/162.06 [4220]E(f91(f890(x42201,x42202),f331(f331(f18(f890(x42201,x42202),x42202,a877),f331(f331(f8(x42201,f891(x42202,a877),f890(x42201,x42202)),x42203),f260(x42201,x42202))),f269(x42201,x42202))),f91(f890(x42201,x42202),f331(f270(x42201,x42202,a877),x42203)))
% 162.26/162.06 [4254]E(f331(f331(f287(f890(a883,x42541),x42541),f323(a883,x42541,a252,x42542)),f331(f331(f18(x42541,x42541,f890(a883,x42541)),f331(f331(f8(a883,f891(x42541,f890(a883,x42541)),x42541),f261(a883,x42541)),x42543)),f5(x42541))),f325(x42541,x42543,x42542))
% 162.26/162.06 [4317]E(f331(f271(x43171,x43171,x43172,x43172,f5(x43171),f5(x43172)),x43173),x43173)
% 162.26/162.06 [4398]E(f331(f145(f884(f884(x43981)),f884(f884(x43981)),f137(f884(x43981)),f119(f884(x43981))),f331(f331(f157(f884(x43981),f884(f884(x43981))),f331(f331(f7(f884(x43981),f884(x43981),f884(f884(x43981))),f331(f331(f8(f891(x43981,f884(x43981)),f891(f884(x43981),f884(f884(x43981))),f884(x43981)),f157(x43981,f884(x43981))),f331(f7(x43981,f884(x43981),f884(x43981)),f154(x43981)))),x43982)),f55(x43981,x43983,x43982))),f55(x43981,f331(a118,x43983),x43982))
% 162.26/162.06 [4470]E(f331(f242(a883,f890(x44701,f885(x44701)),f2(a883),f331(f270(x44701,f885(x44701),a883),f331(f331(f7(x44701,a883,f891(f885(x44701),a883)),f331(f331(f8(f891(f885(x44701),f891(a883,a883)),f891(a883,f891(f885(x44701),a883)),x44701),f7(f885(x44701),a883,a883)),f331(f331(f8(f891(f885(x44701),a883),f891(f885(x44701),f891(a883,a883)),x44701),f331(f8(a883,f891(a883,a883),f885(x44701)),f81(a883))),f331(f331(f7(x44701,f891(f885(x44701),a883),f891(f885(x44701),a883)),f331(f331(f8(f891(a883,a883),f891(f891(f885(x44701),a883),f891(f885(x44701),a883)),x44701),f8(a883,a883,f885(x44701))),f331(f331(f8(a883,f891(a883,a883),x44701),f81(a883)),x44702))),f132(x44701,x44702))))),f79(a883)))),f331(f138(x44701),x44703)),f331(f132(x44701,x44702),x44703))
% 162.26/162.06 [4472]E(f331(f331(f89(a1,x44721),f230(f331(f331(f74(f890(a1,a1),a1,x44721,f269(a1,a1)),f224(x44721)),x44722),f331(f331(f74(f890(a1,a1),a1,x44721,f269(a1,a1)),f224(x44721)),x44723))),f331(f331(f18(a1,a1,x44721),f331(f331(f8(a1,f891(a1,x44721),a1),f213(x44721)),f331(f331(f18(a1,a1,a1),f331(f331(f8(a1,f891(a1,a1),a1),f81(a1)),f331(f331(f8(a1,a1,a1),f331(f82(a1),f331(f331(f74(f890(a1,a1),a1,x44721,f260(a1,a1)),f224(x44721)),x44722))),f331(f331(f7(a1,a1,a1),f39(a1)),f331(f331(f74(f890(a1,a1),a1,x44721,f269(a1,a1)),f224(x44721)),x44722))))),f331(f331(f8(a1,a1,a1),f331(f82(a1),f331(f331(f74(f890(a1,a1),a1,x44721,f260(a1,a1)),f224(x44721)),x44723))),f331(f331(f7(a1,a1,a1),f39(a1)),f331(f331(f74(f890(a1,a1),a1,x44721,f269(a1,a1)),f224(x44721)),x44723)))))),f5(a1))),f235(x44721,x44722,x44723))
% 162.26/162.06 [4509]~E(f331(f331(f154(x45091),x45092),x45093),x45093)
% 162.26/162.06 [4518]~E(f331(f331(f154(x45181),x45182),x45183),f119(x45181))
% 162.26/162.06 [4540]~E(f331(f331(f309(x45401),x45402),x45403),f196(f891(x45401,a877)))
% 162.26/162.06 [4567]~E(f331(f310(x45671,f891(x45671,a877),x45672),x45673),f331(f308(x45671),x45673))
% 162.26/162.06 [3361]E(f331(f331(f162(x33611,f119(x33611)),x33612),x33613),f119(x33611))
% 162.26/162.06 [3362]E(f331(f144(x33621),f331(f331(f154(x33621),x33622),x33623)),x33622)
% 162.26/162.06 [3363]E(f331(f174(x33631),f331(f331(f154(x33631),x33632),x33633)),x33633)
% 162.26/162.06 [3407]E(f331(f331(f141(x34071),f79(a883)),f331(f331(f154(x34071),x34072),x34073)),x34073)
% 162.26/162.06 [3439]E(f120(x34391,f331(f331(f141(x34391),x34392),x34393)),f331(f331(f141(x34391),x34392),f120(x34391,x34393)))
% 162.26/162.06 [3441]E(f331(f331(f162(x34411,x34412),x34413),f331(f331(f168(x34411),x34412),x34413)),x34412)
% 162.26/162.06 [3464]E(f331(f331(f309(x34641),x34642),f331(f331(f309(x34641),x34642),x34643)),f331(f331(f309(x34641),x34642),x34643))
% 162.26/162.06 [3475]E(f331(f331(f180(x34751,x34752),f119(f890(x34751,x34752))),x34753),f199(x34752))
% 162.26/162.06 [3478]E(f331(f331(f309(x34781),x34782),f331(f175(x34781),x34783)),f331(f175(x34781),f331(f331(f154(x34781),x34782),x34783)))
% 162.26/162.06 [3480]E(f331(f331(f141(x34801),x34802),f331(f174(x34801),x34803)),f331(f174(x34801),f331(f331(f141(x34801),x34802),x34803)))
% 162.26/162.06 [3490]E(f331(f331(f176(x34901),f79(a883)),f331(f331(f154(x34901),x34902),x34903)),f331(f331(f154(x34901),x34902),f119(x34901)))
% 162.26/162.06 [3535]E(f331(f64(x35351,x35352),f331(f331(f309(x35351),x35353),f196(f891(x35351,a877)))),x35353)
% 162.26/162.06 [3577]E(f331(f331(f81(a883),x35771),f331(f331(f81(a883),x35772),x35773)),f331(f331(f81(a883),x35772),f331(f331(f81(a883),x35771),x35773)))
% 162.26/162.06 [3578]E(f331(f331(f81(a1),x35781),f331(f331(f81(a1),x35782),x35783)),f331(f331(f81(a1),x35782),f331(f331(f81(a1),x35781),x35783)))
% 162.26/162.06 [3583]E(f331(f331(f268(x35831,x35832),f196(f891(x35831,a877))),x35833),f196(f891(f890(x35831,x35832),a877)))
% 162.26/162.06 [3607]E(f331(f331(f107(f891(x36071,a877)),x36072),x36073),f331(f331(f107(f891(x36071,a877)),x36073),x36072))
% 162.26/162.06 [3608]E(f331(f331(f108(f891(x36081,a877)),x36082),x36083),f331(f331(f108(f891(x36081,a877)),x36083),x36082))
% 162.26/162.06 [3610]E(f331(f331(f137(x36101),x36102),f331(f331(f154(x36101),x36103),f119(x36101))),f331(f171(x36101),f331(f331(f154(x36101),x36103),x36102)))
% 162.26/162.06 [3611]E(f331(f331(f137(x36111),f331(f172(x36111),x36112)),f331(f172(x36111),x36113)),f331(f172(x36111),f331(f331(f137(x36111),x36113),x36112)))
% 162.26/162.06 [3619]E(f331(f174(x36191),f331(f331(f176(x36191),f331(a118,x36192)),x36193)),f331(f331(f176(x36191),x36192),f331(f174(x36191),x36193)))
% 162.26/162.06 [3626]P24(f331(f331(f333(x36261),x36262),f331(f331(f309(x36261),x36262),x36263)))
% 162.26/162.06 [3630]E(f331(f331(f43(x36301,f891(x36302,a877)),f196(f891(x36301,a877))),x36303),f256(f891(x36302,a877)))
% 162.26/162.06 [3633]E(f331(f285(x36331,x36331,f258(x36331,x36332)),x36333),f331(f331(f108(f891(x36331,a877)),x36332),x36333))
% 162.26/162.06 [3647]E(f331(f197(f884(x36471)),f331(f331(f154(x36471),x36472),x36473)),f331(f331(f81(a883),f331(f197(f884(x36471)),x36473)),f331(a118,f2(a883))))
% 162.26/162.06 [3653]E(f120(x36531,f331(f331(f137(x36531),x36532),f331(f331(f154(x36531),x36533),f119(x36531)))),x36532)
% 162.26/162.06 [3654]E(f147(x36541,f331(f331(f137(x36541),x36542),f331(f331(f154(x36541),x36543),f119(x36541)))),x36543)
% 162.26/162.06 [3660]E(f331(f331(f137(x36601),f331(f331(f176(x36601),x36602),x36603)),f331(f331(f141(x36601),x36602),x36603)),x36603)
% 162.26/162.06 [3669]E(f331(f331(f22(a883),f331(f331(f81(a883),x36691),x36692)),f331(f331(f81(a883),x36693),x36692)),f331(f331(f22(a883),x36691),x36693))
% 162.26/162.06 [3670]E(f331(f331(f22(a883),f331(f331(f81(a883),x36701),x36702)),f331(f331(f81(a883),x36701),x36703)),f331(f331(f22(a883),x36702),x36703))
% 162.26/162.06 [3677]E(f331(f331(f137(x36771),f331(f172(x36771),x36772)),f331(f331(f154(x36771),x36773),f119(x36771))),f331(f172(x36771),f331(f331(f154(x36771),x36773),x36772)))
% 162.26/162.06 [3679]E(f331(f331(f81(a883),f331(f197(f884(x36791)),x36792)),f331(f197(f884(x36791)),x36793)),f331(f197(f884(x36791)),f331(f331(f137(x36791),x36792),x36793)))
% 162.26/162.06 [3689]E(f331(f331(f107(f891(x36891,a877)),f331(f175(x36891),x36892)),f331(f175(x36891),x36893)),f331(f175(x36891),f331(f331(f137(x36891),x36892),x36893)))
% 162.26/162.06 [3690]E(f45(a883,f331(f331(f82(a883),x36901),x36902),f331(f331(f82(a883),x36901),x36903)),f331(f331(f82(a883),x36901),f45(a883,x36902,x36903)))
% 162.26/162.06 [3703]E(f331(f331(f176(x37031),f331(f331(f22(a883),x37032),f79(a883))),f331(f174(x37031),x37033)),f331(f174(x37031),f331(f331(f176(x37031),x37032),x37033)))
% 162.26/162.06 [3708]E(f331(f331(f108(f891(x37081,a877)),x37082),f331(f80(f891(x37081,a877)),x37083)),f331(f331(f22(f891(x37081,a877)),x37082),x37083))
% 162.26/162.06 [3709]E(f331(f331(f22(f891(x37091,a877)),x37092),f331(f80(f891(x37091,a877)),x37093)),f331(f331(f108(f891(x37091,a877)),x37092),x37093))
% 162.26/162.06 [3725]E(f331(f331(f268(x37251,x37252),x37253),f331(f16(f891(x37252,a877),x37251),f196(f891(x37252,a877)))),f196(f891(f890(x37251,x37252),a877)))
% 162.26/162.06 [3727]E(f331(f331(f22(a883),f331(f331(f82(a883),x37271),x37272)),f331(f331(f82(a883),x37271),x37273)),f331(f331(f82(a883),x37271),f331(f331(f22(a883),x37272),x37273)))
% 162.26/162.06 [3728]E(f331(f331(f81(a883),f331(f331(f82(a883),x37281),x37282)),f331(f331(f82(a883),x37281),x37283)),f331(f331(f82(a883),x37281),f331(f331(f81(a883),x37282),x37283)))
% 162.26/162.06 [3729]E(f331(f331(f22(a1),f331(f331(f82(a1),x37291),x37292)),f331(f331(f82(a1),x37291),x37293)),f331(f331(f82(a1),x37291),f331(f331(f22(a1),x37292),x37293)))
% 162.26/162.06 [3730]E(f331(f331(f81(a1),f331(f331(f82(a1),x37301),x37302)),f331(f331(f82(a1),x37301),x37303)),f331(f331(f82(a1),x37301),f331(f331(f81(a1),x37302),x37303)))
% 162.26/162.06 [3731]E(f331(f331(f82(a1),f331(f331(f262(a1),x37311),x37312)),f331(f331(f262(a1),x37311),x37313)),f331(f331(f262(a1),x37311),f331(f331(f81(a883),x37312),x37313)))
% 162.26/162.06 [3744]E(f331(f331(f42(x37441,f891(x37442,a877)),x37443),f331(f16(f891(x37442,a877),x37441),f196(f891(x37442,a877)))),f196(f891(x37442,a877)))
% 162.26/162.06 [3746]E(f45(a883,f331(f331(f82(a883),x37461),x37462),f331(f331(f82(a883),x37463),x37462)),f331(f331(f82(a883),f45(a883,x37461,x37463)),x37462))
% 162.26/162.06 [3750]E(f45(a1,f331(f331(f22(a1),x37501),f45(a1,x37502,x37503)),x37503),f45(a1,f331(f331(f22(a1),x37501),x37502),x37503))
% 162.26/162.06 [3751]E(f45(a1,f331(f331(f82(a1),x37511),f45(a1,x37512,x37513)),x37513),f45(a1,f331(f331(f82(a1),x37511),x37512),x37513))
% 162.26/162.06 [3752]P24(f331(f331(f247(f891(x37521,a877)),x37522),f331(f331(f309(x37521),x37523),x37522)))
% 162.26/162.06 [3755]E(f331(f310(f890(x37551,x37552),x37551,f260(x37551,x37552)),f331(f175(f890(x37551,x37552)),x37553)),f186(x37551,x37552,f331(f180(x37551,x37552),x37553)))
% 162.26/162.06 [3807]P24(f331(f62(x38071),f186(x38071,x38072,f331(f180(x38071,x38072),x38073))))
% 162.26/162.06 [3832]E(f331(f331(f43(f891(x38321,a877),f891(x38321,a877)),x38322),f331(f107(f891(x38321,a877)),x38323)),f331(f331(f107(f891(x38321,a877)),x38323),f41(f891(x38321,a877),x38322)))
% 162.26/162.06 [3833]E(f331(f331(f42(f891(x38331,a877),f891(x38331,a877)),x38332),f331(f108(f891(x38331,a877)),x38333)),f331(f331(f108(f891(x38331,a877)),x38333),f40(f891(x38331,a877),x38332)))
% 162.26/162.06 [3841]E(f331(f175(x38411),f331(f331(f331(f191(f884(x38411),f884(x38411)),x38412),f171(x38411)),x38413)),f331(f175(x38411),x38413))
% 162.26/162.06 [3845]E(f331(f331(f176(x38451),f331(f197(f884(x38451)),f179(x38451,x38452,x38453))),x38453),f179(x38451,x38452,x38453))
% 162.26/162.06 [3846]E(f186(x38461,x38462,f331(f331(f8(x38462,f887(x38462),x38461),f239(x38462)),x38463)),f256(f891(x38461,a877)))
% 162.26/162.06 [3850]E(f331(f197(f884(x38501)),f331(f331(f331(f191(f884(x38501),f884(x38501)),x38502),f171(x38501)),x38503)),f331(f197(f884(x38501)),x38503))
% 162.26/162.06 [3853]E(f331(f331(f270(x38531,x38532,x38532),f331(f16(f891(x38532,x38532),x38531),f5(x38532))),x38533),f331(f269(x38531,x38532),x38533))
% 162.26/162.06 [3859]E(f45(a1,f331(f331(f22(a1),f45(a1,x38591,x38592)),x38593),x38592),f45(a1,f331(f331(f22(a1),x38591),x38593),x38592))
% 162.26/162.06 [3860]E(f45(a1,f331(f331(f262(a1),f45(a1,x38601,x38602)),x38603),x38602),f45(a1,f331(f331(f262(a1),x38601),x38603),x38602))
% 162.26/162.06 [3863]E(f331(f331(f42(f891(f890(x38631,x38632),a877),f891(x38632,a877)),x38633),f257(x38631,x38632)),f331(f257(x38631,x38632),f40(f891(f890(x38631,x38632),a877),x38633)))
% 162.26/162.06 [3864]E(f331(f331(f42(f891(f890(x38641,x38642),a877),f891(x38641,a877)),x38643),f259(x38641,x38642)),f331(f259(x38641,x38642),f40(f891(f890(x38641,x38642),a877),x38643)))
% 162.26/162.06 [3887]E(f331(f74(x38871,x38871,x38871,x38872),f331(f331(f191(x38871,x38871),x38873),x38872)),f331(f331(f191(x38871,x38871),f331(a118,x38873)),x38872))
% 162.26/162.06 [3897]E(f242(f887(x38971),x38972,f199(x38971),f331(f331(f8(x38971,f887(x38971),x38972),f239(x38971)),x38973)),f331(f210(x38972,x38971),x38973))
% 162.26/162.06 [3904]E(f331(f331(f141(x39041),f331(f331(f22(a883),f331(f197(f884(x39041)),x39042)),x39043)),f331(f172(x39041),x39042)),f331(f172(x39041),f331(f331(f176(x39041),x39043),x39042)))
% 162.26/162.06 [3905]E(f331(f331(f176(x39051),f331(f331(f22(a883),f331(f197(f884(x39051)),x39052)),x39053)),f331(f172(x39051),x39052)),f331(f172(x39051),f331(f331(f141(x39051),x39053),x39052)))
% 162.26/162.06 [3908]E(f331(f331(f81(a883),f331(f169(a883),f331(f331(f157(x39081,a883),x39082),x39083))),f331(f197(f884(x39081)),x39083)),f158(x39081,x39082,x39083))
% 162.26/162.06 [3926]E(f331(f171(x39261),f331(f331(f331(f191(f884(x39261),f884(x39261)),x39262),f171(x39261)),x39263)),f331(f331(f331(f191(f884(x39261),f884(x39261)),f331(a118,x39262)),f171(x39261)),x39263))
% 162.26/162.06 [3943]P24(f331(f331(f247(a883),f331(f197(f884(x39431)),f331(f139(x39431,x39432),x39433))),f331(f197(f884(x39431)),x39433)))
% 162.26/162.06 [3959]E(f331(f331(f107(f891(f891(x39591,a877),a877)),f331(f308(x39591),x39592)),f331(f310(f891(x39591,a877),f891(x39591,a877),f331(f309(x39591),x39593)),f331(f308(x39591),x39592))),f331(f308(x39591),f331(f331(f309(x39591),x39593),x39592)))
% 162.26/162.06 [3978]P20(x39781,x39782,f331(f331(f309(f882(x39781)),f331(f331(f331(f93(x39781),x39783),a24),x39783)),f196(f891(f882(x39781),a877))))
% 162.26/162.06 [3993]P24(f331(f331(f247(a883),f331(f197(f884(x39931)),f179(x39931,x39932,x39933))),f331(f197(f884(x39931)),x39933)))
% 162.26/162.06 [4000]E(f331(f259(x40001,x40002),f331(f253(f890(x40001,x40002)),f331(f270(x40001,x40002,a877),x40003))),f331(f253(x40001),f331(f331(f8(f891(x40002,a877),a877,x40001),f87(x40002)),x40003)))
% 162.26/162.06 [4010]E(f331(f310(a883,a883,f331(f331(f7(a883,a883,a883),f81(a883)),x40101)),f302(a883,x40102,x40103)),f302(a883,f331(f331(f81(a883),x40102),x40101),f331(f331(f81(a883),x40103),x40101)))
% 162.26/162.06 [4013]P24(f331(f62(f887(x40131)),f331(f310(x40132,f887(x40131),f331(f180(x40132,x40131),x40133)),f256(f891(x40132,a877)))))
% 162.26/162.06 [4026]E(f331(f310(a883,a883,f331(f331(f7(a883,a883,a883),f81(a883)),x40261)),f331(f301(a883,x40262),x40263)),f331(f301(a883,f331(f331(f81(a883),x40262),x40261)),f331(f331(f81(a883),x40263),x40261)))
% 162.26/162.06 [4043]E(f331(f331(f184(x40431,x40432),f331(f331(f157(f890(x40431,x40432),x40431),f260(x40431,x40432)),x40433)),f331(f331(f157(f890(x40431,x40432),x40432),f269(x40431,x40432)),x40433)),x40433)
% 162.26/162.06 [4048]E(f331(f331(f81(a883),f331(f331(f82(a883),x40481),f45(a883,f331(f331(f39(a883),x40482),x40481),x40483))),f45(a883,x40482,x40481)),f45(a883,x40482,f331(f331(f82(a883),x40481),x40483)))
% 162.26/162.06 [4061]E(f331(f331(f137(x40611),x40612),f331(f145(f884(x40611),f884(x40611),f137(x40611),f119(x40611)),x40613)),f331(f145(f884(x40611),f884(x40611),f137(x40611),x40612),x40613))
% 162.26/162.06 [4078]P24(f331(f331(f333(f890(x40781,x40781)),f331(f331(f261(x40781,x40781),x40782),x40782)),f331(f331(f191(f890(x40781,x40781),a877),f2(a883)),x40783)))
% 162.26/162.06 [4084]E(f331(f253(x40841),f331(f331(f8(f891(x40842,a877),a877,x40841),f87(x40842)),f331(f7(x40842,x40841,a877),x40843))),f331(f257(x40842,x40841),f331(f253(f890(x40842,x40841)),f331(f270(x40842,x40841,a877),x40843))))
% 162.26/162.06 [4102]E(f331(f331(f107(f891(x41021,a877)),f331(f331(f42(a883,f891(x41021,a877)),f302(a883,f79(a883),x41022)),x41023)),f331(x41023,f2(a883))),f331(f331(f42(a883,f891(x41021,a877)),f331(f300(a883),x41022)),x41023))
% 162.26/162.06 [4117]E(f331(f145(f884(x41171),f884(x41171),f137(x41171),f119(x41171)),f331(f331(f157(f884(x41171),f884(x41171)),f139(x41171,x41172)),x41173)),f331(f139(x41171,x41172),f331(f145(f884(x41171),f884(x41171),f137(x41171),f119(x41171)),x41173)))
% 162.26/162.06 [4122]E(f331(f269(f884(x41221),f884(x41221)),f170(x41221,x41222,x41223)),f331(f139(x41221,f331(f74(a877,a877,x41221,a326),x41222)),x41223))
% 162.26/162.06 [4136]E(f331(f331(f43(x41361,f891(x41362,a877)),f256(f891(x41361,a877))),f331(f331(f8(f891(x41362,a877),f891(x41362,a877),x41361),f253(x41362)),f331(f7(x41362,x41361,a877),x41363))),f331(f253(x41362),f331(f331(f8(f891(x41361,a877),a877,x41362),f88(x41361)),x41363)))
% 162.26/162.06 [4165]E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f82(a1),x41651),f331(f331(f39(a1),x41652),x41651))),f45(a1,x41652,x41651))),x41653),f331(f331(f81(a1),x41652),x41653))
% 162.26/162.06 [4205]E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f82(a1),f331(f331(f39(a1),x42051),x42052)),x42052)),f45(a1,x42051,x42052))),x42053),f331(f331(f81(a1),x42051),x42053))
% 162.26/162.06 [4236]E(f86(f890(x42361,x42362),f331(f270(x42361,x42362,a877),f331(f331(f8(f891(x42362,f890(x42361,x42362)),f891(x42362,a877),x42361),f331(f8(f890(x42361,x42362),a877,x42362),x42363)),f261(x42361,x42362)))),f86(f890(x42361,x42362),x42363))
% 162.26/162.06 [4237]E(f91(f890(x42371,x42372),f331(f270(x42371,x42372,a877),f331(f331(f8(f891(x42372,f890(x42371,x42372)),f891(x42372,a877),x42371),f331(f8(f890(x42371,x42372),a877,x42372),x42373)),f261(x42371,x42372)))),f91(f890(x42371,x42372),x42373))
% 162.26/162.06 [4266]P24(f331(f331(f247(f891(x42661,a877)),f40(f891(x42661,a877),f331(f331(f108(f891(f891(x42661,a877),a877)),x42662),x42663))),f331(f331(f108(f891(x42661,a877)),f40(f891(x42661,a877),x42662)),f40(f891(x42661,a877),x42663))))
% 162.26/162.06 [4267]E(f331(f172(x42671),f331(f331(f331(f191(f884(x42671),f884(x42671)),f331(f331(f22(a883),f331(f197(f884(x42671)),x42672)),f45(a883,x42673,f331(f197(f884(x42671)),x42672)))),f171(x42671)),x42672)),f331(f331(f331(f191(f884(x42671),f884(x42671)),x42673),f171(x42671)),f331(f172(x42671),x42672)))
% 162.26/162.06 [4280]E(f331(f253(x42801),f331(f331(f8(a877,a877,x42801),a326),f331(f331(f7(x42801,f887(x42802),a877),f331(f331(f8(f887(x42802),f891(f887(x42802),a877),x42801),a328),x42803)),f199(x42802)))),f186(x42801,x42802,x42803))
% 162.26/162.06 [4307]P24(f331(f331(f247(a883),f331(f197(f884(x43071)),f331(f331(f141(x43071),f331(f197(f884(x43071)),f179(x43071,x43072,x43073))),x43073))),f331(f197(f884(x43071)),x43073)))
% 162.26/162.06 [4346]E(f331(f253(x43461),f331(f331(f8(f891(x43462,a877),a877,x43461),f87(x43462)),f331(f331(f8(f887(x43461),f891(x43462,a877),x43461),f331(f7(x43462,f887(x43461),a877),f331(f331(f8(f887(x43461),f891(f887(x43461),a877),x43462),a328),x43463))),f239(x43461)))),f188(x43462,x43461,x43463))
% 162.26/162.06 [4578]~P24(f331(f63(x45781,x45782,f196(f891(x45781,a877))),x45783))
% 162.26/162.06 [4589]~P24(f331(f331(f333(f890(x45891,x45891)),f331(f331(f261(x45891,x45891),x45892),x45893)),f156(x45891,f119(f891(x45891,a883)))))
% 162.26/162.06 [3620]E(f331(f197(f884(x36201)),f331(f331(f176(x36201),x36202),x36203)),f331(f331(f251(a883),f331(f197(f884(x36201)),x36203)),x36202))
% 162.26/162.06 [3621]E(f331(f197(f884(x36211)),f331(f331(f141(x36211),x36212),x36213)),f331(f331(f22(a883),f331(f197(f884(x36211)),x36213)),x36212))
% 162.26/162.06 [3646]E(f331(f197(f884(f884(x36461))),f55(x36461,x36462,x36463)),f331(f331(f262(a883),f331(f197(f884(x36461)),x36463)),x36462))
% 162.26/162.06 [3662]E(f331(f331(f39(a883),f331(f331(f39(a883),x36621),x36622)),x36623),f331(f331(f39(a883),x36621),f331(f331(f82(a883),x36622),x36623)))
% 162.26/162.06 [3663]E(f331(f331(f22(a883),f331(f331(f22(a883),x36631),x36632)),x36633),f331(f331(f22(a883),x36631),f331(f331(f81(a883),x36632),x36633)))
% 162.26/162.06 [3664]E(f331(f331(f81(a883),f331(f331(f81(a883),x36641),x36642)),x36643),f331(f331(f81(a883),x36641),f331(f331(f81(a883),x36642),x36643)))
% 162.26/162.06 [3665]E(f331(f331(f81(a1),f331(f331(f81(a1),x36651),x36652)),x36653),f331(f331(f81(a1),x36651),f331(f331(f81(a1),x36652),x36653)))
% 162.26/162.06 [3666]E(f331(f331(f82(a883),f331(f331(f82(a883),x36661),x36662)),x36663),f331(f331(f82(a883),x36661),f331(f331(f82(a883),x36662),x36663)))
% 162.26/162.06 [3667]E(f331(f331(f82(a1),f331(f331(f82(a1),x36671),x36672)),x36673),f331(f331(f82(a1),x36671),f331(f331(f82(a1),x36672),x36673)))
% 162.26/162.06 [3668]E(f331(f331(f262(a1),f331(f331(f262(a1),x36681),x36682)),x36683),f331(f331(f262(a1),x36681),f331(f331(f82(a883),x36682),x36683)))
% 162.26/162.06 [3687]E(f165(x36871,f331(f331(f154(f891(x36871,a877)),x36872),x36873)),f178(x36871,x36872,f165(x36871,x36873)))
% 162.26/162.06 [3726]E(f331(f331(f22(a883),f331(f331(f22(a883),x37261),x37262)),x37263),f331(f331(f22(a883),f331(f331(f22(a883),x37261),x37263)),x37262))
% 162.26/162.06 [3732]E(f331(f239(f890(x37321,f885(x37321))),f331(f331(f261(x37321,f885(x37321)),x37322),x37323)),f331(f138(x37321),f130(x37321,x37322,x37323)))
% 162.26/162.06 [3735]E(f331(f331(f108(f891(x37351,a877)),x37352),f331(f331(f22(f891(x37351,a877)),x37353),x37352)),f196(f891(x37351,a877)))
% 162.26/162.06 [3780]E(f41(f891(x37801,a877),f331(f331(f309(f891(x37801,a877)),x37802),x37803)),f331(f331(f108(f891(x37801,a877)),x37802),f41(f891(x37801,a877),x37803)))
% 162.26/162.06 [3781]E(f40(f891(x37811,a877),f331(f331(f309(f891(x37811,a877)),x37812),x37813)),f331(f331(f107(f891(x37811,a877)),x37812),f40(f891(x37811,a877),x37813)))
% 162.26/162.06 [3783]E(f331(f331(f22(a883),f331(f331(f82(a883),x37831),x37832)),f331(f331(f82(a883),x37833),x37832)),f331(f331(f82(a883),f331(f331(f22(a883),x37831),x37833)),x37832))
% 162.26/162.06 [3784]E(f331(f331(f81(a883),f331(f331(f82(a883),x37841),x37842)),f331(f331(f82(a883),x37843),x37842)),f331(f331(f82(a883),f331(f331(f81(a883),x37841),x37843)),x37842))
% 162.26/162.06 [3785]E(f331(f331(f22(a1),f331(f331(f82(a1),x37851),x37852)),f331(f331(f82(a1),x37853),x37852)),f331(f331(f82(a1),f331(f331(f22(a1),x37851),x37853)),x37852))
% 162.26/162.06 [3786]E(f331(f331(f81(a1),f331(f331(f82(a1),x37861),x37862)),f331(f331(f82(a1),x37863),x37862)),f331(f331(f82(a1),f331(f331(f81(a1),x37861),x37863)),x37862))
% 162.26/162.06 [3787]E(f331(f331(f251(a883),f331(f331(f22(a883),x37871),x37872)),f331(f331(f22(a883),x37873),x37872)),f331(f331(f22(a883),f331(f331(f251(a883),x37871),x37873)),x37872))
% 162.26/162.06 [3810]E(f331(f331(f108(f891(f884(x38101),a877)),f163(x38101,x38102)),f163(x38101,x38103)),f163(x38101,f331(f331(f108(f891(x38101,a877)),x38102),x38103)))
% 162.26/162.06 [3812]E(f331(f331(f107(f891(x38121,a877)),x38122),f331(f331(f22(f891(x38121,a877)),x38123),x38122)),f331(f331(f107(f891(x38121,a877)),x38122),x38123))
% 162.26/162.06 [3813]E(f331(f331(f107(f891(x38131,a877)),x38132),f331(f331(f107(f891(x38131,a877)),x38132),x38133)),f331(f331(f107(f891(x38131,a877)),x38132),x38133))
% 162.26/162.06 [3814]E(f331(f331(f108(f891(x38141,a877)),x38142),f331(f331(f108(f891(x38141,a877)),x38142),x38143)),f331(f331(f108(f891(x38141,a877)),x38142),x38143))
% 162.26/162.06 [3826]E(f331(f331(f288(x38261,x38262,x38262),x38263),f307(x38262,f196(f891(f890(x38262,x38262),a877)))),x38263)
% 162.26/162.06 [3829]E(f331(f331(f107(f891(x38291,a877)),f331(f331(f309(x38291),x38292),f196(f891(x38291,a877)))),x38293),f331(f331(f309(x38291),x38292),x38293))
% 162.26/162.06 [3844]E(f331(f331(f22(a883),f331(f331(f22(a883),f331(a118,x38441)),x38442)),f331(a118,x38443)),f331(f331(f22(a883),f331(f331(f22(a883),x38441),x38442)),x38443))
% 162.26/162.06 [3871]E(f331(f331(f108(f891(f891(x38711,a877),a877)),f331(f308(x38711),x38712)),f331(f308(x38711),x38713)),f331(f308(x38711),f331(f331(f108(f891(x38711,a877)),x38712),x38713)))
% 162.26/162.06 [3875]E(f331(f331(f107(f891(x38751,a877)),f331(f80(f891(x38751,a877)),x38752)),x38753),f331(f80(f891(x38751,a877)),f331(f331(f22(f891(x38751,a877)),x38752),x38753)))
% 162.26/162.06 [3885]E(f331(f331(f309(x38851),x38852),f331(f331(f22(f891(x38851,a877)),x38853),f331(f331(f309(x38851),x38852),f196(f891(x38851,a877))))),f331(f331(f309(x38851),x38852),x38853))
% 162.26/162.06 [3894]P24(f331(f331(f247(f891(x38941,a877)),x38942),f331(f331(f107(f891(x38941,a877)),x38943),x38942)))
% 162.26/162.06 [3895]P24(f331(f331(f247(f891(x38951,a877)),x38952),f331(f331(f107(f891(x38951,a877)),x38952),x38953)))
% 162.26/162.06 [3898]E(f331(f331(f108(f891(x38981,a877)),f331(f80(f891(x38981,a877)),x38982)),f331(f80(f891(x38981,a877)),x38983)),f331(f80(f891(x38981,a877)),f331(f331(f107(f891(x38981,a877)),x38982),x38983)))
% 162.26/162.06 [3899]E(f331(f331(f107(f891(x38991,a877)),f331(f80(f891(x38991,a877)),x38992)),f331(f80(f891(x38991,a877)),x38993)),f331(f80(f891(x38991,a877)),f331(f331(f108(f891(x38991,a877)),x38992),x38993)))
% 162.26/162.06 [3913]P24(f331(f331(f247(f891(x39131,a877)),f331(f175(x39131),x39132)),f331(f175(x39131),f331(f331(f154(x39131),x39133),x39132))))
% 162.26/162.06 [3922]E(f331(f331(f107(f891(x39221,a877)),f331(f331(f22(f891(x39221,a877)),x39222),x39223)),f331(f331(f108(f891(x39221,a877)),x39222),x39223)),x39222)
% 162.26/162.06 [3980]E(f331(f331(f9(x39801,a1),f331(f331(f8(a883,a1,x39801),f106(a1)),x39802)),x39803),f331(f106(a1),f331(f331(f9(x39801,a883),x39802),x39803)))
% 162.26/162.06 [3981]E(f331(f331(f6(x39811,a1),f331(f331(f8(a883,a1,x39811),f106(a1)),x39812)),x39813),f331(f106(a1),f331(f331(f6(x39811,a883),x39812),x39813)))
% 162.26/162.06 [4028]E(f331(f331(f137(x40281),f179(x40281,x40282,x40283)),f331(f331(f141(x40281),f331(f197(f884(x40281)),f179(x40281,x40282,x40283))),x40283)),x40283)
% 162.26/162.06 [4032]E(f331(f80(f891(f890(x40321,x40322),a877)),f331(f331(f268(x40321,x40322),x40323),f331(f16(f891(x40322,a877),x40321),f256(f891(x40322,a877))))),f331(f331(f268(x40321,x40322),f331(f80(f891(x40321,a877)),x40323)),f331(f16(f891(x40322,a877),x40321),f256(f891(x40322,a877)))))
% 162.26/162.06 [4033]E(f331(f80(f891(f890(x40331,x40332),a877)),f331(f331(f268(x40331,x40332),f256(f891(x40331,a877))),f331(f16(f891(x40332,a877),x40331),x40333))),f331(f331(f268(x40331,x40332),f256(f891(x40331,a877))),f331(f16(f891(x40332,a877),x40331),f331(f80(f891(x40332,a877)),x40333))))
% 162.26/162.06 [4079]E(f331(f331(f42(f891(x40791,a877),f891(x40791,a877)),x40792),f331(f331(f7(f891(x40791,a877),f891(x40791,a877),f891(x40791,a877)),f108(f891(x40791,a877))),x40793)),f331(f331(f108(f891(x40791,a877)),f40(f891(x40791,a877),x40792)),x40793))
% 162.26/162.06 [4087]E(f331(f145(f884(x40871),f884(x40871),f137(x40871),f119(x40871)),f331(f331(f154(f884(x40871)),x40872),x40873)),f331(f331(f137(x40871),x40872),f331(f145(f884(x40871),f884(x40871),f137(x40871),f119(x40871)),x40873)))
% 162.26/162.06 [4108]E(f331(f331(f309(f891(x41081,a877)),f331(f285(x41081,x41081,x41082),f331(f331(f309(x41081),x41083),f196(f891(x41081,a877))))),f196(f891(f891(x41081,a877),a877))),f331(f331(f61(x41081),f331(f331(f309(x41081),x41083),f196(f891(x41081,a877)))),x41082))
% 162.26/162.06 [4118]E(f331(f331(f81(a883),f331(f331(f82(a883),x41181),f331(f331(f39(a883),x41182),x41183))),f331(f331(f39(a883),f331(f331(f82(a883),x41181),f45(a883,x41182,x41183))),x41183)),f331(f331(f39(a883),f331(f331(f82(a883),x41181),x41182)),x41183))
% 162.26/162.06 [4119]E(f331(f331(f81(a1),f331(f331(f82(a1),x41191),f331(f331(f39(a1),x41192),x41193))),f331(f331(f39(a1),f331(f331(f82(a1),x41191),f45(a1,x41192,x41193))),x41193)),f331(f331(f39(a1),f331(f331(f82(a1),x41191),x41192)),x41193))
% 162.26/162.06 [4152]E(f331(f331(f22(f891(x41521,a877)),f331(f175(x41521),x41522)),f331(f331(f309(x41521),x41523),f196(f891(x41521,a877)))),f331(f175(x41521),f331(f139(x41521,f331(f331(f8(a877,a877,x41521),a326),f331(a328,x41523))),x41522)))
% 162.26/162.06 [4202]E(f331(f331(f137(x42021),f331(f145(f884(x42021),f884(x42021),f137(x42021),f119(x42021)),x42022)),f331(f145(f884(x42021),f884(x42021),f137(x42021),f119(x42021)),x42023)),f331(f145(f884(x42021),f884(x42021),f137(x42021),f119(x42021)),f331(f331(f137(f884(x42021)),x42022),x42023)))
% 162.26/162.06 [4208]E(f331(f331(f261(f884(x42081),f884(x42081)),f331(f139(x42081,x42082),x42083)),f331(f139(x42081,f331(f74(a877,a877,x42081,a326),x42082)),x42083)),f170(x42081,x42082,x42083))
% 162.26/162.06 [4212]E(f331(f331(f81(a883),f331(f331(f81(a883),f331(f331(f39(a883),x42121),x42122)),f331(f331(f39(a883),x42123),x42122))),f331(f331(f39(a883),f331(f331(f81(a883),f45(a883,x42121,x42122)),f45(a883,x42123,x42122))),x42122)),f331(f331(f39(a883),f331(f331(f81(a883),x42121),x42123)),x42122))
% 162.26/162.06 [4213]E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f39(a1),x42131),x42132)),f331(f331(f39(a1),x42133),x42132))),f331(f331(f39(a1),f331(f331(f81(a1),f45(a1,x42131,x42132)),f45(a1,x42133,x42132))),x42132)),f331(f331(f39(a1),f331(f331(f81(a1),x42131),x42133)),x42132))
% 162.26/162.06 [4270]E(f331(f331(f108(f891(f884(x42701),a877)),f331(f331(f7(f884(x42701),f891(f884(x42701),a877),a877),f333(f884(x42701))),f164(x42701,x42702))),f331(f331(f7(f884(x42701),f891(f884(x42701),a877),a877),f333(f884(x42701))),f164(x42701,x42703))),f163(x42701,f331(f331(f108(f891(x42701,a877)),f331(f331(f7(x42701,f891(x42701,a877),a877),f333(x42701)),x42702)),f331(f331(f7(x42701,f891(x42701,a877),a877),f333(x42701)),x42703))))
% 162.26/162.06 [4282]E(f331(f253(x42821),f331(f331(f18(x42821,a877,a877),f331(f331(f8(a877,f891(a877,a877),x42821),a330),f331(f331(f7(x42821,x42821,a877),a328),x42822))),f331(f331(f7(x42821,f891(x42821,a877),a877),f333(x42821)),x42823))),f331(f331(f309(x42821),x42822),x42823))
% 162.26/162.06 [4304]E(f331(f331(f89(f884(f884(x43041)),f884(f884(x43041))),f54(x43041,x43042)),f331(f331(f18(f884(f884(x43041)),f884(f884(x43041)),f884(f884(x43041))),f331(f331(f8(f884(f884(x43041)),f891(f884(f884(x43041)),f884(f884(x43041))),f884(f884(x43041))),f137(f884(x43041))),f331(f157(f884(x43041),f884(x43041)),f331(f154(x43041),x43043)))),f5(f884(f884(x43041))))),f54(x43041,f331(f331(f154(x43041),x43043),x43042)))
% 162.26/162.06 [4308]E(f331(f253(x43081),f331(f331(f18(x43081,a877,a877),f331(f331(f8(a877,f891(a877,a877),x43081),a330),f331(f331(f7(x43081,f891(x43081,a877),a877),f333(x43081)),x43082))),f331(f331(f7(x43081,f891(x43081,a877),a877),f333(x43081)),x43083))),f331(f331(f107(f891(x43081,a877)),x43082),x43083))
% 162.26/162.06 [4309]E(f331(f253(x43091),f331(f331(f18(x43091,a877,a877),f331(f331(f8(a877,f891(a877,a877),x43091),a329),f331(f331(f7(x43091,f891(x43091,a877),a877),f333(x43091)),x43092))),f331(f331(f7(x43091,f891(x43091,a877),a877),f333(x43091)),x43093))),f331(f331(f108(f891(x43091,a877)),x43092),x43093))
% 162.26/162.06 [4399]E(f331(f331(f42(x43991,f891(f891(x43991,a877),a877)),x43992),f331(f331(f7(x43991,f891(f891(x43991,a877),a877),f891(f891(x43991,a877),a877)),f331(f331(f8(f891(x43991,a877),f891(f891(f891(x43991,a877),a877),f891(f891(x43991,a877),a877)),x43991),f309(f891(x43991,a877))),f331(f331(f8(f891(x43991,a877),f891(x43991,a877),x43991),f285(x43991,x43991,x43993)),f331(f331(f7(x43991,f891(x43991,a877),f891(x43991,a877)),f309(x43991)),f196(f891(x43991,a877)))))),f196(f891(f891(x43991,a877),a877)))),f331(f331(f61(x43991),x43992),x43993))
% 162.26/162.06 [4408]E(f331(f331(f213(x44081),f331(f331(f82(a1),f331(f331(f74(f890(a1,a1),a1,x44081,f260(a1,a1)),f224(x44081)),x44082)),f331(f331(f74(f890(a1,a1),a1,x44081,f260(a1,a1)),f224(x44081)),x44083))),f331(f331(f82(a1),f331(f331(f74(f890(a1,a1),a1,x44081,f269(a1,a1)),f224(x44081)),x44082)),f331(f331(f74(f890(a1,a1),a1,x44081,f269(a1,a1)),f224(x44081)),x44083))),f233(x44081,x44082,x44083))
% 162.26/162.06 [4412]E(f331(f253(f884(x44121)),f331(f331(f18(f884(x44121),a877,a877),f331(f331(f8(a877,f891(a877,a877),f884(x44121)),a329),f331(f331(f7(f884(x44121),a883,a877),f331(f331(f8(a883,f891(a883,a877),f884(x44121)),a328),f197(f884(x44121)))),x44122))),f331(f331(f7(f884(x44121),f891(x44121,a877),a877),f331(f331(f8(f891(x44121,a877),f891(f891(x44121,a877),a877),f884(x44121)),f247(f891(x44121,a877))),f175(x44121))),f331(f175(x44121),x44123)))),f331(f175(f884(x44121)),f55(x44121,x44122,x44123)))
% 162.26/162.06 [3800]E(f45(a883,f331(f331(f81(a883),f331(f331(f82(a883),x38001),x38002)),x38003),x38002),f45(a883,x38003,x38002))
% 162.26/162.06 [3843]E(f142(a883,f331(f301(a883,f331(f331(f81(a883),x38431),x38432)),x38433)),f331(f331(f141(a883),x38432),f142(a883,f331(f301(a883,x38431),x38433))))
% 162.26/162.06 [3884]E(f331(f331(f81(a1),f331(f106(a1),x38841)),f331(f331(f81(a1),f331(f106(a1),x38842)),x38843)),f331(f331(f81(a1),f331(f106(a1),f331(f331(f81(a883),x38841),x38842))),x38843))
% 162.26/162.06 [3890]E(f331(f331(f22(f891(x38901,a877)),f331(f331(f22(f891(x38901,a877)),x38902),x38903)),x38903),f331(f331(f22(f891(x38901,a877)),x38902),x38903))
% 162.26/162.06 [3891]E(f331(f331(f107(f891(x38911,a877)),f331(f331(f22(f891(x38911,a877)),x38912),x38913)),x38913),f331(f331(f107(f891(x38911,a877)),x38912),x38913))
% 162.26/162.06 [3914]E(f331(f331(f288(x39141,x39141,x39142),f307(x39141,f196(f891(f890(x39141,x39141),a877)))),x39143),x39143)
% 162.26/162.06 [3920]E(f331(f331(f107(f891(x39201,a877)),f331(f284(x39201),x39202)),f331(f284(x39201),x39203)),f331(f284(x39201),f331(f331(f107(f891(f890(x39201,x39201),a877)),x39202),x39203)))
% 162.26/162.06 [3931]E(f275(x39311,f331(f331(f154(f890(a105,x39311)),f331(f331(f261(a105,x39311),f2(a105)),x39312)),x39313)),f275(x39311,x39313))
% 162.26/162.06 [3934]E(f331(f331(f108(f891(x39341,a877)),f41(f891(x39341,a877),x39342)),f41(f891(x39341,a877),x39343)),f41(f891(x39341,a877),f331(f331(f107(f891(f891(x39341,a877),a877)),x39342),x39343)))
% 162.26/162.06 [3935]E(f331(f331(f107(f891(x39351,a877)),f40(f891(x39351,a877),x39352)),f40(f891(x39351,a877),x39353)),f40(f891(x39351,a877),f331(f331(f107(f891(f891(x39351,a877),a877)),x39352),x39353)))
% 162.26/162.06 [3973]E(f331(f331(f288(x39731,x39731,x39731),f331(f331(f191(f890(x39731,x39731),a877),x39732),x39733)),x39733),f331(f331(f191(f890(x39731,x39731),a877),f331(a118,x39732)),x39733))
% 162.26/162.06 [4019]P24(f331(f331(f247(f891(x40191,a877)),f331(f331(f22(f891(x40191,a877)),x40192),x40193)),x40192))
% 162.26/162.06 [4020]P24(f331(f331(f247(f891(x40201,a877)),f331(f331(f108(f891(x40201,a877)),x40202),x40203)),x40203))
% 162.26/162.06 [4021]P24(f331(f331(f247(f891(x40211,a877)),f331(f331(f108(f891(x40211,a877)),x40212),x40213)),x40212))
% 162.26/162.06 [4045]E(f307(x40451,f331(f331(f107(f891(f890(x40451,x40451),a877)),f307(x40451,x40452)),f307(x40451,x40453))),f307(x40451,f331(f331(f107(f891(f890(x40451,x40451),a877)),x40452),x40453)))
% 162.26/162.06 [4049]E(f40(f891(x40491,a877),f331(f331(f309(f891(x40491,a877)),x40492),f331(f331(f309(f891(x40491,a877)),x40493),f196(f891(f891(x40491,a877),a877))))),f331(f331(f107(f891(x40491,a877)),x40492),x40493))
% 162.26/162.06 [4050]E(f41(f891(x40501,a877),f331(f331(f309(f891(x40501,a877)),x40502),f331(f331(f309(f891(x40501,a877)),x40503),f196(f891(f891(x40501,a877),a877))))),f331(f331(f108(f891(x40501,a877)),x40502),x40503))
% 162.26/162.06 [4056]E(f331(f331(f288(x40561,x40561,x40561),f331(f331(f191(f890(x40561,x40561),a877),x40562),x40563)),x40563),f331(f331(f288(x40561,x40561,x40561),x40563),f331(f331(f191(f890(x40561,x40561),a877),x40562),x40563)))
% 162.26/162.06 [4123]E(f331(f331(f107(f891(x41231,a877)),f331(f253(x41231),f331(f331(f7(x41231,x41231,a877),a328),x41232))),x41233),f331(f331(f309(x41231),x41232),x41233))
% 162.26/162.06 [4124]E(f331(a111,f331(f331(f9(x41241,a1),f331(f331(f8(a883,a1,x41241),f106(a1)),x41242)),x41243)),f331(f331(f9(x41241,a883),x41242),x41243))
% 162.26/162.06 [4125]E(f331(a111,f331(f331(f6(x41251,a1),f331(f331(f8(a883,a1,x41251),f106(a1)),x41252)),x41253)),f331(f331(f6(x41251,a883),x41252),x41253))
% 162.26/162.06 [4199]E(f331(f159(f884(x41991),x41991,f331(f174(x41991),x41992),f331(f16(f891(f884(x41991),f884(x41991)),x41991),f331(f331(f7(f884(x41991),f884(x41991),f884(x41991)),f137(x41991)),x41992))),x41993),f331(f174(x41991),f331(f331(f137(x41991),x41993),x41992)))
% 162.26/162.06 [4230]P24(f331(f331(f247(f891(f891(x42301,a877),a877)),f331(f331(f107(f891(f891(x42301,a877),a877)),f331(f308(x42301),x42302)),f331(f308(x42301),x42303))),f331(f308(x42301),f331(f331(f107(f891(x42301,a877)),x42302),x42303))))
% 162.26/162.06 [4323]E(f331(f253(x43231),f331(f331(f18(x43231,a877,a877),f331(f331(f8(a877,f891(a877,a877),x43231),a329),f331(f331(f7(x43231,f891(x43231,a877),a877),f333(x43231)),x43232))),f331(f331(f8(a877,a877,x43231),a326),f331(f331(f7(x43231,f891(x43231,a877),a877),f333(x43231)),x43233)))),f331(f331(f22(f891(x43231,a877)),x43232),x43233))
% 162.26/162.06 [4347]E(f331(f38(a883),f331(f253(a883),f331(f331(f18(a883,a877,a877),f331(f331(f8(a877,f891(a877,a877),a883),a329),f331(f331(f7(a883,a883,a877),f248(a883)),f331(f197(f884(x43471)),x43472)))),f331(f331(f8(x43471,a877,a883),x43473),f331(f168(x43471),x43472))))),f331(f197(f884(x43471)),f331(f139(x43471,x43473),x43472)))
% 162.26/162.06 [4349]E(f331(f197(f884(x43491)),f177(x43491,x43492,x43493)),f331(f38(a883),f331(f253(a883),f331(f331(f18(a883,a877,a877),f331(f331(f8(a877,f891(a877,a877),a883),a329),f331(f331(f7(a883,a883,a877),f248(a883)),f331(f197(f884(x43491)),x43492)))),f331(f331(f7(a883,f891(a883,a877),a877),f333(a883)),x43493)))))
% 162.26/162.06 [4460]E(f331(f331(f108(f891(f890(f884(x44601),f884(x44601)),a877)),f331(f310(f890(f890(x44601,f884(x44601)),f890(x44601,f884(x44601))),f890(f884(x44601),f884(x44601)),f271(f890(x44601,f884(x44601)),f884(x44601),f890(x44601,f884(x44601)),f884(x44601),f331(f270(x44601,f884(x44601),f884(x44601)),f154(x44601)),f331(f270(x44601,f884(x44601),f884(x44601)),f154(x44601)))),f323(x44601,f884(x44601),x44602,f331(f146(x44601,x44602),x44603)))),f331(f253(f890(f884(x44601),f884(x44601))),f331(f270(f884(x44601),f884(x44601),a877),f331(f331(f7(f884(x44601),f891(f884(x44601),a877),f891(f884(x44601),a877)),f331(f331(f8(f891(a877,a877),f891(f891(f884(x44601),a877),f891(f884(x44601),a877)),f884(x44601)),f8(a877,a877,f884(x44601))),f331(f331(f8(a877,f891(a877,a877),f884(x44601)),a329),f331(f331(f7(f884(x44601),a883,a877),f331(f331(f8(a883,f891(a883,a877),f884(x44601)),a328),f197(f884(x44601)))),f331(a118,x44603))))),f331(f331(f7(f884(x44601),a883,a877),f331(f331(f8(a883,f891(a883,a877),f884(x44601)),a328),f197(f884(x44601)))),f331(a118,x44603)))))),f331(f146(x44601,x44602),f331(a118,x44603)))
% 162.26/162.06 [3936]E(f45(a883,f331(a118,f331(f331(f81(a883),f331(f331(f82(a883),x39361),x39362)),x39363)),x39362),f45(a883,f331(a118,x39363),x39362))
% 162.26/162.06 [4185]E(f331(f253(x41851),f331(f331(f18(x41851,a877,a877),f331(f331(f8(a877,f891(a877,a877),x41851),a329),x41852)),x41853)),f331(f331(f108(f891(x41851,a877)),f331(f253(x41851),x41852)),f331(f253(x41851),x41853)))
% 162.26/162.06 [4186]E(f331(f253(x41861),f331(f331(f18(x41861,a877,a877),f331(f331(f8(a877,f891(a877,a877),x41861),a330),x41862)),x41863)),f331(f331(f107(f891(x41861,a877)),f331(f253(x41861),x41862)),f331(f253(x41861),x41863)))
% 162.26/162.06 [4188]E(f331(f331(f137(x41881),f331(f331(f141(x41881),f45(a883,x41882,f331(f197(f884(x41881)),x41883))),x41883)),f331(f331(f176(x41881),f45(a883,x41882,f331(f197(f884(x41881)),x41883))),x41883)),f331(f331(f331(f191(f884(x41881),f884(x41881)),x41882),f171(x41881)),x41883))
% 162.26/162.06 [4193]E(f331(f253(x41931),f331(f331(f18(x41931,a877,a877),f331(f331(f8(a877,f891(a877,a877),x41931),a334),x41932)),x41933)),f331(f331(f107(f891(x41931,a877)),f331(f80(f891(x41931,a877)),f331(f253(x41931),x41932))),f331(f253(x41931),x41933)))
% 162.26/162.06 [4214]E(f331(f331(f81(a883),f331(f197(f884(x42141)),f331(f139(x42141,x42142),x42143))),f331(f197(f884(x42141)),f331(f139(x42141,f331(f331(f8(a877,a877,x42141),a326),x42142)),x42143))),f331(f197(f884(x42141)),x42143))
% 162.26/162.06 [4239]P24(f331(f331(f247(f891(x42391,a877)),f331(f331(f107(f891(x42391,a877)),f41(f891(x42391,a877),x42392)),f41(f891(x42391,a877),x42393))),f41(f891(x42391,a877),f331(f331(f108(f891(f891(x42391,a877),a877)),x42392),x42393))))
% 162.26/162.06 [4252]E(f331(f175(x42521),f331(f139(x42521,f331(f331(f8(a877,a877,x42521),a326),f331(f331(f7(x42521,x42521,a877),a328),x42522))),x42523)),f331(f331(f22(f891(x42521,a877)),f331(f175(x42521),x42523)),f331(f331(f309(x42521),x42522),f196(f891(x42521,a877)))))
% 162.26/162.06 [4261]P24(f331(f331(f247(f891(f890(x42611,x42611),a877)),f331(f331(f107(f891(f890(x42611,x42611),a877)),f307(x42611,x42612)),f307(x42611,x42613))),f307(x42611,f331(f331(f107(f891(f890(x42611,x42611),a877)),x42612),x42613))))
% 162.26/162.06 [4287]E(f331(f331(f82(a883),f331(a118,f331(a118,f2(a883)))),f331(f331(f6(a883,a883),f331(f331(f8(a883,a883,a883),f331(f81(a883),x42871)),f331(f331(f7(a883,a883,a883),f82(a883)),x42872))),f331(f254(a883),x42873))),f331(f331(f82(a883),x42873),f331(f331(f81(a883),x42871),f331(f331(f81(a883),x42871),f331(f331(f82(a883),f331(f331(f22(a883),x42873),f79(a883))),x42872)))))
% 162.26/162.06 [4299]E(f331(f253(x42991),f331(f331(f18(x42991,a877,a877),f331(f331(f8(a877,f891(a877,a877),x42991),a329),f331(f331(f7(x42991,f891(x42991,a877),a877),f333(x42991)),f331(f175(x42991),x42992)))),x42993)),f331(f175(x42991),f331(f139(x42991,x42993),x42992)))
% 162.26/162.06 [4459]E(f331(f253(x44591),f331(f331(f8(f891(a883,a877),a877,x44591),f87(a883)),f331(f331(f7(x44591,f891(a883,a877),f891(a883,a877)),f331(f331(f8(f891(a883,f891(a877,a877)),f891(f891(a883,a877),f891(a883,a877)),x44591),f18(a883,a877,a877)),f331(f331(f8(f891(a883,a877),f891(a883,f891(a877,a877)),x44591),f331(f8(a877,f891(a877,a877),a883),a329)),f331(f331(f7(x44591,f891(a883,x44591),f891(a883,a877)),f331(f331(f8(f891(x44591,a877),f891(f891(a883,x44591),f891(a883,a877)),x44591),f8(x44591,a877,a883)),a328)),f331(f168(x44591),x44592))))),f331(f331(f18(a883,a877,a877),f331(f331(f8(a877,f891(a877,a877),a883),a329),f331(f331(f7(a883,a883,a877),f248(a883)),f331(f197(f884(x44591)),x44592)))),f331(f331(f7(a883,f891(a883,a877),a877),f333(a883)),x44593))))),f331(f175(x44591),f177(x44591,x44592,x44593)))
% 162.26/162.06 [4336]E(f331(f253(x43361),f331(f331(f18(x43361,a877,a877),f331(f331(f8(a877,f891(a877,a877),x43361),a334),f331(f331(f8(a877,a877,x43361),a326),f331(f331(f7(x43361,x43361,a877),a328),x43362)))),x43363)),f331(f331(f309(x43361),x43362),f331(f253(x43361),x43363)))
% 162.26/162.06 [4374]E(f331(f331(f157(f890(x43741,a883),x43741),f260(x43741,a883)),f331(f139(f890(x43741,a883),f331(f331(f7(f890(x43741,a883),f891(a883,a877),a877),f331(f331(f8(a883,f891(f891(a883,a877),a877),f890(x43741,a883)),f333(a883)),f269(x43741,a883))),x43742)),f331(f331(f184(x43741,a883),x43743),f142(a883,f331(f301(a883,f2(a883)),f331(f197(f884(x43741)),x43743)))))),f177(x43741,x43743,x43742))
% 162.26/162.06 [4444]E(f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f331(f331(f6(a883,a1),f331(f331(f8(a1,a1,a883),f331(f81(a1),x44441)),f331(f331(f7(a883,a1,a1),f331(f331(f8(a1,f891(a1,a1),a883),f82(a1)),f106(a1))),x44442))),f331(f254(a883),x44443))),f331(f331(f82(a1),f331(f106(a1),x44443)),f331(f331(f81(a1),x44441),f331(f331(f81(a1),x44441),f331(f331(f82(a1),f331(f106(a1),f331(f331(f22(a883),x44443),f79(a883)))),x44442)))))
% 162.26/162.06 [4453]E(f331(f253(f890(x44531,x44532)),f331(f270(x44531,x44532,a877),f331(f331(f7(x44531,f891(f890(x44532,x44531),a877),f891(x44532,a877)),f331(f331(f8(f891(x44532,f891(f891(f890(x44532,x44531),a877),a877)),f891(f891(f890(x44532,x44531),a877),f891(x44532,a877)),x44531),f7(x44532,f891(f890(x44532,x44531),a877),a877)),f331(f331(f8(f891(x44532,f890(x44532,x44531)),f891(x44532,f891(f891(f890(x44532,x44531),a877),a877)),x44531),f331(f8(f890(x44532,x44531),f891(f891(f890(x44532,x44531),a877),a877),x44532),f333(f890(x44532,x44531)))),f331(f7(x44532,x44531,f890(x44532,x44531)),f261(x44532,x44531))))),x44533))),f331(f286(x44532,x44531),x44533))
% 162.26/162.06 [4474]E(f331(f253(f884(x44741)),f331(f331(f8(f891(x44741,a877),a877,f884(x44741)),f87(x44741)),f331(f331(f8(f891(x44741,f891(f884(x44741),a877)),f891(x44741,a877),f884(x44741)),f331(f8(f891(f884(x44741),a877),a877,x44741),f87(f884(x44741)))),f331(f331(f7(f884(x44741),f891(x44741,f891(f884(x44741),a877)),f891(x44741,f891(f884(x44741),a877))),f331(f331(f8(f891(x44741,f891(f891(f884(x44741),a877),f891(f884(x44741),a877))),f891(f891(x44741,f891(f884(x44741),a877)),f891(x44741,f891(f884(x44741),a877))),f884(x44741)),f18(x44741,f891(f884(x44741),a877),f891(f884(x44741),a877))),f331(f331(f8(f891(x44741,f891(f884(x44741),f891(a877,a877))),f891(x44741,f891(f891(f884(x44741),a877),f891(f884(x44741),a877))),f884(x44741)),f331(f8(f891(f884(x44741),f891(a877,a877)),f891(f891(f884(x44741),a877),f891(f884(x44741),a877)),x44741),f18(f884(x44741),a877,a877))),f331(f331(f8(f891(x44741,f891(f884(x44741),a877)),f891(x44741,f891(f884(x44741),f891(a877,a877))),f884(x44741)),f331(f8(f891(f884(x44741),a877),f891(f884(x44741),f891(a877,a877)),x44741),f331(f8(a877,f891(a877,a877),f884(x44741)),a329))),f331(f331(f7(f884(x44741),f891(x44741,f891(f884(x44741),f884(x44741))),f891(x44741,f891(f884(x44741),a877))),f331(f331(f8(f891(f891(f884(x44741),f884(x44741)),f891(f884(x44741),a877)),f891(f891(x44741,f891(f884(x44741),f884(x44741))),f891(x44741,f891(f884(x44741),a877))),f884(x44741)),f8(f891(f884(x44741),f884(x44741)),f891(f884(x44741),a877),x44741)),f331(f331(f8(f891(f884(x44741),a877),f891(f891(f884(x44741),f884(x44741)),f891(f884(x44741),a877)),f884(x44741)),f8(f884(x44741),a877,f884(x44741))),a328))),f154(x44741)))))),f331(f331(f7(x44741,f891(f884(x44741),a877),f891(f884(x44741),a877)),f331(f331(f8(f891(a877,a877),f891(f891(f884(x44741),a877),f891(f884(x44741),a877)),x44741),f8(a877,a877,f884(x44741))),f331(f331(f8(a877,f891(a877,a877),x44741),a329),f331(f331(f7(x44741,f891(x44741,a877),a877),f333(x44741)),x44742)))),f331(f331(f7(f884(x44741),f891(f884(x44741),a877),a877),f333(f884(x44741))),x44743)))))),f178(x44741,x44742,x44743))
% 162.26/162.06 [4475]E(f331(f331(f89(a1,f890(a1,a1)),f331(f331(f22(a1),x44751),x44752)),f331(f331(f7(a1,f890(a1,a1),f890(a1,a1)),f331(f331(f18(a1,f890(a1,a1),f891(f890(a1,a1),f890(a1,a1))),f331(f331(f8(a877,f891(f890(a1,a1),f891(f890(a1,a1),f890(a1,a1))),a1),f102(f890(a1,a1))),f331(f247(a1),f2(a1)))),f331(f261(a1,a1),f331(f331(f81(a1),f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x44753)),f79(a1))))),f331(f331(f261(a1,a1),f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x44753)),x44751))),f331(f44(x44752),f331(f331(f261(a1,a1),x44753),x44751)))
% 162.26/162.06 [4503]~E(f33(x45031,x45032),f34(x45033,x45034))
% 162.26/162.06 [4521]~E(f331(a28,x45211),f29(x45212,x45213,x45214))
% 162.26/162.06 [4522]~E(f331(a28,x45221),f31(x45222,x45223,x45224))
% 162.26/162.06 [4523]~E(f331(a28,x45231),f30(x45232,x45233,x45234))
% 162.26/162.06 [4524]~E(f29(x45241,x45242,x45243),f331(a28,x45244))
% 162.26/162.06 [4525]~E(f31(x45251,x45252,x45253),f331(a28,x45254))
% 162.26/162.06 [4526]~E(f30(x45261,x45262,x45263),f331(a28,x45264))
% 162.26/162.06 [3499]E(f331(f331(f331(f73(x34991,x34992),x34993),x34994),f331(x34993,x34994)),x34993)
% 162.26/162.06 [3507]E(f122(x35071,f331(x35072,x35073),f331(x35074,x35073)),f331(f215(x35071,x35072,x35074),x35073))
% 162.26/162.06 [3558]E(f331(f331(f263(x35581,x35582,x35583),x35584),f2(a883)),x35582)
% 162.26/162.06 [3598]E(f193(x35981,x35982,x35983,f331(a118,x35984)),f331(x35983,x35984))
% 162.26/162.06 [3638]E(f173(x36381,x36382,f173(x36381,x36383,x36384)),f173(x36381,x36383,f173(x36381,x36382,x36384)))
% 162.26/162.06 [3639]E(f122(x36391,f130(x36391,x36392,x36393),x36394),f130(x36391,x36392,f122(x36391,x36393,x36394)))
% 162.26/162.06 [3769]E(f331(f242(x37691,x37692,x37693,x37694),f199(x37692)),x37693)
% 162.26/162.06 [3771]E(f331(f159(x37711,x37712,x37713,x37714),f119(x37712)),x37713)
% 162.26/162.06 [3772]E(f331(f145(x37721,x37722,x37723,x37724),f119(x37722)),x37724)
% 162.26/162.06 [3881]E(f331(f242(f887(x38811),x38812,f199(x38811),f331(f16(f887(x38811),x38812),f199(x38811))),f331(x38813,x38814)),f199(x38811))
% 162.26/162.06 [3923]E(f331(f331(f107(f891(x39231,a877)),f186(x39231,x39232,x39233)),f186(x39231,x39232,x39234)),f186(x39231,x39232,f187(x39231,x39232,x39234,x39233)))
% 162.26/162.06 [3957]E(f331(f331(f272(x39571,x39572,x39573,f890(x39572,x39573)),x39574),f261(x39572,x39573)),x39574)
% 162.26/162.06 [3966]E(f243(x39661,x39662,x39663,x39664,f199(x39662)),x39663)
% 162.26/162.06 [3967]E(f189(x39671,x39672,x39673,x39674,f119(x39672)),x39673)
% 162.26/162.06 [3968]E(f189(x39681,x39682,x39683,f119(x39681),x39684),x39683)
% 162.26/162.06 [4246]P42(x42461,x42462,x42463,x42464,f196(f891(x42461,a877)),x42464)
% 162.26/162.06 [3303]E(f331(f331(f16(x33031,x33032),x33033),x33034),x33033)
% 162.26/162.06 [3420]E(f331(f331(f210(x34201,x34202),x34203),f331(f239(x34201),x34204)),f331(f239(x34202),f331(x34203,x34204)))
% 162.26/162.06 [3589]E(f173(x35891,x35892,f331(f139(x35891,x35893),x35894)),f331(f139(x35891,x35893),f173(x35891,x35892,x35894)))
% 162.26/162.06 [3622]E(f331(f331(f65(x36221,x36222,x36223),x36224),f196(f891(x36221,a877))),x36224)
% 162.26/162.06 [3645]E(f331(f331(f168(x36451),f331(f331(f154(x36451),x36452),x36453)),f331(a118,x36454)),f331(f331(f168(x36451),x36453),x36454))
% 162.26/162.06 [3688]P30(x36881,f2(a883),f331(f331(f331(f93(x36881),x36882),f331(a28,x36883)),x36884))
% 162.26/162.06 [3713]E(f331(f331(x37131,x37132),f331(f192(x37133,x37134,x37131),x37132)),f331(f192(x37133,x37134,x37131),f331(a118,x37132)))
% 162.26/162.06 [3805]E(f331(f331(f162(x38051,f331(f331(f154(x38051),x38052),x38053)),f2(a883)),x38054),f331(f331(f154(x38051),x38054),x38053))
% 162.26/162.06 [3816]E(f331(f331(f42(f891(x38161,a877),f891(x38162,a877)),x38163),f310(x38161,x38162,x38164)),f331(f310(x38161,x38162,x38164),f40(f891(x38161,a877),x38163)))
% 162.26/162.06 [3817]E(f331(f331(f42(f891(x38171,a877),f891(x38172,a877)),x38173),f311(x38172,x38171,x38174)),f331(f311(x38172,x38171,x38174),f40(f891(x38171,a877),x38173)))
% 162.26/162.06 [3907]E(f186(x39071,x39072,f190(x39071,x39072,x39073,x39074)),f331(f331(f108(f891(x39071,a877)),f186(x39071,x39072,x39073)),x39074))
% 162.26/162.06 [3911]E(f331(f132(x39111,x39112),f130(x39111,x39113,x39114)),f331(f331(f81(a883),f331(f331(f81(a883),f331(x39112,x39113)),f331(f132(x39111,x39112),x39114))),f331(a118,f2(a883))))
% 162.26/162.06 [3930]E(f331(f145(x39301,x39302,f331(f7(x39302,x39301,x39301),x39303),x39304),f331(f172(x39302),f119(x39302))),x39304)
% 162.26/162.06 [3979]E(f77(x39791,x39792,x39793,x39794,f196(f891(x39791,a877))),x39793)
% 162.26/162.06 [4022]E(f331(f331(f331(f331(f73(x40221,f887(x40222)),f331(f16(f887(x40222),x40221),f199(x40222))),x40223),f199(x40222)),x40224),f199(x40222))
% 162.26/162.06 [4168]E(f331(f270(x41681,x41682,x41683),f331(f331(f8(f891(x41682,f890(x41681,x41682)),f891(x41682,x41683),x41681),f331(f8(f890(x41681,x41682),x41683,x41682),x41684)),f261(x41681,x41682))),x41684)
% 162.26/162.06 [3497]E(f331(f269(x34971,x34972),f331(f331(f261(x34971,x34972),x34973),x34974)),x34974)
% 162.26/162.06 [3498]E(f331(f260(x34981,x34982),f331(f331(f261(x34981,x34982),x34983),x34984)),x34983)
% 162.26/162.06 [3533]E(f331(f197(f884(x35331)),f331(f331(f157(x35332,x35331),x35333),x35334)),f331(f197(f884(x35332)),x35334))
% 162.26/162.06 [3534]E(f331(f197(f884(x35341)),f331(f331(f162(x35341,x35342),x35343),x35344)),f331(f197(f884(x35341)),x35342))
% 162.26/162.06 [3552]E(f331(f331(f141(x35521),f331(a118,x35522)),f331(f331(f154(x35521),x35523),x35524)),f331(f331(f141(x35521),x35522),x35524))
% 162.26/162.06 [3624]E(f331(f331(f309(x36241),x36242),f331(f331(f309(x36241),x36243),x36244)),f331(f331(f309(x36241),x36243),f331(f331(f309(x36241),x36242),x36244)))
% 162.26/162.06 [3627]E(f331(f331(f157(x36271,x36272),x36273),f120(x36271,x36274)),f120(x36272,f331(f331(f157(x36271,x36272),x36273),x36274)))
% 162.26/162.06 [3643]E(f331(f172(x36431),f331(f331(f157(x36432,x36431),x36433),x36434)),f331(f331(f157(x36432,x36431),x36433),f331(f172(x36432),x36434)))
% 162.26/162.06 [3644]E(f331(f331(f157(x36441,x36442),x36443),f331(f174(x36441),x36444)),f331(f174(x36442),f331(f331(f157(x36441,x36442),x36443),x36444)))
% 162.26/162.06 [3657]E(f331(f331(f176(x36571),f331(a118,x36572)),f331(f331(f154(x36571),x36573),x36574)),f331(f331(f154(x36571),x36573),f331(f331(f176(x36571),x36572),x36574)))
% 162.26/162.06 [3661]E(f331(f175(x36611),f331(f331(f157(x36612,x36611),x36613),x36614)),f331(f310(x36612,x36611,x36613),f331(f175(x36612),x36614)))
% 162.26/162.06 [3712]E(f17(x37121,x37122,x37123,f331(a3,f331(a118,f331(a19,x37124)))),f331(x37123,x37124))
% 162.26/162.06 [3715]E(f331(f331(f137(x37151),f331(f139(x37151,x37152),x37153)),f331(f139(x37151,x37152),x37154)),f331(f139(x37151,x37152),f331(f331(f137(x37151),x37153),x37154)))
% 162.26/162.06 [3723]E(f155(x37231,f331(f331(f157(x37232,x37231),x37233),f155(x37232,x37234))),f155(x37231,f331(f331(f157(x37232,x37231),x37233),x37234)))
% 162.26/162.06 [3738]E(f331(f286(x37381,x37381),f331(f331(f287(x37382,x37381),x37383),x37384)),f331(f331(f287(x37382,x37381),f331(f286(x37382,x37382),x37383)),x37384))
% 162.26/162.06 [3747]E(f331(f331(f288(x37471,x37472,x37473),x37474),f196(f891(f890(x37472,x37473),a877))),f196(f891(f890(x37471,x37473),a877)))
% 162.26/162.06 [3748]E(f331(f331(f176(x37481),f331(f331(f22(a883),x37482),x37483)),f331(f331(f141(x37481),x37483),x37484)),f331(f331(f141(x37481),x37483),f331(f331(f176(x37481),x37482),x37484)))
% 162.26/162.06 [3797]E(f41(f891(x37971,a877),f331(f310(x37972,f891(x37971,a877),x37973),x37974)),f331(f331(f43(x37972,f891(x37971,a877)),x37974),x37973))
% 162.26/162.06 [3798]E(f40(f891(x37981,a877),f331(f310(x37982,f891(x37981,a877),x37983),x37984)),f331(f331(f42(x37982,f891(x37981,a877)),x37984),x37983))
% 162.26/162.06 [3799]E(f331(f197(f884(f890(x37991,x37992))),f331(f331(f184(x37991,x37992),x37993),x37994)),f331(f331(f251(a883),f331(f197(f884(x37991)),x37993)),f331(f197(f884(x37992)),x37994)))
% 162.26/162.06 [3801]E(f331(f311(x38011,x38012,x38013),f331(f80(f891(x38012,a877)),x38014)),f331(f80(f891(x38011,a877)),f331(f311(x38011,x38012,x38013),x38014)))
% 162.26/162.06 [3831]E(f331(f190(x38311,x38312,x38313,f196(f891(x38311,a877))),x38314),f199(x38312))
% 162.26/162.06 [3849]E(f331(f311(x38491,x38492,x38493),f331(f253(x38492),x38494)),f331(f253(x38491),f331(f331(f8(x38492,a877,x38491),x38494),x38493)))
% 162.26/162.06 [3866]E(f331(f331(f168(x38661),f331(f331(f137(x38661),x38662),f331(f331(f154(x38661),x38663),x38664))),f331(f197(f884(x38661)),x38662)),x38663)
% 162.26/162.06 [3870]E(f331(f190(x38701,x38702,f331(f16(f887(x38702),x38701),f199(x38702)),x38703),x38704),f199(x38702))
% 162.26/162.06 [3888]E(f331(f310(x38881,x38882,x38883),f331(f311(x38881,x38882,x38883),x38884)),f331(f331(f108(f891(x38882,a877)),x38884),f331(f310(x38881,x38882,x38883),f256(f891(x38881,a877)))))
% 162.26/162.06 [3906]P24(f331(f331(f333(x39061),f331(x39062,x39063)),f331(f310(x39064,x39061,x39062),f256(f891(x39064,a877)))))
% 162.26/162.06 [3919]E(f331(f331(f268(x39191,x39192),f331(f175(x39191),x39193)),f331(f16(f891(x39192,a877),x39191),f331(f175(x39192),x39194))),f331(f175(f890(x39191,x39192)),f60(x39191,x39192,x39193,x39194)))
% 162.26/162.06 [3933]E(f158(x39331,x39332,f331(f331(f154(x39331),x39333),x39334)),f331(f331(f81(a883),f331(f331(f81(a883),f331(x39332,x39333)),f158(x39331,x39332,x39334))),f331(a118,f2(a883))))
% 162.26/162.06 [3949]E(f193(f884(x39491),f331(f331(f154(x39491),x39492),x39493),f331(f331(f7(a883,f884(x39491),f884(x39491)),f141(x39491)),x39493),x39494),f331(f331(f141(x39491),x39494),f331(f331(f154(x39491),x39492),x39493)))
% 162.26/162.06 [3950]P21(x39501,f890(x39502,x39501),f335(x39503,x39504,x39502,x39501),f331(f331(f42(x39502,f891(x39501,a877)),x39504),x39503))
% 162.26/162.06 [3958]E(f331(f331(f22(f891(x39581,a877)),f331(f331(f22(f891(x39581,a877)),x39582),x39583)),f331(f331(f309(x39581),x39584),f196(f891(x39581,a877)))),f331(f331(f22(f891(x39581,a877)),x39582),f331(f331(f309(x39581),x39584),x39583)))
% 162.26/162.06 [3971]E(f331(f331(f191(f891(x39711,x39712),f891(x39711,x39712)),x39713),f74(x39712,x39712,x39711,x39714)),f74(x39712,x39712,x39711,f331(f331(f191(x39712,x39712),x39713),x39714)))
% 162.26/162.06 [4044]E(f331(f331(f331(f191(f884(x40441),f884(x40441)),x40442),f171(x40441)),f331(f331(f331(f191(f884(x40441),f884(x40441)),x40443),f171(x40441)),x40444)),f331(f331(f331(f191(f884(x40441),f884(x40441)),f331(f331(f81(a883),x40442),x40443)),f171(x40441)),x40444))
% 162.26/162.06 [4126]P24(f331(f331(f247(f891(x41261,a877)),f331(f175(x41261),f331(f331(f162(x41261,x41262),x41263),x41264))),f331(f331(f309(x41261),x41264),f331(f175(x41261),x41262))))
% 162.26/162.06 [4156]E(f331(f331(f42(f891(x41561,a877),f891(f890(x41561,x41562),a877)),x41563),f331(f331(f7(f891(x41561,a877),f891(x41561,f891(x41562,a877)),f891(f890(x41561,x41562),a877)),f268(x41561,x41562)),x41564)),f331(f331(f268(x41561,x41562),f40(f891(x41561,a877),x41563)),x41564))
% 162.26/162.06 [4198]E(f221(x41981,x41982,x41983,f331(f74(x41982,f891(a105,f891(a105,f891(f890(a105,a105),f891(a105,f885(x41982))))),x41981,f216(x41982)),x41984)),f222(x41981,x41982,x41984,x41983))
% 162.26/162.06 [4217]E(f218(x42171,x42172,x42173,f331(f74(x42172,f891(a105,f891(a105,f891(f890(a105,a105),f891(a105,f885(f887(x42172)))))),x42171,f217(x42172)),x42174)),f219(x42171,x42172,x42174,x42173))
% 162.26/162.06 [4224]P24(f331(f67(x42241,x42242,x42243,x42244,f196(f891(x42241,a877))),x42244))
% 162.26/162.06 [4265]E(f331(f331(f42(x42651,f891(x42652,a877)),x42653),f331(f331(f7(x42651,f891(x42652,a877),f891(x42652,a877)),f331(f331(f8(x42652,f891(f891(x42652,a877),f891(x42652,a877)),x42651),f309(x42652)),x42654)),f196(f891(x42652,a877)))),f331(f310(x42651,x42652,x42654),x42653))
% 162.26/162.06 [4272]P24(f331(f331(f247(f891(x42721,a877)),f331(f257(x42722,x42721),f331(f331(f108(f891(f890(x42722,x42721),a877)),x42723),x42724))),f331(f331(f108(f891(x42721,a877)),f331(f257(x42722,x42721),x42723)),f331(f257(x42722,x42721),x42724))))
% 162.26/162.06 [4273]P24(f331(f331(f247(f891(x42731,a877)),f331(f259(x42731,x42732),f331(f331(f108(f891(f890(x42731,x42732),a877)),x42733),x42734))),f331(f331(f108(f891(x42731,a877)),f331(f259(x42731,x42732),x42733)),f331(f259(x42731,x42732),x42734))))
% 162.26/162.06 [4333]P24(f331(f331(f247(f891(f890(x43331,x43332),a877)),f331(f310(x43332,f890(x43331,x43332),f335(x43333,x43334,x43331,x43332)),f331(f331(f42(x43331,f891(x43332,a877)),x43334),x43333))),f331(f331(f268(x43331,x43332),x43334),x43333)))
% 162.26/162.06 [4334]E(f331(f124(x43341,f890(x43341,x43342),x43343),f331(f331(f8(f891(x43342,f885(f890(x43341,x43342))),f885(f890(x43341,x43342)),x43341),f124(x43342,f890(x43341,x43342),x43344)),f331(f331(f8(f891(x43342,f890(x43341,x43342)),f891(x43342,f885(f890(x43341,x43342))),x43341),f331(f8(f890(x43341,x43342),f885(f890(x43341,x43342)),x43342),f129(f890(x43341,x43342)))),f261(x43341,x43342)))),f134(x43341,x43342,x43343,x43344))
% 162.26/162.06 [4380]E(f86(f890(x43801,x43802),f331(f270(x43801,x43802,a877),f331(f331(f7(x43801,f891(x43802,a877),f891(x43802,a877)),f331(f331(f8(f891(a877,a877),f891(f891(x43802,a877),f891(x43802,a877)),x43801),f8(a877,a877,x43802)),f331(f331(f8(a877,f891(a877,a877),x43801),a329),f331(a328,x43803)))),f331(a328,x43804)))),f331(f331(f261(x43801,x43802),x43803),x43804))
% 162.26/162.06 [4381]E(f91(f890(x43811,x43812),f331(f270(x43811,x43812,a877),f331(f331(f7(x43811,f891(x43812,a877),f891(x43812,a877)),f331(f331(f8(f891(a877,a877),f891(f891(x43812,a877),f891(x43812,a877)),x43811),f8(a877,a877,x43812)),f331(f331(f8(a877,f891(a877,a877),x43811),a329),f331(a328,x43813)))),f331(a328,x43814)))),f331(f331(f261(x43811,x43812),x43813),x43814))
% 162.26/162.06 [4461]E(f331(f331(f270(f884(x44611),f884(x44611),f890(f884(x44611),f884(x44611))),f331(f331(f18(f884(x44611),f891(f884(x44611),f890(f884(x44611),f884(x44611))),f891(f884(x44611),f890(f884(x44611),f884(x44611)))),f331(f331(f8(f891(f884(x44611),f891(f890(f884(x44611),f884(x44611)),f890(f884(x44611),f884(x44611)))),f891(f891(f884(x44611),f890(f884(x44611),f884(x44611))),f891(f884(x44611),f890(f884(x44611),f884(x44611)))),f884(x44611)),f18(f884(x44611),f890(f884(x44611),f884(x44611)),f890(f884(x44611),f884(x44611)))),f331(f331(f8(f891(f884(x44611),f890(f884(x44611),f884(x44611))),f891(f884(x44611),f891(f890(f884(x44611),f884(x44611)),f890(f884(x44611),f884(x44611)))),f884(x44611)),f331(f8(f890(f884(x44611),f884(x44611)),f891(f890(f884(x44611),f884(x44611)),f890(f884(x44611),f884(x44611))),f884(x44611)),f331(f102(f890(f884(x44611),f884(x44611))),f331(x44612,x44613)))),f331(f331(f8(f884(x44611),f891(f884(x44611),f890(f884(x44611),f884(x44611))),f884(x44611)),f261(f884(x44611),f884(x44611))),f331(f154(x44611),x44613))))),f331(f331(f7(f884(x44611),f891(f884(x44611),f884(x44611)),f891(f884(x44611),f890(f884(x44611),f884(x44611)))),f331(f331(f8(f891(f884(x44611),f890(f884(x44611),f884(x44611))),f891(f891(f884(x44611),f884(x44611)),f891(f884(x44611),f890(f884(x44611),f884(x44611)))),f884(x44611)),f8(f884(x44611),f890(f884(x44611),f884(x44611)),f884(x44611))),f261(f884(x44611),f884(x44611)))),f331(f154(x44611),x44613)))),f170(x44611,x44612,x44614)),f170(x44611,x44612,f331(f331(f154(x44611),x44613),x44614)))
% 162.26/162.06 [4467]E(f331(f145(f891(x44671,f887(x44672)),f890(x44671,x44672),f331(f7(f890(x44671,x44672),f891(x44671,f887(x44672)),f891(x44671,f887(x44672))),f331(f270(x44671,x44672,f891(f891(x44671,f887(x44672)),f891(x44671,f887(x44672)))),f331(f331(f7(x44671,f891(x44672,f887(x44672)),f891(x44672,f891(f891(x44671,f887(x44672)),f891(x44671,f887(x44672))))),f331(f331(f8(f891(f887(x44672),f891(f891(x44671,f887(x44672)),f891(x44671,f887(x44672)))),f891(f891(x44672,f887(x44672)),f891(x44672,f891(f891(x44671,f887(x44672)),f891(x44671,f887(x44672))))),x44671),f8(f887(x44672),f891(f891(x44671,f887(x44672)),f891(x44671,f887(x44672))),x44672)),f331(f331(f8(f891(f891(x44671,f887(x44672)),f891(f887(x44672),f891(x44671,f887(x44672)))),f891(f887(x44672),f891(f891(x44671,f887(x44672)),f891(x44671,f887(x44672)))),x44671),f7(f891(x44671,f887(x44672)),f887(x44672),f891(x44671,f887(x44672)))),f331(f7(f891(x44671,f887(x44672)),x44671,f891(f887(x44672),f891(x44671,f887(x44672)))),f73(x44671,f887(x44672)))))),f239(x44672)))),x44673),f331(f172(f890(x44671,x44672)),x44674)),f187(x44671,x44672,x44673,f331(f180(x44671,x44672),x44674)))
% 162.26/162.06 [3572]E(f331(f197(f882(x35721)),f331(f331(f331(f93(x35721),x35722),x35723),x35724)),f2(a883))
% 162.26/162.06 [3691]E(f331(f331(f176(x36911),x36912),f331(f331(f176(x36911),x36913),x36914)),f331(f331(f176(x36911),f331(f331(f251(a883),x36912),x36913)),x36914))
% 162.26/162.06 [3692]E(f331(f331(f141(x36921),x36922),f331(f331(f141(x36921),x36923),x36924)),f331(f331(f141(x36921),f331(f331(f81(a883),x36922),x36923)),x36924))
% 162.26/162.06 [3704]E(f331(f331(f137(x37041),f331(f331(f154(x37041),x37042),x37043)),x37044),f331(f331(f154(x37041),x37042),f331(f331(f137(x37041),x37043),x37044)))
% 162.26/162.06 [3705]E(f331(f331(f137(x37051),f331(f331(f137(x37051),x37052),x37053)),x37054),f331(f331(f137(x37051),x37052),f331(f331(f137(x37051),x37053),x37054)))
% 162.26/162.06 [3782]E(f331(f331(f168(x37821),f331(f331(f154(x37821),x37822),x37823)),x37824),f193(x37821,x37822,f331(f168(x37821),x37823),x37824))
% 162.26/162.06 [3790]E(f331(f331(f191(x37901,x37901),x37902),f331(f331(f191(x37901,x37901),x37903),x37904)),f331(f331(f191(x37901,x37901),f331(f331(f82(a883),x37903),x37902)),x37904))
% 162.26/162.06 [3819]E(f331(f331(f107(f891(x38191,a877)),x38192),f331(f331(f309(x38191),x38193),x38194)),f331(f331(f309(x38191),x38193),f331(f331(f107(f891(x38191,a877)),x38192),x38194)))
% 162.26/162.06 [3834]E(f331(f331(f331(f191(x38341,x38341),x38342),x38343),f331(x38343,x38344)),f331(x38343,f331(f331(f331(f191(x38341,x38341),x38342),x38343),x38344)))
% 162.26/162.06 [3839]E(f331(f331(f288(x38391,x38392,x38393),f196(f891(f890(x38391,x38392),a877))),x38394),f196(f891(f890(x38391,x38393),a877)))
% 162.26/162.06 [3855]E(f331(f331(f107(f891(x38551,a877)),f331(f331(f309(x38551),x38552),x38553)),x38554),f331(f331(f309(x38551),x38552),f331(f331(f107(f891(x38551,a877)),x38553),x38554)))
% 162.26/162.06 [3872]E(f187(x38721,x38722,f331(f180(x38721,x38722),x38723),f331(f180(x38721,x38722),x38724)),f331(f180(x38721,x38722),f331(f331(f137(f890(x38721,x38722)),x38724),x38723)))
% 162.26/162.06 [3873]E(f331(f38(f890(x38731,x38732)),f331(f331(f268(x38731,x38732),x38733),f331(f16(f891(x38732,a877),x38731),x38734))),f331(f331(f82(a883),f331(f38(x38731),x38733)),f331(f38(x38732),x38734)))
% 162.26/162.06 [3879]E(f331(f331(f108(f891(x38791,a877)),f331(f331(f309(x38791),x38792),x38793)),f331(f331(f309(x38791),x38792),x38794)),f331(f331(f309(x38791),x38792),f331(f331(f108(f891(x38791,a877)),x38793),x38794)))
% 162.26/162.06 [3892]E(f331(f331(f107(f891(x38921,a877)),x38922),f331(f331(f107(f891(x38921,a877)),x38923),x38924)),f331(f331(f107(f891(x38921,a877)),x38923),f331(f331(f107(f891(x38921,a877)),x38922),x38924)))
% 162.26/162.06 [3893]E(f331(f331(f108(f891(x38931,a877)),x38932),f331(f331(f108(f891(x38931,a877)),x38933),x38934)),f331(f331(f108(f891(x38931,a877)),x38933),f331(f331(f108(f891(x38931,a877)),x38932),x38934)))
% 162.26/162.06 [3902]E(f65(x39021,x39022,f331(f331(f8(x39022,f891(x39022,x39022),x39021),x39023),x39024)),f331(f66(x39022,x39021,x39023),x39024))
% 162.26/162.06 [3912]E(f182(x39121,f331(f331(f157(f884(x39122),f884(x39121)),f331(f157(x39122,x39121),x39123)),x39124)),f331(f331(f157(f884(x39122),f884(x39121)),f331(f157(x39122,x39121),x39123)),f182(x39122,x39124)))
% 162.26/162.06 [3929]E(f331(f145(f884(x39291),f884(x39291),f137(x39291),f119(x39291)),f331(f331(f157(x39292,f884(x39291)),x39293),x39294)),f167(x39292,x39291,x39293,x39294))
% 162.26/162.06 [3932]E(f190(x39321,x39322,x39323,f331(f80(f891(x39321,a877)),f331(f331(f309(x39321),x39324),f196(f891(x39321,a877))))),f331(f331(f331(f73(x39321,f887(x39322)),x39323),x39324),f199(x39322)))
% 162.26/162.06 [3975]E(f331(f331(f331(f73(x39751,f887(x39752)),f331(f180(x39751,x39752),x39753)),f331(f260(x39751,x39752),x39754)),f331(f239(x39752),f331(f269(x39751,x39752),x39754))),f331(f180(x39751,x39752),f331(f331(f154(f890(x39751,x39752)),x39754),x39753)))
% 162.26/162.06 [3992]E(f331(f74(x39921,x39921,x39921,f331(f331(f191(x39921,x39921),x39922),x39923)),f331(f331(f191(x39921,x39921),x39924),x39923)),f331(f331(f191(x39921,x39921),f331(f331(f81(a883),x39922),x39924)),x39923))
% 162.26/162.06 [4014]E(f331(f331(f108(f891(x40141,a877)),f331(f331(f22(f891(x40141,a877)),x40142),x40143)),f331(f331(f22(f891(x40141,a877)),x40142),x40144)),f331(f331(f22(f891(x40141,a877)),x40142),f331(f331(f107(f891(x40141,a877)),x40143),x40144)))
% 162.26/162.06 [4015]E(f331(f331(f107(f891(x40151,a877)),f331(f331(f22(f891(x40151,a877)),x40152),x40153)),f331(f331(f22(f891(x40151,a877)),x40152),x40154)),f331(f331(f22(f891(x40151,a877)),x40152),f331(f331(f108(f891(x40151,a877)),x40153),x40154)))
% 162.26/162.06 [4016]E(f331(f331(f108(f891(x40161,a877)),f331(f331(f107(f891(x40161,a877)),x40162),x40163)),f331(f331(f107(f891(x40161,a877)),x40162),x40164)),f331(f331(f107(f891(x40161,a877)),x40162),f331(f331(f108(f891(x40161,a877)),x40163),x40164)))
% 162.26/162.06 [4017]E(f331(f331(f22(f891(x40171,a877)),f331(f331(f108(f891(x40171,a877)),x40172),x40173)),f331(f331(f108(f891(x40171,a877)),x40172),x40174)),f331(f331(f108(f891(x40171,a877)),x40172),f331(f331(f22(f891(x40171,a877)),x40173),x40174)))
% 162.26/162.06 [4018]E(f331(f331(f107(f891(x40181,a877)),f331(f331(f108(f891(x40181,a877)),x40182),x40183)),f331(f331(f108(f891(x40181,a877)),x40182),x40184)),f331(f331(f108(f891(x40181,a877)),x40182),f331(f331(f107(f891(x40181,a877)),x40183),x40184)))
% 162.26/162.06 [4024]E(f331(f38(f890(x40241,x40242)),f331(f331(f268(x40241,x40242),f331(f331(f309(x40241),x40243),f196(f891(x40241,a877)))),f331(f16(f891(x40242,a877),x40241),x40244))),f331(f38(x40242),x40244))
% 162.26/162.06 [4059]E(f331(f331(f43(x40591,f891(x40592,a877)),x40593),f331(f331(f8(f891(x40592,a877),f891(x40592,a877),x40591),f80(f891(x40592,a877))),x40594)),f331(f80(f891(x40592,a877)),f331(f331(f42(x40591,f891(x40592,a877)),x40593),x40594)))
% 162.26/162.06 [4060]E(f331(f331(f42(x40601,f891(x40602,a877)),x40603),f331(f331(f8(f891(x40602,a877),f891(x40602,a877),x40601),f80(f891(x40602,a877))),x40604)),f331(f80(f891(x40602,a877)),f331(f331(f43(x40601,f891(x40602,a877)),x40603),x40604)))
% 162.26/162.06 [4072]E(f331(f331(f288(x40721,x40721,x40721),f331(f331(f191(f890(x40721,x40721),a877),x40722),x40723)),f331(f331(f191(f890(x40721,x40721),a877),x40724),x40723)),f331(f331(f191(f890(x40721,x40721),a877),f331(f331(f81(a883),x40722),x40724)),x40723))
% 162.26/162.06 [4103]E(f331(f331(f43(x41031,f891(f891(x41032,a877),a877)),x41033),f331(f331(f8(f891(x41032,a877),f891(f891(x41032,a877),a877),x41031),f308(x41032)),x41034)),f331(f308(x41032),f331(f331(f43(x41031,f891(x41032,a877)),x41033),x41034)))
% 162.26/162.06 [4130]E(f331(f331(f42(f891(x41301,a877),f891(x41302,a877)),x41303),f331(f331(f7(f891(x41301,a877),f891(x41301,f891(x41302,a877)),f891(x41302,a877)),f42(x41301,f891(x41302,a877))),x41304)),f331(f331(f42(x41301,f891(x41302,a877)),f40(f891(x41301,a877),x41303)),x41304))
% 162.26/162.06 [4131]E(f331(f331(f43(f891(x41311,a877),f891(x41312,a877)),x41313),f331(f331(f7(f891(x41311,a877),f891(x41311,f891(x41312,a877)),f891(x41312,a877)),f43(x41311,f891(x41312,a877))),x41314)),f331(f331(f43(x41311,f891(x41312,a877)),f40(f891(x41311,a877),x41313)),x41314))
% 162.26/162.06 [4134]E(f331(f331(f157(x41341,x41342),x41343),f331(f145(f884(x41341),f884(x41341),f137(x41341),f119(x41341)),x41344)),f331(f145(f884(x41342),f884(x41342),f137(x41342),f119(x41342)),f331(f331(f157(f884(x41341),f884(x41342)),f331(f157(x41341,x41342),x41343)),x41344)))
% 162.26/162.06 [4138]E(f193(f884(x41381),f119(x41381),f331(f331(f8(f884(x41381),f884(x41381),a883),f331(f154(x41381),x41382)),f331(f331(f7(a883,f884(x41381),f884(x41381)),f176(x41381)),x41383)),x41384),f331(f331(f176(x41381),x41384),f331(f331(f154(x41381),x41382),x41383)))
% 162.26/162.06 [4178]P24(f331(f331(f247(f891(x41781,a877)),f331(f310(x41782,x41781,x41783),f331(f311(x41782,x41781,x41783),x41784))),x41784))
% 162.26/162.06 [4181]E(f331(f310(f890(x41811,x41812),f890(x41812,x41811),f331(f270(x41811,x41812,f890(x41812,x41811)),f331(f7(x41812,x41811,f890(x41812,x41811)),f261(x41812,x41811)))),f331(f331(f268(x41811,x41812),x41813),f331(f16(f891(x41812,a877),x41811),x41814))),f331(f331(f268(x41812,x41811),x41814),f331(f16(f891(x41811,a877),x41812),x41813)))
% 162.26/162.06 [4190]E(f331(f331(f42(x41901,f891(x41902,a877)),x41903),f331(f331(f8(f891(x41901,a877),f891(x41902,a877),x41901),f285(x41901,x41902,x41904)),f331(f331(f7(x41901,f891(x41901,a877),f891(x41901,a877)),f309(x41901)),f196(f891(x41901,a877))))),f331(f285(x41901,x41902,x41904),x41903))
% 162.26/162.06 [4191]E(f331(f331(f42(x41911,f891(x41912,a877)),x41913),f331(f331(f8(f891(x41911,a877),f891(x41912,a877),x41911),f311(x41912,x41911,x41914)),f331(f331(f7(x41911,f891(x41911,a877),f891(x41911,a877)),f309(x41911)),f196(f891(x41911,a877))))),f331(f311(x41912,x41911,x41914),x41913))
% 162.26/162.06 [4286]E(f331(f331(f108(f891(x42861,a877)),f331(f331(f108(f891(x42861,a877)),f331(f331(f107(f891(x42861,a877)),x42862),x42863)),f331(f331(f107(f891(x42861,a877)),x42863),x42864))),f331(f331(f107(f891(x42861,a877)),x42864),x42862)),f331(f331(f107(f891(x42861,a877)),f331(f331(f107(f891(x42861,a877)),f331(f331(f108(f891(x42861,a877)),x42862),x42863)),f331(f331(f108(f891(x42861,a877)),x42863),x42864))),f331(f331(f108(f891(x42861,a877)),x42864),x42862)))
% 162.26/162.06 [4348]E(f331(f145(f884(x43481),f884(x43481),f137(x43481),f119(x43481)),f331(f331(f157(x43482,f884(x43481)),f331(f331(f7(x43482,f884(x43481),f884(x43481)),f331(f331(f8(x43481,f891(f884(x43481),f884(x43481)),x43482),f154(x43481)),x43483)),f119(x43481))),x43484)),f331(f331(f157(x43482,x43481),x43483),x43484))
% 162.26/162.06 [4364]E(f331(f331(f89(a1,x43641),f331(f110(a1),f331(f331(f81(a1),x43642),a103))),f331(f331(f18(a1,x43641,x43641),f331(f331(f7(a1,x43641,f891(x43641,x43641)),f331(f331(f8(a877,f891(x43641,f891(x43641,x43641)),a1),f102(x43641)),a202)),x43643)),f331(f331(f8(a883,x43641,a1),x43644),a111))),f193(x43641,x43643,x43644,f331(f110(a883),x43642)))
% 162.26/162.06 [4583]~P24(f331(f331(f196(f891(x45831,f891(x45832,a877))),x45833),x45834))
% 162.26/162.06 [3842]E(f331(f331(f168(x38421),f331(f331(f137(x38421),x38422),x38423)),f331(f331(f81(a883),f331(f197(f884(x38421)),x38422)),x38424)),f331(f331(f168(x38421),x38423),x38424))
% 162.26/162.06 [3848]E(f331(f331(f141(x38481),x38482),f331(f331(f176(x38481),f331(f331(f81(a883),x38483),x38482)),x38484)),f331(f331(f176(x38481),x38483),f331(f331(f141(x38481),x38482),x38484)))
% 162.26/162.06 [3947]E(f331(f331(f107(f891(x39471,a877)),f331(f257(x39472,x39471),x39473)),f331(f257(x39472,x39471),x39474)),f331(f257(x39472,x39471),f331(f331(f107(f891(f890(x39472,x39471),a877)),x39473),x39474)))
% 162.26/162.06 [3948]E(f331(f331(f107(f891(x39481,a877)),f331(f259(x39481,x39482),x39483)),f331(f259(x39481,x39482),x39484)),f331(f259(x39481,x39482),f331(f331(f107(f891(f890(x39481,x39482),a877)),x39483),x39484)))
% 162.26/162.06 [3952]E(f331(f331(f22(f891(x39521,a877)),f331(f331(f108(f891(x39521,a877)),x39522),x39523)),x39524),f331(f331(f108(f891(x39521,a877)),x39522),f331(f331(f22(f891(x39521,a877)),x39523),x39524)))
% 162.26/162.06 [3953]E(f331(f331(f107(f891(x39531,a877)),f331(f331(f107(f891(x39531,a877)),x39532),x39533)),x39534),f331(f331(f107(f891(x39531,a877)),x39532),f331(f331(f107(f891(x39531,a877)),x39533),x39534)))
% 162.26/162.06 [3954]E(f331(f331(f108(f891(x39541,a877)),f331(f331(f108(f891(x39541,a877)),x39542),x39543)),x39544),f331(f331(f108(f891(x39541,a877)),x39542),f331(f331(f108(f891(x39541,a877)),x39543),x39544)))
% 162.26/162.06 [3994]E(f331(f331(f107(f891(f890(x39941,x39942),a877)),f331(f286(x39942,x39941),x39943)),f331(f286(x39942,x39941),x39944)),f331(f286(x39942,x39941),f331(f331(f107(f891(f890(x39942,x39941),a877)),x39943),x39944)))
% 162.26/162.06 [3995]E(f331(f331(f108(f891(f890(x39951,x39952),a877)),f331(f286(x39952,x39951),x39953)),f331(f286(x39952,x39951),x39954)),f331(f286(x39952,x39951),f331(f331(f108(f891(f890(x39952,x39951),a877)),x39953),x39954)))
% 162.26/162.06 [4062]E(f331(f331(f107(f891(x40621,a877)),f331(f331(f22(f891(x40621,a877)),x40622),x40623)),f331(f331(f22(f891(x40621,a877)),x40624),x40623)),f331(f331(f22(f891(x40621,a877)),f331(f331(f107(f891(x40621,a877)),x40622),x40624)),x40623))
% 162.26/162.06 [4063]E(f331(f331(f108(f891(x40631,a877)),f331(f331(f107(f891(x40631,a877)),x40632),x40633)),f331(f331(f107(f891(x40631,a877)),x40634),x40633)),f331(f331(f107(f891(x40631,a877)),f331(f331(f108(f891(x40631,a877)),x40632),x40634)),x40633))
% 162.26/162.06 [4064]E(f331(f331(f22(f891(x40641,a877)),f331(f331(f108(f891(x40641,a877)),x40642),x40643)),f331(f331(f108(f891(x40641,a877)),x40644),x40643)),f331(f331(f108(f891(x40641,a877)),f331(f331(f22(f891(x40641,a877)),x40642),x40644)),x40643))
% 162.26/162.06 [4065]E(f331(f331(f107(f891(x40651,a877)),f331(f331(f108(f891(x40651,a877)),x40652),x40653)),f331(f331(f108(f891(x40651,a877)),x40654),x40653)),f331(f331(f108(f891(x40651,a877)),f331(f331(f107(f891(x40651,a877)),x40652),x40654)),x40653))
% 162.26/162.06 [4066]E(f331(f331(f22(f891(x40661,a877)),f331(f331(f108(f891(x40661,a877)),x40662),x40663)),f331(f331(f108(f891(x40661,a877)),x40664),x40663)),f331(f331(f22(f891(x40661,a877)),f331(f331(f108(f891(x40661,a877)),x40662),x40663)),x40664))
% 162.26/162.06 [4075]E(f331(f331(f22(f891(x40751,a877)),f331(f331(f22(f891(x40751,a877)),x40752),f331(f331(f309(x40751),x40753),f196(f891(x40751,a877))))),x40754),f331(f331(f22(f891(x40751,a877)),x40752),f331(f331(f309(x40751),x40753),x40754)))
% 162.26/162.06 [4127]E(f331(f331(f107(f891(x41271,a877)),f331(f331(f309(x41271),x41272),f331(f331(f309(x41271),x41273),f196(f891(x41271,a877))))),f331(f284(x41271),x41274)),f331(f284(x41271),f331(f331(f309(f890(x41271,x41271)),f331(f331(f261(x41271,x41271),x41272),x41273)),x41274)))
% 162.26/162.06 [4153]E(f331(f331(f42(a883,f891(x41531,a877)),f331(f300(a883),x41532)),f331(f331(f8(a883,f891(x41531,a877),a883),x41533),f331(f331(f7(a883,a883,a883),f81(a883)),x41534))),f331(f331(f42(a883,f891(x41531,a877)),f302(a883,x41534,f331(f331(f81(a883),x41532),x41534))),x41533))
% 162.26/162.06 [4154]E(f178(x41541,f331(f285(x41541,x41541,x41542),f331(f331(f309(x41541),x41543),f196(f891(x41541,a877)))),f331(f285(f884(x41541),f884(x41541),f161(x41541,x41542)),f331(f331(f309(f884(x41541)),x41544),f196(f891(f884(x41541),a877))))),f331(f285(f884(x41541),f884(x41541),f161(x41541,x41542)),f331(f331(f309(f884(x41541)),f331(f331(f154(x41541),x41543),x41544)),f196(f891(f884(x41541),a877)))))
% 162.26/162.06 [4222]E(f331(f180(x42221,x42222),f331(f331(f157(x42221,f890(x42221,x42222)),f331(f331(f18(x42221,x42222,f890(x42221,x42222)),f261(x42221,x42222)),x42223)),x42224)),f190(x42221,x42222,f331(f74(x42222,f887(x42222),x42221,f239(x42222)),x42223),f331(f175(x42221),x42224)))
% 162.26/162.06 [4228]E(f331(f253(x42281),f331(f331(f7(x42281,f891(x42282,a877),a877),f331(f331(f8(x42282,f891(f891(x42282,a877),a877),x42281),f333(x42282)),x42283)),x42284)),f331(f311(x42281,x42282,x42283),x42284))
% 162.26/162.06 [4316]E(f331(f253(x43161),f331(f331(f7(x43161,f891(f890(x43162,x43161),a877),a877),f331(f331(f8(f890(x43162,x43161),f891(f891(f890(x43162,x43161),a877),a877),x43161),f333(f890(x43162,x43161))),f331(f261(x43162,x43161),x43163))),x43164)),f331(f285(x43162,x43161,x43164),f331(f331(f309(x43162),x43163),f196(f891(x43162,a877)))))
% 162.26/162.06 [4332]E(f331(f331(f157(f890(x43321,a883),x43321),f260(x43321,a883)),f331(f139(f890(x43321,a883),f331(f331(f8(a883,a877,f890(x43321,a883)),x43322),f331(f331(f8(a883,a883,f890(x43321,a883)),a118),f269(x43321,a883)))),f331(f331(f184(x43321,a883),x43323),x43324))),f331(f331(f157(f890(x43321,a883),x43321),f260(x43321,a883)),f331(f139(f890(x43321,a883),f331(f331(f8(a883,a877,f890(x43321,a883)),x43322),f269(x43321,a883))),f331(f331(f184(x43321,a883),x43323),f331(f331(f157(a883,a883),a118),x43324)))))
% 162.26/162.06 [4340]P24(f331(f331(f247(f891(f891(x43401,a877),a877)),f331(f331(f42(x43402,f891(f891(x43401,a877),a877)),x43403),f331(f331(f8(f891(x43401,a877),f891(f891(x43401,a877),a877),x43402),f308(x43401)),x43404))),f331(f308(x43401),f331(f331(f42(x43402,f891(x43401,a877)),x43403),x43404))))
% 162.26/162.06 [4386]E(f331(f331(f89(a1,x43861),f331(f110(a1),f331(f331(f81(a1),x43862),a103))),f331(f331(f18(a1,x43861,x43861),f331(f331(f7(a1,x43861,f891(x43861,x43861)),f331(f331(f8(a877,f891(x43861,f891(x43861,x43861)),a1),f102(x43861)),a202)),x43863)),f331(f331(f18(a1,x43861,x43861),f331(f331(f8(a883,f891(x43861,x43861),a1),x43864),a111)),f331(f331(f8(a883,x43861,a1),f192(x43861,x43863,x43864)),a111)))),f331(f192(x43861,x43863,x43864),f331(f110(a883),x43862)))
% 162.26/162.06 [4389]E(f331(f331(f157(x43891,x43892),f331(f74(f887(x43892),x43892,x43891,f244(x43892)),x43893)),f331(f139(x43891,f331(f331(f8(a877,a877,x43891),a326),f331(f331(f7(x43891,f887(x43892),a877),f331(f331(f8(f887(x43892),f891(f887(x43892),a877),x43891),a328),x43893)),f199(x43892)))),x43894)),f166(x43891,x43892,x43893,x43894))
% 162.26/162.06 [4418]E(f331(f253(f890(x44181,x44182)),f331(f270(x44181,x44182,a877),f331(f331(f7(x44181,f891(x44182,a877),f891(x44182,a877)),f331(f331(f8(f891(a877,a877),f891(f891(x44182,a877),f891(x44182,a877)),x44181),f8(a877,a877,x44182)),f331(f331(f8(a877,f891(a877,a877),x44181),a329),f331(f331(f7(x44181,f891(x44181,a877),a877),f333(x44181)),x44183)))),f331(f331(f7(x44182,f891(x44182,a877),a877),f333(x44182)),x44184)))),f234(x44181,x44182,x44183,x44184))
% 162.26/162.06 [4456]E(f331(f331(f42(x44561,f891(f890(x44561,x44562),a877)),x44563),f331(f331(f18(x44561,f891(x44562,f891(f890(x44561,x44562),a877)),f891(f890(x44561,x44562),a877)),f331(f331(f8(f891(x44562,a877),f891(f891(x44562,f891(f890(x44561,x44562),a877)),f891(f890(x44561,x44562),a877)),x44561),f42(x44562,f891(f890(x44561,x44562),a877))),x44564)),f331(f331(f7(x44561,f891(f890(x44561,x44562),a877),f891(x44562,f891(f890(x44561,x44562),a877))),f331(f331(f8(f891(x44562,f891(f891(f890(x44561,x44562),a877),f891(f890(x44561,x44562),a877))),f891(f891(f890(x44561,x44562),a877),f891(x44562,f891(f890(x44561,x44562),a877))),x44561),f7(x44562,f891(f890(x44561,x44562),a877),f891(f890(x44561,x44562),a877))),f331(f331(f8(f891(x44562,f890(x44561,x44562)),f891(x44562,f891(f891(f890(x44561,x44562),a877),f891(f890(x44561,x44562),a877))),x44561),f331(f8(f890(x44561,x44562),f891(f891(f890(x44561,x44562),a877),f891(f890(x44561,x44562),a877)),x44562),f309(f890(x44561,x44562)))),f261(x44561,x44562)))),f196(f891(f890(x44561,x44562),a877))))),f331(f331(f268(x44561,x44562),x44563),x44564))
% 162.26/162.06 [4003]E(f331(f331(f137(x40031),f331(f331(f176(x40031),x40032),x40033)),f331(f331(f176(x40031),f331(f331(f22(a883),x40032),f331(f197(f884(x40031)),x40033))),x40034)),f331(f331(f176(x40031),x40032),f331(f331(f137(x40031),x40033),x40034)))
% 162.26/162.06 [4004]E(f331(f331(f137(x40041),f331(f331(f141(x40041),x40042),x40043)),f331(f331(f141(x40041),f331(f331(f22(a883),x40042),f331(f197(f884(x40041)),x40043))),x40044)),f331(f331(f141(x40041),x40042),f331(f331(f137(x40041),x40043),x40044)))
% 162.26/162.06 [4053]E(f331(f331(f81(a883),f331(f331(f82(a883),x40531),x40532)),f331(f331(f81(a883),f331(f331(f82(a883),x40533),x40532)),x40534)),f331(f331(f81(a883),f331(f331(f82(a883),f331(f331(f81(a883),x40531),x40533)),x40532)),x40534))
% 162.26/162.06 [4249]P24(f331(f331(f247(f891(x42491,a877)),f331(f331(f22(f891(x42491,a877)),f331(f257(x42492,x42491),x42493)),f331(f257(x42492,x42491),x42494))),f331(f257(x42492,x42491),f331(f331(f22(f891(f890(x42492,x42491),a877)),x42493),x42494))))
% 162.26/162.06 [4250]P24(f331(f331(f247(f891(x42501,a877)),f331(f331(f22(f891(x42501,a877)),f331(f259(x42501,x42502),x42503)),f331(f259(x42501,x42502),x42504))),f331(f259(x42501,x42502),f331(f331(f22(f891(f890(x42501,x42502),a877)),x42503),x42504))))
% 162.26/162.06 [4366]E(f331(f331(f81(a1),f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),x43661),x43662)),f196(f891(f890(a883,a883),a877)))))),f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),x43663),x43664)),f196(f891(f890(a883,a883),a877)))))),f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),f331(f331(f81(a883),x43661),x43663)),f331(f331(f81(a883),x43662),x43664))),f196(f891(f890(a883,a883),a877))))))
% 162.26/162.06 [4413]E(f331(f331(f82(a1),f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),x44131),x44132)),f196(f891(f890(a883,a883),a877)))))),f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),x44133),x44134)),f196(f891(f890(a883,a883),a877)))))),f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),f331(f331(f81(a883),f331(f331(f82(a883),x44131),x44133)),f331(f331(f82(a883),x44132),x44134))),f331(f331(f81(a883),f331(f331(f82(a883),x44131),x44134)),f331(f331(f82(a883),x44132),x44133)))),f196(f891(f890(a883,a883),a877))))))
% 162.26/162.06 [4439]E(f331(f253(x44391),f331(f331(f8(f891(x44392,a877),a877,x44391),f88(x44392)),f331(f331(f8(f891(x44392,a877),f891(x44392,a877),x44391),f331(f18(x44392,a877,a877),f331(f331(f8(a877,f891(a877,a877),x44392),a334),f331(f331(f7(x44392,f891(x44392,a877),a877),f333(x44392)),x44393)))),f331(f331(f7(x44391,f891(x44392,f891(x44391,a877)),f891(x44392,a877)),f331(f331(f8(f891(f891(x44391,a877),a877),f891(f891(x44392,f891(x44391,a877)),f891(x44392,a877)),x44391),f8(f891(x44391,a877),a877,x44392)),f333(x44391))),x44394)))),f331(f331(f43(x44392,f891(x44391,a877)),x44393),x44394))
% 162.26/162.06 [4471]E(f331(f331(f288(x44711,x44711,x44711),f331(f331(f309(f890(x44711,x44711)),f331(f331(f261(x44711,x44711),x44712),x44713)),x44714)),f307(x44711,f331(f331(f309(f890(x44711,x44711)),f331(f331(f261(x44711,x44711),x44712),x44713)),x44714))),f331(f331(f107(f891(f890(x44711,x44711),a877)),f331(f331(f288(x44711,x44711,x44711),x44714),f307(x44711,x44714))),f331(f253(f890(x44711,x44711)),f331(f270(x44711,x44711,a877),f331(f331(f7(x44711,f891(x44711,a877),f891(x44711,a877)),f331(f331(f8(f891(a877,a877),f891(f891(x44711,a877),f891(x44711,a877)),x44711),f8(a877,a877,x44711)),f331(f331(f8(a877,f891(a877,a877),x44711),a329),f331(f331(f7(x44711,f891(f890(x44711,x44711),a877),a877),f331(f331(f8(f890(x44711,x44711),f891(f891(f890(x44711,x44711),a877),a877),x44711),f333(f890(x44711,x44711))),f331(f331(f7(x44711,x44711,f890(x44711,x44711)),f261(x44711,x44711)),x44712))),f307(x44711,x44714))))),f331(f331(f7(x44711,f891(f890(x44711,x44711),a877),a877),f331(f331(f8(f890(x44711,x44711),f891(f891(f890(x44711,x44711),a877),a877),x44711),f333(f890(x44711,x44711))),f331(f261(x44711,x44711),x44713))),f307(x44711,x44714)))))))
% 162.26/162.06 [4251]E(f331(f139(x42511,f331(f331(f18(x42511,a877,a877),f331(f331(f8(a877,f891(a877,a877),x42511),a329),x42512)),x42513)),x42514),f331(f139(x42511,x42513),f331(f139(x42511,x42512),x42514)))
% 162.26/162.06 [4360]E(f331(f331(f137(x43601),f331(f331(f331(f102(f884(x43601)),f331(f331(f333(a883),f2(a883)),x43602)),f331(f331(f154(x43601),x43603),f119(x43601))),f119(x43601))),f177(x43601,x43604,f331(f253(a883),f331(f331(f7(a883,f891(a883,a877),a877),f331(f331(f8(a883,f891(f891(a883,a877),a877),a883),f333(a883)),a118)),x43602)))),f177(x43601,f331(f331(f154(x43601),x43603),x43604),x43602))
% 162.26/162.06 [4465]E(f331(f253(f890(x44651,x44652)),f331(f331(f8(f891(a883,a877),a877,f890(x44651,x44652)),f87(a883)),f331(f331(f7(f890(x44651,x44652),f891(a883,a877),f891(a883,a877)),f331(f331(f8(f891(a883,f891(a877,a877)),f891(f891(a883,a877),f891(a883,a877)),f890(x44651,x44652)),f18(a883,a877,a877)),f331(f331(f8(f891(a883,a877),f891(a883,f891(a877,a877)),f890(x44651,x44652)),f331(f8(a877,f891(a877,a877),a883),a329)),f331(f331(f7(f890(x44651,x44652),f891(a883,f890(x44651,x44652)),f891(a883,a877)),f331(f331(f8(f891(f890(x44651,x44652),a877),f891(f891(a883,f890(x44651,x44652)),f891(a883,a877)),f890(x44651,x44652)),f8(f890(x44651,x44652),a877,a883)),a328)),f331(f331(f18(a883,x44652,f890(x44651,x44652)),f331(f331(f8(x44651,f891(x44652,f890(x44651,x44652)),a883),f261(x44651,x44652)),f331(f168(x44651),x44653))),f331(f168(x44652),x44654)))))),f331(f331(f7(a883,a883,a877),f248(a883)),f331(f331(f251(a883),f331(f197(f884(x44651)),x44653)),f331(f197(f884(x44652)),x44654)))))),f331(f175(f890(x44651,x44652)),f331(f331(f184(x44651,x44652),x44653),x44654)))
% 162.26/162.06 [4379]E(f331(f253(f890(x43791,x43792)),f331(f270(x43791,x43792,a877),f331(f331(f7(x43791,f891(x43792,a877),f891(x43792,a877)),f331(f331(f8(f891(a877,a877),f891(f891(x43792,a877),f891(x43792,a877)),x43791),f8(a877,a877,x43792)),f331(f331(f8(a877,f891(a877,a877),x43791),a329),x43793))),x43794))),f331(f331(f268(x43791,x43792),f331(f253(x43791),x43793)),f331(f16(f891(x43792,a877),x43791),f331(f253(x43792),x43794))))
% 162.26/162.06 [4382]E(f331(f253(f890(x43821,x43822)),f331(f270(x43821,x43822,a877),f331(f331(f18(x43821,f891(x43822,a877),f891(x43822,a877)),f331(f331(f8(f891(a877,a877),f891(f891(x43822,a877),f891(x43822,a877)),x43821),f8(a877,a877,x43822)),f331(f331(f8(a877,f891(a877,a877),x43821),a329),x43823))),x43824))),f331(f331(f268(x43821,x43822),f331(f253(x43821),x43823)),f331(f331(f8(f891(x43822,a877),f891(x43822,a877),x43821),f253(x43822)),x43824)))
% 162.26/162.06 [4396]E(f331(f253(x43961),f331(f331(f8(f891(x43962,a877),a877,x43961),f88(x43962)),f331(f331(f8(f891(x43962,a877),f891(x43962,a877),x43961),f331(f18(x43962,a877,a877),f331(f331(f8(a877,f891(a877,a877),x43962),a334),f331(f331(f7(x43962,f891(x43962,a877),a877),f333(x43962)),x43963)))),x43964))),f331(f331(f43(x43962,f891(x43961,a877)),x43963),f331(f331(f8(f891(x43961,a877),f891(x43961,a877),x43962),f253(x43961)),f331(f7(x43961,x43962,a877),x43964))))
% 162.26/162.06 [4451]E(f331(f331(f157(f890(x44511,a883),x44511),f260(x44511,a883)),f331(f139(f890(x44511,a883),f331(f331(f7(f890(x44511,a883),f891(a883,a877),a877),f331(f331(f8(a883,f891(f891(a883,a877),a877),f890(x44511,a883)),f333(a883)),f269(x44511,a883))),x44512)),f331(f331(f184(x44511,a883),x44513),f142(a883,f331(f301(a883,x44514),f331(f331(f81(a883),x44514),f331(f197(f884(x44511)),x44513))))))),f331(f331(f157(f890(x44511,a883),x44511),f260(x44511,a883)),f331(f139(f890(x44511,a883),f331(f331(f7(f890(x44511,a883),f891(a883,a877),a877),f331(f331(f8(a883,f891(f891(a883,a877),a877),f890(x44511,a883)),f333(a883)),f331(f331(f7(f890(x44511,a883),a883,a883),f331(f331(f8(a883,f891(a883,a883),f890(x44511,a883)),f81(a883)),f269(x44511,a883))),x44514))),x44512)),f331(f331(f184(x44511,a883),x44513),f142(a883,f331(f301(a883,f2(a883)),f331(f197(f884(x44511)),x44513)))))))
% 162.26/162.06 [4452]E(f331(a118,f331(f331(f246(a883),f331(f197(f884(x44521)),x44522)),f331(f145(a883,f884(x44523),f331(f7(f884(x44523),a883,a883),f331(f331(f8(a883,f891(a883,a883),f884(x44523)),f246(a883)),f331(f331(f7(f884(x44523),a883,a883),f331(f331(f8(a883,f891(a883,a883),f884(x44523)),f22(a883)),f197(f884(x44523)))),f331(a118,f2(a883))))),f2(a883)),f331(f172(f884(x44523)),f331(f139(f884(x44523),f331(f331(f8(a877,a877,f884(x44523)),a326),f331(f331(f7(f884(x44523),f884(x44523),a877),a328),f119(x44523)))),x44524))))),f331(f331(f246(a883),f331(a118,f331(f197(f884(x44521)),x44522))),f331(f145(a883,f884(x44523),f331(f7(f884(x44523),a883,a883),f331(f331(f8(a883,f891(a883,a883),f884(x44523)),f246(a883)),f197(f884(x44523)))),f2(a883)),f331(f172(f884(x44523)),x44524))))
% 162.26/162.06 [4395]E(f331(f331(f137(x43951),f177(x43951,x43952,x43953)),f177(x43951,x43954,f331(f253(a883),f331(f331(f7(a883,f891(a883,a877),a877),f331(f331(f8(a883,f891(f891(a883,a877),a877),a883),f333(a883)),f331(f331(f7(a883,a883,a883),f81(a883)),f331(f197(f884(x43951)),x43952)))),x43953)))),f177(x43951,f331(f331(f137(x43951),x43952),x43954),x43953))
% 162.26/162.06 [4458]E(f331(f331(f154(f884(x44581)),f331(f331(f154(x44581),x44582),f331(f145(f884(x44581),f884(x44581),f137(x44581),f119(x44581)),f331(f331(f157(f884(x44581),f884(x44581)),f159(f884(x44581),x44581,f119(x44581),f331(f331(f8(f884(x44581),f891(f884(x44581),f884(x44581)),x44581),f16(f884(x44581),f884(x44581))),f331(f331(f7(x44581,f884(x44581),f884(x44581)),f154(x44581)),f119(x44581))))),x44583)))),f182(x44581,f331(f331(f154(f884(x44581)),x44584),f331(f145(f884(f884(x44581)),f884(f884(x44581)),f137(f884(x44581)),f119(f884(x44581))),f331(f331(f157(f884(x44581),f884(f884(x44581))),f159(f884(f884(x44581)),x44581,f119(f884(x44581)),f331(f16(f891(f884(x44581),f884(f884(x44581))),x44581),f331(f331(f7(f884(x44581),f884(f884(x44581)),f884(f884(x44581))),f154(f884(x44581))),f119(f884(x44581)))))),x44583))))),f182(x44581,f331(f331(f154(f884(x44581)),f331(f331(f154(x44581),x44582),x44584)),x44583)))
% 162.26/162.06 [4466]E(f331(f253(f890(x44661,x44661)),f331(f270(x44661,x44661,a877),f331(f331(f7(x44661,f891(f890(x44662,x44662),a877),f891(x44661,a877)),f331(f331(f8(f891(x44661,f891(f891(f890(x44662,x44662),a877),a877)),f891(f891(f890(x44662,x44662),a877),f891(x44661,a877)),x44661),f7(x44661,f891(f890(x44662,x44662),a877),a877)),f331(f331(f8(f891(x44661,f890(x44662,x44662)),f891(x44661,f891(f891(f890(x44662,x44662),a877),a877)),x44661),f331(f8(f890(x44662,x44662),f891(f891(f890(x44662,x44662),a877),a877),x44661),f333(f890(x44662,x44662)))),f331(f331(f7(x44661,f891(x44661,x44662),f891(x44661,f890(x44662,x44662))),f331(f331(f8(f891(x44662,f890(x44662,x44662)),f891(f891(x44661,x44662),f891(x44661,f890(x44662,x44662))),x44661),f8(x44662,f890(x44662,x44662),x44661)),f331(f331(f8(x44662,f891(x44662,f890(x44662,x44662)),x44661),f261(x44662,x44662)),x44663))),x44663)))),x44664))),f331(f331(f287(x44662,x44661),x44664),x44663))
% 162.26/162.06 [4527]~E(f34(x45271,x45272),f29(x45273,x45274,x45275))
% 162.26/162.06 [4528]~E(f34(x45281,x45282),f31(x45283,x45284,x45285))
% 162.26/162.06 [4529]~E(f34(x45291,x45292),f30(x45293,x45294,x45295))
% 162.26/162.06 [4530]~E(f33(x45301,x45302),f29(x45303,x45304,x45305))
% 162.26/162.06 [4531]~E(f33(x45311,x45312),f31(x45313,x45314,x45315))
% 162.26/162.06 [4532]~E(f33(x45321,x45322),f30(x45323,x45324,x45325))
% 162.26/162.06 [4533]~E(f29(x45331,x45332,x45333),f34(x45334,x45335))
% 162.26/162.06 [4534]~E(f29(x45341,x45342,x45343),f33(x45344,x45345))
% 162.26/162.06 [4535]~E(f31(x45351,x45352,x45353),f34(x45354,x45355))
% 162.26/162.06 [4536]~E(f31(x45361,x45362,x45363),f33(x45364,x45365))
% 162.26/162.06 [4537]~E(f30(x45371,x45372,x45373),f34(x45374,x45375))
% 162.26/162.06 [4538]~E(f30(x45381,x45382,x45383),f33(x45384,x45385))
% 162.26/162.06 [3945]E(f331(f187(x39451,x39452,x39453,x39454),x39455),f331(f242(f887(x39452),x39452,f331(x39453,x39455),f239(x39452)),f331(x39454,x39455)))
% 162.26/162.06 [4029]E(f187(x40291,x40292,f187(x40291,x40292,x40293,x40294),x40295),f187(x40291,x40292,x40293,f187(x40291,x40292,x40294,x40295)))
% 162.26/162.06 [4204]E(f331(f331(f107(f891(x42041,a877)),f331(f175(x42041),f331(f331(f176(x42041),f331(f197(f884(x42042)),x42043)),x42044))),f186(x42041,x42042,x42045)),f186(x42041,x42042,f189(x42041,x42042,x42045,x42044,x42043)))
% 162.26/162.06 [3778]E(f331(f331(f270(x37781,x37782,x37783),x37784),x37785),f331(f331(x37784,f331(f260(x37781,x37782),x37785)),f331(f269(x37781,x37782),x37785)))
% 162.26/162.06 [3802]E(f331(f242(x38021,x38022,x38023,x38024),f331(f239(x38022),x38025)),f331(x38024,x38025))
% 162.26/162.06 [3811]E(f331(f331(f331(f66(x38111,x38112,x38113),x38114),x38115),f196(f891(x38112,a877))),x38115)
% 162.26/162.06 [3976]E(f243(x39761,x39762,x39763,x39764,f331(f239(x39762),x39765)),f331(x39764,x39765))
% 162.26/162.06 [4081]E(f331(f74(f887(x40811),f887(x40812),f887(x40813),f331(f210(x40811,x40812),x40814)),f331(f210(x40813,x40811),x40815)),f331(f210(x40813,x40812),f331(f74(x40811,x40812,x40813,x40814),x40815)))
% 162.26/162.06 [4083]E(f331(f74(f884(x40831),f884(x40832),f884(x40833),f331(f157(x40831,x40832),x40834)),f331(f157(x40833,x40831),x40835)),f331(f157(x40833,x40832),f331(f74(x40831,x40832,x40833,x40834),x40835)))
% 162.26/162.06 [4135]E(f331(f242(x41351,f890(x41352,f885(x41352)),x41353,f331(f270(x41352,f885(x41352),x41351),x41354)),f331(f138(x41352),x41355)),f133(x41351,x41352,x41353,x41354,x41355))
% 162.26/162.06 [4155]E(f86(x41551,f67(x41552,x41551,x41553,x41554,x41555)),f331(f331(f65(x41552,x41551,x41553),x41554),x41555))
% 162.26/162.06 [4192]E(f331(f331(f81(a883),f331(f331(f81(a883),f331(x41921,f331(f260(x41922,x41923),x41924))),f331(x41925,f331(f269(x41922,x41923),x41924)))),f331(a118,f2(a883))),f274(x41922,x41923,x41921,x41925,x41924))
% 162.26/162.06 [4391]E(f166(x43911,x43912,f331(f331(f7(x43911,f887(x43912),f887(x43912)),f331(f331(f18(x43911,f887(x43912),f891(f887(x43912),f887(x43912))),f331(f331(f8(a877,f891(f887(x43912),f891(f887(x43912),f887(x43912))),x43911),f102(f887(x43912))),x43913)),f331(f331(f8(x43912,f887(x43912),x43911),f239(x43912)),x43914))),f199(x43912)),x43915),f331(f331(f157(x43911,x43912),x43914),f331(f139(x43911,x43913),x43915)))
% 162.26/162.06 [4575]~E(f331(f331(f331(f73(x45751,f887(x45752)),x45753),x45754),f331(f239(x45752),x45755)),f331(f16(f887(x45752),x45751),f199(x45752)))
% 162.26/162.06 [3716]E(f331(f331(f176(x37161),x37162),f331(f331(f157(x37163,x37161),x37164),x37165)),f331(f331(f157(x37163,x37161),x37164),f331(f331(f176(x37163),x37162),x37165)))
% 162.26/162.06 [3717]E(f331(f331(f141(x37171),x37172),f331(f331(f157(x37173,x37171),x37174),x37175)),f331(f331(f157(x37173,x37171),x37174),f331(f331(f141(x37173),x37172),x37175)))
% 162.26/162.06 [3742]E(f331(f331(f157(x37421,x37422),x37423),f331(f331(f154(x37421),x37424),x37425)),f331(f331(f154(x37422),f331(x37423,x37424)),f331(f331(f157(x37421,x37422),x37423),x37425)))
% 162.26/162.06 [3806]E(f331(f310(x38061,x38062,x38063),f331(f331(f309(x38061),x38064),x38065)),f331(f331(f309(x38062),f331(x38063,x38064)),f331(f310(x38061,x38062,x38063),x38065)))
% 162.26/162.06 [3868]E(f331(f331(f184(x38681,x38682),f331(f331(f176(x38681),x38683),x38684)),f331(f331(f176(x38682),x38683),x38685)),f331(f331(f176(f890(x38681,x38682)),x38683),f331(f331(f184(x38681,x38682),x38684),x38685)))
% 162.26/162.06 [3869]E(f331(f331(f184(x38691,x38692),f331(f331(f141(x38691),x38693),x38694)),f331(f331(f141(x38692),x38693),x38695)),f331(f331(f141(f890(x38691,x38692)),x38693),f331(f331(f184(x38691,x38692),x38694),x38695)))
% 162.26/162.06 [3878]E(f331(f331(f162(x38781,f331(f331(f154(x38781),x38782),x38783)),f331(a118,x38784)),x38785),f331(f331(f154(x38781),x38782),f331(f331(f162(x38781,x38783),x38784),x38785)))
% 162.26/162.06 [3880]E(f331(f242(f887(x38801),x38802,f199(x38801),x38803),f331(f331(f16(f887(x38802),x38804),f199(x38802)),x38805)),f199(x38801))
% 162.26/162.06 [3882]E(f331(f331(f137(x38821),f331(f331(f157(x38822,x38821),x38823),x38824)),f331(f331(f157(x38822,x38821),x38823),x38825)),f331(f331(f157(x38822,x38821),x38823),f331(f331(f137(x38822),x38824),x38825)))
% 162.26/162.06 [3886]E(f331(f331(x38861,x38862),f331(f331(f263(x38863,x38864,x38861),x38862),x38865)),f331(f331(f263(x38863,x38864,x38861),x38862),f331(a118,x38865)))
% 162.26/162.06 [3915]E(f167(x39151,x39152,x39153,f331(f331(f154(x39151),x39154),x39155)),f331(f331(f137(x39152),f331(x39153,x39154)),f167(x39151,x39152,x39153,x39155)))
% 162.26/162.06 [3927]E(f331(f331(f288(x39271,x39272,x39273),f331(f286(x39272,x39271),x39274)),f331(f286(x39273,x39272),x39275)),f331(f286(x39273,x39271),f331(f331(f288(x39273,x39272,x39271),x39275),x39274)))
% 162.26/162.06 [3962]E(f331(f331(f331(f191(f884(x39621),f884(x39621)),x39622),f171(x39621)),f331(f331(f157(x39623,x39621),x39624),x39625)),f331(f331(f157(x39623,x39621),x39624),f331(f331(f331(f191(f884(x39623),f884(x39623)),x39622),f171(x39623)),x39625)))
% 162.26/162.06 [3963]E(f331(f331(f272(x39631,x39632,x39631,x39633),f331(f261(x39632,x39631),x39634)),x39635),f331(x39635,x39634))
% 162.26/162.06 [3990]E(f158(x39901,x39902,f331(f331(f157(x39903,x39901),x39904),x39905)),f158(x39903,f331(f74(x39901,a883,x39903,x39902),x39904),x39905))
% 162.26/162.06 [4051]E(f331(f331(f74(f887(x40511),f887(x40512),x40513,f331(f210(x40511,x40512),x40514)),f331(f16(f887(x40511),x40513),f199(x40511))),x40515),f199(x40512))
% 162.26/162.06 [4052]E(f179(f890(x40521,x40522),f331(f74(x40522,a877,f890(x40521,x40522),x40523),f269(x40521,x40522)),f331(f331(f184(x40521,x40522),x40524),x40525)),f331(f331(f184(x40521,x40522),x40524),f179(x40522,x40523,x40525)))
% 162.26/162.06 [4057]E(f331(f310(x40571,x40572,f331(f331(f8(x40573,x40572,x40571),x40574),x40575)),f256(f891(x40571,a877))),f331(f310(x40573,x40572,x40574),f331(f310(x40571,x40573,x40575),f256(f891(x40571,a877)))))
% 162.26/162.06 [4068]E(f179(f890(x40681,x40682),f331(f74(x40681,a877,f890(x40681,x40682),x40683),f260(x40681,x40682)),f331(f331(f184(x40681,x40682),x40684),x40685)),f331(f331(f184(x40681,x40682),f179(x40681,x40683,x40684)),x40685))
% 162.26/162.06 [4088]E(f331(f331(f107(f891(x40881,a877)),f331(f311(x40881,x40882,x40883),f331(f331(f309(x40882),x40884),f196(f891(x40882,a877))))),f331(f311(x40881,x40882,x40883),x40885)),f331(f311(x40881,x40882,x40883),f331(f331(f309(x40882),x40884),x40885)))
% 162.26/162.06 [4143]E(f331(f331(f137(f890(x41431,x41432)),f331(f331(f157(x41432,f890(x41431,x41432)),f331(f261(x41431,x41432),x41433)),x41434)),f60(x41431,x41432,x41435,x41434)),f60(x41431,x41432,f331(f331(f154(x41431),x41433),x41435),x41434))
% 162.26/162.06 [4144]E(f331(f331(f157(x41441,x41442),x41443),f179(x41441,f331(f74(x41442,a877,x41441,x41444),x41443),x41445)),f179(x41442,x41444,f331(f331(f157(x41441,x41442),x41443),x41445)))
% 162.26/162.06 [4150]E(f331(f145(x41501,x41502,f331(f7(x41502,x41501,x41501),f331(f7(x41501,x41502,x41501),x41503)),x41504),f331(f172(x41502),f331(f172(x41502),x41505))),f331(f145(x41501,x41502,x41503,x41504),x41505))
% 162.26/162.06 [4151]E(f331(f331(f331(f73(x41511,f887(x41512)),f190(x41511,x41512,x41513,x41514)),x41515),f331(x41513,x41515)),f190(x41511,x41512,x41513,f331(f331(f309(x41511),x41515),x41514)))
% 162.26/162.06 [4225]E(f331(f242(f884(x42251),x42251,f166(x42252,x42251,x42253,x42254),f331(f331(f7(x42251,f884(x42251),f884(x42251)),f154(x42251)),f166(x42252,x42251,x42253,x42254))),f331(x42253,x42255)),f166(x42252,x42251,x42253,f331(f331(f154(x42252),x42255),x42254)))
% 162.26/162.06 [4259]P24(f331(f331(f247(f891(x42591,a877)),f331(f310(x42592,x42591,x42593),f331(f331(f108(f891(x42592,a877)),x42594),x42595))),f331(f331(f108(f891(x42591,a877)),f331(f310(x42592,x42591,x42593),x42594)),f331(f310(x42592,x42591,x42593),x42595))))
% 162.26/162.06 [4260]P24(f331(f331(f247(f891(x42601,a877)),f331(f285(x42602,x42601,x42603),f331(f331(f108(f891(x42602,a877)),x42604),x42605))),f331(f331(f108(f891(x42601,a877)),f331(f285(x42602,x42601,x42603),x42604)),f331(f285(x42602,x42601,x42603),x42605))))
% 162.26/162.06 [4367]E(f331(f269(x43671,x43672),f331(f271(x43673,x43671,x43672,x43672,x43674,f35(x43672)),x43675)),f331(f269(x43673,x43672),x43675))
% 162.26/162.06 [4368]E(f331(f260(x43681,x43682),f331(f271(x43681,x43681,x43683,x43682,f35(x43681),x43684),x43685)),f331(f260(x43681,x43683),x43685))
% 162.26/162.06 [4462]E(f331(f145(f891(x44621,f887(x44622)),f890(x44621,x44622),f331(f331(f8(f891(x44621,f891(x44622,f891(x44621,f887(x44622)))),f891(f890(x44621,x44622),f891(x44621,f887(x44622))),f891(x44621,f887(x44622))),f270(x44621,x44622,f891(x44621,f887(x44622)))),f331(f331(f7(f891(x44621,f887(x44622)),f891(x44622,f887(x44622)),f891(x44621,f891(x44622,f891(x44621,f887(x44622))))),f331(f331(f8(f891(x44621,f891(f891(x44622,f887(x44622)),f891(x44622,f891(x44621,f887(x44622))))),f891(f891(x44622,f887(x44622)),f891(x44621,f891(x44622,f891(x44621,f887(x44622))))),f891(x44621,f887(x44622))),f7(x44621,f891(x44622,f887(x44622)),f891(x44622,f891(x44621,f887(x44622))))),f331(f331(f8(f891(x44621,f891(f887(x44622),f891(x44621,f887(x44622)))),f891(x44621,f891(f891(x44622,f887(x44622)),f891(x44622,f891(x44621,f887(x44622))))),f891(x44621,f887(x44622))),f331(f8(f891(f887(x44622),f891(x44621,f887(x44622))),f891(f891(x44622,f887(x44622)),f891(x44622,f891(x44621,f887(x44622)))),x44621),f8(f887(x44622),f891(x44621,f887(x44622)),x44622))),f73(x44621,f887(x44622))))),f239(x44622))),x44623),f331(f331(f184(x44621,x44622),x44624),x44625)),f189(x44621,x44622,x44623,x44624,x44625))
% 162.26/162.06 [4464]P20(x44641,x44642,f331(f331(f309(f882(x44641)),f331(f331(f331(f93(x44641),f331(f331(f7(x44641,f891(a878,a877),f891(a878,a877)),f331(f331(f8(f891(a878,f891(a877,a877)),f891(f891(a878,a877),f891(a878,a877)),x44641),f18(a878,a877,a877)),f331(f331(f8(f891(a878,a877),f891(a878,f891(a877,a877)),x44641),f331(f8(a877,f891(a877,a877),a878),a329)),x44643))),f331(f331(f8(a877,a877,a878),a326),x44644))),f33(x44644,x44645)),x44643)),f196(f891(f882(x44641),a877))))
% 162.26/162.06 [3559]E(f331(f331(f331(f331(f216(x35591),x35592),x35593),x35594),x35595),f211(x35591,x35592))
% 162.26/162.06 [3560]E(f331(f331(f331(f331(f217(x35601),x35602),x35603),x35604),x35605),f201(x35601,x35602))
% 162.26/162.06 [3606]E(f99(x36061,x36062,f331(f331(f331(f93(x36061),x36063),x36064),x36065)),f2(a883))
% 162.26/162.06 [3700]E(f331(f331(f331(f331(f73(x37001,x37002),x37003),x37004),x37005),x37004),x37005)
% 162.26/162.06 [3916]E(f331(f331(f42(x39161,f891(x39162,a877)),f331(f331(f309(x39161),x39163),x39164)),x39165),f331(f331(f107(f891(x39162,a877)),f331(x39165,x39163)),f331(f331(f42(x39161,f891(x39162,a877)),x39164),x39165)))
% 162.26/162.06 [3917]E(f331(f331(f43(x39171,f891(x39172,a877)),f331(f331(f309(x39171),x39173),x39174)),x39175),f331(f331(f108(f891(x39172,a877)),f331(x39175,x39173)),f331(f331(f43(x39171,f891(x39172,a877)),x39174),x39175)))
% 162.26/162.06 [3970]E(f331(f124(x39701,x39702,f331(x39703,x39704)),f331(f331(f7(x39701,a105,f885(x39702)),x39705),x39704)),f331(f208(x39701,x39702,x39703,x39705),x39704))
% 162.26/162.06 [3983]E(f331(f331(f107(f891(x39831,a877)),f331(f310(x39832,x39831,x39833),x39834)),f331(f310(x39832,x39831,x39833),x39835)),f331(f310(x39832,x39831,x39833),f331(f331(f107(f891(x39832,a877)),x39834),x39835)))
% 162.26/162.06 [3984]E(f331(f331(f107(f891(x39841,a877)),f331(f285(x39842,x39841,x39843),x39844)),f331(f285(x39842,x39841,x39843),x39845)),f331(f285(x39842,x39841,x39843),f331(f331(f107(f891(x39842,a877)),x39844),x39845)))
% 162.26/162.06 [3985]E(f331(f331(f22(f891(x39851,a877)),f331(f311(x39851,x39852,x39853),x39854)),f331(f311(x39851,x39852,x39853),x39855)),f331(f311(x39851,x39852,x39853),f331(f331(f22(f891(x39852,a877)),x39854),x39855)))
% 162.26/162.06 [3986]E(f331(f331(f107(f891(x39861,a877)),f331(f311(x39861,x39862,x39863),x39864)),f331(f311(x39861,x39862,x39863),x39865)),f331(f311(x39861,x39862,x39863),f331(f331(f107(f891(x39862,a877)),x39864),x39865)))
% 162.26/162.06 [3987]E(f331(f331(f108(f891(x39871,a877)),f331(f311(x39871,x39872,x39873),x39874)),f331(f311(x39871,x39872,x39873),x39875)),f331(f311(x39871,x39872,x39873),f331(f331(f108(f891(x39872,a877)),x39874),x39875)))
% 162.26/162.06 [3989]E(f190(x39891,x39892,f190(x39891,x39892,x39893,x39894),x39895),f190(x39891,x39892,x39893,f331(f331(f108(f891(x39891,a877)),x39894),x39895)))
% 162.26/162.06 [4047]E(f331(f331(f162(x40471,f331(f331(f137(x40471),x40472),f331(f331(f154(x40471),x40473),x40474))),f331(f197(f884(x40471)),x40472)),x40475),f331(f331(f137(x40471),x40472),f331(f331(f154(x40471),x40475),x40474)))
% 162.26/162.06 [4055]E(f331(f331(f43(x40551,f891(x40552,a877)),x40553),f331(f331(f8(f891(x40552,a877),f891(x40552,a877),x40551),f331(f309(x40552),x40554)),x40555)),f331(f331(f309(x40552),x40554),f331(f331(f43(x40551,f891(x40552,a877)),x40553),x40555)))
% 162.26/162.06 [4121]E(f190(x41211,x41212,f331(f331(f331(f73(x41211,f887(x41212)),x41213),x41214),f331(f239(x41212),x41215)),f331(f80(f891(x41211,a877)),f331(f331(f309(x41211),x41214),f196(f891(x41211,a877))))),f190(x41211,x41212,x41213,f331(f80(f891(x41211,a877)),f331(f331(f309(x41211),x41214),f196(f891(x41211,a877))))))
% 162.26/162.06 [4209]E(f331(f331(f157(x42091,x42092),x42093),f331(f139(x42091,f331(f74(x42092,a877,x42091,x42094),x42093)),x42095)),f331(f139(x42092,x42094),f331(f331(f157(x42091,x42092),x42093),x42095)))
% 162.26/162.06 [4216]E(f331(f197(f884(x42161)),f331(f139(x42161,x42162),f331(f331(f157(x42163,x42161),x42164),x42165))),f331(f197(f884(x42163)),f331(f139(x42163,f331(f74(x42161,a877,x42163,x42162),x42164)),x42165)))
% 162.26/162.06 [4353]E(f331(f331(f107(f891(x43531,a877)),f331(f331(f22(f891(x43531,a877)),f186(x43531,x43532,x43533)),f331(f253(x43531),f331(f331(f7(x43531,f891(x43531,a877),a877),f333(x43531)),f331(f331(f22(f891(x43531,a877)),x43534),f186(x43531,x43532,x43535)))))),f331(f253(x43531),f331(f331(f7(x43531,f891(x43531,a877),a877),f333(x43531)),f331(f331(f108(f891(x43531,a877)),x43534),f186(x43531,x43532,x43535))))),f186(x43531,x43532,f77(x43531,f887(x43532),x43533,x43535,x43534)))
% 162.26/162.06 [4446]E(f331(f159(f884(f890(x44461,x44462)),x44462,f119(f890(x44461,x44462)),f331(f331(f7(x44462,f891(f884(x44462),f884(f890(x44461,x44462))),f891(f884(x44462),f884(f890(x44461,x44462)))),f331(f331(f8(f891(f884(f890(x44461,x44462)),f884(f890(x44461,x44462))),f891(f891(f884(x44462),f884(f890(x44461,x44462))),f891(f884(x44462),f884(f890(x44461,x44462)))),x44462),f8(f884(f890(x44461,x44462)),f884(f890(x44461,x44462)),f884(x44462))),f331(f331(f8(f890(x44461,x44462),f891(f884(f890(x44461,x44462)),f884(f890(x44461,x44462))),x44462),f154(f890(x44461,x44462))),f331(f261(x44461,x44462),x44463)))),f331(f184(x44461,x44462),x44464))),x44465),f331(f331(f184(x44461,x44462),f331(f331(f154(x44461),x44463),x44464)),x44465))
% 162.26/162.06 [3910]E(f331(f331(f162(x39101,f331(f331(f162(x39101,x39102),x39103),x39104)),x39103),x39105),f331(f331(f162(x39101,x39102),x39103),x39105))
% 162.26/162.06 [3964]E(f331(f257(x39641,x39642),f331(f331(f309(f890(x39641,x39642)),f331(f331(f261(x39641,x39642),x39643),x39644)),x39645)),f331(f331(f309(x39642),x39644),f331(f257(x39641,x39642),x39645)))
% 162.26/162.06 [3965]E(f331(f259(x39651,x39652),f331(f331(f309(f890(x39651,x39652)),f331(f331(f261(x39651,x39652),x39653),x39654)),x39655)),f331(f331(f309(x39651),x39653),f331(f259(x39651,x39652),x39655)))
% 162.26/162.06 [4011]E(f126(x40111,x40112,f331(x40113,x40114),f331(f331(f7(x40111,a105,f885(f887(x40112))),x40115),x40114)),f331(f206(x40111,x40112,x40113,x40115),x40114))
% 162.26/162.06 [4040]E(f331(f331(f22(f891(f890(x40401,x40402),a877)),f331(f331(f268(x40401,x40402),x40403),x40404)),f331(f331(f268(x40401,x40402),x40405),x40404)),f331(f331(f268(x40401,x40402),f331(f331(f22(f891(x40401,a877)),x40403),x40405)),x40404))
% 162.26/162.06 [4041]E(f331(f331(f107(f891(f890(x40411,x40412),a877)),f331(f331(f268(x40411,x40412),x40413),x40414)),f331(f331(f268(x40411,x40412),x40415),x40414)),f331(f331(f268(x40411,x40412),f331(f331(f107(f891(x40411,a877)),x40413),x40415)),x40414))
% 162.26/162.06 [4042]E(f331(f331(f108(f891(f890(x40421,x40422),a877)),f331(f331(f268(x40421,x40422),x40423),x40424)),f331(f331(f268(x40421,x40422),x40425),x40424)),f331(f331(f268(x40421,x40422),f331(f331(f108(f891(x40421,a877)),x40423),x40425)),x40424))
% 162.26/162.06 [4099]E(f331(f331(f107(f891(x40991,a877)),f331(f331(f42(x40992,f891(x40991,a877)),x40993),x40994)),f331(f331(f42(x40992,f891(x40991,a877)),x40995),x40994)),f331(f331(f42(x40992,f891(x40991,a877)),f331(f331(f107(f891(x40992,a877)),x40993),x40995)),x40994))
% 162.26/162.06 [4100]E(f331(f331(f108(f891(x41001,a877)),f331(f331(f43(x41002,f891(x41001,a877)),x41003),x41004)),f331(f331(f43(x41002,f891(x41001,a877)),x41005),x41004)),f331(f331(f43(x41002,f891(x41001,a877)),f331(f331(f107(f891(x41002,a877)),x41003),x41005)),x41004))
% 162.26/162.06 [4114]E(f331(f331(f42(x41141,f891(x41142,a877)),x41143),f331(f331(f8(f891(x41142,a877),f891(x41142,a877),x41141),f331(f22(f891(x41142,a877)),x41144)),x41145)),f331(f331(f22(f891(x41142,a877)),x41144),f331(f331(f43(x41141,f891(x41142,a877)),x41143),x41145)))
% 162.26/162.06 [4115]E(f331(f331(f42(x41151,f891(x41152,a877)),x41153),f331(f331(f8(f891(x41152,a877),f891(x41152,a877),x41151),f331(f108(f891(x41152,a877)),x41154)),x41155)),f331(f331(f108(f891(x41152,a877)),x41154),f331(f331(f42(x41151,f891(x41152,a877)),x41153),x41155)))
% 162.26/162.06 [4116]E(f331(f331(f43(x41161,f891(x41162,a877)),x41163),f331(f331(f8(f891(x41162,a877),f891(x41162,a877),x41161),f331(f107(f891(x41162,a877)),x41164)),x41165)),f331(f331(f107(f891(x41162,a877)),x41164),f331(f331(f43(x41161,f891(x41162,a877)),x41163),x41165)))
% 162.26/162.06 [4149]E(f187(x41491,x41492,x41493,f331(f180(x41491,x41492),f331(f172(f890(x41491,x41492)),f331(f331(f184(x41491,x41492),x41494),x41495)))),f189(x41491,x41492,x41493,x41494,x41495))
% 162.26/162.06 [4169]E(f193(f884(x41691),f331(f331(f154(x41691),x41692),x41693),f331(f331(f8(f884(x41691),f884(x41691),a883),f331(f154(x41691),x41694)),f331(f331(f7(a883,x41691,f884(x41691)),f162(x41691,x41693)),x41692)),x41695),f331(f331(f162(x41691,f331(f331(f154(x41691),x41694),x41693)),x41695),x41692))
% 162.26/162.06 [4173]E(f331(f331(f42(x41731,f891(f890(x41732,x41733),a877)),x41734),f331(f331(f8(f891(f890(x41733,x41732),a877),f891(f890(x41732,x41733),a877),x41731),f286(x41733,x41732)),x41735)),f331(f286(x41733,x41732),f331(f331(f42(x41731,f891(f890(x41733,x41732),a877)),x41734),x41735)))
% 162.26/162.06 [4174]E(f331(f331(f43(x41741,f891(f890(x41742,x41743),a877)),x41744),f331(f331(f8(f891(f890(x41743,x41742),a877),f891(f890(x41742,x41743),a877),x41741),f286(x41743,x41742)),x41745)),f331(f286(x41743,x41742),f331(f331(f43(x41741,f891(f890(x41743,x41742),a877)),x41744),x41745)))
% 162.26/162.06 [4234]E(f186(x42341,x42342,f331(f331(f18(x42341,f887(x42343),f887(x42342)),f331(f331(f8(f891(x42343,x42342),f891(f887(x42343),f887(x42342)),x42341),f210(x42343,x42342)),x42344)),x42345)),f186(x42341,x42343,x42345))
% 162.26/162.06 [4285]P24(f331(f331(f247(f891(x42851,a877)),f331(f331(f22(f891(x42851,a877)),f331(f310(x42852,x42851,x42853),x42854)),f331(f310(x42852,x42851,x42853),x42855))),f331(f310(x42852,x42851,x42853),f331(f331(f22(f891(x42852,a877)),x42854),x42855))))
% 162.26/162.06 [4450]E(f331(f159(f884(f890(x44501,x44502)),x44501,f119(f890(x44501,x44502)),f331(f331(f7(x44501,f891(f884(x44501),f884(f890(x44501,x44502))),f891(f884(x44501),f884(f890(x44501,x44502)))),f331(f331(f8(f891(f884(f890(x44501,x44502)),f884(f890(x44501,x44502))),f891(f891(f884(x44501),f884(f890(x44501,x44502))),f891(f884(x44501),f884(f890(x44501,x44502)))),x44501),f8(f884(f890(x44501,x44502)),f884(f890(x44501,x44502)),f884(x44501))),f331(f331(f8(f890(x44501,x44502),f891(f884(f890(x44501,x44502)),f884(f890(x44501,x44502))),x44501),f154(f890(x44501,x44502))),f331(f331(f7(x44501,x44502,f890(x44501,x44502)),f261(x44501,x44502)),x44503)))),f331(f331(f7(f884(x44501),f884(x44502),f884(f890(x44501,x44502))),f184(x44501,x44502)),x44504))),x44505),f331(f331(f184(x44501,x44502),x44505),f331(f331(f154(x44502),x44503),x44504)))
% 162.26/162.06 [4137]E(f331(f331(f107(f891(x41371,a877)),f331(f285(x41372,x41371,x41373),x41374)),f331(f285(x41372,x41371,x41375),x41374)),f331(f285(x41372,x41371,f331(f331(f107(f891(f890(x41372,x41371),a877)),x41373),x41375)),x41374))
% 162.26/162.06 [4176]E(f331(f331(f137(f890(x41761,x41762)),f331(f331(f184(x41761,x41762),x41763),f331(f331(f176(x41762),f331(f197(f884(x41761)),x41763)),x41764))),f331(f331(f184(x41761,x41762),x41765),f331(f331(f141(x41762),f331(f197(f884(x41761)),x41763)),x41764))),f331(f331(f184(x41761,x41762),f331(f331(f137(x41761),x41763),x41765)),x41764))
% 162.26/162.06 [4290]E(f331(f331(f268(x42901,x42902),x42903),f331(f331(f18(x42901,f891(x42902,a877),f891(x42902,a877)),f331(f331(f8(f891(x42902,a877),f891(f891(x42902,a877),f891(x42902,a877)),x42901),f22(f891(x42902,a877))),x42904)),x42905)),f331(f331(f22(f891(f890(x42901,x42902),a877)),f331(f331(f268(x42901,x42902),x42903),x42904)),f331(f331(f268(x42901,x42902),x42903),x42905)))
% 162.26/162.06 [4291]E(f331(f331(f268(x42911,x42912),x42913),f331(f331(f18(x42911,f891(x42912,a877),f891(x42912,a877)),f331(f331(f8(f891(x42912,a877),f891(f891(x42912,a877),f891(x42912,a877)),x42911),f107(f891(x42912,a877))),x42914)),x42915)),f331(f331(f107(f891(f890(x42911,x42912),a877)),f331(f331(f268(x42911,x42912),x42913),x42914)),f331(f331(f268(x42911,x42912),x42913),x42915)))
% 162.26/162.06 [4292]E(f331(f331(f268(x42921,x42922),x42923),f331(f331(f18(x42921,f891(x42922,a877),f891(x42922,a877)),f331(f331(f8(f891(x42922,a877),f891(f891(x42922,a877),f891(x42922,a877)),x42921),f108(f891(x42922,a877))),x42924)),x42925)),f331(f331(f108(f891(f890(x42921,x42922),a877)),f331(f331(f268(x42921,x42922),x42923),x42924)),f331(f331(f268(x42921,x42922),x42923),x42925)))
% 162.26/162.06 [4296]E(f331(f331(f42(x42961,f891(x42962,a877)),x42963),f331(f331(f7(x42961,f891(x42962,a877),f891(x42962,a877)),f331(f331(f8(f891(x42962,a877),f891(f891(x42962,a877),f891(x42962,a877)),x42961),f22(f891(x42962,a877))),x42964)),x42965)),f331(f331(f22(f891(x42962,a877)),f331(f331(f42(x42961,f891(x42962,a877)),x42963),x42964)),x42965))
% 162.26/162.06 [4297]E(f331(f331(f42(x42971,f891(x42972,a877)),x42973),f331(f331(f7(x42971,f891(x42972,a877),f891(x42972,a877)),f331(f331(f8(f891(x42972,a877),f891(f891(x42972,a877),f891(x42972,a877)),x42971),f108(f891(x42972,a877))),x42974)),x42975)),f331(f331(f108(f891(x42972,a877)),f331(f331(f42(x42971,f891(x42972,a877)),x42973),x42974)),x42975))
% 162.26/162.06 [4298]E(f331(f331(f43(x42981,f891(x42982,a877)),x42983),f331(f331(f7(x42981,f891(x42982,a877),f891(x42982,a877)),f331(f331(f8(f891(x42982,a877),f891(f891(x42982,a877),f891(x42982,a877)),x42981),f107(f891(x42982,a877))),x42984)),x42985)),f331(f331(f107(f891(x42982,a877)),f331(f331(f43(x42981,f891(x42982,a877)),x42983),x42984)),x42985))
% 162.26/162.06 [4302]E(f331(f331(f42(x43021,f891(x43022,a877)),x43023),f331(f331(f18(x43021,f891(x43022,a877),f891(x43022,a877)),f331(f331(f8(f891(x43022,a877),f891(f891(x43022,a877),f891(x43022,a877)),x43021),f107(f891(x43022,a877))),x43024)),x43025)),f331(f331(f107(f891(x43022,a877)),f331(f331(f42(x43021,f891(x43022,a877)),x43023),x43024)),f331(f331(f42(x43021,f891(x43022,a877)),x43023),x43025)))
% 162.26/162.06 [4303]E(f331(f331(f43(x43031,f891(x43032,a877)),x43033),f331(f331(f18(x43031,f891(x43032,a877),f891(x43032,a877)),f331(f331(f8(f891(x43032,a877),f891(f891(x43032,a877),f891(x43032,a877)),x43031),f108(f891(x43032,a877))),x43034)),x43035)),f331(f331(f108(f891(x43032,a877)),f331(f331(f43(x43031,f891(x43032,a877)),x43033),x43034)),f331(f331(f43(x43031,f891(x43032,a877)),x43033),x43035)))
% 162.26/162.06 [4313]E(f331(f331(f42(x43131,f891(x43132,a877)),x43133),f331(f331(f18(x43131,f891(x43132,a877),f891(x43132,a877)),f331(f331(f8(f891(x43132,a877),f891(f891(x43132,a877),f891(x43132,a877)),x43131),f107(f891(x43132,a877))),x43134)),x43135)),f331(f331(f107(f891(x43132,a877)),f40(f891(x43132,a877),f331(f310(x43131,f891(x43132,a877),x43134),x43133))),f40(f891(x43132,a877),f331(f310(x43131,f891(x43132,a877),x43135),x43133))))
% 162.26/162.06 [4314]E(f331(f331(f43(x43141,f891(x43142,a877)),x43143),f331(f331(f18(x43141,f891(x43142,a877),f891(x43142,a877)),f331(f331(f8(f891(x43142,a877),f891(f891(x43142,a877),f891(x43142,a877)),x43141),f108(f891(x43142,a877))),x43144)),x43145)),f331(f331(f108(f891(x43142,a877)),f41(f891(x43142,a877),f331(f310(x43141,f891(x43142,a877),x43144),x43143))),f41(f891(x43142,a877),f331(f310(x43141,f891(x43142,a877),x43145),x43143))))
% 162.26/162.06 [4350]E(f331(f331(f141(x43501),f331(f197(f884(x43501)),f179(x43501,x43502,f331(f331(f157(x43503,x43501),x43504),x43505)))),f331(f331(f157(x43503,x43501),x43504),x43505)),f331(f331(f157(x43503,x43501),x43504),f331(f331(f141(x43503),f331(f197(f884(x43503)),f179(x43503,f331(f74(x43501,a877,x43503,x43502),x43504),x43505))),x43505)))
% 162.26/162.06 [4227]E(f331(f331(f137(f890(x42271,x42272)),f331(f331(f184(x42271,x42272),f331(f331(f176(x42271),f331(f197(f884(x42272)),x42273)),x42274)),x42273)),f331(f331(f184(x42271,x42272),f331(f331(f141(x42271),f331(f197(f884(x42272)),x42273)),x42274)),x42275)),f331(f331(f184(x42271,x42272),x42274),f331(f331(f137(x42272),x42273),x42275)))
% 162.26/162.06 [4341]E(f86(x43411,f331(f331(f18(x43411,a877,a877),f331(f331(f8(a877,f891(a877,a877),x43411),a329),f331(f331(f7(x43411,f891(x43411,a877),a877),f333(x43411)),x43412))),f331(f331(f7(x43411,x43413,a877),f331(f331(f8(x43413,f891(x43413,a877),x43411),a328),x43414)),x43415))),f331(f78(x43411,x43413,x43412,x43414),x43415))
% 162.26/162.06 [4397]E(f331(f331(f89(a1,x43971),f331(f110(a1),f331(f331(f81(a1),x43972),a103))),f331(f331(f18(a1,x43971,x43971),f331(f331(f7(a1,x43971,f891(x43971,x43971)),f331(f331(f8(a877,f891(x43971,f891(x43971,x43971)),a1),f102(x43971)),a202)),f193(x43971,x43973,x43974,x43975))),f331(f331(f8(a883,x43971,a1),x43974),f331(f331(f7(a1,a883,a883),f331(f331(f8(a883,f891(a883,a883),a1),f81(a883)),a111)),x43975)))),f193(x43971,x43973,x43974,f331(f331(f81(a883),f331(f110(a883),x43972)),x43975)))
% 162.26/162.06 [4447]E(f331(f180(x44471,x44472),f331(f331(f157(f890(x44471,x44473),f890(x44471,x44472)),f331(f270(x44471,x44473,f890(x44471,x44472)),f331(f331(f7(x44471,f891(x44473,x44472),f891(x44473,f890(x44471,x44472))),f331(f331(f8(f891(x44472,f890(x44471,x44472)),f891(f891(x44473,x44472),f891(x44473,f890(x44471,x44472))),x44471),f8(x44472,f890(x44471,x44472),x44473)),f261(x44471,x44472))),x44474))),x44475)),f331(f74(f887(x44473),f887(x44472),x44471,f331(f210(x44473,x44472),x44474)),f331(f180(x44471,x44473),x44475)))
% 162.26/162.06 [4390]E(f186(x43901,x43902,f331(f331(f18(x43901,f887(x43902),f887(x43902)),f331(f331(f18(x43901,f887(x43902),f891(f887(x43902),f887(x43902))),f331(f331(f8(a877,f891(f887(x43902),f891(f887(x43902),f887(x43902))),x43901),f102(f887(x43902))),x43903)),x43904)),x43905)),f331(f331(f107(f891(x43901,a877)),f331(f331(f108(f891(x43901,a877)),f186(x43901,x43902,x43904)),f331(f253(x43901),x43903))),f331(f331(f108(f891(x43901,a877)),f186(x43901,x43902,x43905)),f331(f253(x43901),f331(f331(f8(a877,a877,x43901),a326),x43903)))))
% 162.26/162.06 [4443]E(f331(f331(f89(a1,x44431),f331(f110(a1),f331(f331(f81(a1),x44432),a103))),f331(f331(f18(a1,x44431,x44431),f331(f331(f7(a1,x44431,f891(x44431,x44431)),f331(f331(f8(a877,f891(x44431,f891(x44431,x44431)),a1),f102(x44431)),a202)),f331(f192(x44431,x44433,x44434),x44435))),f331(f331(f18(a1,x44431,x44431),f331(f331(f8(a883,f891(x44431,x44431),a1),x44434),f331(f331(f7(a1,a883,a883),f331(f331(f8(a883,f891(a883,a883),a1),f81(a883)),a111)),x44435))),f331(f331(f8(a883,x44431,a1),f192(x44431,x44433,x44434)),f331(f331(f7(a1,a883,a883),f331(f331(f8(a883,f891(a883,a883),a1),f81(a883)),a111)),x44435))))),f331(f192(x44431,x44433,x44434),f331(f331(f81(a883),f331(f110(a883),x44432)),x44435)))
% 162.26/162.06 [4476]E(f331(f253(f890(x44761,x44762)),f331(f270(x44761,x44762,a877),f331(f331(f8(f891(x44762,f891(x44763,a877)),f891(x44762,a877),x44761),f331(f8(f891(x44763,a877),a877,x44762),f87(x44763))),f331(f331(f7(x44761,f891(x44762,f891(x44763,a877)),f891(x44762,f891(x44763,a877))),f331(f331(f8(f891(f891(x44763,a877),f891(x44763,a877)),f891(f891(x44762,f891(x44763,a877)),f891(x44762,f891(x44763,a877))),x44761),f8(f891(x44763,a877),f891(x44763,a877),x44762)),f331(f331(f8(f891(x44763,f891(a877,a877)),f891(f891(x44763,a877),f891(x44763,a877)),x44761),f18(x44763,a877,a877)),f331(f331(f8(f891(x44763,a877),f891(x44763,f891(a877,a877)),x44761),f331(f8(a877,f891(a877,a877),x44763),a329)),f331(f331(f7(x44761,f891(f890(x44761,x44763),a877),f891(x44763,a877)),f331(f331(f8(f891(x44763,f891(f891(f890(x44761,x44763),a877),a877)),f891(f891(f890(x44761,x44763),a877),f891(x44763,a877)),x44761),f7(x44763,f891(f890(x44761,x44763),a877),a877)),f331(f331(f8(f891(x44763,f890(x44761,x44763)),f891(x44763,f891(f891(f890(x44761,x44763),a877),a877)),x44761),f331(f8(f890(x44761,x44763),f891(f891(f890(x44761,x44763),a877),a877),x44763),f333(f890(x44761,x44763)))),f261(x44761,x44763)))),x44764))))),f331(f331(f7(x44762,f891(f890(x44763,x44762),a877),f891(x44763,a877)),f331(f331(f8(f891(x44763,f891(f891(f890(x44763,x44762),a877),a877)),f891(f891(f890(x44763,x44762),a877),f891(x44763,a877)),x44762),f7(x44763,f891(f890(x44763,x44762),a877),a877)),f331(f331(f8(f891(x44763,f890(x44763,x44762)),f891(x44763,f891(f891(f890(x44763,x44762),a877),a877)),x44762),f331(f8(f890(x44763,x44762),f891(f891(f890(x44763,x44762),a877),a877),x44763),f333(f890(x44763,x44762)))),f331(f7(x44763,x44762,f890(x44763,x44762)),f261(x44763,x44762))))),x44765))))),f331(f331(f288(x44761,x44763,x44762),x44764),x44765))
% 162.26/162.06 [4559]~E(f31(x45591,x45592,x45593),f29(x45594,x45595,x45596))
% 162.26/162.06 [4562]~E(f30(x45621,x45622,x45623),f29(x45624,x45625,x45626))
% 162.26/162.06 [4563]~E(f30(x45631,x45632,x45633),f31(x45634,x45635,x45636))
% 162.26/162.06 [3999]E(f133(x39991,x39992,x39993,x39994,f130(x39992,x39995,x39996)),f331(f331(x39994,x39995),x39996))
% 162.26/162.06 [4206]E(f189(x42061,x42062,f187(x42061,x42062,x42063,x42064),x42065,x42066),f187(x42061,x42062,x42063,f189(x42061,x42062,x42064,x42065,x42066)))
% 162.26/162.06 [4330]E(f331(f74(f890(x43301,x43302),x43302,f890(x43303,x43304),f269(x43301,x43302)),f271(x43303,x43301,x43304,x43302,x43305,x43306)),f331(f74(x43304,x43302,f890(x43303,x43304),x43306),f269(x43303,x43304)))
% 162.26/162.06 [4331]E(f331(f74(f890(x43311,x43312),x43311,f890(x43313,x43314),f260(x43311,x43312)),f271(x43313,x43311,x43314,x43312,x43315,x43316)),f331(f74(x43313,x43311,f890(x43313,x43314),x43315),f260(x43313,x43314)))
% 162.26/162.06 [3939]E(f331(f331(f74(x39391,x39392,x39393,x39394),x39395),x39396),f331(x39394,f331(x39395,x39396)))
% 162.26/162.06 [3741]E(f331(f331(f270(x37411,x37412,x37413),x37414),f331(f331(f261(x37411,x37412),x37415),x37416)),f331(f331(x37414,x37415),x37416))
% 162.26/162.06 [3803]E(f331(f331(f331(f8(x38031,x38032,x38033),x38034),x38035),x38036),f331(x38034,f331(x38035,x38036)))
% 162.26/162.06 [3804]E(f331(f331(f331(f7(x38041,x38042,x38043),x38044),x38045),x38046),f331(f331(x38044,x38046),x38045))
% 162.26/162.06 [3821]E(f331(f331(f331(f18(x38211,x38212,x38213),x38214),x38215),x38216),f331(f331(x38214,x38216),f331(x38215,x38216)))
% 162.26/162.06 [3840]E(f331(f159(x38401,x38402,x38403,x38404),f331(f331(f154(x38402),x38405),x38406)),f331(f331(x38404,x38405),x38406))
% 162.26/162.06 [3944]E(f331(f331(f154(f890(x39441,x39442)),f331(f331(f261(x39441,x39442),x39443),x39444)),f331(f331(f184(x39441,x39442),x39445),x39446)),f331(f331(f184(x39441,x39442),f331(f331(f154(x39441),x39443),x39445)),f331(f331(f154(x39442),x39444),x39446)))
% 162.26/162.06 [3946]E(f331(f331(f157(x39461,x39462),x39463),f331(f331(f162(x39461,x39464),x39465),x39466)),f331(f331(f162(x39462,f331(f331(f157(x39461,x39462),x39463),x39464)),x39465),f331(x39463,x39466)))
% 162.26/162.06 [3988]E(f331(f145(x39881,x39882,x39883,x39884),f331(f331(f154(x39882),x39885),x39886)),f331(f145(x39881,x39882,x39883,f331(f331(x39883,x39884),x39885)),x39886))
% 162.26/162.06 [4012]E(f273(x40121,x40122,x40123,x40124,f331(f331(f261(x40121,x40122),x40125),x40126)),f331(f331(x40124,x40125),x40126))
% 162.26/162.06 [4093]E(f331(f331(f42(x40931,f891(x40932,a877)),x40933),f331(f74(x40934,f891(x40932,a877),x40931,x40935),x40936)),f331(f331(f42(x40934,f891(x40932,a877)),f331(f310(x40931,x40934,x40936),x40933)),x40935))
% 162.26/162.06 [4140]E(f331(f331(f210(x41401,x41402),x41403),f331(f331(f210(x41404,x41401),x41405),x41406)),f331(f331(f210(x41404,x41402),f331(f74(x41401,x41402,x41404,x41403),x41405)),x41406))
% 162.26/162.06 [4142]E(f331(f331(f157(x41421,x41422),x41423),f331(f331(f157(x41424,x41421),x41425),x41426)),f331(f331(f157(x41424,x41422),f331(f74(x41421,x41422,x41424,x41423),x41425)),x41426))
% 162.26/162.06 [4147]E(f331(f310(x41471,x41472,f331(f74(x41473,x41472,x41471,x41474),x41475)),x41476),f331(f310(x41473,x41472,x41474),f331(f310(x41471,x41473,x41475),x41476)))
% 162.26/162.06 [4148]E(f331(f311(x41481,x41482,f331(f74(x41483,x41482,x41481,x41484),x41485)),x41486),f331(f311(x41481,x41483,x41485),f331(f311(x41483,x41482,x41484),x41486)))
% 162.26/162.06 [4175]E(f187(x41751,x41752,x41753,f331(f331(f331(f73(x41751,f887(x41752)),x41754),x41755),f331(f239(x41752),x41756))),f331(f331(f331(f73(x41751,f887(x41752)),f187(x41751,x41752,x41753,x41754)),x41755),f331(f239(x41752),x41756)))
% 162.26/162.06 [4177]E(f331(f145(x41771,x41772,x41773,f331(f145(x41771,x41772,x41773,x41774),x41775)),x41776),f331(f145(x41771,x41772,x41773,x41774),f331(f331(f137(x41772),x41775),x41776)))
% 162.26/162.06 [4318]E(f331(f271(x43181,x43181,x43182,x43183,f35(x43181),x43184),f331(f331(f261(x43181,x43182),x43185),x43186)),f331(f331(f261(x43181,x43183),x43185),f331(x43184,x43186)))
% 162.26/162.06 [4319]E(f331(f271(x43191,x43192,x43193,x43193,x43194,f35(x43193)),f331(f331(f261(x43191,x43193),x43195),x43196)),f331(f331(f261(x43192,x43193),f331(x43194,x43195)),x43196))
% 162.26/162.06 [4423]E(f331(f331(f157(f890(x44231,x44232),f890(x44231,x44233)),f331(f270(x44231,x44232,f890(x44231,x44233)),f331(f331(f7(x44231,f891(x44232,x44233),f891(x44232,f890(x44231,x44233))),f331(f331(f8(f891(x44233,f890(x44231,x44233)),f891(f891(x44232,x44233),f891(x44232,f890(x44231,x44233))),x44231),f8(x44233,f890(x44231,x44233),x44232)),f261(x44231,x44233))),x44234))),f331(f331(f184(x44231,x44232),x44235),x44236)),f331(f331(f184(x44231,x44233),x44235),f331(f331(f157(x44232,x44233),x44234),x44236)))
% 162.26/162.06 [3808]E(f100(x38081,x38082,x38083,f331(f331(f331(f93(x38081),x38084),x38085),x38086)),f331(f331(f331(x38083,x38084),x38085),x38086))
% 162.26/162.06 [3809]E(f101(x38091,x38092,x38093,f331(f331(f331(f93(x38091),x38094),x38095),x38096)),f331(f331(f331(x38093,x38094),x38095),x38096))
% 162.26/162.06 [3998]E(f331(f331(f74(x39981,x39982,x39983,f331(f16(x39982,x39981),x39984)),x39985),x39986),x39984)
% 162.26/162.06 [4031]E(f331(f310(x40311,x40312,x40313),f331(f310(x40314,x40311,x40315),x40316)),f331(f310(x40314,x40312,f331(f331(f8(x40311,x40312,x40314),x40313),x40315)),x40316))
% 162.26/162.06 [4036]E(f331(f331(f42(x40361,f891(x40362,a877)),f331(f310(x40363,x40361,x40364),x40365)),x40366),f331(f331(f42(x40363,f891(x40362,a877)),x40365),f331(f331(f8(x40361,f891(x40362,a877),x40363),x40366),x40364)))
% 162.26/162.06 [4037]E(f331(f331(f43(x40371,f891(x40372,a877)),f331(f310(x40373,x40371,x40374),x40375)),x40376),f331(f331(f43(x40373,f891(x40372,a877)),x40375),f331(f331(f8(x40371,f891(x40372,a877),x40373),x40376),x40374)))
% 162.26/162.06 [4038]E(f331(f331(f42(x40381,f891(x40382,a877)),x40383),f331(f331(f8(x40384,f891(x40382,a877),x40381),x40385),x40386)),f331(f331(f42(x40384,f891(x40382,a877)),f331(f310(x40381,x40384,x40386),x40383)),x40385))
% 162.26/162.06 [4039]E(f331(f331(f43(x40391,f891(x40392,a877)),x40393),f331(f331(f8(x40394,f891(x40392,a877),x40391),x40395),x40396)),f331(f331(f43(x40394,f891(x40392,a877)),f331(f310(x40391,x40394,x40396),x40393)),x40395))
% 162.26/162.06 [4095]E(f331(f331(f42(x40951,f891(x40952,a877)),x40953),f331(f331(f8(f891(x40954,a877),f891(x40952,a877),x40951),f310(x40954,x40952,x40955)),x40956)),f331(f310(x40954,x40952,x40955),f331(f331(f42(x40951,f891(x40954,a877)),x40953),x40956)))
% 162.26/162.06 [4096]E(f331(f331(f42(x40961,f891(x40962,a877)),x40963),f331(f331(f8(f891(x40964,a877),f891(x40962,a877),x40961),f285(x40964,x40962,x40965)),x40966)),f331(f285(x40964,x40962,x40965),f331(f331(f42(x40961,f891(x40964,a877)),x40963),x40966)))
% 162.26/162.06 [4097]E(f331(f331(f42(x40971,f891(x40972,a877)),x40973),f331(f331(f8(f891(x40974,a877),f891(x40972,a877),x40971),f311(x40972,x40974,x40975)),x40976)),f331(f311(x40972,x40974,x40975),f331(f331(f42(x40971,f891(x40974,a877)),x40973),x40976)))
% 162.26/162.06 [4098]E(f331(f331(f43(x40981,f891(x40982,a877)),x40983),f331(f331(f8(f891(x40984,a877),f891(x40982,a877),x40981),f311(x40982,x40984,x40985)),x40986)),f331(f311(x40982,x40984,x40985),f331(f331(f43(x40981,f891(x40984,a877)),x40983),x40986)))
% 162.26/162.06 [4183]E(f331(f145(x41831,x41832,f331(f7(x41832,x41831,x41831),x41833),x41834),f331(f172(x41832),f331(f331(f154(x41832),x41835),x41836))),f331(f331(x41833,x41835),f331(f145(x41831,x41832,f331(f7(x41832,x41831,x41831),x41833),x41834),f331(f172(x41832),x41836))))
% 162.26/162.06 [4247]E(f331(f331(f18(f890(x42471,x42472),x42472,x42473),f331(f331(f8(x42474,f891(x42472,x42473),f890(x42471,x42472)),x42475),f331(f331(f8(x42471,x42474,f890(x42471,x42472)),x42476),f260(x42471,x42472)))),f269(x42471,x42472)),f331(f270(x42471,x42472,x42473),f331(f331(f8(x42474,f891(x42472,x42473),x42471),x42475),x42476)))
% 162.26/162.06 [4253]E(f331(f145(x42531,x42532,f331(f7(x42532,x42531,x42531),x42533),f331(f145(x42531,x42532,f331(f7(x42532,x42531,x42531),x42533),x42534),f331(f172(x42532),x42535))),f331(f172(x42532),x42536)),f331(f145(x42531,x42532,f331(f7(x42532,x42531,x42531),x42533),x42534),f331(f172(x42532),f331(f331(f137(x42532),x42536),x42535))))
% 162.26/162.06 [4255]E(f331(f331(f157(f890(x42551,x42552),f890(x42553,x42552)),f331(f270(x42551,x42552,f890(x42553,x42552)),f331(f331(f8(x42553,f891(x42552,f890(x42553,x42552)),x42551),f261(x42553,x42552)),x42554))),f331(f331(f184(x42551,x42552),x42555),x42556)),f331(f331(f184(x42553,x42552),f331(f331(f157(x42551,x42553),x42554),x42555)),x42556))
% 162.26/162.06 [4306]P24(f331(f331(f247(f891(x43061,a877)),f331(f285(x43062,x43061,x43063),f331(f331(f43(x43064,f891(x43062,a877)),x43065),x43066))),f331(f331(f43(x43064,f891(x43061,a877)),x43065),f331(f331(f8(f891(x43062,a877),f891(x43061,a877),x43064),f285(x43062,x43061,x43063)),x43066))))
% 162.26/162.06 [4107]E(f331(f331(f184(x41071,x41072),f331(f331(f162(x41071,x41073),x41074),f331(f260(x41071,x41072),x41075))),f331(f331(f162(x41072,x41076),x41074),f331(f269(x41071,x41072),x41075))),f331(f331(f162(f890(x41071,x41072),f331(f331(f184(x41071,x41072),x41073),x41076)),x41074),x41075))
% 162.26/162.06 [4164]E(f331(f331(f107(f891(f890(x41641,x41642),a877)),f331(f331(f288(x41641,x41643,x41642),x41644),x41645)),f331(f331(f288(x41641,x41643,x41642),x41644),x41646)),f331(f331(f288(x41641,x41643,x41642),x41644),f331(f331(f107(f891(f890(x41643,x41642),a877)),x41645),x41646)))
% 162.26/162.06 [4268]E(f331(f331(f309(f890(x42681,x42682)),f331(f331(f261(x42681,x42682),x42683),x42684)),f331(f331(f107(f891(f890(x42681,x42682),a877)),f331(f331(f268(x42681,x42682),x42685),f331(f16(f891(x42682,a877),x42681),f331(f331(f309(x42682),x42684),x42686)))),f331(f331(f268(x42681,x42682),f331(f331(f309(x42681),x42683),x42685)),f331(f16(f891(x42682,a877),x42681),x42686)))),f331(f331(f268(x42681,x42682),f331(f331(f309(x42681),x42683),x42685)),f331(f16(f891(x42682,a877),x42681),f331(f331(f309(x42682),x42684),x42686))))
% 162.26/162.06 [4345]E(f331(f331(f108(f891(x43451,a877)),f331(f311(x43451,x43452,f331(f74(f890(x43452,x43453),x43452,x43451,f260(x43452,x43453)),x43454)),x43455)),f331(f311(x43451,x43453,f331(f74(f890(x43452,x43453),x43453,x43451,f269(x43452,x43453)),x43454)),x43456)),f331(f311(x43451,f890(x43452,x43453),x43454),f331(f331(f268(x43452,x43453),x43455),f331(f16(f891(x43453,a877),x43452),x43456))))
% 162.26/162.06 [4092]E(f331(f331(f331(f73(x40921,x40922),f331(f331(f331(f73(x40921,x40922),x40923),x40924),x40925)),x40924),x40926),f331(f331(f331(f73(x40921,x40922),x40923),x40924),x40926))
% 162.26/162.06 [4189]E(f331(f331(f107(f891(f890(x41891,x41892),a877)),f331(f331(f288(x41891,x41893,x41892),x41894),x41895)),f331(f331(f288(x41891,x41893,x41892),x41896),x41895)),f331(f331(f288(x41891,x41893,x41892),f331(f331(f107(f891(f890(x41891,x41893),a877)),x41894),x41896)),x41895))
% 162.26/162.06 [4328]E(f331(f331(f42(x43281,f891(x43282,a877)),x43283),f331(f331(f7(x43281,f891(x43284,f891(x43282,a877)),f891(x43282,a877)),f331(f331(f8(f891(x43284,a877),f891(f891(x43284,f891(x43282,a877)),f891(x43282,a877)),x43281),f42(x43284,f891(x43282,a877))),x43285)),x43286)),f331(f331(f42(x43284,f891(x43282,a877)),f331(f331(f42(x43281,f891(x43284,a877)),x43283),x43285)),x43286))
% 162.26/162.06 [4329]E(f331(f331(f43(x43291,f891(x43292,a877)),x43293),f331(f331(f7(x43291,f891(x43294,f891(x43292,a877)),f891(x43292,a877)),f331(f331(f8(f891(x43294,a877),f891(f891(x43294,f891(x43292,a877)),f891(x43292,a877)),x43291),f43(x43294,f891(x43292,a877))),x43295)),x43296)),f331(f331(f43(x43294,f891(x43292,a877)),f331(f331(f42(x43291,f891(x43294,a877)),x43293),x43295)),x43296))
% 162.26/162.06 [4385]E(f331(f270(x43851,x43852,f890(x43853,x43854)),f331(f331(f7(x43851,f891(x43852,x43854),f891(x43852,f890(x43853,x43854))),f331(f331(f8(f891(x43854,f890(x43853,x43854)),f891(f891(x43852,x43854),f891(x43852,f890(x43853,x43854))),x43851),f8(x43854,f890(x43853,x43854),x43852)),f331(f331(f8(x43853,f891(x43854,f890(x43853,x43854)),x43851),f261(x43853,x43854)),x43855))),x43856)),f271(x43851,x43853,x43852,x43854,x43855,x43856))
% 162.26/162.06 [4305]E(f331(f331(f331(f73(x43051,f887(x43052)),f190(x43051,x43052,x43053,f331(f331(f22(f891(x43051,a877)),x43054),f331(f331(f309(x43051),x43055),f196(f891(x43051,a877)))))),x43055),x43056),f331(f331(f331(f73(x43051,f887(x43052)),f190(x43051,x43052,x43053,x43054)),x43055),x43056))
% 162.26/162.06 [4416]E(f331(f310(x44161,x44162,f331(f331(f18(x44161,x44162,x44162),f331(f331(f18(x44161,x44162,f891(x44162,x44162)),f331(f331(f8(a877,f891(x44162,f891(x44162,x44162)),x44161),f102(x44162)),x44163)),x44164)),x44165)),x44166),f331(f331(f107(f891(x44162,a877)),f331(f310(x44161,x44162,x44164),f331(f331(f108(f891(x44161,a877)),x44166),f331(f253(x44161),x44163)))),f331(f310(x44161,x44162,x44165),f331(f331(f108(f891(x44161,a877)),x44166),f331(f253(x44161),f331(f331(f8(a877,a877,x44161),a326),x44163))))))
% 162.26/162.06 [4429]E(f331(f310(x44291,f890(x44292,x44293),f331(f331(f18(x44291,x44293,f890(x44292,x44293)),f331(f331(f8(x44292,f891(x44293,f890(x44292,x44293)),x44291),f261(x44292,x44293)),x44294)),x44295)),x44296),f331(f331(f268(x44292,x44293),f331(f310(x44291,x44292,x44294),x44296)),f331(f331(f8(f891(x44291,a877),f891(x44293,a877),x44292),f310(x44291,x44293,x44295)),f331(f331(f7(x44292,f891(x44291,a877),f891(x44291,a877)),f331(f331(f8(f891(x44291,a877),f891(f891(x44291,a877),f891(x44291,a877)),x44292),f108(f891(x44291,a877))),f331(f331(f8(f891(x44292,a877),f891(x44291,a877),x44292),f311(x44291,x44292,x44294)),f331(f331(f7(x44292,f891(x44292,a877),f891(x44292,a877)),f309(x44292)),f196(f891(x44292,a877)))))),x44296))))
% 162.26/162.06 [4369]E(f331(f269(x43691,x43692),f331(f271(x43693,x43691,x43694,x43692,x43695,x43696),x43697)),f331(x43696,f331(f269(x43693,x43694),x43697)))
% 162.26/162.06 [4370]E(f331(f260(x43701,x43702),f331(f271(x43703,x43701,x43704,x43702,x43705,x43706),x43707)),f331(x43705,f331(f260(x43703,x43704),x43707)))
% 162.26/162.06 [4069]E(f331(f331(f184(x40691,x40692),f331(f331(f162(x40691,x40693),x40694),x40695)),f331(f331(f162(x40692,x40696),x40694),x40697)),f331(f331(f162(f890(x40691,x40692),f331(f331(f184(x40691,x40692),x40693),x40696)),x40694),f331(f331(f261(x40691,x40692),x40695),x40697)))
% 162.26/162.06 [4133]E(f331(f331(f331(f272(x41331,x41332,x41333,x41334),x41335),x41336),x41337),f331(f331(f270(x41332,x41333,x41334),x41336),f331(x41335,x41337)))
% 162.26/162.06 [4146]E(f331(f331(f331(f272(x41461,x41462,x41463,x41464),x41465),x41466),x41467),f331(f331(x41466,f331(f260(x41462,x41463),f331(x41465,x41467))),f331(f269(x41462,x41463),f331(x41465,x41467))))
% 162.26/162.06 [4179]E(f189(x41791,x41792,f331(f331(f331(f73(x41791,f887(x41792)),x41793),x41794),f331(f239(x41792),x41795)),x41796,x41797),f189(x41791,x41792,x41793,f331(f331(f154(x41791),x41794),x41796),f331(f331(f154(x41792),x41795),x41797)))
% 162.26/162.06 [4200]E(f331(f74(x42001,x42002,x42003,x42004),f331(f74(x42005,x42001,x42003,x42006),x42007)),f331(f74(x42005,x42002,x42003,f331(f74(x42001,x42002,x42005,x42004),x42006)),x42007))
% 162.26/162.06 [4263]E(f331(f74(f887(x42631),f887(x42632),x42633,f331(f210(x42631,x42632),x42634)),f331(f331(f331(f73(x42633,f887(x42631)),x42635),x42636),f331(f239(x42631),x42637))),f331(f331(f331(f73(x42633,f887(x42632)),f331(f74(f887(x42631),f887(x42632),x42633,f331(f210(x42631,x42632),x42634)),x42635)),x42636),f331(f239(x42632),f331(x42634,x42637))))
% 162.26/162.06 [4392]E(f331(f271(x43921,x43922,x43923,x43923,x43924,f35(x43923)),f331(f271(x43921,x43921,x43925,x43923,f35(x43921),x43926),x43927)),f331(f331(f261(x43922,x43923),f331(x43924,f331(f260(x43921,x43925),x43927))),f331(x43926,f331(f269(x43921,x43925),x43927))))
% 162.26/162.06 [4393]E(f331(f271(x43931,x43931,x43932,x43933,f35(x43931),x43934),f331(f271(x43935,x43931,x43932,x43932,x43936,f35(x43932)),x43937)),f331(f331(f261(x43931,x43933),f331(x43936,f331(f260(x43935,x43932),x43937))),f331(x43934,f331(f269(x43935,x43932),x43937))))
% 162.26/162.06 [4414]E(f331(f271(x44141,x44142,x44143,x44143,x44144,f35(x44143)),f331(f271(x44145,x44141,x44143,x44143,x44146,f35(x44143)),x44147)),f331(f271(x44145,x44142,x44143,x44143,f331(f74(x44141,x44142,x44145,x44144),x44146),f35(x44143)),x44147))
% 162.26/162.06 [4415]E(f331(f271(x44151,x44151,x44152,x44153,f35(x44151),x44154),f331(f271(x44151,x44151,x44155,x44152,f35(x44151),x44156),x44157)),f331(f271(x44151,x44151,x44155,x44153,f35(x44151),f331(f74(x44152,x44153,x44155,x44154),x44156)),x44157))
% 162.26/162.06 [4426]E(f331(f271(x44261,x44262,x44263,x44263,x44264,f35(x44263)),f331(f271(x44261,x44261,x44265,x44263,f35(x44261),x44266),x44267)),f331(f271(x44262,x44262,x44265,x44263,f35(x44262),x44266),f331(f271(x44261,x44262,x44265,x44265,x44264,f35(x44265)),x44267)))
% 162.26/162.06 [4104]E(f331(f331(f288(x41041,x41042,x41043),f331(f331(f288(x41041,x41044,x41042),x41045),x41046)),x41047),f331(f331(f288(x41041,x41044,x41043),x41045),f331(f331(f288(x41044,x41042,x41043),x41046),x41047)))
% 162.26/162.06 [4170]E(f331(f331(f270(x41701,x41702,x41703),f331(f74(x41704,f891(x41702,x41703),x41701,x41705),x41706)),x41707),f331(f331(x41705,f331(x41706,f331(f260(x41701,x41702),x41707))),f331(f269(x41701,x41702),x41707)))
% 162.26/162.06 [4229]E(f331(f74(x42291,x42292,x42293,x42294),f331(f331(f331(f73(x42293,x42291),x42295),x42296),x42297)),f331(f331(f331(f73(x42293,x42292),f331(f74(x42291,x42292,x42293,x42294),x42295)),x42296),f331(x42294,x42297)))
% 162.26/162.06 [4258]E(f331(f145(x42581,x42582,f331(f7(x42582,x42581,x42581),x42583),x42584),f331(f172(x42582),f331(f331(f157(x42585,x42582),x42586),x42587))),f331(f145(x42581,x42585,f331(f7(x42585,x42581,x42581),f331(f74(x42582,f891(x42581,x42581),x42585,x42583),x42586)),x42584),f331(f172(x42585),x42587)))
% 162.26/162.06 [4201]E(f331(f331(f42(x42011,f891(f890(x42012,x42013),a877)),x42014),f331(f331(f8(f891(f890(x42015,x42013),a877),f891(f890(x42012,x42013),a877),x42011),f331(f288(x42012,x42015,x42013),x42016)),x42017)),f331(f331(f288(x42012,x42015,x42013),x42016),f331(f331(f42(x42011,f891(f890(x42015,x42013),a877)),x42014),x42017)))
% 162.26/162.06 [4351]E(f331(f331(f42(x43511,f891(f890(x43512,x43513),a877)),x43514),f331(f331(f7(x43511,f891(f890(x43515,x43513),a877),f891(f890(x43512,x43513),a877)),f331(f331(f8(f891(f890(x43512,x43515),a877),f891(f891(f890(x43515,x43513),a877),f891(f890(x43512,x43513),a877)),x43511),f288(x43512,x43515,x43513)),x43516)),x43517)),f331(f331(f288(x43512,x43515,x43513),f331(f331(f42(x43511,f891(f890(x43512,x43515),a877)),x43514),x43516)),x43517))
% 162.26/162.06 [4352]E(f331(f145(x43521,x43522,f331(f331(f7(x43521,f891(x43522,x43523),f891(x43522,x43521)),f331(f331(f8(f891(x43523,x43521),f891(f891(x43522,x43523),f891(x43522,x43521)),x43521),f8(x43523,x43521,x43522)),x43524)),x43525),x43526),x43527),f331(f145(x43521,x43523,x43524,x43526),f331(f331(f157(x43522,x43523),x43525),x43527)))
% 162.26/162.06 [4427]E(f331(f331(f43(x44271,f891(x44272,a877)),x44273),f331(f331(f8(f891(x44274,f891(x44272,a877)),f891(x44272,a877),x44271),f331(f43(x44274,f891(x44272,a877)),x44275)),f331(f331(f7(x44271,f891(x44274,f891(x44272,a877)),f891(x44274,f891(x44272,a877))),f331(f331(f8(f891(f891(x44272,a877),f891(x44272,a877)),f891(f891(x44274,f891(x44272,a877)),f891(x44274,f891(x44272,a877))),x44271),f8(f891(x44272,a877),f891(x44272,a877),x44274)),f331(f331(f8(f891(x44272,a877),f891(f891(x44272,a877),f891(x44272,a877)),x44271),f107(f891(x44272,a877))),x44276))),x44277))),f331(f331(f107(f891(x44272,a877)),f331(f331(f43(x44271,f891(x44272,a877)),x44273),x44276)),f331(f331(f43(x44274,f891(x44272,a877)),x44275),x44277)))
% 162.26/162.06 [4428]E(f331(f331(f42(x44281,f891(x44282,a877)),x44283),f331(f331(f8(f891(x44284,f891(x44282,a877)),f891(x44282,a877),x44281),f331(f42(x44284,f891(x44282,a877)),x44285)),f331(f331(f7(x44281,f891(x44284,f891(x44282,a877)),f891(x44284,f891(x44282,a877))),f331(f331(f8(f891(f891(x44282,a877),f891(x44282,a877)),f891(f891(x44284,f891(x44282,a877)),f891(x44284,f891(x44282,a877))),x44281),f8(f891(x44282,a877),f891(x44282,a877),x44284)),f331(f331(f8(f891(x44282,a877),f891(f891(x44282,a877),f891(x44282,a877)),x44281),f108(f891(x44282,a877))),x44286))),x44287))),f331(f331(f108(f891(x44282,a877)),f331(f331(f42(x44281,f891(x44282,a877)),x44283),x44286)),f331(f331(f42(x44284,f891(x44282,a877)),x44285),x44287)))
% 162.26/162.06 [4419]E(f208(x44191,x44192,f331(f331(f331(x44193,x44194),x44195),x44196),f331(f331(f7(x44191,f890(a105,a105),f891(a105,f885(x44192))),f331(f331(f7(x44191,a105,f891(f890(a105,a105),f891(a105,f885(x44192)))),f331(f331(f7(x44191,a105,f891(a105,f891(f890(a105,a105),f891(a105,f885(x44192))))),x44197),x44194)),x44195)),x44196)),f331(f331(f331(f221(x44191,x44192,x44193,x44197),x44194),x44195),x44196))
% 162.26/162.06 [4430]E(f209(x44301,x44302,f331(f331(f331(x44303,x44304),x44305),x44306),f331(f331(f7(x44301,f890(a105,a105),f891(a105,f885(x44302))),f331(f331(f7(x44301,a105,f891(f890(a105,a105),f891(a105,f885(x44302)))),f331(f331(f7(x44301,a105,f891(a105,f891(f890(a105,a105),f891(a105,f885(x44302))))),x44307),x44304)),x44305)),x44306)),f223(x44301,x44302,x44303,x44307,x44304,x44305,x44306))
% 162.26/162.06 [4425]E(f206(x44251,x44252,f331(f331(f331(x44253,x44254),x44255),x44256),f331(f331(f7(x44251,f890(a105,a105),f891(a105,f885(f887(x44252)))),f331(f331(f7(x44251,a105,f891(f890(a105,a105),f891(a105,f885(f887(x44252))))),f331(f331(f7(x44251,a105,f891(a105,f891(f890(a105,a105),f891(a105,f885(f887(x44252)))))),x44257),x44254)),x44255)),x44256)),f331(f331(f331(f218(x44251,x44252,x44253,x44257),x44254),x44255),x44256))
% 162.26/162.06 [4440]E(f207(x44401,x44402,f331(f331(f331(x44403,x44404),x44405),x44406),f331(f331(f7(x44401,f890(a105,a105),f891(a105,f885(f887(x44402)))),f331(f331(f7(x44401,a105,f891(f890(a105,a105),f891(a105,f885(f887(x44402))))),f331(f331(f7(x44401,a105,f891(a105,f891(f890(a105,a105),f891(a105,f885(f887(x44402)))))),x44407),x44404)),x44405)),x44406)),f220(x44401,x44402,x44403,x44407,x44404,x44405,x44406))
% 162.26/162.06 [4320]E(f331(f271(x43201,x43202,x43203,x43204,x43205,x43206),f331(f331(f261(x43201,x43203),x43207),x43208)),f331(f331(f261(x43202,x43204),f331(x43205,x43207)),f331(x43206,x43208)))
% 162.26/162.06 [4442]E(f331(f331(f157(f890(x44421,x44422),f890(x44423,x44424)),f331(f270(x44421,x44422,f890(x44423,x44424)),f331(f331(f7(x44421,f891(x44422,x44424),f891(x44422,f890(x44423,x44424))),f331(f331(f8(f891(x44424,f890(x44423,x44424)),f891(f891(x44422,x44424),f891(x44422,f890(x44423,x44424))),x44421),f8(x44424,f890(x44423,x44424),x44422)),f331(f331(f8(x44423,f891(x44424,f890(x44423,x44424)),x44421),f261(x44423,x44424)),x44425))),x44426))),f331(f331(f184(x44421,x44422),x44427),x44428)),f331(f331(f184(x44423,x44424),f331(f331(f157(x44421,x44423),x44425),x44427)),f331(f331(f157(x44422,x44424),x44426),x44428)))
% 162.26/162.06 [4448]E(f331(f331(f157(f890(x44481,x44482),x44483),f331(f270(x44481,x44482,x44483),f331(f331(f8(f891(x44482,f890(x44481,x44484)),f891(x44482,x44483),x44481),f331(f8(f890(x44481,x44484),x44483,x44482),x44485)),f331(f331(f7(x44481,f891(x44482,x44484),f891(x44482,f890(x44481,x44484))),f331(f331(f8(f891(x44484,f890(x44481,x44484)),f891(f891(x44482,x44484),f891(x44482,f890(x44481,x44484))),x44481),f8(x44484,f890(x44481,x44484),x44482)),f261(x44481,x44484))),x44486)))),f331(f331(f184(x44481,x44482),x44487),x44488)),f331(f331(f157(f890(x44481,x44484),x44483),x44485),f331(f331(f184(x44481,x44484),x44487),f331(f331(f157(x44482,x44484),x44486),x44488))))
% 162.26/162.06 [4361]E(f331(f331(f157(f890(x43611,x43612),x43613),f331(f270(x43611,x43612,x43613),f331(f331(f8(f891(x43612,f890(x43614,x43612)),f891(x43612,x43613),x43611),f331(f8(f890(x43614,x43612),x43613,x43612),x43615)),f331(f331(f8(x43614,f891(x43612,f890(x43614,x43612)),x43611),f261(x43614,x43612)),x43616)))),f331(f331(f184(x43611,x43612),x43617),x43618)),f331(f331(f157(f890(x43614,x43612),x43613),x43615),f331(f331(f184(x43614,x43612),f331(f331(f157(x43611,x43614),x43616),x43617)),x43618)))
% 162.26/162.06 [4311]E(f331(f331(f270(x43111,x43112,x43113),f331(f331(f8(f891(x43112,f890(x43114,x43115)),f891(x43112,x43113),x43111),f331(f8(f890(x43114,x43115),x43113,x43112),f331(f270(x43114,x43115,x43113),x43116))),x43117)),x43118),f331(f331(f270(x43114,x43115,x43113),x43116),f331(f331(f270(x43111,x43112,f890(x43114,x43115)),x43117),x43118)))
% 162.26/162.06 [4449]E(f331(f331(f42(f890(x44491,x44492),f891(f890(x44493,x44494),a877)),f331(f331(f268(x44491,x44492),x44495),f331(f16(f891(x44492,a877),x44491),x44496))),f331(f270(x44491,x44492,f891(f890(x44493,x44494),a877)),f331(f331(f7(x44491,f891(x44492,f891(x44493,f891(x44494,a877))),f891(x44492,f891(f890(x44493,x44494),a877))),f331(f331(f8(f891(f891(x44493,f891(x44494,a877)),f891(f890(x44493,x44494),a877)),f891(f891(x44492,f891(x44493,f891(x44494,a877))),f891(x44492,f891(f890(x44493,x44494),a877))),x44491),f8(f891(x44493,f891(x44494,a877)),f891(f890(x44493,x44494),a877),x44492)),f331(f331(f8(f891(x44493,a877),f891(f891(x44493,f891(x44494,a877)),f891(f890(x44493,x44494),a877)),x44491),f268(x44493,x44494)),x44497))),f331(f331(f8(f891(x44494,a877),f891(x44493,f891(x44494,a877)),x44492),f16(f891(x44494,a877),x44493)),x44498)))),f331(f331(f268(x44493,x44494),f331(f331(f42(x44491,f891(x44493,a877)),x44495),x44497)),f331(f16(f891(x44494,a877),x44493),f331(f331(f42(x44492,f891(x44494,a877)),x44496),x44498))))
% 162.26/162.06 [4375]E(f331(f331(f272(x43751,x43752,x43753,x43754),f331(f331(f272(x43751,x43755,x43756,f890(x43752,x43753)),x43757),x43758)),x43759),f331(f331(f272(x43751,x43755,x43756,x43754),x43757),f331(f331(f7(x43755,f891(x43752,f891(x43753,x43754)),f891(x43756,x43754)),f331(f331(f8(f891(x43756,f890(x43752,x43753)),f891(f891(x43752,f891(x43753,x43754)),f891(x43756,x43754)),x43755),f272(x43756,x43752,x43753,x43754)),x43758)),x43759)))
% 162.26/162.06 [4411]E(f331(f74(f890(x44111,x44112),f890(x44113,x44114),f890(x44115,x44116),f271(x44111,x44113,x44112,x44114,x44117,x44118)),f271(x44115,x44111,x44116,x44112,x44119,x441110)),f271(x44115,x44113,x44116,x44114,f331(f74(x44111,x44113,x44115,x44117),x44119),f331(f74(x44112,x44114,x44116,x44118),x441110)))
% 162.26/162.06 [4417]E(f331(f271(x44171,x44172,x44173,x44174,x44175,x44176),f331(f271(x44177,x44171,x44178,x44173,x44179,x441710),x441711)),f331(f271(x44177,x44172,x44178,x44174,f331(f74(x44171,x44172,x44177,x44175),x44179),f331(f74(x44173,x44174,x44178,x44176),x441710)),x441711))
% 162.26/162.06 [4601]~P93(x46011)+E(f92(x46011),a328)
% 162.26/162.06 [4602]~P26(x46021)+P26(f887(x46021))
% 162.26/162.06 [4603]~P60(x46031)+P60(f887(x46031))
% 162.26/162.06 [4604]~P104(x46041)+P104(f884(x46041))
% 162.26/162.06 [4607]~P142(x46071)+~E(f79(x46071),f2(x46071))
% 162.26/162.06 [4609]~E(x46091,f2(a105))+E(f331(a20,x46091),f2(a1))
% 162.26/162.06 [4610]~E(x46101,f2(a1))+E(f83(a1,x46101),f2(a1))
% 162.26/162.06 [4617]~P143(x46171)+P31(x46171,f2(x46171))
% 162.26/162.06 [4619]~P107(x46191)+P29(x46191,f119(x46191))
% 162.26/162.06 [4629]P24(x46291)+P24(f331(a326,x46291))
% 162.26/162.06 [4672]~P143(x46721)+~P31(x46721,f79(x46721))
% 162.26/162.06 [4717]~P24(x47171)+~P24(f331(a326,x47171))
% 162.26/162.06 [4741]E(f331(a111,x47411),f2(a883))+~P24(f331(a202,x47411))
% 162.26/162.06 [4805]~P71(x48051)+P12(x48051,x48051,f82(x48051))
% 162.26/162.06 [4806]~P95(x48061)+P11(x48061,x48061,f82(x48061))
% 162.26/162.06 [4807]~P101(x48071)+P11(x48071,x48071,f107(x48071))
% 162.26/162.06 [4808]~P107(x48081)+P11(x48081,x48081,f251(x48081))
% 162.26/162.06 [4809]~P107(x48091)+P11(x48091,x48091,f246(x48091))
% 162.26/162.06 [4810]~P102(x48101)+P11(x48101,x48101,f108(x48101))
% 162.26/162.06 [4614]~E(x46141,f2(a883))+E(f331(f106(a1),x46141),f2(a1))
% 162.26/162.06 [4622]~P94(x46221)+E(f331(f110(x46221),a84),f2(x46221))
% 162.26/162.06 [4625]~E(f601(x46251),f2(a883))+E(f331(f169(a883),x46251),f2(a883))
% 162.26/162.06 [4626]~P109(x46261)+E(f249(x46261,f247(x46261)),f251(x46261))
% 162.26/162.06 [4627]~P109(x46271)+E(f250(x46271,f247(x46271)),f246(x46271))
% 162.26/162.06 [4628]~P88(x46281)+E(f83(x46281,f2(x46281)),f2(x46281))
% 162.26/162.06 [4637]~P143(x46371)+E(f331(f106(x46371),f79(a883)),f79(x46371))
% 162.26/162.06 [4638]~P143(x46381)+E(f331(f106(x46381),f2(a883)),f2(x46381))
% 162.26/162.06 [4639]~P138(x46391)+E(f331(f109(x46391),f79(a1)),f79(x46391))
% 162.26/162.06 [4640]~P138(x46401)+E(f331(f109(x46401),f2(a1)),f2(x46401))
% 162.26/162.06 [4641]E(x46411,f2(a883))+~E(f331(f106(a1),x46411),f2(a1))
% 162.26/162.06 [4666]~P85(x46661)+E(f331(f80(x46661),f196(x46661)),f256(x46661))
% 162.26/162.06 [4667]~P66(x46671)+E(f331(f80(x46671),f2(x46671)),f2(x46671))
% 162.26/162.06 [4668]~P85(x46681)+E(f331(f80(x46681),f256(x46681)),f196(x46681))
% 162.26/162.06 [4669]~P111(x46691)+E(f331(f76(x46691),f79(x46691)),f79(x46691))
% 162.26/162.06 [4670]~P83(x46701)+E(f331(f76(x46701),f2(x46701)),f2(x46701))
% 162.26/162.06 [4671]~P80(x46711)+E(f331(f169(x46711),f119(x46711)),f2(x46711))
% 162.26/162.06 [4692]~P37(x46921)+P40(f331(f175(a1),x46921))
% 162.26/162.06 [4722]~P94(x47221)+E(f331(f80(x47221),f79(x47221)),f331(f110(x47221),a103))
% 162.26/162.06 [4740]~P94(x47401)+P31(x47401,f331(f110(x47401),a84))
% 162.26/162.06 [4757]~P60(x47571)+E(f331(f175(x47571),f56(x47571)),f256(f891(x47571,a877)))
% 162.26/162.06 [4767]P37(x47671)+~P40(f331(f175(a1),x47671))
% 162.26/162.06 [4768]~P60(x47681)+P24(f331(f140(x47681),f56(x47681)))
% 162.26/162.06 [4811]E(f331(f106(a1),f331(a111,x48111)),x48111)+P24(f331(a202,x48111))
% 162.26/162.06 [4828]~P109(x48281)+E(f95(x48281,x48281,f5(x48281)),f96(x48281))
% 162.26/162.06 [4879]~P115(x48791)+E(f263(x48791,f79(x48791),f82(x48791)),f262(x48791))
% 162.26/162.06 [4909]~P94(x49091)+~P31(x49091,f331(f110(x49091),a103))
% 162.26/162.06 [4920]E(f331(a26,x49201),f199(a879))+P24(f331(a25,f331(a28,x49201)))
% 162.26/162.06 [5050]E(f331(f76(a1),x50501),x50501)+P24(f331(f331(f248(a1),x50501),f2(a1)))
% 162.26/162.06 [5071]~E(f331(a111,x50711),f2(a883))+P24(f331(f331(f247(a1),x50711),f2(a1)))
% 162.26/162.06 [5131]~P24(f331(a202,x51311))+P24(f331(f331(f248(a1),x51311),f2(a1)))
% 162.26/162.06 [5170]~P138(x51701)+P24(f331(f331(f333(x51701),f79(x51701)),f116(x51701)))
% 162.26/162.06 [5171]~P143(x51711)+P24(f331(f331(f333(x51711),f79(x51711)),f194(x51711)))
% 162.26/162.06 [5172]~P138(x51721)+P24(f331(f331(f333(x51721),f2(x51721)),f116(x51721)))
% 162.26/162.06 [5173]~P143(x51731)+P24(f331(f331(f333(x51731),f2(x51731)),f194(x51731)))
% 162.26/162.06 [5174]~P110(x51741)+P24(f331(f331(f248(x51741),f2(x51741)),f79(x51741)))
% 162.26/162.06 [5175]~P110(x51751)+P24(f331(f331(f247(x51751),f2(x51751)),f79(x51751)))
% 162.26/162.06 [5178]E(f331(f239(a879),f545(x51781)),f331(a26,x51781))+~P24(f331(a25,f331(a28,x51781)))
% 162.26/162.06 [5179]E(f331(f239(a879),f723(x51791)),f331(a26,x51791))+~P24(f331(a25,f331(a28,x51791)))
% 162.26/162.06 [5234]E(x52341,f2(a883))+~P24(f331(f331(f247(a883),x52341),f2(a883)))
% 162.26/162.06 [5279]E(f331(a111,x52791),f2(a883))+~P24(f331(f331(f247(a1),x52791),f2(a1)))
% 162.26/162.06 [5342]P24(f331(a202,x53421))+~P24(f331(f331(f248(a1),x53421),f2(a1)))
% 162.26/162.06 [5347]~P107(x53471)+P12(x53471,f884(x53471),f151(x53471,x53471,f5(x53471)))
% 162.26/162.06 [5365]P40(x53651)+~P24(f331(f331(f247(a1),f2(a1)),f338(x53651)))
% 162.26/162.06 [5371]E(f331(f76(a1),x53711),f331(f80(a1),x53711))+~P24(f331(f331(f248(a1),x53711),f2(a1)))
% 162.26/162.06 [5543]~P110(x55431)+~P24(f331(f331(f248(x55431),f79(x55431)),f2(x55431)))
% 162.26/162.06 [5544]~P110(x55441)+~P24(f331(f331(f247(x55441),f79(x55441)),f2(x55441)))
% 162.26/162.06 [5554]~E(x55541,f2(a1))+P24(f331(f331(f248(a1),f331(f76(a1),x55541)),f79(a1)))
% 162.26/162.06 [5555]~E(x55551,f2(a883))+P24(f331(f331(f247(a1),f331(f106(a1),x55551)),f2(a1)))
% 162.26/162.06 [5675]~P80(x56751)+E(f145(x56751,x56751,f81(x56751),f2(x56751)),f169(x56751))
% 162.26/162.06 [5846]~P103(x58461)+P21(a883,x58461,f106(x58461),f256(f891(a883,a877)))
% 162.26/162.06 [6042]E(x60421,f2(a883))+~P24(f331(f331(f247(a1),f331(f106(a1),x60421)),f2(a1)))
% 162.26/162.06 [6043]E(x60431,f2(a1))+~P24(f331(f331(f248(a1),f331(f76(a1),x60431)),f79(a1)))
% 162.26/162.06 [7905]E(x79051,f331(a3,f2(a883)))+P24(f331(f331(f248(a883),f331(f331(f22(a883),f331(a19,x79051)),f331(a118,f2(a883)))),f331(a19,x79051)))
% 162.26/162.06 [8749]~P24(f331(f331(f248(a1),x87491),f2(a1)))+P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x87491)),x87491)),f2(a1)))
% 162.26/162.06 [9133]P24(f331(f331(f248(a1),x91331),f2(a1)))+~P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x91331)),x91331)),f2(a1)))
% 162.26/162.06 [9589]~P24(f331(f331(f248(a1),x95891),f2(a1)))+P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x95891)),x95891)),a103)),f2(a1)))
% 162.26/162.06 [9759]P24(f331(f331(f248(a1),x97591),f2(a1)))+~P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x97591)),x97591)),a103)),f2(a1)))
% 162.26/162.06 [4726]E(x47261,f2(a1))+E(f331(f331(f39(a1),x47261),x47261),f79(a1))
% 162.26/162.06 [4869]~P27(x48691)+E(f41(x48691,f196(f891(x48691,a877))),f256(x48691))
% 162.26/162.06 [4870]~P27(x48701)+E(f41(x48701,f256(f891(x48701,a877))),f196(x48701))
% 162.26/162.06 [4871]~P27(x48711)+E(f40(x48711,f196(f891(x48711,a877))),f196(x48711))
% 162.26/162.06 [4872]~P27(x48721)+E(f40(x48721,f256(f891(x48721,a877))),f256(x48721))
% 162.26/162.06 [4873]~P107(x48731)+E(f142(x48731,f196(f891(x48731,a877))),f119(x48731))
% 162.26/162.06 [5009]E(x50091,f2(a883))+P24(f331(f331(f248(a883),f2(a883)),x50091))
% 162.26/162.06 [5028]~P28(x50281)+P24(f331(f331(f247(a1),f2(a1)),x50281))
% 162.26/162.06 [5062]~E(f331(f110(a883),x50621),f2(a883))+P24(f331(f331(f247(a1),x50621),a84))
% 162.26/162.06 [5067]P40(x50671)+P24(f331(f331(f333(a1),f338(x50671)),x50671))
% 162.26/162.06 [5068]E(x50681,f331(a3,f2(a883)))+P24(f331(f331(f247(a105),f79(a105)),x50681))
% 162.26/162.06 [5105]P24(f331(a202,x51051))+P24(f331(f331(f247(a1),f2(a1)),x51051))
% 162.26/162.06 [5152]E(f331(f106(a1),f331(a111,x51521)),f2(a1))+P24(f331(f331(f247(a1),f2(a1)),x51521))
% 162.26/162.06 [5220]E(f331(f106(a1),f331(f110(a883),x52201)),f331(f110(a1),x52201))+P24(f331(a202,f331(f110(a1),x52201)))
% 162.26/162.06 [5240]E(f331(f110(a883),x52401),f2(a883))+~P24(f331(a202,f331(f110(a1),x52401)))
% 162.26/162.06 [5241]E(f331(f110(a883),x52411),f2(a883))+~P24(f331(f331(f247(a1),x52411),a84))
% 162.26/162.06 [5276]P28(x52761)+~P24(f331(f331(f247(a1),f2(a1)),x52761))
% 162.26/162.06 [5350]E(f331(a118,f724(x53501)),x53501)+~P24(f331(f331(f248(a883),f2(a883)),x53501))
% 162.26/162.06 [5359]E(f331(a118,f331(f110(a883),x53591)),f79(a883))+~P24(f331(a202,f331(f110(a1),x53591)))
% 162.26/162.06 [5367]E(f331(f106(a1),f393(x53671)),x53671)+~P24(f331(f331(f248(a1),f2(a1)),x53671))
% 162.26/162.06 [5375]~E(x53751,f331(a3,f2(a883)))+~P24(f331(f331(f247(a105),f79(a105)),x53751))
% 162.26/162.06 [5382]E(f331(f106(a1),f331(f110(a883),x53821)),f2(a1))+~P24(f331(a202,f331(f110(a1),x53821)))
% 162.26/162.06 [5408]E(f331(f169(a883),x54081),f2(a883))+P24(f331(f331(f333(a883),f601(x54081)),f331(f175(a883),x54081)))
% 162.26/162.06 [5429]E(f331(f106(a1),f331(a111,x54291)),x54291)+~P24(f331(f331(f247(a1),f2(a1)),x54291))
% 162.26/162.06 [5438]~P24(f331(a202,x54381))+~P24(f331(f331(f247(a1),f2(a1)),x54381))
% 162.26/162.06 [5536]E(f331(f331(f81(a883),f79(a883)),f331(f110(a883),x55361)),f79(a883))+~P24(f331(f331(f248(a1),x55361),a84))
% 162.26/162.06 [5594]E(x55941,f2(a883))+~P24(f331(f331(f248(a883),x55941),f331(a118,f2(a883))))
% 162.26/162.06 [5634]E(f331(f331(f22(a883),f331(f110(a883),x56341)),f79(a883)),f2(a883))+~P24(f331(f331(f247(a1),x56341),a84))
% 162.26/162.06 [5635]E(f331(f331(f81(a883),f331(f110(a883),x56351)),f79(a883)),f79(a883))+~P24(f331(f331(f248(a1),x56351),a84))
% 162.26/162.06 [5645]~P40(x56451)+E(f331(f38(a883),f331(f310(a1,a883,a111),x56451)),f331(f38(a1),x56451))
% 162.26/162.06 [5676]~P107(x56761)+E(f250(x56761,f331(f7(x56761,x56761,a877),f247(x56761))),f251(x56761))
% 162.26/162.06 [5677]~P107(x56771)+E(f249(x56771,f331(f7(x56771,x56771,a877),f247(x56771))),f246(x56771))
% 162.26/162.06 [5687]E(f45(a883,f331(a118,f2(a883)),f331(f110(a883),x56871)),f331(a118,f2(a883)))+~P24(f331(a202,f331(f110(a1),x56871)))
% 162.26/162.06 [5696]P24(f331(f331(f248(a1),f2(a1)),x56961))+~P24(f331(f331(f247(a1),f79(a1)),x56961))
% 162.26/162.06 [5697]~P24(f331(f331(f248(a1),f2(a1)),x56971))+P24(f331(f331(f247(a1),f79(a1)),x56971))
% 162.26/162.06 [5708]E(f331(a118,f331(f331(f22(a883),x57081),f79(a883))),x57081)+~P24(f331(f331(f248(a883),f2(a883)),x57081))
% 162.26/162.06 [5765]P24(f331(f331(f248(a883),f2(a883)),f393(x57651)))+~P24(f331(f331(f248(a1),f2(a1)),x57651))
% 162.26/162.06 [5824]E(f45(a1,f331(f110(a1),a103),x58241),f331(f331(f22(a1),x58241),f79(a1)))+~P24(f331(f331(f248(a1),f2(a1)),x58241))
% 162.26/162.06 [5858]~P24(f331(f331(f248(a1),a84),x58581))+P24(f331(f331(f248(a883),f2(a883)),f331(f110(a883),x58581)))
% 162.26/162.06 [5908]P24(f331(f331(f248(a883),f2(a883)),f331(a111,x59081)))+~P24(f331(f331(f248(a1),f2(a1)),x59081))
% 162.26/162.06 [5959]~P24(f331(f331(f248(a883),f2(a883)),x59591))+P24(f331(f331(f248(a1),f2(a1)),f331(f106(a1),x59591)))
% 162.26/162.06 [5997]~P24(f331(f331(f248(a883),f2(a883)),f331(a111,x59971)))+P24(f331(f331(f248(a1),f2(a1)),x59971))
% 162.26/162.06 [6012]~P40(x60121)+E(f331(f310(a883,a1,f106(a1)),f331(f310(a1,a883,a111),x60121)),x60121)
% 162.26/162.06 [6023]P24(f331(f331(f248(a1),a84),x60231))+~P24(f331(f331(f248(a883),f2(a883)),f331(f110(a883),x60231)))
% 162.26/162.06 [6071]~P60(x60711)+E(f331(f331(f154(f887(x60711)),f199(x60711)),f331(f331(f157(x60711,f887(x60711)),f239(x60711)),f56(x60711))),f56(f887(x60711)))
% 162.26/162.06 [6082]P24(f331(f331(f248(a883),f2(a883)),x60821))+~P24(f331(f331(f248(a1),f2(a1)),f331(f106(a1),x60821)))
% 162.26/162.06 [6194]E(f331(f310(a883,a1,f106(a1)),f331(f254(a883),f331(a111,x61941))),f331(f301(a1,f2(a1)),x61941))+~P24(f331(f331(f247(a1),f2(a1)),x61941))
% 162.26/162.06 [6209]~P110(x62091)+P24(f331(f331(f248(x62091),f2(x62091)),f331(f331(f81(x62091),f79(x62091)),f79(x62091))))
% 162.26/162.06 [6260]P24(f331(f331(f248(a883),f331(a118,f2(a883))),f331(a111,x62601)))+~P24(f331(f331(f248(a1),f79(a1)),x62601))
% 162.26/162.06 [6352]E(x63521,f2(a1))+P24(f331(f49(f2(a1),x63521),f331(f331(f261(a1,a1),f2(a1)),f2(a1))))
% 162.26/162.06 [6518]~P24(f331(f331(f248(a883),f331(a118,f2(a883))),f331(a111,x65181)))+P24(f331(f331(f248(a1),f79(a1)),x65181))
% 162.26/162.06 [6931]~P117(x69311)+P38(x69311,f331(f253(f890(x69311,x69311)),f331(f270(x69311,x69311,a877),f248(x69311))))
% 162.26/162.06 [5581]E(f331(f110(a883),f331(f331(f22(a1),x55811),a103)),f331(a118,f331(f110(a883),x55811)))+P24(f331(a202,f331(f110(a1),x55811)))
% 162.26/162.06 [5597]~P37(x55971)+E(f331(f331(f157(a883,a1),f106(a1)),f331(f331(f157(a1,a883),a111),x55971)),x55971)
% 162.26/162.06 [5714]E(f331(f80(a1),f331(f106(a1),f331(a118,f374(x57141)))),x57141)+~P24(f331(f331(f248(a1),x57141),f2(a1)))
% 162.26/162.06 [5724]E(f331(f331(f81(a883),f79(a883)),f331(f110(a883),x57241)),f331(f110(a883),f331(f331(f22(a1),x57241),a103)))+P24(f331(f331(f248(a1),x57241),a84))
% 162.26/162.06 [5767]E(f331(f331(f39(a1),f331(f110(a1),a103)),x57671),f331(f110(a1),a103))+~P24(f331(f331(f248(a1),f2(a1)),x57671))
% 162.26/162.06 [5854]E(f331(f331(f22(a883),f331(f110(a883),x58541)),f79(a883)),f331(f110(a883),f331(f331(f81(a1),x58541),a103)))+P24(f331(f331(f247(a1),x58541),a84))
% 162.26/162.06 [5855]E(f331(f331(f81(a883),f331(f110(a883),x58551)),f79(a883)),f331(f110(a883),f331(f331(f22(a1),x58551),a103)))+P24(f331(f331(f248(a1),x58551),a84))
% 162.26/162.06 [5896]E(f331(a111,f331(f331(f81(a1),f79(a1)),x58961)),f331(a118,f331(a111,x58961)))+~P24(f331(f331(f247(a1),f2(a1)),x58961))
% 162.26/162.06 [5932]E(f331(a118,f331(f331(f22(a883),x59321),f331(a118,f2(a883)))),x59321)+~P24(f331(f331(f248(a883),f2(a883)),x59321))
% 162.26/162.06 [6142]E(f45(a883,f331(a118,f2(a883)),f331(f110(a883),x61421)),f331(a111,f45(a1,f79(a1),f331(f110(a1),x61421))))+P24(f331(a202,f331(f110(a1),x61421)))
% 162.26/162.06 [6365]~P24(f331(f62(x63651),f256(f891(x63651,a877))))+P24(f331(f62(f887(x63651)),f256(f891(f887(x63651),a877))))
% 162.26/162.06 [6451]~P24(f331(f331(f247(a1),f2(a1)),x64511))+P24(f331(f331(f248(a1),f2(a1)),f331(f331(f81(a1),f79(a1)),x64511)))
% 162.26/162.06 [6458]E(f331(f260(a1,a1),f47(f79(a1),f331(f110(a1),x64581))),f331(f331(f39(a1),f79(a1)),f331(f110(a1),x64581)))+~P24(f331(f331(f247(a1),f2(a1)),f331(f110(a1),x64581)))
% 162.26/162.06 [6477]E(f331(f269(a1,a1),f47(f79(a1),f331(f110(a1),x64771))),f45(a1,f79(a1),f331(f110(a1),x64771)))+~P24(f331(f331(f247(a1),f2(a1)),f331(f110(a1),x64771)))
% 162.26/162.06 [6489]P24(f331(f62(x64891),f256(f891(x64891,a877))))+~P24(f331(f62(f887(x64891)),f256(f891(f887(x64891),a877))))
% 162.26/162.06 [6826]~P24(f331(f62(x68261),f256(f891(x68261,a877))))+P24(f331(f331(f248(a883),f2(a883)),f331(f38(x68261),f256(f891(x68261,a877)))))
% 162.26/162.06 [7399]P24(f331(f62(a883),x73991))+~P24(f331(f62(a1),f331(f310(a883,a1,f106(a1)),x73991)))
% 162.26/162.06 [5610]~E(a103,x56101)+E(f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x56101)),x56101),a103)
% 162.26/162.06 [5611]~E(x56111,a103)+E(f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x56111)),x56111),a103)
% 162.26/162.06 [6151]E(x61511,a103)+~E(f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x61511)),x61511),a103)
% 162.26/162.06 [6152]E(a103,x61521)+~E(f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x61521)),x61521),a103)
% 162.26/162.06 [6420]~E(f331(f110(a883),x64201),f2(a883))+P24(f331(a202,f331(f110(a1),f331(f331(f81(a1),x64201),a103))))
% 162.26/162.06 [7078]E(f331(f110(a883),x70781),f2(a883))+~P24(f331(a202,f331(f110(a1),f331(f331(f81(a1),x70781),a103))))
% 162.26/162.06 [7675]E(f331(a113,f535(x76751)),x76751)+~P24(f331(f331(f333(f891(f890(a883,a883),a877)),x76751),a104))
% 162.26/162.06 [6532]~P94(x65321)+E(f331(f110(x65321),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)),f79(x65321))
% 162.26/162.06 [6948]~P24(f331(a202,f331(f110(a1),x69481)))+E(f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x69481)),x69481)),f2(a883))
% 162.26/162.06 [7855]~P24(f331(f331(f248(a1),f331(f110(a1),x78551)),f2(a1)))+E(f331(f260(a1,a1),f331(a51,f50(f331(f80(a1),f79(a1)),f331(f80(a1),f331(f110(a1),x78551))))),f331(f331(f39(a1),f79(a1)),f331(f110(a1),x78551)))
% 162.26/162.06 [7863]~P24(f331(f331(f248(a1),f331(f110(a1),x78631)),f2(a1)))+E(f331(f269(a1,a1),f331(a51,f50(f331(f80(a1),f79(a1)),f331(f80(a1),f331(f110(a1),x78631))))),f45(a1,f79(a1),f331(f110(a1),x78631)))
% 162.26/162.06 [8047]~P24(f331(f331(f247(a1),a84),x80471))+P24(f331(f331(f248(a1),a84),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x80471)),x80471)))
% 162.26/162.06 [8048]~P24(f331(f331(f248(a1),a103),x80481))+P24(f331(f331(f248(a1),a103),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x80481)),x80481)))
% 162.26/162.06 [8049]~P24(f331(f331(f247(a1),a84),x80491))+P24(f331(f331(f247(a1),a84),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x80491)),x80491)))
% 162.26/162.06 [8050]~P24(f331(f331(f247(a1),a103),x80501))+P24(f331(f331(f247(a1),a103),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x80501)),x80501)))
% 162.26/162.06 [8051]~P24(f331(f331(f92(a1),a103),x80511))+P24(f331(f331(f92(a1),a103),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x80511)),x80511)))
% 162.26/162.06 [8386]~P94(x83861)+~P31(x83861,f331(f110(x83861),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)))
% 162.26/162.06 [8510]P24(f331(f331(f248(a1),a103),x85101))+~P24(f331(f331(f248(a1),a103),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x85101)),x85101)))
% 162.26/162.06 [8511]P24(f331(f331(f247(a1),a84),x85111))+~P24(f331(f331(f248(a1),a84),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x85111)),x85111)))
% 162.26/162.06 [8512]P24(f331(f331(f247(a1),a84),x85121))+~P24(f331(f331(f247(a1),a84),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x85121)),x85121)))
% 162.26/162.06 [8513]P24(f331(f331(f247(a1),a103),x85131))+~P24(f331(f331(f247(a1),a103),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x85131)),x85131)))
% 162.26/162.06 [8514]P24(f331(f331(f92(a1),a103),x85141))+~P24(f331(f331(f92(a1),a103),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x85141)),x85141)))
% 162.26/162.06 [8721]E(f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x87211)),x87211)),f331(f331(f89(a883,a883),f331(f110(a883),x87211)),f331(f331(f8(a883,a883,a883),a118),f331(f331(f18(a883,a883,a883),f81(a883)),f5(a883)))))+P24(f331(a202,f331(f110(a1),x87211)))
% 162.26/162.06 [9561]E(x95611,f196(f891(f890(a883,a883),a877)))+P24(f331(f331(f333(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877))),f331(f331(f261(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),x95611),f196(f891(f890(a883,a883),a877)))),a69))
% 162.26/162.06 [7765]~E(a84,x77651)+E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x77651)),x77651)),a103),a84)
% 162.26/162.06 [7766]~E(x77661,a84)+E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x77661)),x77661)),a103),a84)
% 162.26/162.06 [8402]E(x84021,a84)+~E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x84021)),x84021)),a103),a84)
% 162.26/162.06 [8403]E(a84,x84031)+~E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x84031)),x84031)),a103),a84)
% 162.26/162.06 [8736]~P24(f331(a202,f331(f110(a1),x87361)))+P24(f331(a202,f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x87361)),x87361))))
% 162.26/162.06 [8737]~P24(f331(f331(f248(a1),x87371),a84))+P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x87371)),x87371)),a84))
% 162.26/162.06 [8738]~P24(f331(f331(f248(a1),x87381),a103))+P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x87381)),x87381)),a103))
% 162.26/162.06 [8739]~P24(f331(f331(f248(a1),x87391),a84))+P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x87391)),x87391)),a84))
% 162.26/162.06 [8740]~P24(f331(f331(f247(a1),x87401),a103))+P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x87401)),x87401)),a103))
% 162.26/162.06 [8741]~P24(f331(f331(f92(a1),x87411),a103))+P24(f331(f331(f92(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x87411)),x87411)),a103))
% 162.26/162.06 [8813]~P24(f331(f331(f247(a1),f2(a1)),f331(f110(a1),x88131)))+P24(f331(f331(f247(a1),f2(a1)),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x88131)),x88131))))
% 162.26/162.06 [9123]P24(f331(a202,f331(f110(a1),x91231)))+~P24(f331(a202,f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x91231)),x91231))))
% 162.26/162.06 [9124]P24(f331(f331(f248(a1),x91241),a84))+~P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x91241)),x91241)),a84))
% 162.26/162.06 [9125]P24(f331(f331(f248(a1),x91251),a84))+~P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x91251)),x91251)),a84))
% 162.26/162.06 [9126]P24(f331(f331(f248(a1),x91261),a103))+~P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x91261)),x91261)),a103))
% 162.26/162.06 [9127]P24(f331(f331(f247(a1),x91271),a103))+~P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x91271)),x91271)),a103))
% 162.26/162.06 [9128]P24(f331(f331(f92(a1),x91281),a103))+~P24(f331(f331(f92(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x91281)),x91281)),a103))
% 162.26/162.06 [9613]~P24(f331(f62(f890(a883,a883)),x96131))+P24(f331(f331(f333(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877))),f331(f331(f261(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),f196(f891(f890(a883,a883),a877))),x96131)),a70))
% 162.26/162.06 [9286]~P24(f331(f331(f248(a1),a84),x92861))+P24(f331(f331(f248(a1),a84),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x92861)),x92861)),a103)))
% 162.26/162.06 [9287]~P24(f331(f331(f248(a1),a103),x92871))+P24(f331(f331(f248(a1),a103),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x92871)),x92871)),a103)))
% 162.26/162.06 [9288]~P24(f331(f331(f247(a1),a84),x92881))+P24(f331(f331(f247(a1),a84),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x92881)),x92881)),a103)))
% 162.26/162.06 [9289]~P24(f331(f331(f248(a1),a103),x92891))+P24(f331(f331(f247(a1),a103),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x92891)),x92891)),a103)))
% 162.26/162.06 [9290]~P24(f331(f331(f92(a1),a84),x92901))+P24(f331(f331(f92(a1),a84),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x92901)),x92901)),a103)))
% 162.26/162.06 [9503]P24(f331(f331(f248(a1),a84),x95031))+~P24(f331(f331(f248(a1),a84),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x95031)),x95031)),a103)))
% 162.26/162.06 [9504]P24(f331(f331(f248(a1),a103),x95041))+~P24(f331(f331(f248(a1),a103),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x95041)),x95041)),a103)))
% 162.26/162.06 [9505]P24(f331(f331(f248(a1),a103),x95051))+~P24(f331(f331(f247(a1),a103),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x95051)),x95051)),a103)))
% 162.26/162.06 [9506]P24(f331(f331(f247(a1),a84),x95061))+~P24(f331(f331(f247(a1),a84),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x95061)),x95061)),a103)))
% 162.26/162.06 [9507]P24(f331(f331(f92(a1),a84),x95071))+~P24(f331(f331(f92(a1),a84),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x95071)),x95071)),a103)))
% 162.26/162.06 [9583]~P24(f331(a202,f331(f110(a1),x95831)))+P24(f331(a202,f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x95831)),x95831)),a103))))
% 162.26/162.06 [9584]~P24(f331(f331(f248(a1),x95841),a84))+P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x95841)),x95841)),a103)),a84))
% 162.26/162.06 [9585]~P24(f331(f331(f247(a1),x95851),a103))+P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x95851)),x95851)),a103)),a103))
% 162.26/162.06 [9586]~P24(f331(f331(f247(a1),x95861),a84))+P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x95861)),x95861)),a103)),a84))
% 162.26/162.06 [9587]~P24(f331(f331(f247(a1),x95871),a103))+P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x95871)),x95871)),a103)),a103))
% 162.26/162.06 [9588]~P24(f331(f331(f92(a1),x95881),a84))+P24(f331(f331(f92(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x95881)),x95881)),a103)),a84))
% 162.26/162.06 [9592]~P24(f331(f331(f247(a1),f2(a1)),f331(f110(a1),x95921)))+P24(f331(f331(f247(a1),f2(a1)),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x95921)),x95921)),a103))))
% 162.26/162.06 [9753]P24(f331(a202,f331(f110(a1),x97531)))+~P24(f331(a202,f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x97531)),x97531)),a103))))
% 162.26/162.06 [9754]P24(f331(f331(f248(a1),x97541),a84))+~P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x97541)),x97541)),a103)),a84))
% 162.26/162.06 [9755]P24(f331(f331(f247(a1),x97551),a84))+~P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x97551)),x97551)),a103)),a84))
% 162.26/162.06 [9756]P24(f331(f331(f247(a1),x97561),a103))+~P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x97561)),x97561)),a103)),a103))
% 162.26/162.06 [9757]P24(f331(f331(f247(a1),x97571),a103))+~P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x97571)),x97571)),a103)),a103))
% 162.26/162.06 [9758]P24(f331(f331(f92(a1),x97581),a84))+~P24(f331(f331(f92(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x97581)),x97581)),a103)),a84))
% 162.26/162.06 [9863]~P94(x98631)+E(f331(f331(f81(x98631),f79(x98631)),f79(x98631)),f331(f110(x98631),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))
% 162.26/162.06 [9939]~P143(x99391)+E(f331(f331(f262(x99391),f79(x99391)),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f79(x99391))
% 162.26/162.06 [9940]~P143(x99401)+E(f331(f331(f262(x99401),f2(x99401)),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f2(x99401))
% 162.26/162.06 [10077]~P24(f331(f331(f248(a883),f79(a883)),x100771))+P24(f331(f331(f248(a883),f2(a883)),f331(f331(f39(a883),x100771),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))))
% 162.26/162.06 [10081]~P24(f331(f331(f248(a883),f2(a883)),x100811))+P24(f331(f331(f248(a883),f2(a883)),f331(f331(f39(a883),f331(f331(f81(a883),x100811),f79(a883))),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))))
% 162.26/162.06 [10100]~E(f45(a883,x101001,f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f79(a883))+P24(f331(f331(f248(a883),f2(a883)),f45(a883,x101001,f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))))
% 162.26/162.06 [10120]E(f45(a883,x101201,f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f79(a883))+~P24(f331(f331(f248(a883),f2(a883)),f45(a883,x101201,f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))))
% 162.26/162.06 [4645]~P38(x46451,x46452)+P55(x46451,x46452)
% 162.26/162.06 [4646]~P43(x46461,x46462)+P55(x46461,x46462)
% 162.26/162.06 [4605]~E(x46051,x46052)+E(f278(x46051,x46052),f79(a105))
% 162.26/162.06 [4608]E(f228(x46081,x46082),x46081)+~E(x46082,f2(a883))
% 162.26/162.06 [4613]P39(x46131,x46132)+~E(x46132,f199(x46131))
% 162.26/162.06 [4616]~E(x46162,f119(x46161))+E(f155(x46161,x46162),f119(x46161))
% 162.26/162.06 [4620]~P39(x46202,x46201)+E(x46201,f199(x46202))
% 162.26/162.06 [4636]~E(f155(x46362,x46361),f119(x46362))+E(x46361,f119(x46362))
% 162.26/162.06 [4650]~P25(x46502)+P25(f891(x46501,x46502))
% 162.26/162.06 [4651]~P65(x46512)+P65(f891(x46511,x46512))
% 162.26/162.06 [4652]~P106(x46522)+P106(f891(x46521,x46522))
% 162.26/162.06 [4653]~P108(x46532)+P108(f891(x46531,x46532))
% 162.26/162.06 [4654]~P109(x46542)+P109(f891(x46541,x46542))
% 162.26/162.06 [4655]~P85(x46552)+P85(f891(x46551,x46552))
% 162.26/162.06 [4656]~P86(x46562)+P86(f891(x46561,x46562))
% 162.26/162.06 [4657]~P96(x46572)+P96(f891(x46571,x46572))
% 162.26/162.06 [4658]~P96(x46582)+P101(f891(x46581,x46582))
% 162.26/162.06 [4659]~P98(x46592)+P97(f891(x46591,x46592))
% 162.26/162.06 [4660]~P27(x46602)+P27(f891(x46601,x46602))
% 162.26/162.06 [4661]~P96(x46612)+P102(f891(x46611,x46612))
% 162.26/162.06 [4662]~P99(x46622)+P99(f891(x46621,x46622))
% 162.26/162.06 [4663]~P98(x46632)+P100(f891(x46631,x46632))
% 162.26/162.06 [4664]~P116(x46642)+P116(f891(x46641,x46642))
% 162.26/162.06 [4665]~P98(x46652)+P98(f891(x46651,x46652))
% 162.26/162.06 [4677]E(x46771,x46772)+~E(f331(a28,x46771),f331(a28,x46772))
% 162.26/162.06 [4679]E(x46791,x46792)+~E(f331(a118,x46791),f331(a118,x46792))
% 162.26/162.06 [4680]E(x46801,x46802)+~E(f331(a113,x46801),f331(a113,x46802))
% 162.26/162.06 [4681]E(x46811,x46812)+~E(f331(a3,x46811),f331(a3,x46812))
% 162.26/162.06 [4683]E(x46831,x46832)+~E(f331(a19,x46831),f331(a19,x46832))
% 162.26/162.06 [4784]~P58(x47841)+E(f45(x47841,x47842,x47842),f2(x47841))
% 162.26/162.06 [4818]~P38(x48181,x48182)+P38(f884(x48181),f149(x48181,x48182))
% 162.26/162.06 [4819]~P38(x48191,x48192)+P38(f884(x48191),f148(x48191,x48192))
% 162.26/162.06 [4914]~P38(x49141,x49142)+P38(f891(x49141,a877),f324(x49141,x49142))
% 162.26/162.06 [4915]~P38(x49151,x49152)+P38(f891(x49151,a877),f322(x49151,x49152))
% 162.26/162.06 [5034]~P28(x50341)+P40(f302(a1,x50341,x50342))
% 162.26/162.06 [5134]~P38(x51341,x51342)+P57(x51341,f68(x51341,x51341,x51342))
% 162.26/162.06 [5639]~P77(x56391)+P21(x56391,x56391,f80(x56391),x56392)
% 162.26/162.06 [4631]~E(x46312,f119(x46311))+E(f331(f171(x46311),x46312),f119(x46311))
% 162.26/162.06 [4632]~E(x46322,f119(x46321))+E(f331(f172(x46321),x46322),f119(x46321))
% 162.26/162.06 [4687]E(x46871,f331(a111,x46872))+~E(f331(f106(a1),x46871),x46872)
% 162.26/162.06 [4690]E(x46901,f119(x46902))+~E(f331(f171(x46902),x46901),f119(x46902))
% 162.26/162.06 [4691]E(x46911,f119(x46912))+~E(f331(f172(x46912),x46911),f119(x46912))
% 162.26/162.06 [4709]~P94(x47091)+E(f331(f110(x47091),x47092),f331(f109(x47091),x47092))
% 162.26/162.06 [4714]~E(x47142,f199(x47141))+E(f240(x47141,x47142),f196(f891(x47141,a877)))
% 162.26/162.06 [4716]~P26(x47161)+P24(f331(f62(x47161),x47162))
% 162.26/162.06 [4723]E(x47231,f199(x47232))+E(f331(f239(x47232),f635(x47232,x47231)),x47231)
% 162.26/162.06 [4724]E(x47241,f199(x47242))+E(f331(f239(x47242),f844(x47242,x47241)),x47241)
% 162.26/162.06 [4725]E(x47251,f199(x47252))+E(f331(f239(x47252),f337(x47252,x47251)),x47251)
% 162.26/162.06 [4727]~E(f636(x47272,x47271),f119(x47271))+E(f182(x47271,x47272),f119(f884(x47271)))
% 162.26/162.06 [4736]~E(x47362,f119(x47361))+E(f331(f175(x47361),x47362),f196(f891(x47361,a877)))
% 162.26/162.06 [4737]~E(x47372,f119(x47371))+E(f196(f891(x47371,a877)),f331(f175(x47371),x47372))
% 162.26/162.06 [4739]E(x47391,x47392)+~E(f331(f106(a1),x47391),f331(f106(a1),x47392))
% 162.26/162.06 [4742]E(f226(x47421,x47422),f2(a883))+P24(f331(f62(x47421),x47422))
% 162.26/162.06 [4762]~P111(x47621)+E(f83(x47621,f83(x47621,x47622)),f83(x47621,x47622))
% 162.26/162.06 [4775]~P79(x47751)+E(f331(f331(f262(x47751),x47752),f79(a883)),x47752)
% 162.26/162.06 [4776]~P118(x47761)+E(f331(f331(f262(x47761),x47762),f79(a883)),x47762)
% 162.26/162.06 [4778]E(x47781,x47782)+E(f278(x47781,x47782),f331(f331(f81(a105),x47782),f79(a105)))
% 162.26/162.06 [4781]E(f331(f38(x47811),x47812),f2(a883))+P24(f331(f62(x47811),x47812))
% 162.26/162.06 [4785]~E(f155(x47851,x47852),x47852)+P24(f331(f140(x47851),x47852))
% 162.26/162.06 [4788]~P66(x47881)+E(f331(f331(f22(x47881),x47882),f2(x47881)),x47882)
% 162.26/162.06 [4789]~P118(x47891)+E(f331(f331(f81(x47891),x47892),f2(x47891)),x47892)
% 162.26/162.06 [4790]~P80(x47901)+E(f331(f331(f81(x47901),x47902),f2(x47901)),x47902)
% 162.26/162.06 [4791]~P74(x47911)+E(f331(f331(f81(x47911),x47912),f2(x47911)),x47912)
% 162.26/162.06 [4792]~P79(x47921)+E(f331(f331(f82(x47921),x47922),f79(x47921)),x47922)
% 162.26/162.06 [4793]~P73(x47931)+E(f331(f331(f82(x47931),x47932),f79(x47931)),x47932)
% 162.26/162.06 [4794]~P118(x47941)+E(f331(f331(f82(x47941),x47942),f79(x47941)),x47942)
% 162.26/162.06 [4795]~P97(x47951)+E(f331(f331(f107(x47951),x47952),f196(x47951)),x47952)
% 162.26/162.06 [4796]~P58(x47961)+E(f331(f331(f39(x47961),x47962),f79(x47961)),x47962)
% 162.26/162.06 [4797]~P119(x47971)+E(f331(f331(f289(x47971),x47972),f79(x47971)),x47972)
% 162.26/162.06 [4798]~P100(x47981)+E(f331(f331(f108(x47981),x47982),f256(x47981)),x47982)
% 162.26/162.06 [4799]~P118(x47991)+E(f331(f331(f262(x47991),x47992),f2(a883)),f79(x47991))
% 162.26/162.06 [4800]~P115(x48001)+E(f331(f331(f262(x48001),x48002),f2(a883)),f79(x48001))
% 162.26/162.06 [4801]~E(x48012,f196(f891(x48011,a877)))+E(f331(f38(x48011),x48012),f2(a883))
% 162.26/162.06 [4812]~P58(x48121)+E(f45(x48121,x48122,f2(x48121)),x48122)
% 162.26/162.06 [4820]~P118(x48201)+E(f331(f331(f82(x48201),x48202),f2(x48201)),f2(x48201))
% 162.26/162.06 [4821]~P131(x48211)+E(f331(f331(f82(x48211),x48212),f2(x48211)),f2(x48211))
% 162.26/162.06 [4822]~P100(x48221)+E(f331(f331(f107(x48221),x48222),f256(x48221)),f256(x48221))
% 162.26/162.06 [4823]~P58(x48231)+E(f331(f331(f39(x48231),x48232),f2(x48231)),f2(x48231))
% 162.26/162.06 [4824]~P120(x48241)+E(f331(f331(f289(x48241),x48242),f2(x48241)),f2(x48241))
% 162.26/162.06 [4825]~P97(x48251)+E(f331(f331(f108(x48251),x48252),f196(x48251)),f196(x48251))
% 162.26/162.06 [4826]E(x48261,f199(x48262))+~E(f240(x48262,x48261),f196(f891(x48262,a877)))
% 162.26/162.06 [4829]~P58(x48291)+E(f45(x48291,x48292,f79(x48291)),f2(x48291))
% 162.26/162.06 [4830]~P58(x48301)+E(f45(x48301,f2(x48301),x48302),f2(x48301))
% 162.26/162.06 [4857]E(x48571,f2(a883))+E(f55(x48572,x48571,f119(x48572)),f119(f884(x48572)))
% 162.26/162.06 [4881]P38(x48811,x48812)+~E(f693(x48812,x48811),f196(f891(x48811,a877)))
% 162.26/162.06 [4882]E(x48821,f119(x48822))+~E(f331(f175(x48822),x48821),f196(f891(x48822,a877)))
% 162.26/162.06 [4883]E(x48831,f119(x48832))+~E(f196(f891(x48832,a877)),f331(f175(x48832),x48831))
% 162.26/162.06 [4886]~E(x48861,x48862)+P24(f331(f331(a328,x48861),x48862))
% 162.26/162.06 [4896]P24(x48961)+P24(f331(f331(a334,x48961),x48962))
% 162.26/162.06 [4897]E(x48971,f119(x48972))+E(f331(f331(f168(x48972),x48971),f2(a883)),f331(f144(x48972),x48971))
% 162.26/162.06 [4900]E(f155(x49001,x49002),x49002)+~P24(f331(f140(x49001),x49002))
% 162.26/162.06 [4905]~P24(x49052)+P24(f331(f331(a334,x49051),x49052))
% 162.26/162.06 [4906]~P24(x49062)+P24(f331(f331(a330,x49061),x49062))
% 162.26/162.06 [4907]~P24(x49071)+P24(f331(f331(a330,x49071),x49072))
% 162.26/162.06 [4917]~E(x49172,f196(f891(x49171,a877)))+P24(f331(f62(x49171),x49172))
% 162.26/162.06 [4918]~E(f602(x49182,x49181),f622(x49182,x49181))+P24(f331(f140(x49181),x49182))
% 162.26/162.06 [4926]E(f331(f253(x49261),x49262),f196(f891(x49261,a877)))+P24(f331(x49262,f544(x49262)))
% 162.26/162.06 [4927]E(f196(f891(x49271,a877)),f331(f253(x49271),x49272))+P24(f331(x49272,f563(x49272)))
% 162.26/162.06 [4991]~P111(x49911)+E(f331(f331(f82(x49911),x49912),f83(x49911,x49912)),f331(f76(x49911),x49912))
% 162.26/162.06 [5002]~E(x50021,f2(a1))+E(f46(x50021,x50022),f331(f331(f261(a1,a1),f2(a1)),f2(a1)))
% 162.26/162.06 [5033]~P55(x50331,x50332)+P55(x50331,f331(f286(x50331,x50331),x50332))
% 162.26/162.06 [5051]~E(f331(a26,x50511),f331(f239(a879),x50512))+P24(f331(a25,f331(a28,x50511)))
% 162.26/162.06 [5056]E(x50561,x50562)+~P24(f331(f331(a328,x50561),x50562))
% 162.26/162.06 [5060]~P24(f331(a25,x50602))+P24(f331(a25,f33(x50601,x50602)))
% 162.26/162.06 [5069]P24(x50691)+~P24(f331(f331(a329,x50692),x50691))
% 162.26/162.06 [5070]P24(x50701)+~P24(f331(f331(a329,x50701),x50702))
% 162.26/162.06 [5074]~P116(x50741)+P24(f331(f331(f247(x50741),x50742),f256(x50741)))
% 162.26/162.06 [5078]E(x50781,x50782)+~E(f331(x50781,f445(x50782,x50781)),f331(x50782,f445(x50782,x50781)))
% 162.26/162.06 [5107]E(x51071,f2(a883))+E(f228(x51071,f45(a883,x51072,x51071)),f228(x51072,x51071))
% 162.26/162.06 [5112]~P107(x51121)+P29(x51121,f331(f331(f154(x51121),x51122),f119(x51121)))
% 162.26/162.06 [5114]E(x51141,f2(a1))+P24(f331(f49(x51142,x51141),f46(x51142,x51141)))
% 162.26/162.06 [5132]~E(x51321,x51322)+P24(f331(f331(f248(a883),x51321),f331(a118,x51322)))
% 162.26/162.06 [5142]~E(x51421,f2(a883))+P24(f331(f331(f248(a883),x51421),f331(a118,x51422)))
% 162.26/162.06 [5151]P24(f331(x51511,x51512))+P24(f331(f331(f247(a1),f2(a1)),f846(x51511)))
% 162.26/162.06 [5188]P24(f331(a25,x51881))+~P24(f331(a25,f33(x51882,x51881)))
% 162.26/162.06 [5190]P24(f331(a25,x51901))+~P24(f331(a25,f34(x51902,x51901)))
% 162.26/162.06 [5192]P24(f331(a25,x51921))+~P24(f331(a25,f34(x51921,x51922)))
% 162.26/162.06 [5224]P55(x52241,x52242)+~P55(x52241,f331(f286(x52241,x52241),x52242))
% 162.26/162.06 [5227]~E(f45(a883,x52272,x52271),f2(a883))+E(f331(f331(f82(a883),x52271),f367(x52271,x52272)),x52272)
% 162.26/162.06 [5228]~E(f45(a1,x52282,x52281),f2(a1))+E(f331(f331(f82(a1),x52281),f339(x52281,x52282)),x52282)
% 162.26/162.06 [5255]~P24(f331(x52551,x52552))+P24(f331(f331(f247(a1),f2(a1)),f845(x52551)))
% 162.26/162.06 [5267]E(f331(f331(f22(a883),f331(a111,x52671)),f331(a111,x52672)),f331(a111,x52671))+~P24(f331(a202,x52672))
% 162.26/162.06 [5299]E(f279(x52991,x52992),f79(a105))+~P24(f331(f331(f247(a105),x52991),f79(a105)))
% 162.26/162.06 [5394]E(f331(f331(f168(x53941),x53942),f602(x53942,x53941)),f331(f331(f168(x53941),x53942),f622(x53942,x53941)))+P24(f331(f140(x53941),x53942))
% 162.26/162.06 [5439]~P24(f331(x54391,f91(x54392,x54391)))+P24(f331(x54391,f637(x54392,x54391)))
% 162.26/162.06 [5502]P57(x55021,x55022)+~P24(f331(f319(x55021,x55022),f565(x55022,x55021)))
% 162.26/162.06 [5646]~E(f331(a118,f45(a883,x56461,x56462)),x56462)+E(f45(a883,f331(a118,x56461),x56462),f2(a883))
% 162.26/162.06 [5703]P38(x57031,x57032)+P24(f331(f331(f333(x57031),f782(x57032,x57031)),f783(x57032,x57031)))
% 162.26/162.06 [5710]~P94(x57101)+P24(f331(f331(f333(x57101),f331(f110(x57101),x57102)),f116(x57101)))
% 162.26/162.06 [5711]~P138(x57111)+P24(f331(f331(f333(x57111),f331(f106(x57111),x57112)),f116(x57111)))
% 162.26/162.06 [5712]~P143(x57121)+P24(f331(f331(f333(x57121),f331(f106(x57121),x57122)),f194(x57121)))
% 162.26/162.06 [5713]~P138(x57131)+P24(f331(f331(f333(x57131),f331(f109(x57131),x57132)),f116(x57131)))
% 162.26/162.06 [5857]E(f331(a118,f45(a883,x58571,x58572)),x58572)+E(f45(a883,f331(a118,x58571),x58572),f331(a118,f45(a883,x58571,x58572)))
% 162.26/162.06 [6272]P38(x62721,x62722)+~P24(f331(f331(f333(x62721),f566(x62722,x62721)),f320(x62721,x62722)))
% 162.26/162.06 [6306]~P110(x63061)+~P24(f331(f331(f248(x63061),f331(f106(x63061),x63062)),f2(x63061)))
% 162.26/162.06 [6307]~P83(x63071)+~P24(f331(f331(f248(x63071),f331(f76(x63071),x63072)),f2(x63071)))
% 162.26/162.06 [6393]P24(f331(f331(f248(a1),x63931),f45(a1,x63932,x63931)))+~P24(f331(f331(f248(a1),x63931),f2(a1)))
% 162.26/162.06 [6491]E(f331(f331(f309(a883),f331(a118,x64911)),f302(a883,x64912,x64911)),f302(a883,x64912,f331(a118,x64911)))+~P24(f331(f331(f247(a883),x64912),f331(a118,x64911)))
% 162.26/162.06 [6576]~P107(x65761)+P29(x65761,f153(x65761,x65761,f5(x65761),x65762))
% 162.26/162.06 [6706]E(f331(f171(x67061),x67062),x67062)+~P24(f331(f331(f247(a883),f331(f197(f884(x67061)),x67062)),f79(a883)))
% 162.26/162.06 [6726]~P83(x67261)+P24(f331(f331(f247(x67261),f331(f80(x67261),f331(f76(x67261),x67262))),f2(x67261)))
% 162.26/162.06 [6759]~P38(x67591,x67592)+P38(x67591,f331(f331(f288(x67591,x67591,x67591),x67592),f307(x67591,x67592)))
% 162.26/162.06 [6970]~P24(f331(f331(f248(a1),x69702),f2(a1)))+P24(f331(f331(f247(a1),f45(a1,x69701,x69702)),f2(a1)))
% 162.26/162.06 [7354]~P143(x73541)+E(f198(x73541,f331(f331(f7(x73541,x73541,x73541),f81(x73541)),f79(x73541)),x73542,f2(x73541)),f331(f106(x73541),x73542))
% 162.26/162.06 [7381]~P124(x73811)+~P24(f331(f331(f248(x73811),f331(f331(f82(x73811),x73812),x73812)),f2(x73811)))
% 162.26/162.06 [10155]~P111(x101551)+~P24(f331(f331(f248(x101551),f331(f331(f262(x101551),x101552),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f2(x101551)))
% 162.26/162.06 [4688]~E(x46882,f119(x46881))+E(f331(f197(f884(x46881)),x46882),f2(a883))
% 162.26/162.06 [4728]~E(x47281,f2(a883))+E(f331(f331(f81(a883),x47281),x47282),x47282)
% 162.26/162.06 [4729]~E(x47292,f2(a883))+E(f331(f331(f82(a883),x47291),x47292),f2(a883))
% 162.26/162.06 [4731]~E(x47311,f2(a883))+E(f331(f331(f82(a883),x47311),x47312),f2(a883))
% 162.26/162.06 [4732]~E(x47322,f2(a1))+E(f331(f331(f39(a1),x47321),x47322),f2(a1))
% 162.26/162.06 [4733]~E(x47332,f2(a883))+E(f331(f331(f262(a883),x47331),x47332),f79(a883))
% 162.26/162.06 [4743]E(x47431,f119(x47432))+~E(f331(f197(f884(x47432)),x47431),f2(a883))
% 162.26/162.06 [4745]~P95(x47451)+E(f331(f331(f82(x47451),x47452),x47452),x47452)
% 162.26/162.06 [4746]~P96(x47461)+E(f331(f331(f107(x47461),x47462),x47462),x47462)
% 162.26/162.06 [4748]~P101(x47481)+E(f331(f331(f107(x47481),x47482),x47482),x47482)
% 162.26/162.06 [4750]~P107(x47501)+E(f331(f331(f251(x47501),x47502),x47502),x47502)
% 162.26/162.06 [4752]~P107(x47521)+E(f331(f331(f246(x47521),x47522),x47522),x47522)
% 162.26/162.06 [4753]~P96(x47531)+E(f331(f331(f108(x47531),x47532),x47532),x47532)
% 162.26/162.06 [4755]~P102(x47551)+E(f331(f331(f108(x47551),x47552),x47552),x47552)
% 162.26/162.06 [4774]~P66(x47741)+E(f331(f331(f22(x47741),x47742),x47742),f2(x47741))
% 162.26/162.06 [4786]~P66(x47861)+E(f331(f80(x47861),f331(f80(x47861),x47862)),x47862)
% 162.26/162.06 [4787]~P85(x47871)+E(f331(f80(x47871),f331(f80(x47871),x47872)),x47872)
% 162.26/162.06 [4804]~E(x48042,f2(a883))+E(f331(f331(f262(a883),x48041),x48042),f331(a118,f2(a883)))
% 162.26/162.06 [4838]~P118(x48381)+E(f331(f331(f81(x48381),f2(x48381)),x48382),x48382)
% 162.26/162.06 [4839]~P80(x48391)+E(f331(f331(f81(x48391),f2(x48391)),x48392),x48392)
% 162.26/162.06 [4840]~P74(x48401)+E(f331(f331(f81(x48401),f2(x48401)),x48402),x48402)
% 162.26/162.06 [4841]~P79(x48411)+E(f331(f331(f82(x48411),f79(x48411)),x48412),x48412)
% 162.26/162.06 [4842]~P73(x48421)+E(f331(f331(f82(x48421),f79(x48421)),x48422),x48422)
% 162.26/162.06 [4843]~P118(x48431)+E(f331(f331(f82(x48431),f79(x48431)),x48432),x48432)
% 162.26/162.06 [4844]~P97(x48441)+E(f331(f331(f107(x48441),f196(x48441)),x48442),x48442)
% 162.26/162.06 [4845]~P100(x48451)+E(f331(f331(f108(x48451),f256(x48451)),x48452),x48452)
% 162.26/162.06 [4862]~P118(x48621)+E(f331(f331(f82(x48621),f2(x48621)),x48622),f2(x48621))
% 162.26/162.06 [4863]~P131(x48631)+E(f331(f331(f82(x48631),f2(x48631)),x48632),f2(x48631))
% 162.26/162.06 [4864]~P100(x48641)+E(f331(f331(f107(x48641),f256(x48641)),x48642),f256(x48641))
% 162.26/162.06 [4865]~P58(x48651)+E(f331(f331(f39(x48651),f2(x48651)),x48652),f2(x48651))
% 162.26/162.06 [4866]~P79(x48661)+E(f331(f331(f262(x48661),f79(x48661)),x48662),f79(x48661))
% 162.26/162.06 [4867]~P119(x48671)+E(f331(f331(f289(x48671),f2(x48671)),x48672),f2(x48671))
% 162.26/162.06 [4868]~P97(x48681)+E(f331(f331(f108(x48681),f196(x48681)),x48682),f196(x48681))
% 162.26/162.06 [4876]E(x48761,f119(x48762))+E(f147(x48762,f331(f172(x48762),x48761)),f331(f144(x48762),x48761))
% 162.26/162.06 [4877]E(x48771,f119(x48772))+E(f331(f144(x48772),f331(f172(x48772),x48771)),f147(x48772,x48771))
% 162.26/162.06 [4878]E(x48781,f2(a883))+~E(f331(f331(f81(a883),x48782),x48781),x48782)
% 162.26/162.06 [4884]~P94(x48841)+E(f331(f109(x48841),f331(f110(a1),x48842)),f331(f110(x48841),x48842))
% 162.26/162.06 [4885]~P138(x48851)+E(f331(f109(x48851),f331(f106(a1),x48852)),f331(f106(x48851),x48852))
% 162.26/162.06 [4892]E(x48921,f79(a883))+~E(f331(f331(f82(a883),x48922),x48921),f79(a883))
% 162.26/162.06 [4893]E(x48931,f79(a883))+~E(f331(f331(f82(a883),x48931),x48932),f79(a883))
% 162.26/162.06 [4894]E(x48941,f2(a883))+~E(f331(f331(f81(a883),x48942),x48941),f2(a883))
% 162.26/162.06 [4895]E(x48951,f2(a883))+~E(f331(f331(f81(a883),x48951),x48952),f2(a883))
% 162.26/162.06 [4910]~P83(x49101)+E(f331(f76(x49101),f331(f80(x49101),x49102)),f331(f76(x49101),x49102))
% 162.26/162.06 [4911]~P111(x49111)+E(f331(f76(x49111),f331(f106(x49111),x49112)),f331(f106(x49111),x49112))
% 162.26/162.06 [4912]~P83(x49121)+E(f331(f76(x49121),f331(f76(x49121),x49122)),f331(f76(x49121),x49122))
% 162.26/162.06 [4913]~P74(x49131)+E(f331(f169(x49131),f331(f172(x49131),x49132)),f331(f169(x49131),x49132))
% 162.26/162.06 [4919]~E(x49191,f331(a118,f2(a883)))+E(f331(f331(f262(a883),x49191),x49192),f331(a118,f2(a883)))
% 162.26/162.06 [4929]~P66(x49291)+E(f331(f331(f22(x49291),f2(x49291)),x49292),f331(f80(x49291),x49292))
% 162.26/162.06 [4930]~E(x49302,f2(a883))+E(f142(a883,f331(f301(a883,x49301),x49302)),f119(a883))
% 162.26/162.06 [4939]~P94(x49391)+E(f331(f331(f81(x49391),x49392),f331(f110(x49391),a84)),x49392)
% 162.26/162.06 [4940]E(x49401,f2(a1))+E(f47(f331(f76(a1),x49402),f331(f76(a1),x49401)),f53(x49402,x49401))
% 162.26/162.06 [4954]~E(x49541,x49542)+P24(f331(f331(f247(a883),x49541),x49542))
% 162.26/162.06 [4961]~E(x49611,f2(a105))+E(f331(f331(f81(a883),f331(a19,x49611)),x49612),x49612)
% 162.26/162.06 [4971]~P28(x49711)+P28(f331(f331(f262(a1),x49711),x49712))
% 162.26/162.06 [4972]~P66(x49721)+E(f331(f331(f81(x49721),x49722),f331(f80(x49721),x49722)),f2(x49721))
% 162.26/162.06 [4973]~P85(x49731)+E(f331(f331(f107(x49731),x49732),f331(f80(x49731),x49732)),f256(x49731))
% 162.26/162.06 [4974]~P85(x49741)+E(f331(f331(f108(x49741),x49742),f331(f80(x49741),x49742)),f196(x49741))
% 162.26/162.06 [4999]E(x49991,f2(a883))+~E(f331(f80(a1),f331(f106(a1),x49992)),f331(f106(a1),x49991))
% 162.26/162.06 [5000]E(x50001,f2(a883))+~E(f331(f80(a1),f331(f106(a1),x50001)),f331(f106(a1),x50002))
% 162.26/162.06 [5010]E(f204(x50101,x50102),f2(a1))+P24(f331(f331(f247(a1),x50102),x50101))
% 162.26/162.06 [5011]E(f181(x50111,x50112),f119(a1))+P24(f331(f331(f247(a1),x50111),x50112))
% 162.26/162.06 [5024]E(x50241,f331(a118,f2(a883)))+~E(f331(f331(f82(a883),x50242),x50241),f331(a118,f2(a883)))
% 162.26/162.06 [5025]E(x50251,f331(a118,f2(a883)))+~E(f331(f331(f82(a883),x50251),x50252),f331(a118,f2(a883)))
% 162.26/162.06 [5026]~P106(x50261)+P24(f331(f331(f247(x50261),x50262),x50262))
% 162.26/162.06 [5027]~P93(x50271)+P24(f331(f331(f92(x50271),x50272),x50272))
% 162.26/162.06 [5030]~P94(x50301)+E(f331(f331(f82(x50301),x50302),f331(f110(x50301),a103)),f331(f80(x50301),x50302))
% 162.26/162.06 [5048]~P94(x50481)+E(f331(f80(x50481),f331(f110(x50481),x50482)),f331(f110(x50481),f331(f80(a1),x50482)))
% 162.26/162.06 [5049]~P138(x50491)+E(f331(f80(x50491),f331(f109(x50491),x50492)),f331(f109(x50491),f331(f80(a1),x50492)))
% 162.26/162.06 [5079]~E(x50791,f331(a118,x50792))+P24(f331(f331(f248(a883),f2(a883)),x50791))
% 162.26/162.06 [5096]~P107(x50961)+E(f331(f80(f891(x50961,a877)),f331(f300(x50961),x50962)),f331(f303(x50961),x50962))
% 162.26/162.06 [5097]~P107(x50971)+E(f331(f80(f891(x50971,a877)),f331(f254(x50971),x50972)),f331(f255(x50971),x50972))
% 162.26/162.06 [5098]~P107(x50981)+E(f331(f80(f891(x50981,a877)),f331(f255(x50981),x50982)),f331(f254(x50981),x50982))
% 162.26/162.06 [5099]~P107(x50991)+E(f331(f80(f891(x50991,a877)),f331(f303(x50991),x50992)),f331(f300(x50991),x50992))
% 162.26/162.06 [5106]~E(f331(f106(a1),x51062),x51061)+P24(f331(f331(f247(a1),f2(a1)),x51061))
% 162.26/162.06 [5113]~E(x51132,f2(a1))+E(f53(x51131,x51132),f331(f331(f261(a1,a1),f2(a1)),f331(f76(a1),x51131)))
% 162.26/162.06 [5115]~P25(x51151)+P24(f331(f331(f247(x51151),f196(x51151)),x51152))
% 162.26/162.06 [5150]~P24(f331(x51501,x51502))+P24(f331(x51501,f331(a111,f845(x51501))))
% 162.26/162.06 [5176]~P111(x51761)+E(f331(f331(f82(x51761),f83(x51761,x51762)),f331(f76(x51761),x51762)),x51762)
% 162.26/162.06 [5177]E(x51771,x51772)+~P24(f331(f331(f203(a24),x51771),x51772))
% 162.26/162.06 [5186]~E(x51862,f2(a883))+E(f86(f890(a883,a883),f48(x51861,x51862)),f331(f331(f261(a883,a883),f2(a883)),x51861))
% 162.26/162.06 [5197]~E(x51971,x51972)+~P24(f331(f331(f248(a883),x51971),x51972))
% 162.26/162.06 [5198]~E(x51981,x51982)+~P24(f331(f331(f248(a1),x51981),x51982))
% 162.26/162.06 [5201]~P143(x52011)+E(f331(f331(f81(x52011),f79(x52011)),f331(f106(x52011),x52012)),f331(f106(x52011),f331(a118,x52012)))
% 162.26/162.06 [5205]~E(x52051,f2(a883))+~P24(f331(f331(f248(a883),x52052),x52051))
% 162.26/162.06 [5221]E(f155(x52211,x52212),x52212)+~E(f331(f197(f884(x52211)),f155(x52211,x52212)),f331(f197(f884(x52211)),x52212))
% 162.26/162.06 [5222]E(f331(f38(x52221),f331(f175(x52221),x52222)),f331(f197(f884(x52221)),x52222))+~P24(f331(f140(x52221),x52222))
% 162.26/162.06 [5232]~P24(f331(x52321,f340(x52321)))+P24(f331(x52321,f331(f106(a1),x52322)))
% 162.26/162.06 [5243]E(f181(x52431,x52432),f119(a1))+~P24(f331(f331(f248(a1),x52432),x52431))
% 162.26/162.06 [5244]E(f279(x52441,x52442),f79(a105))+~P24(f331(f331(f248(a105),x52442),x52441))
% 162.26/162.06 [5245]E(f128(x52451,x52452),f121(a1))+~P24(f331(f331(f248(a1),x52451),x52452))
% 162.26/162.06 [5248]~P108(x52481)+E(f302(x52481,x52482,x52482),f331(f331(f309(x52481),x52482),f196(f891(x52481,a877))))
% 162.26/162.06 [5270]~E(f331(f331(f22(a883),x52701),x52702),f2(a883))+P24(f331(f331(f247(a883),x52701),x52702))
% 162.26/162.06 [5271]~E(f331(f331(f22(a1),x52711),x52712),f2(a1))+P24(f331(f331(f92(a1),x52711),x52712))
% 162.26/162.06 [5296]~E(x52962,f2(a883))+E(f55(x52961,x52962,f119(x52961)),f331(f331(f154(f884(x52961)),f119(x52961)),f119(f884(x52961))))
% 162.26/162.06 [5300]~P106(x53001)+~P24(f331(f331(f248(x53001),x53002),x53002))
% 162.26/162.06 [5303]~E(f45(a1,x53031,x53032),f2(a1))+E(f45(a1,x53031,f331(f80(a1),x53032)),f2(a1))
% 162.26/162.06 [5305]~E(f45(a1,x53051,x53052),f2(a1))+E(f45(a1,f331(f80(a1),x53051),x53052),f2(a1))
% 162.26/162.06 [5313]E(f331(f301(a883,x53131),f331(a118,x53132)),f196(f891(a883,a877)))+P24(f331(f331(f247(a883),x53131),x53132))
% 162.26/162.06 [5333]E(f142(a883,f331(f301(a883,x53331),x53332)),f119(a883))+P24(f331(f331(f248(a883),x53331),x53332))
% 162.26/162.06 [5338]~E(f331(f38(x53381),f331(f175(x53381),x53382)),f331(f197(f884(x53381)),x53382))+P24(f331(f140(x53381),x53382))
% 162.26/162.06 [5343]~P24(f331(f140(x53431),x53432))+P24(f331(f140(x53431),f331(f171(x53431),x53432)))
% 162.26/162.06 [5344]~P24(f331(f140(x53441),x53442))+P24(f331(f140(x53441),f331(f174(x53441),x53442)))
% 162.26/162.06 [5345]~P24(f331(f140(x53451),x53452))+P24(f331(f140(x53451),f331(f172(x53451),x53452)))
% 162.26/162.06 [5352]P24(f331(x53521,x53522))+~P24(f331(x53521,f331(a111,f846(x53521))))
% 162.26/162.06 [5353]P24(f331(f331(f247(a883),x53532),x53531))+P24(f331(f331(f247(a883),x53531),x53532))
% 162.26/162.06 [5354]P24(f331(f331(f247(a1),x53542),x53541))+P24(f331(f331(f247(a1),x53541),x53542))
% 162.26/162.06 [5357]~P83(x53571)+P24(f331(f331(f247(x53571),x53572),f331(f76(x53571),x53572)))
% 162.26/162.06 [5360]P24(f331(x53601,f341(x53601)))+~P24(f331(x53601,f331(f106(a1),x53602)))
% 162.26/162.06 [5386]E(f331(f331(f22(a883),x53861),x53862),f2(a883))+~P24(f331(f331(f247(a883),x53861),x53862))
% 162.26/162.06 [5387]E(f331(f331(f22(a1),x53871),x53872),f2(a1))+~P24(f331(f331(f92(a1),x53871),x53872))
% 162.26/162.06 [5388]E(f331(f331(f39(a883),x53881),x53882),f2(a883))+~P24(f331(f331(f248(a883),x53881),x53882))
% 162.26/162.06 [5406]E(f45(a883,x54061,x54062),x54061)+~P24(f331(f331(f248(a883),x54061),x54062))
% 162.26/162.06 [5415]E(f45(a1,x54151,f331(f80(a1),x54152)),f290(x54151,x54152))+P24(f331(f331(f247(a1),f2(a1)),x54152))
% 162.26/162.06 [5427]E(f331(f331(f22(a1),x54271),x54272),f204(x54271,x54272))+~P24(f331(f331(f247(a1),x54272),x54271))
% 162.26/162.06 [5446]P24(f331(f331(f247(a1),f2(a1)),f340(x54461)))+P24(f331(x54461,f331(f106(a1),x54462)))
% 162.26/162.06 [5458]~P60(x54581)+P24(f331(f331(f333(x54581),x54582),f331(f175(x54581),f56(x54581))))
% 162.26/162.06 [5460]~P110(x54601)+P24(f331(f331(f247(x54601),f2(x54601)),f331(f106(x54601),x54602)))
% 162.26/162.06 [5461]~P83(x54611)+P24(f331(f331(f247(x54611),f2(x54611)),f331(f76(x54611),x54612)))
% 162.26/162.06 [5488]E(f331(f331(f81(a883),x54881),f696(x54882,x54881)),x54882)+~P24(f331(f331(f247(a883),x54881),x54882))
% 162.26/162.06 [5503]E(f302(a1,x55031,x55032),f196(f891(a1,a877)))+~P24(f331(f331(f248(a1),x55032),x55031))
% 162.26/162.06 [5506]~P111(x55061)+E(f331(f331(f82(x55061),f331(f76(x55061),x55062)),f331(f76(x55061),x55062)),f331(f331(f82(x55061),x55062),x55062))
% 162.26/162.06 [5512]E(f142(a883,f331(f301(a883,x55121),f331(a118,x55122))),f119(a883))+P24(f331(f331(f247(a883),x55121),x55122))
% 162.26/162.06 [5514]E(f331(f331(f39(a1),x55141),x55142),f291(x55141,x55142))+~P24(f331(f331(f247(a1),f2(a1)),x55142))
% 162.26/162.06 [5534]P24(f331(f140(x55341),x55342))+~P24(f331(f140(x55341),f331(f171(x55341),x55342)))
% 162.26/162.06 [5535]P24(f331(f140(x55351),x55352))+~P24(f331(f140(x55351),f331(f172(x55351),x55352)))
% 162.26/162.06 [5556]P24(f331(f62(a883),x55561))+P24(f331(f331(f333(a883),f368(x55561,x55562)),x55561))
% 162.26/162.06 [5557]P24(f331(f62(a883),x55571))+P24(f331(f331(f333(a883),f370(x55571,x55572)),x55571))
% 162.26/162.06 [5558]P24(f331(f331(f248(a883),x55582),f331(a118,x55581)))+P24(f331(f331(f248(a883),x55581),x55582))
% 162.26/162.06 [5559]E(f45(a1,x55591,x55592),f290(x55591,x55592))+~P24(f331(f331(f247(a1),f2(a1)),x55592))
% 162.26/162.06 [5562]E(f142(a883,f331(f301(a883,x55621),x55622)),f119(a883))+~P24(f331(f331(f247(a883),x55622),x55621))
% 162.26/162.06 [5563]~P77(x55631)+E(f331(f310(x55631,x55631,f80(x55631)),f331(f300(x55631),x55632)),f331(f255(x55631),f331(f80(x55631),x55632)))
% 162.26/162.06 [5564]~P77(x55641)+E(f331(f310(x55641,x55641,f80(x55641)),f331(f254(x55641),x55642)),f331(f303(x55641),f331(f80(x55641),x55642)))
% 162.26/162.06 [5565]~P77(x55651)+E(f331(f310(x55651,x55651,f80(x55651)),f331(f255(x55651),x55652)),f331(f300(x55651),f331(f80(x55651),x55652)))
% 162.26/162.06 [5566]~P77(x55661)+E(f331(f310(x55661,x55661,f80(x55661)),f331(f303(x55661),x55662)),f331(f254(x55661),f331(f80(x55661),x55662)))
% 162.26/162.06 [5577]E(x55771,f196(f891(x55772,a877)))+P24(f331(f331(f333(x55772),f448(x55771,x55772)),x55771))
% 162.26/162.06 [5578]E(x55781,f196(f891(x55782,a877)))+P24(f331(f331(f333(x55782),f470(x55781,x55782)),x55781))
% 162.26/162.06 [5589]~P24(f331(f331(f248(a883),x55891),x55892))+P24(f331(f331(f247(a883),x55891),x55892))
% 162.26/162.06 [5590]~P24(f331(f331(f248(a1),x55901),x55902))+P24(f331(f331(f247(a1),x55901),x55902))
% 162.26/162.06 [5606]E(f47(x56061,x56062),f331(f331(f261(a1,a1),f2(a1)),x56061))+~P24(f331(f331(f248(a1),x56061),x56062))
% 162.26/162.06 [5607]E(f227(f331(f80(a1),x56071),f331(f80(a1),x56072)),f227(x56071,x56072))+~P24(f331(f331(f248(a1),x56072),f2(a1)))
% 162.26/162.06 [5620]E(x56201,x56202)+~E(f331(a3,f331(a118,f331(a19,x56201))),f331(a3,f331(a118,f331(a19,x56202))))
% 162.26/162.06 [5625]E(f47(x56251,x56252),f331(f331(f261(a1,a1),f2(a1)),x56251))+~P24(f331(f331(f247(a1),x56252),f2(a1)))
% 162.26/162.06 [5652]E(f45(a883,f331(f110(a883),x56521),f331(f110(a883),x56522)),f2(a883))+~P24(f331(a202,f331(f110(a1),x56521)))
% 162.26/162.06 [5667]P24(f331(f331(f247(a1),f2(a1)),f341(x56671)))+~P24(f331(x56671,f331(f106(a1),x56672)))
% 162.26/162.06 [5701]P40(f302(a1,x57011,x57012))+~P24(f331(f331(f247(a1),f2(a1)),x57011))
% 162.26/162.06 [5706]~P24(f331(f62(x57061),x57062))+P24(f331(f62(f891(x57061,a877)),f331(f308(x57061),x57062)))
% 162.26/162.06 [5719]E(f331(f331(f81(a1),x57191),f331(f106(a1),f347(x57192,x57191))),x57192)+~P24(f331(f331(f247(a1),x57191),x57192))
% 162.26/162.06 [5727]P24(f331(f331(f247(a883),x57271),x57272))+P24(f331(f331(f247(a883),f331(a118,x57272)),x57271))
% 162.26/162.06 [5771]E(f331(f331(f39(a883),f331(f110(a883),x57711)),f331(f110(a883),x57712)),f2(a883))+~P24(f331(a202,f331(f110(a1),x57711)))
% 162.26/162.06 [5772]E(f331(f331(f82(a883),f331(f110(a883),x57721)),f331(f110(a883),x57722)),f2(a883))+~P24(f331(f331(f248(a1),x57721),a84))
% 162.26/162.06 [5774]P24(f331(f331(f248(a883),x57741),f331(a118,x57742)))+~P24(f331(f331(f248(a883),x57741),x57742))
% 162.26/162.06 [5776]P24(f331(f331(f248(a883),x57761),f331(a118,x57762)))+~P24(f331(f331(f247(a883),x57761),x57762))
% 162.26/162.06 [5778]P24(f331(f331(f247(a883),x57781),f331(a118,x57782)))+~P24(f331(f331(f247(a883),x57781),x57782))
% 162.26/162.06 [5781]~E(x57811,x57812)+P24(f331(f331(f248(a1),x57811),f331(f331(f81(a1),x57812),f79(a1))))
% 162.26/162.06 [5784]E(f45(a1,x57841,x57842),f2(a1))+E(f331(f331(f22(a1),x57842),f45(a1,x57841,x57842)),f45(a1,f331(f80(a1),x57841),x57842))
% 162.26/162.06 [5793]E(x57931,f119(x57932))+P24(f331(f331(f333(x57932),f147(x57932,x57931)),f331(f175(x57932),x57931)))
% 162.26/162.06 [5805]E(f86(f890(a883,a883),f48(x58051,x58052)),f331(f331(f261(a883,a883),f2(a883)),x58051))+~P24(f331(f331(f248(a883),x58051),x58052))
% 162.26/162.06 [5838]E(f331(f331(f22(a883),f331(f110(a883),x58381)),f331(f110(a883),x58382)),f331(f110(a883),x58381))+~P24(f331(f331(f248(a1),x58382),a84))
% 162.26/162.06 [5839]E(f331(f331(f81(a883),f331(f110(a883),x58391)),f331(f110(a883),x58392)),f331(f110(a883),x58392))+~P24(f331(f331(f248(a1),x58391),a84))
% 162.26/162.06 [5844]E(f331(a118,f331(f331(f81(a883),x58441),f623(x58442,x58441))),x58442)+~P24(f331(f331(f248(a883),x58441),x58442))
% 162.26/162.06 [5867]P24(f331(x58671,x58672))+~P24(f331(x58671,f331(a90,f603(x58672,x58671))))
% 162.26/162.06 [5875]~P24(f331(f331(f248(a883),x58751),f331(a118,x58752)))+P24(f331(f331(f247(a883),x58751),x58752))
% 162.26/162.06 [5921]E(f331(f331(f309(a883),x59211),f331(f301(a883,x59212),x59211)),f331(f301(a883,x59212),f331(a118,x59211)))+~P24(f331(f331(f247(a883),x59212),x59211))
% 162.26/162.06 [5925]E(x59251,f119(x59252))+E(f331(f331(f137(x59252),f120(x59252,x59251)),f331(f331(f154(x59252),f147(x59252,x59251)),f119(x59252))),x59251)
% 162.26/162.06 [5938]P24(f331(f62(x59381),x59382))+~P24(f331(f331(f248(a883),f2(a883)),f331(f38(x59381),x59382)))
% 162.26/162.06 [5940]~E(x59401,f196(f891(x59402,a877)))+~P24(f331(f331(f248(a883),f2(a883)),f331(f38(x59402),x59401)))
% 162.26/162.06 [5952]~P24(f331(f331(f248(a883),x59521),x59522))+P24(f331(f331(f247(a883),f331(a118,x59521)),x59522))
% 162.26/162.06 [5960]~P107(x59601)+E(f153(x59601,x59601,f5(x59601),f155(x59601,x59602)),f142(x59601,f331(f175(x59601),x59602)))
% 162.26/162.06 [5963]E(x59631,f119(x59632))+P24(f331(f331(f333(x59632),f331(f144(x59632),x59631)),f331(f175(x59632),x59631)))
% 162.26/162.06 [5969]~P110(x59691)+P24(f331(f331(f248(x59691),x59692),f331(f331(f81(x59691),x59692),f79(x59691))))
% 162.26/162.06 [5971]~P83(x59711)+P24(f331(f331(f247(x59711),f331(f80(x59711),x59712)),f331(f76(x59711),x59712)))
% 162.26/162.06 [6004]P24(f331(f62(a883),x60041))+~P24(f331(f331(f248(a883),f370(x60041,x60042)),x60042))
% 162.26/162.06 [6005]P24(f331(f62(a883),x60051))+~P24(f331(f331(f247(a883),f368(x60051,x60052)),x60052))
% 162.26/162.06 [6009]~P24(f331(f62(f890(x60091,x60091)),x60092))+P24(f331(f62(x60091),f331(f284(x60091),x60092)))
% 162.26/162.06 [6063]~P24(f331(f331(f248(a883),x60632),f331(a118,x60631)))+~P24(f331(f331(f248(a883),x60631),x60632))
% 162.26/162.06 [6064]~P108(x60641)+E(f331(f331(f108(f891(x60641,a877)),f331(f300(x60641),x60642)),f331(f255(x60641),x60642)),f331(f331(f309(x60641),x60642),f196(f891(x60641,a877))))
% 162.26/162.06 [6077]P24(f331(f62(x60771),x60772))+~P24(f331(f62(f891(x60771,a877)),f331(f308(x60771),x60772)))
% 162.26/162.06 [6102]P24(f331(f331(f248(a883),f331(a118,x61021)),f331(a118,x61022)))+~P24(f331(f331(f248(a883),x61021),x61022))
% 162.26/162.06 [6103]P24(f331(f331(f248(a883),f331(a19,x61031)),f331(a19,x61032)))+~P24(f331(f331(f248(a105),x61031),x61032))
% 162.26/162.06 [6104]P24(f331(f331(f248(a105),f331(a3,x61041)),f331(a3,x61042)))+~P24(f331(f331(f248(a883),x61041),x61042))
% 162.26/162.06 [6105]P24(f331(f331(f247(a883),f331(a118,x61051)),f331(a118,x61052)))+~P24(f331(f331(f247(a883),x61051),x61052))
% 162.26/162.06 [6106]P24(f331(f331(f247(a883),f331(a19,x61061)),f331(a19,x61062)))+~P24(f331(f331(f247(a105),x61061),x61062))
% 162.26/162.06 [6107]P24(f331(f331(f247(a105),f331(a3,x61071)),f331(a3,x61072)))+~P24(f331(f331(f247(a883),x61071),x61072))
% 162.26/162.06 [6110]E(x61101,x61102)+~E(f331(f310(a883,a1,f106(a1)),x61101),f331(f310(a883,a1,f106(a1)),x61102))
% 162.26/162.06 [6126]P24(f331(f331(f248(a883),x61261),x61262))+~P24(f331(f331(f248(a883),f331(a118,x61261)),x61262))
% 162.26/162.06 [6129]P24(f331(f331(f248(a883),x61291),x61292))+~P24(f331(f331(f247(a883),f331(a118,x61291)),x61292))
% 162.26/162.06 [6130]P24(f331(f331(f247(a883),x61301),x61302))+~P24(f331(f331(f247(a883),f331(a118,x61301)),x61302))
% 162.26/162.06 [6145]E(f45(a1,x61451,x61452),f2(a1))+E(f331(f331(f22(a1),f45(a1,x61451,x61452)),x61452),f45(a1,x61451,f331(f80(a1),x61452)))
% 162.26/162.06 [6212]E(f331(f38(f891(x62121,a877)),f331(f308(x62121),x62122)),f331(f331(f262(a883),f331(a118,f331(a118,f2(a883)))),f331(f38(x62121),x62122)))+~P24(f331(f62(x62121),x62122))
% 162.26/162.06 [6215]E(x62151,f119(x62152))+E(f331(f331(f168(x62152),x62151),f331(f331(f22(a883),f331(f197(f884(x62152)),x62151)),f79(a883))),f147(x62152,x62151))
% 162.26/162.06 [6240]E(x62401,f119(x62402))+E(f331(f331(f137(x62402),f331(f174(x62402),x62401)),f331(f331(f154(x62402),f331(f144(x62402),x62401)),f119(x62402))),f331(f171(x62402),x62401))
% 162.26/162.06 [6269]~P24(f331(f62(x62691),f40(f891(x62691,a877),x62692)))+P24(f331(f62(f891(x62691,a877)),x62692))
% 162.26/162.06 [6292]P24(f331(f331(f247(a883),f331(f110(a883),x62921)),f331(f110(a883),x62922)))+~P24(f331(f331(f247(a1),x62921),a84))
% 162.26/162.06 [6308]~P24(f331(f331(f248(a1),x63081),x63082))+P24(f331(f331(f248(a1),x63081),f331(f331(f81(a1),x63082),f79(a1))))
% 162.26/162.06 [6309]~P24(f331(f331(f247(a1),x63091),x63092))+P24(f331(f331(f248(a1),x63091),f331(f331(f81(a1),x63092),f79(a1))))
% 162.26/162.06 [6310]~P24(f331(f331(f248(a1),x63101),x63102))+P24(f331(f331(f247(a1),x63101),f331(f331(f22(a1),x63102),f79(a1))))
% 162.26/162.06 [6312]~P24(f331(f331(f248(a1),x63121),x63122))+P24(f331(f331(f248(a1),f331(f110(a1),x63121)),f331(f110(a1),x63122)))
% 162.26/162.06 [6314]~P24(f331(f331(f248(a883),x63141),x63142))+P24(f331(f331(f248(a1),f331(f106(a1),x63141)),f331(f106(a1),x63142)))
% 162.26/162.07 [6315]~P24(f331(f331(f247(a1),x63151),x63152))+P24(f331(f331(f247(a883),f331(f110(a883),x63151)),f331(f110(a883),x63152)))
% 162.26/162.07 [6316]~P24(f331(f331(f247(a1),x63161),x63162))+P24(f331(f331(f247(a1),f331(f110(a1),x63161)),f331(f110(a1),x63162)))
% 162.26/162.07 [6318]~P24(f331(f331(f247(a883),x63181),x63182))+P24(f331(f331(f247(a1),f331(f106(a1),x63181)),f331(f106(a1),x63182)))
% 162.26/162.07 [6319]~P24(f331(f331(f92(a1),x63191),x63192))+P24(f331(f331(f92(a1),f331(f110(a1),x63191)),f331(f110(a1),x63192)))
% 162.26/162.07 [6337]~P24(f331(f331(f247(a883),x63371),x63372))+~P24(f331(f331(f247(a883),f331(a118,x63372)),x63371))
% 162.26/162.07 [6380]~P24(f331(f331(f248(a883),f331(a118,x63801)),f331(a118,x63802)))+P24(f331(f331(f248(a883),x63801),x63802))
% 162.26/162.07 [6381]~P24(f331(f331(f248(a105),f331(a3,x63811)),f331(a3,x63812)))+P24(f331(f331(f248(a883),x63811),x63812))
% 162.26/162.07 [6382]~P24(f331(f331(f248(a883),f331(a111,x63821)),f331(a111,x63822)))+P24(f331(f331(f248(a1),x63821),x63822))
% 162.26/162.07 [6383]~P24(f331(f331(f248(a883),f331(a19,x63831)),f331(a19,x63832)))+P24(f331(f331(f248(a105),x63831),x63832))
% 162.26/162.07 [6384]~P24(f331(f331(f247(a883),f331(a118,x63841)),f331(a118,x63842)))+P24(f331(f331(f247(a883),x63841),x63842))
% 162.26/162.07 [6385]~P24(f331(f331(f247(a105),f331(a3,x63851)),f331(a3,x63852)))+P24(f331(f331(f247(a883),x63851),x63852))
% 162.26/162.07 [6386]~P24(f331(f331(f247(a883),f331(a19,x63861)),f331(a19,x63862)))+P24(f331(f331(f247(a105),x63861),x63862))
% 162.26/162.07 [6426]~P24(f331(f331(f248(a883),f331(a111,x64262)),f331(a111,x64261)))+P24(f331(f331(f248(a1),f2(a1)),x64261))
% 162.26/162.07 [6457]P24(f331(f331(f247(a1),f2(a1)),f45(a1,x64571,x64572)))+~P24(f331(f331(f248(a1),f2(a1)),x64572))
% 162.26/162.07 [6612]P38(x66121,x66122)+~E(f331(f331(f288(x66121,x66121,x66121),x66122),x66122),f196(f891(f890(x66121,x66121),a877)))
% 162.26/162.07 [6624]~P38(x66241,x66242)+P38(x66241,f331(f331(f288(x66241,x66241,x66241),x66242),x66242))
% 162.26/162.07 [6636]P24(f331(f331(f248(a1),x66361),x66362))+~P24(f331(f331(f247(a1),x66361),f331(f331(f22(a1),x66362),f79(a1))))
% 162.26/162.07 [6637]P24(f331(f331(f247(a1),x66371),x66372))+~P24(f331(f331(f248(a1),x66371),f331(f331(f81(a1),x66372),f79(a1))))
% 162.26/162.07 [6640]P24(f331(f331(f248(a883),x66401),x66402))+~P24(f331(f331(f248(a1),f331(f106(a1),x66401)),f331(f106(a1),x66402)))
% 162.26/162.07 [6641]P24(f331(f331(f248(a1),x66411),x66412))+~P24(f331(f331(f248(a883),f331(f110(a883),x66411)),f331(f110(a883),x66412)))
% 162.26/162.07 [6642]P24(f331(f331(f248(a1),x66421),x66422))+~P24(f331(f331(f248(a1),f331(f110(a1),x66421)),f331(f110(a1),x66422)))
% 162.26/162.07 [6644]P24(f331(f331(f247(a883),x66441),x66442))+~P24(f331(f331(f247(a1),f331(f106(a1),x66441)),f331(f106(a1),x66442)))
% 162.26/162.07 [6645]P24(f331(f331(f247(a1),x66451),x66452))+~P24(f331(f331(f247(a1),f331(f110(a1),x66451)),f331(f110(a1),x66452)))
% 162.26/162.07 [6646]P24(f331(f331(f92(a1),x66461),x66462))+~P24(f331(f331(f92(a1),f331(f110(a1),x66461)),f331(f110(a1),x66462)))
% 162.26/162.07 [6739]~E(f671(x67392,x67391),f119(x67391))+E(f331(f145(f884(x67391),f884(x67391),f137(x67391),f119(x67391)),x67392),f119(x67391))
% 162.26/162.07 [6740]~E(f672(x67402,x67401),f119(x67401))+E(f331(f145(f884(x67401),f884(x67401),f137(x67401),f119(x67401)),x67402),f119(x67401))
% 162.26/162.07 [6747]~P27(x67471)+E(f331(f145(x67471,x67471,f108(x67471),f256(x67471)),x67472),f41(x67471,f331(f175(x67471),x67472)))
% 162.26/162.07 [6748]~P27(x67481)+E(f331(f145(x67481,x67481,f107(x67481),f196(x67481)),x67482),f40(x67481,f331(f175(x67481),x67482)))
% 162.26/162.07 [6760]E(x67601,f2(a105))+E(f331(f331(f81(a883),f331(a19,f331(f331(f22(a105),x67601),f79(a105)))),f331(a118,x67602)),f331(f331(f81(a883),f331(a19,x67601)),x67602))
% 162.26/162.07 [6804]P24(f331(f331(f248(a1),f331(f331(f22(a1),x68041),x68042)),f2(a1)))+~P24(f331(f331(f248(a1),x68041),x68042))
% 162.26/162.07 [6828]~P107(x68281)+E(f331(f331(f107(f891(x68281,a877)),f331(f331(f309(x68281),x68282),f196(f891(x68281,a877)))),f331(f303(x68281),x68282)),f331(f255(x68281),x68282))
% 162.26/162.07 [6900]~P57(x69001,x69002)+P38(x69001,f331(f253(f890(x69001,x69001)),f331(f270(x69001,x69001,a877),x69002)))
% 162.26/162.07 [6901]~P57(x69011,x69012)+P55(x69011,f331(f253(f890(x69011,x69011)),f331(f270(x69011,x69011,a877),x69012)))
% 162.26/162.07 [6902]E(x69021,f196(f891(x69022,a877)))+~P24(f331(f331(f247(f891(x69022,a877)),x69021),f196(f891(x69022,a877))))
% 162.26/162.07 [6986]~P24(f331(f331(f248(a883),f2(a883)),x69862))+P24(f331(f331(f248(a883),f45(a883,x69861,x69862)),x69862))
% 162.26/162.07 [6988]~P24(f331(f331(f248(a1),f2(a1)),x69882))+P24(f331(f331(f248(a1),f45(a1,x69881,x69882)),x69882))
% 162.26/162.07 [6989]~P24(f331(f331(f248(a883),f2(a883)),x69892))+P24(f331(f331(f247(a883),f45(a883,x69891,x69892)),x69892))
% 162.26/162.07 [6990]~P24(f331(f331(f247(a1),f2(a1)),x69901))+P24(f331(f331(f247(a1),f45(a1,x69901,x69902)),x69901))
% 162.26/162.07 [7068]~P108(x70681)+E(f331(f331(f22(f891(x70681,a877)),f331(f331(f309(x70681),x70682),f196(f891(x70681,a877)))),f331(f254(x70681),x70682)),f331(f331(f309(x70681),x70682),f196(f891(x70681,a877))))
% 162.26/162.07 [7140]~P50(x71401,x71402)+P48(x71401,f256(f891(x71401,a877)),f331(f253(f890(x71401,x71401)),f331(f270(x71401,x71401,a877),x71402)))
% 162.26/162.07 [7141]P24(f331(x71411,x71412))+P24(f331(f331(f333(f891(f890(a883,a883),a877)),f603(x71412,x71411)),a104))
% 162.26/162.07 [7186]E(f331(f331(f137(a883),f142(a883,f331(f301(a883,x71861),x71862))),f331(f331(f154(a883),x71862),f119(a883))),f142(a883,f331(f301(a883,x71861),f331(a118,x71862))))+~P24(f331(f331(f247(a883),x71861),x71862))
% 162.26/162.07 [7316]E(x73161,f2(a883))+~E(f331(f145(a883,a883,f81(a883),x73161),x73162),f2(a883))
% 162.26/162.07 [7344]~P24(f331(f331(f248(a1),f331(f331(f22(a1),x73441),x73442)),f2(a1)))+P24(f331(f331(f248(a1),x73441),x73442))
% 162.26/162.07 [7372]P38(x73721,x73722)+~P38(x73721,f331(f331(f288(x73721,x73721,x73721),x73722),x73722))
% 162.26/162.07 [7402]~P24(f331(f331(f247(a883),f331(a118,x74021)),x74022))+P24(f193(a877,a245,f331(f247(a883),x74021),x74022))
% 162.26/162.07 [7557]P21(a883,a883,f331(f331(f7(a883,a883,a883),f22(a883)),x75571),x75572)+P24(f331(f331(f333(a883),f704(x75571,x75572)),x75572))
% 162.26/162.07 [7611]E(f331(f331(f331(f66(a883,x76111,f81(a883)),f331(f16(a883,x76111),f79(a883))),f2(a883)),x76112),f331(f38(x76111),x76112))+~P24(f331(f62(x76111),x76112))
% 162.26/162.07 [7653]P21(a883,a883,f331(f331(f7(a883,a883,a883),f22(a883)),x76531),x76532)+~P24(f331(f331(f247(a883),x76531),f704(x76531,x76532)))
% 162.26/162.07 [7710]P38(x77101,x77102)+P24(f331(f331(f247(f891(x77101,a877)),f693(x77102,x77101)),f331(f285(x77101,x77101,x77102),f693(x77102,x77101))))
% 162.26/162.07 [7715]P57(x77151,x77152)+~P38(x77151,f331(f253(f890(x77151,x77151)),f331(f270(x77151,x77151,a877),x77152)))
% 162.26/162.07 [7787]P24(f331(f331(f247(a883),f331(a118,x77871)),x77872))+~P24(f193(a877,a245,f331(f247(a883),x77871),x77872))
% 162.26/162.07 [7843]P24(f331(f331(f333(f890(a883,a883)),f331(f331(f261(a883,a883),x78431),x78432)),f307(a883,a321)))+~P24(f331(f331(f247(a883),x78431),x78432))
% 162.26/162.07 [7930]P50(x79301,x79302)+~P48(x79301,f256(f891(x79301,a877)),f331(f253(f890(x79301,x79301)),f331(f270(x79301,x79301,a877),x79302)))
% 162.26/162.07 [7989]~P24(f331(f140(x79891),x79892))+P24(f331(f140(f891(x79891,a877)),f331(f331(f157(f884(x79891),f891(x79891,a877)),f175(x79891)),f54(x79891,x79892))))
% 162.26/162.07 [8201]~P38(x82011,f331(f286(x82011,x82011),x82012))+P38(x82011,f331(f286(x82011,x82011),f331(f331(f288(x82011,x82011,x82011),x82012),f307(x82011,x82012))))
% 162.26/162.07 [8319]P24(f331(f62(f890(x83191,x83191)),f331(f331(f288(x83191,x83191,x83191),x83192),f307(x83191,x83192))))+~P24(f331(f62(f890(x83191,x83191)),x83192))
% 162.26/162.07 [8347]E(x83471,f2(a1))+P24(f331(f49(x83472,x83471),f331(f331(f261(a1,a1),f331(f331(f39(a1),x83472),x83471)),f45(a1,x83472,x83471))))
% 162.26/162.07 [8358]~P24(f331(f331(f333(f890(a883,a883)),f331(f331(f261(a883,a883),x83581),x83582)),f307(a883,a321)))+P24(f331(f331(f247(a883),x83581),x83582))
% 162.26/162.07 [8375]~P80(x83751)+E(f331(f145(x83751,x83751,f331(f7(x83751,x83751,x83751),f81(x83751)),f2(x83751)),f331(f172(x83751),x83752)),f331(f145(x83751,x83751,f81(x83751),f2(x83751)),x83752))
% 162.26/162.07 [8553]~P107(x85531)+E(f331(f145(f884(x85531),x85531,f331(f7(x85531,f884(x85531),f884(x85531)),f151(x85531,x85531,f5(x85531))),f119(x85531)),x85532),f153(x85531,x85531,f5(x85531),x85532))
% 162.26/162.07 [8662]P24(f331(f331(f333(f890(a883,a883)),f331(f331(f261(a883,a883),x86621),x86622)),f331(f331(f288(a883,a883,a883),a321),f307(a883,a321))))+~P24(f331(f331(f248(a883),x86621),x86622))
% 162.26/162.07 [8703]~P24(f331(f62(f890(x87031,x87031)),f331(f331(f288(x87031,x87031,x87031),x87032),f307(x87031,x87032))))+P24(f331(f62(f890(x87031,x87031)),x87032))
% 162.26/162.07 [8960]P55(x89601,x89602)+P24(f331(f331(f333(f890(x89601,x89601)),f331(f331(f261(x89601,x89601),f757(x89602,x89601)),f757(x89602,x89601))),f331(f331(f288(x89601,x89601,x89601),x89602),f307(x89601,x89602))))
% 162.26/162.07 [8961]P55(x89611,x89612)+P24(f331(f331(f333(f890(x89611,x89611)),f331(f331(f261(x89611,x89611),f765(x89612,x89611)),f765(x89612,x89611))),f331(f331(f288(x89611,x89611,x89611),x89612),f307(x89611,x89612))))
% 162.26/162.07 [9063]~P24(f331(f331(f333(f890(a883,a883)),f331(f331(f261(a883,a883),x90631),x90632)),f331(f331(f288(a883,a883,a883),a321),f307(a883,a321))))+P24(f331(f331(f248(a883),x90631),x90632))
% 162.26/162.07 [5092]~P94(x50921)+E(f331(f331(f81(x50921),f331(f110(x50921),a84)),x50922),x50922)
% 162.26/162.07 [5120]~P66(x51201)+E(f331(f331(f81(x51201),f331(f80(x51201),x51202)),x51202),f2(x51201))
% 162.26/162.07 [5121]~P70(x51211)+E(f331(f331(f81(x51211),f331(f80(x51211),x51212)),x51212),f2(x51211))
% 162.26/162.07 [5122]~P85(x51221)+E(f331(f331(f107(x51221),f331(f80(x51221),x51222)),x51222),f256(x51221))
% 162.26/162.07 [5123]~P85(x51231)+E(f331(f331(f108(x51231),f331(f80(x51231),x51232)),x51232),f196(x51231))
% 162.26/162.07 [5154]~P94(x51541)+E(f331(f331(f82(x51541),f331(f110(x51541),a103)),x51542),f331(f80(x51541),x51542))
% 162.26/162.07 [5327]~P114(x53271)+E(f331(f331(f82(x53271),f331(f80(x53271),f79(x53271))),x53272),f331(f80(x53271),x53272))
% 162.26/162.07 [5370]E(f331(f76(a1),x53701),f79(a1))+~E(f331(f76(a1),f331(f331(f82(a1),x53701),x53702)),f79(a1))
% 162.26/162.07 [5463]~P94(x54631)+E(f331(f331(f81(x54631),f79(x54631)),f331(f110(x54631),x54632)),f331(f110(x54631),f331(f331(f22(a1),x54632),a103)))
% 162.26/162.07 [5515]~P96(x55151)+E(f13(x55151,f331(f331(f309(x55151),x55152),f196(f891(x55151,a877)))),x55152)
% 162.26/162.07 [5516]~P107(x55161)+E(f14(x55161,f331(f331(f309(x55161),x55162),f196(f891(x55161,a877)))),x55162)
% 162.26/162.07 [5517]~P107(x55171)+E(f15(x55171,f331(f331(f309(x55171),x55172),f196(f891(x55171,a877)))),x55172)
% 162.26/162.07 [5518]~P96(x55181)+E(f10(x55181,f331(f331(f309(x55181),x55182),f196(f891(x55181,a877)))),x55182)
% 162.26/162.07 [5519]~P27(x55191)+E(f41(x55191,f331(f331(f309(x55191),x55192),f196(f891(x55191,a877)))),x55192)
% 162.26/162.07 [5520]~P27(x55201)+E(f40(x55201,f331(f331(f309(x55201),x55202),f196(f891(x55201,a877)))),x55202)
% 162.26/162.07 [5542]E(f331(f331(f81(a883),x55421),f331(f331(f22(a883),x55422),x55421)),x55422)+P24(f331(f331(f248(a883),x55422),x55421))
% 162.26/162.07 [5572]E(x55721,f119(x55722))+P24(f331(f331(f248(a883),f2(a883)),f331(f197(f884(x55722)),x55721)))
% 162.26/162.07 [5698]~P107(x56981)+E(f11(x56981,f251(x56981),f331(f331(f309(x56981),x56982),f196(f891(x56981,a877)))),x56982)
% 162.26/162.07 [5699]~P107(x56991)+E(f12(x56991,f246(x56991),f331(f331(f309(x56991),x56992),f196(f891(x56991,a877)))),x56992)
% 162.26/162.07 [5761]E(f331(f331(f22(a883),x57611),f331(f331(f22(a883),x57611),x57612)),x57612)+~P24(f331(f331(f247(a883),x57612),x57611))
% 162.26/162.07 [5762]E(f331(f331(f81(a883),x57621),f331(f331(f22(a883),x57622),x57621)),x57622)+~P24(f331(f331(f247(a883),x57621),x57622))
% 162.26/162.07 [5783]E(f45(a883,f331(f331(f22(a883),x57831),x57832),x57832),f45(a883,x57831,x57832))+P24(f331(f331(f248(a883),x57831),x57832))
% 162.26/162.07 [5794]E(f331(f80(a1),f331(f331(f39(a1),x57941),f331(f80(a1),x57942))),f291(x57941,x57942))+P24(f331(f331(f247(a1),f2(a1)),x57942))
% 162.26/162.07 [5796]~E(x57962,f2(a883))+P24(f331(f331(f248(a883),f2(a883)),f331(f331(f262(a883),x57961),x57962)))
% 162.26/162.07 [5847]~P94(x58471)+E(f331(f331(f81(x58471),f331(f80(x58471),f79(x58471))),f331(f110(x58471),x58472)),f331(f110(x58471),f331(f331(f81(a1),x58472),a103)))
% 162.26/162.07 [5848]E(f331(f331(f262(a883),f331(f110(a883),x58481)),x58482),f331(f331(f262(a883),f2(a883)),x58482))+~P24(f331(a202,f331(f110(a1),x58481)))
% 162.26/162.07 [5944]E(f331(f144(a883),f142(a883,f331(f301(a883,x59441),x59442))),x59441)+~P24(f331(f331(f248(a883),x59441),x59442))
% 162.26/162.07 [5964]E(f331(f331(f82(a883),f331(f110(a883),x59641)),f331(f110(a883),x59642)),f331(f110(a883),f331(f331(f82(a1),x59641),x59642)))+P24(f331(f331(f248(a1),x59641),a84))
% 162.26/162.07 [5970]~P124(x59701)+P24(f331(f331(f247(x59701),f2(x59701)),f331(f331(f82(x59701),x59702),x59702)))
% 162.26/162.07 [5982]E(f331(f331(f22(a883),f331(a118,x59821)),x59822),f331(a118,f331(f331(f22(a883),x59821),x59822)))+~P24(f331(f331(f247(a883),x59822),x59821))
% 162.26/162.07 [5985]E(f45(a883,f331(f331(f22(a883),x59851),x59852),x59852),f45(a883,x59851,x59852))+~P24(f331(f331(f247(a883),x59852),x59851))
% 162.26/162.07 [6038]E(f331(f331(f262(a883),f331(a111,x60381)),x60382),f331(a111,f331(f331(f262(a1),x60381),x60382)))+~P24(f331(f331(f247(a1),f2(a1)),x60381))
% 162.26/162.07 [6054]P24(f331(f140(x60541),x60542))+P24(f331(f331(f248(a883),f602(x60542,x60541)),f331(f197(f884(x60541)),x60542)))
% 162.26/162.07 [6055]P24(f331(f140(x60551),x60552))+P24(f331(f331(f248(a883),f622(x60552,x60551)),f331(f197(f884(x60551)),x60552)))
% 162.26/162.07 [6070]~E(x60701,f119(x60702))+~P24(f331(f331(f248(a883),f2(a883)),f331(f197(f884(x60702)),x60701)))
% 162.26/162.07 [6084]E(f147(a883,f142(a883,f331(f301(a883,x60841),x60842))),f331(f331(f22(a883),x60842),f79(a883)))+~P24(f331(f331(f248(a883),x60841),x60842))
% 162.26/162.07 [6087]E(f331(f331(f81(a1),x60871),f331(f106(a1),f331(a118,f349(x60872,x60871)))),x60872)+~P24(f331(f331(f248(a1),x60871),x60872))
% 162.26/162.07 [6094]E(x60941,f2(a883))+E(f331(f331(f82(a883),x60942),f331(f331(f262(a883),x60942),f331(f331(f22(a883),x60941),f79(a883)))),f331(f331(f262(a883),x60942),x60941))
% 162.26/162.07 [6120]E(f331(f331(f82(a883),f331(a111,x61201)),f331(a111,x61202)),f331(a111,f331(f331(f82(a1),x61201),x61202)))+~P24(f331(f331(f247(a1),f2(a1)),x61201))
% 162.26/162.07 [6121]E(f331(f331(f39(a883),f331(a111,x61211)),f331(a111,x61212)),f331(a111,f331(f331(f39(a1),x61211),x61212)))+~P24(f331(f331(f247(a1),f2(a1)),x61211))
% 162.26/162.07 [6135]~P118(x61351)+E(f331(f331(f81(x61351),x61352),x61352),f331(f331(f82(x61351),f331(f331(f81(x61351),f79(x61351)),f79(x61351))),x61352))
% 162.26/162.07 [6154]E(f331(f331(f22(a1),f331(f106(a1),x61541)),f331(f106(a1),x61542)),f331(f106(a1),f331(f331(f22(a883),x61541),x61542)))+~P24(f331(f331(f247(a883),x61542),x61541))
% 162.26/162.07 [6156]E(f331(f331(f261(a1,a1),f331(f110(a1),a103)),f331(f331(f81(a1),x61561),x61562)),f50(x61561,x61562))+~P24(f331(f331(f247(a1),x61562),f2(a1)))
% 162.26/162.07 [6191]E(f182(x61911,x61912),f119(f884(x61911)))+P24(f331(f331(f333(f884(x61911)),f636(x61912,x61911)),f331(f175(f884(x61911)),x61912)))
% 162.26/162.07 [6200]E(f122(a1,f331(f129(a1),x62001),f128(x62002,f331(f331(f81(a1),x62001),f79(a1)))),f128(x62002,x62001))+P24(f331(f331(f248(a1),x62002),x62001))
% 162.26/162.07 [6275]E(f331(f331(f154(a1),x62751),f181(f331(f331(f81(a1),x62751),f79(a1)),x62752)),f181(x62751,x62752))+~P24(f331(f331(f247(a1),x62751),x62752))
% 162.26/162.07 [6311]~P24(f331(f331(f248(a883),x63112),x63111))+P24(f331(f331(f248(a883),f2(a883)),f331(f331(f22(a883),x63111),x63112)))
% 162.26/162.07 [6340]~P24(f331(f331(f248(a883),x63401),f331(a111,x63402)))+P24(f331(f331(f248(a1),f331(f106(a1),x63401)),x63402))
% 162.26/162.07 [6371]~P107(x63711)+E(f331(f331(f107(f891(x63711,a877)),f331(f254(x63711),x63712)),f331(f331(f309(x63711),x63712),f196(f891(x63711,a877)))),f331(f300(x63711),x63712))
% 162.26/162.07 [6374]~P24(f331(f331(f248(a883),f2(a883)),x63741))+P24(f331(f331(f248(a883),f2(a883)),f331(f331(f262(a883),x63741),x63742)))
% 162.26/162.07 [6375]~P24(f331(f331(f247(a1),f2(a1)),x63751))+P24(f331(f331(f247(a1),f2(a1)),f331(f331(f262(a1),x63751),x63752)))
% 162.26/162.07 [6402]~E(f331(x64021,f2(a883)),f2(a883))+E(f331(f331(f6(a883,a883),x64021),f302(a883,f331(a118,f2(a883)),x64022)),f331(f331(f6(a883,a883),x64021),f302(a883,f2(a883),x64022)))
% 162.26/162.07 [6480]E(f331(f331(f309(a1),x64801),f302(a1,f331(f331(f81(a1),x64801),f79(a1)),x64802)),f302(a1,x64801,x64802))+P24(f331(f331(f248(a1),x64802),x64801))
% 162.26/162.07 [6481]P24(f331(f331(f248(a883),x64811),f331(a111,x64812)))+~P24(f331(f331(f248(a1),f331(f106(a1),x64811)),x64812))
% 162.26/162.07 [6579]E(f331(a111,f331(f331(f39(a1),f331(f110(a1),x65791)),f331(f110(a1),x65792))),f331(f331(f39(a883),f331(f110(a883),x65791)),f331(f110(a883),x65792)))+P24(f331(a202,f331(f110(a1),x65791)))
% 162.26/162.07 [6638]P24(f331(f331(f248(a883),x66381),x66382))+~P24(f331(f331(f248(a883),f2(a883)),f331(f331(f22(a883),x66382),x66381)))
% 162.26/162.07 [6682]P24(f331(f331(f248(a883),f2(a883)),x66821))+~P24(f331(f331(f248(a883),f2(a883)),f331(f331(f82(a883),x66822),x66821)))
% 162.26/162.07 [6683]P24(f331(f331(f248(a883),f2(a883)),x66831))+~P24(f331(f331(f248(a883),f2(a883)),f331(f331(f82(a883),x66831),x66832)))
% 162.26/162.07 [6700]~P24(f331(f331(f247(a1),x67001),f2(a1)))+E(f331(f331(f82(a883),f331(a111,f331(f80(a1),x67001))),f331(a111,f331(f80(a1),x67002))),f331(a111,f331(f331(f82(a1),x67001),x67002)))
% 162.26/162.07 [6758]~E(x67582,f196(f891(x67581,a877)))+P24(f331(f331(f247(f891(x67581,a877)),x67582),f331(f80(f891(x67581,a877)),x67582)))
% 162.26/162.07 [6868]~P24(f331(f331(f248(a1),x68681),x68682))+P24(f331(f331(f247(a1),f331(f331(f81(a1),x68681),f79(a1))),x68682))
% 162.26/162.07 [6932]E(x69321,f2(a883))+~P24(f331(f331(f247(a1),f331(f106(a1),x69322)),f331(f80(a1),f331(f106(a1),x69321))))
% 162.26/162.07 [6933]E(x69331,f2(a883))+~P24(f331(f331(f247(a1),f331(f106(a1),x69331)),f331(f80(a1),f331(f106(a1),x69332))))
% 162.26/162.07 [7039]E(f331(f331(f261(a1,a1),f331(f110(a1),a103)),f331(f331(f81(a1),x70391),x70392)),f50(x70391,x70392))+~P24(f331(f331(f247(a1),f2(a1)),f331(f331(f81(a1),x70391),x70392)))
% 162.26/162.07 [7080]~P22(x70801,x70802)+P38(x70801,f331(f260(f891(f890(x70801,x70801),a877),f891(f890(x70801,x70801),a877)),x70802))
% 162.26/162.07 [7098]~P24(f331(f331(f247(a883),f331(a118,f2(a883))),x70981))+P24(f331(f331(f247(a883),f331(a118,f2(a883))),f331(f331(f262(a883),x70981),x70982)))
% 162.26/162.07 [7318]~P24(f331(f331(f248(a883),f2(a883)),x73181))+P24(f331(f331(f248(a883),f331(f331(f22(a883),x73181),f331(a118,x73182))),x73181))
% 162.26/162.07 [7355]P24(f331(f331(f247(a883),f331(a118,f2(a883))),x73551))+~P24(f331(f331(f247(a883),f331(a118,f2(a883))),f331(f331(f82(a883),x73552),x73551)))
% 162.26/162.07 [7356]P24(f331(f331(f247(a883),f331(a118,f2(a883))),x73561))+~P24(f331(f331(f247(a883),f331(a118,f2(a883))),f331(f331(f82(a883),x73561),x73562)))
% 162.26/162.07 [7359]P24(f331(f331(f247(a883),f331(f331(f168(a883),x73591),x73592)),f331(f169(a883),x73591)))+~P24(f331(f331(f248(a883),x73592),f331(f197(f884(a883)),x73591)))
% 162.26/162.07 [7401]P24(f331(f331(f248(a1),x74011),x74012))+~P24(f331(f331(f247(a1),f331(f331(f81(a1),x74011),f79(a1))),x74012))
% 162.26/162.07 [7446]P24(f331(f62(x74461),f256(f891(x74461,a877))))+~P24(f331(f62(f891(x74462,x74461)),f256(f891(f891(x74462,x74461),a877))))
% 162.26/162.07 [7447]P24(f331(f62(x74471),f256(f891(x74471,a877))))+~P24(f331(f62(f889(x74472,x74471)),f256(f891(f889(x74472,x74471),a877))))
% 162.26/162.07 [7448]P24(f331(f62(x74481),f256(f891(x74481,a877))))+~P24(f331(f62(f889(x74481,x74482)),f256(f891(f889(x74481,x74482),a877))))
% 162.26/162.07 [7487]E(x74871,f196(f891(x74872,a877)))+~P24(f331(f331(f247(f891(x74872,a877)),x74871),f331(f80(f891(x74872,a877)),x74871)))
% 162.26/162.07 [7621]E(f331(f145(f884(x76211),f884(x76211),f137(x76211),f119(x76211)),x76212),f119(x76211))+P24(f331(f331(f333(f884(x76211)),f671(x76212,x76211)),f331(f175(f884(x76211)),x76212)))
% 162.26/162.07 [7622]E(f331(f145(f884(x76221),f884(x76221),f137(x76221),f119(x76221)),x76222),f119(x76221))+P24(f331(f331(f333(f884(x76221)),f672(x76222,x76221)),f331(f175(f884(x76221)),x76222)))
% 162.26/162.07 [7949]~P118(x79491)+E(f331(f331(f82(x79491),f331(f331(f81(x79491),f79(x79491)),f79(x79491))),f331(f331(f6(a883,x79491),f106(x79491)),f302(a883,f79(a883),x79492))),f331(f331(f82(x79491),f331(f106(x79491),x79492)),f331(f331(f81(x79491),f331(f106(x79491),x79492)),f79(x79491))))
% 162.26/162.07 [8005]P24(f331(f331(f333(a883),x80051),x80052))+~P24(f331(f331(f333(a1),f331(f106(a1),x80051)),f331(f310(a883,a1,f106(a1)),x80052)))
% 162.26/162.07 [8171]~P24(f331(f62(x81711),x81712))+E(f331(f310(a883,x81711,f568(x81712,x81711)),f331(f253(a883),f331(f331(f7(a883,a883,a877),f248(a883)),f569(x81712,x81711)))),x81712)
% 162.26/162.07 [8453]P49(x84531,x84532)+P24(f331(f331(f333(f890(x84531,x84531)),f331(f331(f261(x84531,x84531),f407(x84532,x84531)),f407(x84532,x84531))),x84532))
% 162.26/162.07 [8699]~P24(f331(f331(f248(f891(a883,a877)),x86991),x86992))+P24(f331(f331(f248(f891(a1,a877)),f331(f310(a883,a1,f106(a1)),x86991)),f331(f310(a883,a1,f106(a1)),x86992)))
% 162.26/162.07 [8729]~P94(x87291)+E(f331(f331(f22(x87291),f79(x87291)),f331(f110(x87291),x87292)),f331(f110(x87291),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)),f331(f80(a1),x87292))))
% 162.26/162.07 [8802]~P24(f331(f331(f333(a883),x88021),f331(f175(a883),x88022)))+P24(f331(f331(f247(a883),x88021),f331(f145(a883,a883,f81(a883),f2(a883)),x88022)))
% 162.26/162.07 [8898]P45(x88981,x88982)+~P24(f331(f331(f333(f890(x88981,x88981)),f331(f331(f261(x88981,x88981),f385(x88982,x88981)),f385(x88982,x88981))),x88982))
% 162.26/162.07 [8975]P20(a878,x89751,f331(f331(f309(f882(a878)),f331(a94,f331(a28,x89752))),f196(f891(f882(a878),a877))))+~P20(a878,f331(f331(f309(f882(a878)),f331(a94,f331(a28,x89752))),x89751),f331(f331(f309(f882(a878)),f331(a94,f331(f244(a879),f331(a26,x89752)))),f196(f891(f882(a878),a877))))
% 162.26/162.07 [9038]~P24(f331(f331(f248(f891(a1,a877)),f331(f310(a883,a1,f106(a1)),x90381)),f331(f310(a883,a1,f106(a1)),x90382)))+P24(f331(f331(f248(f891(a883,a877)),x90381),x90382))
% 162.26/162.07 [9039]~P24(f331(f331(f247(f891(a1,a877)),f331(f310(a883,a1,f106(a1)),x90391)),f331(f310(a883,a1,f106(a1)),x90392)))+P24(f331(f331(f247(f891(a883,a877)),x90391),x90392))
% 162.26/162.07 [10019]~P104(x100191)+E(f122(f884(x100191),f331(f129(f884(x100191)),f119(x100191)),f331(f331(f331(f102(f885(f884(x100191))),f331(f331(f248(a1),f2(a1)),x100192)),f331(f124(f890(x100191,f884(x100191)),f884(x100191),f134(x100191,f884(x100191),f135(x100191,f331(f331(f22(a1),x100192),f79(a1))),f135(f884(x100191),f331(f331(f22(a1),x100192),f79(a1))))),f331(f270(x100191,f884(x100191),f885(f884(x100191))),f331(f331(f8(f891(f884(x100191),f884(x100191)),f891(f884(x100191),f885(f884(x100191))),x100191),f331(f8(f884(x100191),f885(f884(x100191)),f884(x100191)),f129(f884(x100191)))),f154(x100191))))),f121(f884(x100191)))),f135(f884(x100191),x100192))
% 162.26/162.07 [10040]~P24(f331(f62(x100401),x100402))+E(f331(f197(f884(x100401)),f91(f884(x100401),f331(f331(f18(f884(x100401),a877,a877),f331(f331(f8(a877,f891(a877,a877),f884(x100401)),a329),f331(f331(f7(f884(x100401),f891(x100401,a877),a877),f331(f331(f8(f891(x100401,a877),f891(f891(x100401,a877),a877),f884(x100401)),a328),f175(x100401))),x100402))),f140(x100401)))),f226(x100401,x100402))
% 162.26/162.07 [10223]~P20(a878,x102231,f331(f331(f309(f882(a878)),f331(a94,x102232)),f196(f891(f882(a878),a877))))+P20(a878,x102231,f331(f331(f309(f882(a878)),f331(f331(f331(f93(a878),f331(f331(f8(f891(a878,f891(a878,a877)),f891(a878,a877),a878),f331(f8(f891(a878,a877),a877,a878),f88(a878))),f331(f331(f8(f891(a878,a877),f891(a878,f891(a878,a877)),a878),f331(f7(a878,f891(a878,a877),f891(a878,a877)),f331(f331(f8(f891(a878,f891(a877,a877)),f891(f891(a878,a877),f891(a878,a877)),a878),f18(a878,a877,a877)),f331(f331(f8(f891(a878,a877),f891(a878,f891(a877,a877)),a878),f331(f8(a877,f891(a877,a877),a878),a334)),f203(x102232))))),a328))),x102232),a328)),f196(f891(f882(a878),a877))))
% 162.26/162.07 [6083]E(f331(f331(f81(a883),f331(f331(f22(a883),x60831),x60832)),x60832),x60831)+~P24(f331(f331(f247(a883),x60832),x60831))
% 162.26/162.07 [6148]E(f331(f331(f39(a883),f331(f331(f82(a883),x61481),x61482)),x61482),x61481)+~P24(f331(f331(f248(a883),f2(a883)),x61482))
% 162.26/162.07 [6149]E(f331(f331(f39(a883),f331(f331(f82(a883),x61491),x61492)),x61491),x61492)+~P24(f331(f331(f248(a883),f2(a883)),x61491))
% 162.26/162.07 [6155]~P74(x61551)+E(f331(f331(f6(a883,x61551),f331(f168(x61551),x61552)),f331(f301(a883,f2(a883)),f331(f197(f884(x61551)),x61552))),f331(f169(x61551),x61552))
% 162.26/162.07 [6267]E(f45(a883,f331(a118,f331(f331(f82(a883),x62671),x62672)),x62671),f79(a883))+~P24(f331(f331(f248(a883),f79(a883)),x62671))
% 162.26/162.07 [6273]E(f331(a118,f331(f331(f81(a883),f331(f110(a883),x62731)),x62732)),f331(f331(f81(a883),f79(a883)),x62732))+~P24(f331(a202,f331(f110(a1),x62731)))
% 162.26/162.07 [6301]E(f331(a111,f331(f331(f262(a1),f331(f110(a1),x63011)),x63012)),f331(f331(f262(a883),f331(f110(a883),x63011)),x63012))+P24(f331(a202,f331(f110(a1),x63011)))
% 162.26/162.07 [6530]E(f331(f331(f22(a883),x65301),f331(f110(a883),f331(f331(f81(a1),x65302),a103))),f331(f331(f22(a883),f331(a118,x65301)),f331(f110(a883),x65302)))+~P24(f331(f331(f248(a1),a84),x65302))
% 162.26/162.07 [6611]E(x66111,f2(a883))+E(f331(a118,f331(f331(f81(a883),f331(f331(f22(a883),x66111),f79(a883))),x66112)),f331(f331(f81(a883),x66111),x66112))
% 162.26/162.07 [6652]E(x66521,f2(a1))+P24(f331(f331(f248(a1),f2(a1)),f331(f331(f262(a1),f331(f76(a1),x66521)),x66522)))
% 162.26/162.07 [6667]~E(x66672,f2(a883))+P24(f331(f331(f248(a1),f2(a1)),f331(f331(f262(a1),f331(f76(a1),x66671)),x66672)))
% 162.26/162.07 [6704]E(x67041,f2(a883))+E(f331(f331(f81(a883),x67042),f331(f331(f82(a883),f331(f331(f22(a883),x67041),f79(a883))),x67042)),f331(f331(f82(a883),x67041),x67042))
% 162.26/162.07 [6752]~P24(f331(f331(f247(a1),x67521),x67522))+P24(f331(f331(f248(a1),f331(f331(f81(a1),x67521),a103)),x67522))
% 162.26/162.07 [6871]E(f331(f331(f154(a883),x68711),f142(a883,f331(f301(a883,f331(a118,x68711)),x68712))),f142(a883,f331(f301(a883,x68711),x68712)))+~P24(f331(f331(f248(a883),x68711),x68712))
% 162.26/162.07 [7074]E(x70741,f119(x70742))+E(f275(x70742,f331(f331(f157(x70742,f890(a105,x70742)),f331(f261(a105,x70742),f79(a105))),x70741)),f282(x70742,x70741))
% 162.26/162.07 [7293]P24(f331(f331(f247(a1),x72931),x72932))+~P24(f331(f331(f248(a1),f331(f331(f81(a1),x72931),a103)),x72932))
% 162.26/162.07 [7294]E(x72941,x72942)+~E(f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x72941)),x72941),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x72942)),x72942))
% 162.26/162.07 [7762]~P24(f331(f331(f248(a883),x77621),x77622))+P24(f331(f331(f333(f890(a883,a883)),f331(f331(f261(a883,a883),x77621),x77622)),a252))
% 162.26/162.07 [7977]~P24(f331(f331(f248(a105),f2(a105)),x79771))+P24(f331(f331(f248(a105),f331(f260(a105,f890(a105,a105)),f331(f276(x79771),x79772))),x79771))
% 162.26/162.07 [8297]~P83(x82971)+P24(f331(f331(f247(x82971),f331(f76(x82971),f331(f169(x82971),x82972))),f331(f169(x82971),f331(f331(f157(x82971,x82971),f76(x82971)),x82972))))
% 162.26/162.07 [8321]P24(f331(f331(f248(a883),x83211),x83212))+~P24(f331(f331(f333(f890(a883,a883)),f331(f331(f261(a883,a883),x83211),x83212)),a252))
% 162.26/162.07 [8476]E(f331(f331(f261(x84761,x84761),f786(x84762,x84761)),f786(x84762,x84761)),x84762)+~P24(f331(f331(f333(f890(x84761,x84761)),x84762),f307(x84761,f196(f891(f890(x84761,x84761),a877)))))
% 162.26/162.07 [8519]E(f331(f301(a883,x85191),f331(f331(f81(a883),x85191),f331(f38(a883),x85192))),x85192)+~P24(f331(f331(f247(f891(a883,a877)),x85192),f331(f301(a883,x85191),f331(f331(f81(a883),x85191),f331(f38(a883),x85192)))))
% 162.26/162.07 [8971]E(f179(f884(x89711),f331(f331(f8(a877,a877,f884(x89711)),a326),f331(f331(f7(f884(x89711),f884(x89711),a877),a328),f119(x89711))),x89712),f182(x89711,f182(x89711,x89712)))+~P29(a883,f331(f172(a883),f331(f331(f157(f884(x89711),a883),f197(f884(x89711))),x89712)))
% 162.26/162.07 [9834]P24(f331(a202,x98342))+E(f331(f331(f89(a1,a883),f331(f331(f22(a1),x98341),x98342)),f331(f331(f18(a1,a883,a883),f331(f331(f7(a1,a883,f891(a883,a883)),f331(f331(f8(a877,f891(a883,f891(a883,a883)),a1),f102(a883)),a202)),f2(a883))),a111)),f331(f331(f22(a883),f331(a111,x98341)),f331(a111,x98342)))
% 162.26/162.07 [9847]E(f331(f331(f89(a1,a883),f331(f110(a1),f331(f331(f81(a1),x98471),f331(f80(a1),x98472)))),f331(f331(f18(a1,a883,a883),f331(f331(f7(a1,a883,f891(a883,a883)),f331(f331(f8(a877,f891(a883,f891(a883,a883)),a1),f102(a883)),a202)),f2(a883))),a111)),f331(f331(f22(a883),f331(f110(a883),x98471)),f331(f110(a883),x98472)))+P24(f331(f331(f248(a1),x98472),a84))
% 162.26/162.07 [9849]~P22(x98491,x98492)+P24(f331(f331(f247(f891(f890(x98491,x98491),a877)),f331(f331(f288(x98491,x98491,x98491),f331(f260(f891(f890(x98491,x98491),a877),f891(f890(x98491,x98491),a877)),x98492)),f331(f269(f891(f890(x98491,x98491),a877),f891(f890(x98491,x98491),a877)),x98492))),f331(f260(f891(f890(x98491,x98491),a877),f891(f890(x98491,x98491),a877)),x98492)))
% 162.26/162.07 [9904]~E(f331(f38(a883),f331(f253(a883),f331(f331(f18(a883,a877,a877),f331(f331(f8(a877,f891(a877,a877),a883),a329),f331(f331(f7(a883,f891(a883,a877),a877),f333(a883)),x99041))),f331(f331(f7(a883,a883,a877),f248(a883)),f331(a118,x99042))))),f2(a883))+~P24(f331(f331(f333(a883),f2(a883)),x99041))
% 162.26/162.07 [10008]~P27(x100081)+E(f40(x100081,f331(f253(x100081),f331(f331(f8(f891(x100081,a877),a877,x100081),f88(x100081)),f331(f331(f8(f891(x100081,a877),f891(x100081,a877),x100081),f331(f18(x100081,a877,a877),f331(f331(f8(a877,f891(a877,a877),x100081),a334),f331(f331(f7(x100081,f891(x100081,a877),a877),f333(x100081)),x100082)))),f247(x100081))))),f41(x100081,x100082))
% 162.26/162.07 [10035]~P38(x100351,x100352)+P57(x100351,f331(f331(f7(x100351,f891(f890(x100351,x100351),a877),f891(x100351,a877)),f331(f331(f8(f891(x100351,f891(f891(f890(x100351,x100351),a877),a877)),f891(f891(f890(x100351,x100351),a877),f891(x100351,a877)),x100351),f7(x100351,f891(f890(x100351,x100351),a877),a877)),f331(f331(f8(f891(x100351,f890(x100351,x100351)),f891(x100351,f891(f891(f890(x100351,x100351),a877),a877)),x100351),f331(f8(f890(x100351,x100351),f891(f891(f890(x100351,x100351),a877),a877),x100351),f333(f890(x100351,x100351)))),f261(x100351,x100351)))),x100352))
% 162.26/162.07 [10036]~P6(x100361,f256(f891(x100361,a877)),x100362)+P5(x100361,f331(f331(f7(x100361,f891(f890(x100361,x100361),a877),f891(x100361,a877)),f331(f331(f8(f891(x100361,f891(f891(f890(x100361,x100361),a877),a877)),f891(f891(f890(x100361,x100361),a877),f891(x100361,a877)),x100361),f7(x100361,f891(f890(x100361,x100361),a877),a877)),f331(f331(f8(f891(x100361,f890(x100361,x100361)),f891(x100361,f891(f891(f890(x100361,x100361),a877),a877)),x100361),f331(f8(f890(x100361,x100361),f891(f891(f890(x100361,x100361),a877),a877),x100361),f333(f890(x100361,x100361)))),f261(x100361,x100361)))),x100362))
% 162.26/162.07 [10067]P38(x100671,x100672)+~P57(x100671,f331(f331(f7(x100671,f891(f890(x100671,x100671),a877),f891(x100671,a877)),f331(f331(f8(f891(x100671,f891(f891(f890(x100671,x100671),a877),a877)),f891(f891(f890(x100671,x100671),a877),f891(x100671,a877)),x100671),f7(x100671,f891(f890(x100671,x100671),a877),a877)),f331(f331(f8(f891(x100671,f890(x100671,x100671)),f891(x100671,f891(f891(f890(x100671,x100671),a877),a877)),x100671),f331(f8(f890(x100671,x100671),f891(f891(f890(x100671,x100671),a877),a877),x100671),f333(f890(x100671,x100671)))),f261(x100671,x100671)))),x100672))
% 162.26/162.07 [10068]P6(x100681,f256(f891(x100681,a877)),x100682)+~P5(x100681,f331(f331(f7(x100681,f891(f890(x100681,x100681),a877),f891(x100681,a877)),f331(f331(f8(f891(x100681,f891(f891(f890(x100681,x100681),a877),a877)),f891(f891(f890(x100681,x100681),a877),f891(x100681,a877)),x100681),f7(x100681,f891(f890(x100681,x100681),a877),a877)),f331(f331(f8(f891(x100681,f890(x100681,x100681)),f891(x100681,f891(f891(f890(x100681,x100681),a877),a877)),x100681),f331(f8(f890(x100681,x100681),f891(f891(f890(x100681,x100681),a877),a877),x100681),f333(f890(x100681,x100681)))),f261(x100681,x100681)))),x100682))
% 162.26/162.07 [7249]E(f331(f331(f81(a883),f331(f110(a883),f331(f331(f22(a1),x72491),a103))),x72492),f331(a118,f331(f331(f81(a883),f331(f110(a883),x72491)),x72492)))+P24(f331(a202,f331(f110(a1),x72491)))
% 162.26/162.07 [7741]~P94(x77411)+E(f331(f331(f81(x77411),f331(f331(f81(x77411),f79(x77411)),f331(f110(x77411),x77412))),f331(f110(x77411),x77412)),f331(f110(x77411),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x77412)),x77412)))
% 162.26/162.07 [9089]~P24(f331(f331(f248(a1),x90891),x90892))+P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x90891)),x90891)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x90892)),x90892)))
% 162.26/162.07 [9091]~P24(f331(f331(f247(a1),x90911),x90912))+P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x90911)),x90911)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x90912)),x90912)))
% 162.26/162.07 [9092]~P24(f331(f331(f92(a1),x90921),x90922))+P24(f331(f331(f92(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x90921)),x90921)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x90922)),x90922)))
% 162.26/162.07 [9332]~P24(f331(f62(x93321),x93322))+P24(f331(f62(f891(x93321,a877)),f331(f253(f891(x93321,a877)),f331(f331(f7(f891(x93321,a877),f891(x93321,a877),a877),f247(f891(x93321,a877))),x93322))))
% 162.26/162.07 [9357]P24(f331(f331(f248(a1),x93571),x93572))+~P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x93571)),x93571)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x93572)),x93572)))
% 162.26/162.07 [9359]P24(f331(f331(f247(a1),x93591),x93592))+~P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x93591)),x93591)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x93592)),x93592)))
% 162.26/162.07 [9360]P24(f331(f331(f92(a1),x93601),x93602))+~P24(f331(f331(f92(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x93601)),x93601)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x93602)),x93602)))
% 162.26/162.07 [9384]~E(f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),x93841),f196(f891(f890(a883,a883),a877)))),f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),x93842),f196(f891(f890(a883,a883),a877)))))+P24(f331(f331(f333(f890(f890(a883,a883),f890(a883,a883))),f331(f331(f261(f890(a883,a883),f890(a883,a883)),x93841),x93842)),a115))
% 162.26/162.07 [9459]E(f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),x94591),f196(f891(f890(a883,a883),a877)))),f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),x94592),f196(f891(f890(a883,a883),a877)))))+~P24(f331(f331(f333(f890(f890(a883,a883),f890(a883,a883))),f331(f331(f261(f890(a883,a883),f890(a883,a883)),x94591),x94592)),a115))
% 162.26/162.07 [9508]P24(f331(f331(f247(a1),f2(a1)),f800(x95081,x95082)))+E(f331(f253(a1),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f247(a1),f2(a1)))),x95081)),f331(f253(a1),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f247(a1),f2(a1)))),x95082)))
% 162.26/162.07 [9624]~P24(f331(f331(f247(a1),x96241),x96242))+P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x96241)),x96241)),a103)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x96242)),x96242)))
% 162.26/162.07 [9626]~P24(f331(f331(f247(a1),x96261),x96262))+P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x96261)),x96261)),a103)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x96262)),x96262)))
% 162.26/162.07 [9782]P24(f331(f331(f247(a1),x97821),x97822))+~P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x97821)),x97821)),a103)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x97822)),x97822)))
% 162.26/162.07 [9784]P24(f331(f331(f247(a1),x97841),x97842))+~P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x97841)),x97841)),a103)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x97842)),x97842)))
% 162.26/162.07 [10018]~P27(x100181)+E(f41(x100181,f331(f253(x100181),f331(f331(f8(f891(x100181,a877),a877,x100181),f88(x100181)),f331(f331(f8(f891(x100181,a877),f891(x100181,a877),x100181),f331(f18(x100181,a877,a877),f331(f331(f8(a877,f891(a877,a877),x100181),a334),f331(f331(f7(x100181,f891(x100181,a877),a877),f333(x100181)),x100182)))),f331(f7(x100181,x100181,a877),f247(x100181)))))),f40(x100181,x100182))
% 162.26/162.07 [10039]P24(f331(f331(f333(a883),f2(a883)),x100391))+E(f331(f38(a883),f331(f253(a883),f331(f331(f18(a883,a877,a877),f331(f331(f8(a877,f891(a877,a877),a883),a329),f331(f331(f7(a883,f891(a883,a877),a877),f331(f331(f8(a883,f891(f891(a883,a877),a877),a883),f333(a883)),a118)),x100391))),f331(f331(f7(a883,a883,a877),f248(a883)),x100392)))),f331(f38(a883),f331(f253(a883),f331(f331(f18(a883,a877,a877),f331(f331(f8(a877,f891(a877,a877),a883),a329),f331(f331(f7(a883,f891(a883,a877),a877),f333(a883)),x100391))),f331(f331(f7(a883,a883,a877),f248(a883)),f331(a118,x100392))))))
% 162.26/162.07 [7808]~P94(x78081)+E(f331(f331(f82(x78081),x78082),f331(f110(x78081),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),x78082)
% 162.26/162.07 [8038]~P94(x80381)+E(f331(f331(f81(x80381),f331(f110(x80381),x80382)),f79(x80381)),f331(f110(x80381),f331(f331(f81(a1),x80382),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))))
% 162.26/162.07 [8083]P24(f331(f331(f247(a1),f2(a1)),f331(f110(a1),x80832)))+E(f331(f331(f262(a1),x80831),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x80832)),x80832))),f79(a1))
% 162.26/162.07 [9098]E(x90981,x90982)+~E(f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x90981)),x90981)),a103),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x90982)),x90982)),a103))
% 162.26/162.07 [9370]~P24(f331(f331(f247(a1),f2(a1)),f331(f110(a1),x93702)))+E(f331(f331(f262(a1),x93701),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x93702)),x93702))),f331(f331(f89(a1,a1),f331(f331(f262(a1),x93701),f331(f110(a883),x93702))),f331(f331(f18(a1,a1,a1),f331(f331(f8(a1,f891(a1,a1),a1),f82(a1)),f331(f82(a1),x93701))),f5(a1))))
% 162.26/162.07 [9744]~P24(f331(f331(f247(a883),f820(x97442,x97441)),f331(x97441,f820(x97442,x97441))))+P24(f331(f62(a883),f331(f253(a883),f331(f331(f7(a883,a883,a877),f331(f331(f8(a883,f891(a883,a877),a883),f247(a883)),x97441)),x97442))))
% 162.26/162.07 [9895]~P24(f331(f331(f248(a883),f331(f110(a883),x98951)),f331(a118,x98952)))+P24(f331(f331(f89(a1,a877),f331(f110(a1),f331(f331(f81(a1),x98951),a103))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a334),f331(f331(f8(a877,a877,a1),a326),a202))),f331(f331(f7(a1,a883,a877),f331(f331(f8(a883,f891(a883,a877),a1),f248(a883)),a111)),x98952))))
% 162.26/162.07 [9896]~P24(f331(f331(f247(a883),f331(f110(a883),x98961)),f331(a118,x98962)))+P24(f331(f331(f89(a1,a877),f331(f110(a1),f331(f331(f81(a1),x98961),a103))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a334),f331(f331(f8(a877,a877,a1),a326),a202))),f331(f331(f7(a1,a883,a877),f331(f331(f8(a883,f891(a883,a877),a1),f247(a883)),a111)),x98962))))
% 162.26/162.07 [9932]P24(f331(f331(f248(a883),f331(f110(a883),x99321)),f331(a118,x99322)))+~P24(f331(f331(f89(a1,a877),f331(f110(a1),f331(f331(f81(a1),x99321),a103))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a334),f331(f331(f8(a877,a877,a1),a326),a202))),f331(f331(f7(a1,a883,a877),f331(f331(f8(a883,f891(a883,a877),a1),f248(a883)),a111)),x99322))))
% 162.26/162.07 [9933]P24(f331(f331(f247(a883),f331(f110(a883),x99331)),f331(a118,x99332)))+~P24(f331(f331(f89(a1,a877),f331(f110(a1),f331(f331(f81(a1),x99331),a103))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a334),f331(f331(f8(a877,a877,a1),a326),a202))),f331(f331(f7(a1,a883,a877),f331(f331(f8(a883,f891(a883,a877),a1),f247(a883)),a111)),x99332))))
% 162.26/162.07 [9962]~P24(f331(f331(f248(a883),f331(a118,x99622)),f331(f110(a883),x99621)))+P24(f331(f331(f89(a1,a877),f331(f110(a1),f331(f331(f81(a1),x99621),a103))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f331(f8(a877,a877,a1),a326),a202))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a334),f331(f331(f8(a877,a877,a1),a326),a202))),f331(f331(f8(a883,a877,a1),f331(f248(a883),x99622)),a111)))))
% 162.26/162.07 [9963]~P24(f331(f331(f247(a883),f331(a118,x99632)),f331(f110(a883),x99631)))+P24(f331(f331(f89(a1,a877),f331(f110(a1),f331(f331(f81(a1),x99631),a103))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f331(f8(a877,a877,a1),a326),a202))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a334),f331(f331(f8(a877,a877,a1),a326),a202))),f331(f331(f8(a883,a877,a1),f331(f247(a883),x99632)),a111)))))
% 162.26/162.07 [10006]P24(f331(f331(f248(a883),f331(a118,x100061)),f331(f110(a883),x100062)))+~P24(f331(f331(f89(a1,a877),f331(f110(a1),f331(f331(f81(a1),x100062),a103))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f331(f8(a877,a877,a1),a326),a202))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a334),f331(f331(f8(a877,a877,a1),a326),a202))),f331(f331(f8(a883,a877,a1),f331(f248(a883),x100061)),a111)))))
% 162.26/162.07 [10007]P24(f331(f331(f247(a883),f331(a118,x100071)),f331(f110(a883),x100072)))+~P24(f331(f331(f89(a1,a877),f331(f110(a1),f331(f331(f81(a1),x100072),a103))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f331(f8(a877,a877,a1),a326),a202))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a334),f331(f331(f8(a877,a877,a1),a326),a202))),f331(f331(f8(a883,a877,a1),f331(f247(a883),x100071)),a111)))))
% 162.26/162.07 [10084]~P24(f331(f331(f333(a883),f2(a883)),x100841))+E(f331(a118,f331(f38(a883),f331(f253(a883),f331(f331(f18(a883,a877,a877),f331(f331(f8(a877,f891(a877,a877),a883),a329),f331(f331(f7(a883,f891(a883,a877),a877),f331(f331(f8(a883,f891(f891(a883,a877),a877),a883),f333(a883)),a118)),x100841))),f331(f331(f7(a883,a883,a877),f248(a883)),x100842))))),f331(f38(a883),f331(f253(a883),f331(f331(f18(a883,a877,a877),f331(f331(f8(a877,f891(a877,a877),a883),a329),f331(f331(f7(a883,f891(a883,a877),a877),f333(a883)),x100841))),f331(f331(f7(a883,a883,a877),f248(a883)),f331(a118,x100842))))))
% 162.26/162.07 [8667]~P94(x86671)+E(f331(f331(f82(x86671),f331(f110(x86671),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),x86672),x86672)
% 162.26/162.07 [8707]~P94(x87071)+E(f331(f331(f81(x87071),f79(x87071)),f331(f110(x87071),x87072)),f331(f110(x87071),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)),x87072)))
% 162.26/162.07 [8745]~P94(x87451)+E(f331(f331(f22(x87451),f331(f110(x87451),x87452)),f79(x87451)),f331(f110(x87451),f331(f331(f81(a1),x87452),f331(f80(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)))))
% 162.26/162.07 [8828]~P94(x88281)+E(f331(f331(f82(x88281),f331(f331(f81(x88281),f79(x88281)),f79(x88281))),f331(f110(x88281),x88282)),f331(f110(x88281),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x88282)),x88282)),a103)))
% 162.26/162.07 [8858]~P24(f331(f331(f248(a883),f331(f110(a883),a84)),x88582))+E(f331(f331(f22(a883),x88581),f331(f331(f22(a883),x88582),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)))),f331(f331(f22(a883),f331(a118,x88581)),x88582))
% 162.26/162.07 [8885]~P94(x88851)+E(f331(f110(x88851),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x88852)),x88852)),a103)),f331(f331(f81(x88851),f331(f331(f81(x88851),f2(x88851)),f331(f110(x88851),x88852))),f331(f110(x88851),x88852)))
% 162.26/162.07 [9473]~P24(f331(f331(f248(a1),x94731),x94732))+P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x94731)),x94731)),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x94732)),x94732)),a103)))
% 162.26/162.07 [9475]~P24(f331(f331(f248(a1),x94751),x94752))+P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x94751)),x94751)),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x94752)),x94752)),a103)))
% 162.26/162.07 [9638]P24(f331(f331(f248(a1),x96381),x96382))+~P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x96381)),x96381)),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x96382)),x96382)),a103)))
% 162.26/162.07 [9640]P24(f331(f331(f248(a1),x96401),x96402))+~P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x96401)),x96401)),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x96402)),x96402)),a103)))
% 162.26/162.07 [9687]~P79(x96871)+E(f331(f331(f262(x96871),x96872),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)))),f331(f331(f82(x96871),f331(f331(f82(x96871),x96872),x96872)),x96872))
% 162.26/162.07 [9736]~P24(f331(f331(f248(a1),x97361),x97362))+P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x97361)),x97361)),a103)),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x97362)),x97362)),a103)))
% 162.26/162.07 [9738]~P24(f331(f331(f247(a1),x97381),x97382))+P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x97381)),x97381)),a103)),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x97382)),x97382)),a103)))
% 162.26/162.07 [9739]~P24(f331(f331(f92(a1),x97391),x97392))+P24(f331(f331(f92(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x97391)),x97391)),a103)),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x97392)),x97392)),a103)))
% 162.26/162.07 [9843]P24(f331(f331(f248(a1),x98431),x98432))+~P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x98431)),x98431)),a103)),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x98432)),x98432)),a103)))
% 162.26/162.07 [9845]P24(f331(f331(f247(a1),x98451),x98452))+~P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x98451)),x98451)),a103)),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x98452)),x98452)),a103)))
% 162.26/162.07 [9846]P24(f331(f331(f92(a1),x98461),x98462))+~P24(f331(f331(f92(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x98461)),x98461)),a103)),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x98462)),x98462)),a103)))
% 162.26/162.07 [9492]~P24(f331(f331(f247(a1),f2(a1)),f331(f110(a1),x94922)))+E(f331(f331(f39(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x94921)),x94921))),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x94922)),x94922)),a103))),f331(f331(f39(a1),f331(f110(a1),x94921)),f331(f110(a1),x94922)))
% 162.26/162.07 [9514]P24(f331(f331(f247(a1),f2(a1)),f331(f110(a1),x95142)))+E(f331(f331(f39(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x95141)),x95141))),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x95142)),x95142)),a103))),f331(f331(f39(a1),f331(f331(f81(a1),f331(f110(a1),x95141)),f79(a1))),f331(f110(a1),x95142)))
% 162.26/162.07 [9996]~E(f331(a118,x99962),f331(f110(a883),x99961))+P24(f331(f331(f89(a1,a877),f331(f110(a1),f331(f331(f81(a1),x99961),a103))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f331(f8(a877,a877,a1),a326),a202))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a334),f331(f331(f8(a877,a877,a1),a326),a202))),f331(f331(f7(a1,a883,a877),f331(f331(f8(a883,f891(a883,a877),a1),a328),a111)),x99962)))))
% 162.26/162.07 [9997]~E(f331(f110(a883),x99971),f331(a118,x99972))+P24(f331(f331(f89(a1,a877),f331(f110(a1),f331(f331(f81(a1),x99971),a103))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f331(f8(a877,a877,a1),a326),a202))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a334),f331(f331(f8(a877,a877,a1),a326),a202))),f331(f331(f7(a1,a883,a877),f331(f331(f8(a883,f891(a883,a877),a1),a328),a111)),x99972)))))
% 162.26/162.07 [10042]E(f331(a118,x100421),f331(f110(a883),x100422))+~P24(f331(f331(f89(a1,a877),f331(f110(a1),f331(f331(f81(a1),x100422),a103))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f331(f8(a877,a877,a1),a326),a202))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a334),f331(f331(f8(a877,a877,a1),a326),a202))),f331(f331(f7(a1,a883,a877),f331(f331(f8(a883,f891(a883,a877),a1),a328),a111)),x100421)))))
% 162.26/162.07 [10043]E(f331(f110(a883),x100431),f331(a118,x100432))+~P24(f331(f331(f89(a1,a877),f331(f110(a1),f331(f331(f81(a1),x100431),a103))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f331(f8(a877,a877,a1),a326),a202))),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a334),f331(f331(f8(a877,a877,a1),a326),a202))),f331(f331(f7(a1,a883,a877),f331(f331(f8(a883,f891(a883,a877),a1),a328),a111)),x100432)))))
% 162.26/162.07 [10141]~P24(f331(f331(f247(a1),f2(a1)),f331(f110(a1),x101412)))+E(f45(a1,f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x101411)),x101411)),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x101412)),x101412)),a103))),f331(f331(f81(a1),f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f45(a1,f331(f110(a1),x101411),f331(f110(a1),x101412)))),f79(a1)))
% 162.26/162.07 [10143]P24(f331(f331(f247(a1),f2(a1)),f331(f110(a1),x101432)))+E(f45(a1,f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x101431)),x101431)),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x101432)),x101432)),a103))),f331(f331(f22(a1),f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f45(a1,f331(f331(f81(a1),f331(f110(a1),x101431)),f79(a1)),f331(f110(a1),x101432)))),f79(a1)))
% 162.26/162.07 [9942]~P118(x99421)+E(f331(f331(f82(x99421),x99422),x99422),f331(f331(f262(x99421),x99422),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))
% 162.26/162.07 [9943]~P79(x99431)+E(f331(f331(f262(x99431),x99432),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f331(f331(f82(x99431),x99432),x99432))
% 162.26/162.07 [9944]~P94(x99441)+E(f331(f331(f82(x99441),x99442),f331(f110(x99441),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f331(f331(f81(x99441),x99442),x99442))
% 162.26/162.07 [10022]~P138(x100221)+E(f331(f331(f262(x100221),f331(f80(x100221),x100222)),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f331(f331(f262(x100221),x100222),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))
% 162.26/162.07 [10023]~P111(x100231)+E(f331(f331(f262(x100231),f331(f76(x100231),x100232)),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f331(f331(f262(x100231),x100232),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))
% 162.26/162.07 [10021]~P94(x100211)+E(f331(f331(f82(x100211),f331(f110(x100211),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x100212),f331(f331(f81(x100211),x100212),x100212))
% 162.26/162.07 [10060]~P111(x100601)+E(f331(f76(x100601),f331(f331(f262(x100601),x100602),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f331(f331(f262(x100601),x100602),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))
% 162.26/162.07 [10075]~P111(x100751)+P24(f331(f331(f247(x100751),f2(x100751)),f331(f331(f262(x100751),x100752),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))))
% 162.26/162.07 [10073]~P94(x100731)+E(f331(f331(f262(x100731),f331(f110(x100731),a103)),f331(f331(f82(a883),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x100732)),f79(x100731))
% 162.26/162.07 [10074]~P138(x100741)+E(f331(f331(f262(x100741),f331(f80(x100741),f79(x100741))),f331(f331(f82(a883),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x100742)),f79(x100741))
% 162.26/162.07 [10168]~P24(f331(f331(f247(a1),f2(a1)),x101682))+E(f45(a1,f331(f331(f81(a1),f79(a1)),f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x101681)),f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x101682)),f331(f331(f81(a1),f79(a1)),f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f45(a1,x101681,x101682))))
% 162.26/162.07 [10179]~P24(f331(f331(f247(a1),f2(a1)),x101792))+E(f331(f331(f39(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x101791))),f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x101792)),f331(f331(f39(a1),x101791),x101792))
% 162.26/162.07 [10180]~P24(f331(f331(f247(a1),x101802),f2(a1)))+E(f331(f331(f39(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x101801))),f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x101802)),f331(f331(f39(a1),f331(f331(f81(a1),x101801),f79(a1))),x101802))
% 162.26/162.07 [10181]~P24(f331(f331(f247(a1),x101812),f2(a1)))+E(f45(a1,f331(f331(f81(a1),f79(a1)),f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x101811)),f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x101812)),f331(f331(f22(a1),f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f45(a1,f331(f331(f81(a1),x101811),f79(a1)),x101812))),f79(a1)))
% 162.26/162.07 [10124]~P94(x101241)+E(f331(f331(f262(x101241),f331(f110(x101241),a103)),f331(a118,f331(f331(f82(a883),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x101242))),f331(f110(x101241),a103))
% 162.26/162.07 [10126]~P138(x101261)+E(f331(f331(f262(x101261),f331(f80(x101261),f79(x101261))),f331(a118,f331(f331(f82(a883),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x101262))),f331(f80(x101261),f79(x101261)))
% 162.26/162.07 [5128]~P20(x51281,x51282,x51283)+P23(x51281,x51282,x51283)
% 162.26/162.07 [8020]~E(x80202,x80203)+P35(x80201,x80201,a328,x80202,x80203)
% 162.26/162.07 [8574]E(x85741,x85742)+~P35(x85743,x85743,a328,x85741,x85742)
% 162.26/162.07 [5133]~P38(x51331,x51333)+P38(x51331,f325(x51331,x51332,x51333))
% 162.26/162.07 [5308]P30(x53081,x53082,x53083)+~P30(x53081,f331(a118,x53082),x53083)
% 162.26/162.07 [5395]~P6(x53951,x53952,x53953)+P6(f884(x53951),f164(x53951,x53952),f161(x53951,x53953))
% 162.26/162.07 [5396]~P48(x53961,x53962,x53963)+P48(f884(x53961),f164(x53961,x53962),f161(x53961,x53963))
% 162.26/162.07 [5508]P52(x55081,x55082,x55083)+~E(f725(x55083,x55082,x55081),f726(x55083,x55082,x55081))
% 162.26/162.07 [5509]P53(x55091,x55092,x55093)+~E(f762(x55093,x55092,x55091),f763(x55093,x55092,x55091))
% 162.26/162.07 [6440]P23(x64401,x64402,x64403)+~P30(x64401,f591(x64403,x64402,x64401),f599(x64403,x64402,x64401))
% 162.26/162.07 [4685]~E(x46851,f199(x46852))+~E(x46851,f331(f239(x46852),x46853))
% 162.26/162.07 [4734]~E(f331(f172(x47342),x47341),x47343)+E(x47341,f331(f172(x47342),x47343))
% 162.26/162.07 [4735]~E(x47352,f331(f172(x47351),x47353))+E(f331(f172(x47351),x47352),x47353)
% 162.26/162.07 [4782]E(x47821,x47822)+~E(f331(f239(x47823),x47821),f331(f239(x47823),x47822))
% 162.26/162.07 [4783]E(x47831,x47832)+~E(f331(f172(x47833),x47831),f331(f172(x47833),x47832))
% 162.26/162.07 [4987]~P5(x49873,x49871)+P24(f331(f331(x49871,x49872),x49872))
% 162.26/162.07 [4988]~P50(x49883,x49881)+P24(f331(f331(x49881,x49882),x49882))
% 162.26/162.07 [4990]~P57(x49901,x49902)+P24(f331(f319(x49901,x49902),x49903))
% 162.26/162.07 [5052]~P38(x50521,x50522)+P38(f884(x50521),f331(f146(x50521,x50522),x50523))
% 162.26/162.07 [5057]~P24(f331(x50572,x50573))+~E(f331(f253(x50571),x50572),f196(f891(x50571,a877)))
% 162.26/162.07 [5058]~P24(f331(x50582,x50583))+~E(f196(f891(x50581,a877)),f331(f253(x50581),x50582))
% 162.26/162.07 [5089]~P24(f331(x50891,x50893))+P24(f331(x50891,f91(x50892,x50891)))
% 162.26/162.07 [5213]~E(x52132,x52133)+P24(f331(f331(f333(x52131),x52132),f331(a328,x52133)))
% 162.26/162.07 [5225]P24(f331(x52251,x52252))+~P24(f331(x52251,f564(x52251,x52253)))
% 162.26/162.07 [5272]E(f331(f172(x52721),x52722),f331(f331(f154(x52721),x52723),f119(x52721)))+~E(x52722,f331(f331(f154(x52721),x52723),f119(x52721)))
% 162.26/162.07 [5273]~E(x52733,f331(f331(f154(x52731),x52732),f119(x52731)))+E(f331(f331(f154(x52731),x52732),f119(x52731)),f331(f172(x52731),x52733))
% 162.26/162.07 [5301]~E(x53013,f331(f16(f887(x53012),x53011),f199(x53012)))+E(f186(x53011,x53012,x53013),f196(f891(x53011,a877)))
% 162.26/162.07 [5322]~P34(x53221,x53222,x53223)+P34(x53221,x53222,f331(f172(x53221),x53223))
% 162.26/162.07 [5323]~P32(x53231,x53232,x53233)+P32(x53231,x53232,f331(f172(x53231),x53233))
% 162.26/162.07 [5326]E(f331(f38(x53261),f722(x53262,x53263,x53261)),x53262)+~E(f331(f38(x53261),x53263),f331(a118,x53262))
% 162.26/162.07 [5332]~P38(x53321,x53323)+P24(f331(f331(f333(x53321),x53322),f320(x53321,x53323)))
% 162.26/162.07 [5335]~E(f331(f172(x53352),x53351),f331(f331(f154(x53352),x53353),f119(x53352)))+E(x53351,f331(f331(f154(x53352),x53353),f119(x53352)))
% 162.26/162.07 [5336]~E(f331(f331(f154(x53362),x53363),f119(x53362)),f331(f172(x53362),x53361))+E(x53361,f331(f331(f154(x53362),x53363),f119(x53362)))
% 162.26/162.07 [5351]E(x53511,f331(f16(f887(x53512),x53513),f199(x53512)))+~E(f186(x53513,x53512,x53511),f196(f891(x53513,a877)))
% 162.26/162.07 [5358]E(f86(f890(a883,a883),f48(x53581,x53582)),x53583)+~P24(f331(f48(x53581,x53582),x53583))
% 162.26/162.07 [5366]~E(x53663,f331(f239(x53661),x53662))+P24(f331(f331(f333(x53661),x53662),f240(x53661,x53663)))
% 162.26/162.07 [5399]P34(x53991,x53992,x53993)+~P34(x53991,x53992,f331(f172(x53991),x53993))
% 162.26/162.07 [5400]P32(x54001,x54002,x54003)+~P32(x54001,x54002,f331(f172(x54001),x54003))
% 162.26/162.07 [5462]~E(x54622,f119(x54621))+P24(f331(f331(f333(f884(x54621)),x54622),f164(x54621,x54623)))
% 162.26/162.07 [5469]~P48(x54691,x54692,x54693)+P48(x54691,x54692,f331(f286(x54691,x54691),x54693))
% 162.26/162.07 [5470]~P53(x54701,x54702,x54703)+P53(x54701,x54702,f331(f286(x54701,x54701),x54703))
% 162.26/162.07 [5489]~P58(x54891)+E(f45(x54891,f45(x54891,x54892,x54893),x54893),f45(x54891,x54892,x54893))
% 162.26/162.07 [5583]E(x55831,x55832)+~P24(f331(f331(f333(x55833),x55831),f331(a328,x55832)))
% 162.26/162.07 [5630]~P143(x56301)+E(f198(x56301,x56302,f2(a883),x56303),x56303)
% 162.26/162.07 [5650]P48(x56501,x56502,x56503)+~P48(x56501,x56502,f331(f286(x56501,x56501),x56503))
% 162.26/162.07 [5651]P53(x56511,x56512,x56513)+~P53(x56511,x56512,f331(f286(x56511,x56511),x56513))
% 162.26/162.07 [5655]~P107(x56552)+E(f153(x56551,x56552,x56553,f119(x56551)),f119(x56551))
% 162.26/162.07 [5668]E(f173(x56681,x56682,f155(x56681,x56683)),f155(x56681,f173(x56681,x56682,x56683)))+~P24(f331(f140(x56681),x56683))
% 162.26/162.07 [5674]E(x56741,f331(f239(x56742),x56743))+~P24(f331(f331(f333(x56742),x56743),f240(x56742,x56741)))
% 162.26/162.07 [5759]~P24(f331(a25,x57593))+P24(f331(a25,f30(x57591,x57592,x57593)))
% 162.26/162.07 [5770]E(f331(f139(x57701,x57702),x57703),f119(x57701))+P24(f331(x57702,f639(x57703,x57702,x57701)))
% 162.26/162.07 [5913]~P24(f331(f140(x59131),x59133))+P24(f331(f140(x59131),f173(x59131,x59132,x59133)))
% 162.26/162.07 [5914]~P24(f331(f140(x59141),x59142))+P24(f331(f140(x59141),f177(x59141,x59142,x59143)))
% 162.26/162.07 [5915]~P24(f331(f140(x59151),x59153))+P24(f331(f140(x59151),f179(x59151,x59152,x59153)))
% 162.26/162.07 [5916]~P24(f331(f140(x59161),x59163))+P24(f331(f140(x59161),f143(x59161,x59162,x59163)))
% 162.26/162.07 [5917]~P146(x59171,x59173,x59172)+P24(f331(x59171,f45(a1,x59172,x59173)))
% 162.26/162.07 [5935]~P34(x59353,x59351,x59352)+P24(f331(x59351,f728(x59352,x59351,x59353)))
% 162.26/162.07 [5936]~P36(x59363,x59361,x59362)+P24(f331(x59361,f811(x59362,x59361,x59363)))
% 162.26/162.07 [5958]E(f331(f139(x59581,x59582),x59583),f179(x59581,x59582,x59583))+P24(f331(x59582,f686(x59583,x59582,x59581)))
% 162.26/162.07 [6000]~P24(f331(f140(x60001),x60003))+P24(f331(f140(f884(x60001)),f55(x60001,x60002,x60003)))
% 162.26/162.07 [6021]P24(f331(a25,f29(x60211,x60212,x60213)))+~P24(f331(a25,f331(a28,x60212)))
% 162.26/162.07 [6033]~P108(x60331)+E(f331(f331(f108(f891(x60331,a877)),f331(f300(x60331),x60332)),f305(x60331,x60332,x60333)),f196(f891(x60331,a877)))
% 162.26/162.07 [6034]~P108(x60341)+E(f331(f331(f108(f891(x60341,a877)),f331(f300(x60341),x60342)),f304(x60341,x60342,x60343)),f196(f891(x60341,a877)))
% 162.26/162.07 [6035]~P108(x60351)+E(f331(f331(f108(f891(x60351,a877)),f331(f254(x60351),x60352)),f302(x60351,x60352,x60353)),f196(f891(x60351,a877)))
% 162.26/162.07 [6184]P24(f331(a25,x61841))+~P24(f331(a25,f30(x61842,x61843,x61841)))
% 162.26/162.07 [6186]P24(f331(a25,x61861))+~P24(f331(a25,f31(x61862,x61863,x61861)))
% 162.26/162.07 [6188]P24(f331(a25,x61881))+~P24(f331(a25,f31(x61882,x61881,x61883)))
% 162.26/162.07 [6263]E(f331(f139(x62631,x62632),x62633),x62633)+~P24(f331(x62632,f640(x62633,x62632,x62631)))
% 162.26/162.07 [6265]E(f331(f331(f309(x62651),f812(x62652,x62653,x62651)),f722(x62652,x62653,x62651)),x62653)+~E(f331(f38(x62651),x62653),f331(a118,x62652))
% 162.26/162.07 [6281]P146(x62811,x62812,x62813)+~P24(f331(x62811,f45(a1,x62813,x62812)))
% 162.26/162.07 [6327]P32(x63271,x63272,x63273)+~P24(f331(x63272,f796(x63272,x63273,x63271)))
% 162.26/162.07 [6328]P32(x63281,x63282,x63283)+~P24(f331(x63282,f809(x63283,x63282,x63281)))
% 162.26/162.07 [6329]P32(x63291,x63292,x63293)+~P24(f331(x63292,f810(x63293,x63292,x63291)))
% 162.26/162.07 [6331]E(f179(x63311,x63312,x63313),x63313)+~P24(f331(x63312,f670(x63313,x63312,x63311)))
% 162.26/162.07 [6367]~P24(f331(a25,f29(x63672,x63671,x63673)))+P24(f331(a25,f331(a28,x63671)))
% 162.26/162.07 [6409]~P24(f331(x64092,f586(x64093,x64092,x64091)))+P24(f331(f265(x64091,x64092),x64093))
% 162.26/162.07 [6410]~P24(f331(x64102,f688(x64103,x64102,x64101)))+P24(f331(f163(x64101,x64102),x64103))
% 162.26/162.07 [6653]~P24(f331(f319(x66531,x66532),f382(x66533,x66532,x66531)))+P24(f331(f319(x66531,x66532),x66533))
% 162.26/162.07 [6654]~P24(f331(f319(x66541,x66542),f386(x66543,x66542,x66541)))+P24(f331(f319(x66541,x66542),x66543))
% 162.26/162.07 [7250]~P58(x72501)+E(f331(f331(f81(x72501),f331(f331(f82(x72501),x72502),f331(f331(f39(x72501),x72503),x72502))),f45(x72501,x72503,x72502)),x72503)
% 162.26/162.07 [7702]E(f331(f331(f261(x77021,x77021),f455(x77022,x77023,x77021)),f455(x77022,x77023,x77021)),x77023)+~P24(f331(f331(f333(f890(x77021,x77021)),x77023),f258(x77021,x77022)))
% 162.26/162.07 [7821]~P24(f331(f331(f333(x78211),f521(x78213,x78212,x78211)),f320(x78211,x78213)))+P24(f331(f331(f333(x78211),x78212),f320(x78211,x78213)))
% 162.26/162.07 [7822]~P24(f331(f331(f333(x78221),f730(x78223,x78222,x78221)),f320(x78221,x78223)))+P24(f331(f331(f333(x78221),x78222),f320(x78221,x78223)))
% 162.26/162.07 [7823]~P24(f331(f331(f333(x78231),f739(x78233,x78232,x78231)),f320(x78231,x78233)))+P24(f331(f331(f333(x78231),x78232),f320(x78231,x78233)))
% 162.26/162.07 [8001]~P58(x80011)+E(f331(f331(f81(x80011),f331(f331(f82(x80011),f331(f331(f39(x80011),x80012),x80013)),x80013)),f45(x80011,x80012,x80013)),x80012)
% 162.26/162.07 [8052]~E(f331(f38(x80521),x80522),f331(a118,x80523))+~P24(f331(f331(f333(x80521),f812(x80523,x80522,x80521)),f722(x80523,x80522,x80521)))
% 162.26/162.07 [8663]P24(f331(f331(f247(f891(f890(x86631,x86631),a877)),f307(x86631,x86632)),f307(x86631,x86633)))+~P24(f331(f331(f247(f891(f890(x86631,x86631),a877)),x86632),f307(x86631,x86633)))
% 162.26/162.07 [8940]E(x89401,f119(x89402))+~P24(f331(f331(f333(f890(f884(x89402),f884(x89402))),f331(f331(f261(f884(x89402),f884(x89402)),x89401),f119(x89402))),f161(x89402,x89403)))
% 162.26/162.07 [8965]E(x89651,f119(x89652))+~P24(f331(f331(f333(f890(f884(x89652),f884(x89652))),f331(f331(f261(f884(x89652),f884(x89652)),f119(x89652)),x89651)),f161(x89652,x89653)))
% 162.26/162.07 [9075]E(f331(f331(f154(x90751),f656(x90752,x90753,x90751)),f657(x90752,x90753,x90751)),x90753)+~P24(f331(f331(f333(f890(f884(x90751),f884(x90751))),f331(f331(f261(f884(x90751),f884(x90751)),f119(x90751)),x90753)),f150(x90751,x90752)))
% 162.26/162.07 [9325]~P124(x93251)+~P24(f331(f331(f248(x93251),f331(f331(f81(x93251),f331(f331(f82(x93251),x93252),x93252)),f331(f331(f82(x93251),x93253),x93253))),f2(x93251)))
% 162.26/162.07 [9379]P24(f331(f62(x93791),x93792))+~P24(f331(f331(f333(f890(f891(x93791,a877),f891(x93791,a877))),f331(f331(f261(f891(x93791,a877),f891(x93791,a877)),x93793),x93792)),f306(x93791)))
% 162.26/162.07 [9679]~P46(x96791,x96792,x96793)+P24(f331(f331(f248(a1),f331(f331(f74(f890(a1,a1),a1,x96791,f260(a1,a1)),f224(x96791)),f235(x96791,x96792,f232(x96791,x96793)))),f2(a1)))
% 162.26/162.07 [9680]~P47(x96801,x96802,x96803)+P24(f331(f331(f247(a1),f331(f331(f74(f890(a1,a1),a1,x96801,f260(a1,a1)),f224(x96801)),f235(x96801,x96802,f232(x96801,x96803)))),f2(a1)))
% 162.26/162.07 [9819]P46(x98191,x98192,x98193)+~P24(f331(f331(f248(a1),f331(f331(f74(f890(a1,a1),a1,x98191,f260(a1,a1)),f224(x98191)),f235(x98191,x98192,f232(x98191,x98193)))),f2(a1)))
% 162.26/162.07 [9820]P47(x98201,x98202,x98203)+~P24(f331(f331(f247(a1),f331(f331(f74(f890(a1,a1),a1,x98201,f260(a1,a1)),f224(x98201)),f235(x98201,x98202,f232(x98201,x98203)))),f2(a1)))
% 162.26/162.07 [10217]~P111(x102171)+~P24(f331(f331(f248(x102171),f331(f331(f81(x102171),f331(f331(f262(x102171),x102172),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f331(f331(f262(x102171),x102173),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))),f2(x102171)))
% 162.26/162.07 [4765]~E(x47653,f119(x47651))+E(f331(f331(f137(x47651),x47652),x47653),x47652)
% 162.26/162.07 [4766]~E(x47662,f119(x47661))+E(f331(f331(f137(x47661),x47662),x47663),x47663)
% 162.26/162.07 [4773]~E(x47732,f2(a883))+E(f331(f331(f176(x47731),x47732),x47733),f119(x47731))
% 162.26/162.07 [4777]~E(x47773,f119(x47771))+E(f331(f331(f176(x47771),x47772),x47773),f119(x47771))
% 162.26/162.07 [4817]~E(x48171,x48173)+E(x48171,f331(f331(f137(x48172),f119(x48172)),x48173))
% 162.26/162.07 [4903]~P25(x49032)+E(f331(f196(f891(x49031,x49032)),x49033),f196(x49032))
% 162.26/162.07 [4904]~P116(x49042)+E(f331(f256(f891(x49041,x49042)),x49043),f256(x49042))
% 162.26/162.07 [4924]E(x49241,f119(x49242))+~E(f331(f331(f137(x49242),x49243),x49241),x49243)
% 162.26/162.07 [4925]E(x49251,f119(x49252))+~E(f331(f331(f137(x49252),x49251),x49253),x49253)
% 162.26/162.07 [4933]E(x49331,f119(x49332))+~E(f331(f331(f137(x49332),x49333),x49331),f119(x49332))
% 162.26/162.07 [4934]E(x49341,f119(x49342))+~E(f331(f331(f137(x49342),x49341),x49343),f119(x49342))
% 162.26/162.07 [4957]~E(x49572,f2(a883))+E(f331(f331(f82(a883),x49571),x49572),f331(f331(f82(a883),x49573),x49572))
% 162.26/162.07 [4959]~E(x49591,f2(a883))+E(f331(f331(f82(a883),x49591),x49592),f331(f331(f82(a883),x49591),x49593))
% 162.26/162.07 [5012]~P118(x50121)+E(f331(f331(f81(x50121),x50122),x50123),f331(f331(f81(x50121),x50123),x50122))
% 162.26/162.07 [5013]~P118(x50131)+E(f331(f331(f82(x50131),x50132),x50133),f331(f331(f82(x50131),x50133),x50132))
% 162.26/162.07 [5014]~P96(x50141)+E(f331(f331(f107(x50141),x50142),x50143),f331(f331(f107(x50141),x50143),x50142))
% 162.26/162.07 [5016]~P101(x50161)+E(f331(f331(f107(x50161),x50162),x50163),f331(f331(f107(x50161),x50163),x50162))
% 162.26/162.07 [5018]~P107(x50181)+E(f331(f331(f251(x50181),x50182),x50183),f331(f331(f251(x50181),x50183),x50182))
% 162.26/162.07 [5020]~P107(x50201)+E(f331(f331(f246(x50201),x50202),x50203),f331(f331(f246(x50201),x50203),x50202))
% 162.26/162.07 [5021]~P96(x50211)+E(f331(f331(f108(x50211),x50212),x50213),f331(f331(f108(x50211),x50213),x50212))
% 162.26/162.07 [5023]~P102(x50231)+E(f331(f331(f108(x50231),x50232),x50233),f331(f331(f108(x50231),x50233),x50232))
% 162.26/162.07 [5084]E(f45(a883,x50841,x50842),f2(a883))+~E(x50841,f331(f331(f82(a883),x50842),x50843))
% 162.26/162.07 [5085]E(f45(a1,x50851,x50852),f2(a1))+~E(x50851,f331(f331(f82(a1),x50852),x50853))
% 162.26/162.07 [5145]E(x51451,x51452)+~E(f331(f331(f81(a883),x51453),x51451),f331(f331(f81(a883),x51453),x51452))
% 162.26/162.07 [5146]E(x51461,x51462)+~E(f331(f331(f81(a883),x51461),x51463),f331(f331(f81(a883),x51462),x51463))
% 162.26/162.07 [5155]~P66(x51551)+E(f331(f331(f81(x51551),x51552),f331(f80(x51551),x51553)),f331(f331(f22(x51551),x51552),x51553))
% 162.26/162.07 [5156]~P70(x51561)+E(f331(f331(f81(x51561),x51562),f331(f80(x51561),x51563)),f331(f331(f22(x51561),x51562),x51563))
% 162.26/162.07 [5157]~P114(x51571)+E(f331(f331(f81(x51571),x51572),f331(f80(x51571),x51573)),f331(f331(f22(x51571),x51572),x51573))
% 162.26/162.07 [5158]~P85(x51581)+E(f331(f331(f108(x51581),x51582),f331(f80(x51581),x51583)),f331(f331(f22(x51581),x51582),x51583))
% 162.26/162.07 [5159]~P66(x51591)+E(f331(f331(f22(x51591),x51592),f331(f80(x51591),x51593)),f331(f331(f81(x51591),x51592),x51593))
% 162.26/162.07 [5206]~P24(f331(x52063,x52062))+P24(f331(f331(f333(x52061),x52062),x52063))
% 162.26/162.07 [5208]~P73(x52082)+E(f331(f331(f9(x52081,x52082),x52083),f196(f891(x52081,a877))),f79(x52082))
% 162.26/162.07 [5210]~P74(x52102)+E(f331(f331(f6(x52101,x52102),x52103),f196(f891(x52101,a877))),f2(x52102))
% 162.26/162.07 [5260]~E(x52602,f331(f331(f81(a883),x52601),x52603))+P24(f331(f331(f247(a883),x52601),x52602))
% 162.26/162.07 [5263]~E(x52632,f196(f891(x52631,a877)))+E(f331(f331(f61(x52631),x52632),x52633),f196(f891(f891(x52631,a877),a877)))
% 162.26/162.07 [5264]~E(x52642,f196(f891(x52641,a877)))+E(f196(f891(f891(x52641,a877),a877)),f331(f331(f61(x52641),x52642),x52643))
% 162.26/162.07 [5340]~E(f331(f257(x53402,x53403),x53401),f196(f891(x53403,a877)))+E(x53401,f196(f891(f890(x53402,x53403),a877)))
% 162.26/162.07 [5341]~E(f331(f259(x53412,x53413),x53411),f196(f891(x53412,a877)))+E(x53411,f196(f891(f890(x53412,x53413),a877)))
% 162.26/162.07 [5372]E(f331(f257(x53721,x53722),x53723),f196(f891(x53722,a877)))+~E(x53723,f196(f891(f890(x53721,x53722),a877)))
% 162.26/162.07 [5373]E(f331(f259(x53731,x53732),x53733),f196(f891(x53731,a877)))+~E(x53733,f196(f891(f890(x53731,x53732),a877)))
% 162.26/162.07 [5377]E(f281(x53771,x53772,x53773),f331(f331(f22(a105),x53772),x53773))+P24(f331(f331(f248(a105),x53772),x53773))
% 162.26/162.07 [5393]P24(f331(x53931,x53932))+~P24(f331(f331(f333(x53933),x53932),x53931))
% 162.26/162.07 [5432]E(x54321,x54322)+~E(f331(f80(f891(x54323,a877)),x54321),f331(f80(f891(x54323,a877)),x54322))
% 162.26/162.07 [5437]E(f313(x54371,x54372,x54373),f199(f884(a327)))+~P24(f331(f331(f248(a1),x54372),x54373))
% 162.26/162.07 [5442]~E(x54421,f196(f891(x54422,a877)))+~P24(f331(f331(f333(x54422),x54423),x54421))
% 162.26/162.07 [5471]~E(x54712,f331(f331(f81(a1),x54711),f331(f106(a1),x54713)))+P24(f331(f331(f247(a1),x54711),x54712))
% 162.26/162.07 [5487]E(f331(f331(f309(x54871),x54872),x54873),x54873)+~P24(f331(f331(f333(x54871),x54872),x54873))
% 162.26/162.07 [5498]E(x54981,f196(f891(x54982,a877)))+~E(f331(f331(f61(x54982),x54981),x54983),f196(f891(f891(x54982,a877),a877)))
% 162.26/162.07 [5499]E(x54991,f196(f891(x54992,a877)))+~E(f196(f891(f891(x54992,a877),a877)),f331(f331(f61(x54992),x54991),x54993))
% 162.26/162.07 [5505]~P125(x55051)+E(f331(f331(f82(x55051),f331(f80(x55051),x55052)),f331(f80(x55051),x55053)),f331(f331(f82(x55051),x55052),x55053))
% 162.26/162.07 [5507]~P61(x55071)+E(f331(f331(f289(x55071),f331(f80(x55071),x55072)),f331(f80(x55071),x55073)),f331(f331(f289(x55071),x55072),x55073))
% 162.26/162.07 [5538]~P24(f331(x55383,x55382))+P24(f331(f331(f333(x55381),x55382),f331(f253(x55381),x55383)))
% 162.26/162.07 [5576]E(f173(x55761,x55762,x55763),x55763)+P24(f331(f331(f333(x55761),x55762),f331(f175(x55761),x55763)))
% 162.26/162.07 [5659]~P24(f331(f140(x56591),x56593))+P24(f331(f140(x56591),f331(f139(x56591,x56592),x56593)))
% 162.26/162.07 [5704]~P58(x57041)+E(f331(f331(f39(x57041),f45(x57041,x57042,x57043)),x57043),f2(x57041))
% 162.26/162.07 [5723]E(f177(x57231,f331(f331(f154(x57231),x57232),f119(x57231)),x57233),f119(x57231))+P24(f331(f331(f333(a883),f2(a883)),x57233))
% 162.26/162.07 [5780]E(f331(f331(f154(x57801),x57802),x57803),f143(x57801,x57802,x57803))+P24(f331(f331(f333(x57801),x57802),f331(f175(x57801),x57803)))
% 162.26/162.07 [5789]E(x57891,x57892)+~E(f331(f331(f82(a883),f331(a118,x57893)),x57891),f331(f331(f82(a883),f331(a118,x57893)),x57892))
% 162.26/162.07 [5790]~E(x57902,f331(f331(f81(a1),x57901),f331(f106(a1),f331(a118,x57903))))+P24(f331(f331(f248(a1),x57901),x57902))
% 162.26/162.07 [5895]~E(x58953,f119(x58951))+E(f331(f331(f331(f191(f884(x58951),f884(x58951)),x58952),f171(x58951)),x58953),f119(x58951))
% 162.26/162.07 [5899]P24(f331(x58991,x58992))+~P24(f331(f331(f333(x58993),x58992),f331(f253(x58993),x58991)))
% 162.26/162.07 [5931]E(x59311,x59312)+~E(f331(f331(f309(x59313),x59311),f196(f891(x59313,a877))),f331(f331(f309(x59313),x59312),f196(f891(x59313,a877))))
% 162.26/162.07 [5941]~P108(x59411)+E(f331(f331(f108(f891(x59411,a877)),f331(f254(x59411),x59412)),f331(f301(x59411,x59412),x59413)),f196(f891(x59411,a877)))
% 162.26/162.07 [5984]E(f143(x59841,x59842,x59843),x59843)+~P24(f331(f331(f333(x59841),x59842),f331(f175(x59841),x59843)))
% 162.26/162.07 [6008]~P77(x60081)+E(f331(f310(x60081,x60081,f80(x60081)),f331(f301(x60081,x60082),x60083)),f304(x60081,f331(f80(x60081),x60083),f331(f80(x60081),x60082)))
% 162.26/162.07 [6017]E(f331(f197(f884(x60171)),f173(x60171,x60172,x60173)),f331(f197(f884(x60171)),x60173))+P24(f331(f331(f333(x60171),x60172),f331(f175(x60171),x60173)))
% 162.26/162.07 [6069]~P108(x60691)+E(f331(f331(f108(f891(x60691,a877)),f331(f301(x60691,x60692),x60693)),f331(f255(x60691),x60693)),f196(f891(x60691,a877)))
% 162.26/162.07 [6092]~P77(x60921)+E(f331(f310(x60921,x60921,f80(x60921)),f305(x60921,x60922,x60923)),f305(x60921,f331(f80(x60921),x60923),f331(f80(x60921),x60922)))
% 162.26/162.07 [6093]~P77(x60931)+E(f331(f310(x60931,x60931,f80(x60931)),f302(x60931,x60932,x60933)),f302(x60931,f331(f80(x60931),x60933),f331(f80(x60931),x60932)))
% 162.26/162.07 [6150]E(f177(x61501,f331(f331(f154(x61501),x61502),f119(x61501)),x61503),f331(f331(f154(x61501),x61502),f119(x61501)))+~P24(f331(f331(f333(a883),f2(a883)),x61503))
% 162.26/162.07 [6159]~P77(x61591)+E(f331(f310(x61591,x61591,f80(x61591)),f304(x61591,x61592,x61593)),f331(f301(x61591,f331(f80(x61591),x61593)),f331(f80(x61591),x61592)))
% 162.26/162.07 [6179]~P59(x61791)+E(f45(x61791,f331(f80(x61791),f45(x61791,x61792,x61793)),x61793),f45(x61791,f331(f80(x61791),x61792),x61793))
% 162.26/162.07 [6278]~P24(f331(f62(f890(x62782,x62781)),x62783))+P24(f331(f62(x62781),f331(f257(x62782,x62781),x62783)))
% 162.26/162.07 [6279]~P24(f331(f62(f890(x62791,x62792)),x62793))+P24(f331(f62(x62791),f331(f259(x62791,x62792),x62793)))
% 162.26/162.07 [6285]~P108(x62851)+E(f331(f331(f108(f891(x62851,a877)),f305(x62851,x62852,x62853)),f331(f255(x62851),x62853)),f196(f891(x62851,a877)))
% 162.26/162.07 [6286]~P108(x62861)+E(f331(f331(f108(f891(x62861,a877)),f304(x62861,x62862,x62863)),f331(f303(x62861),x62863)),f196(f891(x62861,a877)))
% 162.26/162.07 [6287]~P108(x62871)+E(f331(f331(f108(f891(x62871,a877)),f302(x62871,x62872,x62873)),f331(f303(x62871),x62873)),f196(f891(x62871,a877)))
% 162.26/162.07 [6350]E(f331(f331(f168(x63501),x63502),f624(x63502,x63503,x63501)),x63503)+~P24(f331(f331(f333(x63501),x63503),f331(f175(x63501),x63502)))
% 162.26/162.07 [6490]E(x64901,f119(x64902))+~E(f331(f331(f331(f191(f884(x64902),f884(x64902)),x64903),f171(x64902)),x64901),f119(x64902))
% 162.26/162.07 [6590]~P24(f331(f62(f890(x65902,x65901)),x65903))+P24(f331(f62(f890(x65901,x65902)),f331(f286(x65902,x65901),x65903)))
% 162.26/162.07 [6741]P53(x67411,x67412,x67413)+P24(f331(f331(f333(x67411),f763(x67413,x67412,x67411)),x67412))
% 162.26/162.07 [6742]P53(x67421,x67422,x67423)+P24(f331(f331(f333(x67421),f762(x67423,x67422,x67421)),x67422))
% 162.26/162.07 [6754]P24(f331(f319(x67541,x67542),x67543))+P24(f331(f331(x67542,f382(x67543,x67542,x67541)),x67543))
% 162.26/162.07 [6755]P24(f331(f319(x67551,x67552),x67553))+P24(f331(f331(x67552,f386(x67553,x67552,x67551)),x67553))
% 162.26/162.07 [6780]E(f331(f197(f884(x67801)),f173(x67801,x67802,x67803)),f331(f331(f22(a883),f331(f197(f884(x67801)),x67803)),f79(a883)))+~P24(f331(f331(f333(x67801),x67802),f331(f175(x67801),x67803)))
% 162.26/162.07 [6818]P24(f331(f265(x68181,x68182),x68183))+P24(f331(f331(f333(x68181),f586(x68183,x68182,x68181)),x68183))
% 162.26/162.07 [6827]~P24(f331(f62(f890(x68272,x68271)),f331(f286(x68271,x68272),x68273)))+P24(f331(f62(f890(x68271,x68272)),x68273))
% 162.26/162.07 [6883]~P24(f331(f331(f333(x68831),x68832),f331(f175(x68831),f120(x68831,x68833))))+P24(f331(f331(f333(x68831),x68832),f331(f175(x68831),x68833)))
% 162.26/162.07 [6888]P23(x68881,x68882,x68883)+P24(f331(f331(f333(f882(x68881)),f599(x68883,x68882,x68881)),x68883))
% 162.26/162.07 [6915]E(f331(f139(x69151,x69152),x69153),x69153)+P24(f331(f331(f333(x69151),f640(x69153,x69152,x69151)),f331(f175(x69151),x69153)))
% 162.26/162.07 [6930]E(f331(f139(x69301,x69302),x69303),f119(x69301))+P24(f331(f331(f333(x69301),f639(x69303,x69302,x69301)),f331(f175(x69301),x69303)))
% 162.26/162.07 [6954]P32(x69541,x69542,x69543)+P24(f331(f331(f333(x69541),f809(x69543,x69542,x69541)),f331(f175(x69541),x69543)))
% 162.26/162.07 [6955]P32(x69551,x69552,x69553)+P24(f331(f331(f333(x69551),f810(x69553,x69552,x69551)),f331(f175(x69551),x69553)))
% 162.26/162.07 [6956]P32(x69561,x69562,x69563)+P24(f331(f331(f333(x69561),f796(x69562,x69563,x69561)),f331(f175(x69561),x69563)))
% 162.26/162.07 [6959]E(f179(x69591,x69592,x69593),x69593)+P24(f331(f331(f333(x69591),f670(x69593,x69592,x69591)),f331(f175(x69591),x69593)))
% 162.26/162.07 [7040]P24(f331(f163(x70401,x70402),x70403))+P24(f331(f331(f333(x70401),f688(x70403,x70402,x70401)),f331(f175(x70401),x70403)))
% 162.26/162.07 [7049]~P34(x70491,x70493,x70492)+P24(f331(f331(f333(x70491),f728(x70492,x70493,x70491)),f331(f175(x70491),x70492)))
% 162.26/162.07 [7050]~P36(x70501,x70503,x70502)+P24(f331(f331(f333(x70501),f811(x70502,x70503,x70501)),f331(f175(x70501),x70502)))
% 162.26/162.07 [7084]P24(f331(f331(f333(x70841),x70842),f798(x70843,x70842,x70841)))+~P24(f331(f331(f333(x70841),x70842),f40(f891(x70841,a877),x70843)))
% 162.26/162.07 [7085]~P74(x70851)+E(f331(f331(f81(x70851),f331(f331(f6(a883,x70851),x70852),f331(f254(a883),x70853))),f331(x70852,x70853)),f331(f331(f6(a883,x70851),x70852),f331(f254(a883),f331(a118,x70853))))
% 162.26/162.07 [7174]~P34(x71742,x71741,x71743)+P24(f331(x71741,f331(f331(f168(x71742),x71743),f748(x71743,x71741,x71742))))
% 162.26/162.07 [7187]~P24(f331(f331(f333(x71871),x71872),f749(x71872,x71873,x71871)))+P24(f331(f331(f333(x71871),x71872),f41(f891(x71871,a877),x71873)))
% 162.26/162.07 [7217]~P74(x72171)+E(f331(f331(f81(x72171),f331(f331(f6(a883,x72171),x72172),f331(f300(a883),x72173))),f331(x72172,f331(a118,x72173))),f331(f331(f6(a883,x72171),x72172),f331(f300(a883),f331(a118,x72173))))
% 162.26/162.07 [7341]P24(f331(f331(f333(f884(x73411)),x73412),f164(x73411,x73413)))+P24(f331(f331(f333(x73411),f625(x73413,x73412,x73411)),f331(f175(x73411),x73412)))
% 162.26/162.07 [7357]~P24(f331(f331(f333(f884(x73571)),x73572),f164(x73571,f320(x73571,x73573))))+P24(f331(f331(f333(f884(x73571)),x73572),f320(f884(x73571),f160(x73571,x73573))))
% 162.26/162.07 [7383]~P24(f331(f331(f333(f884(x73831)),x73832),f320(f884(x73831),f160(x73831,x73833))))+P24(f331(f331(f333(f884(x73831)),x73832),f164(x73831,f320(x73831,x73833))))
% 162.26/162.07 [7419]E(f331(f331(f331(f191(f884(x74191),f884(x74191)),x74192),f171(x74191)),x74193),x74193)+~P24(f331(f331(f247(a883),f331(f197(f884(x74191)),x74193)),f79(a883)))
% 162.26/162.07 [7455]E(f331(f331(f137(x74551),f785(x74552,x74553,x74551)),f331(f331(f154(x74551),x74553),f790(x74552,x74553,x74551))),x74552)+~P24(f331(f331(f333(x74551),x74553),f331(f175(x74551),x74552)))
% 162.26/162.07 [7456]E(f331(f331(f137(x74561),f791(x74562,x74563,x74561)),f331(f331(f154(x74561),x74563),f792(x74562,x74563,x74561))),x74562)+~P24(f331(f331(f333(x74561),x74563),f331(f175(x74561),x74562)))
% 162.26/162.07 [7457]E(f331(f331(f137(x74571),f793(x74572,x74573,x74571)),f331(f331(f154(x74571),x74573),f794(x74572,x74573,x74571))),x74572)+~P24(f331(f331(f333(x74571),x74573),f331(f175(x74571),x74572)))
% 162.26/162.07 [7478]~P21(x74781,x74782,x74783,f256(f891(x74781,a877)))+P21(f884(x74781),f884(x74782),f331(f157(x74781,x74782),x74783),f256(f891(f884(x74781),a877)))
% 162.26/162.07 [7624]E(x76241,f331(f331(f81(a883),f331(f331(f82(a883),f331(f260(a883,a883),x76242)),x76243)),f331(f269(a883,a883),x76242)))+~P24(f331(f48(x76241,x76243),x76242))
% 162.26/162.07 [7632]P21(x76321,x76322,x76323,f256(f891(x76321,a877)))+~P21(f884(x76321),f884(x76322),f331(f157(x76321,x76322),x76323),f256(f891(f884(x76321),a877)))
% 162.26/162.07 [7670]~P24(f331(f331(f203(x76701),x76702),x76703))+P24(f331(f331(f331(f331(a205,x76701),x76702),f533(x76703,x76702,x76701)),x76703))
% 162.26/162.07 [7674]P24(f331(f331(f333(f891(x76741,a877)),f749(x76742,x76743,x76741)),x76743))+P24(f331(f331(f333(x76741),x76742),f41(f891(x76741,a877),x76743)))
% 162.26/162.07 [7768]P24(f331(f331(f333(f884(x77681)),x77682),f164(x77681,x77683)))+~P24(f331(f331(f333(x77681),f625(x77683,x77682,x77681)),x77683))
% 162.26/162.07 [7865]P32(x78651,x78652,x78653)+~P24(f331(x78652,f331(f331(f168(x78651),x78653),f797(x78653,x78652,x78651))))
% 162.26/162.07 [7890]E(x78901,x78902)+~E(f331(f331(f7(x78903,f891(x78903,a877),a877),f333(x78903)),x78901),f331(f331(f7(x78903,f891(x78903,a877),a877),f333(x78903)),x78902))
% 162.26/162.07 [7896]~P24(f331(f331(f333(f890(x78961,x78961)),x78963),f258(x78961,x78962)))+P24(f331(f331(f333(x78961),f455(x78962,x78963,x78961)),x78962))
% 162.26/162.07 [7898]~P24(f331(f331(f333(x78981),x78983),f40(f891(x78981,a877),x78982)))+P24(f331(f331(f333(f891(x78981,a877)),f798(x78982,x78983,x78981)),x78982))
% 162.26/162.07 [8078]~P24(f331(f331(f333(x80781),x80782),f331(f175(x80781),f791(x80783,x80782,x80781))))+~P24(f331(f331(f333(x80781),x80782),f331(f175(x80781),x80783)))
% 162.26/162.07 [8079]~P24(f331(f331(f333(x80791),x80792),f331(f175(x80791),f794(x80793,x80792,x80791))))+~P24(f331(f331(f333(x80791),x80792),f331(f175(x80791),x80793)))
% 162.26/162.07 [8170]E(f331(f242(f887(f884(a327)),f884(a327),f313(x81701,x81702,f331(f331(f81(a1),x81703),f79(a1))),f239(f884(a327))),f331(x81701,x81703)),f313(x81701,x81702,x81703))+P24(f331(f331(f248(a1),x81702),x81703))
% 162.26/162.07 [8270]E(x82701,f119(x82702))+P24(f331(f331(f333(x82702),f331(f260(x82702,f890(a105,a105)),f331(f282(x82702,x82701),x82703))),f331(f175(x82702),x82701)))
% 162.26/162.07 [8363]~P69(x83631)+E(f331(f145(x83631,x83631,f331(f7(x83631,x83631,x83631),f81(x83631)),x83632),f331(f172(x83631),x83633)),f331(f145(x83631,x83631,f81(x83631),x83632),x83633))
% 162.26/162.07 [8848]~P107(x88481)+E(f331(f175(x88481),f152(x88481,x88481,f5(x88481),x88482,x88483)),f331(f331(f309(x88481),x88482),f331(f175(x88481),x88483)))
% 162.26/162.07 [8860]P24(f331(f331(f248(a883),f2(a883)),f766(x88601,x88602,x88603)))+~P24(f331(f331(f333(f890(x88603,x88603)),x88602),f331(f331(f288(x88603,x88603,x88603),x88601),f307(x88603,x88601))))
% 162.26/162.07 [9144]~P55(x91441,x91442)+~P24(f331(f331(f333(f890(x91441,x91441)),f331(f331(f261(x91441,x91441),x91443),x91443)),f331(f331(f288(x91441,x91441,x91441),x91442),f307(x91441,x91442))))
% 162.26/162.07 [9280]~E(f331(f331(f108(f891(f890(x92801,x92801),a877)),f331(f286(x92801,x92801),x92802)),f307(x92801,x92802)),f196(f891(f890(x92801,x92801),a877)))+~P24(f331(f331(f333(f890(x92801,x92801)),f331(f331(f261(x92801,x92801),x92803),x92803)),f331(f331(f288(x92801,x92801,x92801),x92802),f307(x92801,x92802))))
% 162.26/162.07 [9454]~P24(f331(f62(x94541),x94542))+P24(f331(f331(f247(a883),f331(f38(x94541),f331(f331(f22(f891(x94541,a877)),x94542),f331(f331(f309(x94541),x94543),f196(f891(x94541,a877)))))),f331(f38(x94541),x94542)))
% 162.26/162.07 [5073]~E(x50733,f119(x50731))+E(f147(x50731,f331(f331(f154(x50731),x50732),x50733)),x50732)
% 162.26/162.07 [5081]~E(x50813,f119(x50811))+E(f120(x50811,f331(f331(f154(x50811),x50812),x50813)),f119(x50811))
% 162.26/162.07 [5109]E(x51091,f119(x51092))+E(f147(x51092,f331(f331(f154(x51092),x51093),x51091)),f147(x51092,x51091))
% 162.26/162.07 [5111]E(x51111,f119(x51112))+E(f147(x51112,f331(f331(f137(x51112),x51113),x51111)),f147(x51112,x51111))
% 162.26/162.07 [5116]~E(x51163,f119(x51161))+E(f120(x51161,f331(f331(f137(x51161),x51162),x51163)),f120(x51161,x51162))
% 162.26/162.07 [5118]~E(x51183,f119(x51181))+E(f147(x51181,f331(f331(f137(x51181),x51182),x51183)),f147(x51181,x51182))
% 162.26/162.07 [5149]E(x51491,f119(x51492))+E(f331(f144(x51492),f331(f331(f137(x51492),x51491),x51493)),f331(f144(x51492),x51491))
% 162.26/162.07 [5180]~E(x51802,f119(x51801))+E(f331(f144(x51801),f331(f331(f137(x51801),x51802),x51803)),f331(f144(x51801),x51803))
% 162.26/162.07 [5235]~P96(x52351)+E(f331(f331(f107(x52351),x52352),f331(f331(f108(x52351),x52352),x52353)),x52352)
% 162.26/162.07 [5236]~P107(x52361)+E(f331(f331(f251(x52361),x52362),f331(f331(f246(x52361),x52362),x52363)),x52362)
% 162.26/162.07 [5237]~P107(x52371)+E(f331(f331(f246(x52371),x52372),f331(f331(f251(x52371),x52372),x52373)),x52372)
% 162.26/162.07 [5238]~P96(x52381)+E(f331(f331(f108(x52381),x52382),f331(f331(f107(x52381),x52382),x52383)),x52382)
% 162.26/162.07 [5258]~P58(x52581)+E(f45(x52581,f331(f331(f82(x52581),x52582),x52583),x52583),f2(x52581))
% 162.26/162.07 [5259]~P58(x52591)+E(f45(x52591,f331(f331(f82(x52591),x52592),x52593),x52592),f2(x52591))
% 162.26/162.07 [5334]~P70(x53341)+E(f331(f80(x53341),f331(f331(f22(x53341),x53342),x53343)),f331(f331(f22(x53341),x53343),x53342))
% 162.26/162.07 [5397]E(x53971,f119(x53972))+E(f120(x53972,f331(f331(f154(x53972),x53973),x53971)),f331(f331(f154(x53972),x53973),f120(x53972,x53971)))
% 162.26/162.07 [5398]E(x53981,f119(x53982))+E(f120(x53982,f331(f331(f137(x53982),x53983),x53981)),f331(f331(f137(x53982),x53983),f120(x53982,x53981)))
% 162.26/162.07 [5401]~P27(x54011)+E(f41(x54011,f331(f331(f309(x54011),x54012),x54013)),f331(f331(f108(x54011),x54012),f41(x54011,x54013)))
% 162.26/162.07 [5402]~P27(x54021)+E(f40(x54021,f331(f331(f309(x54021),x54022),x54023)),f331(f331(f107(x54021),x54022),f40(x54021,x54023)))
% 162.26/162.07 [5447]~P95(x54471)+E(f331(f331(f82(x54471),x54472),f331(f331(f82(x54471),x54472),x54473)),f331(f331(f82(x54471),x54472),x54473))
% 162.26/162.07 [5448]~P96(x54481)+E(f331(f331(f107(x54481),x54482),f331(f331(f107(x54481),x54482),x54483)),f331(f331(f107(x54481),x54482),x54483))
% 162.26/162.07 [5450]~P101(x54501)+E(f331(f331(f107(x54501),x54502),f331(f331(f107(x54501),x54502),x54503)),f331(f331(f107(x54501),x54502),x54503))
% 162.26/162.07 [5452]~P107(x54521)+E(f331(f331(f251(x54521),x54522),f331(f331(f251(x54521),x54522),x54523)),f331(f331(f251(x54521),x54522),x54523))
% 162.26/162.07 [5454]~P107(x54541)+E(f331(f331(f246(x54541),x54542),f331(f331(f246(x54541),x54542),x54543)),f331(f331(f246(x54541),x54542),x54543))
% 162.26/162.07 [5455]~P96(x54551)+E(f331(f331(f108(x54551),x54552),f331(f331(f108(x54551),x54552),x54553)),f331(f331(f108(x54551),x54552),x54553))
% 162.26/162.07 [5457]~P102(x54571)+E(f331(f331(f108(x54571),x54572),f331(f331(f108(x54571),x54572),x54573)),f331(f331(f108(x54571),x54572),x54573))
% 162.26/162.07 [5465]~P58(x54651)+E(f45(x54651,f331(f331(f81(x54651),x54652),x54653),x54653),f45(x54651,x54652,x54653))
% 162.26/162.07 [5466]~P58(x54661)+E(f45(x54661,f331(f331(f81(x54661),x54662),x54663),x54662),f45(x54661,x54663,x54662))
% 162.26/162.07 [5472]~P125(x54721)+E(f331(f331(f82(x54721),x54722),f331(f80(x54721),x54723)),f331(f80(x54721),f331(f331(f82(x54721),x54722),x54723)))
% 162.26/162.07 [5473]~P61(x54731)+E(f331(f331(f289(x54731),x54732),f331(f80(x54731),x54733)),f331(f80(x54731),f331(f331(f289(x54731),x54732),x54733)))
% 162.26/162.07 [5474]~P80(x54741)+E(f331(f331(f81(x54741),x54742),f331(f169(x54741),x54743)),f331(f169(x54741),f331(f331(f154(x54741),x54742),x54743)))
% 162.26/162.07 [5504]~P125(x55041)+E(f331(f331(f82(x55041),f331(f80(x55041),x55042)),x55043),f331(f331(f82(x55041),x55042),f331(f80(x55041),x55043)))
% 162.26/162.07 [5511]~P6(x55111,x55112,x55113)+E(f40(f891(x55111,a877),f331(f331(f61(x55111),x55112),x55113)),x55112)
% 162.26/162.07 [5568]~P115(x55681)+E(f331(f331(f82(x55681),x55682),f331(f331(f262(x55681),x55682),x55683)),f331(f331(f262(x55681),x55682),f331(a118,x55683)))
% 162.26/162.07 [5569]~P118(x55691)+E(f331(f331(f82(x55691),x55692),f331(f331(f262(x55691),x55692),x55693)),f331(f331(f262(x55691),x55692),f331(a118,x55693)))
% 162.26/162.07 [5579]~P66(x55791)+E(f331(f331(f81(x55791),f331(f80(x55791),x55792)),f331(f331(f81(x55791),x55792),x55793)),x55793)
% 162.26/162.07 [5602]~P143(x56021)+E(f331(f331(f262(x56021),f331(f106(x56021),x56022)),x56023),f331(f106(x56021),f331(f331(f262(a883),x56022),x56023)))
% 162.26/162.07 [5603]~P138(x56031)+E(f331(f331(f262(x56031),f331(f109(x56031),x56032)),x56033),f331(f109(x56031),f331(f331(f262(a1),x56032),x56033)))
% 162.26/162.07 [5608]~P83(x56081)+E(f331(f76(x56081),f331(f331(f22(x56081),x56082),x56083)),f331(f76(x56081),f331(f331(f22(x56081),x56083),x56082)))
% 162.26/162.07 [5612]~P111(x56121)+E(f331(f331(f82(x56121),f83(x56121,x56122)),f83(x56121,x56123)),f83(x56121,f331(f331(f82(x56121),x56122),x56123)))
% 162.26/162.07 [5616]E(x56161,f119(x56162))+E(f331(f331(f137(x56162),f331(f174(x56162),x56161)),x56163),f331(f174(x56162),f331(f331(f137(x56162),x56161),x56163)))
% 162.26/162.07 [5621]~E(x56212,f331(a118,f331(f331(f81(a883),x56211),x56213)))+P24(f331(f331(f248(a883),x56211),x56212))
% 162.26/162.07 [5622]~P125(x56221)+E(f331(f331(f82(x56221),f331(f80(x56221),x56222)),x56223),f331(f80(x56221),f331(f331(f82(x56221),x56222),x56223)))
% 162.26/162.07 [5623]~P119(x56231)+E(f331(f331(f289(x56231),f331(f80(x56231),x56232)),x56233),f331(f80(x56231),f331(f331(f289(x56231),x56232),x56233)))
% 162.26/162.07 [5624]~P111(x56241)+E(f331(f331(f262(x56241),f331(f76(x56241),x56242)),x56243),f331(f76(x56241),f331(f331(f262(x56241),x56242),x56243)))
% 162.26/162.07 [5722]E(f449(x57221,x57222,x57223),f464(x57221,x57222,x57223))+E(f331(f331(f108(f891(x57223,a877)),x57222),x57221),f196(f891(x57223,a877)))
% 162.26/162.07 [5736]~P73(x57362)+E(f331(f331(f9(x57361,x57362),f331(f16(x57362,x57361),f79(x57362))),x57363),f79(x57362))
% 162.26/162.07 [5737]~P74(x57372)+E(f331(f331(f6(x57371,x57372),f331(f16(x57372,x57371),f2(x57372))),x57373),f2(x57372))
% 162.26/162.07 [5739]~P94(x57391)+E(f331(f331(f22(x57391),f331(f110(x57391),x57392)),f331(f110(x57391),x57393)),f331(f110(x57391),f331(f331(f22(a1),x57392),x57393)))
% 162.26/162.07 [5742]~P143(x57421)+E(f331(f331(f81(x57421),f331(f106(x57421),x57422)),f331(f106(x57421),x57423)),f331(f106(x57421),f331(f331(f81(a883),x57422),x57423)))
% 162.26/162.07 [5743]~P143(x57431)+E(f331(f331(f82(x57431),f331(f106(x57431),x57432)),f331(f106(x57431),x57433)),f331(f106(x57431),f331(f331(f82(a883),x57432),x57433)))
% 162.26/162.07 [5744]~P138(x57441)+E(f331(f331(f22(x57441),f331(f109(x57441),x57442)),f331(f109(x57441),x57443)),f331(f109(x57441),f331(f331(f22(a1),x57442),x57443)))
% 162.26/162.07 [5745]~P138(x57451)+E(f331(f331(f81(x57451),f331(f109(x57451),x57452)),f331(f109(x57451),x57453)),f331(f109(x57451),f331(f331(f81(a1),x57452),x57453)))
% 162.26/162.07 [5746]~P138(x57461)+E(f331(f331(f82(x57461),f331(f109(x57461),x57462)),f331(f109(x57461),x57463)),f331(f109(x57461),f331(f331(f82(a1),x57462),x57463)))
% 162.26/162.07 [5747]~P94(x57471)+E(f331(f331(f81(x57471),f331(f110(x57471),x57472)),f331(f110(x57471),x57473)),f331(f110(x57471),f331(f331(f81(a1),x57472),x57473)))
% 162.26/162.07 [5748]~P94(x57481)+E(f331(f331(f82(x57481),f331(f110(x57481),x57482)),f331(f110(x57481),x57483)),f331(f110(x57481),f331(f331(f82(a1),x57482),x57483)))
% 162.26/162.07 [5797]~E(x57973,x57972)+P24(f331(f331(f247(f891(x57971,a877)),x57972),x57973))
% 162.26/162.07 [5803]~E(x58032,x58033)+P24(f331(f331(f247(f891(x58031,a877)),x58032),x58033))
% 162.26/162.07 [5808]~P66(x58081)+E(f331(f331(f81(x58081),f331(f80(x58081),x58082)),f331(f80(x58081),x58083)),f331(f80(x58081),f331(f331(f81(x58081),x58083),x58082)))
% 162.26/162.07 [5809]~P70(x58091)+E(f331(f331(f81(x58091),f331(f80(x58091),x58092)),f331(f80(x58091),x58093)),f331(f80(x58091),f331(f331(f81(x58091),x58092),x58093)))
% 162.26/162.07 [5810]~P85(x58101)+E(f331(f331(f108(x58101),f331(f80(x58101),x58102)),f331(f80(x58101),x58103)),f331(f80(x58101),f331(f331(f107(x58101),x58102),x58103)))
% 162.26/162.07 [5811]~P75(x58111)+E(f331(f331(f246(x58111),f331(f80(x58111),x58112)),f331(f80(x58111),x58113)),f331(f80(x58111),f331(f331(f251(x58111),x58112),x58113)))
% 162.26/162.07 [5812]~P75(x58121)+E(f331(f331(f251(x58121),f331(f80(x58121),x58122)),f331(f80(x58121),x58123)),f331(f80(x58121),f331(f331(f246(x58121),x58122),x58123)))
% 162.26/162.07 [5813]~P85(x58131)+E(f331(f331(f107(x58131),f331(f80(x58131),x58132)),f331(f80(x58131),x58133)),f331(f80(x58131),f331(f331(f108(x58131),x58132),x58133)))
% 162.26/162.07 [5814]~P111(x58141)+E(f331(f331(f82(x58141),f331(f76(x58141),x58142)),f331(f76(x58141),x58143)),f331(f76(x58141),f331(f331(f82(x58141),x58142),x58143)))
% 162.26/162.07 [5815]~P63(x58151)+E(f331(f331(f289(x58151),f331(f76(x58151),x58152)),f331(f76(x58151),x58153)),f331(f76(x58151),f331(f331(f289(x58151),x58152),x58153)))
% 162.26/162.07 [5816]~P80(x58161)+E(f331(f331(f81(x58161),f331(f169(x58161),x58162)),f331(f169(x58161),x58163)),f331(f169(x58161),f331(f331(f137(x58161),x58162),x58163)))
% 162.26/162.07 [5817]E(x58171,f196(f891(x58172,a877)))+~E(f331(f331(f107(f891(x58172,a877)),x58173),x58171),f196(f891(x58172,a877)))
% 162.26/162.07 [5818]E(x58181,f196(f891(x58182,a877)))+~E(f331(f331(f107(f891(x58182,a877)),x58181),x58183),f196(f891(x58182,a877)))
% 162.26/162.07 [5819]~P147(x58191,x58193,x58192)+P24(f331(x58191,f331(f331(f39(a1),x58192),x58193)))
% 162.26/162.07 [5869]~P24(f331(f62(x58691),x58693))+P24(f331(f62(x58691),f331(f331(f309(x58691),x58692),x58693)))
% 162.26/162.07 [5870]~P24(f331(f140(x58701),x58703))+P24(f331(f140(x58701),f331(f331(f176(x58701),x58702),x58703)))
% 162.26/162.07 [5871]~P24(f331(f140(x58711),x58713))+P24(f331(f140(x58711),f331(f331(f141(x58711),x58712),x58713)))
% 162.26/162.07 [5900]~P96(x59001)+P24(f331(f331(f247(x59001),x59002),f331(f331(f107(x59001),x59003),x59002)))
% 162.26/162.07 [5901]~P101(x59011)+P24(f331(f331(f247(x59011),x59012),f331(f331(f107(x59011),x59013),x59012)))
% 162.26/162.07 [5902]~P96(x59021)+P24(f331(f331(f247(x59021),x59022),f331(f331(f107(x59021),x59022),x59023)))
% 162.26/162.07 [5903]~P101(x59031)+P24(f331(f331(f247(x59031),x59032),f331(f331(f107(x59031),x59032),x59033)))
% 162.26/162.07 [5904]~P107(x59041)+P24(f331(f331(f247(x59041),x59042),f331(f331(f246(x59041),x59043),x59042)))
% 162.26/162.07 [5905]~P107(x59051)+P24(f331(f331(f247(x59051),x59052),f331(f331(f246(x59051),x59052),x59053)))
% 162.26/162.07 [5919]~E(x59191,f2(a883))+E(f331(f331(f39(a883),f331(f331(f82(a883),x59191),x59192)),f331(f331(f82(a883),x59191),x59193)),f2(a883))
% 162.26/162.07 [5987]P24(f331(x59871,x59872))+P24(f331(f331(f203(f33(x59871,x59873)),x59872),x59872))
% 162.26/162.07 [6002]~P94(x60021)+E(f331(f331(f22(x60021),f331(f110(x60021),x60022)),f331(f110(x60021),x60023)),f331(f110(x60021),f331(f331(f81(a1),x60022),f331(f80(a1),x60023))))
% 162.26/162.07 [6056]E(x60561,f2(a883))+E(f331(f331(f39(a883),f331(f331(f82(a883),x60561),x60562)),f331(f331(f82(a883),x60561),x60563)),f331(f331(f39(a883),x60562),x60563))
% 162.26/162.07 [6090]E(f155(x60901,f331(f331(f154(x60901),x60902),x60903)),f331(f331(f154(x60901),x60902),f155(x60901,x60903)))+P24(f331(f331(f333(x60901),x60902),f331(f175(x60901),x60903)))
% 162.26/162.07 [6124]P147(x61241,x61242,x61243)+~P24(f331(x61241,f331(f331(f39(a1),x61243),x61242)))
% 162.26/162.07 [6196]E(x61961,f119(x61962))+E(f331(f331(f154(x61962),f331(f144(x61962),x61961)),f331(f331(f176(x61962),x61963),f331(f174(x61962),x61961))),f331(f331(f176(x61962),f331(a118,x61963)),x61961))
% 162.26/162.07 [6203]E(f331(f331(f22(f891(x62031,a877)),x62032),x62033),x62032)+~E(f331(f331(f108(f891(x62031,a877)),x62032),x62033),f196(f891(x62031,a877)))
% 162.26/162.07 [6216]E(f155(x62161,f331(f331(f154(x62161),x62162),x62163)),f155(x62161,x62163))+~P24(f331(f331(f333(x62161),x62162),f331(f175(x62161),x62163)))
% 162.26/162.07 [6248]~P24(f331(f331(f248(a883),x62481),x62483))+P24(f331(f331(f248(a883),x62481),f331(f331(f81(a883),x62482),x62483)))
% 162.26/162.07 [6250]~P24(f331(f331(f248(a883),x62501),x62502))+P24(f331(f331(f248(a883),x62501),f331(f331(f81(a883),x62502),x62503)))
% 162.26/162.07 [6252]~P24(f331(f331(f247(a883),x62521),x62523))+P24(f331(f331(f247(a883),x62521),f331(f331(f81(a883),x62522),x62523)))
% 162.26/162.07 [6254]~P24(f331(f331(f247(a883),x62541),x62542))+P24(f331(f331(f247(a883),x62541),f331(f331(f81(a883),x62542),x62543)))
% 162.26/162.07 [6293]P24(f331(f62(x62931),x62932))+~P24(f331(f62(x62931),f331(f331(f309(x62931),x62933),x62932)))
% 162.26/162.07 [6294]P24(f331(f140(x62941),x62942))+~P24(f331(f140(x62941),f331(f331(f154(x62941),x62943),x62942)))
% 162.26/162.07 [6295]P24(f331(f140(x62951),x62952))+~P24(f331(f140(x62951),f331(f331(f137(x62951),x62953),x62952)))
% 162.26/162.07 [6296]P24(f331(f140(x62961),x62962))+~P24(f331(f140(x62961),f331(f331(f137(x62961),x62962),x62963)))
% 162.26/162.07 [6339]~P118(x63391)+E(f331(f331(f81(x63391),x63392),f331(f331(f82(x63391),x63393),x63392)),f331(f331(f82(x63391),f331(f331(f81(x63391),x63393),f79(x63391))),x63392))
% 162.26/162.07 [6387]~E(x63871,x63872)+~P24(f331(f331(f248(f891(x63873,a877)),x63871),x63872))
% 162.26/162.07 [6431]P24(f331(f331(f333(x64311),x64312),x64313))+P24(f331(f331(f333(x64311),x64312),f331(f80(f891(x64311,a877)),x64313)))
% 162.26/162.07 [6437]E(f147(x64371,f331(f331(f141(x64371),x64372),x64373)),f147(x64371,x64373))+~P24(f331(f331(f248(a883),x64372),f331(f197(f884(x64371)),x64373)))
% 162.26/162.07 [6438]E(f331(f331(f176(x64381),x64382),f120(x64381,x64383)),f331(f331(f176(x64381),x64382),x64383))+~P24(f331(f331(f248(a883),x64382),f331(f197(f884(x64381)),x64383)))
% 162.26/162.07 [6492]E(f331(f331(f331(f191(f884(x64921),f884(x64921)),x64922),f171(x64921)),x64923),x64923)+~E(f45(a883,x64922,f331(f197(f884(x64921)),x64923)),f2(a883))
% 162.26/162.07 [6499]~P6(x64991,x64993,x64992)+E(f331(f331(f288(x64991,x64991,x64991),f331(f286(x64991,x64991),x64992)),x64992),x64992)
% 162.26/162.07 [6539]~E(f331(f331(f107(f891(x65391,a877)),x65392),x65393),x65393)+P24(f331(f331(f247(f891(x65391,a877)),x65392),x65393))
% 162.26/162.07 [6544]~P52(x65441,x65441,x65443)+P52(x65441,x65441,f331(f331(f191(f890(x65441,x65441),a877),x65442),x65443))
% 162.26/162.07 [6546]~P24(f331(f331(f333(x65461),x65463),f331(f175(x65461),x65462)))+P24(f331(f331(f248(a883),f2(a883)),f331(f197(f884(x65461)),x65462)))
% 162.26/162.07 [6572]~P83(x65721)+E(f331(f76(x65721),f331(f331(f81(x65721),f331(f76(x65721),x65722)),f331(f76(x65721),x65723))),f331(f331(f81(x65721),f331(f76(x65721),x65722)),f331(f76(x65721),x65723)))
% 162.26/162.07 [6583]E(f331(f331(f39(a883),f331(f331(f82(a883),x65831),x65832)),f331(f331(f82(a883),x65831),x65833)),f331(f331(f39(a883),x65832),x65833))+~P24(f331(f331(f248(a883),f2(a883)),x65831))
% 162.26/162.07 [6631]E(x66311,x66312)+~P24(f331(f331(f331(f331(a205,a24),x66311),x66313),x66312))
% 162.26/162.07 [6720]~P24(f331(f62(x67201),x67203))+E(f331(f331(f65(x67201,f891(x67201,a877),f309(x67201)),x67202),x67203),f331(f331(f107(f891(x67201,a877)),x67203),x67202))
% 162.26/162.07 [6773]E(f331(f331(f107(f891(x67731,a877)),x67732),x67733),x67732)+~P24(f331(f331(f247(f891(x67731,a877)),x67733),x67732))
% 162.26/162.07 [6775]E(f331(f331(f107(f891(x67751,a877)),x67752),x67753),x67753)+~P24(f331(f331(f247(f891(x67751,a877)),x67752),x67753))
% 162.26/162.07 [6776]E(f331(f331(f108(f891(x67761,a877)),x67762),x67763),x67763)+~P24(f331(f331(f247(f891(x67761,a877)),x67763),x67762))
% 162.26/162.07 [6777]E(f331(f331(f108(f891(x67771,a877)),x67772),x67773),x67772)+~P24(f331(f331(f247(f891(x67771,a877)),x67772),x67773))
% 162.26/162.07 [6825]~P24(f331(f140(x68251),x68252))+E(f331(f331(f22(f891(x68251,a877)),f331(f175(x68251),x68252)),f331(f331(f309(x68251),x68253),f196(f891(x68251,a877)))),f331(f175(x68251),f173(x68251,x68253,x68252)))
% 162.26/162.07 [6878]P38(x68781,x68782)+~P38(x68781,f331(f331(f191(f890(x68781,x68781),a877),x68783),x68782))
% 162.26/162.07 [6941]P24(f331(f49(x69411,x69412),f331(a51,x69413)))+~P24(f331(f49(f331(f80(a1),x69411),f331(f80(a1),x69412)),x69413))
% 162.26/162.07 [6946]E(f331(f331(f22(f891(x69461,a877)),f331(f331(f309(x69461),x69462),x69463)),f331(f331(f309(x69461),x69462),f196(f891(x69461,a877)))),x69463)+P24(f331(f331(f333(x69461),x69462),x69463))
% 162.26/162.07 [6968]E(f331(f331(f108(f891(x69681,a877)),f331(f175(x69681),x69682)),f331(f175(x69681),x69683)),f196(f891(x69681,a877)))+~P24(f331(f140(x69681),f331(f331(f137(x69681),x69682),x69683)))
% 162.26/162.07 [6984]~P24(f331(f331(f333(x69841),x69842),f331(f175(x69841),x69843)))+~P24(f331(f140(x69841),f331(f331(f154(x69841),x69842),x69843)))
% 162.26/162.07 [7056]P32(x70561,x70562,x70563)+P24(f331(f331(f248(a883),f797(x70563,x70562,x70561)),f331(f197(f884(x70561)),x70563)))
% 162.26/162.07 [7066]E(f331(f331(f108(f891(x70661,a877)),x70662),x70663),f196(f891(x70661,a877)))+P24(f331(f331(f333(x70661),f449(x70663,x70662,x70661)),x70662))
% 162.26/162.07 [7067]E(f331(f331(f108(f891(x70671,a877)),x70672),x70673),f196(f891(x70671,a877)))+P24(f331(f331(f333(x70671),f464(x70673,x70672,x70671)),x70673))
% 162.26/162.07 [7071]E(f120(x70711,f331(f331(f176(x70711),x70712),x70713)),f331(f331(f176(x70711),f331(f331(f22(a883),x70712),f79(a883))),x70713))+~P24(f331(f331(f247(a883),x70712),f331(f197(f884(x70711)),x70713)))
% 162.26/162.07 [7129]~P34(x71293,x71292,x71291)+P24(f331(f331(f248(a883),f748(x71291,x71292,x71293)),f331(f197(f884(x71293)),x71291)))
% 162.26/162.07 [7147]P24(f331(f331(f248(a883),f2(a883)),x71471))+P24(f331(f331(f247(a883),f331(f331(f82(a883),x71472),x71471)),f331(f331(f82(a883),x71473),x71471)))
% 162.26/162.07 [7148]P24(f331(f331(f248(a883),f2(a883)),x71481))+P24(f331(f331(f247(a883),f331(f331(f82(a883),x71481),x71482)),f331(f331(f82(a883),x71481),x71483)))
% 162.26/162.07 [7151]~P24(f331(f331(f333(x71511),x71512),x71513))+~P24(f331(f331(f333(x71511),x71512),f331(f80(f891(x71511,a877)),x71513)))
% 162.26/162.07 [7158]~P24(f331(f331(f248(f891(x71581,a877)),x71582),x71583))+P24(f331(f331(f247(f891(x71581,a877)),x71582),x71583))
% 162.26/162.07 [7257]~P24(f331(f331(f248(a883),x72572),x72573))+P24(f331(f331(f248(a883),f331(f331(f81(a883),x72571),x72572)),f331(f331(f81(a883),x72571),x72573)))
% 162.26/162.07 [7258]~P24(f331(f331(f248(a883),x72581),x72583))+P24(f331(f331(f248(a883),f331(f331(f81(a883),x72581),x72582)),f331(f331(f81(a883),x72583),x72582)))
% 162.26/162.07 [7259]~P24(f331(f331(f248(a1),x72591),x72593))+P24(f331(f331(f248(a1),f331(f331(f81(a1),x72591),x72592)),f331(f331(f81(a1),x72593),x72592)))
% 162.26/162.07 [7260]~P24(f331(f331(f247(a883),x72603),x72602))+P24(f331(f331(f247(a883),f331(f331(f22(a883),x72601),x72602)),f331(f331(f22(a883),x72601),x72603)))
% 162.26/162.07 [7261]~P24(f331(f331(f247(a883),x72611),x72613))+P24(f331(f331(f247(a883),f331(f331(f22(a883),x72611),x72612)),f331(f331(f22(a883),x72613),x72612)))
% 162.26/162.07 [7262]~P24(f331(f331(f247(a883),x72622),x72623))+P24(f331(f331(f247(a883),f331(f331(f81(a883),x72621),x72622)),f331(f331(f81(a883),x72621),x72623)))
% 162.26/162.07 [7263]~P24(f331(f331(f247(a883),x72631),x72633))+P24(f331(f331(f247(a883),f331(f331(f81(a883),x72631),x72632)),f331(f331(f81(a883),x72633),x72632)))
% 162.26/162.07 [7265]~P24(f331(f331(f247(a883),x72652),x72653))+P24(f331(f331(f247(a883),f331(f331(f82(a883),x72651),x72652)),f331(f331(f82(a883),x72651),x72653)))
% 162.26/162.07 [7267]~P24(f331(f331(f247(a883),x72671),x72673))+P24(f331(f331(f247(a883),f331(f331(f82(a883),x72671),x72672)),f331(f331(f82(a883),x72673),x72672)))
% 162.26/162.07 [7268]~P24(f331(f331(f247(a883),x72681),x72683))+P24(f331(f331(f247(a883),f331(f331(f39(a883),x72681),x72682)),f331(f331(f39(a883),x72683),x72682)))
% 162.26/162.07 [7269]~P24(f331(f331(f247(a1),x72692),x72693))+P24(f331(f331(f247(a1),f331(f331(f81(a1),x72691),x72692)),f331(f331(f81(a1),x72691),x72693)))
% 162.26/162.07 [7340]E(x73401,x73402)+~P24(f331(f331(f333(x73403),x73401),f331(f331(f309(x73403),x73402),f196(f891(x73403,a877)))))
% 162.26/162.07 [7342]~E(f331(f331(f108(f891(x73421,a877)),x73422),x73423),f196(f891(x73421,a877)))+P24(f331(f331(f247(f891(x73421,a877)),x73422),f331(f80(f891(x73421,a877)),x73423)))
% 162.26/162.07 [7350]P24(f331(f331(f333(f891(x73501,a877)),x73502),f331(f308(x73501),x73503)))+~P24(f331(f331(f247(f891(x73501,a877)),x73502),x73503))
% 162.26/162.07 [7403]E(f331(f331(f154(x74031),f331(f331(f168(x74031),x74032),x74033)),f331(f331(f141(x74031),f331(a118,x74033)),x74032)),f331(f331(f141(x74031),x74033),x74032))+~P24(f331(f331(f248(a883),x74033),f331(f197(f884(x74031)),x74032)))
% 162.26/162.07 [7430]P24(f331(f331(f333(f890(x74301,x74301)),x74302),f307(x74301,x74303)))+~P24(f331(f331(f333(f890(x74301,x74301)),x74302),x74303))
% 162.26/162.07 [7441]~P24(f331(f331(f333(f891(x74411,a877)),x74412),f331(f308(x74411),x74413)))+P24(f331(f331(f247(f891(x74411,a877)),x74412),x74413))
% 162.26/162.07 [7484]P24(f331(f331(f247(f891(x74841,a877)),x74842),f40(f891(x74841,a877),x74843)))+~P24(f331(f331(f333(f891(x74841,a877)),x74842),x74843))
% 162.26/162.07 [7509]~P138(x75091)+E(f331(f331(f82(x75091),f331(f331(f262(x75091),f331(f80(x75091),f79(x75091))),x75092)),f331(f331(f262(x75091),x75093),x75092)),f331(f331(f262(x75091),f331(f80(x75091),x75093)),x75092))
% 162.26/162.07 [7531]E(f331(f331(f168(x75311),x75312),f331(f331(f22(a883),f331(f197(f884(x75311)),x75312)),f331(a118,x75313))),f331(f331(f168(x75311),f331(f172(x75311),x75312)),x75313))+~P24(f331(f331(f248(a883),x75313),f331(f197(f884(x75311)),x75312)))
% 162.26/162.07 [7548]~E(f331(f331(f108(f891(x75481,a877)),f528(x75483,x75482,x75481)),x75483),f196(f891(x75481,a877)))+E(f331(f331(f108(f891(x75481,a877)),f40(f891(x75481,a877),x75482)),x75483),f196(f891(x75481,a877)))
% 162.26/162.07 [7606]~P24(f331(f331(f333(x76063),x76062),f331(f175(x76063),x76061)))+P24(f331(f331(f248(a883),f624(x76061,x76062,x76063)),f331(f197(f884(x76063)),x76061)))
% 162.26/162.07 [7614]P24(f331(f331(f333(x76141),f331(f331(f168(x76141),x76142),x76143)),f331(f175(x76141),x76142)))+~P24(f331(f331(f248(a883),x76143),f331(f197(f884(x76141)),x76142)))
% 162.26/162.07 [7713]~P24(f331(x77132,f678(x77133,x77132,x77131)))+E(f331(f331(f141(x77131),f331(f197(f884(x77131)),f179(x77131,x77132,x77133))),x77133),f119(x77131))
% 162.26/162.07 [7723]P24(f331(f331(f247(f891(f884(x77231),a877)),f164(x77231,x77232)),f164(x77231,x77233)))+~P24(f331(f331(f247(f891(x77231,a877)),x77232),x77233))
% 162.26/162.07 [7724]P24(f331(f331(f247(f891(f884(x77241),a877)),f163(x77241,x77242)),f163(x77241,x77243)))+~P24(f331(f331(f247(f891(x77241,a877)),x77242),x77243))
% 162.26/162.07 [7753]E(f331(f331(f108(f891(x77531,a877)),f40(f891(x77531,a877),x77532)),x77533),f196(f891(x77531,a877)))+P24(f331(f331(f333(f891(x77531,a877)),f528(x77533,x77532,x77531)),x77532))
% 162.26/162.07 [7756]~P24(f331(f331(f333(f891(x77561,a877)),x77563),x77562))+P24(f331(f331(f247(f891(x77561,a877)),f41(f891(x77561,a877),x77562)),x77563))
% 162.26/162.07 [7758]E(f331(f331(f108(f891(x77581,a877)),x77582),x77583),f196(f891(x77581,a877)))+~P24(f331(f331(f247(f891(x77581,a877)),x77582),f331(f80(f891(x77581,a877)),x77583)))
% 162.26/162.07 [7807]E(f331(f331(f22(a883),f331(f331(f81(a883),f331(f169(a883),x78071)),x78072)),f331(f331(f168(a883),x78071),x78073)),f331(f169(a883),f331(f331(f162(a883,x78071),x78073),x78072)))+~P24(f331(f331(f248(a883),x78073),f331(f197(f884(a883)),x78071)))
% 162.26/162.07 [7858]P24(f331(f331(f248(a883),x78581),x78582))+~P24(f331(f331(f248(a883),f331(f331(f81(a883),x78583),x78581)),f331(f331(f81(a883),x78583),x78582)))
% 162.26/162.07 [7859]P24(f331(f331(f248(a883),x78591),x78592))+~P24(f331(f331(f248(a883),f331(f331(f82(a883),x78593),x78591)),f331(f331(f82(a883),x78593),x78592)))
% 162.26/162.07 [7860]P24(f331(f331(f248(a883),x78601),x78602))+~P24(f331(f331(f248(a883),f331(f331(f82(a883),x78601),x78603)),f331(f331(f82(a883),x78602),x78603)))
% 162.26/162.07 [7861]P24(f331(f331(f247(a883),x78611),x78612))+~P24(f331(f331(f247(a883),f331(f331(f81(a883),x78613),x78611)),f331(f331(f81(a883),x78613),x78612)))
% 162.26/162.07 [7888]P24(f331(f331(f248(a883),f2(a883)),x78881))+~P24(f331(f331(f248(a883),f331(f331(f82(a883),x78882),x78881)),f331(f331(f82(a883),x78883),x78881)))
% 162.26/162.07 [7889]P24(f331(f331(f248(a883),f2(a883)),x78891))+~P24(f331(f331(f248(a883),f331(f331(f82(a883),x78891),x78892)),f331(f331(f82(a883),x78891),x78893)))
% 162.26/162.07 [7957]E(f264(x79571,x79572,x79573),x79572)+~P24(f331(f331(f247(f891(x79571,a877)),x79573),f331(f331(f309(x79571),x79572),f196(f891(x79571,a877)))))
% 162.26/162.07 [8014]~P24(f331(f140(x80141),x80143))+E(f331(f139(x80141,f331(f331(f8(a877,a877,x80141),a326),f331(a328,x80142))),x80143),f173(x80141,x80142,x80143))
% 162.26/162.07 [8037]E(f331(f331(f141(x80371),f331(f197(f884(x80371)),f179(x80371,x80372,x80373))),x80373),f119(x80371))+P24(f331(f331(f333(x80371),f678(x80373,x80372,x80371)),f331(f175(x80371),x80373)))
% 162.26/162.07 [8042]E(f331(f331(f137(x80421),f331(f331(f176(x80421),x80422),x80423)),f331(f331(f154(x80421),f331(f331(f168(x80421),x80423),x80422)),f119(x80421))),f331(f331(f176(x80421),f331(a118,x80422)),x80423))+~P24(f331(f331(f248(a883),x80422),f331(f197(f884(x80421)),x80423)))
% 162.26/162.07 [8109]E(f331(f139(x81091,f331(f331(f8(a877,a877,x81091),a326),f331(a328,x81092))),x81093),x81093)+P24(f331(f331(f333(x81091),x81092),f331(f175(x81091),x81093)))
% 162.26/162.07 [8117]P24(f331(f331(f247(f891(f891(x81171,a877),a877)),f265(x81171,x81172)),f265(x81171,x81173)))+~P24(f331(f331(f247(f891(x81171,a877)),x81172),x81173))
% 162.26/162.07 [8161]~P24(f331(f140(x81611),x81613))+P24(f331(f140(x81611),f331(f331(f331(f191(f884(x81611),f884(x81611)),x81612),f171(x81611)),x81613)))
% 162.26/162.07 [8166]~P24(f331(f331(f248(a883),x81662),x81663))+P24(f331(f331(f248(a883),f331(f331(f82(a883),f331(a118,x81661)),x81662)),f331(f331(f82(a883),f331(a118,x81661)),x81663)))
% 162.26/162.07 [8189]P24(f331(f331(f247(f891(f891(x81891,a877),a877)),f331(f308(x81891),x81892)),f331(f308(x81891),x81893)))+~P24(f331(f331(f247(f891(x81891,a877)),x81892),x81893))
% 162.26/162.07 [8346]~P24(f331(f331(f247(f891(x83461,a877)),x83463),x83462))+P24(f331(f331(f247(f891(x83461,a877)),f331(f80(f891(x83461,a877)),x83462)),f331(f80(f891(x83461,a877)),x83463)))
% 162.26/162.07 [8378]E(f331(f310(a883,a883,f331(f331(f7(a883,a883,a883),f22(a883)),x83781)),f331(f301(a883,x83782),x83783)),f331(f301(a883,f331(f331(f22(a883),x83782),x83781)),f331(f331(f22(a883),x83783),x83781)))+~P24(f331(f331(f248(a883),x83781),x83783))
% 162.26/162.07 [8401]~P80(x84011)+E(f331(f331(f81(x84011),x84012),f331(f145(x84011,x84011,f81(x84011),f2(x84011)),x84013)),f331(f145(x84011,x84011,f81(x84011),x84012),x84013))
% 162.26/162.07 [8486]~P83(x84861)+P24(f331(f331(f247(x84861),f331(f76(x84861),f331(f331(f22(x84861),x84862),x84863))),f331(f331(f81(x84861),f331(f76(x84861),x84862)),f331(f76(x84861),x84863))))
% 162.26/162.07 [8487]~P83(x84871)+P24(f331(f331(f247(x84871),f331(f76(x84871),f331(f331(f81(x84871),x84872),x84873))),f331(f331(f81(x84871),f331(f76(x84871),x84872)),f331(f76(x84871),x84873))))
% 162.26/162.07 [8497]E(f331(f331(f81(a1),f331(f331(f82(a1),x84971),f45(a1,f331(f331(f39(a1),x84972),x84971),x84973))),f45(a1,x84972,x84971)),f45(a1,x84972,f331(f331(f82(a1),x84971),x84973)))+~P24(f331(f331(f248(a1),f2(a1)),x84973))
% 162.26/162.07 [8502]E(f331(f331(f137(x85021),f331(f331(f176(x85021),x85022),x85023)),f331(f331(f154(x85021),f331(f144(x85021),f331(f331(f141(x85021),x85022),x85023))),f119(x85021))),f331(f331(f176(x85021),f331(a118,x85022)),x85023))+~P24(f331(f331(f248(a883),x85022),f331(f197(f884(x85021)),x85023)))
% 162.26/162.07 [8526]E(f331(f277(x85261,f331(f331(f157(x85261,f890(a105,x85261)),f331(f261(a105,x85261),f79(a105))),x85262)),f331(a3,x85263)),f331(f331(f168(x85261),x85262),x85263))+~P24(f331(f331(f248(a883),x85263),f331(f197(f884(x85261)),x85262)))
% 162.26/162.07 [8590]P24(f331(f331(f333(f890(x85901,x85901)),x85902),f331(f331(f288(x85901,x85901,x85901),x85903),f307(x85901,x85903))))+~P24(f331(f331(f333(f890(x85901,x85901)),x85902),x85903))
% 162.26/162.07 [8611]P24(f331(f331(f247(a883),x86111),x86112))+~P24(f331(f331(f247(a883),f331(f331(f82(a883),f331(a118,x86113)),x86111)),f331(f331(f82(a883),f331(a118,x86113)),x86112)))
% 162.26/162.07 [8625]P24(f331(f331(f247(f891(x86251,a877)),x86252),x86253))+~P24(f331(f331(f247(f891(x86251,a877)),f331(f80(f891(x86251,a877)),x86253)),f331(f80(f891(x86251,a877)),x86252)))
% 162.26/162.07 [8644]P24(f331(f140(x86441),x86442))+~P24(f331(f140(x86441),f331(f331(f331(f191(f884(x86441),f884(x86441)),x86443),f171(x86441)),x86442)))
% 162.26/162.07 [8695]E(f331(f310(f890(x86951,x86952),x86952,f269(x86951,x86952)),f331(f175(f890(x86951,x86952)),x86953)),f188(x86951,x86952,f331(f180(x86951,x86952),x86953)))+~P24(f331(f140(x86951),f331(f331(f157(f890(x86951,x86952),x86951),f260(x86951,x86952)),x86953)))
% 162.26/162.07 [8704]E(f331(f285(x87041,x87041,f307(x87041,x87042)),x87043),x87043)+~P24(f331(f331(f247(f891(x87041,a877)),f331(f285(x87041,x87041,x87042),x87043)),x87043))
% 162.26/162.07 [8747]~P107(x87471)+P29(x87471,f331(f139(x87471,f331(f331(f7(x87471,x87471,a877),a328),f331(x87472,x87473))),x87473))
% 162.26/162.07 [8753]~P24(f331(f331(f247(a883),x87531),x87532))+P24(f331(f331(f247(a883),x87531),f331(f145(a883,a883,f81(a883),x87532),x87533)))
% 162.26/162.07 [8833]~P24(f331(f331(f333(f890(x88331,x88331)),x88332),f307(x88331,x88333)))+P24(f331(f331(f333(f890(x88331,x88331)),x88332),f331(f331(f191(f890(x88331,x88331),a877),f764(x88333,x88332,x88331)),x88333)))
% 162.26/162.07 [8926]~P80(x89261)+E(f331(f331(f81(x89261),x89262),f331(f145(x89261,x89261,f331(f7(x89261,x89261,x89261),f81(x89261)),f2(x89261)),f331(f172(x89261),x89263))),f331(f145(x89261,x89261,f81(x89261),x89262),x89263))
% 162.26/162.07 [9192]P52(x91921,x91922,x91923)+P24(f331(f331(f333(f890(x91921,x91922)),f331(f331(f261(x91921,x91922),f761(x91923,x91922,x91921)),f726(x91923,x91922,x91921))),x91923))
% 162.26/162.07 [9193]P52(x91931,x91932,x91933)+P24(f331(f331(f333(f890(x91931,x91932)),f331(f331(f261(x91931,x91932),f761(x91933,x91932,x91931)),f725(x91933,x91932,x91931))),x91933))
% 162.26/162.07 [9262]~P24(f331(f331(f333(f890(x92621,x92621)),x92622),f331(f331(f288(x92621,x92621,x92621),x92623),f307(x92621,x92623))))+P24(f331(f331(f333(f890(x92621,x92621)),x92622),f331(f331(f191(f890(x92621,x92621),a877),f766(x92623,x92622,x92621)),x92623)))
% 162.26/162.07 [9263]~P24(f331(x92631,f331(f331(f168(x92632),x92633),f331(f197(f884(x92632)),f179(x92632,x92631,x92633)))))+~P24(f331(f331(f248(a883),f331(f197(f884(x92632)),f179(x92632,x92631,x92633))),f331(f197(f884(x92632)),x92633)))
% 162.26/162.07 [9355]~P24(f331(f331(f247(f891(x93551,a877)),x93552),x93553))+P24(f331(f331(f247(f891(x93551,a877)),f331(f331(f7(x93551,f891(x93551,a877),a877),f333(x93551)),x93552)),f331(f331(f7(x93551,f891(x93551,a877),a877),f333(x93551)),x93553)))
% 162.26/162.07 [9405]~P24(f331(f331(f333(f890(f891(x94051,a877),f891(x94051,a877))),f331(f331(f261(f891(x94051,a877),f891(x94051,a877)),x94052),x94053)),f306(x94051)))+P24(f331(f331(f248(f891(x94051,a877)),x94052),x94053))
% 162.26/162.07 [9430]P53(x94301,x94302,x94303)+~P24(f331(f331(f333(f890(x94301,x94301)),f331(f331(f261(x94301,x94301),f763(x94303,x94302,x94301)),f762(x94303,x94302,x94301))),x94303))
% 162.26/162.07 [9431]P53(x94311,x94312,x94313)+~P24(f331(f331(f333(f890(x94311,x94311)),f331(f331(f261(x94311,x94311),f762(x94313,x94312,x94311)),f763(x94313,x94312,x94311))),x94313))
% 162.26/162.07 [9465]~P24(f331(f331(f333(f890(f884(x94651),f884(x94651))),f331(f331(f261(f884(x94651),f884(x94651)),x94652),x94652)),f150(x94651,x94653)))+P24(f331(f331(f333(f890(x94651,x94651)),f331(f331(f261(x94651,x94651),f632(x94652,x94653,x94651)),f632(x94652,x94653,x94651))),x94653))
% 162.26/162.07 [9530]P24(f331(f331(f247(f891(x95301,a877)),x95302),x95303))+~P24(f331(f331(f247(f891(x95301,a877)),f331(f331(f7(x95301,f891(x95301,a877),a877),f333(x95301)),x95302)),f331(f331(f7(x95301,f891(x95301,a877),a877),f333(x95301)),x95303)))
% 162.26/162.07 [9617]E(f331(f331(f22(a883),f331(f331(f6(a883,a883),x96171),f331(f254(a883),x96172))),f331(f331(f6(a883,a883),x96173),f331(f254(a883),x96172))),f331(f331(f6(a883,a883),f331(f331(f18(a883,a883,a883),f331(f331(f8(a883,f891(a883,a883),a883),f22(a883)),x96171)),x96173)),f331(f254(a883),x96172)))+~P24(f331(f331(f247(a883),f331(x96173,f488(x96172,x96171,x96173))),f331(x96171,f488(x96172,x96171,x96173))))
% 162.26/162.07 [9927]E(f331(f253(f890(x99271,x99272)),f331(f270(x99271,x99272,a877),f331(f331(f7(x99271,f891(x99272,f887(x99272)),f891(x99272,a877)),f331(f331(f8(f891(f887(x99272),a877),f891(f891(x99272,f887(x99272)),f891(x99272,a877)),x99271),f8(f887(x99272),a877,x99272)),f331(f331(f8(f887(x99272),f891(f887(x99272),a877),x99271),a328),f331(f180(x99271,x99272),x99273)))),f239(x99272)))),f331(f175(f890(x99271,x99272)),x99273))+~P24(f331(f140(x99271),f331(f331(f157(f890(x99271,x99272),x99271),f260(x99271,x99272)),x99273)))
% 162.26/162.07 [5656]~P66(x56561)+E(f331(f331(f22(x56561),f331(f331(f81(x56561),x56562),x56563)),x56563),x56562)
% 162.26/162.07 [5657]~P66(x56571)+E(f331(f331(f81(x56571),f331(f331(f22(x56571),x56572),x56573)),x56573),x56572)
% 162.26/162.07 [5877]~P66(x58771)+E(f331(f331(f81(x58771),x58772),f331(f331(f81(x58771),f331(f80(x58771),x58772)),x58773)),x58773)
% 162.26/162.07 [5961]~P79(x59611)+E(f331(f331(f82(x59611),f331(f331(f262(x59611),x59612),x59613)),x59612),f331(f331(f262(x59611),x59612),f331(a118,x59613)))
% 162.26/162.07 [5962]~P118(x59621)+E(f331(f331(f82(x59621),f331(f331(f262(x59621),x59622),x59623)),x59622),f331(f331(f262(x59621),x59622),f331(a118,x59623)))
% 162.26/162.07 [6176]~P111(x61761)+E(f331(f76(x61761),f331(f331(f262(x61761),f331(f80(x61761),x61762)),x61763)),f331(f76(x61761),f331(f331(f262(x61761),x61762),x61763)))
% 162.26/162.07 [6224]~P79(x62241)+E(f331(f331(f82(x62241),f331(f331(f262(x62241),x62242),x62243)),x62242),f331(f331(f82(x62241),x62242),f331(f331(f262(x62241),x62242),x62243)))
% 162.26/162.07 [6284]E(f331(f331(f22(a105),f331(f331(f81(a105),x62841),x62842)),x62843),f281(x62841,x62842,x62843))+~P24(f331(f331(f248(a105),x62842),x62843))
% 162.26/162.07 [6304]~E(f331(f331(f141(x63041),x63043),x63042),f119(x63041))+P24(f331(f331(f247(a883),f331(f197(f884(x63041)),x63042)),x63043))
% 162.26/162.07 [6436]E(f331(f331(f82(a883),f331(f110(a883),x64361)),f331(f331(f82(a883),f331(f110(a883),x64362)),x64363)),f2(a883))+~P24(f331(f331(f248(a1),x64361),a84))
% 162.26/162.07 [6452]~P61(x64521)+E(f331(f331(f262(x64521),f331(f331(f289(x64521),f79(x64521)),x64522)),x64523),f331(f331(f289(x64521),f79(x64521)),f331(f331(f262(x64521),x64522),x64523)))
% 162.26/162.07 [6524]E(f331(f331(f22(a883),f331(f331(f81(a883),x65241),x65242)),x65243),f331(f331(f22(a883),x65241),f331(f331(f22(a883),x65243),x65242)))+~P24(f331(f331(f247(a883),x65242),x65243))
% 162.26/162.07 [6526]E(f331(f331(f22(a883),f331(f331(f81(a883),x65261),x65262)),x65263),f331(f331(f81(a883),x65261),f331(f331(f22(a883),x65262),x65263)))+~P24(f331(f331(f247(a883),x65263),x65262))
% 162.26/162.07 [6563]~P107(x65631)+P24(f331(f331(f247(x65631),f331(f331(f251(x65631),x65632),x65633)),x65633))
% 162.26/162.07 [6564]~P107(x65641)+P24(f331(f331(f247(x65641),f331(f331(f251(x65641),x65642),x65643)),x65642))
% 162.26/162.07 [6565]~P96(x65651)+P24(f331(f331(f247(x65651),f331(f331(f108(x65651),x65652),x65653)),x65653))
% 162.26/162.07 [6566]~P102(x65661)+P24(f331(f331(f247(x65661),f331(f331(f108(x65661),x65662),x65663)),x65663))
% 162.26/162.07 [6567]~P96(x65671)+P24(f331(f331(f247(x65671),f331(f331(f108(x65671),x65672),x65673)),x65672))
% 162.26/162.07 [6568]~P102(x65681)+P24(f331(f331(f247(x65681),f331(f331(f108(x65681),x65682),x65683)),x65682))
% 162.26/162.07 [6582]E(f331(f331(f39(a1),f331(f331(f39(a1),x65821),x65822)),x65823),f331(f331(f39(a1),x65821),f331(f331(f82(a1),x65822),x65823)))+~P24(f331(f331(f248(a1),f2(a1)),x65823))
% 162.26/162.07 [6634]~P118(x66341)+E(f331(f331(f81(x66341),f331(f331(f82(x66341),x66342),x66343)),x66343),f331(f331(f82(x66341),f331(f331(f81(x66341),x66342),f79(x66341))),x66343))
% 162.26/162.07 [6635]~P94(x66351)+E(f331(f331(f82(x66351),f331(f80(x66351),f331(f110(x66351),x66352))),x66353),f331(f331(f82(x66351),f331(f110(x66351),f331(f80(a1),x66352))),x66353))
% 162.26/162.07 [6707]~P80(x67071)+E(f331(f169(x67071),f331(f331(f157(x67072,x67071),f331(f16(x67071,x67072),f2(x67071))),x67073)),f2(x67071))
% 162.26/162.07 [6723]E(f331(f331(f81(a883),f331(f110(a883),x67231)),f331(f331(f81(a883),f331(f110(a883),x67232)),x67233)),f331(f331(f81(a883),f331(f110(a883),x67232)),x67233))+~P24(f331(a202,f331(f110(a1),x67231)))
% 162.26/162.07 [6737]~P27(x67371)+E(f41(x67371,f331(f331(f309(x67371),x67372),f331(f331(f309(x67371),x67373),f196(f891(x67371,a877))))),f331(f331(f108(x67371),x67372),x67373))
% 162.26/162.07 [6738]~P27(x67381)+E(f40(x67381,f331(f331(f309(x67381),x67382),f331(f331(f309(x67381),x67383),f196(f891(x67381,a877))))),f331(f331(f107(x67381),x67382),x67383))
% 162.26/162.07 [6761]E(f331(f331(f176(x67611),x67612),x67613),x67613)+~P24(f331(f331(f247(a883),f331(f197(f884(x67611)),x67613)),x67612))
% 162.26/162.07 [6768]E(f331(f331(f141(x67681),x67682),x67683),f119(x67681))+~P24(f331(f331(f247(a883),f331(f197(f884(x67681)),x67683)),x67682))
% 162.26/162.07 [6779]E(f331(f331(f81(a883),f331(f331(f22(a883),x67791),x67792)),x67793),f331(f331(f22(a883),f331(f331(f81(a883),x67791),x67793)),x67792))+~P24(f331(f331(f247(a883),x67792),x67791))
% 162.26/162.07 [6793]~P24(f331(f331(f248(a883),x67931),x67933))+P24(f331(f331(f248(a883),f331(f331(f22(a883),x67931),x67932)),x67933))
% 162.26/162.07 [6819]~P107(x68191)+E(f173(x68191,x68192,f331(f331(f151(x68191,x68191,f5(x68191)),x68192),x68193)),x68193)
% 162.26/162.07 [6903]E(f331(f331(f22(a883),f331(f331(f81(a883),x69031),x69032)),f331(a118,x69033)),f331(f331(f22(a883),x69031),f331(a118,f331(f331(f22(a883),x69033),x69032))))+~P24(f331(f331(f247(a883),x69032),x69033))
% 162.26/162.07 [6904]~P111(x69041)+P24(f331(f331(f247(x69041),f2(x69041)),f331(f331(f262(x69041),f331(f76(x69041),x69042)),x69043)))
% 162.26/162.07 [6952]P20(x69521,x69522,x69523)+~P24(f331(f331(f247(f891(f882(x69521),a877)),x69523),x69522))
% 162.26/162.07 [6995]~P24(f331(f62(x69951),x69952))+P24(f331(f62(x69951),f331(f331(f22(f891(x69951,a877)),x69952),x69953)))
% 162.26/162.07 [6996]~P24(f331(f62(x69961),x69963))+P24(f331(f62(x69961),f331(f331(f108(f891(x69961,a877)),x69962),x69963)))
% 162.26/162.07 [6997]~P24(f331(f62(x69971),x69972))+P24(f331(f62(x69971),f331(f331(f108(f891(x69971,a877)),x69972),x69973)))
% 162.26/162.07 [7137]~P38(x71371,x71373)+P38(x71371,f331(f331(f108(f891(f890(x71371,x71371),a877)),x71372),x71373))
% 162.26/162.07 [7138]~P38(x71381,x71382)+P38(x71381,f331(f331(f108(f891(f890(x71381,x71381),a877)),x71382),x71383))
% 162.26/162.07 [7253]~P96(x72531)+E(f13(x72531,f331(f175(x72531),f331(f331(f154(x72531),x72532),x72533))),f331(f145(x72531,x72531,f107(x72531),x72532),x72533))
% 162.26/162.07 [7254]~P107(x72541)+E(f14(x72541,f331(f175(x72541),f331(f331(f154(x72541),x72542),x72543))),f331(f145(x72541,x72541,f251(x72541),x72542),x72543))
% 162.26/162.07 [7255]~P107(x72551)+E(f15(x72551,f331(f175(x72551),f331(f331(f154(x72551),x72552),x72553))),f331(f145(x72551,x72551,f246(x72551),x72552),x72553))
% 162.26/162.07 [7256]~P96(x72561)+E(f10(x72561,f331(f175(x72561),f331(f331(f154(x72561),x72562),x72563))),f331(f145(x72561,x72561,f108(x72561),x72562),x72563))
% 162.26/162.07 [7312]~P24(f331(f62(x73121),x73122))+P24(f331(f331(f247(a883),f331(f38(x73121),x73122)),f331(f38(x73121),f331(f331(f309(x73121),x73123),x73122))))
% 162.26/162.07 [7313]E(f331(f331(f107(f891(a883,a877)),f331(f301(a883,x73131),x73132)),f331(f301(a883,x73132),f331(f331(f81(a883),x73132),x73133))),f331(f301(a883,x73131),f331(f331(f81(a883),x73132),x73133)))+~P24(f331(f331(f247(a883),x73131),x73132))
% 162.26/162.07 [7321]P24(f331(f331(f248(a883),x73211),x73212))+~P24(f331(f331(f248(a883),f331(f331(f81(a883),x73211),x73213)),x73212))
% 162.26/162.07 [7324]P24(f331(f331(f247(a883),x73241),x73242))+~P24(f331(f331(f247(a883),f331(f331(f81(a883),x73243),x73241)),x73242))
% 162.26/162.07 [7325]P24(f331(f331(f247(a883),x73251),x73252))+~P24(f331(f331(f247(a883),f331(f331(f81(a883),x73251),x73253)),x73252))
% 162.26/162.07 [7366]~P107(x73661)+E(f11(x73661,f251(x73661),f331(f175(x73661),f331(f331(f154(x73661),x73662),x73663))),f331(f145(x73661,x73661,f251(x73661),x73662),x73663))
% 162.26/162.07 [7367]~P107(x73671)+E(f12(x73671,f246(x73671),f331(f175(x73671),f331(f331(f154(x73671),x73672),x73673))),f331(f145(x73671,x73671,f246(x73671),x73672),x73673))
% 162.26/162.07 [7371]~E(x73712,f196(f891(f890(x73711,x73711),a877)))+P24(f331(f331(f247(f891(f890(x73711,x73711),a877)),x73712),x73713))
% 162.26/162.07 [7479]E(f331(f331(f107(f891(x74791,a877)),x74792),f331(f331(f22(f891(x74791,a877)),x74793),x74792)),x74793)+~P24(f331(f331(f247(f891(x74791,a877)),x74792),x74793))
% 162.26/162.07 [7480]~P24(f331(f331(f248(a883),x74801),f331(f331(f22(a883),x74803),x74802)))+P24(f331(f331(f248(a883),f331(f331(f81(a883),x74801),x74802)),x74803))
% 162.26/162.07 [7481]~P24(f331(f331(f247(a883),x74811),f331(f331(f81(a883),x74813),x74812)))+P24(f331(f331(f247(a883),f331(f331(f22(a883),x74811),x74812)),x74813))
% 162.26/162.07 [7538]E(x75381,f119(x75382))+E(f331(f144(x75382),f331(f331(f331(f191(f884(x75382),f884(x75382)),x75383),f171(x75382)),x75381)),f331(f331(f168(x75382),x75381),f45(a883,x75383,f331(f197(f884(x75382)),x75381))))
% 162.26/162.07 [7547]E(f331(f331(f309(x75471),x75472),f331(f331(f22(f891(x75471,a877)),x75473),f331(f331(f309(x75471),x75472),f196(f891(x75471,a877))))),x75473)+~P24(f331(f331(f333(x75471),x75472),x75473))
% 162.26/162.07 [7704]P24(f331(f331(f248(a883),x77041),f331(f331(f22(a883),x77042),x77043)))+~P24(f331(f331(f248(a883),f331(f331(f81(a883),x77041),x77043)),x77042))
% 162.26/162.07 [7705]P24(f331(f331(f247(a883),x77051),f331(f331(f81(a883),x77052),x77053)))+~P24(f331(f331(f247(a883),f331(f331(f22(a883),x77051),x77053)),x77052))
% 162.26/162.07 [7727]P24(f331(f62(x77271),x77272))+~P24(f331(f62(x77271),f331(f331(f107(f891(x77271,a877)),x77273),x77272)))
% 162.26/162.07 [7728]P24(f331(f62(x77281),x77282))+~P24(f331(f62(x77281),f331(f331(f107(f891(x77281,a877)),x77282),x77283)))
% 162.26/162.07 [7806]~P45(x78061,x78063)+P24(f331(f331(f333(f890(x78061,x78061)),f331(f331(f261(x78061,x78061),x78062),x78062)),x78063))
% 162.26/162.07 [7931]E(f331(f331(f168(a883),f142(a883,f331(f301(a883,x79311),x79312))),x79313),f331(f331(f81(a883),x79311),x79313))+~P24(f331(f331(f248(a883),f331(f331(f81(a883),x79311),x79313)),x79312))
% 162.26/162.07 [7998]~P24(f331(f331(f203(f331(a28,x79981)),x79982),x79983))+P24(f331(f331(f203(f331(f244(a879),f331(a26,x79981))),x79982),x79983))
% 162.26/162.07 [8003]E(f331(f331(f176(a883),x80031),f142(a883,f331(f301(a883,x80032),x80033))),f142(a883,f331(f301(a883,x80032),f331(f331(f81(a883),x80032),x80031))))+~P24(f331(f331(f247(a883),f331(f331(f81(a883),x80032),x80031)),x80033))
% 162.26/162.07 [8269]P24(f331(f331(f203(f331(a28,x82691)),x82692),x82693))+~P24(f331(f331(f203(f331(f244(a879),f331(a26,x82691))),x82692),x82693))
% 162.26/162.07 [8325]E(f331(f331(f137(x83251),f331(f331(f176(x83251),x83252),x83253)),f331(f331(f154(x83251),f331(f331(f168(x83251),x83253),x83252)),f331(f331(f141(x83251),f331(a118,x83252)),x83253))),x83253)+~P24(f331(f331(f248(a883),x83252),f331(f197(f884(x83251)),x83253)))
% 162.26/162.07 [8333]P24(f331(f331(f247(f891(x83331,a877)),f319(x83331,x83332)),f319(x83331,x83333)))+~P24(f331(f331(f247(f891(x83331,f891(x83331,a877))),x83333),x83332))
% 162.26/162.07 [8335]~P53(x83351,x83352,x83353)+P53(x83351,x83352,f331(f331(f22(f891(f890(x83351,x83351),a877)),x83353),f307(x83351,f196(f891(f890(x83351,x83351),a877)))))
% 162.26/162.07 [8352]P24(f331(f331(f247(f891(x83521,a877)),f320(x83521,x83522)),f320(x83521,x83523)))+~P24(f331(f331(f247(f891(f890(x83521,x83521),a877)),x83523),x83522))
% 162.26/162.07 [8359]~P124(x83591)+P24(f331(f331(f247(x83591),f2(x83591)),f331(f331(f81(x83591),f331(f331(f82(x83591),x83592),x83592)),f331(f331(f82(x83591),x83593),x83593))))
% 162.26/162.07 [8394]P24(f331(f331(f247(f891(x83941,a877)),f331(f284(x83941),x83942)),f331(f284(x83941),x83943)))+~P24(f331(f331(f247(f891(f890(x83941,x83941),a877)),x83942),x83943))
% 162.26/162.07 [8424]~P49(x84241,x84242)+~P24(f331(f331(f333(f890(x84241,x84241)),f331(f331(f261(x84241,x84241),x84243),x84243)),x84242))
% 162.26/162.07 [8426]~P38(x84261,x84262)+~P24(f331(f331(f333(f890(x84261,x84261)),f331(f331(f261(x84261,x84261),x84263),x84263)),x84262))
% 162.26/162.07 [8488]P24(f331(f331(f247(f891(x84881,a877)),f41(f891(x84881,a877),x84882)),f41(f891(x84881,a877),x84883)))+~P24(f331(f331(f247(f891(f891(x84881,a877),a877)),x84883),x84882))
% 162.26/162.07 [8489]P24(f331(f331(f247(f891(x84891,a877)),f40(f891(x84891,a877),x84892)),f40(f891(x84891,a877),x84893)))+~P24(f331(f331(f247(f891(f891(x84891,a877),a877)),x84892),x84893))
% 162.26/162.07 [8545]~P6(x85451,x85453,x85452)+P24(f331(f331(f247(f891(f890(x85451,x85451),a877)),x85452),f331(f331(f268(x85451,x85451),x85453),f331(f16(f891(x85451,a877),x85451),x85453))))
% 162.26/162.07 [8546]~P48(x85461,x85463,x85462)+P24(f331(f331(f247(f891(f890(x85461,x85461),a877)),x85462),f331(f331(f268(x85461,x85461),x85463),f331(f16(f891(x85461,a877),x85461),x85463))))
% 162.26/162.07 [8591]~P83(x85911)+P24(f331(f331(f247(x85911),f331(f331(f22(x85911),f331(f76(x85911),x85912)),f331(f76(x85911),x85913))),f331(f76(x85911),f331(f331(f22(x85911),x85913),x85912))))
% 162.26/162.07 [8592]~P83(x85921)+P24(f331(f331(f247(x85921),f331(f331(f22(x85921),f331(f76(x85921),x85922)),f331(f76(x85921),x85923))),f331(f76(x85921),f331(f331(f22(x85921),x85922),x85923))))
% 162.26/162.07 [8623]P24(f331(f331(f247(f891(f890(x86231,x86231),a877)),f307(x86231,x86232)),f307(x86231,x86233)))+~P24(f331(f331(f247(f891(f890(x86231,x86231),a877)),x86232),x86233))
% 162.26/162.07 [8770]P53(x87701,x87702,x87703)+~P53(x87701,x87702,f331(f331(f22(f891(f890(x87701,x87701),a877)),x87703),f307(x87701,f196(f891(f890(x87701,x87701),a877)))))
% 162.26/162.07 [8788]P24(f331(f331(f247(f891(f890(f884(x87881),f884(x87881)),a877)),f161(x87881,x87882)),f161(x87881,x87883)))+~P24(f331(f331(f247(f891(f890(x87881,x87881),a877)),x87882),x87883))
% 162.26/162.07 [8789]P24(f331(f331(f247(f891(f890(f884(x87891),f884(x87891)),a877)),f160(x87891,x87892)),f160(x87891,x87893)))+~P24(f331(f331(f247(f891(f890(x87891,x87891),a877)),x87892),x87893))
% 162.26/162.07 [8810]~P48(x88101,x88103,x88102)+P24(f331(f331(f247(f891(f890(x88101,x88101),a877)),x88102),f331(f331(f288(x88101,x88101,x88101),f331(f286(x88101,x88101),x88102)),x88102)))
% 162.26/162.07 [8861]~P24(f331(f140(x88611),x88612))+E(f331(f139(x88611,f331(f331(f7(x88611,f891(x88611,a877),a877),f333(x88611)),f331(f175(x88611),f177(x88611,x88612,x88613)))),x88612),f177(x88611,x88612,x88613))
% 162.26/162.07 [8924]E(x89241,x89242)+~P24(f331(f331(f333(f890(x89243,x89243)),f331(f331(f261(x89243,x89243),x89241),x89242)),f307(x89243,f196(f891(f890(x89243,x89243),a877)))))
% 162.26/162.07 [9009]P24(f331(f331(f333(x90091),x90092),f320(x90091,x90093)))+P24(f331(f331(f333(f890(x90091,x90091)),f331(f331(f261(x90091,x90091),f521(x90093,x90092,x90091)),x90092)),x90093))
% 162.26/162.07 [9010]P24(f331(f331(f333(x90101),x90102),f320(x90101,x90103)))+P24(f331(f331(f333(f890(x90101,x90101)),f331(f331(f261(x90101,x90101),f730(x90103,x90102,x90101)),x90102)),x90103))
% 162.26/162.07 [9011]P24(f331(f331(f333(x90111),x90112),f320(x90111,x90113)))+P24(f331(f331(f333(f890(x90111,x90111)),f331(f331(f261(x90111,x90111),f739(x90113,x90112,x90111)),x90112)),x90113))
% 162.26/162.07 [9084]~P24(f331(f331(f333(f884(x90841)),x90843),f164(x90841,x90842)))+P24(f331(f163(x90841,f331(f331(f7(x90841,f891(x90841,a877),a877),f333(x90841)),x90842)),x90843))
% 162.26/162.07 [9111]P24(f331(x91113,x91112))+E(f331(f253(x91111),f331(f331(f18(x91111,a877,a877),f331(f331(f8(a877,f891(a877,a877),x91111),a329),f331(a328,x91112))),x91113)),f196(f891(x91111,a877)))
% 162.26/162.07 [9135]~P83(x91351)+P24(f331(f331(f247(x91351),f331(f76(x91351),f331(f331(f22(x91351),f331(f76(x91351),x91352)),f331(f76(x91351),x91353)))),f331(f76(x91351),f331(f331(f22(x91351),x91352),x91353))))
% 162.26/162.07 [9151]~P24(f331(x91513,x91512))+E(f331(f253(x91511),f331(f331(f18(x91511,a877,a877),f331(f331(f8(a877,f891(a877,a877),x91511),a329),f331(a328,x91512))),x91513)),f331(f331(f309(x91511),x91512),f196(f891(x91511,a877))))
% 162.26/162.07 [9158]~P24(f331(f331(f333(f891(x91581,a877)),x91583),f331(f308(x91581),x91582)))+P24(f331(f265(x91581,f331(f331(f7(x91581,f891(x91581,a877),a877),f333(x91581)),x91582)),x91583))
% 162.26/162.07 [9191]P38(x91911,x91912)+P24(f331(f331(f333(f890(x91911,x91911)),f331(f331(f261(x91911,x91911),f331(f578(x91912,x91911),f331(a118,x91913))),f331(f578(x91912,x91911),x91913))),x91912))
% 162.26/162.07 [9334]P24(f331(f331(f333(f884(x93341)),x93342),f164(x93341,x93343)))+~P24(f331(f163(x93341,f331(f331(f7(x93341,f891(x93341,a877),a877),f333(x93341)),x93343)),x93342))
% 162.26/162.07 [9347]P24(f331(f331(f333(f891(x93471,a877)),x93472),f331(f308(x93471),x93473)))+~P24(f331(f265(x93471,f331(f331(f7(x93471,f891(x93471,a877),a877),f333(x93471)),x93473)),x93472))
% 162.26/162.07 [9401]P24(f331(f331(f333(x94011),f331(f277(x94011,x94012),x94013)),f331(f175(x94011),f331(f331(f157(f890(a105,x94011),x94011),f269(a105,x94011)),x94012))))+~P24(f331(f331(f248(a105),x94013),f331(f169(a105),f331(f331(f157(f890(a105,x94011),a105),f260(a105,x94011)),x94012))))
% 162.26/162.07 [9447]P24(f331(f331(f247(f891(f890(f884(x94471),f884(x94471)),a877)),f161(x94471,x94472)),f331(f331(f268(f884(x94471),f884(x94471)),f164(x94471,x94473)),f331(f16(f891(f884(x94471),a877),f884(x94471)),f164(x94471,x94473)))))+~P24(f331(f331(f247(f891(f890(x94471,x94471),a877)),x94472),f331(f331(f268(x94471,x94471),x94473),f331(f16(f891(x94471,a877),x94471),x94473))))
% 162.26/162.07 [9468]P24(f331(f331(f333(x94681),f331(f260(x94681,f890(a105,a105)),f331(f275(x94681,x94682),x94683))),f331(f175(x94681),f331(f331(f157(f890(a105,x94681),x94681),f269(a105,x94681)),x94682))))+~P24(f331(f331(f248(a105),f2(a105)),f331(f169(a105),f331(f331(f157(f890(a105,x94681),a105),f260(a105,x94681)),x94682))))
% 162.26/162.07 [9493]~P24(f331(f331(f247(f891(f890(x94931,x94931),a877)),x94932),f331(f331(f268(x94931,x94931),x94933),f331(f16(f891(x94931,a877),x94931),x94933))))+P24(f331(f331(f247(f891(f890(x94931,x94931),a877)),f331(f331(f288(x94931,x94931,x94931),x94932),f307(x94931,x94932))),f331(f331(f268(x94931,x94931),x94933),f331(f16(f891(x94931,a877),x94931),x94933))))
% 162.26/162.07 [9822]~P38(x98221,x98222)+~P24(f331(f331(f333(f890(x98221,x98221)),f331(f331(f261(x98221,x98221),f331(x98223,f331(a118,f579(x98222,x98221,x98223)))),f331(x98223,f579(x98222,x98221,x98223)))),x98222))
% 162.26/162.07 [9823]~P38(x98231,x98232)+~P24(f331(f331(f333(f890(x98231,x98231)),f331(f331(f261(x98231,x98231),f331(x98233,f331(a118,f756(x98233,x98232,x98231)))),f331(x98233,f756(x98233,x98232,x98231)))),x98232))
% 162.26/162.07 [10053]P24(f331(f331(f247(f891(f890(f891(x100531,a877),f891(x100531,a877)),a877)),f331(f331(f288(f891(x100531,a877),f891(x100531,a877),f891(x100531,a877)),f324(x100531,x100532)),f331(f331(f107(f891(f890(f891(x100531,a877),f891(x100531,a877)),a877)),f324(x100531,x100533)),f331(f331(f309(f890(f891(x100531,a877),f891(x100531,a877))),f331(f331(f261(f891(x100531,a877),f891(x100531,a877)),f196(f891(x100531,a877))),f196(f891(x100531,a877)))),f196(f891(f890(f891(x100531,a877),f891(x100531,a877)),a877)))))),f324(x100531,x100532)))+~P24(f331(f331(f247(f891(f890(x100531,x100531),a877)),f331(f331(f288(x100531,x100531,x100531),x100532),x100533)),x100532))
% 162.26/162.07 [10054]P24(f331(f331(f247(f891(f890(f891(x100541,a877),f891(x100541,a877)),a877)),f331(f331(f288(f891(x100541,a877),f891(x100541,a877),f891(x100541,a877)),f322(x100541,x100542)),f331(f331(f107(f891(f890(f891(x100541,a877),f891(x100541,a877)),a877)),f322(x100541,x100543)),f331(f331(f309(f890(f891(x100541,a877),f891(x100541,a877))),f331(f331(f261(f891(x100541,a877),f891(x100541,a877)),f196(f891(x100541,a877))),f196(f891(x100541,a877)))),f196(f891(f890(f891(x100541,a877),f891(x100541,a877)),a877)))))),f322(x100541,x100542)))+~P24(f331(f331(f247(f891(f890(x100541,x100541),a877)),f331(f331(f288(x100541,x100541,x100541),x100542),x100543)),x100542))
% 162.26/162.07 [7252]~P24(f331(f331(f247(a883),x72522),x72521))+E(f331(f331(f22(a883),f331(a118,f331(f331(f22(a883),x72521),x72522))),x72523),f331(f331(f22(a883),f331(a118,x72521)),f331(f331(f81(a883),x72522),x72523)))
% 162.26/162.07 [7286]~P58(x72861)+E(f331(f331(f81(x72861),f45(x72861,x72862,x72863)),f331(f331(f82(x72861),f331(f331(f39(x72861),x72862),x72863)),x72863)),x72862)
% 162.26/162.07 [7485]E(f331(f331(f82(a883),f331(f110(a883),x74851)),f331(f331(f82(a883),f331(f110(a883),x74852)),x74853)),f331(f331(f82(a883),f331(f110(a883),f331(f331(f82(a1),x74851),x74852))),x74853))+P24(f331(f331(f248(a1),x74851),a84))
% 162.26/162.07 [7940]~P24(f331(f331(f247(a883),x79403),x79402))+P24(f331(f331(f247(a883),x79401),f331(f331(f22(a883),f331(f331(f81(a883),x79402),x79401)),x79403)))
% 162.26/162.07 [8151]~P24(f331(f331(f247(a883),x81511),x81512))+E(f331(f331(f137(a883),f142(a883,f331(f301(a883,x81511),x81512))),f142(a883,f331(f301(a883,x81512),f331(f331(f81(a883),x81512),x81513)))),f142(a883,f331(f301(a883,x81511),f331(f331(f81(a883),x81512),x81513))))
% 162.26/162.07 [8398]~P24(f331(f62(x83981),x83982))+E(f331(a118,f331(f38(x83981),f331(f331(f22(f891(x83981,a877)),x83982),f331(f331(f309(x83981),x83983),f196(f891(x83981,a877)))))),f331(f38(x83981),f331(f331(f309(x83981),x83983),x83982)))
% 162.26/162.07 [8450]~P24(f331(f62(x84501),x84502))+E(f331(f331(f81(a883),f79(a883)),f331(f38(x84501),f331(f331(f22(f891(x84501,a877)),x84502),f331(f331(f309(x84501),x84503),f196(f891(x84501,a877)))))),f331(f38(x84501),f331(f331(f309(x84501),x84503),x84502)))
% 162.26/162.07 [8632]E(f331(f331(f22(a883),f331(f38(x86321),x86322)),f331(f38(x86321),f331(f331(f108(f891(x86321,a877)),x86322),x86323))),f331(f38(x86321),f331(f331(f22(f891(x86321,a877)),x86322),x86323)))+~P24(f331(f62(x86321),f331(f331(f108(f891(x86321,a877)),x86322),x86323)))
% 162.26/162.07 [8856]~P28(f331(x88562,f396(x88562,x88563,x88561)))+E(f331(f106(a1),f331(f331(f9(x88561,a883),f331(f331(f8(a1,a883,x88561),a111),x88562)),x88563)),f331(f331(f9(x88561,a1),x88562),x88563))
% 162.26/162.07 [8857]~P28(f331(x88572,f457(x88572,x88573,x88571)))+E(f331(f106(a1),f331(f331(f6(x88571,a883),f331(f331(f8(a1,a883,x88571),a111),x88572)),x88573)),f331(f331(f6(x88571,a1),x88572),x88573))
% 162.26/162.07 [8906]~P24(f331(f62(x89061),x89063))+P24(f331(f331(f247(a883),f331(f331(f22(a883),f331(f38(x89061),x89062)),f331(f38(x89061),x89063))),f331(f38(x89061),f331(f331(f22(f891(x89061,a877)),x89062),x89063))))
% 162.26/162.07 [8932]P24(f331(f331(f333(x89321),f396(x89322,x89323,x89321)),x89323))+E(f331(f106(a1),f331(f331(f9(x89321,a883),f331(f331(f8(a1,a883,x89321),a111),x89322)),x89323)),f331(f331(f9(x89321,a1),x89322),x89323))
% 162.26/162.07 [8933]P24(f331(f331(f333(x89331),f457(x89332,x89333,x89331)),x89333))+E(f331(f106(a1),f331(f331(f6(x89331,a883),f331(f331(f8(a1,a883,x89331),a111),x89332)),x89333)),f331(f331(f6(x89331,a1),x89332),x89333))
% 162.26/162.07 [9001]E(f86(x90011,f331(f331(f7(x90011,f891(x90011,a877),a877),f333(x90011)),f331(f331(f22(f891(x90011,a877)),x90012),f331(f331(f309(x90011),x90013),f196(f891(x90011,a877)))))),f264(x90011,x90013,x90012))+P24(f331(f331(f247(f891(x90011,a877)),x90012),f331(f331(f309(x90011),x90013),f196(f891(x90011,a877)))))
% 162.26/162.07 [9348]E(f331(f331(f157(f884(x93481),x93481),f331(f331(f7(f884(x93481),a883,x93481),f168(x93481)),x93482)),f331(f139(f884(x93481),f331(f331(f8(a883,a877,f884(x93481)),f331(f248(a883),x93482)),f197(f884(x93481)))),x93483)),f331(f331(f168(f884(x93481)),f182(x93481,x93483)),x93482))+~P24(f331(f331(f248(a883),x93482),f331(f197(f884(f884(x93481))),f182(x93481,x93483))))
% 162.26/162.07 [9416]E(f331(f139(x94161,x94162),x94163),f179(x94161,x94162,x94163))+P24(f331(f331(f333(x94161),f686(x94163,x94162,x94161)),f331(f175(x94161),f331(f331(f141(x94161),f331(f197(f884(x94161)),f179(x94161,x94162,x94163))),x94163))))
% 162.26/162.07 [9568]E(f331(f331(f141(x95681),f331(f197(f884(x95681)),f179(x95681,x95682,x95683))),x95683),f119(x95681))+~P24(f331(x95682,f331(f144(x95681),f331(f331(f141(x95681),f331(f197(f884(x95681)),f179(x95681,x95682,x95683))),x95683))))
% 162.26/162.07 [9672]~P24(f331(f331(f333(f890(x96721,x96721)),x96722),f307(x96721,x96723)))+P24(f331(f331(f333(f890(x96721,x96721)),x96722),f331(f331(f42(a883,f891(f890(x96721,x96721),a877)),f256(f891(a883,a877))),f331(f331(f7(a883,f891(f890(x96721,x96721),a877),f891(f890(x96721,x96721),a877)),f191(f890(x96721,x96721),a877)),x96723))))
% 162.26/162.07 [9729]~P24(f331(f331(f247(f891(x97291,a877)),f331(f331(f42(a883,f891(x97291,a877)),f331(f301(a883,f2(a883)),f512(x97293,x97292,x97291))),x97292)),x97293))+P24(f331(f331(f247(f891(x97291,a877)),f331(f331(f42(a883,f891(x97291,a877)),f256(f891(a883,a877))),x97292)),x97293))
% 162.26/162.07 [9801]~P24(f331(f331(f248(a1),f2(a1)),x98013))+P24(f331(f331(f248(a1),x98011),f331(f331(f81(a1),x98012),f331(f331(f82(a1),f331(f331(f81(a1),f331(f76(a1),f331(f331(f22(a1),x98012),x98011))),f79(a1))),x98013))))
% 162.26/162.07 [9809]~P38(x98091,f331(f331(f107(f891(f890(x98091,x98091),a877)),x98092),x98093))+P38(x98091,f331(f331(f107(f891(f890(x98091,x98091),a877)),f331(f331(f107(f891(f890(x98091,x98091),a877)),f331(f331(f288(x98091,x98091,x98091),x98092),x98092)),f331(f331(f288(x98091,x98091,x98091),x98093),x98092))),x98093))
% 162.26/162.07 [9887]P38(x98871,f331(f331(f107(f891(f890(x98871,x98871),a877)),x98872),x98873))+~P38(x98871,f331(f331(f107(f891(f890(x98871,x98871),a877)),f331(f331(f107(f891(f890(x98871,x98871),a877)),f331(f331(f288(x98871,x98871,x98871),x98872),x98872)),f331(f331(f288(x98871,x98871,x98871),x98873),x98872))),x98873))
% 162.26/162.07 [9422]~P138(x94221)+E(f331(f109(x94221),f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),x94222),x94223)),f196(f891(f890(a883,a883),a877)))))),f331(f331(f22(x94221),f331(f106(x94221),x94222)),f331(f106(x94221),x94223)))
% 162.26/162.07 [9517]P24(f331(x95173,x95172))+E(f331(f253(x95171),f331(f331(f18(x95171,a877,a877),f331(f331(f8(a877,f891(a877,a877),x95171),a329),f331(f331(f7(x95171,x95171,a877),a328),x95172))),x95173)),f196(f891(x95171,a877)))
% 162.26/162.07 [9519]~P24(f331(x95193,x95192))+E(f331(f253(x95191),f331(f331(f18(x95191,a877,a877),f331(f331(f8(a877,f891(a877,a877),x95191),a329),f331(f331(f7(x95191,x95191,a877),a328),x95192))),x95193)),f331(f331(f309(x95191),x95192),f196(f891(x95191,a877))))
% 162.26/162.07 [9879]~P24(f331(f62(x98791),x98793))+E(f331(f331(f65(x98791,f891(x98791,a877),f331(f331(f8(f891(x98791,a877),f891(f891(x98791,a877),f891(x98791,a877)),x98791),f331(f7(f891(x98791,a877),f891(x98791,a877),f891(x98791,a877)),f22(f891(x98791,a877)))),f331(f331(f7(x98791,f891(x98791,a877),f891(x98791,a877)),f309(x98791)),f196(f891(x98791,a877))))),x98792),x98793),f331(f331(f22(f891(x98791,a877)),x98792),x98793))
% 162.26/162.07 [9910]~P24(f331(f331(f248(a1),f2(a1)),x99103))+P24(f331(f331(f248(a1),f331(f331(f22(a1),x99101),f331(f331(f82(a1),f331(f331(f81(a1),f331(f76(a1),f331(f331(f22(a1),x99101),x99102))),f79(a1))),x99103))),x99102))
% 162.26/162.07 [10147]~P24(f331(f331(f333(x101471),x101473),f320(x101471,x101472)))+P24(f331(f319(x101471,f331(f331(f7(x101471,f891(f890(x101471,x101471),a877),f891(x101471,a877)),f331(f331(f8(f891(x101471,f891(f891(f890(x101471,x101471),a877),a877)),f891(f891(f890(x101471,x101471),a877),f891(x101471,a877)),x101471),f7(x101471,f891(f890(x101471,x101471),a877),a877)),f331(f331(f8(f891(x101471,f890(x101471,x101471)),f891(x101471,f891(f891(f890(x101471,x101471),a877),a877)),x101471),f331(f8(f890(x101471,x101471),f891(f891(f890(x101471,x101471),a877),a877),x101471),f333(f890(x101471,x101471)))),f261(x101471,x101471)))),x101472)),x101473))
% 162.26/162.07 [10161]P24(f331(f331(f333(x101611),x101612),f320(x101611,x101613)))+~P24(f331(f319(x101611,f331(f331(f7(x101611,f891(f890(x101611,x101611),a877),f891(x101611,a877)),f331(f331(f8(f891(x101611,f891(f891(f890(x101611,x101611),a877),a877)),f891(f891(f890(x101611,x101611),a877),f891(x101611,a877)),x101611),f7(x101611,f891(f890(x101611,x101611),a877),a877)),f331(f331(f8(f891(x101611,f890(x101611,x101611)),f891(x101611,f891(f891(f890(x101611,x101611),a877),a877)),x101611),f331(f8(f890(x101611,x101611),f891(f891(f890(x101611,x101611),a877),a877),x101611),f333(f890(x101611,x101611)))),f261(x101611,x101611)))),x101613)),x101612))
% 162.26/162.07 [9727]~P24(f331(f62(x97271),f331(f253(x97271),x97273)))+P24(f331(f62(x97271),f331(f253(x97271),f331(f331(f18(x97271,a877,a877),f331(f331(f8(a877,f891(a877,a877),x97271),a329),x97272)),x97273))))
% 162.26/162.07 [9728]~P24(f331(f62(x97281),f331(f253(x97281),x97282)))+P24(f331(f62(x97281),f331(f253(x97281),f331(f331(f18(x97281,a877,a877),f331(f331(f8(a877,f891(a877,a877),x97281),a329),x97282)),x97283))))
% 162.26/162.07 [9840]P24(f331(f62(x98401),f331(f253(x98401),x98402)))+~P24(f331(f62(x98401),f331(f253(x98401),f331(f331(f18(x98401,a877,a877),f331(f331(f8(a877,f891(a877,a877),x98401),a330),x98403)),x98402))))
% 162.26/162.07 [9841]P24(f331(f62(x98411),f331(f253(x98411),x98412)))+~P24(f331(f62(x98411),f331(f253(x98411),f331(f331(f18(x98411,a877,a877),f331(f331(f8(a877,f891(a877,a877),x98411),a330),x98412)),x98413))))
% 162.26/162.07 [10109]~P24(f331(f62(x101091),x101092))+P24(f331(f62(f884(x101091)),f331(f253(f884(x101091)),f331(f331(f18(f884(x101091),a877,a877),f331(f331(f8(a877,f891(a877,a877),f884(x101091)),a329),f331(f331(f7(f884(x101091),f891(x101091,a877),a877),f331(f331(f8(f891(x101091,a877),f891(f891(x101091,a877),a877),f884(x101091)),f247(f891(x101091,a877))),f175(x101091))),x101092))),f331(f331(f7(f884(x101091),a883,a877),f331(f331(f8(a883,f891(a883,a877),f884(x101091)),a328),f197(f884(x101091)))),x101093)))))
% 162.26/162.07 [10110]~P24(f331(f62(x101101),x101102))+P24(f331(f62(f884(x101101)),f331(f253(f884(x101101)),f331(f331(f18(f884(x101101),a877,a877),f331(f331(f8(a877,f891(a877,a877),f884(x101101)),a329),f331(f331(f7(f884(x101101),f891(x101101,a877),a877),f331(f331(f8(f891(x101101,a877),f891(f891(x101101,a877),a877),f884(x101101)),f247(f891(x101101,a877))),f175(x101101))),x101102))),f331(f331(f7(f884(x101101),a883,a877),f331(f331(f8(a883,f891(a883,a877),f884(x101101)),f247(a883)),f197(f884(x101101)))),x101103)))))
% 162.26/162.07 [9388]~P94(x93881)+E(f331(f331(f262(x93881),x93882),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x93883)),x93883)),a103))),f331(f331(f89(x93881,x93881),f331(f331(f262(x93881),x93882),f331(f110(a883),x93883))),f331(f331(f18(x93881,x93881,x93881),f82(x93881)),f5(x93881))))
% 162.26/162.07 [10078]~P118(x100781)+E(f331(f331(f262(x100781),x100782),f331(f331(f82(a883),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x100783)),f331(f331(f82(x100781),f331(f331(f262(x100781),x100782),x100783)),f331(f331(f262(x100781),x100782),x100783)))
% 162.26/162.07 [10090]~P79(x100901)+E(f331(f331(f262(x100901),f331(f331(f262(x100901),x100902),x100903)),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f331(f331(f262(x100901),x100902),f331(f331(f82(a883),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x100903)))
% 162.26/162.07 [10125]~P138(x101251)+E(f331(f331(f262(x101251),f331(f80(x101251),x101252)),f331(f331(f82(a883),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x101253)),f331(f331(f262(x101251),x101252),f331(f331(f82(a883),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x101253)))
% 162.26/162.07 [10185]~P111(x101851)+P24(f331(f331(f247(x101851),f2(x101851)),f331(f331(f81(x101851),f331(f331(f262(x101851),x101852),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f331(f331(f262(x101851),x101853),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))))
% 162.26/162.07 [10133]~P118(x101331)+E(f331(f331(f262(x101331),x101332),f331(a118,f331(f331(f82(a883),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x101333))),f331(f331(f82(x101331),x101332),f331(f331(f82(x101331),f331(f331(f262(x101331),x101332),x101333)),f331(f331(f262(x101331),x101332),x101333))))
% 162.26/162.07 [10153]~P79(x101531)+E(f331(f331(f82(x101531),x101532),f331(f331(f262(x101531),f331(f331(f262(x101531),x101532),x101533)),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f331(f331(f262(x101531),x101532),f331(a118,f331(f331(f82(a883),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x101533))))
% 162.26/162.07 [10167]~P111(x101671)+P24(f331(f331(f247(x101671),f2(x101671)),f331(f331(f262(x101671),x101672),f331(f331(f82(a883),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x101673))))
% 162.26/162.07 [10204]~P94(x102041)+E(f331(f331(f22(x102041),f331(f331(f81(x102041),f331(f331(f262(x102041),x102042),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f331(f331(f262(x102041),x102043),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))),f331(f331(f82(x102041),f331(f331(f82(x102041),f331(f110(x102041),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x102042)),x102043)),f331(f331(f262(x102041),f331(f331(f22(x102041),x102042),x102043)),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))
% 162.26/162.07 [10205]~P94(x102051)+E(f331(f331(f81(x102051),f331(f331(f81(x102051),f331(f331(f262(x102051),x102052),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f331(f331(f262(x102051),x102053),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))),f331(f331(f82(x102051),f331(f331(f82(x102051),f331(f110(x102051),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x102052)),x102053)),f331(f331(f262(x102051),f331(f331(f81(x102051),x102052),x102053)),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))
% 162.26/162.07 [10232]~P30(x102321,x102322,x102323)+P24(f100(x102321,a877,f331(f331(f8(f891(a879,f891(f891(x102321,f891(a878,a877)),f891(x102321,a877))),f891(a879,f891(f891(x102321,f891(a878,a877)),a877)),f891(x102321,f891(a878,a877))),f331(f8(f891(f891(x102321,f891(a878,a877)),f891(x102321,a877)),f891(f891(x102321,f891(a878,a877)),a877),a879),f331(f8(f891(x102321,a877),a877,f891(x102321,f891(a878,a877))),f88(x102321)))),f331(f331(f8(f891(a879,f891(f891(x102321,f891(a878,a877)),f891(x102321,f891(a878,a877)))),f891(a879,f891(f891(x102321,f891(a878,a877)),f891(x102321,a877))),f891(x102321,f891(a878,a877))),f331(f8(f891(f891(x102321,f891(a878,a877)),f891(x102321,f891(a878,a877))),f891(f891(x102321,f891(a878,a877)),f891(x102321,a877)),a879),f331(f8(f891(x102321,f891(a878,a877)),f891(x102321,a877),f891(x102321,f891(a878,a877))),f331(f8(f891(a878,a877),a877,x102321),f88(a878))))),f331(f331(f7(f891(x102321,f891(a878,a877)),f891(a879,f891(f891(x102321,f891(a878,a877)),f891(x102321,f891(a878,a877)))),f891(a879,f891(f891(x102321,f891(a878,a877)),f891(x102321,f891(a878,a877))))),f331(f331(f8(f891(f891(f891(x102321,f891(a878,a877)),f891(x102321,f891(a878,a877))),f891(f891(x102321,f891(a878,a877)),f891(x102321,f891(a878,a877)))),f891(f891(a879,f891(f891(x102321,f891(a878,a877)),f891(x102321,f891(a878,a877)))),f891(a879,f891(f891(x102321,f891(a878,a877)),f891(x102321,f891(a878,a877))))),f891(x102321,f891(a878,a877))),f8(f891(f891(x102321,f891(a878,a877)),f891(x102321,f891(a878,a877))),f891(f891(x102321,f891(a878,a877)),f891(x102321,f891(a878,a877))),a879)),f331(f331(f8(f891(f891(x102321,f891(a878,a877)),f891(x102321,f891(a878,a877))),f891(f891(f891(x102321,f891(a878,a877)),f891(x102321,f891(a878,a877))),f891(f891(x102321,f891(a878,a877)),f891(x102321,f891(a878,a877)))),f891(x102321,f891(a878,a877))),f8(f891(x102321,f891(a878,a877)),f891(x102321,f891(a878,a877)),f891(x102321,f891(a878,a877)))),f331(f331(f8(f891(x102321,f891(f891(a878,a877),f891(a878,a877))),f891(f891(x102321,f891(a878,a877)),f891(x102321,f891(a878,a877))),f891(x102321,f891(a878,a877))),f18(x102321,f891(a878,a877),f891(a878,a877))),f331(f331(f8(f891(x102321,f891(a878,f891(a877,a877))),f891(x102321,f891(f891(a878,a877),f891(a878,a877))),f891(x102321,f891(a878,a877))),f331(f8(f891(a878,f891(a877,a877)),f891(f891(a878,a877),f891(a878,a877)),x102321),f18(a878,a877,a877))),f331(f8(f891(a878,a877),f891(a878,f891(a877,a877)),x102321),f331(f8(a877,f891(a877,a877),a878),a334))))))),f331(f331(f8(f891(f891(x102321,f891(a878,a877)),f891(x102321,f891(a878,f891(a878,a877)))),f891(f891(x102321,f891(a878,a877)),f891(x102321,f891(a878,a877))),a879),f331(f8(f891(x102321,f891(a878,f891(a878,a877))),f891(x102321,f891(a878,a877)),f891(x102321,f891(a878,a877))),f331(f8(f891(a878,f891(a878,a877)),f891(a878,a877),x102321),f331(f8(f891(a878,a877),a877,a878),f88(a878))))),f331(f331(f8(f891(f891(a878,a877),f891(a878,f891(a878,a877))),f891(f891(x102321,f891(a878,a877)),f891(x102321,f891(a878,f891(a878,a877)))),a879),f8(f891(a878,a877),f891(a878,f891(a878,a877)),x102321)),f331(f331(f8(f891(a878,f891(f891(a878,a877),f891(a878,a877))),f891(f891(a878,a877),f891(a878,f891(a878,a877))),a879),f7(a878,f891(a878,a877),f891(a878,a877))),f331(f331(f8(f891(a878,f891(a878,f891(a877,a877))),f891(a878,f891(f891(a878,a877),f891(a878,a877))),a879),f331(f8(f891(a878,f891(a877,a877)),f891(f891(a878,a877),f891(a878,a877)),a878),f18(a878,a877,a877))),f331(f331(f8(f891(a878,f891(a878,a877)),f891(a878,f891(a878,f891(a877,a877))),a879),f331(f8(f891(a878,a877),f891(a878,f891(a877,a877)),a878),f331(f8(a877,f891(a877,a877),a878),a334))),f331(f331(f7(a879,a883,f891(a878,f891(a878,a877))),f331(f331(f8(f891(a878,f891(a883,f891(a878,a877))),f891(a883,f891(a878,f891(a878,a877))),a879),f7(a878,a883,f891(a878,a877))),a205)),x102322))))))))),x102323))
% 162.26/162.07 [10234]P30(x102341,x102342,x102343)+~P24(f100(x102341,a877,f331(f331(f8(f891(a879,f891(f891(x102341,f891(a878,a877)),f891(x102341,a877))),f891(a879,f891(f891(x102341,f891(a878,a877)),a877)),f891(x102341,f891(a878,a877))),f331(f8(f891(f891(x102341,f891(a878,a877)),f891(x102341,a877)),f891(f891(x102341,f891(a878,a877)),a877),a879),f331(f8(f891(x102341,a877),a877,f891(x102341,f891(a878,a877))),f88(x102341)))),f331(f331(f8(f891(a879,f891(f891(x102341,f891(a878,a877)),f891(x102341,f891(a878,a877)))),f891(a879,f891(f891(x102341,f891(a878,a877)),f891(x102341,a877))),f891(x102341,f891(a878,a877))),f331(f8(f891(f891(x102341,f891(a878,a877)),f891(x102341,f891(a878,a877))),f891(f891(x102341,f891(a878,a877)),f891(x102341,a877)),a879),f331(f8(f891(x102341,f891(a878,a877)),f891(x102341,a877),f891(x102341,f891(a878,a877))),f331(f8(f891(a878,a877),a877,x102341),f88(a878))))),f331(f331(f7(f891(x102341,f891(a878,a877)),f891(a879,f891(f891(x102341,f891(a878,a877)),f891(x102341,f891(a878,a877)))),f891(a879,f891(f891(x102341,f891(a878,a877)),f891(x102341,f891(a878,a877))))),f331(f331(f8(f891(f891(f891(x102341,f891(a878,a877)),f891(x102341,f891(a878,a877))),f891(f891(x102341,f891(a878,a877)),f891(x102341,f891(a878,a877)))),f891(f891(a879,f891(f891(x102341,f891(a878,a877)),f891(x102341,f891(a878,a877)))),f891(a879,f891(f891(x102341,f891(a878,a877)),f891(x102341,f891(a878,a877))))),f891(x102341,f891(a878,a877))),f8(f891(f891(x102341,f891(a878,a877)),f891(x102341,f891(a878,a877))),f891(f891(x102341,f891(a878,a877)),f891(x102341,f891(a878,a877))),a879)),f331(f331(f8(f891(f891(x102341,f891(a878,a877)),f891(x102341,f891(a878,a877))),f891(f891(f891(x102341,f891(a878,a877)),f891(x102341,f891(a878,a877))),f891(f891(x102341,f891(a878,a877)),f891(x102341,f891(a878,a877)))),f891(x102341,f891(a878,a877))),f8(f891(x102341,f891(a878,a877)),f891(x102341,f891(a878,a877)),f891(x102341,f891(a878,a877)))),f331(f331(f8(f891(x102341,f891(f891(a878,a877),f891(a878,a877))),f891(f891(x102341,f891(a878,a877)),f891(x102341,f891(a878,a877))),f891(x102341,f891(a878,a877))),f18(x102341,f891(a878,a877),f891(a878,a877))),f331(f331(f8(f891(x102341,f891(a878,f891(a877,a877))),f891(x102341,f891(f891(a878,a877),f891(a878,a877))),f891(x102341,f891(a878,a877))),f331(f8(f891(a878,f891(a877,a877)),f891(f891(a878,a877),f891(a878,a877)),x102341),f18(a878,a877,a877))),f331(f8(f891(a878,a877),f891(a878,f891(a877,a877)),x102341),f331(f8(a877,f891(a877,a877),a878),a334))))))),f331(f331(f8(f891(f891(x102341,f891(a878,a877)),f891(x102341,f891(a878,f891(a878,a877)))),f891(f891(x102341,f891(a878,a877)),f891(x102341,f891(a878,a877))),a879),f331(f8(f891(x102341,f891(a878,f891(a878,a877))),f891(x102341,f891(a878,a877)),f891(x102341,f891(a878,a877))),f331(f8(f891(a878,f891(a878,a877)),f891(a878,a877),x102341),f331(f8(f891(a878,a877),a877,a878),f88(a878))))),f331(f331(f8(f891(f891(a878,a877),f891(a878,f891(a878,a877))),f891(f891(x102341,f891(a878,a877)),f891(x102341,f891(a878,f891(a878,a877)))),a879),f8(f891(a878,a877),f891(a878,f891(a878,a877)),x102341)),f331(f331(f8(f891(a878,f891(f891(a878,a877),f891(a878,a877))),f891(f891(a878,a877),f891(a878,f891(a878,a877))),a879),f7(a878,f891(a878,a877),f891(a878,a877))),f331(f331(f8(f891(a878,f891(a878,f891(a877,a877))),f891(a878,f891(f891(a878,a877),f891(a878,a877))),a879),f331(f8(f891(a878,f891(a877,a877)),f891(f891(a878,a877),f891(a878,a877)),a878),f18(a878,a877,a877))),f331(f331(f8(f891(a878,f891(a878,a877)),f891(a878,f891(a878,f891(a877,a877))),a879),f331(f8(f891(a878,a877),f891(a878,f891(a877,a877)),a878),f331(f8(a877,f891(a877,a877),a878),a334))),f331(f331(f7(a879,a883,f891(a878,f891(a878,a877))),f331(f331(f8(f891(a878,f891(a883,f891(a878,a877))),f891(a883,f891(a878,f891(a878,a877))),a879),f7(a878,a883,f891(a878,a877))),a205)),x102342))))))))),x102343))
% 162.26/162.07 [4705]E(x47051,x47052)+~E(f34(x47053,x47051),f34(x47054,x47052))
% 162.26/162.07 [4706]E(x47061,x47062)+~E(f34(x47061,x47063),f34(x47062,x47064))
% 162.26/162.07 [4707]E(x47071,x47072)+~E(f33(x47073,x47071),f33(x47074,x47072))
% 162.26/162.07 [4708]E(x47081,x47082)+~E(f33(x47081,x47083),f33(x47082,x47084))
% 162.26/162.07 [7747]P21(x77471,x77472,x77473,x77474)+~E(f471(x77474,x77473,x77472,x77471),f483(x77474,x77473,x77472,x77471))
% 162.26/162.07 [8035]P35(x80351,x80352,x80353,x80354,f119(x80352))+~E(x80354,f119(x80351))
% 162.26/162.07 [8036]P35(x80361,x80362,x80363,f119(x80361),x80364)+~E(x80364,f119(x80362))
% 162.26/162.07 [8254]~P21(x82541,f887(x82542),x82544,f186(x82541,x82542,x82544))+P21(x82541,f887(x82542),f187(x82541,x82542,x82543,x82544),f186(x82541,x82542,x82544))
% 162.26/162.07 [8464]~P21(x84641,f887(x84642),f187(x84641,x84642,x84644,x84643),f186(x84641,x84642,x84643))+P21(x84641,f887(x84642),x84643,f186(x84641,x84642,x84643))
% 162.26/162.07 [8581]~P35(x85812,x85813,x85814,x85811,f119(x85813))+E(x85811,f119(x85812))
% 162.26/162.07 [8582]~P35(x85823,x85822,x85824,f119(x85823),x85821)+E(x85821,f119(x85822))
% 162.26/162.07 [5077]~P13(x50773,x50771,x50774)+E(f331(f331(x50771,x50772),x50772),x50772)
% 162.26/162.07 [5369]~E(x53694,f196(f891(x53691,a877)))+E(f331(f310(x53691,x53692,x53693),x53694),f196(f891(x53692,a877)))
% 162.26/162.07 [5637]~E(f331(f310(x56372,x56373,x56374),x56371),f196(f891(x56373,a877)))+E(x56371,f196(f891(x56372,a877)))
% 162.26/162.07 [5920]~P107(x59202)+E(f331(f331(f151(x59201,x59202,x59203),x59204),f119(x59201)),f331(f331(f154(x59201),x59204),f119(x59201)))
% 162.26/162.07 [5957]E(f331(x59571,x59572),f199(x59573))+P24(f331(f331(f333(x59574),x59572),f186(x59574,x59573,x59571)))
% 162.26/162.07 [6277]~E(x62771,f196(f891(x62772,a877)))+~P24(f331(f63(x62772,x62773,x62771),x62774))
% 162.26/162.07 [6299]~P56(x62991,x62993,x62994,x62992)+P24(f331(f62(x62991),x62992))
% 162.26/162.07 [6300]~P56(x63001,x63003,x63002,x63004)+P24(f331(f62(x63001),x63002))
% 162.26/162.07 [6305]~P56(x63052,x63053,x63054,x63051)+~E(x63051,f196(f891(x63052,a877)))
% 162.26/162.07 [6336]~P108(x63361)+E(f331(f331(f108(f891(x63361,a877)),f331(f301(x63361,x63362),x63363)),f302(x63361,x63363,x63364)),f196(f891(x63361,a877)))
% 162.26/162.07 [6361]~P24(f331(f331(x63613,x63614),x63612))+P24(f331(f331(f333(x63611),x63612),f292(x63611,x63613,x63614)))
% 162.26/162.07 [6362]~P24(f331(f331(x63623,x63624),x63622))+P24(f331(f331(f333(x63621),x63622),f293(x63621,x63623,x63624)))
% 162.26/162.07 [6363]~P24(f331(f331(x63633,x63632),x63634))+P24(f331(f331(f333(x63631),x63632),f294(x63631,x63633,x63634)))
% 162.26/162.07 [6364]~P24(f331(f331(x63643,x63642),x63644))+P24(f331(f331(f333(x63641),x63642),f297(x63641,x63643,x63644)))
% 162.26/162.07 [6503]~P108(x65031)+E(f331(f331(f108(f891(x65031,a877)),f305(x65031,x65032,x65033)),f302(x65031,x65033,x65034)),f196(f891(x65031,a877)))
% 162.26/162.07 [6504]~P108(x65041)+E(f331(f331(f108(f891(x65041,a877)),f304(x65041,x65042,x65043)),f305(x65041,x65043,x65044)),f196(f891(x65041,a877)))
% 162.26/162.07 [6505]~P108(x65051)+E(f331(f331(f108(f891(x65051,a877)),f304(x65051,x65052,x65053)),f304(x65051,x65053,x65054)),f196(f891(x65051,a877)))
% 162.26/162.07 [6506]~P108(x65061)+E(f331(f331(f108(f891(x65061,a877)),f302(x65061,x65062,x65063)),f305(x65061,x65063,x65064)),f196(f891(x65061,a877)))
% 162.26/162.07 [6507]~P108(x65071)+E(f331(f331(f108(f891(x65071,a877)),f302(x65071,x65072,x65073)),f304(x65071,x65073,x65074)),f196(f891(x65071,a877)))
% 162.26/162.07 [6542]P24(f331(f331(x65421,x65422),f577(x65422,x65421)))+~P24(f331(f266(x65423,x65424,x65421),x65422))
% 162.26/162.07 [6591]~E(f331(x65911,x65912),f199(x65913))+~P24(f331(f331(f333(x65914),x65912),f186(x65914,x65913,x65911)))
% 162.26/162.07 [6620]~P107(x66202)+E(f331(f175(x66201),f153(x66201,x66202,x66203,x66204)),f331(f175(x66201),x66204))
% 162.26/162.07 [6672]~P143(x66721)+E(f198(x66721,x66722,f331(a118,x66723),x66724),f198(x66721,x66722,x66723,f331(x66722,x66724)))
% 162.26/162.07 [6732]~P24(f331(f331(f333(x67324),x67323),f292(x67324,x67321,x67322)))+P24(f331(f331(x67321,x67322),x67323))
% 162.26/162.07 [6733]~P24(f331(f331(f333(x67334),x67333),f293(x67334,x67331,x67332)))+P24(f331(f331(x67331,x67332),x67333))
% 162.26/162.07 [6734]~P24(f331(f331(f333(x67344),x67342),f294(x67344,x67341,x67343)))+P24(f331(f331(x67341,x67342),x67343))
% 162.26/162.07 [6735]~P24(f331(f331(f333(x67354),x67352),f297(x67354,x67351,x67353)))+P24(f331(f331(x67351,x67352),x67353))
% 162.26/162.07 [6806]E(f331(f38(f889(x68061,x68062)),f318(x68061,x68062,x68063,x68064)),f2(a883))+P24(f331(f62(x68062),x68064))
% 162.26/162.07 [6807]E(f331(f38(f889(x68071,x68072)),f318(x68071,x68072,x68073,x68074)),f2(a883))+P24(f331(f62(x68071),x68073))
% 162.26/162.07 [7004]~P11(x70044,x70041,x70042)+E(f331(f74(x70041,x70041,x70041,f331(x70042,x70043)),f331(x70042,x70043)),f331(x70042,x70043))
% 162.26/162.07 [7786]~P24(f331(x77861,x77864))+P24(f331(x77861,f97(x77862,a883,x77863,x77861)))
% 162.26/162.07 [7866]~E(x78662,x78663)+P24(f331(f331(f333(f890(x78661,x78661)),f331(f331(f261(x78661,x78661),x78662),x78663)),f307(x78661,x78664)))
% 162.26/162.07 [7895]~P21(x78951,x78952,x78953,f256(f891(x78951,a877)))+E(f331(f78(x78951,x78952,f256(f891(x78951,a877)),x78953),f331(x78953,x78954)),x78954)
% 162.26/162.07 [7981]~P24(f331(f331(f333(f884(x79811)),f331(f331(f154(x79811),x79814),x79812)),f164(x79811,x79813)))+P24(f331(f331(f333(f884(x79811)),x79812),f164(x79811,x79813)))
% 162.26/162.07 [7982]~P24(f331(f331(f333(f884(x79821)),f331(f331(f137(x79821),x79824),x79822)),f164(x79821,x79823)))+P24(f331(f331(f333(f884(x79821)),x79822),f164(x79821,x79823)))
% 162.26/162.07 [7983]~P24(f331(f331(f333(f884(x79831)),f331(f331(f137(x79831),x79832),x79834)),f164(x79831,x79833)))+P24(f331(f331(f333(f884(x79831)),x79832),f164(x79831,x79833)))
% 162.26/162.07 [7999]~P107(x79991)+P29(x79991,f331(f331(f157(x79992,x79991),x79993),f153(x79992,x79991,x79993,x79994)))
% 162.26/162.07 [8102]P21(x81024,x81023,x81021,x81022)+E(f331(x81021,f471(x81022,x81021,x81023,x81024)),f331(x81021,f483(x81022,x81021,x81023,x81024)))
% 162.26/162.07 [8116]E(f187(x81161,x81162,x81163,x81164),f187(x81161,x81162,x81164,x81163))+~E(f331(f331(f108(f891(x81161,a877)),f186(x81161,x81162,x81163)),f186(x81161,x81162,x81164)),f196(f891(x81161,a877)))
% 162.26/162.07 [8218]~P21(x82182,x82181,x82184,x82183)+P21(x82181,x82182,f78(x82182,x82181,x82183,x82184),f331(f310(x82182,x82181,x82184),x82183))
% 162.26/162.07 [8350]P38(f890(x83502,x83504),f283(x83502,x83504,x83501,x83503))+P24(f331(x83501,f583(x83502,x83503,x83504,x83501)))
% 162.26/162.07 [8471]E(x84711,x84712)+~P24(f331(f331(f333(f890(x84713,x84713)),f331(f331(f261(x84713,x84713),x84711),x84712)),f258(x84713,x84714)))
% 162.26/162.07 [8537]~P24(f331(f62(f889(x85373,x85371)),f318(x85373,x85371,x85374,x85372)))+P24(f331(f62(x85371),x85372))
% 162.26/162.07 [8538]~P24(f331(f62(f889(x85381,x85383)),f318(x85381,x85383,x85382,x85384)))+P24(f331(f62(x85381),x85382))
% 162.26/162.07 [8706]P38(f890(x87061,x87062),f283(x87061,x87062,x87063,x87064))+~P38(x87062,f331(x87064,f583(x87061,x87064,x87062,x87063)))
% 162.26/162.07 [9267]E(f331(f331(f162(x92671,x92672),f630(x92673,x92674,x92672,x92671)),f631(x92673,x92674,x92672,x92671)),x92674)+~P24(f331(f331(f333(f890(f884(x92671),f884(x92671))),f331(f331(f261(f884(x92671),f884(x92671)),x92672),x92674)),f160(x92671,x92673)))
% 162.26/162.07 [9268]~P24(f331(x92683,x92684))+P24(f331(f331(f247(a883),f331(x92681,f97(x92682,a883,x92681,x92683))),f331(x92681,x92684)))
% 162.26/162.07 [9277]~P24(f331(f331(f333(f890(f884(x92771),f884(x92771))),f331(f331(f261(f884(x92771),f884(x92771)),x92772),x92773)),f148(x92771,x92774)))+P24(f331(f331(f333(f890(f884(x92771),f884(x92771))),f331(f331(f261(f884(x92771),f884(x92771)),x92772),x92773)),f150(x92771,x92774)))
% 162.26/162.07 [9385]P24(f331(f62(x93851),x93852))+~P24(f331(f331(f333(f890(f891(x93851,a877),f891(x93851,a877))),f331(f331(f261(f891(x93851,a877),f891(x93851,a877)),x93853),x93852)),f322(x93851,x93854)))
% 162.26/162.07 [9386]P24(f331(f62(x93861),x93862))+~P24(f331(f331(f333(f890(f891(x93861,a877),f891(x93861,a877))),f331(f331(f261(f891(x93861,a877),f891(x93861,a877)),x93862),x93863)),f322(x93861,x93864)))
% 162.26/162.07 [9387]~E(x93871,f196(f891(x93872,a877)))+~P24(f331(f331(f333(f890(f891(x93872,a877),f891(x93872,a877))),f331(f331(f261(f891(x93872,a877),f891(x93872,a877)),x93873),x93871)),f322(x93872,x93874)))
% 162.26/162.07 [10034]P9(x100341,x100342,x100343,x100344)+~P24(f331(f331(f270(x100341,x100341,a877),f331(f331(f7(x100341,f891(x100341,x100342),f891(x100341,a877)),f331(f331(f8(f891(x100342,a877),f891(f891(x100341,x100342),f891(x100341,a877)),x100341),f8(x100342,a877,x100341)),f331(f331(f8(x100342,f891(x100342,a877),x100341),a328),x100344))),x100344)),f595(x100344,x100343,x100342,x100341)))
% 162.26/162.07 [4978]~E(x49784,f199(x49781))+E(f331(f331(f210(x49781,x49782),x49783),x49784),f199(x49782))
% 162.26/162.07 [4979]~E(x49794,f119(x49791))+E(f331(f331(f157(x49791,x49792),x49793),x49794),f119(x49792))
% 162.26/162.07 [4980]~E(x49802,f119(x49801))+E(f331(f331(f162(x49801,x49802),x49803),x49804),f119(x49801))
% 162.26/162.07 [5215]E(x52151,f199(x52152))+~E(f331(f331(f210(x52152,x52153),x52154),x52151),f199(x52153))
% 162.26/162.07 [5216]E(x52161,f119(x52162))+~E(f331(f331(f157(x52162,x52163),x52164),x52161),f119(x52163))
% 162.26/162.07 [5217]E(x52171,f119(x52172))+~E(f331(f331(f162(x52172,x52171),x52173),x52174),f119(x52172))
% 162.26/162.07 [5250]E(x52501,x52502)+~E(f331(f331(f137(x52503),x52504),x52501),f331(f331(f137(x52503),x52504),x52502))
% 162.26/162.07 [5251]E(x52511,x52512)+~E(f331(f331(f137(x52513),x52511),x52514),f331(f331(f137(x52513),x52512),x52514))
% 162.26/162.07 [5407]P24(f331(x54073,x54072))+E(f173(x54071,x54072,f331(f139(x54071,x54073),x54074)),f331(f139(x54071,x54073),x54074))
% 162.26/162.07 [5410]~P24(f331(x54102,x54103))+P34(x54101,x54102,f331(f331(f154(x54101),x54103),x54104))
% 162.26/162.07 [5419]E(x54191,x54192)+~E(f142(a883,f331(f301(a883,x54191),x54193)),f331(f331(f154(a883),x54192),x54194))
% 162.26/162.07 [5467]~P22(x54672,x54673)+P22(x54671,f331(f331(f75(x54672,x54671),x54673),x54674))
% 162.26/162.07 [5468]~P38(x54682,x54683)+P38(x54681,f331(f331(f287(x54682,x54681),x54683),x54684))
% 162.26/162.07 [5591]~P34(x55911,x55912,x55914)+P34(x55911,x55912,f331(f331(f154(x55911),x55913),x55914))
% 162.26/162.07 [5592]~P34(x55921,x55922,x55924)+P34(x55921,x55922,f331(f331(f137(x55921),x55923),x55924))
% 162.26/162.07 [5593]~P34(x55931,x55932,x55933)+P34(x55931,x55932,f331(f331(f137(x55931),x55933),x55934))
% 162.26/162.07 [5680]~E(x56801,f119(x56802))+~E(f331(f331(f137(x56802),x56803),f331(f331(f154(x56802),x56804),f119(x56802))),x56801)
% 162.26/162.07 [5705]~P32(x57053,x57051,f331(f331(f154(x57053),x57052),x57054))+P24(f331(x57051,x57052))
% 162.26/162.07 [5715]E(f120(x57151,x57152),x57153)+~E(f331(f331(f137(x57151),x57153),f331(f331(f154(x57151),x57154),f119(x57151))),x57152)
% 162.26/162.07 [5716]E(f147(x57161,x57162),x57163)+~E(f331(f331(f137(x57161),x57164),f331(f331(f154(x57161),x57163),f119(x57161))),x57162)
% 162.26/162.07 [5825]~E(f142(a883,f331(f301(a883,x58251),x58252)),f331(f331(f154(a883),x58253),x58254))+P24(f331(f331(f248(a883),x58251),x58252))
% 162.26/162.07 [5833]P32(x58331,x58332,x58333)+~P32(x58331,x58332,f331(f331(f154(x58331),x58334),x58333))
% 162.26/162.07 [5834]P32(x58341,x58342,x58343)+~P32(x58341,x58342,f331(f331(f137(x58341),x58344),x58343))
% 162.26/162.07 [5835]P32(x58351,x58352,x58353)+~P32(x58351,x58352,f331(f331(f137(x58351),x58353),x58354))
% 162.26/162.07 [6024]E(x60241,f331(f331(f137(x60242),f331(f172(x60242),x60243)),f331(f331(f154(x60242),x60244),f119(x60242))))+~E(f331(f172(x60242),x60241),f331(f331(f154(x60242),x60244),x60243))
% 162.26/162.07 [6198]~P108(x61981)+E(f331(f331(f108(f891(x61981,a877)),f331(f301(x61981,x61982),x61983)),f331(f301(x61981,x61983),x61984)),f196(f891(x61981,a877)))
% 162.26/162.07 [6235]~P74(x62351)+E(f331(f169(x62351),f331(f331(f157(a1,x62351),x62352),f181(x62353,x62354))),f331(f331(f6(a1,x62351),x62352),f331(f175(a1),f181(x62353,x62354))))
% 162.26/162.07 [6236]~P74(x62361)+E(f331(f331(f6(a1,x62361),x62362),f331(f175(a1),f181(x62363,x62364))),f331(f169(x62361),f331(f331(f157(a1,x62361),x62362),f181(x62363,x62364))))
% 162.26/162.07 [6376]~E(x63762,f331(f331(f137(x63761),f331(f172(x63761),x63764)),f331(f331(f154(x63761),x63763),f119(x63761))))+E(f331(f172(x63761),x63762),f331(f331(f154(x63761),x63763),x63764))
% 162.26/162.07 [6391]~P15(x63912,x63913,x63914,x63911)+E(f331(x63911,f196(f891(x63912,a877))),f35(x63913))
% 162.26/162.07 [6417]~P108(x64171)+E(f331(f331(f108(f891(x64171,a877)),f305(x64171,x64172,x64173)),f331(f301(x64171,x64173),x64174)),f196(f891(x64171,a877)))
% 162.26/162.07 [6621]E(x66211,f196(f891(x66212,a877)))+~E(f318(x66213,x66212,x66214,x66211),f196(f891(f889(x66213,x66212),a877)))
% 162.26/162.07 [6622]E(x66221,f196(f891(x66222,a877)))+~E(f318(x66222,x66223,x66221,x66224),f196(f891(f889(x66222,x66223),a877)))
% 162.26/162.07 [6691]~P107(x66912)+E(f331(f197(f884(x66911)),f153(x66911,x66912,x66913,x66914)),f331(f197(f884(x66911)),x66914))
% 162.26/162.07 [6703]~P24(f331(f267(x67033,x67034,x67031),x67032))+P24(f331(f331(x67031,f567(x67032,x67031)),x67032))
% 162.26/162.07 [6743]~P24(f331(f62(x67432),x67434))+P24(f331(f62(x67431),f331(f310(x67432,x67431,x67433),x67434)))
% 162.26/162.07 [6964]~P21(x69642,x69641,x69643,x69644)+E(f331(f38(x69641),f331(f310(x69642,x69641,x69643),x69644)),f331(f38(x69642),x69644))
% 162.26/162.07 [6983]E(f331(f310(x69831,x69832,x69833),f331(f311(x69831,x69832,x69833),x69834)),x69834)+~E(f331(f310(x69831,x69832,x69833),f256(f891(x69831,a877))),f256(f891(x69832,a877)))
% 162.26/162.07 [7380]~P21(x73801,x73802,x73803,f256(f891(x73801,a877)))+E(f331(f311(x73801,x73802,x73803),f331(f310(x73801,x73802,x73803),x73804)),x73804)
% 162.26/162.07 [7707]P24(f331(x77071,x77072))+~P24(f331(f331(f333(x77073),x77072),f331(f175(x77073),f179(x77073,x77071,x77074))))
% 162.26/162.07 [7818]~P24(f331(f331(f333(f884(x78181)),f331(f331(f154(x78181),x78182),x78184)),f164(x78181,x78183)))+P24(f331(f331(f333(x78181),x78182),x78183))
% 162.26/162.07 [7936]~P24(f331(f331(f333(x79361),x79362),f331(f175(x79361),f173(x79361,x79364,x79363))))+P24(f331(f331(f333(x79361),x79362),f331(f175(x79361),x79363)))
% 162.26/162.07 [7938]~P24(f331(f331(f333(x79381),x79382),f331(f175(x79381),f177(x79381,x79383,x79384))))+P24(f331(f331(f333(x79381),x79382),f331(f175(x79381),x79383)))
% 162.26/162.07 [7939]~P24(f331(f331(f333(x79391),x79392),f331(f175(x79391),f179(x79391,x79394,x79393))))+P24(f331(f331(f333(x79391),x79392),f331(f175(x79391),x79393)))
% 162.26/162.07 [7948]E(f331(f197(f884(x79481)),x79482),x79483)+~P24(f331(f331(f333(f884(x79481)),x79482),f331(f175(f884(x79481)),f55(x79481,x79483,x79484))))
% 162.26/162.07 [8053]P24(f331(x80533,x80532))+E(f331(f139(x80531,f331(f331(f8(a877,a877,x80531),a326),f331(a328,x80532))),f331(f139(x80531,x80533),x80534)),f331(f139(x80531,x80533),x80534))
% 162.26/162.07 [8168]E(f331(f331(f168(x81681),f179(x81681,x81682,x81683)),x81684),f331(f331(f168(x81681),x81683),x81684))+~P24(f331(f331(f248(a883),x81684),f331(f197(f884(x81681)),f179(x81681,x81682,x81683))))
% 162.26/162.07 [8252]~P74(x82521)+E(f331(f331(f6(a883,x82521),f331(f331(f8(a883,x82521,a883),x82522),a118)),f331(f301(a883,x82523),x82524)),f331(f331(f6(a883,x82521),x82522),f331(f301(a883,f331(a118,x82523)),f331(a118,x82524))))
% 162.26/162.07 [8261]~P74(x82611)+E(f331(f331(f6(a883,x82611),f331(f331(f8(a883,x82611,a883),x82612),a118)),f302(a883,x82613,x82614)),f331(f331(f6(a883,x82611),x82612),f302(a883,f331(a118,x82613),f331(a118,x82614))))
% 162.26/162.07 [8388]~P21(x83881,x83883,x83884,f256(f891(x83881,a877)))+P21(x83881,f891(x83882,x83883),f331(f331(f8(x83883,f891(x83882,x83883),x83881),f16(x83883,x83882)),x83884),f256(f891(x83881,a877)))
% 162.26/162.07 [8477]~P21(x84772,x84771,x84774,x84773)+E(f331(f310(x84771,x84772,f78(x84772,x84771,x84773,x84774)),f331(f310(x84772,x84771,x84774),x84773)),x84773)
% 162.26/162.07 [8539]~P24(f331(f331(f333(f890(x85391,x85391)),f331(f331(f261(x85391,x85391),x85392),x85394)),f258(x85391,x85393)))+P24(f331(f331(f333(x85391),x85392),x85393))
% 162.26/162.07 [8628]E(f331(f331(f331(f73(x86281,f887(x86282)),f331(f16(f887(x86282),x86281),f199(x86282))),x86283),f331(f239(x86282),f839(x86283,x86284,x86282,x86281))),x86284)+~E(f186(x86281,x86282,x86284),f331(f331(f309(x86281),x86283),f196(f891(x86281,a877))))
% 162.26/162.07 [8742]~E(f331(f331(f6(x87421,a883),x87424),x87423),f331(a118,x87422))+P24(f331(f331(f333(x87421),f719(x87422,x87423,x87424,x87421)),x87423))
% 162.26/162.07 [8762]~E(f331(f331(f6(x87624,a883),x87621),x87623),f331(a118,x87622))+P24(f331(f331(f248(a883),f2(a883)),f331(x87621,f719(x87622,x87623,x87621,x87624))))
% 162.26/162.07 [8773]~P24(f331(f62(x87732),x87734))+P24(f331(f331(f247(a883),f331(f38(x87731),f331(f310(x87732,x87731,x87733),x87734))),f331(f38(x87732),x87734)))
% 162.26/162.07 [8774]E(f331(f331(f261(x87741,x87742),f802(x87743,x87744,x87742,x87741)),f803(x87743,x87744,x87742,x87741)),x87744)+~P24(f331(f331(f333(f890(x87741,x87742)),x87744),f331(f286(x87742,x87741),x87743)))
% 162.26/162.07 [8782]P21(x87821,x87822,x87823,x87824)+P24(f331(f331(f333(x87821),f471(x87824,x87823,x87822,x87821)),x87824))
% 162.26/162.07 [8783]P21(x87831,x87832,x87833,x87834)+P24(f331(f331(f333(x87831),f483(x87834,x87833,x87832,x87831)),x87834))
% 162.26/162.07 [8847]P9(x88471,x88472,x88473,x88474)+P24(f331(f331(f333(f890(x88471,x88471)),f595(x88474,x88473,x88472,x88471)),x88473))
% 162.26/162.07 [8910]P24(f331(x89101,x89102))+~P24(f331(x89101,f331(f331(f261(x89103,x89104),f389(x89104,x89103,x89101)),f390(x89104,x89103,x89101))))
% 162.26/162.07 [8927]E(f331(f197(f884(x89271)),x89272),f331(f197(f884(x89271)),x89273))+~P24(f331(f331(f333(f890(f884(x89271),f884(x89271))),f331(f331(f261(f884(x89271),f884(x89271)),x89272),x89273)),f148(x89271,x89274)))
% 162.26/162.07 [8930]E(f331(f197(f884(x89301)),x89302),f331(f197(f884(x89301)),x89303))+~P24(f331(f331(f333(f890(f884(x89301),f884(x89301))),f331(f331(f261(f884(x89301),f884(x89301)),x89302),x89303)),f161(x89301,x89304)))
% 162.26/162.07 [8931]E(f331(f197(f884(x89311)),x89312),f331(f197(f884(x89311)),x89313))+~P24(f331(f331(f333(f890(f884(x89311),f884(x89311))),f331(f331(f261(f884(x89311),f884(x89311)),x89312),x89313)),f160(x89311,x89314)))
% 162.26/162.07 [9005]P24(f331(f331(f247(a883),f158(x90051,x90052,x90053)),f158(x90051,x90054,x90053)))+P24(f331(f331(f333(x90051),f628(x90054,x90052,x90053,x90051)),f331(f175(x90051),x90053)))
% 162.26/162.07 [9008]E(f331(f197(f884(x90081)),x90082),f331(f197(f884(x90081)),x90083))+~P24(f331(f331(f333(f890(f884(x90081),f884(x90081))),f331(f331(f261(f884(x90081),f884(x90081)),x90082),x90083)),f307(f884(x90081),f160(x90081,x90084))))
% 162.26/162.07 [9239]~P21(x92391,x92392,x92393,x92394)+~P24(f331(f331(f248(a883),f331(f38(x92392),f331(f310(x92391,x92392,x92393),x92394))),f331(f38(x92391),x92394)))
% 162.26/162.07 [9293]~P24(f331(f331(f333(f890(f884(x92931),f884(x92931))),f331(f331(f261(f884(x92931),f884(x92931)),x92932),x92933)),f160(x92931,x92934)))+P24(f331(f331(f333(f890(f884(x92931),f884(x92931))),f331(f331(f261(f884(x92931),f884(x92931)),x92932),x92933)),f161(x92931,f307(x92931,x92934))))
% 162.26/162.07 [9297]~P24(f331(f331(f333(f890(f884(x92971),f884(x92971))),f331(f331(f261(f884(x92971),f884(x92971)),x92972),x92973)),f161(x92971,x92974)))+P24(f331(f331(f333(f890(f884(x92971),f884(x92971))),f331(f331(f261(f884(x92971),f884(x92971)),x92972),x92973)),f307(f884(x92971),f160(x92971,x92974))))
% 162.26/162.07 [9309]P24(f331(f331(f333(f890(x93091,x93091)),f331(f331(f261(x93091,x93091),x93092),x93093)),f307(x93091,x93094)))+~P24(f331(f331(f333(f890(x93091,x93091)),f331(f331(f261(x93091,x93091),x93092),x93093)),f331(f331(f288(x93091,x93091,x93091),x93094),f307(x93091,x93094))))
% 162.26/162.07 [9494]E(f331(f331(f137(x94941),f650(x94942,x94943,x94944,x94941)),f331(f331(f154(x94941),f651(x94942,x94943,x94944,x94941)),f653(x94942,x94943,x94944,x94941))),x94944)+~P24(f331(f331(f333(f890(f884(x94941),f884(x94941))),f331(f331(f261(f884(x94941),f884(x94941)),x94944),x94943)),f160(x94941,x94942)))
% 162.26/162.07 [9495]E(f331(f331(f137(x94951),f650(x94952,x94953,x94954,x94951)),f331(f331(f154(x94951),f652(x94952,x94953,x94954,x94951)),f653(x94952,x94953,x94954,x94951))),x94953)+~P24(f331(f331(f333(f890(f884(x94951),f884(x94951))),f331(f331(f261(f884(x94951),f884(x94951)),x94954),x94953)),f160(x94951,x94952)))
% 162.26/162.07 [9575]P24(f331(f331(f333(f890(x95751,x95751)),f331(f331(f261(x95751,x95751),x95752),f787(x95753,x95754,x95752,x95751))),f307(x95751,x95753)))+~P24(f331(f331(f333(f890(x95751,x95751)),f331(f331(f261(x95751,x95751),x95752),x95754)),f331(f331(f288(x95751,x95751,x95751),x95753),f307(x95751,x95753))))
% 162.26/162.07 [9657]P24(f331(f331(f247(a883),f158(x96571,x96572,x96573)),f158(x96571,x96574,x96573)))+~P24(f331(f331(f248(a883),f331(x96572,f628(x96574,x96572,x96573,x96571))),f331(x96574,f628(x96574,x96572,x96573,x96571))))
% 162.26/162.07 [9723]P24(f331(f331(f333(f890(x97231,x97231)),f331(f331(f261(x97231,x97231),f772(x97232,x97233,x97234,x97231)),x97233)),f307(x97231,x97232)))+~P24(f331(f331(f333(f890(x97231,x97231)),f331(f331(f261(x97231,x97231),x97234),x97233)),f331(f331(f288(x97231,x97231,x97231),x97232),f307(x97231,x97232))))
% 162.26/162.07 [5231]~E(x52312,x52313)+E(f173(x52311,x52312,f331(f331(f154(x52311),x52313),x52314)),x52314)
% 162.26/162.07 [5361]P24(f331(x53612,x53613))+E(f179(x53611,x53612,f331(f331(f154(x53611),x53613),x53614)),f119(x53611))
% 162.26/162.07 [5431]~P86(x54312)+E(f331(f331(f80(f891(x54311,x54312)),x54313),x54314),f331(f80(x54312),f331(x54313,x54314)))
% 162.26/162.07 [5443]~E(x54432,f2(a883))+E(f331(f331(f141(x54431),x54432),f331(f331(f154(x54431),x54433),x54434)),f331(f331(f154(x54431),x54433),x54434))
% 162.26/162.07 [5444]P24(f331(x54442,x54443))+E(f331(f139(x54441,x54442),f331(f331(f154(x54441),x54443),x54444)),f331(f139(x54441,x54442),x54444))
% 162.26/162.07 [5574]~E(x55742,x55744)+P24(f331(f331(f331(f309(x55741),x55742),x55743),x55744))
% 162.26/162.07 [5582]E(x55821,f119(x55822))+E(f147(x55823,f331(f331(f157(x55822,x55823),x55824),x55821)),f331(x55824,f147(x55822,x55821)))
% 162.26/162.07 [5596]~E(x55961,f64(x55962,x55964))+E(f331(x55961,f331(f331(f309(x55962),x55963),f196(f891(x55962,a877)))),x55963)
% 162.26/162.07 [5632]E(x56321,f119(x56322))+E(f331(f144(x56323),f331(f331(f157(x56322,x56323),x56324),x56321)),f331(x56324,f331(f144(x56322),x56321)))
% 162.26/162.07 [5734]~P24(f331(x57343,x57344))+P24(f331(f331(f331(f309(x57341),x57342),x57343),x57344))
% 162.26/162.07 [5850]~P14(x58502,x58504,x58501)+E(f331(x58501,f331(f331(f309(x58502),x58503),f196(f891(x58502,a877)))),x58503)
% 162.26/162.07 [5874]~E(x58742,x58743)+P24(f331(f331(f333(x58741),x58742),f331(f331(f309(x58741),x58743),x58744)))
% 162.26/162.07 [5878]~P118(x58781)+E(f331(f331(f81(x58781),x58782),f331(f331(f81(x58781),x58783),x58784)),f331(f331(f81(x58781),x58783),f331(f331(f81(x58781),x58782),x58784)))
% 162.26/162.07 [5879]~P118(x58791)+E(f331(f331(f82(x58791),x58792),f331(f331(f82(x58791),x58793),x58794)),f331(f331(f82(x58791),x58793),f331(f331(f82(x58791),x58792),x58794)))
% 162.26/162.07 [5880]~P96(x58801)+E(f331(f331(f107(x58801),x58802),f331(f331(f107(x58801),x58803),x58804)),f331(f331(f107(x58801),x58803),f331(f331(f107(x58801),x58802),x58804)))
% 162.26/162.07 [5882]~P101(x58821)+E(f331(f331(f107(x58821),x58822),f331(f331(f107(x58821),x58823),x58824)),f331(f331(f107(x58821),x58823),f331(f331(f107(x58821),x58822),x58824)))
% 162.26/162.07 [5884]~P107(x58841)+E(f331(f331(f251(x58841),x58842),f331(f331(f251(x58841),x58843),x58844)),f331(f331(f251(x58841),x58843),f331(f331(f251(x58841),x58842),x58844)))
% 162.26/162.07 [5886]~P107(x58861)+E(f331(f331(f246(x58861),x58862),f331(f331(f246(x58861),x58863),x58864)),f331(f331(f246(x58861),x58863),f331(f331(f246(x58861),x58862),x58864)))
% 162.26/162.07 [5887]~P96(x58871)+E(f331(f331(f108(x58871),x58872),f331(f331(f108(x58871),x58873),x58874)),f331(f331(f108(x58871),x58873),f331(f331(f108(x58871),x58872),x58874)))
% 162.26/162.07 [5889]~P102(x58891)+E(f331(f331(f108(x58891),x58892),f331(f331(f108(x58891),x58893),x58894)),f331(f331(f108(x58891),x58893),f331(f331(f108(x58891),x58892),x58894)))
% 162.26/162.07 [5894]E(x58941,x58942)+E(f173(x58943,x58941,f331(f331(f154(x58943),x58942),x58944)),f331(f331(f154(x58943),x58942),f173(x58943,x58941,x58944)))
% 162.26/162.07 [5907]~P24(f331(x59072,x59073))+E(f331(f139(x59071,x59072),f331(f331(f154(x59071),x59073),x59074)),f331(f331(f154(x59071),x59073),f331(f139(x59071,x59072),x59074)))
% 162.26/162.07 [6044]~P24(f331(x60442,x60443))+E(f179(x60441,x60442,f331(f331(f154(x60441),x60443),x60444)),f331(f331(f154(x60441),x60443),f179(x60441,x60442,x60444)))
% 162.26/162.07 [6095]P20(x60951,x60952,x60953)+~P20(x60951,x60952,f331(f331(f309(f882(x60951)),x60954),x60953))
% 162.26/162.07 [6108]E(x61081,f196(f891(x61082,a877)))+E(f331(f331(f42(x61082,f891(x61083,a877)),x61081),f331(f16(f891(x61083,a877),x61082),x61084)),x61084)
% 162.26/162.07 [6109]E(x61091,f196(f891(x61092,a877)))+E(f331(f331(f43(x61092,f891(x61093,a877)),x61091),f331(f16(f891(x61093,a877),x61092),x61094)),x61094)
% 162.26/162.07 [6118]~E(x61184,f196(f891(x61182,a877)))+E(f331(f331(f268(x61181,x61182),x61183),f331(f16(f891(x61182,a877),x61181),x61184)),f196(f891(f890(x61181,x61182),a877)))
% 162.26/162.07 [6119]~E(x61193,f196(f891(x61191,a877)))+E(f331(f331(f268(x61191,x61192),x61193),f331(f16(f891(x61192,a877),x61191),x61194)),f196(f891(f890(x61191,x61192),a877)))
% 162.26/162.07 [6167]E(x61671,f2(a883))+E(f331(f331(f141(x61672),x61671),f331(f331(f154(x61672),x61673),x61674)),f331(f331(f141(x61672),f331(f331(f22(a883),x61671),f79(a883))),x61674))
% 162.26/162.07 [6192]E(x61921,f196(f891(x61922,a877)))+E(f331(f310(x61922,x61923,f331(f16(x61923,x61922),x61924)),x61921),f331(f331(f309(x61923),x61924),f196(f891(x61923,a877))))
% 162.26/162.07 [6195]E(f331(f311(x61951,x61952,f331(f16(x61952,x61951),x61953)),x61954),f196(f891(x61951,a877)))+P24(f331(f331(f333(x61952),x61953),x61954))
% 162.26/162.07 [6261]~E(x62613,f196(f891(x62611,a877)))+E(f331(f331(f42(x62611,f891(x62612,a877)),x62613),f331(f16(f891(x62612,a877),x62611),x62614)),f196(f891(x62612,a877)))
% 162.26/162.07 [6262]~E(x62623,f196(f891(x62621,a877)))+E(f331(f331(f43(x62621,f891(x62622,a877)),x62623),f331(f16(f891(x62622,a877),x62621),x62624)),f256(f891(x62622,a877)))
% 162.26/162.07 [6264]~P58(x62641)+E(f45(x62641,f331(f331(f82(x62641),x62642),x62643),f331(f331(f82(x62641),x62642),x62644)),f331(f331(f82(x62641),x62642),f45(x62641,x62643,x62644)))
% 162.26/162.07 [6427]E(f331(f311(x64271,x64272,f331(f16(x64272,x64271),x64273)),x64274),f256(f891(x64271,a877)))+~P24(f331(f331(f333(x64272),x64273),x64274))
% 162.26/162.07 [6450]~P24(f331(f331(f333(x64501),x64502),x64504))+P24(f331(f331(f333(x64501),x64502),f331(f331(f309(x64501),x64503),x64504)))
% 162.26/162.07 [6455]P24(f331(x64551,x64552))+~P24(f331(f163(x64553,x64551),f331(f331(f154(x64553),x64552),x64554)))
% 162.26/162.07 [6464]~E(x64643,f331(f331(f22(a883),f331(f197(f884(x64641)),x64642)),f79(a883)))+E(f120(x64641,f331(f331(f162(x64641,x64642),x64643),x64644)),f120(x64641,x64642))
% 162.26/162.07 [6482]~P107(x64821)+E(f331(f331(f108(f891(x64821,a877)),f331(f300(x64821),x64822)),f302(x64821,x64823,x64824)),f302(x64821,x64823,f331(f331(f251(x64821),x64822),x64824)))
% 162.26/162.07 [6483]~P107(x64831)+E(f331(f331(f108(f891(x64831,a877)),f331(f255(x64831),x64832)),f302(x64831,x64833,x64834)),f302(x64831,f331(f331(f246(x64831),x64832),x64833),x64834))
% 162.26/162.07 [6498]E(f331(f331(f108(f891(x64981,a877)),x64982),f331(f331(f309(x64981),x64983),x64984)),f331(f331(f108(f891(x64981,a877)),x64982),x64984))+P24(f331(f331(f333(x64981),x64983),x64982))
% 162.26/162.07 [6510]E(f173(x65101,x65102,f331(f331(f137(x65101),x65103),x65104)),f331(f331(f137(x65101),x65103),f173(x65101,x65102,x65104)))+P24(f331(f331(f333(x65101),x65102),f331(f175(x65101),x65103)))
% 162.26/162.07 [6514]~P79(x65141)+E(f331(f331(f82(x65141),f331(f331(f262(x65141),x65142),x65143)),f331(f331(f262(x65141),x65142),x65144)),f331(f331(f262(x65141),x65142),f331(f331(f81(a883),x65143),x65144)))
% 162.26/162.07 [6515]~P118(x65151)+E(f331(f331(f82(x65151),f331(f331(f262(x65151),x65152),x65153)),f331(f331(f262(x65151),x65152),x65154)),f331(f331(f262(x65151),x65152),f331(f331(f81(a883),x65153),x65154)))
% 162.26/162.07 [6549]~P118(x65491)+E(f331(f331(f81(x65491),f331(f331(f82(x65491),x65492),x65493)),f331(f331(f82(x65491),x65492),x65494)),f331(f331(f82(x65491),x65492),f331(f331(f81(x65491),x65493),x65494)))
% 162.26/162.07 [6550]~P99(x65501)+E(f331(f331(f108(x65501),f331(f331(f107(x65501),x65502),x65503)),f331(f331(f107(x65501),x65502),x65504)),f331(f331(f107(x65501),x65502),f331(f331(f108(x65501),x65503),x65504)))
% 162.26/162.07 [6551]~P107(x65511)+E(f331(f331(f246(x65511),f331(f331(f251(x65511),x65512),x65513)),f331(f331(f251(x65511),x65512),x65514)),f331(f331(f251(x65511),x65512),f331(f331(f246(x65511),x65513),x65514)))
% 162.26/162.07 [6552]~P107(x65521)+E(f331(f331(f251(x65521),f331(f331(f246(x65521),x65522),x65523)),f331(f331(f246(x65521),x65522),x65524)),f331(f331(f246(x65521),x65522),f331(f331(f251(x65521),x65523),x65524)))
% 162.26/162.07 [6553]~P99(x65531)+E(f331(f331(f107(x65531),f331(f331(f108(x65531),x65532),x65533)),f331(f331(f108(x65531),x65532),x65534)),f331(f331(f108(x65531),x65532),f331(f331(f107(x65531),x65533),x65534)))
% 162.26/162.07 [6585]~P58(x65851)+E(f45(x65851,f331(f331(f82(x65851),x65852),x65853),f331(f331(f82(x65851),x65854),x65853)),f331(f331(f82(x65851),f45(x65851,x65852,x65854)),x65853))
% 162.26/162.07 [6588]~E(f331(f197(f884(x65881)),x65883),f331(f197(f884(x65882)),x65884))+E(f331(f331(f157(f890(x65881,x65882),x65882),f269(x65881,x65882)),f331(f331(f184(x65881,x65882),x65883),x65884)),x65884)
% 162.26/162.07 [6589]~E(f331(f197(f884(x65891)),x65893),f331(f197(f884(x65892)),x65894))+E(f331(f331(f157(f890(x65891,x65892),x65891),f260(x65891,x65892)),f331(f331(f184(x65891,x65892),x65893),x65894)),x65893)
% 162.26/162.07 [6595]P24(f331(f163(x65951,x65952),x65953))+~P24(f331(f163(x65951,x65952),f331(f331(f154(x65951),x65954),x65953)))
% 162.26/162.07 [6596]P24(f331(f163(x65961,x65962),x65963))+~P24(f331(f163(x65961,x65962),f331(f331(f137(x65961),x65964),x65963)))
% 162.26/162.07 [6597]P24(f331(f163(x65971,x65972),x65973))+~P24(f331(f163(x65971,x65972),f331(f331(f137(x65971),x65973),x65974)))
% 162.26/162.07 [6602]~P59(x66021)+E(f45(x66021,f331(f331(f22(x66021),x66022),f45(x66021,x66023,x66024)),x66024),f45(x66021,f331(f331(f22(x66021),x66022),x66023),x66024))
% 162.26/162.07 [6604]~P58(x66041)+E(f45(x66041,f331(f331(f82(x66041),x66042),f45(x66041,x66043,x66044)),x66044),f45(x66041,f331(f331(f82(x66041),x66042),x66043),x66044))
% 162.26/162.07 [6605]~P58(x66051)+E(f45(x66051,f331(f331(f81(x66051),x66052),f45(x66051,x66053,x66054)),x66054),f45(x66051,f331(f331(f81(x66051),x66052),x66053),x66054))
% 162.26/162.07 [6685]~P107(x66851)+E(f331(f331(f108(f891(x66851,a877)),f302(x66851,x66852,x66853)),f331(f300(x66851),x66854)),f302(x66851,x66852,f331(f331(f251(x66851),x66853),x66854)))
% 162.26/162.07 [6686]~P107(x66861)+E(f331(f331(f108(f891(x66861,a877)),f302(x66861,x66862,x66863)),f331(f255(x66861),x66864)),f302(x66861,f331(f331(f246(x66861),x66862),x66864),x66863))
% 162.26/162.07 [6689]~E(f331(f197(f884(x66891)),x66893),f331(f197(f884(x66892)),x66894))+E(f331(f331(f184(x66891,x66892),f331(f172(x66891),x66893)),f331(f172(x66892),x66894)),f331(f172(f890(x66891,x66892)),f331(f331(f184(x66891,x66892),x66893),x66894)))
% 162.26/162.07 [6699]E(x66991,f331(f331(f22(a883),f331(f197(f884(x66992)),x66993)),f79(a883)))+E(f120(x66992,f331(f331(f162(x66992,x66993),x66991),x66994)),f331(f331(f162(x66992,f120(x66992,x66993)),x66991),x66994))
% 162.26/162.07 [6714]~P24(f331(f140(x67142),x67144))+P24(f331(f140(f890(x67141,x67142)),f331(f331(f184(x67141,x67142),x67143),x67144)))
% 162.26/162.07 [6715]~P24(f331(f140(x67151),x67153))+P24(f331(f140(f890(x67151,x67152)),f331(f331(f184(x67151,x67152),x67153),x67154)))
% 162.26/162.07 [6967]E(f331(f331(f39(a883),x69671),x69672),x69673)+~P24(f331(f48(x69671,x69672),f331(f331(f261(a883,a883),x69673),x69674)))
% 162.26/162.07 [6991]E(f45(a883,x69911,x69912),x69913)+~P24(f331(f48(x69911,x69912),f331(f331(f261(a883,a883),x69914),x69913)))
% 162.26/162.07 [6994]P24(f331(f140(x69941),x69942))+~P24(f331(f140(x69943),f331(f331(f157(x69941,x69943),x69944),x69942)))
% 162.26/162.07 [7002]~P20(x70021,x70022,f331(f331(f309(f882(x70021)),x70023),x70024))+P20(x70021,x70022,f331(f331(f309(f882(x70021)),x70023),f196(f891(f882(x70021),a877))))
% 162.26/162.07 [7008]P24(f331(f331(f203(x70081),x70082),x70083))+~P24(f331(f331(f331(f331(a205,x70081),x70082),x70084),x70083))
% 162.26/162.07 [7079]E(f173(x70791,x70792,f331(f331(f137(x70791),x70793),x70794)),f331(f331(f137(x70791),f173(x70791,x70792,x70793)),x70794))+~P24(f331(f331(f333(x70791),x70792),f331(f175(x70791),x70793)))
% 162.26/162.07 [7169]~P59(x71691)+E(f45(x71691,f331(f331(f22(x71691),f45(x71691,x71692,x71693)),x71694),x71693),f45(x71691,f331(f331(f22(x71691),x71692),x71694),x71693))
% 162.26/162.07 [7172]~P58(x71721)+E(f45(x71721,f331(f331(f81(x71721),f45(x71721,x71722,x71723)),x71724),x71723),f45(x71721,f331(f331(f81(x71721),x71722),x71724),x71723))
% 162.26/162.07 [7173]~P58(x71731)+E(f45(x71731,f331(f331(f82(x71731),f45(x71731,x71732,x71733)),x71734),x71733),f45(x71731,f331(f331(f82(x71731),x71732),x71734),x71733))
% 162.26/162.07 [7352]~E(x73521,f331(f331(f154(x73522),x73523),x73524))+~P24(f331(f331(f247(a883),f331(f197(f884(x73522)),x73521)),f331(f197(f884(x73522)),x73524)))
% 162.26/162.07 [7427]~E(f331(f180(x74271,x74272),x74273),f331(f180(x74271,x74272),x74274))+E(f331(f310(f890(x74271,x74272),x74271,f260(x74271,x74272)),f331(f175(f890(x74271,x74272)),x74273)),f331(f310(f890(x74271,x74272),x74271,f260(x74271,x74272)),f331(f175(f890(x74271,x74272)),x74274)))
% 162.26/162.07 [7558]P21(x75581,x75582,x75583,f331(f175(x75581),x75584))+~P24(f331(f140(x75582),f331(f331(f157(x75581,x75582),x75583),x75584)))
% 162.26/162.07 [7630]~P24(f331(f331(f247(f891(x76301,a877)),x76302),x76304))+P24(f331(f331(f247(f891(x76301,a877)),x76302),f331(f331(f309(x76301),x76303),x76304)))
% 162.26/162.07 [7663]~P59(x76631)+E(f45(x76631,f331(f331(f22(x76631),f45(x76631,x76632,x76633)),f45(x76631,x76634,x76633)),x76633),f45(x76631,f331(f331(f22(x76631),x76632),x76634),x76633))
% 162.26/162.07 [7664]~P58(x76641)+E(f45(x76641,f331(f331(f81(x76641),f45(x76641,x76642,x76643)),f45(x76641,x76644,x76643)),x76643),f45(x76641,f331(f331(f81(x76641),x76642),x76644),x76643))
% 162.26/162.07 [7665]~P58(x76651)+E(f45(x76651,f331(f331(f82(x76651),f45(x76651,x76652,x76653)),f45(x76651,x76654,x76653)),x76653),f45(x76651,f331(f331(f82(x76651),x76652),x76654),x76653))
% 162.26/162.07 [7763]P24(f331(f331(f331(f331(a205,x77631),x77632),f331(a118,x77633)),x77634))+~P24(f331(f331(f331(f331(a205,x77631),x77632),x77633),x77634))
% 162.26/162.07 [7772]~E(f331(x77724,f350(x77724,x77723,x77721,x77722)),f196(f891(x77722,a877)))+E(f331(f331(f42(x77721,f891(x77722,a877)),x77723),x77724),f196(f891(x77722,a877)))
% 162.26/162.07 [7773]~E(f331(x77734,f498(x77734,x77733,x77731,x77732)),f256(f891(x77732,a877)))+E(f331(f331(f43(x77731,f891(x77732,a877)),x77733),x77734),f256(f891(x77732,a877)))
% 162.26/162.07 [7774]~E(f331(x77744,f358(x77744,x77743,x77742,x77741)),f196(f891(x77742,a877)))+E(f331(f331(f42(x77741,f891(x77742,a877)),x77743),x77744),f196(f891(x77742,a877)))
% 162.26/162.07 [7775]~E(f331(x77754,f507(x77754,x77753,x77752,x77751)),f256(f891(x77752,a877)))+E(f331(f331(f43(x77751,f891(x77752,a877)),x77753),x77754),f256(f891(x77752,a877)))
% 162.26/162.07 [8169]P24(f331(x81691,x81692))+~P24(f331(f331(f333(x81693),x81692),f331(f331(f108(f891(x81693,a877)),x81694),f331(f253(x81693),x81691))))
% 162.26/162.07 [8207]~P24(f331(f331(f247(f891(x82071,a877)),x82073),x82074))+P24(f331(f331(f247(f891(x82071,a877)),f331(f331(f309(x82071),x82072),x82073)),f331(f331(f309(x82071),x82072),x82074)))
% 162.26/162.07 [8370]P24(f331(f331(f203(x83701),x83702),f456(x83703,x83702,x83704,x83701)))+~P24(f331(f331(f203(f34(x83701,x83704)),x83702),x83703))
% 162.26/162.07 [8379]P24(f331(x83792,x83793))+E(f331(f331(f141(x83791),f331(f197(f884(x83791)),f179(x83791,x83792,f331(f331(f154(x83791),x83793),x83794)))),f331(f331(f154(x83791),x83793),x83794)),f331(f331(f154(x83791),x83793),x83794))
% 162.26/162.07 [8491]~P24(f331(f331(f248(a883),f331(x84914,x84912)),f331(x84914,x84913)))+P24(f331(f331(f333(f890(x84911,x84911)),f331(f331(f261(x84911,x84911),x84912),x84913)),f331(f331(f287(a883,x84911),a252),x84914)))
% 162.26/162.07 [8584]~P24(f331(x85842,f720(x85844,x85842,x85843,x85841)))+E(f179(x85841,x85842,f331(f331(f137(x85841),x85843),x85844)),f331(f331(f137(x85841),x85843),f179(x85841,x85842,x85844)))
% 162.26/162.07 [8649]P21(f884(x86491),f884(x86492),f331(f157(x86491,x86492),x86493),x86494)+~P21(x86491,x86492,x86493,f40(f891(x86491,a877),f331(f310(f884(x86491),f891(x86491,a877),f175(x86491)),x86494)))
% 162.26/162.07 [8714]~P24(f331(x87142,x87143))+E(f331(f331(f141(x87141),f331(f197(f884(x87141)),f179(x87141,x87142,f331(f331(f154(x87141),x87143),x87144)))),f331(f331(f154(x87141),x87143),x87144)),f331(f331(f141(x87141),f331(f197(f884(x87141)),f179(x87141,x87142,x87144))),x87144))
% 162.26/162.07 [8754]~E(x87542,x87543)+E(f331(f139(x87541,f331(f331(f8(a877,a877,x87541),a326),f331(a328,x87542))),f331(f331(f154(x87541),x87543),x87544)),f331(f139(x87541,f331(f331(f8(a877,a877,x87541),a326),f331(a328,x87542))),x87544))
% 162.26/162.07 [8763]E(f331(f331(f42(x87631,f891(x87632,a877)),x87633),x87634),f196(f891(x87632,a877)))+P24(f331(f331(f333(x87631),f350(x87634,x87633,x87631,x87632)),x87633))
% 162.26/162.07 [8764]E(f331(f331(f43(x87641,f891(x87642,a877)),x87643),x87644),f256(f891(x87642,a877)))+P24(f331(f331(f333(x87641),f498(x87644,x87643,x87641,x87642)),x87643))
% 162.26/162.07 [8765]E(f331(f331(f42(x87651,f891(x87652,a877)),x87653),x87654),f196(f891(x87652,a877)))+P24(f331(f331(f333(x87651),f358(x87654,x87653,x87652,x87651)),x87653))
% 162.26/162.07 [8766]E(f331(f331(f43(x87661,f891(x87662,a877)),x87663),x87664),f256(f891(x87662,a877)))+P24(f331(f331(f333(x87661),f507(x87664,x87663,x87662,x87661)),x87663))
% 162.26/162.07 [8804]P24(f331(f331(f248(a883),f331(x88041,x88042)),f331(x88041,x88043)))+~P24(f331(f331(f333(f890(x88044,x88044)),f331(f331(f261(x88044,x88044),x88042),x88043)),f331(f331(f287(a883,x88044),a252),x88041)))
% 162.26/162.07 [8826]E(f179(x88261,x88262,f331(f331(f137(x88261),x88263),x88264)),f331(f331(f137(x88261),x88263),f179(x88261,x88262,x88264)))+P24(f331(f331(f333(x88261),f720(x88264,x88262,x88263,x88261)),f331(f175(x88261),x88263)))
% 162.26/162.07 [8864]P24(f331(f331(f203(x88641),f456(x88642,x88643,x88641,x88644)),x88642))+~P24(f331(f331(f203(f34(x88644,x88641)),x88643),x88642))
% 162.26/162.07 [8994]P24(f331(f331(f333(x89941),f462(x89942,x89943,x89944,x89941)),x89943))+~P24(f331(f331(f333(f891(x89941,a877)),x89944),f331(f331(f61(x89941),x89943),x89942)))
% 162.26/162.07 [8997]E(x89971,x89972)+~P24(f331(f331(f333(f890(x89973,x89973)),f331(f331(f261(x89973,x89973),x89971),x89972)),f331(f331(f191(f890(x89973,x89973),a877),f2(a883)),x89974)))
% 162.26/162.07 [9062]E(f331(f285(x90621,x90621,x90622),f331(f331(f309(x90621),f462(x90622,x90623,x90624,x90621)),f196(f891(x90621,a877)))),x90624)+~P24(f331(f331(f333(f891(x90621,a877)),x90624),f331(f331(f61(x90621),x90623),x90622)))
% 162.26/162.07 [9068]~P24(f331(f331(f333(f890(x90681,x90681)),f331(f331(f261(x90681,x90681),x90683),x90682)),f307(x90681,x90684)))+P24(f331(f331(f333(f890(x90681,x90681)),f331(f331(f261(x90681,x90681),x90682),x90683)),f307(x90681,f331(f286(x90681,x90681),x90684))))
% 162.26/162.07 [9080]~P58(x90801)+E(f331(f331(f81(x90801),f331(f331(f81(x90801),f331(f331(f82(x90801),x90802),f331(f331(f39(x90801),x90803),x90802))),f45(x90801,x90803,x90802))),x90804),f331(f331(f81(x90801),x90803),x90804))
% 162.26/162.07 [9095]~P24(f331(f331(f333(x90951),x90953),x90954))+P24(f331(f331(f333(f891(x90951,a877)),f331(f285(x90951,x90951,x90952),f331(f331(f309(x90951),x90953),f196(f891(x90951,a877))))),f331(f331(f61(x90951),x90954),x90952)))
% 162.26/162.07 [9107]P24(f331(f331(f333(f890(x91071,x91071)),f331(f331(f261(x91071,x91071),x91072),x91073)),f307(x91071,x91074)))+~P24(f331(f331(f333(f890(x91071,x91071)),f331(f331(f261(x91071,x91071),x91073),x91072)),f307(x91071,f331(f286(x91071,x91071),x91074))))
% 162.26/162.07 [9202]E(f331(f331(f162(x92021,f331(f172(x92021),x92022)),f331(f331(f22(a883),f331(f331(f22(a883),f331(f197(f884(x92021)),x92022)),x92023)),f79(a883))),x92024),f331(f172(x92021),f331(f331(f162(x92021,x92022),x92023),x92024)))+~P24(f331(f331(f248(a883),x92023),f331(f197(f884(x92021)),x92022)))
% 162.26/162.07 [9205]~P24(f331(x92052,f711(x92054,x92052,x92053,x92051)))+E(f331(f331(f141(x92051),f331(f197(f884(x92051)),f179(x92051,x92052,f331(f331(f137(x92051),x92053),x92054)))),f331(f331(f137(x92051),x92053),x92054)),f331(f331(f141(x92051),f331(f197(f884(x92051)),f179(x92051,x92052,x92054))),x92054))
% 162.26/162.07 [9245]~P21(x92452,x92451,x92453,f256(f891(x92452,a877)))+P24(f331(f331(f247(f891(x92451,a877)),f331(f310(x92452,x92451,x92453),f331(f80(f891(x92452,a877)),x92454))),f331(f80(f891(x92451,a877)),f331(f310(x92452,x92451,x92453),x92454))))
% 162.26/162.07 [9258]~P27(x92581)+E(f331(f145(x92581,x92582,f331(f7(x92582,x92581,x92581),f331(f331(f8(x92581,f891(x92581,x92581),x92582),f107(x92581)),x92583)),f196(x92581)),x92584),f331(f331(f42(x92582,x92581),f331(f175(x92582),x92584)),x92583))
% 162.26/162.07 [9259]~P27(x92591)+E(f331(f145(x92591,x92592,f331(f7(x92592,x92591,x92591),f331(f331(f8(x92591,f891(x92591,x92591),x92592),f108(x92591)),x92593)),f256(x92591)),x92594),f331(f331(f43(x92592,x92591),f331(f175(x92592),x92594)),x92593))
% 162.26/162.07 [9273]E(f331(f331(f141(x92731),f331(f197(f884(x92731)),f179(x92731,x92732,f331(f331(f137(x92731),x92733),x92734)))),f331(f331(f137(x92731),x92733),x92734)),f331(f331(f141(x92731),f331(f197(f884(x92731)),f179(x92731,x92732,x92734))),x92734))+P24(f331(f331(f333(x92731),f711(x92734,x92732,x92733,x92731)),f331(f175(x92731),x92733)))
% 162.26/162.07 [9342]~P24(f331(f331(f333(f890(f884(x93424),f884(x93424))),f331(f331(f261(f884(x93424),f884(x93424)),x93423),x93422)),f160(x93424,x93421)))+P24(f331(f331(f248(a883),f630(x93421,x93422,x93423,x93424)),f331(f197(f884(x93424)),x93423)))
% 162.26/162.07 [9343]~P58(x93431)+E(f331(f331(f81(x93431),f331(f331(f81(x93431),f331(f331(f82(x93431),f331(f331(f39(x93431),x93432),x93433)),x93433)),f45(x93431,x93432,x93433))),x93434),f331(f331(f81(x93431),x93432),x93434))
% 162.26/162.07 [9375]~P24(f331(f331(f333(f890(f884(x93751),f884(x93751))),f331(f331(f261(f884(x93751),f884(x93751)),x93752),x93753)),f331(f286(f884(x93751),f884(x93751)),f160(x93751,x93754))))+P24(f331(f331(f333(f890(f884(x93751),f884(x93751))),f331(f331(f261(f884(x93751),f884(x93751)),x93752),x93753)),f160(x93751,f331(f286(x93751,x93751),x93754))))
% 162.26/162.07 [9376]P24(f331(f331(f333(f890(f884(x93761),f884(x93761))),f331(f331(f261(f884(x93761),f884(x93761)),x93762),x93763)),f331(f286(f884(x93761),f884(x93761)),f160(x93761,x93764))))+~P24(f331(f331(f333(f890(f884(x93761),f884(x93761))),f331(f331(f261(f884(x93761),f884(x93761)),x93762),x93763)),f160(x93761,f331(f286(x93761,x93761),x93764))))
% 162.26/162.07 [9403]~P24(f331(f331(f333(x94031),x94033),f331(f259(x94031,x94032),x94034)))+P24(f331(f331(f333(f890(x94031,x94032)),f331(f331(f261(x94031,x94032),x94033),f581(x94034,x94032,x94033,x94031))),x94034))
% 162.26/162.07 [9404]~P24(f331(f331(f333(x94041),x94043),f331(f259(x94041,x94042),x94044)))+P24(f331(f331(f333(f890(x94041,x94042)),f331(f331(f261(x94041,x94042),x94043),f582(x94044,x94042,x94043,x94041))),x94044))
% 162.26/162.07 [9525]~P24(f331(f62(f887(x95251)),f331(f310(x95252,f887(x95251),x95253),f256(f891(x95252,a877)))))+P24(f331(f62(f887(x95251)),f331(f310(x95252,f887(x95251),f187(x95252,x95251,x95253,f331(f180(x95252,x95251),x95254))),f256(f891(x95252,a877)))))
% 162.26/162.07 [9570]~P24(f331(f331(f333(f890(x95701,x95701)),f331(f331(f261(x95701,x95701),x95702),x95704)),f331(f331(f288(x95701,x95701,x95701),x95703),f307(x95701,x95703))))+P24(f331(f331(f333(f890(x95701,x95701)),f331(f331(f261(x95701,x95701),x95702),f772(x95703,x95704,x95702,x95701))),x95703))
% 162.26/162.07 [9762]~P24(f331(f331(f333(f890(x97622,x97621)),x97624),f331(f286(x97621,x97622),x97623)))+P24(f331(f331(f333(f890(x97621,x97622)),f331(f331(f261(x97621,x97622),f803(x97623,x97624,x97621,x97622)),f802(x97623,x97624,x97621,x97622))),x97623))
% 162.26/162.07 [9793]~P24(f331(f331(f333(f890(f884(x97931),f884(x97931))),f331(f331(f261(f884(x97931),f884(x97931)),x97934),x97933)),f160(x97931,x97932)))+P24(f331(f331(f333(f890(x97931,x97931)),f331(f331(f261(x97931,x97931),f651(x97932,x97933,x97934,x97931)),f652(x97932,x97933,x97934,x97931))),x97932))
% 162.26/162.07 [9881]~P24(f331(f331(f333(f890(f884(x98811),f884(x98811))),f331(f331(f261(f884(x98811),f884(x98811)),x98812),x98814)),f160(x98811,x98813)))+P24(f331(f331(f333(f890(x98811,x98811)),f331(f331(f261(x98811,x98811),f331(f331(f168(x98811),x98812),f630(x98813,x98814,x98812,x98811))),f631(x98813,x98814,x98812,x98811))),x98813))
% 162.26/162.07 [9902]~P24(f331(f62(x99022),x99024))+E(f331(f331(f331(f66(f891(x99021,a877),x99022,f107(f891(x99021,a877))),f331(f331(f7(x99022,f891(x99021,a877),f891(x99021,a877)),f331(f331(f8(x99021,f891(f891(x99021,a877),f891(x99021,a877)),x99022),f309(x99021)),x99023)),f196(f891(x99021,a877)))),f196(f891(x99021,a877))),x99024),f331(f310(x99022,x99021,x99023),x99024))
% 162.26/162.07 [9982]~P21(x99821,x99822,x99823,f256(f891(x99821,a877)))+P24(f331(f331(f247(f891(x99821,a877)),f331(f311(x99821,x99822,x99823),f331(f331(f309(x99822),x99824),f196(f891(x99822,a877))))),f331(f331(f309(x99821),f86(x99821,f331(f331(f7(x99821,x99822,a877),f331(f331(f8(x99822,f891(x99822,a877),x99821),a328),x99823)),x99824))),f196(f891(x99821,a877)))))
% 162.26/162.07 [5641]~E(f331(f331(f137(x56411),x56412),x56414),x56413)+E(f331(f331(f176(x56411),f331(f197(f884(x56411)),x56412)),x56413),x56412)
% 162.26/162.07 [5642]~E(f331(f331(f137(x56422),x56423),x56421),x56424)+E(x56421,f331(f331(f141(x56422),f331(f197(f884(x56422)),x56423)),x56424))
% 162.26/162.07 [5653]~E(x56534,f2(a883))+E(f331(f331(f168(x56531),f331(f331(f154(x56531),x56532),x56533)),x56534),x56532)
% 162.26/162.07 [6180]~P118(x61801)+E(f331(f331(f262(x61801),f331(f331(f262(x61801),x61802),x61803)),x61804),f331(f331(f262(x61801),x61802),f331(f331(f82(a883),x61803),x61804)))
% 162.26/162.07 [6181]~P79(x61811)+E(f331(f331(f262(x61811),f331(f331(f262(x61811),x61812),x61813)),x61814),f331(f331(f262(x61811),x61812),f331(f331(f82(a883),x61813),x61814)))
% 162.26/162.07 [6193]E(x61931,f2(a883))+E(f331(f331(f168(x61932),f331(f331(f154(x61932),x61933),x61934)),x61931),f331(f331(f168(x61932),x61934),f331(f331(f22(a883),x61931),f79(a883))))
% 162.26/162.07 [6219]~P119(x62191)+E(f331(f331(f289(x62191),f331(f331(f82(x62191),x62192),x62193)),x62194),f331(f331(f82(x62191),x62192),f331(f331(f289(x62191),x62193),x62194)))
% 162.26/162.07 [6220]~P69(x62201)+E(f331(f331(f81(x62201),f331(f331(f81(x62201),x62202),x62203)),x62204),f331(f331(f81(x62201),x62202),f331(f331(f81(x62201),x62203),x62204)))
% 162.26/162.07 [6221]~P118(x62211)+E(f331(f331(f81(x62211),f331(f331(f81(x62211),x62212),x62213)),x62214),f331(f331(f81(x62211),x62212),f331(f331(f81(x62211),x62213),x62214)))
% 162.26/162.07 [6222]~P71(x62221)+E(f331(f331(f82(x62221),f331(f331(f82(x62221),x62222),x62223)),x62224),f331(f331(f82(x62221),x62222),f331(f331(f82(x62221),x62223),x62224)))
% 162.26/162.07 [6223]~P118(x62231)+E(f331(f331(f82(x62231),f331(f331(f82(x62231),x62232),x62233)),x62234),f331(f331(f82(x62231),x62232),f331(f331(f82(x62231),x62233),x62234)))
% 162.26/162.07 [6225]~P96(x62251)+E(f331(f331(f107(x62251),f331(f331(f107(x62251),x62252),x62253)),x62254),f331(f331(f107(x62251),x62252),f331(f331(f107(x62251),x62253),x62254)))
% 162.26/162.07 [6227]~P101(x62271)+E(f331(f331(f107(x62271),f331(f331(f107(x62271),x62272),x62273)),x62274),f331(f331(f107(x62271),x62272),f331(f331(f107(x62271),x62273),x62274)))
% 162.26/162.07 [6229]~P107(x62291)+E(f331(f331(f251(x62291),f331(f331(f251(x62291),x62292),x62293)),x62294),f331(f331(f251(x62291),x62292),f331(f331(f251(x62291),x62293),x62294)))
% 162.26/162.07 [6231]~P107(x62311)+E(f331(f331(f246(x62311),f331(f331(f246(x62311),x62312),x62313)),x62314),f331(f331(f246(x62311),x62312),f331(f331(f246(x62311),x62313),x62314)))
% 162.26/162.07 [6232]~P96(x62321)+E(f331(f331(f108(x62321),f331(f331(f108(x62321),x62322),x62323)),x62324),f331(f331(f108(x62321),x62322),f331(f331(f108(x62321),x62323),x62324)))
% 162.26/162.07 [6234]~P102(x62341)+E(f331(f331(f108(x62341),f331(f331(f108(x62341),x62342),x62343)),x62344),f331(f331(f108(x62341),x62342),f331(f331(f108(x62341),x62343),x62344)))
% 162.26/162.07 [6245]~P58(x62451)+E(f45(x62451,f331(f331(f81(x62451),x62452),f331(f331(f82(x62451),x62453),x62454)),x62454),f45(x62451,x62452,x62454))
% 162.26/162.07 [6246]~P58(x62461)+E(f45(x62461,f331(f331(f81(x62461),x62462),f331(f331(f82(x62461),x62463),x62464)),x62463),f45(x62461,x62462,x62463))
% 162.26/162.07 [6377]E(f331(f331(f168(x63771),f331(f331(f176(x63771),x63772),x63773)),x63774),f331(f331(f168(x63771),x63773),x63774))+~P24(f331(f331(f248(a883),x63774),x63772))
% 162.26/162.07 [6547]~P118(x65471)+E(f331(f331(f81(x65471),f331(f331(f81(x65471),x65472),x65473)),x65474),f331(f331(f81(x65471),f331(f331(f81(x65471),x65472),x65474)),x65473))
% 162.26/162.07 [6548]~P118(x65481)+E(f331(f331(f82(x65481),f331(f331(f82(x65481),x65482),x65483)),x65484),f331(f331(f82(x65481),f331(f331(f82(x65481),x65482),x65484)),x65483))
% 162.26/162.07 [6608]~P143(x66082)+E(f331(f331(f6(x66081,x66082),f331(f16(x66082,x66081),x66083)),x66084),f331(f331(f82(x66082),f331(f106(x66082),f331(f38(x66081),x66084))),x66083))
% 162.26/162.07 [6771]E(f331(f331(f108(f891(x67711,a877)),f331(f331(f309(x67711),x67712),x67713)),x67714),f331(f331(f108(f891(x67711,a877)),x67713),x67714))+P24(f331(f331(f333(x67711),x67712),x67714))
% 162.26/162.07 [6837]~P77(x68371)+E(f331(f331(f251(x68371),f331(f331(f22(x68371),x68372),x68373)),f331(f331(f22(x68371),x68374),x68373)),f331(f331(f22(x68371),f331(f331(f251(x68371),x68372),x68374)),x68373))
% 162.26/162.07 [6838]~P77(x68381)+E(f331(f331(f246(x68381),f331(f331(f22(x68381),x68382),x68383)),f331(f331(f22(x68381),x68384),x68383)),f331(f331(f22(x68381),f331(f331(f246(x68381),x68382),x68384)),x68383))
% 162.26/162.07 [6839]~P81(x68391)+E(f331(f331(f251(x68391),f331(f331(f81(x68391),x68392),x68393)),f331(f331(f81(x68391),x68394),x68393)),f331(f331(f81(x68391),f331(f331(f251(x68391),x68392),x68394)),x68393))
% 162.26/162.07 [6840]~P81(x68401)+E(f331(f331(f246(x68401),f331(f331(f81(x68401),x68402),x68403)),f331(f331(f81(x68401),x68404),x68403)),f331(f331(f81(x68401),f331(f331(f246(x68401),x68402),x68404)),x68403))
% 162.26/162.07 [6841]~P113(x68411)+E(f331(f331(f81(x68411),f331(f331(f82(x68411),x68412),x68413)),f331(f331(f82(x68411),x68414),x68413)),f331(f331(f82(x68411),f331(f331(f81(x68411),x68412),x68414)),x68413))
% 162.26/162.07 [6843]~P99(x68431)+E(f331(f331(f108(x68431),f331(f331(f107(x68431),x68432),x68433)),f331(f331(f107(x68431),x68434),x68433)),f331(f331(f107(x68431),f331(f331(f108(x68431),x68432),x68434)),x68433))
% 162.26/162.07 [6844]~P107(x68441)+E(f331(f331(f246(x68441),f331(f331(f251(x68441),x68442),x68443)),f331(f331(f251(x68441),x68444),x68443)),f331(f331(f251(x68441),f331(f331(f246(x68441),x68442),x68444)),x68443))
% 162.26/162.07 [6845]~P107(x68451)+E(f331(f331(f251(x68451),f331(f331(f246(x68451),x68452),x68453)),f331(f331(f246(x68451),x68454),x68453)),f331(f331(f246(x68451),f331(f331(f251(x68451),x68452),x68454)),x68453))
% 162.26/162.07 [6846]~P73(x68461)+E(f331(f331(f82(x68461),f331(f331(f262(x68461),x68462),x68463)),f331(f331(f262(x68461),x68464),x68463)),f331(f331(f262(x68461),f331(f331(f82(x68461),x68462),x68464)),x68463))
% 162.26/162.07 [6847]~P118(x68471)+E(f331(f331(f82(x68471),f331(f331(f262(x68471),x68472),x68473)),f331(f331(f262(x68471),x68474),x68473)),f331(f331(f262(x68471),f331(f331(f82(x68471),x68472),x68474)),x68473))
% 162.26/162.07 [6848]~P61(x68481)+E(f331(f331(f289(x68481),f331(f331(f262(x68481),x68482),x68483)),f331(f331(f262(x68481),x68484),x68483)),f331(f331(f262(x68481),f331(f331(f289(x68481),x68482),x68484)),x68483))
% 162.26/162.07 [6849]~P119(x68491)+E(f331(f331(f22(x68491),f331(f331(f289(x68491),x68492),x68493)),f331(f331(f289(x68491),x68494),x68493)),f331(f331(f289(x68491),f331(f331(f22(x68491),x68492),x68494)),x68493))
% 162.26/162.07 [6850]~P119(x68501)+E(f331(f331(f81(x68501),f331(f331(f289(x68501),x68502),x68503)),f331(f331(f289(x68501),x68504),x68503)),f331(f331(f289(x68501),f331(f331(f81(x68501),x68502),x68504)),x68503))
% 162.26/162.07 [6851]~P99(x68511)+E(f331(f331(f107(x68511),f331(f331(f108(x68511),x68512),x68513)),f331(f331(f108(x68511),x68514),x68513)),f331(f331(f108(x68511),f331(f331(f107(x68511),x68512),x68514)),x68513))
% 162.26/162.07 [6852]~P118(x68521)+E(f331(f331(f81(x68521),f331(f331(f82(x68521),x68522),x68523)),f331(f331(f82(x68521),x68524),x68523)),f331(f331(f82(x68521),f331(f331(f81(x68521),x68522),x68524)),x68523))
% 162.26/162.07 [6884]E(f331(f331(f162(x68841,x68842),x68843),x68844),x68842)+~P24(f331(f331(f247(a883),f331(f197(f884(x68841)),x68842)),x68843))
% 162.26/162.07 [6906]~P24(f331(x69063,x69064))+P24(f331(f331(f331(f107(f891(x69061,a877)),x69062),x69063),x69064))
% 162.26/162.07 [6908]~P24(f331(x69082,x69084))+P24(f331(f331(f331(f107(f891(x69081,a877)),x69082),x69083),x69084))
% 162.26/162.07 [6929]E(f331(f331(f168(x69291),f331(f331(f137(x69291),x69292),x69293)),x69294),f331(f331(f168(x69291),x69292),x69294))+~P24(f331(f331(f248(a883),x69294),f331(f197(f884(x69291)),x69292)))
% 162.26/162.07 [6939]E(f331(f331(f22(f891(x69391,a877)),f331(f331(f309(x69391),x69392),x69393)),x69394),f331(f331(f22(f891(x69391,a877)),x69393),x69394))+~P24(f331(f331(f333(x69391),x69392),x69394))
% 162.26/162.07 [6981]~E(f142(a883,f331(f301(a883,x69811),x69812)),f331(f331(f154(a883),x69814),x69813))+E(f142(a883,f331(f301(a883,f331(f331(f81(a883),x69811),f79(a883))),x69812)),x69813)
% 162.26/162.07 [7054]E(x70541,f2(a883))+E(f331(f331(f154(x70542),x70543),f331(f331(f176(x70542),f331(f331(f22(a883),x70541),f79(a883))),x70544)),f331(f331(f176(x70542),x70541),f331(f331(f154(x70542),x70543),x70544)))
% 162.26/162.07 [7153]E(f331(f331(f168(x71531),x71532),f331(f331(f22(a883),x71533),f331(f197(f884(x71531)),x71534))),f331(f331(f168(x71531),f331(f331(f137(x71531),x71534),x71532)),x71533))+P24(f331(f331(f248(a883),x71533),f331(f197(f884(x71531)),x71534)))
% 162.26/162.07 [7183]E(f331(f331(f108(f891(x71831,a877)),x71832),f331(f331(f309(x71831),x71833),x71834)),f331(f331(f309(x71831),x71833),f331(f331(f108(f891(x71831,a877)),x71832),x71834)))+~P24(f331(f331(f333(x71831),x71833),x71832))
% 162.26/162.07 [7218]E(f331(f331(f168(x72181),f331(f331(f162(x72181,x72182),x72183),x72184)),x72183),x72184)+~P24(f331(f331(f248(a883),x72183),f331(f197(f884(x72181)),x72182)))
% 162.26/162.07 [7239]E(x72391,f196(f891(x72392,a877)))+E(f331(f310(f890(x72393,x72392),x72393,f260(x72393,x72392)),f331(f331(f268(x72393,x72392),x72394),f331(f16(f891(x72392,a877),x72393),x72391))),x72394)
% 162.26/162.07 [7240]E(x72401,f196(f891(x72402,a877)))+E(f331(f310(f890(x72402,x72403),x72403,f269(x72402,x72403)),f331(f331(f268(x72402,x72403),x72401),f331(f16(f891(x72403,a877),x72402),x72404))),x72404)
% 162.26/162.07 [7303]E(f331(f331(f22(f891(x73031,a877)),f331(f331(f309(x73031),x73032),x73033)),x73034),f331(f331(f309(x73031),x73032),f331(f331(f22(f891(x73031,a877)),x73033),x73034)))+P24(f331(f331(f333(x73031),x73032),x73034))
% 162.26/162.07 [7328]P24(f331(x73281,x73282))+P24(f331(f331(f331(f331(a205,f33(x73281,x73283)),x73282),x73284),x73282))
% 162.26/162.07 [7335]~E(x73354,f196(f891(x73352,a877)))+E(f331(f310(f890(x73351,x73352),x73351,f260(x73351,x73352)),f331(f331(f268(x73351,x73352),x73353),f331(f16(f891(x73352,a877),x73351),x73354))),f196(f891(x73351,a877)))
% 162.26/162.07 [7336]~E(x73363,f196(f891(x73361,a877)))+E(f331(f310(f890(x73361,x73362),x73362,f269(x73361,x73362)),f331(f331(f268(x73361,x73362),x73363),f331(f16(f891(x73362,a877),x73361),x73364))),f196(f891(x73362,a877)))
% 162.26/162.07 [7392]~P24(f331(f331(f333(x73921),x73922),x73924))+P24(f331(f331(f333(x73921),x73922),f331(f331(f107(f891(x73921,a877)),x73923),x73924)))
% 162.26/162.07 [7395]~P24(f331(f331(f333(x73951),x73952),x73953))+P24(f331(f331(f333(x73951),x73952),f331(f331(f107(f891(x73951,a877)),x73953),x73954)))
% 162.26/162.07 [7414]E(f331(f331(f108(f891(x74141,a877)),f331(f331(f309(x74141),x74142),x74143)),x74144),f331(f331(f309(x74141),x74142),f331(f331(f108(f891(x74141,a877)),x74143),x74144)))+~P24(f331(f331(f333(x74141),x74142),x74144))
% 162.26/162.07 [7685]P24(f331(x76851,x76852))+~P24(f331(f331(f331(f108(f891(x76853,a877)),x76854),x76851),x76852))
% 162.26/162.07 [7686]P24(f331(x76861,x76862))+~P24(f331(f331(f331(f108(f891(x76863,a877)),x76861),x76864),x76862))
% 162.26/162.07 [7689]E(f331(f331(f6(x76891,a883),x76892),f331(f331(f22(f891(x76891,a877)),x76893),f331(f331(f309(x76891),x76894),f196(f891(x76891,a877))))),f331(f331(f6(x76891,a883),x76892),x76893))+P24(f331(f331(f333(x76891),x76894),x76893))
% 162.26/162.07 [7695]~P74(x76951)+E(f331(f169(x76951),f331(f331(f157(a883,x76951),x76952),f142(a883,f331(f301(a883,x76953),x76954)))),f331(f331(f6(a883,x76951),x76952),f331(f175(a883),f142(a883,f331(f301(a883,x76953),x76954)))))
% 162.26/162.07 [7696]~P74(x76961)+E(f331(f331(f6(a883,x76961),x76962),f331(f175(a883),f142(a883,f331(f301(a883,x76963),x76964)))),f331(f169(x76961),f331(f331(f157(a883,x76961),x76962),f142(a883,f331(f301(a883,x76963),x76964)))))
% 162.26/162.07 [7810]~E(x78103,x78104)+P24(f331(f63(x78101,x78102,f331(f331(f309(x78101),x78103),f196(f891(x78101,a877)))),x78104))
% 162.26/162.07 [7903]P24(f331(f331(f333(x79031),x79032),f331(f175(x79031),x79033)))+~P24(f331(f331(f333(x79031),x79032),f331(f175(x79031),f331(f331(f176(x79031),x79034),x79033))))
% 162.26/162.07 [7904]P24(f331(f331(f333(x79041),x79042),f331(f175(x79041),x79043)))+~P24(f331(f331(f333(x79041),x79042),f331(f175(x79041),f331(f331(f141(x79041),x79044),x79043))))
% 162.26/162.07 [7971]P24(f331(f331(f333(x79711),x79712),x79713))+~P24(f331(f331(f333(x79711),x79712),f331(f331(f22(f891(x79711,a877)),x79713),x79714)))
% 162.26/162.07 [7973]P24(f331(f331(f333(x79731),x79732),x79733))+~P24(f331(f331(f333(x79731),x79732),f331(f331(f108(f891(x79731,a877)),x79734),x79733)))
% 162.26/162.07 [7976]P24(f331(f331(f333(x79761),x79762),x79763))+~P24(f331(f331(f333(x79761),x79762),f331(f331(f108(f891(x79761,a877)),x79763),x79764)))
% 162.26/162.07 [7994]E(f331(f331(f137(x79941),f331(f331(f176(x79941),x79942),x79943)),f331(f331(f154(x79941),x79944),f331(f331(f141(x79941),f331(a118,x79942)),x79943))),f331(f331(f162(x79941,x79943),x79942),x79944))+~P24(f331(f331(f248(a883),x79942),f331(f197(f884(x79941)),x79943)))
% 162.26/162.07 [8019]P24(f331(f331(f333(x80191),x80192),x80193))+~P24(f331(f331(f247(f891(x80191,a877)),f331(f331(f309(x80191),x80192),x80194)),x80193))
% 162.26/162.07 [8058]~P24(f331(f331(f333(x80581),x80582),x80583))+~P24(f331(f331(f333(x80581),x80582),f331(f331(f22(f891(x80581,a877)),x80584),x80583)))
% 162.26/162.07 [8090]~P24(f331(f331(f248(a883),x80904),f331(f197(f884(x80901)),x80903)))+P24(f331(f331(f333(x80901),x80902),f331(f175(x80901),f331(f331(f162(x80901,x80903),x80904),x80902))))
% 162.26/162.07 [8146]E(f331(f331(f168(x81461),f331(f331(f141(x81461),x81462),x81463)),x81464),f331(f331(f168(x81461),x81463),f331(f331(f81(a883),x81462),x81464)))+~P24(f331(f331(f247(a883),f331(f331(f81(a883),x81462),x81464)),f331(f197(f884(x81461)),x81463)))
% 162.26/162.07 [8156]~P143(x81562)+E(f331(f331(f6(x81561,x81562),f331(f331(f8(a883,x81562,x81561),f106(x81562)),x81563)),x81564),f331(f106(x81562),f331(f331(f6(x81561,a883),x81563),x81564)))
% 162.26/162.07 [8157]~P138(x81572)+E(f331(f331(f6(x81571,x81572),f331(f331(f8(a1,x81572,x81571),f109(x81572)),x81573)),x81574),f331(f109(x81572),f331(f331(f6(x81571,a1),x81573),x81574)))
% 162.26/162.07 [8209]~P64(x82092)+E(f331(f331(f9(x82091,x82092),f331(f331(f8(x82092,x82092,x82091),f76(x82092)),x82093)),x82094),f331(f76(x82092),f331(f331(f9(x82091,x82092),x82093),x82094)))
% 162.26/162.07 [8210]~P70(x82102)+E(f331(f331(f6(x82101,x82102),f331(f331(f8(x82102,x82102,x82101),f80(x82102)),x82103)),x82104),f331(f80(x82102),f331(f331(f6(x82101,x82102),x82103),x82104)))
% 162.26/162.07 [8212]E(f331(f331(f6(x82121,a883),x82122),f331(f331(f22(f891(x82121,a877)),x82123),f331(f331(f309(x82121),x82124),f196(f891(x82121,a877))))),f331(f331(f22(a883),f331(f331(f6(x82121,a883),x82122),x82123)),f331(x82122,x82124)))+~P24(f331(f331(f333(x82121),x82124),x82123))
% 162.26/162.07 [8231]P24(f331(f331(f247(f891(x82311,a877)),x82312),x82313))+~P24(f331(f331(f247(f891(x82311,a877)),f331(f331(f309(x82311),x82314),x82312)),x82313))
% 162.26/162.07 [8433]E(f331(a118,f590(x84331,x84332,x84333,x84334)),x84332)+~P24(f331(f331(f331(f331(a205,f331(a28,x84334)),x84333),x84332),x84331))
% 162.26/162.07 [8435]E(f331(f331(f180(x84351,x84352),x84353),x84354),f199(x84352))+P24(f331(f331(f333(x84351),x84354),f331(f310(f890(x84351,x84352),x84351,f260(x84351,x84352)),f331(f175(f890(x84351,x84352)),x84353))))
% 162.26/162.07 [8437]P38(x84371,x84372)+~P38(x84371,f331(f331(f309(f890(x84371,x84371)),f331(f331(f261(x84371,x84371),x84373),x84374)),x84372))
% 162.26/162.07 [8438]P55(x84381,x84382)+~P55(x84381,f331(f331(f309(f890(x84381,x84381)),f331(f331(f261(x84381,x84381),x84383),x84384)),x84382))
% 162.26/162.07 [8447]~P107(x84471)+E(f331(f331(f151(x84471,x84471,f5(x84471)),x84472),f331(f331(f151(x84471,x84471,f5(x84471)),x84473),x84474)),f331(f331(f151(x84471,x84471,f5(x84471)),x84473),f331(f331(f151(x84471,x84471,f5(x84471)),x84472),x84474)))
% 162.26/162.07 [8457]E(x84571,x84572)+~P24(f331(f63(x84573,x84574,f331(f331(f309(x84573),x84571),f196(f891(x84573,a877)))),x84572))
% 162.26/162.07 [8467]E(f331(f331(f137(x84671),f331(f331(f176(x84671),x84672),x84673)),f331(f331(f176(x84671),x84674),f331(f331(f141(x84671),x84672),x84673))),f331(f331(f176(x84671),f331(f331(f81(a883),x84672),x84674)),x84673))+~P24(f331(f331(f247(a883),f331(f331(f81(a883),x84672),x84674)),f331(f197(f884(x84671)),x84673)))
% 162.26/162.07 [8504]P24(f331(f62(x85041),x85042))+~E(x85042,f331(f310(a883,x85041,x85043),f331(f253(a883),f331(f331(f7(a883,a883,a877),f248(a883)),x85044))))
% 162.26/162.07 [8529]~P89(x85291)+E(f331(f145(x85291,x85291,f81(x85291),f331(f331(f81(x85291),x85292),x85293)),x85294),f331(f331(f81(x85291),x85292),f331(f145(x85291,x85291,f81(x85291),x85293),x85294)))
% 162.26/162.07 [8562]P24(f331(f331(f247(f891(x85621,a877)),f331(f259(x85621,x85622),x85623)),f331(f259(x85621,x85622),x85624)))+~P24(f331(f331(f247(f891(f890(x85621,x85622),a877)),x85623),x85624))
% 162.26/162.07 [8575]~P24(f331(f331(f247(a883),x85752),x85754))+P24(f331(f331(f247(f891(x85751,a877)),f331(f175(x85751),f331(f331(f176(x85751),x85752),x85753))),f331(f175(x85751),f331(f331(f176(x85751),x85754),x85753))))
% 162.26/162.07 [8576]~P24(f331(f331(f247(a883),x85764),x85762))+P24(f331(f331(f247(f891(x85761,a877)),f331(f175(x85761),f331(f331(f141(x85761),x85762),x85763))),f331(f175(x85761),f331(f331(f141(x85761),x85764),x85763))))
% 162.26/162.07 [8630]~P24(f331(f62(x86301),f331(f331(f22(f891(x86301,a877)),x86302),x86304)))+P24(f331(f62(x86301),f331(f331(f22(f891(x86301,a877)),x86302),f331(f331(f309(x86301),x86303),x86304))))
% 162.26/162.07 [8660]P24(f331(f331(f333(f890(x86601,x86601)),x86602),f307(x86601,x86603)))+~P24(f331(f331(f333(f890(x86601,x86601)),x86602),f331(f331(f191(f890(x86601,x86601),a877),x86604),x86603)))
% 162.26/162.07 [8730]~P24(f331(f62(x87301),f331(f331(f22(f891(x87301,a877)),x87302),f331(f331(f309(x87301),x87304),x87303))))+P24(f331(f62(x87301),f331(f331(f22(f891(x87301,a877)),x87302),x87303)))
% 162.26/162.07 [8888]~E(f331(f331(f180(x88881,x88882),x88883),x88884),f199(x88882))+~P24(f331(f331(f333(x88881),x88884),f331(f310(f890(x88881,x88882),x88881,f260(x88881,x88882)),f331(f175(f890(x88881,x88882)),x88883))))
% 162.26/162.07 [8953]~P96(x89531)+P24(f331(f331(f247(x89531),f331(f331(f107(x89531),x89532),f331(f331(f108(x89531),x89533),x89534))),f331(f331(f108(x89531),f331(f331(f107(x89531),x89532),x89533)),f331(f331(f107(x89531),x89532),x89534))))
% 162.26/162.07 [8954]~P107(x89541)+P24(f331(f331(f247(x89541),f331(f331(f246(x89541),x89542),f331(f331(f251(x89541),x89543),x89544))),f331(f331(f251(x89541),f331(f331(f246(x89541),x89542),x89543)),f331(f331(f246(x89541),x89542),x89544))))
% 162.26/162.07 [9086]E(x90861,x90862)+~P24(f331(f331(f333(f890(x90863,x90863)),f331(f331(f261(x90863,x90863),x90861),x90862)),f331(f175(f890(x90863,x90863)),f331(f331(f184(x90863,x90863),x90864),x90864))))
% 162.26/162.07 [9121]~P24(f331(f331(f333(f890(x91211,x91211)),f331(f331(f261(x91211,x91211),x91213),x91212)),f307(x91211,x91214)))+~P38(x91211,f331(f331(f309(f890(x91211,x91211)),f331(f331(f261(x91211,x91211),x91212),x91213)),x91214))
% 162.26/162.07 [9122]~P24(f331(f331(f333(f890(x91221,x91221)),f331(f331(f261(x91221,x91221),x91223),x91222)),f307(x91221,x91224)))+~P55(x91221,f331(f331(f309(f890(x91221,x91221)),f331(f331(f261(x91221,x91221),x91222),x91223)),x91224))
% 162.26/162.07 [9134]E(x91341,x91342)+E(f331(f139(x91343,f331(f331(f8(a877,a877,x91343),a326),f331(a328,x91341))),f331(f331(f154(x91343),x91342),x91344)),f331(f331(f154(x91343),x91342),f331(f139(x91343,f331(f331(f8(a877,a877,x91343),a326),f331(a328,x91341))),x91344)))
% 162.26/162.07 [9180]~P96(x91801)+P24(f331(f331(f247(x91801),f331(f331(f107(x91801),f331(f331(f108(x91801),x91802),x91803)),f331(f331(f108(x91801),x91802),x91804))),f331(f331(f108(x91801),x91802),f331(f331(f107(x91801),x91803),x91804))))
% 162.26/162.07 [9181]~P107(x91811)+P24(f331(f331(f247(x91811),f331(f331(f246(x91811),f331(f331(f251(x91811),x91812),x91813)),f331(f331(f251(x91811),x91812),x91814))),f331(f331(f251(x91811),x91812),f331(f331(f246(x91811),x91813),x91814))))
% 162.26/162.07 [9254]~E(f331(f310(x92542,x92541,x92543),f256(f891(x92542,a877))),f256(f891(x92541,a877)))+P24(f331(f331(f247(f891(x92541,a877)),f331(f80(f891(x92541,a877)),f331(f310(x92542,x92541,x92543),x92544))),f331(f310(x92542,x92541,x92543),f331(f80(f891(x92542,a877)),x92544))))
% 162.26/162.07 [9335]P24(f331(f331(f331(f331(a205,f331(f244(a879),f331(a26,x93351))),x93352),f590(x93353,x93354,x93352,x93351)),x93353))+~P24(f331(f331(f331(f331(a205,f331(a28,x93351)),x93352),x93354),x93353))
% 162.26/162.07 [9591]P24(f331(f331(f333(f890(x95911,x95911)),f331(f331(f261(x95911,x95911),x95912),x95913)),f331(f286(x95911,x95911),f331(f331(f288(x95911,x95911,x95911),x95914),f307(x95911,x95914)))))+~P24(f331(f331(f333(f890(x95911,x95911)),f331(f331(f261(x95911,x95911),x95912),x95913)),f331(f331(f288(x95911,x95911,x95911),f331(f286(x95911,x95911),x95914)),f307(x95911,f331(f286(x95911,x95911),x95914)))))
% 162.26/162.07 [9593]~P24(f331(f331(f333(f890(x95931,x95931)),f331(f331(f261(x95931,x95931),x95932),x95933)),f331(f286(x95931,x95931),f331(f331(f288(x95931,x95931,x95931),x95934),f307(x95931,x95934)))))+P24(f331(f331(f333(f890(x95931,x95931)),f331(f331(f261(x95931,x95931),x95932),x95933)),f331(f331(f288(x95931,x95931,x95931),f331(f286(x95931,x95931),x95934)),f307(x95931,f331(f286(x95931,x95931),x95934)))))
% 162.26/162.07 [9614]~P24(f331(f331(f333(x96142),x96144),f331(f257(x96141,x96142),x96143)))+P24(f331(f331(f333(f890(x96141,x96142)),f331(f331(f261(x96141,x96142),f574(x96143,x96141,x96144,x96142)),x96144)),x96143))
% 162.26/162.07 [9615]~P24(f331(f331(f333(x96152),x96154),f331(f257(x96151,x96152),x96153)))+P24(f331(f331(f333(f890(x96151,x96152)),f331(f331(f261(x96151,x96152),f575(x96153,x96151,x96154,x96152)),x96154)),x96153))
% 162.26/162.07 [9646]~P24(f331(f331(f333(x96461),x96464),f331(f331(f107(f891(x96461,a877)),x96462),x96463)))+P24(f331(f331(f331(f107(f891(x96461,a877)),f331(f331(f7(x96461,f891(x96461,a877),a877),f333(x96461)),x96462)),f331(f331(f7(x96461,f891(x96461,a877),a877),f333(x96461)),x96463)),x96464))
% 162.26/162.07 [9647]~P24(f331(f331(f333(x96471),x96474),f331(f331(f108(f891(x96471,a877)),x96472),x96473)))+P24(f331(f331(f331(f108(f891(x96471,a877)),f331(f331(f7(x96471,f891(x96471,a877),a877),f333(x96471)),x96472)),f331(f331(f7(x96471,f891(x96471,a877),a877),f333(x96471)),x96473)),x96474))
% 162.26/162.07 [9721]~P24(f331(f331(f333(f890(x97211,x97211)),f331(f331(f261(x97211,x97211),x97214),x97213)),f331(f331(f288(x97211,x97211,x97211),x97212),f307(x97211,x97212))))+P24(f331(f331(f333(f890(x97211,x97211)),f331(f331(f261(x97211,x97211),f787(x97212,x97213,x97214,x97211)),x97213)),x97212))
% 162.26/162.07 [9777]P24(f331(f331(f333(x97771),x97772),f331(f331(f107(f891(x97771,a877)),x97773),x97774)))+~P24(f331(f331(f331(f107(f891(x97771,a877)),f331(f331(f7(x97771,f891(x97771,a877),a877),f333(x97771)),x97773)),f331(f331(f7(x97771,f891(x97771,a877),a877),f333(x97771)),x97774)),x97772))
% 162.26/162.07 [9778]P24(f331(f331(f333(x97781),x97782),f331(f331(f108(f891(x97781,a877)),x97783),x97784)))+~P24(f331(f331(f331(f108(f891(x97781,a877)),f331(f331(f7(x97781,f891(x97781,a877),a877),f333(x97781)),x97783)),f331(f331(f7(x97781,f891(x97781,a877),a877),f333(x97781)),x97784)),x97782))
% 162.26/162.07 [10037]P33(x100371,f331(f331(f7(x100371,f891(f890(x100371,x100371),a877),f891(x100371,a877)),f331(f331(f8(f891(x100371,f891(f891(f890(x100371,x100371),a877),a877)),f891(f891(f890(x100371,x100371),a877),f891(x100371,a877)),x100371),f7(x100371,f891(f890(x100371,x100371),a877),a877)),f331(f331(f8(f891(x100371,f890(x100371,x100371)),f891(x100371,f891(f891(f890(x100371,x100371),a877),a877)),x100371),f331(f8(f890(x100371,x100371),f891(f891(f890(x100371,x100371),a877),a877),x100371),f333(f890(x100371,x100371)))),f261(x100371,x100371)))),x100372),x100373,x100374)+~P24(f331(f331(f333(f890(f884(x100371),f884(x100371))),f331(f331(f261(f884(x100371),f884(x100371)),x100373),x100374)),f161(x100371,x100372)))
% 162.26/162.07 [10041]P56(x100411,f331(f331(f7(x100411,f891(f890(x100411,x100411),a877),f891(x100411,a877)),f331(f331(f8(f891(x100411,f891(f891(f890(x100411,x100411),a877),a877)),f891(f891(f890(x100411,x100411),a877),f891(x100411,a877)),x100411),f7(x100411,f891(f890(x100411,x100411),a877),a877)),f331(f331(f8(f891(x100411,f890(x100411,x100411)),f891(x100411,f891(f891(f890(x100411,x100411),a877),a877)),x100411),f331(f8(f890(x100411,x100411),f891(f891(f890(x100411,x100411),a877),a877),x100411),f333(f890(x100411,x100411)))),f261(x100411,x100411)))),x100412),x100413,x100414)+~P24(f331(f331(f333(f890(f891(x100411,a877),f891(x100411,a877))),f331(f331(f261(f891(x100411,a877),f891(x100411,a877)),x100413),x100414)),f322(x100411,x100412)))
% 162.26/162.07 [10066]E(x100661,x100662)+~E(f331(f331(f7(x100663,f891(f890(x100663,x100664),a877),f891(x100664,a877)),f331(f331(f8(f891(x100664,f891(f891(f890(x100663,x100664),a877),a877)),f891(f891(f890(x100663,x100664),a877),f891(x100664,a877)),x100663),f7(x100664,f891(f890(x100663,x100664),a877),a877)),f331(f331(f8(f891(x100664,f890(x100663,x100664)),f891(x100664,f891(f891(f890(x100663,x100664),a877),a877)),x100663),f331(f8(f890(x100663,x100664),f891(f891(f890(x100663,x100664),a877),a877),x100664),f333(f890(x100663,x100664)))),f261(x100663,x100664)))),x100661),f331(f331(f7(x100663,f891(f890(x100663,x100664),a877),f891(x100664,a877)),f331(f331(f8(f891(x100664,f891(f891(f890(x100663,x100664),a877),a877)),f891(f891(f890(x100663,x100664),a877),f891(x100664,a877)),x100663),f7(x100664,f891(f890(x100663,x100664),a877),a877)),f331(f331(f8(f891(x100664,f890(x100663,x100664)),f891(x100664,f891(f891(f890(x100663,x100664),a877),a877)),x100663),f331(f8(f890(x100663,x100664),f891(f891(f890(x100663,x100664),a877),a877),x100664),f333(f890(x100663,x100664)))),f261(x100663,x100664)))),x100662))
% 162.26/162.07 [10070]~P33(x100701,f331(f331(f7(x100701,f891(f890(x100701,x100701),a877),f891(x100701,a877)),f331(f331(f8(f891(x100701,f891(f891(f890(x100701,x100701),a877),a877)),f891(f891(f890(x100701,x100701),a877),f891(x100701,a877)),x100701),f7(x100701,f891(f890(x100701,x100701),a877),a877)),f331(f331(f8(f891(x100701,f890(x100701,x100701)),f891(x100701,f891(f891(f890(x100701,x100701),a877),a877)),x100701),f331(f8(f890(x100701,x100701),f891(f891(f890(x100701,x100701),a877),a877),x100701),f333(f890(x100701,x100701)))),f261(x100701,x100701)))),x100704),x100702,x100703)+P24(f331(f331(f333(f890(f884(x100701),f884(x100701))),f331(f331(f261(f884(x100701),f884(x100701)),x100702),x100703)),f161(x100701,x100704)))
% 162.26/162.07 [10071]~P56(x100711,f331(f331(f7(x100711,f891(f890(x100711,x100711),a877),f891(x100711,a877)),f331(f331(f8(f891(x100711,f891(f891(f890(x100711,x100711),a877),a877)),f891(f891(f890(x100711,x100711),a877),f891(x100711,a877)),x100711),f7(x100711,f891(f890(x100711,x100711),a877),a877)),f331(f331(f8(f891(x100711,f890(x100711,x100711)),f891(x100711,f891(f891(f890(x100711,x100711),a877),a877)),x100711),f331(f8(f890(x100711,x100711),f891(f891(f890(x100711,x100711),a877),a877),x100711),f333(f890(x100711,x100711)))),f261(x100711,x100711)))),x100714),x100712,x100713)+P24(f331(f331(f333(f890(f891(x100711,a877),f891(x100711,a877))),f331(f331(f261(f891(x100711,a877),f891(x100711,a877)),x100712),x100713)),f322(x100711,x100714)))
% 162.26/162.07 [7466]~P94(x74661)+E(f331(f331(f81(x74661),f331(f110(x74661),x74662)),f331(f331(f22(x74661),f331(f110(x74661),x74663)),x74664)),f331(f331(f22(x74661),f331(f110(x74661),f331(f331(f81(a1),x74662),x74663))),x74664))
% 162.26/162.07 [7467]~P94(x74671)+E(f331(f331(f81(x74671),f331(f110(x74671),x74672)),f331(f331(f81(x74671),f331(f110(x74671),x74673)),x74674)),f331(f331(f81(x74671),f331(f110(x74671),f331(f331(f81(a1),x74672),x74673))),x74674))
% 162.26/162.07 [7468]~P94(x74681)+E(f331(f331(f82(x74681),f331(f110(x74681),x74682)),f331(f331(f82(x74681),f331(f110(x74681),x74683)),x74684)),f331(f331(f82(x74681),f331(f110(x74681),f331(f331(f82(a1),x74682),x74683))),x74684))
% 162.26/162.07 [7510]~P143(x75101)+E(f331(f169(x75101),f331(f331(f157(x75102,x75101),f331(f16(x75101,x75102),x75103)),x75104)),f331(f331(f82(x75101),f331(f106(x75101),f331(f197(f884(x75102)),x75104))),x75103))
% 162.26/162.07 [7740]E(f331(f277(x77401,f331(f331(f154(f890(a105,x77401)),x77402),x77403)),x77404),f331(f269(a105,x77401),x77402))+~P24(f331(f331(f248(a105),x77404),f331(f260(a105,x77401),x77402)))
% 162.26/162.07 [7788]~P94(x77881)+E(f331(f331(f81(x77881),f331(f110(x77881),x77882)),f331(f331(f22(x77881),x77883),f331(f110(x77881),x77884))),f331(f331(f81(x77881),f331(f110(x77881),f331(f331(f81(a1),x77882),f331(f80(a1),x77884)))),x77883))
% 162.26/162.07 [7911]E(f331(f277(x79111,x79112),f331(f331(f22(a105),x79113),f331(f260(a105,x79111),x79114))),f331(f277(x79111,f331(f331(f154(f890(a105,x79111)),x79114),x79112)),x79113))+P24(f331(f331(f248(a105),x79113),f331(f260(a105,x79111),x79114)))
% 162.26/162.07 [8354]~P24(f331(f331(f333(x83541),x83542),f331(f175(x83541),f120(x83541,x83544))))+P24(f331(f331(f333(x83541),x83542),f331(f175(x83541),f120(x83541,f331(f331(f137(x83541),x83543),x83544)))))
% 162.26/162.07 [8355]~P24(f331(f331(f333(x83551),x83552),f331(f175(x83551),f120(x83551,x83553))))+P24(f331(f331(f333(x83551),x83552),f331(f175(x83551),f120(x83551,f331(f331(f137(x83551),x83553),x83554)))))
% 162.26/162.07 [8374]E(f331(f331(f107(f891(x83741,a877)),f331(f331(f108(f891(x83741,a877)),x83742),x83743)),x83744),f331(f331(f108(f891(x83741,a877)),x83742),f331(f331(f107(f891(x83741,a877)),x83743),x83744)))+~P24(f331(f331(f247(f891(x83741,a877)),x83744),x83742))
% 162.26/162.07 [8671]~E(f331(f331(f107(f891(x86711,a877)),f331(f331(f108(f891(x86711,a877)),x86713),x86714)),x86712),f331(f331(f108(f891(x86711,a877)),x86713),f331(f331(f107(f891(x86711,a877)),x86714),x86712)))+P24(f331(f331(f247(f891(x86711,a877)),x86712),x86713))
% 162.26/162.07 [8959]~P24(f331(f331(f247(f891(x89591,a877)),x89592),f331(f331(f107(f891(x89591,a877)),x89593),x89594)))+P24(f331(f331(f247(f891(x89591,a877)),f331(f331(f22(f891(x89591,a877)),x89592),x89593)),x89594))
% 162.26/162.07 [9018]~P24(f331(f331(f331(f331(a205,f331(a28,x90181)),x90182),f331(a118,x90183)),x90184))+P24(f331(f331(f331(f331(a205,f331(f244(a879),f331(a26,x90181))),x90182),x90183),x90184))
% 162.26/162.07 [9064]P24(f331(f331(f247(f891(x90641,a877)),x90642),f331(f331(f107(f891(x90641,a877)),x90643),x90644)))+~P24(f331(f331(f247(f891(x90641,a877)),f331(f331(f22(f891(x90641,a877)),x90642),x90643)),x90644))
% 162.26/162.07 [9120]P24(f331(f331(f331(f331(a205,f331(a28,x91201)),x91202),f331(a118,x91203)),x91204))+~P24(f331(f331(f331(f331(a205,f331(f244(a879),f331(a26,x91201))),x91202),x91203),x91204))
% 162.26/162.07 [9161]~P83(x91611)+E(f331(f76(x91611),f331(f331(f6(x91612,x91611),f331(f331(f8(x91611,x91611,x91612),f76(x91611)),x91613)),x91614)),f331(f331(f6(x91612,x91611),f331(f331(f8(x91611,x91611,x91612),f76(x91611)),x91613)),x91614))
% 162.26/162.07 [9333]~P83(x93331)+P24(f331(f331(f247(x93331),f2(x93331)),f331(f331(f6(x93332,x93331),f331(f331(f8(x93331,x93331,x93332),f76(x93331)),x93333)),x93334)))
% 162.26/162.07 [9338]~P70(x93381)+E(f331(f169(x93381),f331(f331(f157(x93382,x93381),f331(f74(x93381,x93381,x93382,f80(x93381)),x93383)),x93384)),f331(f80(x93381),f331(f169(x93381),f331(f331(f157(x93382,x93381),x93383),x93384))))
% 162.26/162.07 [9467]~P83(x94671)+P24(f331(f331(f247(x94671),f331(f76(x94671),f331(f331(f6(x94672,x94671),x94673),x94674))),f331(f331(f6(x94672,x94671),f331(f331(f8(x94671,x94671,x94672),f76(x94671)),x94673)),x94674)))
% 162.26/162.07 [9510]~E(f331(f331(f81(a883),x95101),x95104),f331(f331(f81(a883),x95103),x95102))+P24(f331(f331(f333(f890(f890(a883,a883),f890(a883,a883))),f331(f331(f261(f890(a883,a883),f890(a883,a883)),f331(f331(f261(a883,a883),x95101),x95102)),f331(f331(f261(a883,a883),x95103),x95104))),a115))
% 162.26/162.07 [9511]~P24(f331(f331(f248(a883),x95111),x95113))+P24(f331(f331(f333(f890(f890(a883,a883),f890(a883,a883))),f331(f331(f261(f890(a883,a883),f890(a883,a883)),f331(f331(f261(a883,a883),x95111),x95112)),f331(f331(f261(a883,a883),x95113),x95114))),a36))
% 162.26/162.07 [9512]~P24(f331(f331(f248(a883),x95121),x95123))+P24(f331(f331(f333(f890(f890(a883,a883),f890(a883,a883))),f331(f331(f261(f890(a883,a883),f890(a883,a883)),f331(f331(f261(a883,a883),x95121),x95122)),f331(f331(f261(a883,a883),x95123),x95124))),a71))
% 162.26/162.07 [9668]E(f331(f331(f81(a883),x96681),x96682),f331(f331(f81(a883),x96683),x96684))+~P24(f331(f331(f333(f890(f890(a883,a883),f890(a883,a883))),f331(f331(f261(f890(a883,a883),f890(a883,a883)),f331(f331(f261(a883,a883),x96681),x96684)),f331(f331(f261(a883,a883),x96683),x96682))),a115))
% 162.26/162.07 [9695]E(f331(f331(f168(x96951),f331(f331(f141(x96951),f331(f197(f884(x96951)),f179(x96951,x96952,x96953))),x96953)),x96954),f331(f331(f168(x96951),x96953),f331(f331(f81(a883),x96954),f331(f197(f884(x96951)),f179(x96951,x96952,x96953)))))+~P24(f331(f331(f248(a883),x96954),f331(f197(f884(x96951)),f331(f331(f141(x96951),f331(f197(f884(x96951)),f179(x96951,x96952,x96953))),x96953))))
% 162.26/162.07 [9712]~P24(f331(f331(f333(x97122),x97124),f331(f331(f42(x97121,f891(x97122,a877)),f256(f891(x97121,a877))),x97123)))+P24(f331(f331(f331(f42(x97121,f891(x97122,a877)),f256(f891(x97121,a877))),f331(f331(f8(f891(x97122,a877),f891(x97122,a877),x97121),f331(f7(x97122,f891(x97122,a877),a877),f333(x97122))),x97123)),x97124))
% 162.26/162.07 [9713]~P24(f331(f331(f333(x97132),x97134),f331(f331(f43(x97131,f891(x97132,a877)),f256(f891(x97131,a877))),x97133)))+P24(f331(f331(f331(f43(x97131,f891(x97132,a877)),f256(f891(x97131,a877))),f331(f331(f8(f891(x97132,a877),f891(x97132,a877),x97131),f331(f7(x97132,f891(x97132,a877),a877),f333(x97132))),x97133)),x97134))
% 162.26/162.07 [9806]~P24(f331(f49(x98061,x98062),f331(f331(f261(a1,a1),x98064),x98063)))+P24(f331(f49(f331(f80(a1),x98061),x98062),f331(f331(f261(a1,a1),f331(f331(f331(f102(a1),f331(f331(a328,x98063),f2(a1))),f331(f80(a1),x98064)),f331(f331(f22(a1),f331(f80(a1),x98064)),f79(a1)))),f331(f331(f331(f102(a1),f331(f331(a328,x98063),f2(a1))),f2(a1)),f331(f331(f22(a1),x98062),x98063)))))
% 162.26/162.07 [9814]P24(f331(f331(f333(x98141),x98142),f331(f331(f42(x98143,f891(x98141,a877)),f256(f891(x98143,a877))),x98144)))+~P24(f331(f331(f331(f42(x98143,f891(x98141,a877)),f256(f891(x98143,a877))),f331(f331(f8(f891(x98141,a877),f891(x98141,a877),x98143),f331(f7(x98141,f891(x98141,a877),a877),f333(x98141))),x98144)),x98142))
% 162.26/162.07 [9815]P24(f331(f331(f333(x98151),x98152),f331(f331(f43(x98153,f891(x98151,a877)),f256(f891(x98153,a877))),x98154)))+~P24(f331(f331(f331(f43(x98153,f891(x98151,a877)),f256(f891(x98153,a877))),f331(f331(f8(f891(x98151,a877),f891(x98151,a877),x98153),f331(f7(x98151,f891(x98151,a877),a877),f333(x98151))),x98154)),x98152))
% 162.26/162.07 [9826]E(f331(f331(f42(a883,f891(x98261,a877)),f256(f891(a883,a877))),x98262),f331(f331(f42(a883,f891(x98261,a877)),f256(f891(a883,a877))),x98263))+~E(f331(f331(f42(a883,f891(x98261,a877)),f331(f301(a883,f2(a883)),f513(x98262,x98264,x98263,x98261))),x98263),f331(f331(f42(a883,f891(x98261,a877)),f331(f301(a883,f2(a883)),f331(f331(f81(a883),f513(x98262,x98264,x98263,x98261)),x98264))),x98262))
% 162.26/162.07 [10159]~P24(f331(f331(f247(f891(f890(x101591,x101592),a877)),x101593),x101594))+P24(f331(f331(f247(f891(x101591,f891(x101592,a877))),f331(f331(f7(x101591,f891(f890(x101591,x101592),a877),f891(x101592,a877)),f331(f331(f8(f891(x101592,f891(f891(f890(x101591,x101592),a877),a877)),f891(f891(f890(x101591,x101592),a877),f891(x101592,a877)),x101591),f7(x101592,f891(f890(x101591,x101592),a877),a877)),f331(f331(f8(f891(x101592,f890(x101591,x101592)),f891(x101592,f891(f891(f890(x101591,x101592),a877),a877)),x101591),f331(f8(f890(x101591,x101592),f891(f891(f890(x101591,x101592),a877),a877),x101592),f333(f890(x101591,x101592)))),f261(x101591,x101592)))),x101593)),f331(f331(f7(x101591,f891(f890(x101591,x101592),a877),f891(x101592,a877)),f331(f331(f8(f891(x101592,f891(f891(f890(x101591,x101592),a877),a877)),f891(f891(f890(x101591,x101592),a877),f891(x101592,a877)),x101591),f7(x101592,f891(f890(x101591,x101592),a877),a877)),f331(f331(f8(f891(x101592,f890(x101591,x101592)),f891(x101592,f891(f891(f890(x101591,x101592),a877),a877)),x101591),f331(f8(f890(x101591,x101592),f891(f891(f890(x101591,x101592),a877),a877),x101592),f333(f890(x101591,x101592)))),f261(x101591,x101592)))),x101594)))
% 162.26/162.07 [10182]P24(f331(f331(f247(f891(f890(x101821,x101822),a877)),x101823),x101824))+~P24(f331(f331(f247(f891(x101821,f891(x101822,a877))),f331(f331(f7(x101821,f891(f890(x101821,x101822),a877),f891(x101822,a877)),f331(f331(f8(f891(x101822,f891(f891(f890(x101821,x101822),a877),a877)),f891(f891(f890(x101821,x101822),a877),f891(x101822,a877)),x101821),f7(x101822,f891(f890(x101821,x101822),a877),a877)),f331(f331(f8(f891(x101822,f890(x101821,x101822)),f891(x101822,f891(f891(f890(x101821,x101822),a877),a877)),x101821),f331(f8(f890(x101821,x101822),f891(f891(f890(x101821,x101822),a877),a877),x101822),f333(f890(x101821,x101822)))),f261(x101821,x101822)))),x101823)),f331(f331(f7(x101821,f891(f890(x101821,x101822),a877),f891(x101822,a877)),f331(f331(f8(f891(x101822,f891(f891(f890(x101821,x101822),a877),a877)),f891(f891(f890(x101821,x101822),a877),f891(x101822,a877)),x101821),f7(x101822,f891(f890(x101821,x101822),a877),a877)),f331(f331(f8(f891(x101822,f890(x101821,x101822)),f891(x101822,f891(f891(f890(x101821,x101822),a877),a877)),x101821),f331(f8(f890(x101821,x101822),f891(f891(f890(x101821,x101822),a877),a877),x101822),f333(f890(x101821,x101822)))),f261(x101821,x101822)))),x101824)))
% 162.26/162.07 [9208]~P24(f331(f331(f333(f890(x92081,x92081)),x92082),f307(x92081,x92084)))+P24(f331(f331(f333(f890(x92081,x92081)),x92082),f307(x92081,f331(f331(f107(f891(f890(x92081,x92081),a877)),x92083),x92084))))
% 162.26/162.07 [9209]~P24(f331(f331(f333(f890(x92091,x92091)),x92092),f307(x92091,x92093)))+P24(f331(f331(f333(f890(x92091,x92091)),x92092),f307(x92091,f331(f331(f107(f891(f890(x92091,x92091),a877)),x92093),x92094))))
% 162.26/162.07 [9576]~E(f331(f175(x95761),x95764),f186(x95761,x95762,x95763))+E(f331(f180(x95761,x95762),f331(f331(f157(x95761,f890(x95761,x95762)),f331(f331(f18(x95761,x95762,f890(x95761,x95762)),f261(x95761,x95762)),f331(f331(f8(f887(x95762),x95762,x95761),f244(x95762)),x95763))),x95764)),x95763)
% 162.26/162.07 [9914]~P24(f331(f331(f248(a883),f331(f331(f81(a883),x99141),x99144)),f331(f331(f81(a883),x99143),x99142)))+P24(f331(f331(f248(a1),f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),x99141),x99142)),f196(f891(f890(a883,a883),a877)))))),f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),x99143),x99144)),f196(f891(f890(a883,a883),a877)))))))
% 162.26/162.07 [9915]~P24(f331(f331(f247(a883),f331(f331(f81(a883),x99151),x99154)),f331(f331(f81(a883),x99153),x99152)))+P24(f331(f331(f247(a1),f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),x99151),x99152)),f196(f891(f890(a883,a883),a877)))))),f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),x99153),x99154)),f196(f891(f890(a883,a883),a877)))))))
% 162.26/162.07 [9980]P24(f331(f331(f248(a883),f331(f331(f81(a883),x99801),x99802)),f331(f331(f81(a883),x99803),x99804)))+~P24(f331(f331(f248(a1),f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),x99801),x99804)),f196(f891(f890(a883,a883),a877)))))),f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),x99803),x99802)),f196(f891(f890(a883,a883),a877)))))))
% 162.26/162.07 [9981]P24(f331(f331(f247(a883),f331(f331(f81(a883),x99811),x99812)),f331(f331(f81(a883),x99813),x99814)))+~P24(f331(f331(f247(a1),f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),x99811),x99814)),f196(f891(f890(a883,a883),a877)))))),f331(a90,f331(f285(f890(a883,a883),f890(a883,a883),a115),f331(f331(f309(f890(a883,a883)),f331(f331(f261(a883,a883),x99813),x99812)),f196(f891(f890(a883,a883),a877)))))))
% 162.26/162.07 [10024]P24(f331(f331(f247(f891(x100241,a877)),f331(f331(f42(a883,f891(x100241,a877)),f256(f891(a883,a877))),x100242)),f331(f331(f42(a883,f891(x100241,a877)),f256(f891(a883,a877))),x100243)))+~P24(f331(f331(f247(f891(x100241,a877)),f331(f331(f42(a883,f891(x100241,a877)),f331(f301(a883,f2(a883)),f506(x100243,x100244,x100242,x100241))),x100242)),f331(f331(f42(a883,f891(x100241,a877)),f331(f301(a883,f2(a883)),f331(f331(f81(a883),f506(x100243,x100244,x100242,x100241)),x100244))),x100243)))
% 162.26/162.07 [10148]~P24(f331(f331(f333(x101482),x101484),f331(f257(x101481,x101482),x101483)))+P24(f331(f267(x101481,x101482,f331(f331(f7(x101481,f891(f890(x101481,x101482),a877),f891(x101482,a877)),f331(f331(f8(f891(x101482,f891(f891(f890(x101481,x101482),a877),a877)),f891(f891(f890(x101481,x101482),a877),f891(x101482,a877)),x101481),f7(x101482,f891(f890(x101481,x101482),a877),a877)),f331(f331(f8(f891(x101482,f890(x101481,x101482)),f891(x101482,f891(f891(f890(x101481,x101482),a877),a877)),x101481),f331(f8(f890(x101481,x101482),f891(f891(f890(x101481,x101482),a877),a877),x101482),f333(f890(x101481,x101482)))),f261(x101481,x101482)))),x101483)),x101484))
% 162.26/162.07 [10149]~P24(f331(f331(f333(x101491),x101494),f331(f259(x101491,x101492),x101493)))+P24(f331(f266(x101491,x101492,f331(f331(f7(x101491,f891(f890(x101491,x101492),a877),f891(x101492,a877)),f331(f331(f8(f891(x101492,f891(f891(f890(x101491,x101492),a877),a877)),f891(f891(f890(x101491,x101492),a877),f891(x101492,a877)),x101491),f7(x101492,f891(f890(x101491,x101492),a877),a877)),f331(f331(f8(f891(x101492,f890(x101491,x101492)),f891(x101492,f891(f891(f890(x101491,x101492),a877),a877)),x101491),f331(f8(f890(x101491,x101492),f891(f891(f890(x101491,x101492),a877),a877),x101492),f333(f890(x101491,x101492)))),f261(x101491,x101492)))),x101493)),x101494))
% 162.26/162.07 [10162]P24(f331(f331(f333(x101621),x101622),f331(f257(x101623,x101621),x101624)))+~P24(f331(f267(x101623,x101621,f331(f331(f7(x101623,f891(f890(x101623,x101621),a877),f891(x101621,a877)),f331(f331(f8(f891(x101621,f891(f891(f890(x101623,x101621),a877),a877)),f891(f891(f890(x101623,x101621),a877),f891(x101621,a877)),x101623),f7(x101621,f891(f890(x101623,x101621),a877),a877)),f331(f331(f8(f891(x101621,f890(x101623,x101621)),f891(x101621,f891(f891(f890(x101623,x101621),a877),a877)),x101623),f331(f8(f890(x101623,x101621),f891(f891(f890(x101623,x101621),a877),a877),x101621),f333(f890(x101623,x101621)))),f261(x101623,x101621)))),x101624)),x101622))
% 162.26/162.07 [10163]P24(f331(f331(f333(x101631),x101632),f331(f259(x101631,x101633),x101634)))+~P24(f331(f266(x101631,x101633,f331(f331(f7(x101631,f891(f890(x101631,x101633),a877),f891(x101633,a877)),f331(f331(f8(f891(x101633,f891(f891(f890(x101631,x101633),a877),a877)),f891(f891(f890(x101631,x101633),a877),f891(x101633,a877)),x101631),f7(x101633,f891(f890(x101631,x101633),a877),a877)),f331(f331(f8(f891(x101633,f890(x101631,x101633)),f891(x101633,f891(f891(f890(x101631,x101633),a877),a877)),x101631),f331(f8(f890(x101631,x101633),f891(f891(f890(x101631,x101633),a877),a877),x101633),f333(f890(x101631,x101633)))),f261(x101631,x101633)))),x101634)),x101632))
% 162.26/162.07 [9836]P24(f331(f163(x98361,x98362),x98363))+~P24(f331(f163(x98361,f331(f331(f18(x98361,a877,a877),f331(f331(f8(a877,f891(a877,a877),x98361),a329),x98364)),x98362)),x98363))
% 162.26/162.07 [9837]P24(f331(f163(x98371,x98372),x98373))+~P24(f331(f163(x98371,f331(f331(f18(x98371,a877,a877),f331(f331(f8(a877,f891(a877,a877),x98371),a329),x98372)),x98374)),x98373))
% 162.26/162.07 [9916]~P118(x99161)+E(f331(f331(f82(x99161),f331(f331(f81(x99161),f79(x99161)),f79(x99161))),f331(f331(f6(a883,x99161),f331(f331(f8(x99161,x99161,a883),f331(f81(x99161),x99162)),f331(f331(f7(a883,x99161,x99161),f331(f331(f8(x99161,f891(x99161,x99161),a883),f82(x99161)),f106(x99161))),x99163))),f331(f254(a883),x99164))),f331(f331(f82(x99161),f331(f106(x99161),x99164)),f331(f331(f81(x99161),x99162),f331(f331(f81(x99161),x99162),f331(f331(f82(x99161),f331(f106(x99161),f331(f331(f22(a883),x99164),f79(a883)))),x99163)))))
% 162.26/162.07 [10044]P24(f331(x100441,f585(x100442,x100443,x100444,x100441)))+P38(x100442,f331(f253(f890(x100442,x100442)),f331(f270(x100442,x100442,a877),f331(f331(f8(f891(x100442,a877),f891(x100442,a877),x100442),f331(f18(x100442,a877,a877),f331(f331(f8(a877,f891(a877,a877),x100442),a329),x100441))),f331(f331(f7(x100442,f891(x100442,x100442),f891(x100442,a877)),f331(f331(f8(f891(x100442,a877),f891(f891(x100442,x100442),f891(x100442,a877)),x100442),f8(x100442,a877,x100442)),a328)),x100443)))))
% 162.26/162.07 [10055]~P24(f331(f331(f248(a883),f331(x100554,f331(x100553,f585(x100551,x100553,x100554,x100552)))),f331(x100554,f585(x100551,x100553,x100554,x100552))))+P38(x100551,f331(f253(f890(x100551,x100551)),f331(f270(x100551,x100551,a877),f331(f331(f8(f891(x100551,a877),f891(x100551,a877),x100551),f331(f18(x100551,a877,a877),f331(f331(f8(a877,f891(a877,a877),x100551),a329),x100552))),f331(f331(f7(x100551,f891(x100551,x100551),f891(x100551,a877)),f331(f331(f8(f891(x100551,a877),f891(f891(x100551,x100551),f891(x100551,a877)),x100551),f8(x100551,a877,x100551)),a328)),x100553)))))
% 162.26/162.07 [10198]~P24(f331(f331(f333(f890(x101981,x101981)),f331(f331(f261(x101981,x101981),x101983),x101984)),f331(f331(f107(f891(f890(x101981,x101981),a877)),x101982),f307(x101981,f196(f891(f890(x101981,x101981),a877))))))+P24(f331(f331(f331(f331(f107(f891(x101981,f891(x101981,a877))),f331(f331(f7(x101981,f891(f890(x101981,x101981),a877),f891(x101981,a877)),f331(f331(f8(f891(x101981,f891(f891(f890(x101981,x101981),a877),a877)),f891(f891(f890(x101981,x101981),a877),f891(x101981,a877)),x101981),f7(x101981,f891(f890(x101981,x101981),a877),a877)),f331(f331(f8(f891(x101981,f890(x101981,x101981)),f891(x101981,f891(f891(f890(x101981,x101981),a877),a877)),x101981),f331(f8(f890(x101981,x101981),f891(f891(f890(x101981,x101981),a877),a877),x101981),f333(f890(x101981,x101981)))),f261(x101981,x101981)))),x101982)),a328),x101983),x101984))
% 162.26/162.07 [10212]P24(f331(f331(f333(f890(x102121,x102121)),f331(f331(f261(x102121,x102121),x102122),x102123)),f331(f331(f107(f891(f890(x102121,x102121),a877)),x102124),f307(x102121,f196(f891(f890(x102121,x102121),a877))))))+~P24(f331(f331(f331(f331(f107(f891(x102121,f891(x102121,a877))),f331(f331(f7(x102121,f891(f890(x102121,x102121),a877),f891(x102121,a877)),f331(f331(f8(f891(x102121,f891(f891(f890(x102121,x102121),a877),a877)),f891(f891(f890(x102121,x102121),a877),f891(x102121,a877)),x102121),f7(x102121,f891(f890(x102121,x102121),a877),a877)),f331(f331(f8(f891(x102121,f890(x102121,x102121)),f891(x102121,f891(f891(f890(x102121,x102121),a877),a877)),x102121),f331(f8(f890(x102121,x102121),f891(f891(f890(x102121,x102121),a877),a877),x102121),f333(f890(x102121,x102121)))),f261(x102121,x102121)))),x102124)),a328),x102122),x102123))
% 162.26/162.07 [10032]~P109(x100323)+E(f91(x100321,f331(f331(f18(x100321,a877,a877),f331(f331(f8(a877,f891(a877,a877),x100321),a329),x100322)),f331(f331(f8(f891(x100321,a877),a877,x100321),f88(x100321)),f331(f331(f8(f891(x100321,a877),f891(x100321,a877),x100321),f331(f18(x100321,a877,a877),f331(f331(f8(a877,f891(a877,a877),x100321),a334),x100322))),f331(f331(f8(x100323,f891(x100321,a877),x100321),f331(f7(x100321,x100323,a877),f331(f331(f8(x100323,f891(x100323,a877),x100321),f247(x100323)),x100324))),x100324))))),f331(f95(x100321,x100323,x100324),x100322))
% 162.26/162.07 [10069]~P109(x100693)+E(f91(x100691,f331(f331(f18(x100691,a877,a877),f331(f331(f8(a877,f891(a877,a877),x100691),a329),x100692)),f331(f331(f8(f891(x100691,a877),a877,x100691),f88(x100691)),f331(f331(f8(f891(x100691,a877),f891(x100691,a877),x100691),f331(f18(x100691,a877,a877),f331(f331(f8(a877,f891(a877,a877),x100691),a334),x100692))),f331(f331(f7(x100691,f891(x100691,x100693),f891(x100691,a877)),f331(f331(f8(f891(x100693,a877),f891(f891(x100691,x100693),f891(x100691,a877)),x100691),f8(x100693,a877,x100691)),f331(f331(f8(x100693,f891(x100693,a877),x100691),f247(x100693)),x100694))),x100694))))),f97(x100691,x100693,x100694,x100692))
% 162.26/162.07 [10145]E(f331(f331(f154(f884(x101451)),f331(f331(f154(x101451),x101452),f331(f145(f884(x101451),f884(x101451),f137(x101451),f119(x101451)),f331(f331(f157(f884(x101451),f884(x101451)),f159(f884(x101451),x101451,f119(x101451),f331(f331(f8(f884(x101451),f891(f884(x101451),f884(x101451)),x101451),f16(f884(x101451),f884(x101451))),f331(f331(f7(x101451,f884(x101451),f884(x101451)),f154(x101451)),f119(x101451))))),x101453)))),f182(x101451,f331(f331(f154(f884(x101451)),x101454),f331(f145(f884(f884(x101451)),f884(f884(x101451)),f137(f884(x101451)),f119(f884(x101451))),f331(f331(f157(f884(x101451),f884(f884(x101451))),f159(f884(f884(x101451)),x101451,f119(f884(x101451)),f331(f16(f891(f884(x101451),f884(f884(x101451))),x101451),f331(f331(f7(f884(x101451),f884(f884(x101451)),f884(f884(x101451))),f154(f884(x101451))),f119(f884(x101451)))))),x101453))))),f182(x101451,f331(f331(f154(f884(x101451)),f331(f331(f154(x101451),x101452),x101454)),x101453)))+~P24(f331(f319(f884(f884(x101451)),f183(x101451)),f331(f331(f154(f884(x101451)),f331(f331(f154(x101451),x101452),x101454)),x101453)))
% 162.26/162.07 [10197]~P24(f331(f62(x101972),f331(f253(x101972),x101974)))+P24(f331(f62(x101971),f331(f253(x101971),f331(f331(f8(f891(x101972,a877),a877,x101971),f87(x101972)),f331(f331(f7(x101971,f891(x101972,a877),f891(x101972,a877)),f331(f331(f8(f891(x101972,f891(a877,a877)),f891(f891(x101972,a877),f891(x101972,a877)),x101971),f18(x101972,a877,a877)),f331(f331(f8(f891(x101972,a877),f891(x101972,f891(a877,a877)),x101971),f331(f8(a877,f891(a877,a877),x101972),a329)),f331(f331(f7(x101971,f891(x101972,x101971),f891(x101972,a877)),f331(f331(f8(f891(x101971,a877),f891(f891(x101972,x101971),f891(x101972,a877)),x101971),f8(x101971,a877,x101972)),a328)),x101973)))),x101974)))))
% 162.26/162.07 [5289]E(x52891,x52892)+~E(f130(x52893,x52894,x52891),f130(x52893,x52895,x52892))
% 162.26/162.07 [5290]E(x52901,x52902)+~E(f130(x52903,x52901,x52904),f130(x52903,x52902,x52905))
% 162.26/162.07 [5666]E(f331(f331(f309(x56661),x56662),f186(x56661,x56663,x56664)),f186(x56661,x56663,x56664))+~E(f331(x56664,x56662),f331(f239(x56663),x56665))
% 162.26/162.07 [6074]P24(f331(f267(x60741,x60742,x60743),x60744))+~P24(f331(f331(x60743,x60745),x60744))
% 162.26/162.07 [6076]P24(f331(f266(x60761,x60762,x60763),x60764))+~P24(f331(f331(x60763,x60764),x60765))
% 162.26/162.07 [6079]~E(f331(x60794,x60792),f331(f239(x60793),x60795))+P24(f331(f331(f333(x60791),x60792),f186(x60791,x60793,x60794)))
% 162.26/162.07 [6080]~E(f331(x60804,x60805),f331(f239(x60801),x60802))+P24(f331(f331(f333(x60801),x60802),f188(x60803,x60801,x60804)))
% 162.26/162.07 [6537]~E(x65375,f2(a105))+E(f331(f209(x65371,x65372,x65373,x65374),x65375),f121(x65372))
% 162.26/162.07 [6538]~E(x65385,f2(a105))+E(f331(f207(x65381,x65382,x65383,x65384),x65385),f131(x65382))
% 162.26/162.07 [6674]~E(x66743,f2(a105))+E(f331(f280(x66741,x66742,x66743,x66744),x66745),f331(f261(x66741,x66742),x66745))
% 162.26/162.07 [6746]~E(f331(x67464,x67465),f199(x67462))+E(f331(f242(f887(x67461),x67462,f199(x67461),x67463),f331(x67464,x67465)),f199(x67461))
% 162.26/162.07 [7347]E(f331(x73471,x73472),f199(x73473))+~E(f331(f187(x73474,x73473,x73475,x73471),x73472),f199(x73473))
% 162.26/162.07 [7348]E(f331(x73481,x73482),f199(x73483))+~E(f331(f187(x73484,x73483,x73481,x73485),x73482),f199(x73483))
% 162.26/162.07 [7384]E(f331(f187(x73841,x73842,x73843,x73844),x73845),f331(x73843,x73845))+P24(f331(f331(f333(x73841),x73845),f186(x73841,x73842,x73844)))
% 162.26/162.07 [7385]E(f331(f187(x73851,x73852,x73853,x73854),x73855),f331(x73854,x73855))+P24(f331(f331(f333(x73851),x73855),f186(x73851,x73852,x73853)))
% 162.26/162.07 [7700]~P16(x77004,x77001,x77002,x77005)+E(f331(f74(x77001,x77001,x77001,f331(x77002,x77003)),f331(x77002,x77003)),f331(x77002,x77003))
% 162.26/162.07 [7745]E(f331(f187(x77451,x77452,x77453,x77454),x77455),f331(x77454,x77455))+~P24(f331(f331(f333(x77451),x77455),f186(x77451,x77452,x77454)))
% 162.26/162.07 [8091]~P12(x80915,x80911,x80912)+E(f331(f74(x80911,x80911,x80911,f331(x80912,x80913)),f331(x80912,x80914)),f331(f74(x80911,x80911,x80911,f331(x80912,x80914)),f331(x80912,x80913)))
% 162.26/162.07 [8413]P24(f331(f331(f333(f890(x84131,x84131)),f331(f331(f261(x84131,x84131),x84132),x84133)),f325(x84131,x84134,x84135)))+~P24(f331(f331(f248(a883),f331(x84134,x84132)),f331(x84134,x84133)))
% 162.26/162.07 [8515]~P24(f331(f331(f333(x85154),x85153),f298(x85154,x85151,x85152,x85155)))+P24(f331(f331(x85151,x85152),x85153))
% 162.26/162.07 [8516]~P24(f331(f331(f333(x85164),x85163),f295(x85164,x85161,x85162,x85165)))+P24(f331(f331(x85161,x85162),x85163))
% 162.26/162.07 [8517]~P24(f331(f331(f333(x85174),x85172),f298(x85174,x85171,x85175,x85173)))+P24(f331(f331(x85171,x85172),x85173))
% 162.26/162.07 [8518]~P24(f331(f331(f333(x85184),x85182),f295(x85184,x85181,x85185,x85183)))+P24(f331(f331(x85181,x85182),x85183))
% 162.26/162.07 [8650]~P54(x86502,x86501,x86505,x86503,x86504)+E(f331(f310(x86501,x86502,x86503),x86504),f256(f891(x86502,a877)))
% 162.26/162.07 [9076]~P35(x90761,x90762,x90763,x90764,x90765)+P35(x90761,x90762,x90763,f331(f172(x90761),x90764),f331(f172(x90762),x90765))
% 162.26/162.07 [9078]~P35(x90781,x90782,x90783,f331(f172(x90781),x90784),x90785)+P35(x90781,x90782,x90783,x90784,f331(f172(x90782),x90785))
% 162.26/162.07 [9079]~P35(x90791,x90792,x90793,x90794,f331(f172(x90792),x90795))+P35(x90791,x90792,x90793,f331(f172(x90791),x90794),x90795)
% 162.26/162.07 [9085]P35(x90851,x90852,x90853,x90854,x90855)+~P35(x90851,x90852,x90853,f331(f172(x90851),x90854),f331(f172(x90852),x90855))
% 162.26/162.07 [9496]P24(f331(f331(f333(f890(f884(x94961),f884(x94961))),f331(f331(f261(f884(x94961),f884(x94961)),f331(f331(f154(x94961),x94962),x94963)),f331(f331(f154(x94961),x94962),x94964))),f160(x94961,x94965)))+~P24(f331(f331(f333(f890(f884(x94961),f884(x94961))),f331(f331(f261(f884(x94961),f884(x94961)),x94963),x94964)),f160(x94961,x94965)))
% 162.26/162.07 [9497]P24(f331(f331(f333(f890(f884(x94971),f884(x94971))),f331(f331(f261(f884(x94971),f884(x94971)),f331(f331(f137(x94971),x94972),x94973)),f331(f331(f137(x94971),x94972),x94974))),f150(x94971,x94975)))+~P24(f331(f331(f333(f890(f884(x94971),f884(x94971))),f331(f331(f261(f884(x94971),f884(x94971)),x94973),x94974)),f150(x94971,x94975)))
% 162.26/162.07 [9702]E(f331(f331(f154(x97021),f616(x97022,x97023,x97024,x97025,x97021)),f617(x97022,x97023,x97024,x97025,x97021)),x97025)+~P24(f331(f331(f333(f890(f884(x97021),f884(x97021))),f331(f331(f261(f884(x97021),f884(x97021)),x97025),f331(f331(f154(x97021),x97024),x97023))),f161(x97021,x97022)))
% 162.26/162.07 [9724]E(f331(f331(f154(x97241),f618(x97242,x97243,x97244,x97245,x97241)),f619(x97242,x97243,x97244,x97245,x97241)),x97243)+~P24(f331(f331(f333(f890(f884(x97241),f884(x97241))),f331(f331(f261(f884(x97241),f884(x97241)),f331(f331(f154(x97241),x97245),x97244)),x97243)),f161(x97241,x97242)))
% 162.26/162.07 [9892]~P24(f331(f331(f333(f890(f884(x98921),f884(x98921))),f331(f331(f261(f884(x98921),f884(x98921)),f331(f331(f154(x98921),x98925),x98922)),x98924)),f161(x98921,x98923)))+P24(f331(f331(f333(f890(f884(x98921),f884(x98921))),f331(f331(f261(f884(x98921),f884(x98921)),x98922),f619(x98923,x98924,x98922,x98925,x98921))),f161(x98921,x98923)))
% 162.26/162.07 [9951]~P24(f331(f331(f333(f890(f884(x99511),f884(x99511))),f331(f331(f261(f884(x99511),f884(x99511)),x99515),f331(f331(f154(x99511),x99514),x99513))),f161(x99511,x99512)))+P24(f331(f331(f333(f890(f884(x99511),f884(x99511))),f331(f331(f261(f884(x99511),f884(x99511)),f617(x99512,x99513,x99514,x99515,x99511)),x99513)),f161(x99511,x99512)))
% 162.26/162.07 [10119]P24(f331(f331(f333(f890(x101191,x101191)),f331(f331(f261(x101191,x101191),f331(x101192,f331(f331(f81(a883),x101193),x101194))),f331(x101192,x101193))),f307(x101191,x101195)))+~P24(f331(f331(f333(f890(x101191,x101191)),f331(f331(f261(x101191,x101191),f331(x101192,f331(a118,f760(x101194,x101193,x101195,x101192,x101191)))),f331(x101192,f760(x101194,x101193,x101195,x101192,x101191)))),f307(x101191,x101195)))
% 162.26/162.07 [5252]E(x52521,x52522)+~E(f331(f331(f154(x52523),x52524),x52521),f331(f331(f154(x52523),x52525),x52522))
% 162.26/162.07 [5253]E(x52531,x52532)+~E(f331(f331(f154(x52533),x52531),x52534),f331(f331(f154(x52533),x52532),x52535))
% 162.26/162.07 [5306]P24(f331(x53061,x53062))+~E(f331(f139(x53063,x53061),x53064),f331(f331(f154(x53063),x53062),x53065))
% 162.26/162.07 [5307]P24(f331(x53071,x53072))+~E(f331(f331(f154(x53073),x53072),x53074),f331(f139(x53073,x53071),x53075))
% 162.26/162.07 [5464]~E(f331(f331(f141(x54641),x54643),x54642),f331(f331(f154(x54641),x54644),x54645))+E(f331(f331(f168(x54641),x54642),x54643),x54644)
% 162.26/162.07 [5595]~P11(x55954,x55955,x55951)+E(f331(f331(x55951,x55952),f331(f331(x55951,x55952),x55953)),f331(f331(x55951,x55952),x55953))
% 162.26/162.07 [6132]~E(x61324,f2(a105))+E(f331(f331(f123(x61321,x61322,x61323),x61324),x61325),f331(f331(f261(f884(x61322),x61321),f119(x61322)),x61325))
% 162.26/162.07 [6202]~P107(x62022)+~E(f331(f331(f151(x62021,x62022,x62023),x62024),x62025),f119(x62021))
% 162.26/162.07 [6574]E(x65741,x65742)+~E(f331(f331(f137(x65743),x65744),f331(f331(f154(x65743),x65741),f119(x65743))),f331(f331(f137(x65743),x65745),f331(f331(f154(x65743),x65742),f119(x65743))))
% 162.26/162.07 [6575]E(x65751,x65752)+~E(f331(f331(f137(x65753),x65751),f331(f331(f154(x65753),x65754),f119(x65753))),f331(f331(f137(x65753),x65752),f331(f331(f154(x65753),x65755),f119(x65753))))
% 162.26/162.07 [6821]E(f331(f190(x68211,x68212,x68213,x68214),x68215),f199(x68212))+P24(f331(f331(f333(x68211),x68215),x68214))
% 162.26/162.07 [6882]E(f331(f331(f309(x68821),f331(x68822,x68823)),f331(f310(x68824,x68821,x68822),x68825)),f331(f310(x68824,x68821,x68822),x68825))+~P24(f331(f331(f333(x68824),x68823),x68825))
% 162.26/162.07 [6889]~P24(f331(x68894,f331(x68893,x68895)))+P24(f331(f331(f311(x68891,x68892,x68893),x68894),x68895))
% 162.26/162.07 [6985]~E(f331(f310(x69851,x69852,x69853),x69854),x69855)+E(f331(f310(f891(x69851,a877),f891(x69852,a877),f310(x69851,x69852,x69853)),f331(f308(x69851),x69854)),f331(f308(x69852),x69855))
% 162.26/162.07 [7017]E(f331(f190(x70171,x70172,x70173,x70174),x70175),f331(x70173,x70175))+~P24(f331(f331(f333(x70171),x70175),x70174))
% 162.26/162.07 [7311]P21(x73111,x73112,x73113,x73114)+~P21(x73111,x73112,x73113,f331(f331(f309(x73111),x73115),x73114))
% 162.26/162.07 [7373]P24(f331(x73731,x73732))+~P24(f331(f331(f98(x73733,x73734,x73731),x73735),x73732))
% 162.26/162.07 [7418]~P24(f331(f331(f333(x74184),x74183),x74185))+P24(f331(f331(f333(x74181),f331(x74182,x74183)),f331(f310(x74184,x74181,x74182),x74185)))
% 162.26/162.07 [7442]~P107(x74422)+E(f153(x74421,x74422,x74423,f331(f139(x74421,x74424),x74425)),f331(f139(x74421,x74424),f153(x74421,x74422,x74423,x74425)))
% 162.26/162.07 [7475]P24(f331(x74751,f331(x74752,x74753)))+~P24(f331(f331(f311(x74754,x74755,x74752),x74751),x74753))
% 162.26/162.07 [7476]P24(f331(f331(x74761,x74762),x74763))+~P24(f331(f331(f98(x74764,x74761,x74765),x74762),x74763))
% 162.26/162.07 [7540]~P24(f331(f331(f333(x75403),f331(x75404,x75402)),x75405))+P24(f331(f331(f333(x75401),x75402),f331(f311(x75401,x75403,x75404),x75405)))
% 162.26/162.07 [7925]~P24(f331(f331(f333(x79255),x79253),f331(f311(x79255,x79251,x79252),x79254)))+P24(f331(f331(f333(x79251),f331(x79252,x79253)),x79254))
% 162.26/162.07 [8158]~E(x81583,f331(f331(f331(f73(x81581,f887(x81582)),f331(f16(f887(x81582),x81581),f199(x81582))),x81584),f331(f239(x81582),x81585)))+E(f186(x81581,x81582,x81583),f331(f331(f309(x81581),x81584),f196(f891(x81581,a877))))
% 162.26/162.07 [8236]~P12(x82362,x82361,x82363)+E(f331(f145(x82361,x82362,f331(f7(x82362,x82361,x82361),x82363),x82364),f155(x82362,x82365)),f331(f331(f65(x82362,x82361,x82363),x82364),f331(f175(x82362),x82365)))
% 162.26/162.07 [8255]E(f331(x82551,f740(x82552,x82551,x82553,x82554)),x82554)+~P24(f331(f331(f333(x82555),x82554),f331(f310(x82553,x82555,x82551),x82552)))
% 162.26/162.07 [8561]~E(x85612,f331(f331(f154(x85611),x85614),x85615))+P24(f331(f331(f333(f890(f884(x85611),f884(x85611))),f331(f331(f261(f884(x85611),f884(x85611)),f119(x85611)),x85612)),f150(x85611,x85613)))
% 162.26/162.07 [8614]~P35(x86141,x86143,x86145,x86142,x86144)+E(f331(f197(f884(x86141)),x86142),f331(f197(f884(x86143)),x86144))
% 162.26/162.07 [8624]P24(f331(f331(f247(f891(x86241,a877)),f331(f331(f43(x86242,f891(x86241,a877)),x86243),x86244)),f331(x86244,x86245)))+~P24(f331(f331(f333(x86242),x86245),x86243))
% 162.26/162.07 [8665]~P54(x86651,x86652,x86653,x86655,x86654)+E(f331(f310(x86651,x86652,x86653),f256(f891(x86651,a877))),x86654)
% 162.26/162.07 [8873]E(f331(f331(f331(f73(x88731,f887(x88732)),f190(x88731,x88732,x88733,x88734)),x88735),f199(x88732)),f190(x88731,x88732,x88733,x88734))+P24(f331(f331(f333(x88731),x88735),x88734))
% 162.26/162.07 [8878]E(f331(f139(x88781,x88782),f732(x88783,x88784,x88785,x88782,x88781)),x88783)+~E(f331(f139(x88781,x88782),x88785),f331(f331(f154(x88781),x88784),x88783))
% 162.26/162.07 [8879]E(f331(f139(x88791,x88792),f734(x88793,x88792,x88794,x88795,x88791)),x88794)+~E(f331(f331(f154(x88791),x88795),x88794),f331(f139(x88791,x88792),x88793))
% 162.26/162.07 [8880]E(f331(x88801,f543(x88802,x88803,x88801,x88804,x88805)),x88802)+~E(f331(f331(f210(x88805,x88804),x88801),x88803),f331(f239(x88804),x88802))
% 162.26/162.07 [8884]E(f331(f239(x88841),f543(x88842,x88843,x88844,x88845,x88841)),x88843)+~E(f331(f331(f210(x88841,x88845),x88844),x88843),f331(f239(x88845),x88842))
% 162.26/162.07 [8981]E(f331(f197(f884(x89811)),x89812),x89813)+~P24(f331(f331(f333(f890(f884(x89811),f884(x89811))),f331(f331(f261(f884(x89811),f884(x89811)),x89814),x89812)),f331(f146(x89811,x89815),x89813)))
% 162.26/162.07 [8982]E(f331(f197(f884(x89821)),x89822),x89823)+~P24(f331(f331(f333(f890(f884(x89821),f884(x89821))),f331(f331(f261(f884(x89821),f884(x89821)),x89822),x89824)),f331(f146(x89821,x89825),x89823)))
% 162.26/162.07 [9042]P24(f331(f331(f333(x90421),f740(x90422,x90423,x90421,x90424)),x90422))+~P24(f331(f331(f333(x90425),x90424),f331(f310(x90421,x90425,x90423),x90422)))
% 162.26/162.07 [9206]E(f331(f310(x92061,x92062,x92063),f753(x92064,x92063,x92061,x92065,x92062)),x92065)+~P24(f331(f331(f247(f891(x92062,a877)),x92065),f331(f310(x92061,x92062,x92063),x92064)))
% 162.26/162.07 [9458]E(f331(x94581,f634(x94582,x94581,x94583,x94584,x94585)),f331(f239(x94585),x94584))+~P24(f331(f331(f333(x94585),x94584),f188(x94583,x94585,f190(x94583,x94585,x94581,x94582))))
% 162.26/162.07 [9518]P24(f331(f331(f333(f890(f884(x95181),f884(x95181))),f331(f331(f261(f884(x95181),f884(x95181)),f331(f331(f154(x95181),x95182),x95183)),f331(f331(f154(x95181),x95182),x95184))),f307(f884(x95181),f160(x95181,x95185))))+~P24(f331(f331(f333(f890(f884(x95181),f884(x95181))),f331(f331(f261(f884(x95181),f884(x95181)),x95183),x95184)),f307(f884(x95181),f160(x95181,x95185))))
% 162.26/162.07 [9549]~E(f331(x95493,f606(x95495,x95494,x95493,x95492,x95491)),f331(x95495,f606(x95495,x95494,x95493,x95492,x95491)))+E(f331(f331(f157(x95491,x95492),x95493),x95494),f331(f331(f157(x95491,x95492),x95495),x95494))
% 162.26/162.07 [9635]~E(f331(f139(x96351,x96355),x96354),f331(f331(f154(x96351),x96353),x96352))+E(f331(f331(f137(x96351),f733(x96352,x96353,x96354,x96355,x96351)),f331(f331(f154(x96351),x96353),f732(x96352,x96353,x96354,x96355,x96351))),x96354)
% 162.26/162.07 [9636]~E(f331(f331(f154(x96361),x96365),x96364),f331(f139(x96361,x96363),x96362))+E(f331(f331(f137(x96361),f735(x96362,x96363,x96364,x96365,x96361)),f331(f331(f154(x96361),x96365),f734(x96362,x96363,x96364,x96365,x96361))),x96362)
% 162.26/162.07 [9642]E(f331(f331(f157(x96421,x96422),x96423),x96424),f331(f331(f157(x96421,x96422),x96425),x96424))+P24(f331(f331(f333(x96421),f606(x96423,x96424,x96425,x96422,x96421)),f331(f175(x96421),x96424)))
% 162.26/162.07 [9669]~P24(f331(f331(f333(x96695),x96694),f331(f285(x96691,x96695,x96693),x96692)))+P24(f331(f331(f333(x96691),f443(x96692,x96693,x96691,x96694,x96695)),x96692))
% 162.26/162.07 [9670]~P24(f331(f331(f333(x96705),x96704),f331(f285(x96701,x96705,x96703),x96702)))+P24(f331(f331(f333(x96701),f491(x96702,x96703,x96701,x96704,x96705)),x96702))
% 162.26/162.07 [9696]~P24(f331(f331(f247(f891(x96965,a877)),x96964),f331(f310(x96961,x96965,x96963),x96962)))+P24(f331(f331(f247(f891(x96961,a877)),f753(x96962,x96963,x96961,x96964,x96965)),x96962))
% 162.26/162.07 [9752]~P24(f331(f331(f333(x97525),x97524),f188(x97521,x97525,f190(x97521,x97525,x97523,x97522))))+P24(f331(f331(f333(x97521),f634(x97522,x97523,x97521,x97524,x97525)),x97522))
% 162.26/162.07 [10165]E(x101651,f2(a105))+E(f331(f242(f890(f884(x101652),x101653),f890(x101652,x101653),f331(f331(f261(f884(x101652),x101653),f119(x101652)),x101654),f331(f270(x101652,x101653,f890(f884(x101652),x101653)),f331(f331(f7(x101652,f891(x101653,f890(f884(x101652),x101653)),f891(x101653,f890(f884(x101652),x101653))),f331(f331(f8(f891(f890(f884(x101652),x101653),f890(f884(x101652),x101653)),f891(f891(x101653,f890(f884(x101652),x101653)),f891(x101653,f890(f884(x101652),x101653))),x101652),f8(f890(f884(x101652),x101653),f890(f884(x101652),x101653),x101653)),f331(f331(f8(f891(f884(x101652),f891(x101653,f890(f884(x101652),x101653))),f891(f890(f884(x101652),x101653),f890(f884(x101652),x101653)),x101652),f270(f884(x101652),x101653,f890(f884(x101652),x101653))),f331(f331(f8(f891(f884(x101652),f884(x101652)),f891(f884(x101652),f891(x101653,f890(f884(x101652),x101653))),x101652),f331(f8(f884(x101652),f891(x101653,f890(f884(x101652),x101653)),f884(x101652)),f261(f884(x101652),x101653))),f154(x101652))))),f331(f123(x101653,x101652,x101655),f331(f331(f22(a105),x101651),f79(a105)))))),f331(x101655,x101654)),f331(f331(f123(x101653,x101652,x101655),x101651),x101654))
% 162.26/162.07 [5477]~E(f331(x54773,x54774),x54775)+E(f331(f331(f331(f73(x54771,x54772),x54773),x54774),x54775),x54773)
% 162.26/162.07 [5918]E(f331(x59181,x59182),x59183)+~E(f331(f331(f331(f73(x59184,x59185),x59181),x59182),x59183),x59181)
% 162.26/162.07 [6013]E(x60131,x60132)+~E(f331(f269(x60133,x60134),f331(f331(f261(x60133,x60134),x60135),x60131)),x60132)
% 162.26/162.07 [6014]E(x60141,x60142)+~E(f331(f260(x60143,x60144),f331(f331(f261(x60143,x60144),x60141),x60145)),x60142)
% 162.26/162.07 [6276]~E(x62763,f331(f331(f137(x62761),x62764),f331(f331(f154(x62761),x62762),x62765)))+P24(f331(f331(f333(x62761),x62762),f331(f175(x62761),x62763)))
% 162.26/162.07 [6661]E(f331(f310(x66611,x66612,f331(f16(x66612,x66611),x66613)),x66614),f331(f331(f309(x66612),x66613),f196(f891(x66612,a877))))+~P24(f331(f331(f333(x66611),x66615),x66614))
% 162.26/162.07 [6731]E(f331(f331(f107(f891(x67311,a877)),f331(f175(x67311),x67312)),f331(f175(x67311),x67313)),f331(f175(x67311),x67314))+~E(f170(x67311,x67315,x67314),f331(f331(f261(f884(x67311),f884(x67311)),x67312),x67313))
% 162.26/162.07 [6824]~P107(x68242)+E(f331(f197(f884(x68241)),f331(f331(f151(x68241,x68242,x68243),x68244),x68245)),f331(a118,f331(f197(f884(x68241)),x68245)))
% 162.26/162.07 [6836]~P107(x68362)+E(f331(f175(x68361),f331(f331(f151(x68361,x68362,x68363),x68364),x68365)),f331(f331(f309(x68361),x68364),f331(f175(x68361),x68365)))
% 162.26/162.07 [7107]~P118(x71071)+E(f331(f331(f81(x71071),f331(f331(f81(x71071),x71072),x71073)),f331(f331(f81(x71071),x71074),x71075)),f331(f331(f81(x71071),f331(f331(f81(x71071),x71072),x71074)),f331(f331(f81(x71071),x71073),x71075)))
% 162.26/162.07 [7108]~P118(x71081)+E(f331(f331(f82(x71081),f331(f331(f82(x71081),x71082),x71083)),f331(f331(f82(x71081),x71084),x71085)),f331(f331(f82(x71081),f331(f331(f82(x71081),x71082),x71084)),f331(f331(f82(x71081),x71083),x71085)))
% 162.26/162.07 [7109]~P61(x71091)+E(f331(f331(f289(x71091),f331(f331(f82(x71091),x71092),x71093)),f331(f331(f82(x71091),x71094),x71095)),f331(f331(f82(x71091),f331(f331(f289(x71091),x71092),x71094)),f331(f331(f289(x71091),x71093),x71095)))
% 162.26/162.07 [7123]~P107(x71231)+E(f305(x71231,f331(f331(f246(x71231),x71232),x71233),f331(f331(f251(x71231),x71234),x71235)),f331(f331(f108(f891(x71231,a877)),f305(x71231,x71232,x71234)),f305(x71231,x71233,x71235)))
% 162.26/162.07 [7124]~P107(x71241)+E(f304(x71241,f331(f331(f246(x71241),x71242),x71243),f331(f331(f251(x71241),x71244),x71245)),f331(f331(f108(f891(x71241,a877)),f304(x71241,x71242,x71244)),f304(x71241,x71243,x71245)))
% 162.26/162.07 [7125]~P107(x71251)+E(f302(x71251,f331(f331(f246(x71251),x71252),x71253),f331(f331(f251(x71251),x71254),x71255)),f331(f331(f108(f891(x71251,a877)),f302(x71251,x71252,x71254)),f302(x71251,x71253,x71255)))
% 162.26/162.07 [7126]~P107(x71261)+E(f331(f331(f108(f891(x71261,a877)),f331(f301(x71261,x71262),x71263)),f331(f301(x71261,x71264),x71265)),f331(f301(x71261,f331(f331(f246(x71261),x71262),x71264)),f331(f331(f251(x71261),x71263),x71265)))
% 162.26/162.07 [7241]~P24(f331(x72411,f387(x72413,x72412,x72411)))+P24(f331(x72411,f331(f331(f261(x72412,x72413),x72414),x72415)))
% 162.26/162.07 [7317]~E(f331(x73173,x73174),f199(x73172))+E(f188(x73171,x73172,f331(f331(f331(f73(x73171,f887(x73172)),x73173),x73174),f331(f239(x73172),x73175))),f331(f331(f309(x73172),x73175),f188(x73171,x73172,x73173)))
% 162.26/162.07 [7338]~E(x73382,f331(x73384,x73385))+P24(f331(f331(f333(x73381),x73382),f331(f310(x73383,x73381,x73384),f256(f891(x73383,a877)))))
% 162.26/162.07 [7396]~E(f331(x73963,x73964),f199(x73962))+E(f331(f331(f22(f891(x73961,a877)),f186(x73961,x73962,x73963)),f331(f331(f309(x73961),x73964),x73965)),f331(f331(f22(f891(x73961,a877)),f186(x73961,x73962,x73963)),x73965))
% 162.26/162.07 [7415]~P12(x74153,x74152,x74154)+P12(x74151,x74152,f331(f331(f8(x74153,f891(x74152,x74152),x74151),x74154),x74155))
% 162.26/162.07 [7416]~P11(x74163,x74162,x74164)+P11(x74161,x74162,f331(f331(f8(x74163,f891(x74162,x74162),x74161),x74164),x74165))
% 162.26/162.07 [7555]~P21(x75551,x75552,x75553,x75554)+P21(x75551,x75552,x75553,f331(f331(f22(f891(x75551,a877)),x75554),x75555))
% 162.26/162.07 [7709]~P24(f331(f331(x77093,x77094),x77095))+P24(f331(f331(f270(x77091,x77092,a877),x77093),f331(f331(f261(x77091,x77092),x77094),x77095)))
% 162.26/162.07 [7824]~P24(f331(x78242,x78244))+~E(f331(f331(f141(x78241),f331(f197(f884(x78241)),f179(x78241,x78242,x78243))),x78243),f331(f331(f154(x78241),x78244),x78245))
% 162.26/162.07 [7844]P21(x78441,x78442,x78443,x78444)+~P21(x78441,x78442,x78443,f331(f331(f107(f891(x78441,a877)),x78445),x78444))
% 162.26/162.07 [7845]P21(x78451,x78452,x78453,x78454)+~P21(x78451,x78452,x78453,f331(f331(f107(f891(x78451,a877)),x78454),x78455))
% 162.26/162.07 [7887]~P107(x78872)+E(f331(f331(f151(x78871,x78872,x78873),x78874),f153(x78871,x78872,x78873,x78875)),f153(x78871,x78872,x78873,f331(f331(f154(x78871),x78874),x78875)))
% 162.26/162.07 [8046]~P30(x80461,f331(a118,x80462),f331(f331(f331(f93(x80461),x80463),f331(a28,x80464)),x80465))+P30(x80461,x80462,f331(f331(f331(f93(x80461),x80463),f331(f244(a879),f331(a26,x80464))),x80465))
% 162.26/162.07 [8185]P30(x81851,f331(a118,x81852),f331(f331(f331(f93(x81851),x81853),f331(a28,x81854)),x81855))+~P30(x81851,x81852,f331(f331(f331(f93(x81851),x81853),f331(f244(a879),f331(a26,x81854))),x81855))
% 162.26/162.07 [8213]~P11(x82132,x82131,x82133)+E(f331(f145(x82131,x82132,f331(f7(x82132,x82131,x82131),x82133),x82134),x82135),f331(f331(f65(x82132,x82131,x82133),x82134),f331(f175(x82132),x82135)))
% 162.26/162.07 [8241]~E(f331(f331(f141(x82411),f331(f197(f884(x82411)),f179(x82411,x82412,x82413))),x82413),f331(f331(f154(x82411),x82414),x82415))+E(f331(f331(f137(x82411),f179(x82411,x82412,x82413)),f331(f331(f154(x82411),x82414),x82415)),x82413)
% 162.26/162.07 [8265]P24(f331(f331(x82651,x82652),x82653))+~P24(f331(f331(f270(x82654,x82655,a877),x82651),f331(f331(f261(x82654,x82655),x82652),x82653)))
% 162.26/162.07 [8324]~E(f331(f331(f180(x83241,x83242),x83245),x83243),f331(f239(x83242),x83244))+P24(f331(f331(f333(f890(x83241,x83242)),f331(f331(f261(x83241,x83242),x83243),x83244)),f331(f175(f890(x83241,x83242)),x83245)))
% 162.26/162.07 [8719]P24(f331(f331(f247(f891(x87191,a877)),f331(f310(x87192,x87191,x87193),x87194)),f331(f310(x87192,x87191,x87193),x87195)))+~P24(f331(f331(f247(f891(x87192,a877)),x87194),x87195))
% 162.26/162.07 [8720]P24(f331(f331(f247(f891(x87201,a877)),f331(f311(x87201,x87202,x87203),x87204)),f331(f311(x87201,x87202,x87203),x87205)))+~P24(f331(f331(f247(f891(x87202,a877)),x87204),x87205))
% 162.26/162.07 [8797]E(x87971,f2(a105))+E(f331(f331(f272(x87972,x87973,x87972,f890(x87973,x87972)),f331(x87974,x87975)),f280(x87973,x87972,f331(f331(f22(a105),x87971),f79(a105)),x87974)),f331(f280(x87973,x87972,x87971,x87974),x87975))
% 162.26/162.07 [9112]P30(x91121,x91122,f331(f331(f331(f93(x91121),x91123),x91124),x91125))+P24(f331(f331(x91123,f549(x91125,x91124,x91123,x91122)),f570(x91125,x91124,x91123,x91122)))
% 162.26/162.07 [9319]E(f331(f239(x93191),f609(x93192,x93193,x93194,x93191,x93195)),f331(f331(f180(x93195,x93191),x93192),x93194))+~P24(f331(f331(f333(f890(x93195,x93191)),f331(f331(f261(x93195,x93191),x93194),x93193)),f331(f175(f890(x93195,x93191)),x93192)))
% 162.26/162.07 [9367]P30(x93671,x93672,f331(f331(f331(f93(x93671),x93673),x93674),x93675))+~P24(f331(f331(x93675,f549(x93675,x93674,x93673,x93672)),f580(x93675,x93674,x93673,x93672)))
% 162.26/162.07 [9419]P30(x94191,x94192,f331(f331(f331(f93(x94191),x94193),x94194),x94195))+P24(f331(f331(f331(f331(a205,x94194),f570(x94195,x94194,x94193,x94192)),x94192),f580(x94195,x94194,x94193,x94192)))
% 162.26/162.07 [9423]~P20(x94231,x94232,f331(f331(f309(f882(x94231)),f331(f331(f331(f93(x94231),x94233),f331(f244(a879),f331(a26,x94234))),x94235)),f196(f891(f882(x94231),a877))))+P20(x94231,x94232,f331(f331(f309(f882(x94231)),f331(f331(f331(f93(x94231),x94233),f331(a28,x94234)),x94235)),f196(f891(f882(x94231),a877))))
% 162.26/162.07 [9449]~P24(f331(f62(x94493),f331(f310(x94492,x94493,x94495),f256(f891(x94492,a877)))))+P24(f331(f62(x94491),f331(f310(x94492,x94491,f331(f331(f8(x94493,x94491,x94492),x94494),x94495)),f256(f891(x94492,a877)))))
% 162.26/162.07 [9471]P24(f331(f331(f247(f891(f891(x94711,a877),a877)),f331(f310(f891(x94712,a877),f891(x94711,a877),f310(x94712,x94711,x94713)),f331(f308(x94712),x94714))),f331(f308(x94711),x94715)))+~P24(f331(f331(f247(f891(x94711,a877)),f331(f310(x94712,x94711,x94713),x94714)),x94715))
% 162.26/162.07 [9488]~P24(f331(f62(f887(x94881)),f331(f310(x94882,f887(x94881),x94883),f256(f891(x94882,a877)))))+P24(f331(f62(f887(x94881)),f331(f310(x94882,f887(x94881),f331(f331(f331(f73(x94882,f887(x94881)),x94883),x94884),f331(f239(x94881),x94885))),f256(f891(x94882,a877)))))
% 162.26/162.07 [9558]E(x95581,x95582)+~P24(f331(f67(x95583,x95584,x95585,x95581,f196(f891(x95583,a877))),x95582))
% 162.26/162.07 [9571]E(f331(f331(f261(x95711,x95712),f554(x95713,x95714,x95715,x95712,x95711)),f555(x95713,x95714,x95715,x95712,x95711)),x95715)+~P24(f331(f331(f333(f890(x95711,x95712)),x95715),f331(f331(f268(x95711,x95712),x95714),x95713)))
% 162.26/162.07 [9674]P24(f331(f331(f333(x96741),f554(x96742,x96743,x96744,x96745,x96741)),x96743))+~P24(f331(f331(f333(f890(x96741,x96745)),x96744),f331(f331(f268(x96741,x96745),x96743),x96742)))
% 162.26/162.07 [9797]P20(x97975,x97974,f331(f331(f309(f882(x97975)),f331(f331(f331(f93(x97975),x97971),x97973),x97972)),f196(f891(f882(x97975),a877))))+P24(f331(f331(x97971,f495(x97972,x97973,x97974,x97975,x97971)),f496(x97972,x97973,x97974,x97975,x97971)))
% 162.26/162.07 [9850]P24(f331(f331(f333(x98501),f555(x98502,x98503,x98504,x98501,x98505)),f331(x98502,f554(x98502,x98503,x98504,x98501,x98505))))+~P24(f331(f331(f333(f890(x98505,x98501)),x98504),f331(f331(f268(x98505,x98501),x98503),x98502)))
% 162.26/162.07 [9868]P24(f331(f331(f333(f890(x98681,x98681)),f331(f331(f261(x98681,x98681),x98682),f777(x98683,x98684,x98685,x98682,x98681))),x98683))+~P24(f331(f331(f333(f890(x98681,x98681)),f331(f331(f261(x98681,x98681),x98682),x98685)),f331(f331(f191(f890(x98681,x98681),a877),f331(a118,x98684)),x98683)))
% 162.26/162.07 [9869]P24(f331(f331(f333(f890(x98691,x98691)),f331(f331(f261(x98691,x98691),x98692),f778(x98693,x98694,x98695,x98692,x98691))),x98693))+~P24(f331(f331(f333(f890(x98691,x98691)),f331(f331(f261(x98691,x98691),x98692),x98695)),f331(f331(f191(f890(x98691,x98691),a877),f331(a118,x98694)),x98693)))
% 162.26/162.07 [9888]~P24(f331(f331(f333(f890(f884(x98881),f884(x98881))),f331(f331(f261(f884(x98881),f884(x98881)),f331(f331(f154(x98881),x98882),x98885)),x98884)),f161(x98881,x98883)))+P24(f331(f331(f333(f890(x98881,x98881)),f331(f331(f261(x98881,x98881),x98882),f618(x98883,x98884,x98885,x98882,x98881))),x98883))
% 162.26/162.07 [9890]~P20(x98901,x98902,f331(f331(f309(f882(x98901)),f331(f331(f331(f93(x98901),f98(x98901,x98903,x98904)),x98905),x98903)),f196(f891(f882(x98901),a877))))+P20(x98901,x98902,f331(f331(f309(f882(x98901)),f331(f331(f331(f93(x98901),x98903),f33(x98904,x98905)),f98(x98901,x98903,f331(f74(a877,a877,a878,a326),x98904)))),f196(f891(f882(x98901),a877))))
% 162.26/162.07 [9891]~P23(x98911,x98912,f331(f331(f309(f882(x98911)),f331(f331(f331(f93(x98911),f98(x98911,x98913,x98914)),x98915),x98913)),f196(f891(f882(x98911),a877))))+P23(x98911,x98912,f331(f331(f309(f882(x98911)),f331(f331(f331(f93(x98911),x98913),f33(x98914,x98915)),f98(x98911,x98913,f331(f74(a877,a877,a878,a326),x98914)))),f196(f891(f882(x98911),a877))))
% 162.26/162.07 [10166]P20(x101661,x101662,f331(f331(f309(f882(x101661)),f331(f331(f331(f93(x101661),x101663),x101664),x101665)),f196(f891(f882(x101661),a877))))+~P20(x101661,x101662,f331(f331(f309(f882(x101661)),f331(f331(f331(f93(x101661),f331(f16(f891(a878,a877),x101661),f331(f331(f7(a878,a878,a877),a328),f496(x101665,x101664,x101662,x101661,x101663)))),x101664),f331(f16(f891(a878,a877),x101661),f331(x101665,f495(x101665,x101664,x101662,x101661,x101663))))),f196(f891(f882(x101661),a877))))
% 162.26/162.07 [6347]P24(f331(x63472,x63474))+E(f179(x63471,x63472,f331(f331(f137(x63471),x63473),f331(f331(f154(x63471),x63474),x63475))),f179(x63471,x63472,x63473))
% 162.26/162.07 [6396]~P65(x63962)+E(f331(f331(f331(f22(f891(x63961,x63962)),x63963),x63964),x63965),f331(f331(f22(x63962),f331(x63963,x63965)),f331(x63964,x63965)))
% 162.26/162.07 [6398]~P96(x63982)+E(f331(f331(f331(f107(f891(x63981,x63982)),x63983),x63984),x63985),f331(f331(f107(x63982),f331(x63983,x63985)),f331(x63984,x63985)))
% 162.26/162.07 [6400]~P96(x64002)+E(f331(f331(f331(f108(f891(x64001,x64002)),x64003),x64004),x64005),f331(f331(f108(x64002),f331(x64003,x64005)),f331(x64004,x64005)))
% 162.26/162.07 [6418]E(x64181,x64182)+E(f331(f331(f168(x64183),f331(f331(f162(x64183,x64184),x64181),x64185)),x64182),f331(f331(f168(x64183),x64184),x64182))
% 162.26/162.07 [6679]~E(x66794,f196(f891(x66793,a877)))+E(f331(f331(f22(f891(x66791,a877)),x66792),f331(f331(f42(x66793,f891(x66791,a877)),x66794),x66795)),x66792)
% 162.26/162.07 [6680]~E(x66804,f196(f891(x66803,a877)))+E(f331(f331(f107(f891(x66801,a877)),x66802),f331(f331(f42(x66803,f891(x66801,a877)),x66804),x66805)),x66802)
% 162.26/162.07 [6681]~E(x66814,f196(f891(x66813,a877)))+E(f331(f331(f108(f891(x66811,a877)),x66812),f331(f331(f43(x66813,f891(x66811,a877)),x66814),x66815)),x66812)
% 162.26/162.07 [6695]~E(x66954,f196(f891(x66953,a877)))+E(f331(f331(f309(x66951),x66952),f331(f331(f42(x66953,f891(x66951,a877)),x66954),x66955)),f331(f331(f309(x66951),x66952),f196(f891(x66951,a877))))
% 162.26/162.07 [7464]E(f331(f331(f168(x74641),f331(f331(f157(x74642,x74641),x74643),x74644)),x74645),f331(x74643,f331(f331(f168(x74642),x74644),x74645)))+~P24(f331(f331(f248(a883),x74645),f331(f197(f884(x74642)),x74644)))
% 162.26/162.07 [7528]E(f331(f331(f107(f891(x75281,a877)),f331(x75282,x75283)),f331(f331(f42(x75284,f891(x75281,a877)),x75285),x75282)),f331(f331(f42(x75284,f891(x75281,a877)),x75285),x75282))+~P24(f331(f331(f333(x75284),x75283),x75285))
% 162.26/162.07 [7529]E(f331(f331(f108(f891(x75291,a877)),f331(x75292,x75293)),f331(f331(f43(x75294,f891(x75291,a877)),x75295),x75292)),f331(f331(f43(x75294,f891(x75291,a877)),x75295),x75292))+~P24(f331(f331(f333(x75294),x75293),x75295))
% 162.26/162.07 [8130]~E(x81303,f196(f891(x81301,a877)))+E(f331(f331(f42(x81301,f891(x81302,a877)),x81303),f331(f331(f8(f891(x81302,a877),f891(x81302,a877),x81301),f331(f309(x81302),x81304)),x81305)),f196(f891(x81302,a877)))
% 162.26/162.07 [8136]~P24(f331(f331(f333(x81364),x81363),x81365))+P24(f331(f331(f247(f891(x81361,a877)),f331(x81362,x81363)),f331(f331(f42(x81364,f891(x81361,a877)),x81365),x81362)))
% 162.26/162.07 [8264]~E(f331(x82644,x82642),x82645)+P24(f331(f331(f333(x82641),x82642),f331(f311(x82641,x82643,x82644),f331(f331(f309(x82643),x82645),f196(f891(x82643,a877))))))
% 162.26/162.07 [8310]~P52(x83101,x83102,f331(f286(x83102,x83101),x83103))+E(f331(f331(f108(f891(x83101,a877)),f331(f285(x83102,x83101,x83103),x83104)),f331(f285(x83102,x83101,x83103),x83105)),f331(f285(x83102,x83101,x83103),f331(f331(f108(f891(x83102,a877)),x83104),x83105)))
% 162.26/162.07 [8383]E(x83831,f2(a105))+E(f331(f124(x83832,x83833,f331(x83834,f331(f331(f22(a105),x83831),f79(a105)))),f331(f331(f7(x83832,a105,f885(x83833)),x83835),x83831)),f331(f209(x83832,x83833,x83834,x83835),x83831))
% 162.26/162.07 [8423]E(x84231,f196(f891(x84232,a877)))+E(f331(f331(f42(x84232,f891(x84233,a877)),x84231),f331(f331(f8(f891(x84233,a877),f891(x84233,a877),x84232),f331(f309(x84233),x84234)),x84235)),f331(f331(f309(x84233),x84234),f331(f331(f42(x84232,f891(x84233,a877)),x84231),x84235)))
% 162.26/162.07 [8478]~P21(x84782,x84781,x84783,f256(f891(x84782,a877)))+E(f331(f331(f22(f891(x84781,a877)),f331(f310(x84782,x84781,x84783),x84784)),f331(f310(x84782,x84781,x84783),x84785)),f331(f310(x84782,x84781,x84783),f331(f331(f22(f891(x84782,a877)),x84784),x84785)))
% 162.26/162.07 [8479]~P21(x84792,x84791,x84793,f256(f891(x84792,a877)))+E(f331(f331(f108(f891(x84791,a877)),f331(f310(x84792,x84791,x84793),x84794)),f331(f310(x84792,x84791,x84793),x84795)),f331(f310(x84792,x84791,x84793),f331(f331(f108(f891(x84792,a877)),x84794),x84795)))
% 162.26/162.07 [8547]~P24(f331(f331(f68(x85471,x85472,x85475),x85473),x85474))+P24(f331(f331(f333(f890(x85471,x85472)),f331(f331(f261(x85471,x85472),x85473),x85474)),x85475))
% 162.26/162.07 [8578]P24(f331(f331(f333(x85781),x85782),f331(f257(x85783,x85781),x85784)))+~P24(f331(f331(f333(f890(x85783,x85781)),f331(f331(f261(x85783,x85781),x85785),x85782)),x85784))
% 162.26/162.07 [8580]P24(f331(f331(f333(x85801),x85802),f331(f259(x85801,x85803),x85804)))+~P24(f331(f331(f333(f890(x85801,x85803)),f331(f331(f261(x85801,x85803),x85802),x85805)),x85804))
% 162.26/162.07 [8705]P24(f331(f331(f68(x87051,x87052,x87053),x87054),x87055))+~P24(f331(f331(f333(f890(x87051,x87052)),f331(f331(f261(x87051,x87052),x87054),x87055)),x87053))
% 162.26/162.07 [8735]E(f331(x87351,x87352),x87353)+~P24(f331(f331(f333(x87354),x87352),f331(f311(x87354,x87355,x87351),f331(f331(f309(x87355),x87353),f196(f891(x87355,a877))))))
% 162.26/162.07 [8978]P24(f331(f331(f333(f890(x89781,x89782)),f331(f331(f261(x89781,x89782),x89783),x89784)),f331(f286(x89782,x89781),x89785)))+~P24(f331(f331(f333(f890(x89782,x89781)),f331(f331(f261(x89782,x89781),x89784),x89783)),x89785))
% 162.26/162.07 [8996]~P24(f331(f331(x89961,x89965),x89964))+P24(f331(f331(x89961,f331(f269(x89962,x89963),f331(f331(f261(x89962,x89963),x89964),x89965))),f331(f260(x89962,x89963),f331(f331(f261(x89962,x89963),x89964),x89965))))
% 162.26/162.07 [9026]~P24(f331(f331(f333(f890(x90262,x90261)),f331(f331(f261(x90262,x90261),x90264),x90263)),f331(f286(x90261,x90262),x90265)))+P24(f331(f331(f333(f890(x90261,x90262)),f331(f331(f261(x90261,x90262),x90263),x90264)),x90265))
% 162.26/162.07 [9049]~P24(f331(f331(f333(f890(x90493,x90491)),f331(f331(f261(x90493,x90491),x90495),x90492)),x90494))+P24(f331(f331(f333(x90491),x90492),f331(f285(x90493,x90491,x90494),f331(f331(f309(x90493),x90495),f196(f891(x90493,a877))))))
% 162.26/162.07 [9093]P24(f331(f331(f333(f890(x90931,x90932)),f331(f331(f261(x90931,x90932),x90933),x90934)),x90935))+~P24(f331(f331(f333(x90932),x90934),f331(f285(x90931,x90932,x90935),f331(f331(f309(x90931),x90933),f196(f891(x90931,a877))))))
% 162.26/162.07 [9115]E(f331(f331(f331(f73(x91151,f887(x91152)),f190(x91151,x91152,x91153,x91154)),x91155),f199(x91152)),f190(x91151,x91152,x91153,f331(f331(f22(f891(x91151,a877)),x91154),f331(f331(f309(x91151),x91155),f196(f891(x91151,a877))))))+~P24(f331(f331(f333(x91151),x91155),x91154))
% 162.26/162.07 [9188]~P74(x91881)+E(f331(f331(f6(a883,x91881),x91882),f302(a883,f331(f331(f81(a883),x91883),x91884),f331(f331(f81(a883),x91885),x91884))),f331(f331(f6(a883,x91881),f331(f331(f8(a883,x91881,a883),x91882),f331(f331(f7(a883,a883,a883),f81(a883)),x91884))),f302(a883,x91883,x91885)))
% 162.26/162.07 [9210]~P74(x92101)+E(f331(f331(f6(a883,x92101),x92102),f331(f301(a883,f331(f331(f81(a883),x92103),x92104)),f331(f331(f81(a883),x92105),x92104))),f331(f331(f6(a883,x92101),f331(f331(f8(a883,x92101,a883),x92102),f331(f331(f7(a883,a883,a883),f81(a883)),x92104))),f331(f301(a883,x92103),x92105)))
% 162.26/162.07 [9264]~P21(x92641,x92642,x92643,f256(f891(x92641,a877)))+E(f331(f331(f157(x92641,x92642),x92643),f331(f139(x92641,f331(f331(f8(a877,a877,x92641),a326),f331(a328,x92644))),x92645)),f331(f139(x92642,f331(f331(f8(a877,a877,x92642),a326),f331(a328,f331(x92643,x92644)))),f331(f331(f157(x92641,x92642),x92643),x92645)))
% 162.26/162.07 [9285]~P21(x92851,x92852,x92853,f331(f331(f309(x92851),x92854),f331(f175(x92851),x92855)))+E(f331(f331(f157(x92851,x92852),x92853),f331(f139(x92851,f331(f331(f8(a877,a877,x92851),a326),f331(a328,x92854))),x92855)),f331(f139(x92852,f331(f331(f8(a877,a877,x92852),a326),f331(a328,f331(x92853,x92854)))),f331(f331(f157(x92851,x92852),x92853),x92855)))
% 162.26/162.07 [9436]P24(f331(f331(f333(f890(f884(x94361),f884(x94361))),f331(f331(f261(f884(x94361),f884(x94361)),f331(f331(f154(x94361),x94362),x94363)),f331(f331(f154(x94361),x94364),x94363))),f160(x94361,x94365)))+~P24(f331(f331(f333(f890(x94361,x94361)),f331(f331(f261(x94361,x94361),x94362),x94364)),x94365))
% 162.26/162.07 [9476]P24(f331(f331(f331(f331(a205,x94761),x94762),x94763),f547(x94764,x94763,x94762,x94765,x94761)))+~P24(f331(f331(f331(f331(a205,f34(x94761,x94765)),x94762),x94763),x94764))
% 162.26/162.07 [9556]P20(x95561,x95562,f331(f331(f309(f882(x95561)),f331(f331(f331(f93(x95561),x95563),f331(a28,x95564)),x95565)),f196(f891(f882(x95561),a877))))+~P20(x95561,f331(f331(f309(f882(x95561)),f331(f331(f331(f93(x95561),x95563),f331(a28,x95564)),x95565)),x95562),f331(f331(f309(f882(x95561)),f331(f331(f331(f93(x95561),x95563),f331(f244(a879),f331(a26,x95564))),x95565)),f196(f891(f882(x95561),a877))))
% 162.26/162.07 [9566]E(f331(f331(f309(x95661),f600(x95662,x95663,x95664,x95665,x95661)),f614(x95662,x95663,x95664,x95665,x95661)),f331(f331(f309(x95661),x95664),x95663))+~P24(f331(f63(x95661,x95665,f331(f331(f309(x95661),x95664),x95663)),x95662))
% 162.26/162.07 [9567]E(f331(f331(f309(x95671),f649(x95672,x95673,x95674,x95675,x95671)),f659(x95672,x95673,x95674,x95675,x95671)),f331(f331(f309(x95671),x95674),x95673))+~P24(f331(f63(x95671,x95675,f331(f331(f309(x95671),x95674),x95673)),x95672))
% 162.26/162.07 [9660]P24(f331(f331(f333(x96601),f514(x96602,x96603,x96604,x96605,x96601)),x96604))+P24(f331(f331(f331(f43(x96601,f891(x96605,a877)),x96604),x96603),x96602))
% 162.26/162.07 [9665]P24(f331(f331(f333(x96651),f509(x96652,x96653,x96651,x96654,x96655)),x96653))+P24(f331(f331(f333(x96655),x96654),f331(f331(f43(x96651,f891(x96655,a877)),x96653),x96652)))
% 162.26/162.07 [9673]P24(f331(f331(f333(x96731),f510(x96732,x96733,x96731,x96734,x96735)),x96733))+P24(f331(f331(f247(f891(x96735,a877)),x96734),f331(f331(f43(x96731,f891(x96735,a877)),x96733),x96732)))
% 162.26/162.07 [9675]P24(f331(f331(x96751,f352(x96752,x96751,x96753,x96754,x96755)),x96752))+~P24(f331(f331(f331(f42(x96755,f891(x96754,a877)),x96753),x96751),x96752))
% 162.26/162.07 [9678]P24(f331(f331(f333(x96781),f352(x96782,x96783,x96784,x96785,x96781)),x96784))+~P24(f331(f331(f331(f42(x96781,f891(x96785,a877)),x96784),x96783),x96782))
% 162.26/162.07 [9689]P24(f331(f331(f333(x96891),f357(x96892,x96893,x96891,x96894,x96895)),x96893))+~P24(f331(f331(f333(x96895),x96894),f331(f331(f42(x96891,f891(x96895,a877)),x96893),x96892)))
% 162.26/162.07 [9694]P24(f331(f331(f333(x96941),x96942),f331(x96943,f357(x96943,x96944,x96945,x96942,x96941))))+~P24(f331(f331(f333(x96941),x96942),f331(f331(f42(x96945,f891(x96941,a877)),x96944),x96943)))
% 162.26/162.07 [9802]~P24(f331(f331(x98024,f514(x98025,x98024,x98023,x98022,x98021)),x98025))+P24(f331(f331(f331(f43(x98021,f891(x98022,a877)),x98023),x98024),x98025))
% 162.26/162.07 [9805]~P24(f331(f331(f333(x98051),x98052),f331(x98055,f509(x98055,x98054,x98053,x98052,x98051))))+P24(f331(f331(f333(x98051),x98052),f331(f331(f43(x98053,f891(x98051,a877)),x98054),x98055)))
% 162.26/162.07 [9807]~P24(f331(f331(f247(f891(x98071,a877)),x98072),f331(x98075,f510(x98075,x98074,x98073,x98072,x98071))))+P24(f331(f331(f247(f891(x98071,a877)),x98072),f331(f331(f43(x98073,f891(x98071,a877)),x98074),x98075)))
% 162.26/162.07 [9854]P24(f331(f331(f331(f331(a205,x98541),f547(x98542,x98543,x98544,x98541,x98545)),x98543),x98542))+~P24(f331(f331(f331(f331(a205,f34(x98545,x98541)),x98544),x98543),x98542))
% 162.26/162.07 [9873]~P24(f331(f331(f333(x98731),f600(x98735,x98734,x98733,x98732,x98731)),f614(x98735,x98734,x98733,x98732,x98731)))+~P24(f331(f63(x98731,x98732,f331(f331(f309(x98731),x98733),x98734)),x98735))
% 162.26/162.07 [9874]~P24(f331(f331(f333(x98741),f649(x98745,x98744,x98743,x98742,x98741)),f659(x98745,x98744,x98743,x98742,x98741)))+~P24(f331(f63(x98741,x98742,f331(f331(f309(x98741),x98743),x98744)),x98745))
% 162.26/162.07 [9875]~P24(f331(f331(f333(f890(x98751,x98751)),f331(f331(f261(x98751,x98751),x98752),x98755)),f331(f331(f191(f890(x98751,x98751),a877),f331(a118,x98754)),x98753)))+P24(f331(f331(f333(f890(x98751,x98751)),f331(f331(f261(x98751,x98751),x98752),f779(x98753,x98754,x98755,x98752,x98751))),f331(f331(f191(f890(x98751,x98751),a877),x98754),x98753)))
% 162.26/162.07 [9882]P24(f331(f67(x98821,x98821,x98822,f600(x98823,x98824,x98825,x98822,x98821),f614(x98823,x98824,x98825,x98822,x98821)),x98823))+~P24(f331(f63(x98821,x98822,f331(f331(f309(x98821),x98825),x98824)),x98823))
% 162.26/162.07 [9883]P24(f331(f67(x98831,x98831,x98832,f649(x98833,x98834,x98835,x98832,x98831),f659(x98833,x98834,x98835,x98832,x98831)),x98833))+~P24(f331(f63(x98831,x98832,f331(f331(f309(x98831),x98835),x98834)),x98833))
% 162.26/162.07 [9894]~P107(x98941)+P29(x98941,f331(f331(f157(x98942,x98941),x98943),f331(f139(x98942,f331(f331(f7(x98942,x98941,a877),f331(f331(f8(x98941,f891(x98941,a877),x98942),a328),x98943)),f331(x98944,x98945))),x98945)))
% 162.26/162.07 [9930]~P24(f331(f331(f333(x99302),x99305),f331(f285(x99301,x99302,x99304),x99303)))+P24(f331(f331(f333(f890(x99301,x99302)),f331(f331(f261(x99301,x99302),f443(x99303,x99304,x99301,x99305,x99302)),x99305)),x99304))
% 162.26/162.07 [9931]~P24(f331(f331(f333(x99312),x99315),f331(f285(x99311,x99312,x99314),x99313)))+P24(f331(f331(f333(f890(x99311,x99312)),f331(f331(f261(x99311,x99312),f491(x99313,x99314,x99311,x99315,x99312)),x99315)),x99314))
% 162.26/162.07 [9936]~P24(f331(f331(f333(f890(x99361,x99361)),f331(f331(f261(x99361,x99361),x99365),x99364)),f331(f331(f191(f890(x99361,x99361),a877),f331(a118,x99363)),x99362)))+P24(f331(f331(f333(f890(x99361,x99361)),f331(f331(f261(x99361,x99361),f779(x99362,x99363,x99364,x99365,x99361)),x99364)),x99362))
% 162.26/162.07 [9948]~P24(f331(f331(f333(f890(x99481,x99481)),f331(f331(f261(x99481,x99481),x99485),x99484)),f331(f331(f191(f890(x99481,x99481),a877),f331(a118,x99483)),x99482)))+P24(f331(f331(f333(f890(x99481,x99481)),f331(f331(f261(x99481,x99481),f777(x99482,x99483,x99484,x99485,x99481)),x99484)),f331(f331(f191(f890(x99481,x99481),a877),x99483),x99482)))
% 162.26/162.07 [9949]~P24(f331(f331(f333(f890(x99491,x99491)),f331(f331(f261(x99491,x99491),x99495),x99494)),f331(f331(f191(f890(x99491,x99491),a877),f331(a118,x99493)),x99492)))+P24(f331(f331(f333(f890(x99491,x99491)),f331(f331(f261(x99491,x99491),f778(x99492,x99493,x99494,x99495,x99491)),x99494)),f331(f331(f191(f890(x99491,x99491),a877),x99493),x99492)))
% 162.26/162.07 [9950]~P24(f331(f331(f333(f890(f884(x99501),f884(x99501))),f331(f331(f261(f884(x99501),f884(x99501)),x99505),f331(f331(f154(x99501),x99504),x99503))),f161(x99501,x99502)))+P24(f331(f331(f333(f890(x99501,x99501)),f331(f331(f261(x99501,x99501),f616(x99502,x99503,x99504,x99505,x99501)),x99504)),x99502))
% 162.26/162.07 [7070]E(x70701,f199(x70702))+E(f186(x70703,x70702,f331(f331(f331(f73(x70703,f887(x70702)),x70704),x70705),x70701)),f331(f331(f309(x70703),x70705),f186(x70703,x70702,x70704)))
% 162.26/162.07 [7549]~E(x75493,f196(f891(x75492,a877)))+E(f331(f331(f107(f891(x75491,a877)),f331(f331(f42(x75492,f891(x75491,a877)),x75493),x75494)),x75495),x75495)
% 162.26/162.07 [7550]~E(x75503,f196(f891(x75502,a877)))+E(f331(f331(f108(f891(x75501,a877)),f331(f331(f43(x75502,f891(x75501,a877)),x75503),x75504)),x75505),x75505)
% 162.26/162.07 [7902]~E(x79025,f199(x79022))+E(f186(x79021,x79022,f331(f331(f331(f73(x79021,f887(x79022)),x79023),x79024),x79025)),f331(f331(f22(f891(x79021,a877)),f186(x79021,x79022,x79023)),f331(f331(f309(x79021),x79024),f196(f891(x79021,a877)))))
% 162.26/162.07 [7965]~E(x79653,f196(f891(x79652,a877)))+E(f331(f331(f22(f891(x79651,a877)),f331(f331(f43(x79652,f891(x79651,a877)),x79653),x79654)),x79655),f331(f331(f22(f891(x79651,a877)),f256(f891(x79651,a877))),x79655))
% 162.26/162.07 [8101]E(f331(f331(f162(x81011,f331(f331(f137(x81011),x81012),x81013)),x81014),x81015),f331(f331(f137(x81011),f331(f331(f162(x81011,x81012),x81014),x81015)),x81013))+~P24(f331(f331(f248(a883),x81014),f331(f197(f884(x81011)),x81012)))
% 162.26/162.07 [8217]P24(f331(f331(f333(x82171),x82175),f331(f175(x82171),x82173)))+E(f331(f331(f180(x82171,x82172),f331(f331(f184(x82171,x82172),x82173),f331(f331(f157(x82171,x82172),x82174),x82173))),x82175),f199(x82172))
% 162.26/162.07 [8334]~P24(f331(f331(f333(x83341),x83345),f331(f175(x83341),x83343)))+E(f331(f331(f180(x83341,x83342),f331(f331(f184(x83341,x83342),x83343),f331(f331(f157(x83341,x83342),x83344),x83343))),x83345),f331(f239(x83342),f331(x83344,x83345)))
% 162.26/162.07 [8373]E(f331(f331(f168(x83731),f331(f331(f157(a883,x83731),x83732),f142(a883,f331(f301(a883,x83733),x83734)))),x83735),f331(x83732,f331(f331(f81(a883),x83733),x83735)))+~P24(f331(f331(f248(a883),x83735),f331(f331(f22(a883),x83734),x83733)))
% 162.26/162.07 [8389]E(x83891,f2(a105))+E(f126(x83892,x83893,f331(x83894,f331(f331(f22(a105),x83891),f79(a105))),f331(f331(f7(x83892,a105,f885(f887(x83893))),x83895),x83891)),f331(f207(x83892,x83893,x83894,x83895),x83891))
% 162.26/162.07 [8410]~E(x84103,f196(f891(x84101,a877)))+E(f331(f331(f42(x84101,f891(x84102,a877)),x84103),f331(f331(f8(f891(x84102,a877),f891(x84102,a877),x84101),f331(f107(f891(x84102,a877)),x84104)),x84105)),f196(f891(x84102,a877)))
% 162.26/162.07 [8411]~E(x84113,f196(f891(x84111,a877)))+E(f331(f331(f43(x84111,f891(x84112,a877)),x84113),f331(f331(f8(f891(x84112,a877),f891(x84112,a877),x84111),f331(f22(f891(x84112,a877)),x84114)),x84115)),f256(f891(x84112,a877)))
% 162.26/162.07 [8412]~E(x84123,f196(f891(x84121,a877)))+E(f331(f331(f43(x84121,f891(x84122,a877)),x84123),f331(f331(f8(f891(x84122,a877),f891(x84122,a877),x84121),f331(f108(f891(x84122,a877)),x84124)),x84125)),f256(f891(x84122,a877)))
% 162.26/162.07 [8417]~P144(x84172)+E(f331(f331(f6(x84171,x84172),f331(f331(f8(x84172,x84172,x84171),f331(f82(x84172),x84173)),x84174)),x84175),f331(f331(f82(x84172),x84173),f331(f331(f6(x84171,x84172),x84174),x84175)))
% 162.26/162.07 [8691]E(x86911,f196(f891(x86912,a877)))+E(f331(f331(f42(x86912,f891(x86913,a877)),x86911),f331(f331(f8(f891(x86913,a877),f891(x86913,a877),x86912),f331(f107(f891(x86913,a877)),x86914)),x86915)),f331(f331(f107(f891(x86913,a877)),x86914),f331(f331(f42(x86912,f891(x86913,a877)),x86911),x86915)))
% 162.26/162.07 [8692]E(x86921,f196(f891(x86922,a877)))+E(f331(f331(f43(x86922,f891(x86923,a877)),x86921),f331(f331(f8(f891(x86923,a877),f891(x86923,a877),x86922),f331(f22(f891(x86923,a877)),x86924)),x86925)),f331(f331(f22(f891(x86923,a877)),x86924),f331(f331(f42(x86922,f891(x86923,a877)),x86921),x86925)))
% 162.26/162.07 [8693]E(x86931,f196(f891(x86932,a877)))+E(f331(f331(f43(x86932,f891(x86933,a877)),x86931),f331(f331(f8(f891(x86933,a877),f891(x86933,a877),x86932),f331(f108(f891(x86933,a877)),x86934)),x86935)),f331(f331(f108(f891(x86933,a877)),x86934),f331(f331(f43(x86932,f891(x86933,a877)),x86931),x86935)))
% 162.26/162.07 [8893]~P24(f331(f331(f248(a883),f331(x88934,x88932)),f331(x88934,x88933)))+P24(f331(f331(f333(f890(x88931,x88931)),f331(f331(f261(x88931,x88931),x88932),x88933)),f156(x88931,f331(f331(f154(f891(x88931,a883)),x88934),x88935))))
% 162.26/162.07 [9155]~P21(x91552,x91551,x91553,f331(f331(f107(f891(x91552,a877)),x91554),x91555))+E(f331(f331(f108(f891(x91551,a877)),f331(f310(x91552,x91551,x91553),f331(f331(f22(f891(x91552,a877)),x91554),x91555))),f331(f310(x91552,x91551,x91553),f331(f331(f22(f891(x91552,a877)),x91555),x91554))),f196(f891(x91551,a877)))
% 162.26/162.07 [9434]~P24(f331(f331(f247(f891(x94343,a877)),f331(f285(x94341,x94343,x94344),x94342)),x94345))+P24(f331(f331(f247(f891(x94341,a877)),x94342),f331(f80(f891(x94341,a877)),f331(f285(x94343,x94341,f331(f286(x94341,x94343),x94344)),f331(f80(f891(x94343,a877)),x94345)))))
% 162.26/162.07 [9457]~P21(x94571,x94572,x94573,f331(f331(f309(x94571),x94574),x94575))+~P24(f331(f331(f333(x94572),f331(x94573,x94574)),f331(f310(x94571,x94572,x94573),f331(f331(f22(f891(x94571,a877)),x94575),f331(f331(f309(x94571),x94574),f196(f891(x94571,a877)))))))
% 162.26/162.07 [9522]P24(f331(f331(f247(f891(x95221,a877)),f331(f285(x95222,x95221,x95223),x95224)),x95225))+~P24(f331(f331(f247(f891(x95222,a877)),x95224),f331(f80(f891(x95222,a877)),f331(f285(x95221,x95222,f331(f286(x95222,x95221),x95223)),f331(f80(f891(x95221,a877)),x95225)))))
% 162.26/162.07 [9602]~P83(x96021)+P24(f331(f331(f247(x96021),f331(f76(x96021),f331(f331(f22(x96021),f331(f331(f81(x96021),x96022),x96023)),f331(f331(f81(x96021),x96024),x96025)))),f331(f331(f81(x96021),f331(f76(x96021),f331(f331(f22(x96021),x96022),x96024))),f331(f76(x96021),f331(f331(f22(x96021),x96023),x96025)))))
% 162.26/162.07 [9709]P24(f331(f331(f333(x97091),f361(x97092,x97093,x97094,x97091,x97095)),x97094))+P24(f331(f331(f247(f891(x97095,a877)),f331(f331(f42(x97091,f891(x97095,a877)),x97094),x97093)),x97092))
% 162.26/162.07 [9912]~P24(f331(f331(f247(f891(x99121,a877)),f331(x99124,f361(x99125,x99124,x99123,x99122,x99121))),x99125))+P24(f331(f331(f247(f891(x99121,a877)),f331(f331(f42(x99122,f891(x99121,a877)),x99123),x99124)),x99125))
% 162.26/162.07 [8528]E(f331(f331(f137(x85281),x85282),f331(f331(f162(x85281,x85283),f331(f331(f22(a883),x85284),f331(f197(f884(x85281)),x85282))),x85285)),f331(f331(f162(x85281,f331(f331(f137(x85281),x85282),x85283)),x85284),x85285))+P24(f331(f331(f248(a883),x85284),f331(f197(f884(x85281)),x85282)))
% 162.26/162.07 [8555]~P139(x85551)+E(f331(f331(f81(x85551),f331(f331(f82(x85551),x85552),x85553)),f331(f331(f81(x85551),f331(f331(f82(x85551),x85554),x85553)),x85555)),f331(f331(f81(x85551),f331(f331(f82(x85551),f331(f331(f81(x85551),x85552),x85554)),x85553)),x85555))
% 162.26/162.07 [9104]~P144(x91041)+E(f331(f169(x91041),f331(f331(f157(x91042,x91041),f331(f331(f8(x91041,x91041,x91042),f331(f82(x91041),x91043)),x91044)),x91045)),f331(f331(f82(x91041),x91043),f331(f169(x91041),f331(f331(f157(x91042,x91041),x91044),x91045))))
% 162.26/162.07 [9284]E(f331(f197(f884(x92841)),f331(f331(f176(x92841),f331(f331(f251(a883),f331(f197(f884(x92841)),x92842)),f331(f197(f884(x92843)),x92844))),x92842)),f331(f197(f884(x92843)),f331(f331(f176(x92843),f331(f331(f251(a883),f331(f197(f884(x92841)),x92842)),f331(f197(f884(x92843)),x92844))),x92844)))+P24(f331(x92845,f331(f331(f184(x92841,x92843),x92842),x92844)))
% 162.26/162.07 [9533]~P144(x95332)+E(f331(f331(f6(x95331,x95332),f331(f331(f7(x95331,x95332,x95332),f331(f331(f8(x95332,f891(x95332,x95332),x95331),f82(x95332)),x95333)),x95334)),x95335),f331(f331(f82(x95332),f331(f331(f6(x95331,x95332),x95333),x95335)),x95334))
% 162.26/162.07 [9534]~P62(x95342)+E(f331(f331(f6(x95341,x95342),f331(f331(f7(x95341,x95342,x95342),f331(f331(f8(x95342,f891(x95342,x95342),x95341),f289(x95342)),x95343)),x95344)),x95345),f331(f331(f289(x95342),f331(f331(f6(x95341,x95342),x95343),x95345)),x95344))
% 162.26/162.07 [9541]~P73(x95412)+E(f331(f331(f9(x95411,x95412),f331(f331(f18(x95411,x95412,x95412),f331(f331(f8(x95412,f891(x95412,x95412),x95411),f82(x95412)),x95413)),x95414)),x95415),f331(f331(f82(x95412),f331(f331(f9(x95411,x95412),x95413),x95415)),f331(f331(f9(x95411,x95412),x95414),x95415)))
% 162.26/162.07 [9542]~P70(x95422)+E(f331(f331(f6(x95421,x95422),f331(f331(f18(x95421,x95422,x95422),f331(f331(f8(x95422,f891(x95422,x95422),x95421),f22(x95422)),x95423)),x95424)),x95425),f331(f331(f22(x95422),f331(f331(f6(x95421,x95422),x95423),x95425)),f331(f331(f6(x95421,x95422),x95424),x95425)))
% 162.26/162.07 [9543]~P74(x95432)+E(f331(f331(f6(x95431,x95432),f331(f331(f18(x95431,x95432,x95432),f331(f331(f8(x95432,f891(x95432,x95432),x95431),f81(x95432)),x95433)),x95434)),x95435),f331(f331(f81(x95432),f331(f331(f6(x95431,x95432),x95433),x95435)),f331(f331(f6(x95431,x95432),x95434),x95435)))
% 162.26/162.07 [9579]~E(x95793,f196(f891(x95791,a877)))+E(f331(f331(f42(x95791,f891(x95792,a877)),x95793),f331(f331(f7(x95791,f891(x95792,a877),f891(x95792,a877)),f331(f331(f8(f891(x95792,a877),f891(f891(x95792,a877),f891(x95792,a877)),x95791),f107(f891(x95792,a877))),x95794)),x95795)),f196(f891(x95792,a877)))
% 162.26/162.07 [9580]~E(x95803,f196(f891(x95801,a877)))+E(f331(f331(f43(x95801,f891(x95802,a877)),x95803),f331(f331(f7(x95801,f891(x95802,a877),f891(x95802,a877)),f331(f331(f8(f891(x95802,a877),f891(f891(x95802,a877),f891(x95802,a877)),x95801),f22(f891(x95802,a877))),x95804)),x95805)),f256(f891(x95802,a877)))
% 162.26/162.07 [9581]~E(x95813,f196(f891(x95811,a877)))+E(f331(f331(f43(x95811,f891(x95812,a877)),x95813),f331(f331(f7(x95811,f891(x95812,a877),f891(x95812,a877)),f331(f331(f8(f891(x95812,a877),f891(f891(x95812,a877),f891(x95812,a877)),x95811),f108(f891(x95812,a877))),x95814)),x95815)),f256(f891(x95812,a877)))
% 162.26/162.07 [9610]E(x96101,f196(f891(x96102,a877)))+E(f331(f331(f42(x96102,f891(x96103,a877)),x96101),f331(f331(f7(x96102,f891(x96103,a877),f891(x96103,a877)),f331(f331(f8(f891(x96103,a877),f891(f891(x96103,a877),f891(x96103,a877)),x96102),f107(f891(x96103,a877))),x96104)),x96105)),f331(f331(f107(f891(x96103,a877)),f331(f331(f42(x96102,f891(x96103,a877)),x96101),x96104)),x96105))
% 162.26/162.07 [9611]E(x96111,f196(f891(x96112,a877)))+E(f331(f331(f43(x96112,f891(x96113,a877)),x96111),f331(f331(f7(x96112,f891(x96113,a877),f891(x96113,a877)),f331(f331(f8(f891(x96113,a877),f891(f891(x96113,a877),f891(x96113,a877)),x96112),f22(f891(x96113,a877))),x96114)),x96115)),f331(f331(f22(f891(x96113,a877)),f331(f331(f43(x96112,f891(x96113,a877)),x96111),x96114)),x96115))
% 162.26/162.07 [9612]E(x96121,f196(f891(x96122,a877)))+E(f331(f331(f43(x96122,f891(x96123,a877)),x96121),f331(f331(f7(x96122,f891(x96123,a877),f891(x96123,a877)),f331(f331(f8(f891(x96123,a877),f891(f891(x96123,a877),f891(x96123,a877)),x96122),f108(f891(x96123,a877))),x96124)),x96125)),f331(f331(f108(f891(x96123,a877)),f331(f331(f43(x96122,f891(x96123,a877)),x96121),x96124)),x96125))
% 162.26/162.07 [9162]~P24(f331(f331(f247(a883),x91621),x91624))+E(f331(f331(f22(a883),f331(f331(f81(a883),f331(f331(f82(a883),x91621),x91622)),x91623)),f331(f331(f81(a883),f331(f331(f82(a883),x91624),x91622)),x91625)),f331(f331(f22(a883),x91623),f331(f331(f81(a883),f331(f331(f82(a883),f331(f331(f22(a883),x91624),x91621)),x91622)),x91625)))
% 162.26/162.07 [9780]~P144(x97801)+E(f331(f169(x97801),f331(f331(f157(x97802,x97801),f331(f331(f7(x97802,x97801,x97801),f331(f331(f8(x97801,f891(x97801,x97801),x97802),f82(x97801)),x97803)),x97804)),x97805)),f331(f331(f82(x97801),f331(f169(x97801),f331(f331(f157(x97802,x97801),x97803),x97805))),x97804))
% 162.26/162.07 [9790]~P70(x97901)+E(f331(f169(x97901),f331(f331(f157(x97902,x97901),f331(f331(f18(x97902,x97901,x97901),f331(f331(f8(x97901,f891(x97901,x97901),x97902),f22(x97901)),x97903)),x97904)),x97905)),f331(f331(f22(x97901),f331(f169(x97901),f331(f331(f157(x97902,x97901),x97903),x97905))),f331(f169(x97901),f331(f331(f157(x97902,x97901),x97904),x97905))))
% 162.26/162.07 [9791]~P74(x97911)+E(f331(f169(x97911),f331(f331(f157(x97912,x97911),f331(f331(f18(x97912,x97911,x97911),f331(f331(f8(x97911,f891(x97911,x97911),x97912),f81(x97911)),x97913)),x97914)),x97915)),f331(f331(f81(x97911),f331(f169(x97911),f331(f331(f157(x97912,x97911),x97913),x97915))),f331(f169(x97911),f331(f331(f157(x97912,x97911),x97914),x97915))))
% 162.26/162.07 [9922]P24(f331(x99221,f331(f331(f184(x99222,x99223),x99224),x99225)))+~P24(f331(x99221,f331(f331(f184(x99222,x99223),f331(f331(f176(x99222),f331(f331(f251(a883),f331(f197(f884(x99222)),x99224)),f331(f197(f884(x99223)),x99225))),x99224)),f331(f331(f176(x99223),f331(f331(f251(a883),f331(f197(f884(x99222)),x99224)),f331(f197(f884(x99223)),x99225))),x99225))))
% 162.26/162.07 [9402]~P24(f331(f331(f247(a883),x94024),x94021))+E(f331(f331(f22(a883),f331(f331(f81(a883),f331(f331(f82(a883),x94021),x94022)),x94023)),f331(f331(f81(a883),f331(f331(f82(a883),x94024),x94022)),x94025)),f331(f331(f22(a883),f331(f331(f81(a883),f331(f331(f82(a883),f331(f331(f22(a883),x94021),x94024)),x94022)),x94023)),x94025))
% 162.26/162.07 [10202]P20(x102021,x102022,f331(f310(a880,f882(x102021),f331(f331(f18(a880,f891(x102021,f891(a878,a877)),f882(x102021)),f331(f331(f18(a880,a879,f891(f891(x102021,f891(a878,a877)),f882(x102021))),f331(f331(f8(f891(x102021,f891(a878,a877)),f891(a879,f891(f891(x102021,f891(a878,a877)),f882(x102021))),a880),f93(x102021)),x102023)),a28)),x102024)),x102025))+~P20(x102021,f331(f331(f107(f891(f882(x102021),a877)),x102022),f331(f310(a880,f882(x102021),f331(f331(f18(a880,f891(x102021,f891(a878,a877)),f882(x102021)),f331(f331(f18(a880,a879,f891(f891(x102021,f891(a878,a877)),f882(x102021))),f331(f331(f8(f891(x102021,f891(a878,a877)),f891(a879,f891(f891(x102021,f891(a878,a877)),f882(x102021))),a880),f93(x102021)),x102023)),a28)),x102024)),x102025)),f331(f310(a880,f882(x102021),f331(f331(f18(a880,f891(x102021,f891(a878,a877)),f882(x102021)),f331(f331(f18(a880,a879,f891(f891(x102021,f891(a878,a877)),f882(x102021))),f331(f331(f8(f891(x102021,f891(a878,a877)),f891(a879,f891(f891(x102021,f891(a878,a877)),f882(x102021))),a880),f93(x102021)),x102023)),f331(f331(f8(f887(a879),a879,a880),f244(a879)),a26))),x102024)),x102025))
% 162.26/162.07 [10203]P23(x102031,x102032,f331(f310(a880,f882(x102031),f331(f331(f18(a880,f891(x102031,f891(a878,a877)),f882(x102031)),f331(f331(f18(a880,a879,f891(f891(x102031,f891(a878,a877)),f882(x102031))),f331(f331(f8(f891(x102031,f891(a878,a877)),f891(a879,f891(f891(x102031,f891(a878,a877)),f882(x102031))),a880),f93(x102031)),x102033)),a28)),x102034)),x102035))+~P23(x102031,f331(f331(f107(f891(f882(x102031),a877)),x102032),f331(f310(a880,f882(x102031),f331(f331(f18(a880,f891(x102031,f891(a878,a877)),f882(x102031)),f331(f331(f18(a880,a879,f891(f891(x102031,f891(a878,a877)),f882(x102031))),f331(f331(f8(f891(x102031,f891(a878,a877)),f891(a879,f891(f891(x102031,f891(a878,a877)),f882(x102031))),a880),f93(x102031)),x102033)),a28)),x102034)),x102035)),f331(f310(a880,f882(x102031),f331(f331(f18(a880,f891(x102031,f891(a878,a877)),f882(x102031)),f331(f331(f18(a880,a879,f891(f891(x102031,f891(a878,a877)),f882(x102031))),f331(f331(f8(f891(x102031,f891(a878,a877)),f891(a879,f891(f891(x102031,f891(a878,a877)),f882(x102031))),a880),f93(x102031)),x102033)),f331(f331(f8(f887(a879),a879,a880),f244(a879)),a26))),x102034)),x102035))
% 162.26/162.07 [5280]E(x52801,x52802)+~E(f29(x52803,x52804,x52801),f29(x52805,x52806,x52802))
% 162.26/162.07 [5281]E(x52811,x52812)+~E(f29(x52813,x52811,x52814),f29(x52815,x52812,x52816))
% 162.26/162.07 [5282]E(x52821,x52822)+~E(f29(x52821,x52823,x52824),f29(x52822,x52825,x52826))
% 162.26/162.07 [5283]E(x52831,x52832)+~E(f31(x52833,x52834,x52831),f31(x52835,x52836,x52832))
% 162.26/162.07 [5284]E(x52841,x52842)+~E(f31(x52843,x52841,x52844),f31(x52845,x52842,x52846))
% 162.26/162.07 [5285]E(x52851,x52852)+~E(f31(x52851,x52853,x52854),f31(x52852,x52855,x52856))
% 162.26/162.07 [5286]E(x52861,x52862)+~E(f30(x52863,x52864,x52861),f30(x52865,x52866,x52862))
% 162.26/162.07 [5287]E(x52871,x52872)+~E(f30(x52873,x52871,x52874),f30(x52875,x52872,x52876))
% 162.26/162.07 [5288]E(x52881,x52882)+~E(f30(x52881,x52883,x52884),f30(x52882,x52885,x52886))
% 162.26/162.07 [6722]E(f331(f187(x67221,x67222,x67223,x67224),x67225),f331(f239(x67222),x67226))+~E(f331(x67224,x67225),f331(f239(x67222),x67226))
% 162.26/162.07 [6856]E(f331(f242(f887(x68561),x68562,f199(x68561),x68563),f331(x68564,x68565)),f331(x68563,x68566))+~E(f331(x68564,x68565),f331(f239(x68562),x68566))
% 162.26/162.07 [8357]~P15(x83575,x83571,x83572,x83576)+E(f331(f74(x83571,x83571,x83571,f331(x83572,x83573)),f331(x83572,x83574)),f331(f74(x83571,x83571,x83571,f331(x83572,x83574)),f331(x83572,x83573)))
% 162.26/162.07 [8594]~P54(x85944,x85945,x85942,x85941,x85946)+E(f331(x85941,f331(x85942,x85943)),x85943)
% 162.26/162.07 [8734]P21(x87341,x87342,x87343,x87344)+~P21(x87341,x87345,f331(f74(x87342,x87345,x87341,x87346),x87343),x87344)
% 162.26/162.07 [8825]~P21(x88254,x88252,f331(f74(x88251,x88252,x88254,x88253),x88255),x88256)+P21(x88251,x88252,x88253,f331(f310(x88254,x88251,x88255),x88256))
% 162.26/162.07 [9544]P24(f331(f62(x95441),x95442))+~P24(f331(f67(x95441,x95443,x95444,x95445,x95442),x95446))
% 162.26/162.07 [9552]~P24(f331(f331(f333(x95524),x95523),f299(x95524,x95525,x95521,x95522,x95526)))+P24(f331(f331(x95521,x95522),x95523))
% 162.26/162.07 [9553]~P24(f331(f331(f333(x95534),x95533),f296(x95534,x95531,x95535,x95532,x95536)))+P24(f331(f331(x95531,x95532),x95533))
% 162.26/162.07 [9554]~P24(f331(f331(f333(x95544),x95542),f299(x95544,x95541,x95545,x95546,x95543)))+P24(f331(f331(x95541,x95542),x95543))
% 162.26/162.07 [9555]~P24(f331(f331(f333(x95554),x95552),f296(x95554,x95555,x95551,x95556,x95553)))+P24(f331(f331(x95551,x95552),x95553))
% 162.26/162.07 [5786]E(x57861,x57862)+~E(f331(f331(f261(x57863,x57864),x57865),x57861),f331(f331(f261(x57863,x57864),x57866),x57862))
% 162.26/162.07 [5788]E(x57881,x57882)+~E(f331(f331(f261(x57883,x57884),x57881),x57885),f331(f331(f261(x57883,x57884),x57882),x57886))
% 162.26/162.07 [5912]~P12(x59125,x59126,x59121)+E(f331(f331(x59121,x59122),f331(f331(x59121,x59123),x59124)),f331(f331(x59121,x59123),f331(f331(x59121,x59122),x59124)))
% 162.26/162.07 [7305]~P33(x73054,x73051,f331(f331(f154(x73054),x73052),x73055),f331(f331(f154(x73054),x73053),x73056))+P24(f331(f331(x73051,x73052),x73053))
% 162.26/162.07 [7660]P33(x76601,x76602,x76603,x76604)+~P33(x76601,x76602,f331(f331(f154(x76601),x76605),x76603),f331(f331(f154(x76601),x76606),x76604))
% 162.26/162.07 [8682]~P54(x86825,x86821,x86822,x86826,x86824)+P24(f331(f331(f333(x86821),f331(x86822,x86823)),x86824))
% 162.26/162.07 [8853]E(f331(f77(x88531,x88532,x88533,x88534,x88535),x88536),f331(x88533,x88536))+P24(f331(f331(f333(x88531),x88536),x88535))
% 162.26/162.07 [8876]~E(x88763,f331(f331(f154(x88761),x88765),x88766))+P24(f331(f331(f333(f890(f884(x88761),f884(x88761))),f331(f331(f261(f884(x88761),f884(x88761)),x88762),f331(f331(f137(x88761),x88762),x88763))),f150(x88761,x88764)))
% 162.26/162.07 [8883]E(f331(f77(x88831,x88832,x88833,x88834,x88835),x88836),f331(x88834,x88836))+~P24(f331(f331(f333(x88831),x88836),x88835))
% 162.26/162.07 [8889]E(f331(f189(x88891,x88892,x88893,x88894,x88895),x88896),f331(x88893,x88896))+P24(f331(f331(f333(x88891),x88896),f331(f175(x88891),x88894)))
% 162.26/162.07 [9108]~P35(x91081,x91082,x91083,x91085,x91086)+P35(x91081,x91082,x91083,f331(f331(f176(x91081),x91084),x91085),f331(f331(f176(x91082),x91084),x91086))
% 162.26/162.07 [9109]~P35(x91091,x91092,x91093,x91095,x91096)+P35(x91091,x91092,x91093,f331(f331(f141(x91091),x91094),x91095),f331(f331(f141(x91092),x91094),x91096))
% 162.26/162.07 [9622]~P19(x96224,x96222,x96225,x96223,x96226,x96221)+E(f331(x96221,f196(f891(x96222,a877))),x96223)
% 162.26/162.07 [9876]~E(f331(x98764,f331(f260(x98761,x98763),x98765)),f331(x98766,f331(f260(x98761,x98763),x98765)))+E(f331(f271(x98761,x98762,x98763,x98763,x98764,f35(x98763)),x98765),f331(f271(x98761,x98762,x98763,x98763,x98766,f35(x98763)),x98765))
% 162.26/162.07 [9877]~E(f331(x98774,f331(f269(x98771,x98772),x98775)),f331(x98776,f331(f269(x98771,x98772),x98775)))+E(f331(f271(x98771,x98771,x98772,x98773,f35(x98771),x98774),x98775),f331(f271(x98771,x98771,x98772,x98773,f35(x98771),x98776),x98775))
% 162.26/162.07 [9919]~E(f331(f271(x99192,x99196,x99193,x99193,x99191,f35(x99193)),x99194),f331(f271(x99192,x99196,x99193,x99193,x99195,f35(x99193)),x99194))+E(f331(x99191,f331(f260(x99192,x99193),x99194)),f331(x99195,f331(f260(x99192,x99193),x99194)))
% 162.26/162.07 [9920]~E(f331(f271(x99202,x99202,x99203,x99206,f35(x99202),x99201),x99204),f331(f271(x99202,x99202,x99203,x99206,f35(x99202),x99205),x99204))+E(f331(x99201,f331(f269(x99202,x99203),x99204)),f331(x99205,f331(f269(x99202,x99203),x99204)))
% 162.26/162.07 [8778]P24(f331(f331(f333(x87781),x87782),x87783))+~P24(f331(f331(f333(f890(x87781,x87784)),f331(f331(f261(x87781,x87784),x87782),x87785)),f331(f331(f268(x87781,x87784),x87783),x87786)))
% 162.26/162.07 [8792]P24(f331(f331(f333(x87921),x87922),f331(x87923,x87924)))+~P24(f331(f331(f333(f890(x87925,x87921)),f331(f331(f261(x87925,x87921),x87924),x87922)),f331(f331(f268(x87925,x87921),x87926),x87923)))
% 162.26/162.07 [8886]~E(f331(f197(f884(x88861)),x88864),f331(f197(f884(x88862)),x88865))+E(f189(x88861,x88862,x88863,x88864,f331(f331(f137(x88862),x88865),x88866)),f189(x88861,x88862,x88863,x88864,x88865))
% 162.26/162.07 [8887]~E(f331(f197(f884(x88871)),x88874),f331(f197(f884(x88872)),x88876))+E(f189(x88871,x88872,x88873,f331(f331(f137(x88871),x88874),x88875),x88876),f189(x88871,x88872,x88873,x88874,x88876))
% 162.26/162.07 [9131]P24(f331(f331(f333(x91311),x91314),f186(x91311,x91312,x91316)))+E(f187(x91311,x91312,f331(f331(f331(f73(x91311,f887(x91312)),x91313),x91314),f331(f239(x91312),x91315)),x91316),f331(f331(f331(f73(x91311,f887(x91312)),f187(x91311,x91312,x91313,x91316)),x91314),f331(f239(x91312),x91315)))
% 162.26/162.07 [9232]P24(f331(f331(f333(f890(x92321,x92321)),f331(f331(f261(x92321,x92321),f331(x92322,x92323)),f331(x92322,x92324))),x92325))+~P24(f331(f331(f333(f890(x92326,x92326)),f331(f331(f261(x92326,x92326),x92323),x92324)),f331(f331(f287(x92321,x92326),x92325),x92322)))
% 162.26/162.07 [9252]~P24(f331(f331(f333(f890(x92524,x92524)),f331(f331(f261(x92524,x92524),f331(x92526,x92522)),f331(x92526,x92523))),x92525))+P24(f331(f331(f333(f890(x92521,x92521)),f331(f331(f261(x92521,x92521),x92522),x92523)),f331(f331(f287(x92524,x92521),x92525),x92526)))
% 162.26/162.07 [9921]E(f331(f331(f261(x99211,x99212),f806(x99213,x99214,x99215,x99216,x99212,x99211)),f807(x99213,x99214,x99215,x99216,x99212,x99211)),x99216)+~P24(f331(f331(f333(f890(x99211,x99212)),x99216),f331(f331(f288(x99211,x99215,x99212),x99214),x99213)))
% 162.26/162.07 [10116]~P24(f331(f331(f333(f890(x101161,x101166)),x101165),f331(f331(f288(x101161,x101162,x101166),x101164),x101163)))+P24(f331(f331(f333(f890(x101161,x101162)),f331(f331(f261(x101161,x101162),f806(x101163,x101164,x101162,x101165,x101166,x101161)),f808(x101163,x101164,x101162,x101165,x101166,x101161))),x101164))
% 162.26/162.07 [10117]~P24(f331(f331(f333(f890(x101176,x101172)),x101175),f331(f331(f288(x101176,x101171,x101172),x101174),x101173)))+P24(f331(f331(f333(f890(x101171,x101172)),f331(f331(f261(x101171,x101172),f808(x101173,x101174,x101171,x101175,x101172,x101176)),f807(x101173,x101174,x101171,x101175,x101172,x101176))),x101173))
% 162.26/162.07 [6190]~E(x61906,x61904)+E(f331(f331(f331(f331(f73(x61901,x61902),x61903),x61904),x61905),x61906),x61905)
% 162.26/162.07 [6239]E(x62391,x62392)+E(f331(f331(f331(f331(f73(x62393,x62394),x62395),x62392),x62396),x62391),f331(x62395,x62391))
% 162.26/162.07 [7729]~P27(x77292)+E(f331(f331(f42(x77291,x77292),x77293),f331(f331(f7(x77291,x77294,x77292),x77295),x77296)),f331(f331(f331(f42(x77291,f891(x77294,x77292)),x77293),x77295),x77296))
% 162.26/162.07 [7730]~P27(x77302)+E(f331(f331(f43(x77301,x77302),x77303),f331(f331(f7(x77301,x77304,x77302),x77305),x77306)),f331(f331(f331(f43(x77301,f891(x77304,x77302)),x77303),x77305),x77306))
% 162.26/162.07 [8505]E(f331(f331(f42(x85051,f891(x85052,a877)),x85053),f331(f331(f8(f891(x85052,a877),f891(x85052,a877),x85051),f331(f309(x85052),x85054)),x85055)),f331(f331(f309(x85052),x85054),f331(f331(f42(x85051,f891(x85052,a877)),x85053),x85055)))+~P24(f331(f331(f333(x85051),x85056),x85053))
% 162.26/162.07 [8938]~P27(x89382)+E(f331(f331(f42(x89381,x89382),x89383),f331(f331(f8(f891(x89384,x89382),x89382,x89381),f331(f42(x89384,x89382),x89385)),f331(f7(x89384,x89381,x89382),x89386))),f331(f331(f42(x89384,x89382),x89385),f331(f331(f8(f891(x89381,x89382),x89382,x89384),f331(f42(x89381,x89382),x89383)),x89386)))
% 162.26/162.07 [8939]~P27(x89392)+E(f331(f331(f43(x89391,x89392),x89393),f331(f331(f8(f891(x89394,x89392),x89392,x89391),f331(f43(x89394,x89392),x89395)),f331(f7(x89394,x89391,x89392),x89396))),f331(f331(f43(x89394,x89392),x89395),f331(f331(f8(f891(x89391,x89392),x89392,x89394),f331(f43(x89391,x89392),x89393)),x89396)))
% 162.26/162.07 [9141]P24(f331(f331(f333(x91411),x91412),f331(f175(x91411),x91413)))+~P24(f331(f331(f333(f890(x91414,x91411)),f331(f331(f261(x91414,x91411),x91415),x91412)),f331(f175(f890(x91414,x91411)),f331(f331(f184(x91414,x91411),x91416),x91413))))
% 162.26/162.07 [9142]P24(f331(f331(f333(x91421),x91422),f331(f175(x91421),x91423)))+~P24(f331(f331(f333(f890(x91421,x91424)),f331(f331(f261(x91421,x91424),x91422),x91425)),f331(f175(f890(x91421,x91424)),f331(f331(f184(x91421,x91424),x91423),x91426))))
% 162.26/162.07 [9246]P24(f331(f331(f247(f891(x92461,a877)),f331(f285(x92462,x92461,x92463),x92464)),x92465))+~P24(f331(f331(f247(f891(f890(x92462,x92461),a877)),x92463),f331(f331(f268(x92462,x92461),x92466),f331(f16(f891(x92461,a877),x92462),x92465))))
% 162.26/162.07 [9435]P24(f331(f331(f333(f890(f884(x94351),f884(x94351))),f331(f331(f261(f884(x94351),f884(x94351)),f331(f331(f154(x94351),x94352),x94353)),f331(f331(f154(x94351),x94354),x94355))),f150(x94351,x94356)))+~P24(f331(f331(f333(f890(x94351,x94351)),f331(f331(f261(x94351,x94351),x94352),x94354)),x94356))
% 162.26/162.07 [9918]E(f331(f331(f261(x99181,x99182),f714(x99183,x99184,x99185,x99182,x99181,x99186)),f715(x99183,x99184,x99185,x99182,x99181,x99186)),x99186)+P24(f331(f331(f333(x99185),x99184),f331(f331(f270(x99181,x99182,f891(x99185,a877)),x99183),x99186)))
% 162.26/162.07 [9923]E(f331(f331(f261(x99231,x99232),f716(x99233,x99234,x99232,x99231,x99235,x99236)),f717(x99233,x99234,x99232,x99231,x99235,x99236)),x99233)+~P24(f331(f331(f333(x99236),x99235),f331(f331(f270(x99231,x99232,f891(x99236,a877)),x99234),x99233)))
% 162.26/162.07 [10065]P24(f331(f331(f333(x100651),x100652),f331(f331(x100653,f716(x100654,x100653,x100655,x100656,x100652,x100651)),f717(x100654,x100653,x100655,x100656,x100652,x100651))))+~P24(f331(f331(f333(x100651),x100652),f331(f331(f270(x100656,x100655,f891(x100651,a877)),x100653),x100654)))
% 162.26/162.07 [10092]~P24(f331(f331(f333(x100921),x100922),f331(f331(x100925,f714(x100925,x100922,x100921,x100924,x100923,x100926)),f715(x100925,x100922,x100921,x100924,x100923,x100926))))+P24(f331(f331(f333(x100921),x100922),f331(f331(f270(x100923,x100924,f891(x100921,a877)),x100925),x100926)))
% 162.26/162.07 [7853]P24(f331(f331(f333(x78531),x78534),x78536))+E(f190(x78531,x78532,f331(f331(f331(f73(x78531,f887(x78532)),x78533),x78534),x78535),x78536),f190(x78531,x78532,x78533,x78536))
% 162.26/162.07 [7920]P24(f331(f331(f333(x79201),x79204),x79206))+E(f331(f310(x79201,x79202,f331(f331(f331(f73(x79201,x79202),x79203),x79204),x79205)),x79206),f331(f310(x79201,x79202,x79203),x79206))
% 162.26/162.07 [7947]P24(f331(f331(f333(x79471),x79474),f331(f175(x79471),x79476)))+E(f331(f331(f157(x79471,x79472),f331(f331(f331(f73(x79471,x79472),x79473),x79474),x79475)),x79476),f331(f331(f157(x79471,x79472),x79473),x79476))
% 162.26/162.07 [8400]E(x84001,x84002)+E(f331(f331(f162(x84003,f331(f331(f162(x84003,x84004),x84001),x84005)),x84002),x84006),f331(f331(f162(x84003,f331(f331(f162(x84003,x84004),x84002),x84006)),x84001),x84005))
% 162.26/162.07 [8944]~P24(f331(f331(f333(x89443),x89446),x89445))+E(f331(f331(f309(x89441),x89442),f331(f310(x89443,x89441,x89444),f331(f331(f22(f891(x89443,a877)),x89445),f331(f331(f309(x89443),x89446),f196(f891(x89443,a877)))))),f331(f310(x89443,x89441,f331(f331(f331(f73(x89443,x89441),x89444),x89446),x89442)),x89445))
% 162.26/162.07 [9731]E(f189(x97311,x97312,x97313,f331(f331(f137(x97311),x97314),f331(f331(f154(x97311),x97315),f119(x97311))),x97316),f331(f331(f331(f73(x97311,f887(x97312)),f189(x97311,x97312,x97313,x97314,x97316)),x97315),f331(f239(x97312),f331(f331(f168(x97312),x97316),f331(f197(f884(x97311)),x97314)))))+~P24(f331(f331(f248(a883),f331(f197(f884(x97311)),x97314)),f331(f197(f884(x97312)),x97316)))
% 162.26/162.07 [8722]~E(x87223,x87226)+E(f331(f331(f180(x87221,x87222),f331(f331(f154(f890(x87221,x87222)),f331(f331(f261(x87221,x87222),x87223),x87224)),x87225)),x87226),f331(f239(x87222),x87224))
% 162.26/162.07 [8750]E(x87501,x87502)+E(f331(f331(f180(x87503,x87504),f331(f331(f154(f890(x87503,x87504)),f331(f331(f261(x87503,x87504),x87501),x87505)),x87506)),x87502),f331(f331(f180(x87503,x87504),x87506),x87502))
% 162.26/162.07 [9020]~P24(f331(f331(x90204,x90205),x90206))+P24(f331(f331(f331(f331(f107(f891(x90201,f891(x90202,a877))),x90203),x90204),x90205),x90206))
% 162.26/162.07 [9022]~P24(f331(f331(x90223,x90225),x90226))+P24(f331(f331(f331(f331(f107(f891(x90221,f891(x90222,a877))),x90223),x90224),x90225),x90226))
% 162.26/162.07 [9306]P24(f331(f331(x93061,x93062),x93063))+~P24(f331(f331(f331(f331(f108(f891(x93064,f891(x93065,a877))),x93066),x93061),x93062),x93063))
% 162.26/162.07 [9307]P24(f331(f331(x93071,x93072),x93073))+~P24(f331(f331(f331(f331(f108(f891(x93074,f891(x93075,a877))),x93071),x93076),x93072),x93073))
% 162.26/162.07 [9765]~P73(x97652)+E(f331(f331(f9(x97651,x97652),f331(f331(f7(x97651,f891(x97653,a877),x97652),f331(f331(f8(f891(x97653,x97652),f891(f891(x97653,a877),x97652),x97651),f9(x97653,x97652)),x97654)),x97655)),x97656),f331(f331(f9(f890(x97651,x97653),x97652),f331(f270(x97651,x97653,x97652),x97654)),f331(f331(f268(x97651,x97653),x97656),f331(f16(f891(x97653,a877),x97651),x97655))))
% 162.26/162.07 [9766]~P74(x97662)+E(f331(f331(f6(x97661,x97662),f331(f331(f7(x97661,f891(x97663,a877),x97662),f331(f331(f8(f891(x97663,x97662),f891(f891(x97663,a877),x97662),x97661),f6(x97663,x97662)),x97664)),x97665)),x97666),f331(f331(f6(f890(x97661,x97663),x97662),f331(f270(x97661,x97663,x97662),x97664)),f331(f331(f268(x97661,x97663),x97666),f331(f16(f891(x97663,a877),x97661),x97665))))
% 162.26/162.07 [9903]~P74(x99032)+E(f331(f331(f6(x99031,x99032),f331(f331(f7(x99031,f891(x99033,a877),x99032),f331(f331(f8(f891(x99033,x99032),f891(f891(x99033,a877),x99032),x99031),f6(x99033,x99032)),f331(f7(x99033,x99031,x99032),x99034))),x99035)),x99036),f331(f331(f6(x99033,x99032),f331(f331(f7(x99033,f891(x99031,a877),x99032),f331(f331(f8(f891(x99031,x99032),f891(f891(x99031,a877),x99032),x99033),f6(x99031,x99032)),x99034)),x99036)),x99035))
% 162.26/162.07 [9590]~P24(f331(f331(f333(x95901),x95905),x95904))+E(f331(f331(f331(f73(x95901,f887(x95902)),f190(x95901,x95902,x95903,f331(f331(f22(f891(x95901,a877)),x95904),f331(f331(f309(x95901),x95905),f196(f891(x95901,a877)))))),x95905),x95906),f190(x95901,x95902,f331(f331(f331(f73(x95901,f887(x95902)),x95903),x95905),x95906),x95904))
% 162.26/162.07 [10210]~P24(f331(f331(f333(f890(x102101,x102102)),f331(f331(f261(x102101,x102102),x102105),x102106)),f331(f331(f107(f891(f890(x102101,x102102),a877)),x102103),x102104)))+P24(f331(f331(f331(f331(f107(f891(x102101,f891(x102102,a877))),f331(f331(f7(x102101,f891(f890(x102101,x102102),a877),f891(x102102,a877)),f331(f331(f8(f891(x102102,f891(f891(f890(x102101,x102102),a877),a877)),f891(f891(f890(x102101,x102102),a877),f891(x102102,a877)),x102101),f7(x102102,f891(f890(x102101,x102102),a877),a877)),f331(f331(f8(f891(x102102,f890(x102101,x102102)),f891(x102102,f891(f891(f890(x102101,x102102),a877),a877)),x102101),f331(f8(f890(x102101,x102102),f891(f891(f890(x102101,x102102),a877),a877),x102102),f333(f890(x102101,x102102)))),f261(x102101,x102102)))),x102103)),f331(f331(f7(x102101,f891(f890(x102101,x102102),a877),f891(x102102,a877)),f331(f331(f8(f891(x102102,f891(f891(f890(x102101,x102102),a877),a877)),f891(f891(f890(x102101,x102102),a877),f891(x102102,a877)),x102101),f7(x102102,f891(f890(x102101,x102102),a877),a877)),f331(f331(f8(f891(x102102,f890(x102101,x102102)),f891(x102102,f891(f891(f890(x102101,x102102),a877),a877)),x102101),f331(f8(f890(x102101,x102102),f891(f891(f890(x102101,x102102),a877),a877),x102102),f333(f890(x102101,x102102)))),f261(x102101,x102102)))),x102104)),x102105),x102106))
% 162.26/162.07 [10211]~P24(f331(f331(f333(f890(x102111,x102112)),f331(f331(f261(x102111,x102112),x102115),x102116)),f331(f331(f108(f891(f890(x102111,x102112),a877)),x102113),x102114)))+P24(f331(f331(f331(f331(f108(f891(x102111,f891(x102112,a877))),f331(f331(f7(x102111,f891(f890(x102111,x102112),a877),f891(x102112,a877)),f331(f331(f8(f891(x102112,f891(f891(f890(x102111,x102112),a877),a877)),f891(f891(f890(x102111,x102112),a877),f891(x102112,a877)),x102111),f7(x102112,f891(f890(x102111,x102112),a877),a877)),f331(f331(f8(f891(x102112,f890(x102111,x102112)),f891(x102112,f891(f891(f890(x102111,x102112),a877),a877)),x102111),f331(f8(f890(x102111,x102112),f891(f891(f890(x102111,x102112),a877),a877),x102112),f333(f890(x102111,x102112)))),f261(x102111,x102112)))),x102113)),f331(f331(f7(x102111,f891(f890(x102111,x102112),a877),f891(x102112,a877)),f331(f331(f8(f891(x102112,f891(f891(f890(x102111,x102112),a877),a877)),f891(f891(f890(x102111,x102112),a877),f891(x102112,a877)),x102111),f7(x102112,f891(f890(x102111,x102112),a877),a877)),f331(f331(f8(f891(x102112,f890(x102111,x102112)),f891(x102112,f891(f891(f890(x102111,x102112),a877),a877)),x102111),f331(f8(f890(x102111,x102112),f891(f891(f890(x102111,x102112),a877),a877),x102112),f333(f890(x102111,x102112)))),f261(x102111,x102112)))),x102114)),x102115),x102116))
% 162.26/162.07 [10220]P24(f331(f331(f333(f890(x102201,x102202)),f331(f331(f261(x102201,x102202),x102203),x102204)),f331(f331(f107(f891(f890(x102201,x102202),a877)),x102205),x102206)))+~P24(f331(f331(f331(f331(f107(f891(x102201,f891(x102202,a877))),f331(f331(f7(x102201,f891(f890(x102201,x102202),a877),f891(x102202,a877)),f331(f331(f8(f891(x102202,f891(f891(f890(x102201,x102202),a877),a877)),f891(f891(f890(x102201,x102202),a877),f891(x102202,a877)),x102201),f7(x102202,f891(f890(x102201,x102202),a877),a877)),f331(f331(f8(f891(x102202,f890(x102201,x102202)),f891(x102202,f891(f891(f890(x102201,x102202),a877),a877)),x102201),f331(f8(f890(x102201,x102202),f891(f891(f890(x102201,x102202),a877),a877),x102202),f333(f890(x102201,x102202)))),f261(x102201,x102202)))),x102205)),f331(f331(f7(x102201,f891(f890(x102201,x102202),a877),f891(x102202,a877)),f331(f331(f8(f891(x102202,f891(f891(f890(x102201,x102202),a877),a877)),f891(f891(f890(x102201,x102202),a877),f891(x102202,a877)),x102201),f7(x102202,f891(f890(x102201,x102202),a877),a877)),f331(f331(f8(f891(x102202,f890(x102201,x102202)),f891(x102202,f891(f891(f890(x102201,x102202),a877),a877)),x102201),f331(f8(f890(x102201,x102202),f891(f891(f890(x102201,x102202),a877),a877),x102202),f333(f890(x102201,x102202)))),f261(x102201,x102202)))),x102206)),x102203),x102204))
% 162.26/162.07 [10221]P24(f331(f331(f333(f890(x102211,x102212)),f331(f331(f261(x102211,x102212),x102213),x102214)),f331(f331(f108(f891(f890(x102211,x102212),a877)),x102215),x102216)))+~P24(f331(f331(f331(f331(f108(f891(x102211,f891(x102212,a877))),f331(f331(f7(x102211,f891(f890(x102211,x102212),a877),f891(x102212,a877)),f331(f331(f8(f891(x102212,f891(f891(f890(x102211,x102212),a877),a877)),f891(f891(f890(x102211,x102212),a877),f891(x102212,a877)),x102211),f7(x102212,f891(f890(x102211,x102212),a877),a877)),f331(f331(f8(f891(x102212,f890(x102211,x102212)),f891(x102212,f891(f891(f890(x102211,x102212),a877),a877)),x102211),f331(f8(f890(x102211,x102212),f891(f891(f890(x102211,x102212),a877),a877),x102212),f333(f890(x102211,x102212)))),f261(x102211,x102212)))),x102215)),f331(f331(f7(x102211,f891(f890(x102211,x102212),a877),f891(x102212,a877)),f331(f331(f8(f891(x102212,f891(f891(f890(x102211,x102212),a877),a877)),f891(f891(f890(x102211,x102212),a877),f891(x102212,a877)),x102211),f7(x102212,f891(f890(x102211,x102212),a877),a877)),f331(f331(f8(f891(x102212,f890(x102211,x102212)),f891(x102212,f891(f891(f890(x102211,x102212),a877),a877)),x102211),f331(f8(f890(x102211,x102212),f891(f891(f890(x102211,x102212),a877),a877),x102212),f333(f890(x102211,x102212)))),f261(x102211,x102212)))),x102216)),x102213),x102214))
% 162.26/162.07 [10199]~P24(f331(f331(f333(f890(x101992,x101993)),f331(f331(f261(x101992,x101993),x101995),x101996)),f331(f331(f42(x101991,f891(f890(x101992,x101993),a877)),f256(f891(x101991,a877))),x101994)))+P24(f331(f331(f331(f331(f42(x101991,f891(x101992,f891(x101993,a877))),f256(f891(x101991,a877))),f331(f331(f8(f891(f890(x101992,x101993),a877),f891(x101992,f891(x101993,a877)),x101991),f331(f7(x101992,f891(f890(x101992,x101993),a877),f891(x101993,a877)),f331(f331(f8(f891(x101993,f891(f891(f890(x101992,x101993),a877),a877)),f891(f891(f890(x101992,x101993),a877),f891(x101993,a877)),x101992),f7(x101993,f891(f890(x101992,x101993),a877),a877)),f331(f331(f8(f891(x101993,f890(x101992,x101993)),f891(x101993,f891(f891(f890(x101992,x101993),a877),a877)),x101992),f331(f8(f890(x101992,x101993),f891(f891(f890(x101992,x101993),a877),a877),x101993),f333(f890(x101992,x101993)))),f261(x101992,x101993))))),x101994)),x101995),x101996))
% 162.26/162.07 [10200]~P24(f331(f331(f333(f890(x102002,x102003)),f331(f331(f261(x102002,x102003),x102005),x102006)),f331(f331(f43(x102001,f891(f890(x102002,x102003),a877)),f256(f891(x102001,a877))),x102004)))+P24(f331(f331(f331(f331(f43(x102001,f891(x102002,f891(x102003,a877))),f256(f891(x102001,a877))),f331(f331(f8(f891(f890(x102002,x102003),a877),f891(x102002,f891(x102003,a877)),x102001),f331(f7(x102002,f891(f890(x102002,x102003),a877),f891(x102003,a877)),f331(f331(f8(f891(x102003,f891(f891(f890(x102002,x102003),a877),a877)),f891(f891(f890(x102002,x102003),a877),f891(x102003,a877)),x102002),f7(x102003,f891(f890(x102002,x102003),a877),a877)),f331(f331(f8(f891(x102003,f890(x102002,x102003)),f891(x102003,f891(f891(f890(x102002,x102003),a877),a877)),x102002),f331(f8(f890(x102002,x102003),f891(f891(f890(x102002,x102003),a877),a877),x102003),f333(f890(x102002,x102003)))),f261(x102002,x102003))))),x102004)),x102005),x102006))
% 162.26/162.07 [10213]P24(f331(f331(f333(f890(x102131,x102132)),f331(f331(f261(x102131,x102132),x102133),x102134)),f331(f331(f42(x102135,f891(f890(x102131,x102132),a877)),f256(f891(x102135,a877))),x102136)))+~P24(f331(f331(f331(f331(f42(x102135,f891(x102131,f891(x102132,a877))),f256(f891(x102135,a877))),f331(f331(f8(f891(f890(x102131,x102132),a877),f891(x102131,f891(x102132,a877)),x102135),f331(f7(x102131,f891(f890(x102131,x102132),a877),f891(x102132,a877)),f331(f331(f8(f891(x102132,f891(f891(f890(x102131,x102132),a877),a877)),f891(f891(f890(x102131,x102132),a877),f891(x102132,a877)),x102131),f7(x102132,f891(f890(x102131,x102132),a877),a877)),f331(f331(f8(f891(x102132,f890(x102131,x102132)),f891(x102132,f891(f891(f890(x102131,x102132),a877),a877)),x102131),f331(f8(f890(x102131,x102132),f891(f891(f890(x102131,x102132),a877),a877),x102132),f333(f890(x102131,x102132)))),f261(x102131,x102132))))),x102136)),x102133),x102134))
% 162.26/162.07 [10214]P24(f331(f331(f333(f890(x102141,x102142)),f331(f331(f261(x102141,x102142),x102143),x102144)),f331(f331(f43(x102145,f891(f890(x102141,x102142),a877)),f256(f891(x102145,a877))),x102146)))+~P24(f331(f331(f331(f331(f43(x102145,f891(x102141,f891(x102142,a877))),f256(f891(x102145,a877))),f331(f331(f8(f891(f890(x102141,x102142),a877),f891(x102141,f891(x102142,a877)),x102145),f331(f7(x102141,f891(f890(x102141,x102142),a877),f891(x102142,a877)),f331(f331(f8(f891(x102142,f891(f891(f890(x102141,x102142),a877),a877)),f891(f891(f890(x102141,x102142),a877),f891(x102142,a877)),x102141),f7(x102142,f891(f890(x102141,x102142),a877),a877)),f331(f331(f8(f891(x102142,f890(x102141,x102142)),f891(x102142,f891(f891(f890(x102141,x102142),a877),a877)),x102141),f331(f8(f890(x102141,x102142),f891(f891(f890(x102141,x102142),a877),a877),x102142),f333(f890(x102141,x102142)))),f261(x102141,x102142))))),x102146)),x102143),x102144))
% 162.26/162.07 [7411]E(f331(x74111,f331(x74112,x74113)),f331(x74114,x74113))+~E(f331(f74(x74115,x74116,x74117,x74111),x74112),x74114)
% 162.26/162.07 [9621]~P18(x96213,x96214,x96211,x96215,x96216,x96217)+E(f331(f331(x96211,x96212),x96212),x96212)
% 162.26/162.07 [9969]~P51(x99695,x99696,x99697,x99691,x99694,x99692,x99693)+P24(f331(f331(x99691,x99692),f576(x99693,x99692,x99694,x99691)))
% 162.26/162.07 [9985]~E(f331(f242(f887(x99857),x99851,f199(x99857),x99855),f331(x99854,x99853)),f331(f239(x99857),x99852))+E(f331(f239(x99851),f384(x99852,x99853,x99854,x99855,x99856,x99857,x99851)),f331(x99854,x99853))
% 162.26/162.07 [9986]~E(f331(f242(f887(x99866),x99867,f199(x99866),x99861),f331(x99864,x99863)),f331(f239(x99866),x99862))+E(f331(x99861,f384(x99862,x99863,x99864,x99861,x99865,x99866,x99867)),f331(f239(x99866),x99862))
% 162.26/162.07 [6015]~E(f331(f331(f157(x60151,x60155),x60156),x60152),f331(f331(f157(x60153,x60155),x60157),x60154))+E(f331(f197(f884(x60151)),x60152),f331(f197(f884(x60153)),x60154))
% 162.26/162.07 [7486]E(x74861,x74862)+~E(f331(f331(f331(f73(x74863,f887(x74864)),x74865),x74866),f331(f239(x74864),x74861)),f331(f331(f331(f73(x74863,f887(x74864)),x74867),x74866),f331(f239(x74864),x74862)))
% 162.26/162.07 [8443]E(f331(x84431,f331(x84432,x84433)),f331(x84434,x84433))+~E(f331(f74(x84435,x84436,x84437,x84431),x84432),f331(f74(x84436,x84436,x84437,f35(x84436)),x84434))
% 162.26/162.07 [8767]~P35(x87674,x87675,x87671,f331(f331(f154(x87674),x87672),x87676),f331(f331(f154(x87675),x87673),x87677))+P24(f331(f331(x87671,x87672),x87673))
% 162.26/162.07 [9150]P35(x91501,x91502,x91503,x91504,x91505)+~P35(x91501,x91502,x91503,f331(f331(f154(x91501),x91506),x91504),f331(f331(f154(x91502),x91507),x91505))
% 162.26/162.07 [9974]~P51(x99745,x99746,x99747,x99744,x99741,x99743,x99742)+P24(f331(f331(x99741,f576(x99742,x99743,x99741,x99744)),x99742))
% 162.26/162.07 [6059]E(x60591,x60592)+~E(f331(f331(f331(f93(x60593),x60594),x60595),x60591),f331(f331(f331(f93(x60593),x60596),x60597),x60592))
% 162.26/162.07 [6060]E(x60601,x60602)+~E(f331(f331(f331(f93(x60603),x60604),x60601),x60605),f331(f331(f331(f93(x60603),x60606),x60602),x60607))
% 162.26/162.07 [6061]E(x60611,x60612)+~E(f331(f331(f331(f93(x60613),x60611),x60614),x60615),f331(f331(f331(f93(x60613),x60612),x60616),x60617))
% 162.26/162.07 [8891]~P16(x88916,x88911,x88913,x88917)+E(f331(f74(x88911,x88911,x88912,f331(x88913,x88914)),f331(f74(x88911,x88911,x88912,f331(x88913,x88914)),x88915)),f331(f74(x88911,x88911,x88912,f331(x88913,x88914)),x88915))
% 162.26/162.07 [9255]~P35(x92553,x92552,x92554,f331(f331(f157(x92551,x92553),x92555),x92556),x92557)+P35(x92551,x92552,f331(f331(f8(x92553,f891(x92552,a877),x92551),x92554),x92555),x92556,x92557)
% 162.26/162.07 [9281]P35(x92811,x92812,x92813,f331(f331(f157(x92814,x92811),x92815),x92816),x92817)+~P35(x92814,x92812,f331(f331(f8(x92811,f891(x92812,a877),x92814),x92813),x92815),x92816,x92817)
% 162.26/162.07 [9711]E(f189(x97111,x97112,f331(f331(f331(f73(x97111,f887(x97112)),x97113),x97114),f331(f239(x97112),x97115)),x97116,x97117),f331(f331(f331(f73(x97111,f887(x97112)),f189(x97111,x97112,x97113,x97116,x97117)),x97114),f331(f239(x97112),x97115)))+P24(f331(f331(f333(x97111),x97114),f331(f175(x97111),x97116)))
% 162.26/162.07 [8890]~P24(f331(f331(f333(x88901),x88902),f331(f331(x88905,x88906),x88907)))+P24(f331(f331(f333(x88901),x88902),f331(f331(f270(x88903,x88904,f891(x88901,a877)),x88905),f331(f331(f261(x88903,x88904),x88906),x88907))))
% 162.26/162.07 [9176]P24(f331(f331(f331(x91761,x91762),x91763),x91764))+~P24(f331(f331(f331(f270(x91765,x91766,f891(x91767,a877)),x91761),f331(f331(f261(x91765,x91766),x91762),x91763)),x91764))
% 162.26/162.07 [9320]P24(f331(f331(f333(x93201),f331(f331(x93202,x93203),x93204)),f331(f310(f890(x93205,x93206),x93201,f331(f270(x93205,x93206,x93201),x93202)),x93207)))+~P24(f331(f331(f333(f890(x93205,x93206)),f331(f331(f261(x93205,x93206),x93203),x93204)),x93207))
% 162.26/162.07 [9671]P24(f331(f331(f333(f890(f884(x96711),f884(x96711))),f331(f331(f261(f884(x96711),f884(x96711)),f331(f331(f137(x96711),x96712),f331(f331(f154(x96711),x96713),x96714))),f331(f331(f137(x96711),x96712),f331(f331(f154(x96711),x96715),x96716)))),f150(x96711,x96717)))+~P24(f331(f331(f333(f890(x96711,x96711)),f331(f331(f261(x96711,x96711),x96713),x96715)),x96717))
% 162.26/162.07 [9733]~P35(x97331,x97333,x97334,x97336,f331(f331(f157(x97332,x97333),x97335),x97337))+P35(x97331,x97332,f331(f331(f7(x97331,f891(x97332,x97333),f891(x97332,a877)),f331(f331(f8(f891(x97333,a877),f891(f891(x97332,x97333),f891(x97332,a877)),x97331),f8(x97333,a877,x97332)),x97334)),x97335),x97336,x97337)
% 162.26/162.07 [9827]P35(x98271,x98272,x98273,x98274,f331(f331(f157(x98275,x98272),x98276),x98277))+~P35(x98271,x98275,f331(f331(f7(x98271,f891(x98275,x98272),f891(x98275,a877)),f331(f331(f8(f891(x98272,a877),f891(f891(x98275,x98272),f891(x98275,a877)),x98271),f8(x98272,a877,x98275)),x98273)),x98276),x98274,x98277)
% 162.26/162.07 [10091]P51(x100911,x100912,x100913,f331(f331(f7(x100911,f891(f890(x100911,x100912),a877),f891(x100912,a877)),f331(f331(f8(f891(x100912,f891(f891(f890(x100911,x100912),a877),a877)),f891(f891(f890(x100911,x100912),a877),f891(x100912,a877)),x100911),f7(x100912,f891(f890(x100911,x100912),a877),a877)),f331(f331(f8(f891(x100912,f890(x100911,x100912)),f891(x100912,f891(f891(f890(x100911,x100912),a877),a877)),x100911),f331(f8(f890(x100911,x100912),f891(f891(f890(x100911,x100912),a877),a877),x100912),f333(f890(x100911,x100912)))),f261(x100911,x100912)))),x100914),f331(f331(f7(x100912,f891(f890(x100912,x100913),a877),f891(x100913,a877)),f331(f331(f8(f891(x100913,f891(f891(f890(x100912,x100913),a877),a877)),f891(f891(f890(x100912,x100913),a877),f891(x100913,a877)),x100912),f7(x100913,f891(f890(x100912,x100913),a877),a877)),f331(f331(f8(f891(x100913,f890(x100912,x100913)),f891(x100913,f891(f891(f890(x100912,x100913),a877),a877)),x100912),f331(f8(f890(x100912,x100913),f891(f891(f890(x100912,x100913),a877),a877),x100913),f333(f890(x100912,x100913)))),f261(x100912,x100913)))),x100915),x100916,x100917)+~P24(f331(f331(f333(f890(x100911,x100913)),f331(f331(f261(x100911,x100913),x100916),x100917)),f331(f331(f288(x100911,x100912,x100913),x100914),x100915)))
% 162.26/162.07 [10144]~P51(x101441,x101445,x101442,f331(f331(f7(x101441,f891(f890(x101441,x101445),a877),f891(x101445,a877)),f331(f331(f8(f891(x101445,f891(f891(f890(x101441,x101445),a877),a877)),f891(f891(f890(x101441,x101445),a877),f891(x101445,a877)),x101441),f7(x101445,f891(f890(x101441,x101445),a877),a877)),f331(f331(f8(f891(x101445,f890(x101441,x101445)),f891(x101445,f891(f891(f890(x101441,x101445),a877),a877)),x101441),f331(f8(f890(x101441,x101445),f891(f891(f890(x101441,x101445),a877),a877),x101445),f333(f890(x101441,x101445)))),f261(x101441,x101445)))),x101446),f331(f331(f7(x101445,f891(f890(x101445,x101442),a877),f891(x101442,a877)),f331(f331(f8(f891(x101442,f891(f891(f890(x101445,x101442),a877),a877)),f891(f891(f890(x101445,x101442),a877),f891(x101442,a877)),x101445),f7(x101442,f891(f890(x101445,x101442),a877),a877)),f331(f331(f8(f891(x101442,f890(x101445,x101442)),f891(x101442,f891(f891(f890(x101445,x101442),a877),a877)),x101445),f331(f8(f890(x101445,x101442),f891(f891(f890(x101445,x101442),a877),a877),x101442),f333(f890(x101445,x101442)))),f261(x101445,x101442)))),x101447),x101443,x101444)+P24(f331(f331(f333(f890(x101441,x101442)),f331(f331(f261(x101441,x101442),x101443),x101444)),f331(f331(f288(x101441,x101445,x101442),x101446),x101447)))
% 162.26/162.07 [9168]E(x91681,x91682)+E(f331(f331(f331(f73(x91683,x91684),f331(f331(f331(f73(x91683,x91684),x91685),x91681),x91686)),x91682),x91687),f331(f331(f331(f73(x91683,x91684),f331(f331(f331(f73(x91683,x91684),x91685),x91682),x91687)),x91681),x91686))
% 162.26/162.07 [9409]E(f189(x94091,x94092,f331(f331(f331(f73(x94091,f887(x94092)),x94093),x94094),f331(f239(x94092),x94095)),x94096,x94097),f189(x94091,x94092,x94093,x94096,x94097))+~P24(f331(f331(f333(x94091),x94094),f331(f175(x94091),f331(f331(f176(x94091),f331(f197(f884(x94092)),x94097)),x94096))))
% 162.26/162.07 [9749]E(f189(x97491,x97492,f331(f331(f331(f73(x97491,f887(x97492)),x97493),x97494),f331(f239(x97492),x97495)),x97496,x97497),f331(f331(f331(f73(x97491,f887(x97492)),f189(x97491,x97492,x97493,x97496,x97497)),x97494),f331(f239(x97492),x97495)))+P24(f331(f331(f333(x97491),x97494),f331(f175(x97491),f331(f331(f176(x97491),f331(f197(f884(x97492)),x97497)),x97496))))
% 162.26/162.07 [10104]P24(f331(f331(f333(x101041),f515(x101042,x101043,x101044,x101045,x101046,x101047,x101041)),x101045))+P24(f331(f331(f331(f331(f43(x101041,f891(x101047,f891(x101046,a877))),x101045),x101044),x101043),x101042))
% 162.26/162.07 [10105]P24(f331(f331(f333(x101051),f354(x101052,x101053,x101054,x101055,x101056,x101057,x101051)),x101055))+~P24(f331(f331(f331(f331(f42(x101051,f891(x101057,f891(x101056,a877))),x101055),x101054),x101053),x101052))
% 162.26/162.07 [10154]P24(f331(f331(f331(x101541,f354(x101542,x101543,x101541,x101544,x101545,x101546,x101547)),x101543),x101542))+~P24(f331(f331(f331(f331(f42(x101547,f891(x101546,f891(x101545,a877))),x101544),x101541),x101543),x101542))
% 162.26/162.07 [10175]~P24(f331(f331(f331(x101755,f515(x101757,x101756,x101755,x101754,x101753,x101752,x101751)),x101756),x101757))+P24(f331(f331(f331(f331(f43(x101751,f891(x101752,f891(x101753,a877))),x101754),x101755),x101756),x101757))
% 162.26/162.07 [10113]~P144(x101132)+E(f331(f331(f6(x101131,x101132),f331(f331(f7(x101131,f891(x101133,a877),x101132),f331(f331(f8(f891(x101133,x101132),f891(f891(x101133,a877),x101132),x101131),f6(x101133,x101132)),f331(f331(f7(x101131,f891(x101133,x101132),f891(x101133,x101132)),f331(f331(f8(f891(x101132,x101132),f891(f891(x101133,x101132),f891(x101133,x101132)),x101131),f8(x101132,x101132,x101133)),f331(f331(f8(x101132,f891(x101132,x101132),x101131),f82(x101132)),x101134))),x101135))),x101136)),x101137),f331(f331(f82(x101132),f331(f331(f6(x101131,x101132),x101134),x101137)),f331(f331(f6(x101133,x101132),x101135),x101136)))
% 162.26/162.07 [9207]~P15(x92077,x92071,x92073,x92078)+E(f331(f74(x92071,x92071,x92072,f331(x92073,x92074)),f331(f74(x92071,x92071,x92072,f331(x92073,x92075)),x92076)),f331(f74(x92071,x92071,x92072,f331(x92073,x92075)),f331(f74(x92071,x92071,x92072,f331(x92073,x92074)),x92076)))
% 162.26/162.07 [10206]E(f331(f331(f261(x102061,x102062),f331(x102063,f556(x102064,x102065,x102063,x102066,x102067,x102068,x102062,x102061))),f331(x102065,f557(x102064,x102065,x102063,x102066,x102067,x102068,x102062,x102061))),x102068)+~P24(f331(f331(f333(f890(x102061,x102062)),x102068),f331(f310(f890(x102067,x102066),f890(x102061,x102062),f271(x102067,x102061,x102066,x102062,x102063,x102065)),x102064)))
% 162.26/162.07 [10227]~P24(f331(f331(f333(f890(x102278,x102277)),x102276),f331(f310(f890(x102271,x102272),f890(x102278,x102277),f271(x102271,x102278,x102272,x102277,x102275,x102274)),x102273)))+P24(f331(f331(f333(f890(x102271,x102272)),f331(f331(f261(x102271,x102272),f556(x102273,x102274,x102275,x102272,x102271,x102276,x102277,x102278)),f557(x102273,x102274,x102275,x102272,x102271,x102276,x102277,x102278))),x102273))
% 162.26/162.08 [9661]P24(f331(f331(f333(f890(f890(x96611,x96612),f890(x96611,x96612))),f331(f331(f261(f890(x96611,x96612),f890(x96611,x96612)),f331(f331(f261(x96611,x96612),x96613),x96614)),f331(f331(f261(x96611,x96612),x96615),x96616))),f323(x96611,x96612,x96617,x96618)))+~P24(f331(f331(f333(f890(x96611,x96611)),f331(f331(f261(x96611,x96611),x96613),x96615)),x96617))
% 162.26/162.08 [10193]E(f331(f145(x101931,x101932,f331(f7(x101932,x101931,x101931),x101933),f331(x101934,x101935)),x101936),f331(x101934,f331(f145(x101937,x101932,f331(f7(x101932,x101937,x101937),x101938),x101935),x101936)))+P24(f331(f331(f333(x101932),f707(x101935,x101938,x101934,x101933,x101937,x101931,x101936,x101932)),f331(f175(x101932),x101936)))
% 162.26/162.08 [10216]~E(f331(f74(x102161,x102161,x102167,f331(x102163,f707(x102165,x102168,x102164,x102163,x102167,x102161,x102166,x102162))),x102164),f331(f74(x102167,x102161,x102167,x102164),f331(x102168,f707(x102165,x102168,x102164,x102163,x102167,x102161,x102166,x102162))))+E(f331(f145(x102161,x102162,f331(f7(x102162,x102161,x102161),x102163),f331(x102164,x102165)),x102166),f331(x102164,f331(f145(x102167,x102162,f331(f7(x102162,x102167,x102167),x102168),x102165),x102166)))
% 162.26/162.08 [8449]E(f331(x84491,f331(x84492,x84493)),f331(x84494,f331(x84495,x84493)))+~E(f331(f74(x84496,x84497,x84498,x84491),x84492),f331(f74(x84499,x84497,x84498,x84494),x84495))
% 162.26/162.08 [10038]P24(f331(f331(f333(f890(x100381,x100382)),f331(f331(f261(x100381,x100382),f331(x100383,x100384)),f331(x100385,x100386))),f331(f310(f890(x100387,x100388),f890(x100381,x100382),f271(x100387,x100381,x100388,x100382,x100383,x100385)),x100389)))+~P24(f331(f331(f333(f890(x100387,x100388)),f331(f331(f261(x100387,x100388),x100384),x100386)),x100389))
% 162.26/162.08 [8715]~E(f331(x87154,f331(x87155,x87156)),f331(x87159,f331(x871510,x871511)))+E(f331(f331(f74(x87151,x87152,x87153,x87154),x87155),x87156),f331(f331(f74(x87157,x87152,x87158,x87159),x871510),x871511))
% 162.26/162.08 [4611]~P107(x46111)+~P101(x46111)+E(f107(x46111),f246(x46111))
% 162.26/162.08 [4612]~P107(x46121)+~P102(x46121)+E(f251(x46121),f108(x46121))
% 162.26/162.08 [4856]~P111(x48561)+~P94(x48561)+E(f331(f76(x48561),f331(f110(x48561),a103)),f79(x48561))
% 162.26/162.08 [5130]E(x51301,f2(a1))+E(f83(a1,x51301),f331(f80(a1),f79(a1)))+P24(f331(f331(f248(a1),f2(a1)),x51301))
% 162.26/162.08 [5346]E(x53461,f2(a1))+E(f83(a1,x53461),f79(a1))+~P24(f331(f331(f248(a1),f2(a1)),x53461))
% 162.26/162.08 [7309]~P40(x73091)+P24(f331(f62(a1),x73091))+~P24(f331(f62(a883),f331(f310(a1,a883,a111),x73091)))
% 162.26/162.08 [8552]~P2(a5000)+~P24(f331(f331(f333(f890(a880,a879)),x85521),f331(f175(f890(a880,a879)),a27)))+P24(f331(f331(f270(a880,a879,a877),f331(f16(f891(a879,a877),a880),a25)),x85521))
% 162.26/162.08 [9620]E(x96201,f196(f891(f890(a883,a883),a877)))+~P24(f331(f62(f890(a883,a883)),x96201))+P24(f331(f331(f333(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877))),f331(f331(f261(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),f196(f891(f890(a883,a883),a877))),x96201)),a37))
% 162.26/162.08 [10063]E(x100631,f2(a883))+E(x100631,f331(a118,f2(a883)))+~P24(f331(f331(f248(a883),x100631),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))
% 162.26/162.08 [10188]E(x101881,f2(a105))+E(f331(f331(f81(a1),f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f331(a20,f331(f331(f39(a105),x101881),f331(f110(a105),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))))),f79(a1)),f331(a20,x101881))+E(f45(a105,x101881,f331(f110(a105),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f2(a105))
% 162.26/162.08 [10121]E(x101211,f2(a105))+~E(f45(a105,x101211,f331(f110(a105),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f2(a105))+E(f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f331(a20,f331(f331(f39(a105),x101211),f331(f110(a105),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))),f331(a20,x101211))
% 162.26/162.08 [4686]~P55(x46861,x46862)+P43(x46861,x46862)+~P44(a877)
% 162.26/162.08 [4623]~P143(x46231)+P31(x46231,x46232)+~E(x46232,f2(x46231))
% 162.26/162.08 [4624]~P107(x46241)+P29(x46241,x46242)+~E(x46242,f119(x46241))
% 162.26/162.08 [4633]~P111(x46331)+~E(x46332,f2(x46331))+E(f83(x46331,x46332),f2(x46331))
% 162.26/162.08 [4634]~P88(x46341)+~E(x46342,f2(x46341))+E(f83(x46341,x46342),f2(x46341))
% 162.26/162.08 [4642]~P143(x46422)+~P31(x46422,x46421)+E(x46421,f2(x46422))
% 162.26/162.08 [4676]~P111(x46762)+~E(f83(x46762,x46761),f2(x46762))+E(x46761,f2(x46762))
% 162.26/162.08 [4693]~P26(x46932)+~P26(x46931)+P26(f891(x46931,x46932))
% 162.26/162.08 [4694]~P26(x46942)+~P26(x46941)+P26(f889(x46941,x46942))
% 162.26/162.08 [4695]~P26(x46952)+~P26(x46951)+P26(f890(x46951,x46952))
% 162.26/162.08 [4696]~P28(x46962)+~P28(x46961)+P28(f204(x46961,x46962))
% 162.26/162.08 [4697]~P145(x46972)+~P145(x46971)+P145(f890(x46971,x46972))
% 162.26/162.08 [4698]~P60(x46982)+~P60(x46981)+P60(f891(x46981,x46982))
% 162.26/162.08 [4699]~P60(x46992)+~P60(x46991)+P60(f889(x46991,x46992))
% 162.26/162.08 [4700]~P60(x47002)+~P60(x47001)+P60(f890(x47001,x47002))
% 162.26/162.08 [4701]~P60(x47011)+~P93(x47012)+P93(f891(x47011,x47012))
% 162.26/162.08 [4702]~P104(x47022)+~P104(x47021)+P104(f890(x47021,x47022))
% 162.26/162.08 [4827]~P107(x48271)+~P29(x48271,x48272)+P29(x48271,f155(x48271,x48272))
% 162.26/162.08 [5063]~P28(x50632)+~P28(x50631)+P28(f45(a1,x50631,x50632))
% 162.26/162.08 [4644]~P75(x46441)+~E(x46442,f2(x46441))+E(f331(f80(x46441),x46442),x46442)
% 162.26/162.08 [4648]~P138(x46481)+~E(x46482,f2(a1))+E(f331(f109(x46481),x46482),f2(x46481))
% 162.26/162.08 [4649]~P91(x46491)+~E(x46492,f2(a1))+E(f331(f109(x46491),x46492),f2(x46491))
% 162.26/162.08 [4673]~P66(x46731)+~E(f2(x46731),x46732)+E(f331(f80(x46731),x46732),f2(x46731))
% 162.26/162.08 [4674]~P66(x46741)+~E(x46742,f2(x46741))+E(f331(f80(x46741),x46742),f2(x46741))
% 162.26/162.08 [4675]~P83(x46751)+~E(x46752,f2(x46751))+E(f331(f76(x46751),x46752),f2(x46751))
% 162.26/162.08 [4704]~P75(x47042)+E(x47041,f2(x47042))+~E(f331(f80(x47042),x47041),x47041)
% 162.26/162.08 [4710]E(x47101,f331(a111,x47102))+~E(x47101,f2(a883))+~E(x47102,f331(f106(a1),x47101))
% 162.26/162.08 [4711]E(f331(a111,x47111),x47112)+~E(x47112,f2(a883))+~E(x47111,f331(f106(a1),x47112))
% 162.26/162.08 [4713]~P91(x47132)+E(x47131,f2(a1))+~E(f331(f109(x47132),x47131),f2(x47132))
% 162.26/162.08 [4718]~P66(x47182)+E(x47181,f2(x47182))+~E(f331(f80(x47182),x47181),f2(x47182))
% 162.26/162.08 [4719]~P83(x47192)+E(x47191,f2(x47192))+~E(f331(f76(x47192),x47191),f2(x47192))
% 162.26/162.08 [4720]~P66(x47201)+E(f2(x47201),x47202)+~E(f331(f80(x47201),x47202),f2(x47201))
% 162.26/162.08 [4859]~P2(a5000)+~E(f331(a26,x48592),f331(f239(a879),x48591))+P24(f331(a25,x48591))
% 162.26/162.08 [4901]~P107(x49011)+~P29(x49011,x49012)+P29(x49011,f331(f174(x49011),x49012))
% 162.26/162.08 [4928]~P24(x49282)+~P24(x49281)+P24(f331(f331(a329,x49281),x49282))
% 162.26/162.08 [4960]~E(f79(a883),f2(a883))+E(f331(f38(x49601),x49602),f2(a883))+~P24(f331(f62(x49601),x49602))
% 162.26/162.08 [4993]~P115(x49931)+~P144(x49931)+E(f331(f331(f262(x49931),f2(x49931)),f331(a118,x49932)),f2(x49931))
% 162.26/162.08 [5031]~P107(x50311)+P29(x50311,f142(x50311,x50312))+~P24(f331(f62(x50311),x50312))
% 162.26/162.08 [5032]~P107(x50321)+P29(x50321,f694(x50322,x50321))+~P24(f331(f62(x50321),x50322))
% 162.26/162.08 [5053]~P107(x50531)+E(f331(f175(x50531),f142(x50531,x50532)),x50532)+~P24(f331(f62(x50531),x50532))
% 162.26/162.08 [5054]~P107(x50541)+E(f331(f175(x50541),f694(x50542,x50541)),x50542)+~P24(f331(f62(x50541),x50542))
% 162.26/162.08 [5083]P24(x50831)+P24(x50832)+~P24(f331(f331(a330,x50832),x50831))
% 162.26/162.08 [5095]E(x50951,f196(f891(x50952,a877)))+~E(f331(f38(x50952),x50951),f2(a883))+~P24(f331(f62(x50952),x50951))
% 162.26/162.08 [5100]P24(x51001)+~P24(x51002)+~P24(f331(f331(a334,x51002),x51001))
% 162.26/162.08 [5147]~P72(x51471)+E(f331(f76(x51471),x51472),x51472)+P24(f331(f331(f248(x51471),x51472),f2(x51471)))
% 162.26/162.08 [5218]~P60(x52182)+~P24(f331(f58(x52182),x52181))+P24(f331(x52181,f661(x52181,x52182)))
% 162.26/162.08 [5219]~P60(x52192)+~P24(f331(f58(x52192),x52191))+P24(f331(x52191,f684(x52191,x52192)))
% 162.26/162.08 [5247]~P24(f331(a25,x52472))+~P24(f331(a25,x52471))+P24(f331(a25,f34(x52471,x52472)))
% 162.26/162.08 [5256]E(x52561,f119(x52562))+P24(f331(f140(x52562),f120(x52562,x52561)))+~P24(f331(f140(x52562),x52561))
% 162.26/162.08 [5261]~P107(x52611)+~P24(f331(f62(x52611),x52612))+P24(f331(f140(x52611),f142(x52611,x52612)))
% 162.26/162.08 [5262]~P107(x52621)+~P24(f331(f62(x52621),x52622))+P24(f331(f140(x52621),f694(x52622,x52621)))
% 162.26/162.08 [5268]~P138(x52681)+E(f331(f106(x52681),f331(a111,x52682)),f331(f109(x52681),x52682))+P24(f331(f331(f248(a1),x52682),f2(a1)))
% 162.26/162.08 [5298]P5(x52982,x52981)+E(f331(x52981,f447(x52981)),f331(x52981,f517(x52981)))+P24(f331(f331(x52981,f447(x52981)),f517(x52981)))
% 162.26/162.08 [5312]E(f331(f106(a1),f346(x53121,x53122)),x53121)+P24(f331(x53122,f331(a111,x53121)))+~P24(f331(x53122,f2(a883)))
% 162.26/162.08 [5324]~P60(x53241)+~P24(f331(x53242,f662(x53242,x53241)))+P24(f331(f59(x53241),x53242))
% 162.26/162.08 [5325]~P60(x53251)+~P24(f331(x53252,f685(x53252,x53251)))+P24(f331(f59(x53251),x53252))
% 162.26/162.08 [5339]~P60(x53392)+~P36(x53392,x53391,f56(x53392))+P24(f331(x53391,f780(x53391,x53392)))
% 162.26/162.08 [5355]~P111(x53551)+~E(f83(x53551,x53552),f331(f80(x53551),f79(x53551)))+P24(f331(f331(f248(x53551),x53552),f2(x53551)))
% 162.26/162.08 [5356]E(x53561,f196(f891(x53562,a877)))+P24(f331(f62(x53562),f373(x53561,x53562)))+~P24(f331(f62(x53562),x53561))
% 162.26/162.08 [5433]~E(x54332,f2(a1))+E(f227(x54331,x54332),f331(f331(f261(a1,a1),f2(a1)),f79(a1)))+P24(f331(f331(f248(a1),x54332),f2(a1)))
% 162.26/162.08 [5434]~E(x54341,f2(a1))+E(f227(x54341,x54342),f331(f331(f261(a1,a1),f2(a1)),f79(a1)))+P24(f331(f331(f248(a1),x54342),f2(a1)))
% 162.26/162.08 [5486]E(f331(f106(a1),f346(x54861,x54862)),x54861)+P24(f331(x54862,f331(a111,x54861)))+P24(f331(f331(f248(a1),x54861),f2(a1)))
% 162.26/162.08 [5510]E(f331(f331(f309(x55102),f403(x55101,x55102)),f373(x55101,x55102)),x55101)+E(x55101,f196(f891(x55102,a877)))+~P24(f331(f62(x55102),x55101))
% 162.26/162.08 [5548]~P111(x55481)+E(f83(x55481,x55482),f331(f80(x55481),f79(x55481)))+~P24(f331(f331(f248(x55481),x55482),f2(x55481)))
% 162.26/162.08 [5549]~P83(x55491)+E(f331(f76(x55491),x55492),f331(f80(x55491),x55492))+~P24(f331(f331(f248(x55491),x55492),f2(x55491)))
% 162.26/162.08 [5550]~P83(x55501)+E(f331(f76(x55501),x55502),f331(f80(x55501),x55502))+~P24(f331(f331(f247(x55501),x55502),f2(x55501)))
% 162.26/162.08 [5551]~P72(x55511)+E(f331(f76(x55511),x55512),f331(f80(x55511),x55512))+~P24(f331(f331(f248(x55511),x55512),f2(x55511)))
% 162.26/162.08 [5647]~P24(f331(x56471,f346(x56472,x56471)))+P24(f331(x56471,f331(a111,x56472)))+~P24(f331(x56471,f2(a883)))
% 162.26/162.08 [5654]E(x56541,f2(a883))+E(f331(a118,f727(x56542,x56541)),x56541)+~P24(f331(f331(f248(a883),x56541),f331(a118,x56542)))
% 162.26/162.08 [5658]P5(x56581,x56582)+~E(f331(x56582,f447(x56582)),f331(x56582,f517(x56582)))+~P24(f331(f331(x56582,f447(x56582)),f517(x56582)))
% 162.26/162.08 [5678]~P107(x56781)+P29(x56781,x56782)+P24(f331(f331(f247(a883),f663(x56782,x56781)),f664(x56782,x56781)))
% 162.26/162.08 [5679]~P107(x56791)+P29(x56791,x56792)+P24(f331(f331(f247(a883),f669(x56792,x56791)),f680(x56792,x56791)))
% 162.26/162.08 [5766]~P83(x57661)+~E(x57662,f2(x57661))+P24(f331(f331(f247(x57661),f331(f76(x57661),x57662)),f2(x57661)))
% 162.26/162.08 [5845]~P60(x58452)+~P60(x58451)+E(f60(x58451,x58452,f56(x58451),f56(x58452)),f56(f890(x58451,x58452)))
% 162.26/162.08 [5849]~P24(f331(x58491,f346(x58492,x58491)))+P24(f331(x58491,f331(a111,x58492)))+P24(f331(f331(f248(a1),x58492),f2(a1)))
% 162.26/162.08 [5872]~P24(f331(x58721,f331(a111,x58722)))+P24(f331(x58721,f2(a883)))+~P24(f331(f331(f248(a1),x58722),f2(a1)))
% 162.26/162.08 [6211]~P111(x62111)+~P24(f331(f331(f248(x62111),x62112),f2(x62111)))+P24(f331(f331(f248(x62111),f83(x62111,x62112)),f2(x62111)))
% 162.26/162.08 [6324]~P111(x63241)+P24(f331(f331(f248(x63241),f331(f109(x63241),x63242)),f2(x63241)))+~P24(f331(f331(f248(a1),x63242),f2(a1)))
% 162.26/162.08 [6325]~P111(x63251)+P24(f331(f331(f247(x63251),f331(f109(x63251),x63252)),f2(x63251)))+~P24(f331(f331(f247(a1),x63252),f2(a1)))
% 162.26/162.08 [6332]~P83(x63322)+E(x63321,f2(x63322))+~P24(f331(f331(f247(x63322),f331(f76(x63322),x63321)),f2(x63322)))
% 162.26/162.08 [6407]~P138(x64071)+~P24(f331(f331(f333(x64071),x64072),f116(x64071)))+P24(f331(f331(f333(x64071),f331(f80(x64071),x64072)),f116(x64071)))
% 162.26/162.08 [6439]~P111(x64391)+~P24(f331(f331(f248(x64391),f83(x64391,x64392)),f2(x64391)))+P24(f331(f331(f248(x64391),x64392),f2(x64391)))
% 162.26/162.08 [6606]~P111(x66062)+~P24(f331(f331(f248(x66062),f331(f109(x66062),x66061)),f2(x66062)))+P24(f331(f331(f248(a1),x66061),f2(a1)))
% 162.26/162.08 [6607]~P111(x66072)+~P24(f331(f331(f247(x66072),f331(f109(x66072),x66071)),f2(x66072)))+P24(f331(f331(f247(a1),x66071),f2(a1)))
% 162.26/162.08 [7100]~P111(x71001)+~P24(f331(f331(f248(x71001),x71002),f2(x71001)))+P24(f331(f331(f248(x71001),f331(f331(f81(x71001),x71002),x71002)),f2(x71001)))
% 162.26/162.08 [7101]~P75(x71011)+~P24(f331(f331(f248(x71011),x71012),f2(x71011)))+P24(f331(f331(f248(x71011),f331(f331(f81(x71011),x71012),x71012)),f2(x71011)))
% 162.26/162.08 [7102]~P75(x71021)+~P24(f331(f331(f247(x71021),x71022),f2(x71021)))+P24(f331(f331(f247(x71021),f331(f331(f81(x71021),x71022),x71022)),f2(x71021)))
% 162.26/162.08 [7654]~P111(x76541)+~P24(f331(f331(f248(x76541),f331(f331(f81(x76541),x76542),x76542)),f2(x76541)))+P24(f331(f331(f248(x76541),x76542),f2(x76541)))
% 162.26/162.08 [7655]~P75(x76551)+~P24(f331(f331(f248(x76551),f331(f331(f81(x76551),x76552),x76552)),f2(x76551)))+P24(f331(f331(f248(x76551),x76552),f2(x76551)))
% 162.26/162.08 [7656]~P75(x76561)+~P24(f331(f331(f247(x76561),f331(f331(f81(x76561),x76562),x76562)),f2(x76561)))+P24(f331(f331(f247(x76561),x76562),f2(x76561)))
% 162.26/162.08 [4759]~E(x47592,f2(a883))+~E(x47591,f2(a883))+E(f331(f331(f81(a883),x47591),x47592),f2(a883))
% 162.26/162.08 [4760]~E(x47602,f79(a883))+~E(x47601,f79(a883))+E(f331(f331(f82(a883),x47601),x47602),f79(a883))
% 162.26/162.08 [4761]~E(x47612,f79(a1))+~E(x47611,f79(a1))+E(f331(f331(f82(a1),x47611),x47612),f79(a1))
% 162.26/162.08 [4813]~P58(x48132)+E(x48131,f2(x48132))+E(f331(f331(f39(x48132),x48131),x48131),f79(x48132))
% 162.26/162.08 [4814]~P119(x48142)+E(x48141,f2(x48142))+E(f331(f331(f289(x48142),x48141),x48141),f79(x48142))
% 162.26/162.08 [4815]~P120(x48152)+E(x48151,f2(x48152))+E(f331(f331(f289(x48152),x48151),x48151),f79(x48152))
% 162.26/162.08 [4832]~P75(x48321)+~E(x48322,f2(x48321))+E(f331(f331(f81(x48321),x48322),x48322),f2(x48321))
% 162.26/162.08 [4835]~P137(x48351)+~E(x48352,f79(x48351))+E(f331(f331(f82(x48351),x48352),x48352),f79(x48351))
% 162.26/162.08 [4836]~P120(x48361)+~E(x48362,f2(x48361))+E(f331(f331(f289(x48361),x48362),x48362),f2(x48361))
% 162.26/162.08 [4880]~E(x48802,f2(a883))+~E(x48801,f2(a883))+E(f331(f80(a1),f331(f106(a1),x48801)),f331(f106(a1),x48802))
% 162.26/162.08 [4898]E(x48981,f79(a883))+E(x48982,f2(a883))+~E(f331(f331(f82(a883),x48982),x48981),x48982)
% 162.26/162.08 [4908]E(x49081,f2(a883))+E(x49082,f2(a883))+~E(f331(f331(f82(a883),x49082),x49081),f2(a883))
% 162.26/162.08 [4937]~E(x49372,f2(a883))+~E(x49371,f331(a118,f2(a883)))+E(f331(f331(f81(a883),x49371),x49372),f331(a118,f2(a883)))
% 162.26/162.08 [4938]~E(x49381,f2(a883))+~E(x49382,f331(a118,f2(a883)))+E(f331(f331(f81(a883),x49381),x49382),f331(a118,f2(a883)))
% 162.26/162.08 [4943]E(x49431,f79(a1))+E(x49432,f331(f110(a1),a103))+~E(f331(f331(f82(a1),x49431),x49432),f79(a1))
% 162.26/162.08 [4944]E(x49441,f79(a1))+E(x49442,f331(f110(a1),a103))+~E(f331(f331(f82(a1),x49442),x49441),f79(a1))
% 162.26/162.08 [4945]E(x49451,f79(a1))+E(x49451,f331(f110(a1),a103))+~E(f331(f331(f82(a1),x49452),x49451),f79(a1))
% 162.26/162.08 [4947]E(x49471,f79(a1))+E(x49471,f331(f110(a1),a103))+~E(f331(f331(f82(a1),x49471),x49472),f79(a1))
% 162.26/162.08 [4964]~P75(x49642)+E(x49641,f2(x49642))+~E(f331(f331(f81(x49642),x49641),x49641),f2(x49642))
% 162.26/162.08 [4970]~E(x49701,f331(f110(a1),a103))+~E(x49702,f331(f110(a1),a103))+E(f331(f331(f82(a1),x49701),x49702),f79(a1))
% 162.26/162.08 [4982]E(x49821,f2(a883))+E(x49822,f2(a883))+~E(f331(f331(f81(a883),x49822),x49821),f331(a118,f2(a883)))
% 162.26/162.08 [4992]~P94(x49921)+~P61(x49921)+E(f331(f331(f289(x49921),x49922),f331(f110(x49921),a84)),f2(x49921))
% 162.26/162.08 [4998]~P137(x49981)+~E(x49982,f331(f80(x49981),f79(x49981)))+E(f331(f331(f82(x49981),x49982),x49982),f79(x49981))
% 162.26/162.08 [5003]~P28(x50032)+~P28(x50031)+P28(f331(f331(f81(a1),x50031),x50032))
% 162.26/162.08 [5004]~P28(x50042)+~P28(x50041)+P28(f331(f331(f82(a1),x50041),x50042))
% 162.26/162.08 [5005]~P28(x50052)+~P28(x50051)+P28(f331(f331(f39(a1),x50051),x50052))
% 162.26/162.08 [5007]~E(x50072,f2(a1))+E(x50071,f2(a1))+E(f46(x50071,x50072),f331(f331(f261(a1,a1),f2(a1)),x50071))
% 162.26/162.08 [5029]~E(x50292,f331(a118,f2(a883)))+~E(x50291,f331(a118,f2(a883)))+E(f331(f331(f82(a883),x50291),x50292),f331(a118,f2(a883)))
% 162.26/162.08 [5044]E(x50441,f2(a883))+E(x50442,f331(a118,f2(a883)))+~E(f331(f331(f262(a883),x50442),x50441),f331(a118,f2(a883)))
% 162.26/162.08 [5045]E(x50451,f2(a883))+E(x50451,f331(a118,f2(a883)))+~E(f331(f331(f81(a883),x50452),x50451),f331(a118,f2(a883)))
% 162.26/162.08 [5046]E(x50461,f2(a883))+E(x50461,f331(a118,f2(a883)))+~E(f331(f331(f81(a883),x50461),x50462),f331(a118,f2(a883)))
% 162.26/162.08 [5055]~P94(x50551)+~P61(x50551)+E(f331(f331(f289(x50551),x50552),f331(f110(x50551),a103)),f331(f80(x50551),x50552))
% 162.26/162.08 [5075]E(x50751,f331(a111,x50752))+~E(x50751,f2(a883))+P24(f331(f331(f247(a1),f2(a1)),x50752))
% 162.26/162.08 [5076]E(f331(a111,x50761),x50762)+~E(x50762,f2(a883))+P24(f331(f331(f247(a1),f2(a1)),x50761))
% 162.26/162.08 [5091]E(x50911,f331(a118,f2(a883)))+E(x50912,f331(a118,f2(a883)))+~E(f331(f331(f81(a883),x50911),x50912),f331(a118,f2(a883)))
% 162.26/162.08 [5101]~E(x51011,f331(a111,x51012))+E(x51011,f2(a883))+P24(f331(f331(f247(a1),f2(a1)),x51012))
% 162.26/162.08 [5102]~E(f331(a111,x51022),x51021)+E(x51021,f2(a883))+P24(f331(f331(f247(a1),f2(a1)),x51022))
% 162.26/162.08 [5124]~P96(x51241)+E(f331(f64(x51241,f107(x51241)),x51242),f13(x51241,x51242))+~P24(f331(f62(x51241),x51242))
% 162.26/162.08 [5125]~P107(x51251)+E(f331(f64(x51251,f251(x51251)),x51252),f14(x51251,x51252))+~P24(f331(f62(x51251),x51252))
% 162.26/162.08 [5126]~P107(x51261)+E(f331(f64(x51261,f246(x51261)),x51262),f15(x51261,x51262))+~P24(f331(f62(x51261),x51262))
% 162.26/162.08 [5127]~P96(x51271)+E(f331(f64(x51271,f108(x51271)),x51272),f10(x51271,x51272))+~P24(f331(f62(x51271),x51272))
% 162.26/162.08 [5129]~P60(x51291)+~P24(f331(x51292,f199(x51291)))+P24(f331(f58(f887(x51291)),x51292))
% 162.26/162.08 [5211]~P60(x52112)+P24(f331(x52111,f199(x52112)))+~P24(f331(f59(f887(x52112)),x52111))
% 162.26/162.08 [5212]E(x52121,x52122)+~E(f331(f331(f22(a883),x52122),x52121),f2(a883))+~E(f331(f331(f22(a883),x52121),x52122),f2(a883))
% 162.26/162.08 [5226]P28(x52261)+~P40(x52262)+~P24(f331(f331(f333(a1),x52261),x52262))
% 162.26/162.08 [5257]~P111(x52571)+~E(f83(x52571,x52572),f79(x52571))+P24(f331(f331(f248(x52571),f2(x52571)),x52572))
% 162.26/162.08 [5269]~P94(x52691)+E(f331(f106(x52691),f331(f110(a883),x52692)),f331(f110(x52691),x52692))+P24(f331(a202,f331(f110(a1),x52692)))
% 162.26/162.08 [5275]~P43(x52751,x52752)+P44(a877)+P24(f331(f62(f890(x52751,x52751)),x52752))
% 162.26/162.08 [5348]~P107(x53481)+E(f331(f64(x53481,f251(x53481)),x53482),f11(x53481,f251(x53481),x53482))+~P24(f331(f62(x53481),x53482))
% 162.26/162.08 [5349]~P107(x53491)+E(f331(f64(x53491,f246(x53491)),x53492),f12(x53491,f246(x53491),x53492))+~P24(f331(f62(x53491),x53492))
% 162.26/162.08 [5363]E(x53631,x53632)+P24(f331(f331(f248(a883),x53632),x53631))+P24(f331(f331(f248(a883),x53631),x53632))
% 162.26/162.08 [5364]E(x53641,x53642)+P24(f331(f331(f248(a1),x53642),x53641))+P24(f331(f331(f248(a1),x53641),x53642))
% 162.26/162.08 [5420]~P94(x54201)+E(f331(f106(x54201),f331(f110(a883),x54202)),f2(x54201))+~P24(f331(a202,f331(f110(a1),x54202)))
% 162.26/162.08 [5423]~E(x54232,f331(a111,x54231))+E(x54231,f331(f106(a1),x54232))+~P24(f331(f331(f247(a1),f2(a1)),x54231))
% 162.26/162.08 [5424]~E(f331(a111,x54241),x54242)+E(x54241,f331(f106(a1),x54242))+~P24(f331(f331(f247(a1),f2(a1)),x54241))
% 162.26/162.08 [5425]~E(x54251,f331(a111,x54252))+E(f331(f106(a1),x54251),x54252)+~P24(f331(f331(f247(a1),f2(a1)),x54252))
% 162.26/162.08 [5435]E(x54351,f331(a111,x54352))+~E(x54352,f331(f106(a1),x54351))+~P24(f331(f331(f247(a1),f2(a1)),x54352))
% 162.26/162.08 [5436]E(f331(a111,x54361),x54362)+~E(x54361,f331(f106(a1),x54362))+~P24(f331(f331(f247(a1),f2(a1)),x54361))
% 162.26/162.08 [5475]~P83(x54752)+E(x54751,f2(x54752))+P24(f331(f331(f248(x54752),f2(x54752)),f331(f76(x54752),x54751)))
% 162.26/162.08 [5541]~P111(x55411)+E(f83(x55411,x55412),f79(x55411))+~P24(f331(f331(f248(x55411),f2(x55411)),x55412))
% 162.26/162.08 [5545]~P94(x55451)+E(f331(f106(x55451),f331(f110(a883),x55452)),f2(x55451))+P24(f331(f331(f247(a1),f2(a1)),f331(f110(a1),x55452)))
% 162.26/162.08 [5552]~P83(x55521)+E(f331(f76(x55521),x55522),x55522)+~P24(f331(f331(f248(x55521),f2(x55521)),x55522))
% 162.26/162.08 [5553]~P83(x55531)+E(f331(f76(x55531),x55532),x55532)+~P24(f331(f331(f247(x55531),f2(x55531)),x55532))
% 162.26/162.08 [5560]E(x55601,f2(a883))+~E(f142(a883,f331(f301(a883,x55602),x55601)),f119(a883))+P24(f331(f331(f247(a883),x55601),x55602))
% 162.26/162.08 [5570]~P74(x55701)+E(f331(f331(f6(x55701,x55701),f5(x55701)),f331(f175(x55701),x55702)),f331(f169(x55701),x55702))+~P24(f331(f140(x55701),x55702))
% 162.26/162.08 [5573]~P138(x55731)+E(f331(f106(x55731),f331(a111,x55732)),f331(f109(x55731),x55732))+~P24(f331(f331(f247(a1),f2(a1)),x55732))
% 162.26/162.08 [5600]E(x56001,x56002)+P24(f331(f331(f248(a883),x56001),x56002))+~P24(f331(f331(f247(a883),x56001),x56002))
% 162.26/162.08 [5601]E(x56011,x56012)+P24(f331(f331(f248(a1),x56011),x56012))+~P24(f331(f331(f247(a1),x56011),x56012))
% 162.26/162.08 [5604]E(x56041,f79(a1))+~E(f331(f331(f82(a1),x56042),x56041),f79(a1))+~P24(f331(f331(f248(a1),f2(a1)),x56042))
% 162.26/162.08 [5605]E(x56051,f79(a1))+~E(f331(f331(f82(a1),x56051),x56052),f79(a1))+~P24(f331(f331(f248(a1),f2(a1)),x56051))
% 162.26/162.08 [5644]~P40(x56442)+P24(f331(f331(f247(a1),f2(a1)),x56441))+~P24(f331(f331(f333(a1),x56441),x56442))
% 162.26/162.08 [5663]~P55(x56631,x56632)+P38(x56631,x56632)+~P24(f331(f62(f890(x56631,x56631)),x56632))
% 162.26/162.08 [5665]~P55(x56651,x56652)+P43(x56651,x56652)+~P24(f331(f62(f890(x56651,x56651)),x56652))
% 162.26/162.08 [5709]E(x57091,f196(f891(x57092,a877)))+~P24(f331(f62(x57092),x57091))+P24(f331(f331(f248(a883),f2(a883)),f331(f38(x57092),x57091)))
% 162.26/162.08 [5735]~P24(f331(x57351,x57352))+P24(f331(x57351,f2(a883)))+P24(f331(f331(f248(a883),f828(x57352,x57351)),x57352))
% 162.26/162.08 [5760]E(x57601,f2(a883))+~E(f331(f169(a883),x57602),f2(a883))+~P24(f331(f331(f333(a883),x57601),f331(f175(a883),x57602)))
% 162.26/162.08 [5826]E(x58261,x58262)+~P24(f331(f331(f247(a883),x58262),x58261))+~P24(f331(f331(f247(a883),x58261),x58262))
% 162.26/162.08 [5827]E(x58271,x58272)+~P24(f331(f331(f247(a1),x58272),x58271))+~P24(f331(f331(f247(a1),x58271),x58272))
% 162.26/162.08 [5828]E(f331(f38(x58281),x58282),f2(a883))+~P24(f331(f62(x58281),x58282))+P24(f331(f331(f333(x58281),f833(x58282,x58281)),x58282))
% 162.26/162.08 [5837]E(f50(x58371,x58372),f46(x58371,x58372))+P24(f331(f331(f247(a1),f2(a1)),x58371))+~P24(f331(f331(f248(a1),f2(a1)),x58372))
% 162.26/162.08 [5861]~P24(f331(x58611,f847(x58611)))+P24(f331(x58611,f331(a111,x58612)))+~P24(f331(f331(f247(a1),f2(a1)),x58612))
% 162.26/162.08 [5863]P24(f331(f331(f248(a883),x58631),f371(x58632)))+~P24(f331(f62(a883),x58632))+~P24(f331(f331(f333(a883),x58631),x58632))
% 162.26/162.08 [5864]P24(f331(f331(f247(a883),x58641),f369(x58642)))+~P24(f331(f62(a883),x58642))+~P24(f331(f331(f333(a883),x58641),x58642))
% 162.26/162.08 [5893]E(x58931,x58932)+~P24(f331(f331(f248(a883),x58931),f331(a118,x58932)))+P24(f331(f331(f248(a883),x58931),x58932))
% 162.26/162.08 [5927]E(x59271,f331(a118,x59272))+~P24(f331(f331(f247(a883),x59271),f331(a118,x59272)))+P24(f331(f331(f247(a883),x59271),x59272))
% 162.26/162.08 [5939]P24(f331(x59391,f852(x59391)))+~P24(f331(x59391,f331(a111,x59392)))+~P24(f331(f331(f247(a1),f2(a1)),x59392))
% 162.26/162.08 [5953]~P24(f331(x59531,x59532))+~P24(f331(f331(f247(a1),f2(a1)),x59532))+P24(f331(x59531,f331(f106(a1),f342(x59531))))
% 162.26/162.08 [5968]~P83(x59682)+~E(x59681,f2(x59682))+~P24(f331(f331(f248(x59682),f2(x59682)),f331(f76(x59682),x59681)))
% 162.26/162.08 [5995]~P55(x59951,x59952)+P38(x59951,f331(f286(x59951,x59951),x59952))+~P24(f331(f62(f890(x59951,x59951)),x59952))
% 162.26/162.08 [6003]~P94(x60031)+E(f331(f106(x60031),f331(f110(a883),x60032)),f331(f110(x60031),x60032))+~P24(f331(f331(f247(a1),f2(a1)),f331(f110(a1),x60032)))
% 162.26/162.08 [6007]E(f331(a118,x60071),x60072)+~P24(f331(f331(f248(a883),x60071),x60072))+P24(f331(f331(f248(a883),f331(a118,x60071)),x60072))
% 162.26/162.08 [6019]E(f331(f331(f39(a1),x60191),x60192),f2(a1))+~P24(f331(f331(f247(a1),x60191),f2(a1)))+~P24(f331(f331(f248(a1),x60192),x60191))
% 162.26/162.08 [6032]E(f45(a1,x60321,x60322),x60321)+~P24(f331(f331(f247(a1),x60321),f2(a1)))+~P24(f331(f331(f248(a1),x60322),x60321))
% 162.26/162.08 [6045]E(f47(x60451,x60452),f46(x60451,x60452))+~P24(f331(f331(f247(a1),f2(a1)),x60451))+~P24(f331(f331(f247(a1),f2(a1)),x60452))
% 162.26/162.08 [6053]E(f331(f331(f39(a1),x60531),x60532),f2(a1))+~P24(f331(f331(f247(a1),f2(a1)),x60531))+~P24(f331(f331(f248(a1),x60531),x60532))
% 162.26/162.08 [6065]E(f45(a883,f331(f110(a883),x60651),f331(f110(a883),x60652)),f331(f110(a883),x60651))+P24(f331(a202,f331(f110(a1),x60651)))+~P24(f331(a202,f331(f110(a1),x60652)))
% 162.26/162.08 [6067]E(f45(a1,x60671,x60672),x60671)+~P24(f331(f331(f247(a1),f2(a1)),x60671))+~P24(f331(f331(f248(a1),x60671),x60672))
% 162.26/162.08 [6068]E(x60681,x60682)+~P24(f331(f331(f248(a883),x60681),f331(a118,x60682)))+~P24(f331(f331(f247(a883),x60682),x60681))
% 162.26/162.08 [6085]~P111(x60851)+~P24(f331(f331(f248(x60851),x60852),f2(x60851)))+P24(f331(f331(f248(x60851),x60852),f331(f80(x60851),x60852)))
% 162.26/162.08 [6086]~P75(x60861)+~P24(f331(f331(f247(x60861),x60862),f2(x60861)))+P24(f331(f331(f247(x60861),x60862),f331(f80(x60861),x60862)))
% 162.26/162.08 [6096]~P27(x60961)+E(f331(f331(f65(x60961,x60961,f108(x60961)),f256(x60961)),x60962),f41(x60961,x60962))+~P24(f331(f62(x60961),x60962))
% 162.26/162.08 [6097]~P27(x60971)+E(f331(f331(f65(x60971,x60971,f107(x60971)),f196(x60971)),x60972),f40(x60971,x60972))+~P24(f331(f62(x60971),x60972))
% 162.26/162.08 [6111]~P110(x61111)+~P24(f331(f331(f248(a883),f2(a883)),x61112))+P24(f331(f331(f248(x61111),f2(x61111)),f331(f106(x61111),x61112)))
% 162.26/162.08 [6112]~P111(x61121)+~P24(f331(f331(f248(a1),f2(a1)),x61122))+P24(f331(f331(f248(x61121),f2(x61121)),f331(f109(x61121),x61122)))
% 162.26/162.08 [6113]~P111(x61131)+~P24(f331(f331(f247(a1),f2(a1)),x61132))+P24(f331(f331(f247(x61131),f2(x61131)),f331(f109(x61131),x61132)))
% 162.26/162.08 [6116]~P28(x61162)+~P28(x61161)+E(f331(f310(a883,a1,f106(a1)),f302(a883,f331(a111,x61161),f331(a111,x61162))),f302(a1,x61161,x61162))
% 162.26/162.08 [6122]P24(f331(x61221,x61222))+~P24(f331(f331(f247(a1),f2(a1)),x61222))+~P24(f331(x61221,f331(f106(a1),f348(x61221))))
% 162.26/162.08 [6147]E(f331(f331(f81(a883),f331(f110(a883),x61471)),f331(f110(a883),x61472)),f331(f110(a883),x61471))+P24(f331(f331(f248(a1),x61471),a84))+~P24(f331(f331(f248(a1),x61472),a84))
% 162.26/162.08 [6153]~P111(x61531)+P24(f331(f331(f248(x61531),f2(x61531)),f83(x61531,x61532)))+~P24(f331(f331(f248(x61531),f2(x61531)),x61532))
% 162.26/162.08 [6164]~P77(x61641)+~P24(f331(f331(f248(x61641),x61642),f2(x61641)))+P24(f331(f331(f248(x61641),f2(x61641)),f331(f80(x61641),x61642)))
% 162.26/162.08 [6165]~P77(x61651)+~P24(f331(f331(f247(x61651),x61652),f2(x61651)))+P24(f331(f331(f247(x61651),f2(x61651)),f331(f80(x61651),x61652)))
% 162.26/162.08 [6168]E(x61681,f256(f891(x61682,a877)))+~E(f331(f38(x61682),x61681),f331(f38(x61682),f256(f891(x61682,a877))))+~P24(f331(f62(x61682),f256(f891(x61682,a877))))
% 162.26/162.08 [6204]~P111(x62041)+P24(f331(f331(f248(x62041),x62042),f2(x62041)))+~P24(f331(f331(f248(x62041),x62042),f331(f80(x62041),x62042)))
% 162.26/162.08 [6205]~P75(x62051)+P24(f331(f331(f247(x62051),x62052),f2(x62051)))+~P24(f331(f331(f247(x62051),x62052),f331(f80(x62051),x62052)))
% 162.26/162.08 [6213]~P94(x62131)+P24(f331(f331(f333(x62131),f331(f110(x62131),x62132)),f194(x62131)))+~P24(f331(f331(f247(a1),a84),x62132))
% 162.26/162.08 [6244]E(x62441,f2(a883))+~P24(f331(f331(f248(a883),x62441),f331(a118,x62442)))+P24(f331(f331(f248(a883),f727(x62442,x62441)),x62442))
% 162.26/162.08 [6266]~P111(x62661)+~P24(f331(f331(f248(x62661),f2(x62661)),f83(x62661,x62662)))+P24(f331(f331(f248(x62661),f2(x62661)),x62662))
% 162.26/162.08 [6268]~E(f331(f110(a883),x62682),f331(f110(a883),x62681))+P24(f331(f331(f247(a1),f331(f110(a1),x62681)),f2(a1)))+~P24(f331(a202,f331(f110(a1),x62682)))
% 162.26/162.08 [6298]E(f331(f260(a1,a1),f50(x62981,x62982)),f331(f331(f39(a1),x62981),x62982))+~P24(f331(f331(f248(a1),x62981),f2(a1)))+~P24(f331(f331(f248(a1),f2(a1)),x62982))
% 162.26/162.08 [6330]E(f331(f269(a1,a1),f50(x63301,x63302)),f45(a1,x63301,x63302))+~P24(f331(f331(f248(a1),x63301),f2(a1)))+~P24(f331(f331(f248(a1),f2(a1)),x63302))
% 162.26/162.08 [6333]~P110(x63332)+~P24(f331(f331(f248(x63332),f2(x63332)),f331(f106(x63332),x63331)))+P24(f331(f331(f248(a883),f2(a883)),x63331))
% 162.26/162.08 [6334]~P111(x63342)+~P24(f331(f331(f248(x63342),f2(x63342)),f331(f109(x63342),x63341)))+P24(f331(f331(f248(a1),f2(a1)),x63341))
% 162.26/162.08 [6335]~P111(x63352)+~P24(f331(f331(f247(x63352),f2(x63352)),f331(f109(x63352),x63351)))+P24(f331(f331(f247(a1),f2(a1)),x63351))
% 162.26/162.08 [6338]E(f331(f260(a1,a1),f47(x63381,x63382)),f331(f331(f39(a1),x63381),x63382))+~P24(f331(f331(f248(a1),f2(a1)),x63381))+~P24(f331(f331(f247(a1),f2(a1)),x63382))
% 162.26/162.08 [6351]E(f331(f269(a1,a1),f47(x63511,x63512)),f45(a1,x63511,x63512))+~P24(f331(f331(f248(a1),f2(a1)),x63511))+~P24(f331(f331(f247(a1),f2(a1)),x63512))
% 162.26/162.08 [6368]~P77(x63681)+P24(f331(f331(f248(x63681),x63682),f2(x63681)))+~P24(f331(f331(f248(x63681),f2(x63681)),f331(f80(x63681),x63682)))
% 162.26/162.08 [6369]~P77(x63691)+P24(f331(f331(f247(x63691),x63692),f2(x63691)))+~P24(f331(f331(f247(x63691),f2(x63691)),f331(f80(x63691),x63692)))
% 162.26/162.08 [6394]P24(f331(f49(x63941,x63942),f50(x63941,x63942)))+~P24(f331(f331(f248(a1),x63941),f2(a1)))+~P24(f331(f331(f248(a1),f2(a1)),x63942))
% 162.26/162.08 [6419]P24(f331(f49(x64191,x64192),f47(x64191,x64192)))+~P24(f331(f331(f248(a1),f2(a1)),x64192))+~P24(f331(f331(f247(a1),f2(a1)),x64191))
% 162.26/162.08 [6462]~P77(x64621)+P24(f331(f331(f248(x64621),f331(f80(x64621),x64622)),f2(x64621)))+~P24(f331(f331(f248(x64621),f2(x64621)),x64622))
% 162.26/162.08 [6463]~P77(x64631)+P24(f331(f331(f247(x64631),f331(f80(x64631),x64632)),f2(x64631)))+~P24(f331(f331(f247(x64631),f2(x64631)),x64632))
% 162.26/162.08 [6479]E(f331(f331(f22(a883),f331(a111,x64791)),f331(a111,x64792)),f331(a111,f204(x64791,x64792)))+~P24(f331(f331(f247(a1),f2(a1)),x64792))+~P24(f331(f331(f247(a1),f2(a1)),x64791))
% 162.26/162.08 [6496]P24(f331(f331(f247(a1),f2(a1)),f204(x64961,x64962)))+~P24(f331(f331(f247(a1),f2(a1)),x64962))+~P24(f331(f331(f247(a1),f2(a1)),x64961))
% 162.26/162.08 [6529]~P24(f331(x65291,x65292))+P24(f331(x65291,f2(a883)))+P24(f331(x65291,f331(f331(f81(a883),f828(x65292,x65291)),f79(a883))))
% 162.26/162.08 [6613]E(f331(f110(a883),x66131),f331(f110(a883),x66132))+~P24(f331(f331(f247(a1),f331(f110(a1),x66132)),f2(a1)))+~P24(f331(a202,f331(f110(a1),x66131)))
% 162.26/162.08 [6623]~E(x66231,f2(a883))+~E(f641(x66232,x66231),f2(a883))+E(f331(f145(a883,a883,f81(a883),x66231),x66232),f2(a883))
% 162.26/162.08 [6649]~P24(f331(f62(x66491),f524(x66492,x66491)))+~P24(f331(f62(f891(x66491,a877)),x66492))+P24(f331(f62(x66491),f40(f891(x66491,a877),x66492)))
% 162.26/162.08 [6655]E(x66551,x66552)+P24(f331(f331(f248(a1),x66551),x66552))+~P24(f331(f331(f248(a1),x66551),f331(f331(f81(a1),x66552),f79(a1))))
% 162.26/162.08 [6657]P24(f331(f331(f248(a883),f331(a111,x66571)),f331(a111,x66572)))+~P24(f331(f331(f248(a1),f2(a1)),x66572))+~P24(f331(f331(f248(a1),x66571),x66572))
% 162.26/162.08 [6658]P24(f331(f331(f248(a883),f331(a111,x66581)),f331(a111,x66582)))+~P24(f331(f331(f247(a1),f2(a1)),x66581))+~P24(f331(f331(f248(a1),x66581),x66582))
% 162.26/162.08 [6659]P24(f331(f331(f247(a883),f331(a111,x66591)),f331(a111,x66592)))+~P24(f331(f331(f248(a1),f2(a1)),x66591))+~P24(f331(f331(f247(a1),x66591),x66592))
% 162.26/162.08 [6660]P24(f331(f331(f247(a883),f331(a111,x66601)),f331(a111,x66602)))+~P24(f331(f331(f247(a1),f2(a1)),x66602))+~P24(f331(f331(f247(a1),x66601),x66602))
% 162.26/162.08 [6671]E(f45(a883,f331(a111,x66711),f331(a111,x66712)),f331(a111,f45(a1,x66711,x66712)))+~P24(f331(f331(f247(a1),f2(a1)),x66712))+~P24(f331(f331(f247(a1),f2(a1)),x66711))
% 162.26/162.08 [6693]~P77(x66931)+~P24(f331(f331(f248(x66931),f331(f80(x66931),x66932)),f2(x66931)))+P24(f331(f331(f248(x66931),f2(x66931)),x66932))
% 162.26/162.08 [6694]~P77(x66941)+~P24(f331(f331(f247(x66941),f331(f80(x66941),x66942)),f2(x66941)))+P24(f331(f331(f247(x66941),f2(x66941)),x66942))
% 162.26/162.08 [6709]~P24(f331(f331(f248(a1),a84),x67092))+~P24(f331(f331(f248(a1),x67091),x67092))+P24(f331(f331(f248(a883),f331(f110(a883),x67091)),f331(f110(a883),x67092)))
% 162.26/162.08 [6794]~P24(f331(f331(f247(a1),f2(a1)),x67941))+P24(f331(f331(f248(a883),f331(a111,x67941)),x67942))+~P24(f331(f331(f248(a1),x67941),f331(f106(a1),x67942)))
% 162.26/162.08 [6810]E(x68101,f2(a1))+E(f45(a1,x68102,x68101),f2(a1))+E(f331(f331(f22(a1),f331(f80(a1),f331(f331(f39(a1),x68102),x68101))),f79(a1)),f331(f331(f39(a1),x68102),f331(f80(a1),x68101)))
% 162.26/162.08 [6823]~P24(f331(f331(f247(a1),f2(a1)),x68231))+~P24(f331(f331(f248(a883),f331(a111,x68231)),x68232))+P24(f331(f331(f248(a1),x68231),f331(f106(a1),x68232)))
% 162.26/162.08 [6860]~P24(f331(f331(f247(a883),f331(a111,x68601)),f331(a111,x68602)))+~P24(f331(f331(f248(a1),f2(a1)),x68601))+P24(f331(f331(f247(a1),x68601),x68602))
% 162.26/162.08 [6861]~P24(f331(f331(f247(a883),f331(a111,x68611)),f331(a111,x68612)))+~P24(f331(f331(f247(a1),f2(a1)),x68612))+P24(f331(f331(f247(a1),x68611),x68612))
% 162.26/162.08 [6887]P24(f331(f331(f247(a1),x68871),x68872))+~P24(f331(f331(f247(a883),f331(f110(a883),x68871)),f331(f110(a883),x68872)))+P24(f331(f331(f247(a1),x68871),a84))
% 162.26/162.08 [6911]P24(f331(f331(f247(a1),f2(a1)),f45(a1,x69111,x69112)))+~P24(f331(f331(f247(a1),f2(a1)),x69112))+~P24(f331(f331(f247(a1),f2(a1)),x69111))
% 162.26/162.08 [7012]P24(f331(f331(f248(a1),a84),x70121))+~P24(f331(f331(f248(a1),x70122),x70121))+~P24(f331(f331(f248(a883),f331(f110(a883),x70122)),f331(f110(a883),x70121)))
% 162.26/162.08 [7063]E(f331(f331(f261(a1,a1),f331(f331(f39(a1),x70631),x70632)),f45(a1,x70631,x70632)),f50(x70631,x70632))+~P24(f331(f331(f248(a1),x70631),f2(a1)))+~P24(f331(f331(f248(a1),f2(a1)),x70632))
% 162.26/162.08 [7083]E(f331(f331(f261(a1,a1),f331(f331(f39(a1),x70831),x70832)),f45(a1,x70831,x70832)),f47(x70831,x70832))+~P24(f331(f331(f247(a1),f2(a1)),x70832))+~P24(f331(f331(f247(a1),f2(a1)),x70831))
% 162.26/162.08 [7134]~P95(x71342)+E(x71341,f119(x71342))+E(f331(f145(x71342,x71342,f82(x71342),f331(f144(x71342),x71341)),f331(f174(x71342),x71341)),f331(f64(x71342,f82(x71342)),f331(f175(x71342),x71341)))
% 162.26/162.08 [7246]~E(x72461,f2(a883))+E(f331(f145(a883,a883,f81(a883),x72461),x72462),f2(a883))+P24(f331(f331(f333(a883),f641(x72462,x72461)),f331(f175(a883),x72462)))
% 162.26/162.08 [7288]~P24(f331(f331(f248(a1),x72882),f2(a1)))+P24(f331(f331(f248(a1),f331(f331(f39(a1),x72881),x72882)),f2(a1)))+~P24(f331(f331(f248(a1),f2(a1)),x72881))
% 162.26/162.08 [7290]~P24(f331(f331(f248(a1),x72901),f2(a1)))+P24(f331(f331(f248(a1),f331(f331(f39(a1),x72901),x72902)),f2(a1)))+~P24(f331(f331(f248(a1),f2(a1)),x72902))
% 162.26/162.08 [7291]~P24(f331(f331(f248(a1),x72912),f2(a1)))+P24(f331(f331(f247(a1),f331(f331(f39(a1),x72911),x72912)),f2(a1)))+~P24(f331(f331(f247(a1),f2(a1)),x72911))
% 162.26/162.08 [7292]~P24(f331(f331(f247(a1),x72921),f2(a1)))+P24(f331(f331(f247(a1),f331(f331(f39(a1),x72921),x72922)),f2(a1)))+~P24(f331(f331(f248(a1),f2(a1)),x72922))
% 162.26/162.08 [7299]P24(f331(f331(f333(f891(x72991,a877)),f524(x72992,x72991)),x72992))+~P24(f331(f62(f891(x72991,a877)),x72992))+P24(f331(f62(x72991),f40(f891(x72991,a877),x72992)))
% 162.26/162.08 [7389]P21(x73891,x73891,x73892,f256(f891(x73891,a877)))+~E(f331(f310(x73891,x73891,x73892),f256(f891(x73891,a877))),f256(f891(x73891,a877)))+~P24(f331(f62(x73891),f256(f891(x73891,a877))))
% 162.26/162.08 [7514]~P21(x75141,x75141,x75142,f256(f891(x75141,a877)))+E(f331(f310(x75141,x75141,x75142),f256(f891(x75141,a877))),f256(f891(x75141,a877)))+~P24(f331(f62(x75141),f256(f891(x75141,a877))))
% 162.26/162.08 [7648]E(f331(f331(f39(a1),x76481),x76482),f331(f110(a1),a103))+~P24(f331(f331(f247(a1),f331(f331(f81(a1),x76481),x76482)),f2(a1)))+~P24(f331(f331(f248(a1),f2(a1)),x76481))
% 162.26/162.08 [7706]~P24(f331(f331(f248(a1),x77062),f2(a1)))+~P24(f331(f331(f248(a1),f331(f331(f39(a1),x77061),x77062)),f2(a1)))+P24(f331(f331(f248(a1),f2(a1)),x77061))
% 162.26/162.08 [7711]E(f331(f331(f81(a1),x77111),x77112),f45(a1,x77111,x77112))+~P24(f331(f331(f247(a1),f331(f331(f81(a1),x77111),x77112)),f2(a1)))+~P24(f331(f331(f248(a1),f2(a1)),x77111))
% 162.26/162.08 [7714]P24(f331(f331(f248(a1),x77141),f2(a1)))+~P24(f331(f331(f248(a1),f331(f331(f39(a1),x77141),x77142)),f2(a1)))+~P24(f331(f331(f248(a1),f2(a1)),x77142))
% 162.26/162.08 [8104]~P60(x81041)+~P24(f331(f59(f887(x81041)),x81042))+P24(f331(f59(x81041),f331(f331(f8(f887(x81041),a877,x81041),x81042),f239(x81041))))
% 162.26/162.08 [8407]~P107(x84071)+P29(x84071,x84072)+~P24(f331(f331(f247(x84071),f331(f331(f168(x84071),x84072),f663(x84072,x84071))),f331(f331(f168(x84071),x84072),f664(x84072,x84071))))
% 162.26/162.08 [8408]~P107(x84081)+P29(x84081,x84082)+~P24(f331(f331(f247(x84081),f331(f331(f168(x84081),x84082),f669(x84082,x84081))),f331(f331(f168(x84081),x84082),f680(x84082,x84081))))
% 162.26/162.08 [8565]~P60(x85651)+P24(f331(f58(f887(x85651)),x85652))+~P24(f331(f58(x85651),f331(f331(f8(f887(x85651),a877,x85651),x85652),f239(x85651))))
% 162.26/162.08 [9746]~P60(x97461)+~P60(x97462)+E(f331(f331(f157(f884(x97461),f891(x97462,x97461)),f331(f331(f8(f891(x97462,f887(x97461)),f891(x97462,x97461),f884(x97461)),f74(f887(x97461),x97461,x97462,f244(x97461))),f331(f331(f8(f884(f890(x97462,x97461)),f891(x97462,f887(x97461)),f884(x97461)),f180(x97462,x97461)),f331(f184(x97462,x97461),f56(x97462))))),f55(x97461,f331(f197(f884(x97462)),f56(x97462)),f56(x97461))),f56(f891(x97462,x97461)))
% 162.26/162.08 [5702]E(x57021,f2(a1))+~E(f45(a1,x57022,x57021),f2(a1))+E(f331(f331(f39(a1),x57022),f331(f80(a1),x57021)),f331(f80(a1),f331(f331(f39(a1),x57022),x57021)))
% 162.26/162.08 [5720]~P40(x57202)+~P40(x57201)+P40(f331(f331(f107(f891(a1,a877)),x57201),x57202))
% 162.26/162.08 [5721]~P40(x57212)+~P40(x57211)+P40(f331(f331(f108(f891(a1,a877)),x57211),x57212))
% 162.26/162.08 [5738]~P94(x57381)+~P61(x57381)+E(f331(f80(x57381),f331(f331(f289(x57381),f79(x57381)),x57382)),f331(f331(f289(x57381),f331(f110(x57381),a103)),x57382))
% 162.26/162.08 [5853]E(x58531,f2(a1))+~E(f45(a1,x58532,x58531),f2(a1))+E(f331(f331(f39(a1),f331(f80(a1),x58532)),x58531),f331(f80(a1),f331(f331(f39(a1),x58532),x58531)))
% 162.26/162.08 [5989]~P107(x59891)+P29(x59891,x59892)+P24(f331(f331(f248(a883),f664(x59892,x59891)),f331(f197(f884(x59891)),x59892)))
% 162.26/162.08 [5990]~P107(x59901)+P29(x59901,x59902)+P24(f331(f331(f248(a883),f680(x59902,x59901)),f331(f197(f884(x59901)),x59902)))
% 162.26/162.08 [6143]~P94(x61431)+~E(f331(f110(x61431),x61432),f2(x61431))+P31(x61431,f331(f110(x61431),f331(f331(f81(a1),x61432),f331(f80(a1),a84))))
% 162.26/162.08 [6144]~P94(x61441)+~E(f331(f110(x61441),x61442),f2(x61441))+P31(x61441,f331(f110(x61441),f331(f331(f81(a1),a84),f331(f80(a1),x61442))))
% 162.26/162.08 [6146]E(f331(a51,f47(f331(f80(a1),x61461),f331(f80(a1),x61462))),f46(x61461,x61462))+P24(f331(f331(f248(a1),f2(a1)),x61462))+P24(f331(f331(f247(a1),f2(a1)),x61461))
% 162.26/162.08 [6274]~E(x62742,f2(a883))+~E(x62741,f2(a883))+P24(f331(f331(f247(a1),f331(f106(a1),x62741)),f331(f80(a1),f331(f106(a1),x62742))))
% 162.26/162.08 [6302]E(f331(f331(f81(a883),f331(f110(a883),x63021)),f331(f110(a883),x63022)),f331(f110(a883),f331(f331(f81(a1),x63021),x63022)))+P24(f331(f331(f248(a1),x63021),a84))+P24(f331(f331(f248(a1),x63022),a84))
% 162.26/162.08 [6428]~P75(x64281)+~P24(f331(f331(f248(x64281),f2(x64281)),x64282))+P24(f331(f331(f248(x64281),f331(f80(x64281),x64282)),x64282))
% 162.26/162.08 [6429]~P75(x64291)+~P24(f331(f331(f247(x64291),f2(x64291)),x64292))+P24(f331(f331(f247(x64291),f331(f80(x64291),x64292)),x64292))
% 162.26/162.08 [6599]E(f331(f331(f22(a883),f331(a111,x65991)),f331(a111,x65992)),f331(a111,f331(f331(f22(a1),x65991),x65992)))+~P24(f331(f331(f247(a1),f2(a1)),x65992))+~P24(f331(f331(f247(a1),x65992),x65991))
% 162.26/162.08 [6632]E(f331(a111,f45(a1,f331(f110(a1),x66321),f331(f110(a1),x66322))),f45(a883,f331(f110(a883),x66321),f331(f110(a883),x66322)))+P24(f331(a202,f331(f110(a1),x66321)))+P24(f331(a202,f331(f110(a1),x66322)))
% 162.26/162.08 [6650]~P75(x66501)+P24(f331(f331(f248(x66501),f2(x66501)),x66502))+~P24(f331(f331(f248(x66501),f331(f80(x66501),x66502)),x66502))
% 162.26/162.08 [6651]~P75(x66511)+P24(f331(f331(f247(x66511),f2(x66511)),x66512))+~P24(f331(f331(f247(x66511),f331(f80(x66511),x66512)),x66512))
% 162.26/162.08 [6662]~P75(x66621)+~P24(f331(f331(f248(x66621),f2(x66621)),x66622))+P24(f331(f331(f248(x66621),f2(x66621)),f331(f331(f81(x66621),x66622),x66622)))
% 162.26/162.08 [6665]~P75(x66651)+~P24(f331(f331(f247(x66651),f2(x66651)),x66652))+P24(f331(f331(f247(x66651),f2(x66651)),f331(f331(f81(x66651),x66652),x66652)))
% 162.26/162.08 [6676]E(f331(f331(f81(a883),f331(a111,x66761)),f331(a111,x66762)),f331(a111,f331(f331(f81(a1),x66761),x66762)))+~P24(f331(f331(f247(a1),f2(a1)),x66762))+~P24(f331(f331(f247(a1),f2(a1)),x66761))
% 162.26/162.08 [6688]E(x66881,f2(a883))+P24(f331(f331(f248(a883),f2(a883)),x66882))+~P24(f331(f331(f248(a883),f2(a883)),f331(f331(f262(a883),x66882),x66881)))
% 162.26/162.08 [6718]~P94(x67181)+E(f331(f110(x67181),x67182),f2(x67181))+~P31(x67181,f331(f110(x67181),f331(f331(f81(a1),a84),f331(f80(a1),x67182))))
% 162.26/162.08 [6719]~P94(x67191)+E(f331(f110(x67191),x67192),f2(x67191))+~P31(x67191,f331(f110(x67191),f331(f331(f81(a1),x67192),f331(f80(a1),a84))))
% 162.26/162.08 [6772]~P24(f331(f62(x67721),x67722))+~P24(f331(f62(x67721),f256(f891(x67721,a877))))+P24(f331(f62(x67721),f331(f80(f891(x67721,a877)),x67722)))
% 162.26/162.08 [6795]~P24(f331(f331(f248(a1),f2(a1)),x67952))+~P24(f331(f331(f247(a1),x67952),x67951))+P24(f331(f331(f248(a1),f2(a1)),f331(f331(f39(a1),x67951),x67952)))
% 162.26/162.08 [6796]~P24(f331(f331(f248(a1),x67962),f2(a1)))+~P24(f331(f331(f247(a1),x67961),f2(a1)))+P24(f331(f331(f247(a1),f2(a1)),f331(f331(f39(a1),x67961),x67962)))
% 162.26/162.08 [6831]~P24(f331(f331(f248(a883),f2(a883)),x68312))+~P24(f331(f331(f248(a883),f2(a883)),x68311))+P24(f331(f331(f248(a883),f2(a883)),f331(f331(f82(a883),x68311),x68312)))
% 162.26/162.08 [6832]~P24(f331(f331(f247(a1),f2(a1)),x68322))+~P24(f331(f331(f247(a1),f2(a1)),x68321))+P24(f331(f331(f247(a1),f2(a1)),f331(f331(f81(a1),x68321),x68322)))
% 162.26/162.08 [6833]~P24(f331(f331(f247(a1),f2(a1)),x68332))+~P24(f331(f331(f247(a1),f2(a1)),x68331))+P24(f331(f331(f247(a1),f2(a1)),f331(f331(f82(a1),x68331),x68332)))
% 162.26/162.08 [6834]~P24(f331(f331(f248(a1),f2(a1)),x68342))+~P24(f331(f331(f247(a1),f2(a1)),x68341))+P24(f331(f331(f247(a1),f2(a1)),f331(f331(f39(a1),x68341),x68342)))
% 162.26/162.08 [6835]~P24(f331(f331(f247(a1),f2(a1)),x68352))+~P24(f331(f331(f247(a1),f2(a1)),x68351))+P24(f331(f331(f247(a1),f2(a1)),f331(f331(f39(a1),x68351),x68352)))
% 162.26/162.08 [6897]E(x68971,f2(a1))+E(f45(a1,x68972,x68971),f2(a1))+E(f331(f331(f22(a1),f331(f80(a1),f331(f331(f39(a1),x68972),x68971))),f79(a1)),f331(f331(f39(a1),f331(f80(a1),x68972)),x68971))
% 162.26/162.08 [6953]P24(f331(f331(f248(a883),f2(a883)),x69531))+P24(f331(f331(f248(a883),f2(a883)),x69532))+~P24(f331(f331(f248(a883),f2(a883)),f331(f331(f81(a883),x69532),x69531)))
% 162.26/162.08 [6957]~P75(x69571)+P24(f331(f331(f248(x69571),f2(x69571)),x69572))+~P24(f331(f331(f248(x69571),f2(x69571)),f331(f331(f81(x69571),x69572),x69572)))
% 162.26/162.08 [6958]~P75(x69581)+P24(f331(f331(f247(x69581),f2(x69581)),x69582))+~P24(f331(f331(f247(x69581),f2(x69581)),f331(f331(f81(x69581),x69582),x69582)))
% 162.26/162.08 [7013]~P24(f331(f62(x70131),x70132))+P24(f331(f62(x70131),f256(f891(x70131,a877))))+~P24(f331(f62(x70131),f331(f80(f891(x70131,a877)),x70132)))
% 162.26/162.08 [7075]P24(f331(f331(f247(a1),x70751),f2(a1)))+~P24(f331(f331(f248(a1),x70752),f2(a1)))+~P24(f331(f331(f247(a1),f2(a1)),f331(f331(f39(a1),x70751),x70752)))
% 162.26/162.08 [7081]~P24(f331(f331(f248(a1),f2(a1)),x70811))+P24(f331(f331(f247(a1),x70811),x70812))+~P24(f331(f331(f248(a1),f2(a1)),f331(f331(f39(a1),x70812),x70811)))
% 162.26/162.08 [7082]~P24(f331(f331(f247(a1),f2(a1)),x70822))+P24(f331(f331(f247(a1),x70821),x70822))+~P24(f331(f331(f248(a1),f2(a1)),f331(f331(f39(a1),x70822),x70821)))
% 162.26/162.08 [7111]P24(f331(f331(f248(a1),f2(a1)),x71111))+~P24(f331(f331(f247(a1),f2(a1)),x71112))+~P24(f331(f331(f248(a1),f2(a1)),f331(f331(f39(a1),x71112),x71111)))
% 162.26/162.08 [7112]P24(f331(f331(f247(a1),f2(a1)),x71121))+~P24(f331(f331(f248(a1),f2(a1)),x71122))+~P24(f331(f331(f247(a1),f2(a1)),f331(f331(f39(a1),x71121),x71122)))
% 162.26/162.08 [7545]~P24(f331(f62(x75452),f256(f891(x75452,a877))))+~P24(f331(f62(x75451),f256(f891(x75451,a877))))+P24(f331(f62(f889(x75451,x75452)),f256(f891(f889(x75451,x75452),a877))))
% 162.26/162.08 [7546]~P24(f331(f62(x75462),f256(f891(x75462,a877))))+~P24(f331(f62(x75461),f256(f891(x75461,a877))))+P24(f331(f62(f890(x75461,x75462)),f256(f891(f890(x75461,x75462),a877))))
% 162.26/162.08 [7612]~P24(f331(f331(f248(a883),f331(a118,f2(a883))),x76121))+~P24(f331(f331(f248(a883),f331(a118,f2(a883))),x76122))+P24(f331(f331(f248(a883),x76121),f331(f331(f82(a883),x76122),x76121)))
% 162.26/162.08 [7613]~P24(f331(f331(f248(a883),f331(a118,f2(a883))),x76131))+~P24(f331(f331(f248(a883),f331(a118,f2(a883))),x76132))+P24(f331(f331(f248(a883),x76131),f331(f331(f82(a883),x76131),x76132)))
% 162.26/162.08 [7647]E(f331(f38(x76471),f256(f891(x76471,a877))),f331(a118,f2(a883)))+P24(f331(f62(x76472),f256(f891(x76472,a877))))+~P24(f331(f62(f891(x76472,x76471)),f256(f891(f891(x76472,x76471),a877))))
% 162.26/162.08 [7776]~P24(f331(f331(f248(a883),f331(a118,f2(a883))),x77762))+~P24(f331(f331(f248(a883),f331(a118,f2(a883))),x77761))+P24(f331(f331(f248(a883),f331(a118,f2(a883))),f331(f331(f82(a883),x77761),x77762)))
% 162.26/162.08 [7777]~P24(f331(f331(f247(a883),f331(a118,f2(a883))),x77771))+~P24(f331(f331(f247(a883),f331(a118,f2(a883))),x77772))+P24(f331(f331(f247(a883),f331(a118,f2(a883))),f331(f331(f82(a883),x77771),x77772)))
% 162.26/162.08 [8460]E(x84601,f119(x84602))+~P24(f331(f140(x84602),x84601))+E(f179(x84602,f331(f331(f8(a877,a877,x84602),a326),f331(f331(f7(x84602,x84602,a877),a328),f147(x84602,x84601))),x84601),f120(x84602,x84601))
% 162.26/162.08 [8557]~P40(x85572)+~P40(x85571)+E(f331(f310(a883,a1,f106(a1)),f331(f331(f107(f891(a883,a877)),f331(f310(a1,a883,a111),x85571)),f331(f310(a1,a883,a111),x85572))),f331(f331(f107(f891(a1,a877)),x85571),x85572))
% 162.26/162.08 [8558]~P40(x85582)+~P40(x85581)+E(f331(f310(a883,a1,f106(a1)),f331(f331(f108(f891(a883,a877)),f331(f310(a1,a883,a111),x85581)),f331(f310(a1,a883,a111),x85582))),f331(f331(f108(f891(a1,a877)),x85581),x85582))
% 162.26/162.08 [9272]~P94(x92721)+~E(f331(f110(x92721),x92722),f79(x92721))+P31(x92721,f331(f110(x92721),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)),f331(f80(a1),x92722))))
% 162.26/162.08 [9489]~P94(x94891)+E(f331(f110(x94891),x94892),f79(x94891))+~P31(x94891,f331(f110(x94891),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)),f331(f80(a1),x94892))))
% 162.26/162.08 [10224]E(x102241,f2(a1))+E(x102242,f2(a1))+E(f331(f271(a1,a1,a1,a1,f35(a1),f331(f82(a1),f83(a1,x102242))),f331(f331(f331(f102(f890(a1,a1)),f331(f331(a328,f83(a1,x102241)),f83(a1,x102242))),f53(x102241,x102242)),f331(f331(f270(a1,a1,f890(a1,a1)),f331(f331(f18(a1,f891(a1,f890(a1,a1)),f891(a1,f890(a1,a1))),f331(f331(f8(f891(a1,f891(f890(a1,a1),f890(a1,a1))),f891(f891(a1,f890(a1,a1)),f891(a1,f890(a1,a1))),a1),f18(a1,f890(a1,a1),f890(a1,a1))),f331(f331(f8(f890(a1,a1),f891(a1,f891(f890(a1,a1),f890(a1,a1))),a1),f331(f7(a1,f890(a1,a1),f891(f890(a1,a1),f890(a1,a1))),f331(f331(f8(a877,f891(f890(a1,a1),f891(f890(a1,a1),f890(a1,a1))),a1),f102(f890(a1,a1))),f331(f331(f7(a1,a1,a877),a328),f2(a1))))),f331(f331(f7(a1,a1,f890(a1,a1)),f331(f331(f8(a1,f891(a1,f890(a1,a1)),a1),f261(a1,a1)),f80(a1))),f2(a1))))),f331(f331(f7(a1,f891(a1,a1),f891(a1,f890(a1,a1))),f331(f331(f8(f891(a1,f890(a1,a1)),f891(f891(a1,a1),f891(a1,f890(a1,a1))),a1),f8(a1,f890(a1,a1),a1)),f331(f331(f8(a1,f891(a1,f890(a1,a1)),a1),f261(a1,a1)),f331(f331(f7(a1,a1,a1),f331(f331(f8(a1,f891(a1,a1),a1),f22(a1)),f80(a1))),f79(a1))))),f331(f22(a1),f331(f76(a1),x102242))))),f53(x102241,x102242)))),f46(x102241,x102242))
% 162.26/162.08 [10225]E(x102251,f2(a1))+E(x102252,f2(a1))+E(f331(f271(a1,a1,a1,a1,f35(a1),f331(f82(a1),f83(a1,x102252))),f331(f331(f331(f102(f890(a1,a1)),f331(f331(a330,f331(f331(a329,f331(f331(f248(a1),f2(a1)),x102252)),f331(f331(f247(a1),f2(a1)),x102251))),f331(f331(a329,f331(f331(f248(a1),x102252),f2(a1))),f331(f331(f248(a1),x102251),f2(a1))))),f53(x102251,x102252)),f331(f331(f270(a1,a1,f890(a1,a1)),f331(f331(f18(a1,f891(a1,f890(a1,a1)),f891(a1,f890(a1,a1))),f331(f331(f8(f891(a1,f891(f890(a1,a1),f890(a1,a1))),f891(f891(a1,f890(a1,a1)),f891(a1,f890(a1,a1))),a1),f18(a1,f890(a1,a1),f890(a1,a1))),f331(f331(f8(f890(a1,a1),f891(a1,f891(f890(a1,a1),f890(a1,a1))),a1),f331(f7(a1,f890(a1,a1),f891(f890(a1,a1),f890(a1,a1))),f331(f331(f8(a877,f891(f890(a1,a1),f891(f890(a1,a1),f890(a1,a1))),a1),f102(f890(a1,a1))),f331(f331(f7(a1,a1,a877),a328),f2(a1))))),f331(f331(f7(a1,a1,f890(a1,a1)),f331(f331(f8(a1,f891(a1,f890(a1,a1)),a1),f261(a1,a1)),f80(a1))),f2(a1))))),f331(f331(f7(a1,f891(a1,a1),f891(a1,f890(a1,a1))),f331(f331(f8(f891(a1,f890(a1,a1)),f891(f891(a1,a1),f891(a1,f890(a1,a1))),a1),f8(a1,f890(a1,a1),a1)),f331(f331(f8(a1,f891(a1,f890(a1,a1)),a1),f261(a1,a1)),f331(f331(f7(a1,a1,a1),f331(f331(f8(a1,f891(a1,a1),a1),f22(a1)),f80(a1))),f79(a1))))),f331(f22(a1),f331(f76(a1),x102252))))),f53(x102251,x102252)))),f46(x102251,x102252))
% 162.26/162.08 [10226]~P1(a5000)+P20(a878,x102261,f331(f331(f309(f882(a878)),f331(a94,x102262)),f196(f891(f882(a878),a877))))+~P20(a878,x102261,f331(f331(f309(f882(a878)),f331(f331(f331(f93(a878),f331(f331(f8(f891(a878,f891(a878,a877)),f891(a878,a877),a878),f331(f8(f891(a878,a877),a877,a878),f88(a878))),f331(f331(f8(f891(a878,a877),f891(a878,f891(a878,a877)),a878),f331(f7(a878,f891(a878,a877),f891(a878,a877)),f331(f331(f8(f891(a878,f891(a877,a877)),f891(f891(a878,a877),f891(a878,a877)),a878),f18(a878,a877,a877)),f331(f331(f8(f891(a878,a877),f891(a878,f891(a877,a877)),a878),f331(f8(a877,f891(a877,a877),a878),a334)),f203(x102262))))),a328))),x102262),a328)),f196(f891(f882(a878),a877))))
% 162.26/162.08 [5728]~P111(x57281)+~P94(x57281)+E(f331(f76(x57281),f331(f331(f262(x57281),f331(f110(x57281),a103)),x57282)),f79(x57281))
% 162.26/162.08 [6214]~P138(x62141)+~P24(f331(f331(f248(a1),x62142),f2(a1)))+E(f331(f80(x62141),f331(f106(x62141),f331(a111,f331(f80(a1),x62142)))),f331(f109(x62141),x62142))
% 162.26/162.08 [6412]P24(f331(f331(f247(a105),x64121),f79(a105)))+E(f331(f331(f81(a105),f79(a105)),f279(x64121,f331(f331(f39(a105),x64122),x64121))),f279(x64121,x64122))+P24(f331(f331(f248(a105),x64122),x64121))
% 162.26/162.08 [6998]~P91(x69981)+~P24(f331(f331(f333(x69981),x69982),f116(x69981)))+~E(f331(f331(f81(x69981),f331(f331(f81(x69981),f79(x69981)),x69982)),x69982),f2(x69981))
% 162.26/162.08 [7113]~P24(f331(f331(f248(a1),x71131),f2(a1)))+~P24(f331(f331(f247(a1),x71132),f2(a1)))+E(f331(f260(a1,a1),f331(a51,f47(f331(f80(a1),x71131),f331(f80(a1),x71132)))),f331(f331(f39(a1),x71131),x71132))
% 162.26/162.08 [7130]~P24(f331(f331(f248(a1),x71301),f2(a1)))+~P24(f331(f331(f247(a1),x71302),f2(a1)))+E(f331(f269(a1,a1),f331(a51,f47(f331(f80(a1),x71301),f331(f80(a1),x71302)))),f45(a1,x71301,x71302))
% 162.26/162.08 [7136]~P24(f331(f331(f248(a1),x71362),f2(a1)))+E(f331(f260(a1,a1),f331(a51,f50(f331(f80(a1),x71361),f331(f80(a1),x71362)))),f331(f331(f39(a1),x71361),x71362))+~P24(f331(f331(f248(a1),f2(a1)),x71361))
% 162.26/162.08 [7154]~P24(f331(f331(f248(a1),x71542),f2(a1)))+E(f331(f269(a1,a1),f331(a51,f50(f331(f80(a1),x71541),f331(f80(a1),x71542)))),f45(a1,x71541,x71542))+~P24(f331(f331(f248(a1),f2(a1)),x71541))
% 162.26/162.08 [7207]E(f331(f331(f39(a1),f331(f331(f262(a1),x72071),x72072)),x72071),f331(f331(f262(a1),x72071),f331(f331(f22(a883),x72072),f331(a118,f2(a883)))))+~P24(f331(f331(f248(a883),f2(a883)),x72072))+~P24(f331(f331(f248(a1),f2(a1)),x72071))
% 162.26/162.08 [7296]~P24(f331(f331(f248(a883),f2(a883)),x72961))+~P24(f331(f331(f248(a883),f2(a883)),x72962))+P24(f331(f331(f248(a883),f331(f331(f22(a883),x72961),x72962)),x72961))
% 162.26/162.08 [7297]~P24(f331(f331(f248(a883),f2(a883)),x72971))+~P24(f331(f331(f248(a883),f79(a883)),x72972))+P24(f331(f331(f248(a883),f331(f331(f39(a883),x72971),x72972)),x72971))
% 162.26/162.08 [7298]~P24(f331(f331(f248(a1),f2(a1)),x72981))+~P24(f331(f331(f248(a1),f79(a1)),x72982))+P24(f331(f331(f248(a1),f331(f331(f39(a1),x72981),x72982)),x72981))
% 162.26/162.08 [7439]E(x74391,f2(a883))+~E(x74392,f2(a1))+~P24(f331(f331(f248(a1),f2(a1)),f331(f331(f262(a1),f331(f76(a1),x74392)),x74391)))
% 162.26/162.08 [7856]~E(x78562,f119(f884(x78561)))+E(f331(f197(f884(f884(x78561))),f182(x78561,x78562)),f2(a883))+~P29(a883,f331(f172(a883),f331(f331(f157(f884(x78561),a883),f197(f884(x78561))),x78562)))
% 162.26/162.08 [8103]P24(f331(x81031,x81032))+~P24(f331(x81031,f331(a113,f558(x81031,x81032))))+~P24(f331(f331(f333(f891(f890(a883,a883),a877)),x81032),a104))
% 162.26/162.08 [8123]E(x81231,f119(f884(x81232)))+E(f331(f197(f884(x81232)),f331(f331(f168(f884(x81232)),x81231),f2(a883))),f331(f197(f884(f884(x81232))),f182(x81232,x81231)))+~P29(a883,f331(f172(a883),f331(f331(f157(f884(x81232),a883),f197(f884(x81232))),x81231)))
% 162.26/162.08 [8812]~P24(f331(f62(x88121),f331(f253(x88121),x88122)))+~P24(f331(f62(x88121),f256(f891(x88121,a877))))+P24(f331(f62(x88121),f331(f253(x88121),f331(f331(f8(a877,a877,x88121),a326),x88122))))
% 162.26/162.08 [8877]E(f331(f331(f261(a883,a883),f331(a118,f331(f331(f39(a883),f331(f331(f22(a883),x88771),x88772)),x88772))),f45(a883,f331(f331(f22(a883),x88771),x88772),x88772)),f86(f890(a883,a883),f48(x88771,x88772)))+~P24(f331(f331(f248(a883),f2(a883)),x88772))+~P24(f331(f331(f247(a883),x88772),x88771))
% 162.26/162.08 [9166]~P24(f331(f62(x91661),f331(f253(x91661),x91662)))+P24(f331(f62(x91661),f256(f891(x91661,a877))))+~P24(f331(f62(x91661),f331(f253(x91661),f331(f331(f8(a877,a877,x91661),a326),x91662))))
% 162.26/162.08 [9913]P22(x99131,x99132)+~P38(x99131,f331(f260(f891(f890(x99131,x99131),a877),f891(f890(x99131,x99131),a877)),x99132))+~P24(f331(f331(f247(f891(f890(x99131,x99131),a877)),f331(f331(f288(x99131,x99131,x99131),f331(f260(f891(f890(x99131,x99131),a877),f891(f890(x99131,x99131),a877)),x99132)),f331(f269(f891(f890(x99131,x99131),a877),f891(f890(x99131,x99131),a877)),x99132))),f331(f260(f891(f890(x99131,x99131),a877),f891(f890(x99131,x99131),a877)),x99132)))
% 162.26/162.08 [7233]~P24(f331(f331(f248(a883),f2(a883)),x72332))+P24(f331(f331(f248(a883),x72331),x72332))+E(f331(a118,f331(f331(f39(a883),f331(f331(f22(a883),x72331),x72332)),x72332)),f331(f331(f39(a883),x72331),x72332))
% 162.26/162.08 [7358]~P24(f331(f331(f248(a883),f2(a883)),x73582))+~P24(f331(f331(f247(a883),x73582),x73581))+E(f331(a118,f331(f331(f39(a883),f331(f331(f22(a883),x73581),x73582)),x73582)),f331(f331(f39(a883),x73581),x73582))
% 162.26/162.08 [8436]~P94(x84361)+~P91(x84361)+~P31(x84361,f331(f110(x84361),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x84362)),x84362)))
% 162.26/162.08 [9061]E(x90611,f2(a883))+E(f331(f331(f270(a883,a883,f890(a883,a883)),f331(f331(f8(a883,f891(a883,f890(a883,a883)),a883),f261(a883,a883)),a118)),f86(f890(a883,a883),f48(f331(f331(f22(a883),x90612),x90611),x90611))),f86(f890(a883,a883),f48(x90612,x90611)))+P24(f331(f331(f248(a883),x90612),x90611))
% 162.26/162.08 [9509]P24(f331(x95092,f800(x95092,x95091)))+P24(f331(x95091,f800(x95092,x95091)))+E(f331(f253(a1),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f247(a1),f2(a1)))),x95091)),f331(f253(a1),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f247(a1),f2(a1)))),x95092)))
% 162.26/162.08 [9513]~P24(f331(x95132,f800(x95132,x95131)))+~P24(f331(x95131,f800(x95132,x95131)))+E(f331(f253(a1),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f247(a1),f2(a1)))),x95131)),f331(f253(a1),f331(f331(f18(a1,a877,a877),f331(f331(f8(a877,f891(a877,a877),a1),a329),f331(f247(a1),f2(a1)))),x95132)))
% 162.26/162.08 [7813]~P94(x78131)+~P62(x78131)+E(f331(f331(f289(x78131),x78132),f331(f110(x78131),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),x78132)
% 162.26/162.08 [9848]~P24(f331(f62(a880),x98482))+P20(a878,x98481,f331(f310(a880,f882(a878),f331(f331(f8(a879,f882(a878),a880),a94),a28)),x98482))+~P20(a878,f331(f331(f107(f891(f882(a878),a877)),x98481),f331(f310(a880,f882(a878),f331(f331(f8(a879,f882(a878),a880),a94),a28)),x98482)),f331(f310(a880,f882(a878),f331(f331(f8(a879,f882(a878),a880),a94),f331(f331(f8(f887(a879),a879,a880),f244(a879)),a26))),x98482))
% 162.26/162.08 [9271]~P94(x92711)+~E(f331(f110(x92711),x92712),f79(x92711))+P31(x92711,f331(f110(x92711),f331(f331(f81(a1),x92712),f331(f80(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)))))
% 162.26/162.08 [9490]~P94(x94901)+E(f331(f110(x94901),x94902),f79(x94901))+~P31(x94901,f331(f110(x94901),f331(f331(f81(a1),x94902),f331(f80(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)))))
% 162.26/162.08 [9937]~P137(x99371)+~E(x99372,f79(x99371))+E(f331(f331(f262(x99371),x99372),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f79(x99371))
% 162.26/162.08 [9938]~P137(x99381)+~E(x99382,f2(x99381))+E(f331(f331(f262(x99381),x99382),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f2(x99381))
% 162.26/162.08 [9941]~P137(x99411)+~E(x99412,f331(f80(x99411),f79(x99411)))+E(f331(f331(f262(x99411),x99412),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f79(x99411))
% 162.26/162.08 [10076]~P111(x100762)+E(x100761,f2(x100762))+P24(f331(f331(f248(x100762),f2(x100762)),f331(f331(f262(x100762),x100761),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))))
% 162.26/162.08 [10114]~P111(x101142)+~E(x101141,f2(x101142))+~P24(f331(f331(f248(x101142),f2(x101142)),f331(f331(f262(x101142),x101141),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))))
% 162.26/162.08 [10127]P24(f331(f331(f247(a1),x101271),f2(a1)))+P24(f331(f331(f248(a1),x101272),x101271))+E(f331(f44(x101271),f47(x101272,f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x101271))),f47(x101272,x101271))
% 162.26/162.08 [10128]~P24(f331(f331(f248(a1),f2(a1)),x101281))+P24(f331(f331(f248(a1),x101282),x101281))+E(f331(f44(x101281),f47(x101282,f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x101281))),f47(x101282,x101281))
% 162.26/162.08 [10129]P24(f331(f331(f247(a1),x101291),f2(a1)))+P24(f331(f331(f247(a1),f2(a1)),f331(f331(f81(a1),x101292),x101291)))+E(f331(f44(x101291),f50(x101292,f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x101291))),f50(x101292,x101291))
% 162.26/162.08 [10130]~P24(f331(f331(f248(a1),f2(a1)),x101301))+P24(f331(f331(f247(a1),f2(a1)),f331(f331(f81(a1),x101302),x101301)))+E(f331(f44(x101301),f50(x101302,f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x101301))),f50(x101302,x101301))
% 162.26/162.08 [10131]~P143(x101311)+~P24(f331(f331(f247(a1),f2(a1)),x101312))+E(f331(f106(x101311),f331(a111,f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x101312))),f331(f331(f81(x101311),f331(f106(x101311),f331(a111,x101312))),f331(f106(x101311),f331(a111,x101312))))
% 162.26/162.08 [5064]~P146(x50641,x50643,x50642)+~E(x50643,f2(a1))+P24(f331(x50641,x50642))
% 162.26/162.08 [5184]~P107(x51841)+~P29(x51841,x51843)+P29(x51841,f173(x51841,x51842,x51843))
% 162.26/162.08 [5185]~P107(x51851)+~P29(x51851,x51853)+P29(x51851,f179(x51851,x51852,x51853))
% 162.26/162.08 [4770]~P66(x47702)+~E(x47703,f331(f80(x47702),x47701))+E(x47701,f331(f80(x47702),x47703))
% 162.26/162.08 [4772]~P66(x47721)+~E(f331(f80(x47721),x47723),x47722)+E(f331(f80(x47721),x47722),x47723)
% 162.26/162.08 [4846]~P66(x48463)+E(x48461,x48462)+~E(f331(f80(x48463),x48461),f331(f80(x48463),x48462))
% 162.26/162.08 [4847]~P85(x48473)+E(x48471,x48472)+~E(f331(f80(x48473),x48471),f331(f80(x48473),x48472))
% 162.26/162.08 [4848]~P103(x48483)+E(x48481,x48482)+~E(f331(f106(x48483),x48481),f331(f106(x48483),x48482))
% 162.26/162.08 [4849]~P91(x48493)+E(x48491,x48492)+~E(f331(f109(x48493),x48491),f331(f109(x48493),x48492))
% 162.26/162.08 [4850]~P107(x48503)+E(x48501,x48502)+~E(f331(f300(x48503),x48501),f331(f300(x48503),x48502))
% 162.26/162.08 [4851]~P107(x48513)+E(x48511,x48512)+~E(f331(f254(x48513),x48511),f331(f254(x48513),x48512))
% 162.26/162.08 [4852]~P107(x48523)+E(x48521,x48522)+~E(f331(f255(x48523),x48521),f331(f255(x48523),x48522))
% 162.26/162.08 [4853]~P107(x48533)+E(x48531,x48532)+~E(f331(f303(x48533),x48531),f331(f303(x48533),x48532))
% 162.26/162.08 [4951]~P60(x49511)+~P24(f331(x49512,x49513))+P24(f331(f58(x49511),x49512))
% 162.26/162.08 [4984]~P60(x49843)+P24(f331(x49841,x49842))+~P24(f331(f59(x49843),x49841))
% 162.26/162.08 [5082]~P147(x50821,x50822,x50823)+~E(x50822,f2(a1))+P24(f331(x50821,f2(a1)))
% 162.26/162.08 [5119]~E(x51191,f2(a883))+E(f722(x51191,x51192,x51193),f196(f891(x51193,a877)))+~E(f331(f38(x51193),x51192),f331(a118,x51191))
% 162.26/162.08 [5274]~E(x52742,f2(a883))+E(f331(f260(a883,a883),x52741),f2(a883))+~P24(f331(f48(x52743,x52742),x52741))
% 162.26/162.08 [5321]P24(f331(x53211,x53212))+~E(x53213,f331(f106(a1),x53212))+~P24(f331(x53211,f331(a111,x53213)))
% 162.26/162.08 [5792]~E(x57923,f2(a883))+~P24(f331(x57921,x57922))+P24(f331(x57921,f45(a883,x57922,x57923)))
% 162.26/162.08 [5923]~P24(f331(a25,x59233))+~P24(f331(a25,x59232))+P24(f331(a25,f31(x59231,x59232,x59233)))
% 162.26/162.08 [5954]~P60(x59543)+~P7(x59543,x59541,x59542)+P24(f331(x59541,f681(x59542,x59541,x59543)))
% 162.26/162.08 [6016]~P104(x60162)+~P104(x60161)+E(f134(x60161,x60162,f135(x60161,x60163),f135(x60162,x60163)),f135(f890(x60161,x60162),x60163))
% 162.26/162.08 [6197]~E(x61973,f2(a883))+P24(f331(x61971,x61972))+~P24(f331(x61971,f45(a883,x61972,x61973)))
% 162.26/162.08 [6342]~P60(x63421)+P8(x63421,x63422,x63423)+~P24(f331(x63422,f682(x63423,x63422,x63421)))
% 162.26/162.08 [6857]E(x68571,f2(a883))+~P24(f331(x68572,f377(x68571,x68573,x68572)))+P24(f331(x68572,f45(a883,x68573,x68571)))
% 162.26/162.08 [6963]~P27(x69631)+~P24(f331(f331(f247(x69631),x69632),f519(x69633,x69632,x69631)))+P24(f331(f331(f247(x69631),x69632),f41(x69631,x69633)))
% 162.26/162.08 [6965]~P24(f331(x69651,x69652))+~P24(f331(x69651,f377(x69653,x69652,x69651)))+P24(f331(x69651,f45(a883,x69652,x69653)))
% 162.26/162.08 [7069]E(x70691,f119(x70692))+E(f331(f331(f154(x70692),f655(x70693,x70691,x70692)),f658(x70693,x70691,x70692)),x70691)+~P24(f331(f331(f333(f884(x70692)),x70691),f164(x70692,x70693)))
% 162.26/162.08 [7099]~P138(x70991)+~P24(f331(f331(f333(x70991),x70992),f116(x70991)))+P24(f331(f331(f333(x70991),f331(f331(f262(x70991),x70992),x70993)),f116(x70991)))
% 162.26/162.08 [7408]P38(x74081,x74082)+~P24(f331(f331(f333(x74081),x74083),f783(x74082,x74081)))+P24(f331(f331(f333(x74081),f799(x74082,x74081,x74083)),f783(x74082,x74081)))
% 162.26/162.08 [7673]E(x76731,f119(x76732))+~P24(f331(f331(f333(f884(x76732)),x76731),f164(x76732,x76733)))+P24(f331(f331(f333(f884(x76732)),f658(x76733,x76731,x76732)),f164(x76732,x76733)))
% 162.26/162.08 [7725]E(x77251,f2(a883))+E(f331(f331(f81(a883),f331(f331(f82(a883),x77251),f379(x77251,x77252,x77253))),f377(x77251,x77252,x77253)),x77252)+P24(f331(x77253,f45(a883,x77252,x77251)))
% 162.26/162.08 [7771]~P24(f331(x77713,x77712))+E(f331(f331(f81(a883),f331(f331(f82(a883),x77711),f379(x77711,x77712,x77713))),f377(x77711,x77712,x77713)),x77712)+P24(f331(x77713,f45(a883,x77712,x77711)))
% 162.26/162.08 [7907]P24(f331(f331(f248(a1),x79071),f363(x79072,x79073,x79071)))+P24(f331(f331(x79073,f331(f331(f39(a1),x79072),x79071)),f45(a1,x79072,x79071)))+~P24(f331(f331(f248(a1),x79071),f2(a1)))
% 162.26/162.08 [8184]P24(f331(f331(x81842,f331(f331(f39(a1),x81841),x81843)),f45(a1,x81841,x81843)))+~P24(f331(f331(f248(a1),x81843),f2(a1)))+P24(f331(f331(f247(a1),f363(x81841,x81842,x81843)),f2(a1)))
% 162.26/162.08 [8360]E(f331(f331(f81(a1),f331(f331(f82(a1),x83601),f366(x83602,x83603,x83601))),f363(x83602,x83603,x83601)),x83602)+P24(f331(f331(x83603,f331(f331(f39(a1),x83602),x83601)),f45(a1,x83602,x83601)))+~P24(f331(f331(f248(a1),x83601),f2(a1)))
% 162.26/162.08 [8601]~P24(f331(f331(x86011,f366(x86012,x86011,x86013)),f363(x86012,x86011,x86013)))+P24(f331(f331(x86011,f331(f331(f39(a1),x86012),x86013)),f45(a1,x86012,x86013)))+~P24(f331(f331(f248(a1),x86013),f2(a1)))
% 162.26/162.08 [8823]~P107(x88231)+~P29(x88231,x88233)+P29(x88231,f152(x88231,x88231,f5(x88231),x88232,x88233))
% 162.26/162.08 [9330]~P123(x93302)+E(x93301,f2(x93302))+~P24(f331(f331(f247(x93302),f331(f331(f81(x93302),f331(f331(f82(x93302),x93303),x93303)),f331(f331(f82(x93302),x93301),x93301))),f2(x93302)))
% 162.26/162.08 [9331]~P123(x93312)+E(x93311,f2(x93312))+~P24(f331(f331(f247(x93312),f331(f331(f81(x93312),f331(f331(f82(x93312),x93311),x93311)),f331(f331(f82(x93312),x93313),x93313))),f2(x93312)))
% 162.26/162.08 [10215]~P111(x102151)+~P24(f331(f331(f248(x102151),x102152),f2(x102151)))+P24(f331(f331(f248(x102151),f331(f331(f262(x102151),x102152),f331(a118,f331(f331(f82(a883),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x102153)))),f2(x102151)))
% 162.26/162.08 [10218]~P111(x102182)+E(x102181,f2(x102182))+~P24(f331(f331(f247(x102182),f331(f331(f81(x102182),f331(f331(f262(x102182),x102183),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f331(f331(f262(x102182),x102181),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))),f2(x102182)))
% 162.26/162.08 [10219]~P111(x102192)+E(x102191,f2(x102192))+~P24(f331(f331(f247(x102192),f331(f331(f81(x102192),f331(f331(f262(x102192),x102191),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f331(f331(f262(x102192),x102193),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))),f2(x102192)))
% 162.26/162.08 [4802]~E(x48022,x48023)+~P66(x48021)+E(f331(f331(f22(x48021),x48022),x48023),f2(x48021))
% 162.26/162.08 [4803]~E(x48032,x48033)+~P70(x48031)+E(f331(f331(f22(x48031),x48032),x48033),f2(x48031))
% 162.26/162.08 [4816]~P141(x48161)+~E(x48163,f2(x48161))+E(f331(f331(f81(x48161),x48162),x48163),x48162)
% 162.26/162.08 [4833]~P140(x48331)+~E(x48333,f2(x48331))+E(f331(f331(f82(x48331),x48332),x48333),f2(x48331))
% 162.26/162.08 [4834]~P140(x48341)+~E(x48342,f2(x48341))+E(f331(f331(f82(x48341),x48342),x48343),f2(x48341))
% 162.26/162.08 [4855]~E(x48553,f119(x48551))+~E(x48552,f119(x48551))+E(f331(f331(f137(x48551),x48552),x48553),f119(x48551))
% 162.26/162.08 [4941]~P141(x49412)+E(x49411,f2(x49412))+~E(f331(f331(f81(x49412),x49413),x49411),x49413)
% 162.26/162.08 [4942]~P66(x49421)+~E(x49422,f331(f80(x49421),x49423))+E(f331(f331(f81(x49421),x49422),x49423),f2(x49421))
% 162.26/162.08 [4949]E(x49491,f119(x49492))+E(x49493,f2(a883))+~E(f331(f331(f176(x49492),x49493),x49491),f119(x49492))
% 162.26/162.08 [4955]~P66(x49553)+E(x49551,x49552)+~E(f331(f331(f22(x49553),x49551),x49552),f2(x49553))
% 162.26/162.08 [4956]~P70(x49563)+E(x49561,x49562)+~E(f331(f331(f22(x49563),x49561),x49562),f2(x49563))
% 162.26/162.08 [4965]~P137(x49652)+E(x49651,f2(x49652))+~E(f331(f331(f262(x49652),x49651),x49653),f2(x49652))
% 162.26/162.08 [4966]~P97(x49662)+E(x49661,f196(x49662))+~E(f331(f331(f107(x49662),x49663),x49661),f196(x49662))
% 162.26/162.08 [4967]~P97(x49672)+E(x49671,f196(x49672))+~E(f331(f331(f107(x49672),x49671),x49673),f196(x49672))
% 162.26/162.08 [4968]~P100(x49682)+E(x49681,f256(x49682))+~E(f331(f331(f108(x49682),x49683),x49681),f256(x49682))
% 162.26/162.08 [4969]~P100(x49692)+E(x49691,f256(x49692))+~E(f331(f331(f108(x49692),x49691),x49693),f256(x49692))
% 162.26/162.08 [5035]~P66(x50352)+E(x50351,f331(f80(x50352),x50353))+~E(f331(f331(f81(x50352),x50351),x50353),f2(x50352))
% 162.26/162.08 [5036]~P66(x50361)+E(f331(f80(x50361),x50362),x50363)+~E(f331(f331(f81(x50361),x50362),x50363),f2(x50361))
% 162.26/162.08 [5038]~E(x50382,x50383)+~P106(x50381)+P24(f331(f331(f247(x50381),x50382),x50383))
% 162.26/162.08 [5040]~E(x50402,x50403)+~P108(x50401)+P24(f331(f331(f247(x50401),x50402),x50403))
% 162.26/162.08 [5041]~E(x50412,x50413)+~P93(x50411)+P24(f331(f331(f92(x50411),x50412),x50413))
% 162.26/162.08 [5135]~P112(x51351)+~E(x51352,f331(f80(x51351),x51353))+E(f331(f331(f82(x51351),x51352),x51352),f331(f331(f82(x51351),x51353),x51353))
% 162.26/162.08 [5143]~P107(x51431)+~P29(x51431,x51433)+P29(x51431,f331(f331(f176(x51431),x51432),x51433))
% 162.26/162.08 [5144]~P107(x51441)+~P29(x51441,x51443)+P29(x51441,f331(f331(f141(x51441),x51442),x51443))
% 162.26/162.08 [5182]E(x51821,x51822)+E(x51823,f2(a883))+~E(f331(f331(f82(a883),x51823),x51821),f331(f331(f82(a883),x51823),x51822))
% 162.26/162.08 [5183]E(x51831,x51832)+E(x51833,f2(a883))+~E(f331(f331(f82(a883),x51831),x51833),f331(f331(f82(a883),x51832),x51833))
% 162.26/162.08 [5265]~E(x52652,x52653)+~P108(x52651)+E(f302(x52651,x52652,x52653),f331(f331(f309(x52651),x52652),f196(f891(x52651,a877))))
% 162.26/162.08 [5309]E(x53091,x53092)+~P93(x53093)+~P24(f331(f331(f92(x53093),x53091),x53092))
% 162.26/162.08 [5319]~E(x53191,x53192)+~P107(x53193)+~P24(f331(f331(f248(x53193),x53191),x53192))
% 162.26/162.08 [5320]~E(x53201,x53202)+~P108(x53203)+~P24(f331(f331(f248(x53203),x53201),x53202))
% 162.26/162.08 [5330]~P108(x53301)+E(f331(f301(x53301,x53302),x53303),f196(f891(x53301,a877)))+P24(f331(f331(f248(x53301),x53302),x53303))
% 162.26/162.08 [5378]~P108(x53781)+E(f304(x53781,x53782,x53783),f196(f891(x53781,a877)))+P24(f331(f331(f248(x53781),x53782),x53783))
% 162.26/162.08 [5379]~P108(x53791)+E(f302(x53791,x53792,x53793),f196(f891(x53791,a877)))+P24(f331(f331(f247(x53791),x53792),x53793))
% 162.26/162.08 [5380]~P108(x53801)+E(f196(f891(x53801,a877)),f304(x53801,x53802,x53803))+P24(f331(f331(f248(x53801),x53802),x53803))
% 162.26/162.08 [5381]~P108(x53811)+E(f196(f891(x53811,a877)),f302(x53811,x53812,x53813))+P24(f331(f331(f247(x53811),x53812),x53813))
% 162.26/162.08 [5389]~P101(x53891)+~E(f331(f331(f107(x53891),x53892),x53893),x53893)+P24(f331(f331(f247(x53891),x53892),x53893))
% 162.26/162.08 [5390]~P107(x53901)+~E(f331(f331(f251(x53901),x53902),x53903),x53902)+P24(f331(f331(f247(x53901),x53902),x53903))
% 162.26/162.08 [5391]~P107(x53911)+~E(f331(f331(f246(x53911),x53912),x53913),x53913)+P24(f331(f331(f247(x53911),x53912),x53913))
% 162.26/162.08 [5392]~P102(x53921)+~E(f331(f331(f108(x53921),x53922),x53923),x53922)+P24(f331(f331(f247(x53921),x53922),x53923))
% 162.26/162.08 [5412]~P107(x54121)+P29(x54121,x54122)+~P29(x54121,f331(f331(f154(x54121),x54123),x54122))
% 162.26/162.08 [5413]~P107(x54131)+P29(x54131,x54132)+~P29(x54131,f331(f331(f137(x54131),x54133),x54132))
% 162.26/162.08 [5414]~P107(x54141)+P29(x54141,x54142)+~P29(x54141,f331(f331(f137(x54141),x54142),x54143))
% 162.26/162.08 [5482]~P107(x54821)+P24(f331(f331(f247(x54821),x54823),x54822))+P24(f331(f331(f248(x54821),x54822),x54823))
% 162.26/162.08 [5484]~P107(x54841)+P24(f331(f331(f247(x54841),x54843),x54842))+P24(f331(f331(f247(x54841),x54842),x54843))
% 162.26/162.08 [5521]~P101(x55211)+E(f331(f331(f107(x55211),x55212),x55213),x55212)+~P24(f331(f331(f247(x55211),x55213),x55212))
% 162.26/162.08 [5523]~P101(x55231)+E(f331(f331(f107(x55231),x55232),x55233),x55233)+~P24(f331(f331(f247(x55231),x55232),x55233))
% 162.26/162.08 [5524]~P107(x55241)+E(f331(f331(f251(x55241),x55242),x55243),x55243)+~P24(f331(f331(f247(x55241),x55243),x55242))
% 162.26/162.08 [5526]~P107(x55261)+E(f331(f331(f251(x55261),x55262),x55263),x55262)+~P24(f331(f331(f247(x55261),x55262),x55263))
% 162.26/162.08 [5527]~P107(x55271)+E(f331(f331(f246(x55271),x55272),x55273),x55272)+~P24(f331(f331(f247(x55271),x55273),x55272))
% 162.26/162.08 [5529]~P107(x55291)+E(f331(f331(f246(x55291),x55292),x55293),x55293)+~P24(f331(f331(f247(x55291),x55292),x55293))
% 162.26/162.08 [5530]~P102(x55301)+E(f331(f331(f108(x55301),x55302),x55303),x55303)+~P24(f331(f331(f247(x55301),x55303),x55302))
% 162.26/162.08 [5532]~P102(x55321)+E(f331(f331(f108(x55321),x55322),x55323),x55322)+~P24(f331(f331(f247(x55321),x55322),x55323))
% 162.26/162.08 [5539]~P119(x55392)+E(x55391,f2(x55392))+E(f331(f331(f289(x55392),f331(f80(x55392),x55393)),f331(f80(x55392),x55391)),f331(f331(f289(x55392),x55393),x55391))
% 162.26/162.08 [5584]~P108(x55841)+E(f331(f301(x55841,x55842),x55843),f196(f891(x55841,a877)))+~P24(f331(f331(f247(x55841),x55843),x55842))
% 162.26/162.08 [5617]~P108(x56171)+E(f305(x56171,x56172,x56173),f196(f891(x56171,a877)))+~P24(f331(f331(f247(x56171),x56173),x56172))
% 162.26/162.08 [5618]~P108(x56181)+E(f304(x56181,x56182,x56183),f196(f891(x56181,a877)))+~P24(f331(f331(f247(x56181),x56183),x56182))
% 162.26/162.08 [5619]~P108(x56191)+E(f302(x56191,x56192,x56193),f196(f891(x56191,a877)))+~P24(f331(f331(f248(x56191),x56193),x56192))
% 162.26/162.08 [5670]~E(f331(f331(f22(a883),x56701),x56703),x56702)+E(x56701,f331(f331(f81(a883),x56702),x56703))+~P24(f331(f331(f247(a883),x56703),x56701))
% 162.26/162.08 [5671]~E(x56711,f331(f331(f81(a883),x56713),x56712))+E(f331(f331(f22(a883),x56711),x56712),x56713)+~P24(f331(f331(f247(a883),x56712),x56711))
% 162.26/162.08 [5717]~P24(f331(x57171,x57173))+P24(f331(x57171,f404(x57171,x57172)))+~P24(f331(f331(f247(a883),x57173),x57172))
% 162.26/162.08 [5718]~P24(f331(x57181,x57183))+P24(f331(x57181,f414(x57181,x57182)))+~P24(f331(f331(f248(a883),x57183),x57182))
% 162.26/162.08 [5726]~P108(x57261)+~E(f331(f301(x57261,x57262),x57263),f196(f891(x57261,a877)))+~P24(f331(f331(f248(x57261),x57262),x57263))
% 162.26/162.08 [5730]~P106(x57301)+~P24(f331(f331(f248(x57301),x57302),x57303))+P24(f331(f331(f247(x57301),x57302),x57303))
% 162.26/162.08 [5732]~P108(x57321)+~P24(f331(f331(f248(x57321),x57322),x57323))+P24(f331(f331(f247(x57321),x57322),x57323))
% 162.26/162.08 [5840]~P108(x58401)+~E(f304(x58401,x58402,x58403),f196(f891(x58401,a877)))+~P24(f331(f331(f248(x58401),x58402),x58403))
% 162.26/162.08 [5841]~P108(x58411)+~E(f302(x58411,x58412,x58413),f196(f891(x58411,a877)))+~P24(f331(f331(f247(x58411),x58412),x58413))
% 162.26/162.08 [5842]~P108(x58421)+~E(f196(f891(x58421,a877)),f304(x58421,x58422,x58423))+~P24(f331(f331(f248(x58421),x58422),x58423))
% 162.26/162.08 [5843]~P108(x58431)+~E(f196(f891(x58431,a877)),f302(x58431,x58432,x58433))+~P24(f331(f331(f247(x58431),x58432),x58433))
% 162.26/162.08 [5851]P24(f331(x58511,x58512))+~P24(f331(x58511,f415(x58511,x58513)))+~P24(f331(f331(f247(a883),x58512),x58513))
% 162.26/162.08 [5852]P24(f331(x58521,x58522))+~P24(f331(x58521,f440(x58521,x58523)))+~P24(f331(f331(f248(a883),x58522),x58523))
% 162.26/162.08 [5860]~E(x58601,f331(a118,x58603))+P24(f331(f331(f248(a883),x58601),f331(a118,x58602)))+~P24(f331(f331(f248(a883),x58603),x58602))
% 162.26/162.08 [5876]E(x58761,x58762)+~E(f331(f331(f82(a883),x58763),x58761),f331(f331(f82(a883),x58763),x58762))+~P24(f331(f331(f248(a883),f2(a883)),x58763))
% 162.26/162.08 [5934]E(f331(x59341,f450(x59341,x59342,x59343)),f79(a883))+~E(f331(f331(f6(x59343,a883),x59341),x59342),f79(a883))+~P24(f331(f62(x59343),x59342))
% 162.26/162.08 [5945]~P27(x59451)+P24(f331(f331(f247(x59451),x59452),f40(x59451,x59453)))+~P24(f331(f331(f333(x59451),x59452),x59453))
% 162.26/162.08 [5975]~P106(x59751)+~P24(f331(f331(f248(x59751),x59753),x59752))+~P24(f331(f331(f248(x59751),x59752),x59753))
% 162.26/162.08 [5976]~P106(x59761)+~P24(f331(f331(f247(x59761),x59763),x59762))+~P24(f331(f331(f248(x59761),x59762),x59763))
% 162.26/162.08 [5977]~P107(x59771)+~P24(f331(f331(f248(x59771),x59773),x59772))+~P24(f331(f331(f248(x59771),x59772),x59773))
% 162.26/162.08 [5980]~P107(x59801)+~P24(f331(f331(f247(x59801),x59803),x59802))+~P24(f331(f331(f248(x59801),x59802),x59803))
% 162.26/162.08 [5981]~P108(x59811)+~P24(f331(f331(f248(x59811),x59813),x59812))+~P24(f331(f331(f248(x59811),x59812),x59813))
% 162.26/162.08 [6010]~E(f331(x60102,f380(x60102,x60103,x60101)),f79(a883))+E(f331(f331(f9(x60101,a883),x60102),x60103),f79(a883))+~P24(f331(f62(x60101),x60103))
% 162.26/162.08 [6011]~E(f331(x60112,f451(x60112,x60113,x60111)),f2(a883))+E(f331(f331(f6(x60111,a883),x60112),x60113),f2(a883))+~P24(f331(f62(x60111),x60113))
% 162.26/162.08 [6025]~P109(x60251)+~P24(f331(f331(f247(x60251),x60253),x60252))+P24(f331(f331(f333(x60251),x60252),f331(f255(x60251),x60253)))
% 162.26/162.08 [6026]~P109(x60261)+~P24(f331(f331(f248(x60261),x60263),x60262))+P24(f331(f331(f333(x60261),x60262),f331(f303(x60261),x60263)))
% 162.26/162.08 [6027]~P109(x60271)+~P24(f331(f331(f247(x60271),x60272),x60273))+P24(f331(f331(f333(x60271),x60272),f331(f300(x60271),x60273)))
% 162.26/162.08 [6028]~P109(x60281)+~P24(f331(f331(f248(x60281),x60282),x60283))+P24(f331(f331(f333(x60281),x60282),f331(f254(x60281),x60283)))
% 162.26/162.08 [6040]E(f331(x60401,f452(x60401,x60402,x60403)),f331(a118,f2(a883)))+~E(f331(f331(f6(x60403,a883),x60401),x60402),f331(a118,f2(a883)))+~P24(f331(f62(x60403),x60402))
% 162.26/162.08 [6123]~P27(x61231)+~P24(f331(f331(f333(x61231),x61233),x61232))+P24(f331(f331(f247(x61231),f41(x61231,x61232)),x61233))
% 162.26/162.08 [6140]~P24(f331(f331(f247(a883),x61401),x61403))+P24(f331(f331(f247(a883),x61401),x61402))+~P24(f331(f331(f247(a883),x61403),x61402))
% 162.26/162.08 [6141]~P24(f331(f331(f247(a1),x61411),x61413))+P24(f331(f331(f247(a1),x61411),x61412))+~P24(f331(f331(f247(a1),x61413),x61412))
% 162.26/162.08 [6160]~P109(x61601)+~P24(f331(f331(f333(x61601),x61603),f331(f303(x61601),x61602)))+P24(f331(f331(f248(x61601),x61602),x61603))
% 162.26/162.08 [6161]~P109(x61611)+~P24(f331(f331(f333(x61611),x61612),f331(f254(x61611),x61613)))+P24(f331(f331(f248(x61611),x61612),x61613))
% 162.26/162.08 [6162]~P109(x61621)+~P24(f331(f331(f333(x61621),x61623),f331(f255(x61621),x61622)))+P24(f331(f331(f247(x61621),x61622),x61623))
% 162.26/162.08 [6163]~P109(x61631)+~P24(f331(f331(f333(x61631),x61632),f331(f300(x61631),x61633)))+P24(f331(f331(f247(x61631),x61632),x61633))
% 162.26/162.08 [6280]P24(f331(x62801,x62802))+~P24(f331(x62801,f589(x62801)))+~P24(f331(f331(f333(x62803),x62802),f256(f891(x62803,a877))))
% 162.26/162.08 [6378]~P63(x63781)+P24(f331(f331(f248(x63781),f2(x63781)),f481(x63783,x63782,x63781)))+P24(f331(f331(f247(x63781),x63782),x63783))
% 162.26/162.08 [6445]~P77(x64451)+~P24(f331(f331(f248(x64451),x64453),f331(f80(x64451),x64452)))+P24(f331(f331(f248(x64451),x64452),f331(f80(x64451),x64453)))
% 162.26/162.08 [6447]~P77(x64471)+~P24(f331(f331(f247(x64471),x64473),f331(f80(x64471),x64472)))+P24(f331(f331(f247(x64471),x64472),f331(f80(x64471),x64473)))
% 162.26/162.08 [6459]~P24(f331(f331(f248(a883),x64591),x64593))+~P24(f331(f331(f248(a883),x64593),x64592))+P24(f331(f331(f248(a883),f331(a118,x64591)),x64592))
% 162.26/162.08 [6485]~P111(x64851)+P24(f331(f331(f248(x64851),f331(f109(x64851),x64852)),f331(f109(x64851),x64853)))+~P24(f331(f331(f248(a1),x64852),x64853))
% 162.26/162.08 [6486]~P110(x64861)+P24(f331(f331(f248(x64861),f331(f106(x64861),x64862)),f331(f106(x64861),x64863)))+~P24(f331(f331(f248(a883),x64862),x64863))
% 162.26/162.08 [6487]~P110(x64871)+P24(f331(f331(f247(x64871),f331(f106(x64871),x64872)),f331(f106(x64871),x64873)))+~P24(f331(f331(f247(a883),x64872),x64873))
% 162.26/162.08 [6488]~P111(x64881)+P24(f331(f331(f247(x64881),f331(f109(x64881),x64882)),f331(f109(x64881),x64883)))+~P24(f331(f331(f247(a1),x64882),x64883))
% 162.26/162.08 [6494]~P107(x64941)+E(f331(f331(f107(f891(x64941,a877)),f331(f254(x64941),x64942)),f331(f301(x64941,x64942),x64943)),f331(f254(x64941),x64943))+~P24(f331(f331(f247(x64941),x64942),x64943))
% 162.26/162.08 [6519]~P77(x65191)+~P24(f331(f331(f248(x65191),x65193),x65192))+P24(f331(f331(f248(x65191),f331(f80(x65191),x65192)),f331(f80(x65191),x65193)))
% 162.26/162.08 [6521]~P77(x65211)+~P24(f331(f331(f247(x65211),x65213),x65212))+P24(f331(f331(f247(x65211),f331(f80(x65211),x65212)),f331(f80(x65211),x65213)))
% 162.26/162.08 [6523]~P85(x65231)+~P24(f331(f331(f247(x65231),x65233),x65232))+P24(f331(f331(f247(x65231),f331(f80(x65231),x65232)),f331(f80(x65231),x65233)))
% 162.26/162.08 [6557]~P107(x65571)+E(f331(f331(f107(f891(x65571,a877)),f331(f300(x65571),x65572)),f305(x65571,x65572,x65573)),f331(f254(x65571),x65573))+~P24(f331(f331(f248(x65571),x65572),x65573))
% 162.26/162.08 [6558]~P107(x65581)+E(f331(f331(f107(f891(x65581,a877)),f331(f300(x65581),x65582)),f304(x65581,x65582,x65583)),f331(f300(x65581),x65583))+~P24(f331(f331(f247(x65581),x65582),x65583))
% 162.26/162.08 [6559]~P107(x65591)+E(f331(f331(f107(f891(x65591,a877)),f331(f254(x65591),x65592)),f302(x65591,x65592,x65593)),f331(f300(x65591),x65593))+~P24(f331(f331(f247(x65591),x65592),x65593))
% 162.26/162.08 [6594]~P107(x65941)+E(f331(f331(f107(f891(x65941,a877)),f331(f301(x65941,x65942),x65943)),f331(f255(x65941),x65943)),f331(f255(x65941),x65942))+~P24(f331(f331(f247(x65941),x65942),x65943))
% 162.26/162.08 [6749]~P107(x67491)+E(f331(f331(f107(f891(x67491,a877)),f305(x67491,x67492,x67493)),f331(f255(x67491),x67493)),f331(f303(x67491),x67492))+~P24(f331(f331(f248(x67491),x67492),x67493))
% 162.26/162.08 [6750]~P107(x67501)+E(f331(f331(f107(f891(x67501,a877)),f304(x67501,x67502,x67503)),f331(f303(x67501),x67503)),f331(f303(x67501),x67502))+~P24(f331(f331(f247(x67501),x67502),x67503))
% 162.26/162.08 [6751]~P107(x67511)+E(f331(f331(f107(f891(x67511,a877)),f302(x67511,x67512,x67513)),f331(f303(x67511),x67513)),f331(f255(x67511),x67512))+~P24(f331(f331(f247(x67511),x67512),x67513))
% 162.26/162.08 [6763]P24(f331(x67631,x67632))+~P24(f331(f331(f247(a883),x67632),x67633))+P24(f331(f331(f333(a883),f415(x67631,x67633)),f302(a883,f2(a883),x67633)))
% 162.26/162.08 [6797]E(x67971,x67972)+~E(f331(f331(f168(x67973),x67971),f607(x67973,x67972,x67971)),f331(f331(f168(x67973),x67972),f607(x67973,x67972,x67971)))+~E(f331(f197(f884(x67973)),x67971),f331(f197(f884(x67973)),x67972))
% 162.26/162.08 [6802]~E(x68023,f331(f331(f39(a883),x68021),x68022))+~P24(f331(f331(f248(a883),f2(a883)),x68022))+P24(f331(f331(f248(a883),x68021),f331(f331(f82(a883),x68022),f331(a118,x68023))))
% 162.26/162.08 [6817]~P24(f331(x68171,x68173))+~P24(f331(f331(f247(a883),x68173),x68172))+P24(f331(f331(f333(a883),f404(x68171,x68172)),f302(a883,f2(a883),x68172)))
% 162.26/162.08 [6854]~P24(f331(x68541,x68543))+P24(f331(x68541,f412(x68541,x68542)))+~P24(f331(f331(f333(a883),x68543),f302(a883,f2(a883),x68542)))
% 162.26/162.08 [6874]~P110(x68743)+~P24(f331(f331(f248(x68743),f331(f106(x68743),x68741)),f331(f106(x68743),x68742)))+P24(f331(f331(f248(a883),x68741),x68742))
% 162.26/162.08 [6875]~P111(x68753)+~P24(f331(f331(f248(x68753),f331(f109(x68753),x68751)),f331(f109(x68753),x68752)))+P24(f331(f331(f248(a1),x68751),x68752))
% 162.26/162.08 [6876]~P110(x68763)+~P24(f331(f331(f247(x68763),f331(f106(x68763),x68761)),f331(f106(x68763),x68762)))+P24(f331(f331(f247(a883),x68761),x68762))
% 162.26/162.08 [6877]~P111(x68773)+~P24(f331(f331(f247(x68773),f331(f109(x68773),x68771)),f331(f109(x68773),x68772)))+P24(f331(f331(f247(a1),x68771),x68772))
% 162.26/162.08 [6891]~P110(x68911)+~P24(f331(f331(f248(x68911),f79(x68911)),x68912))+P24(f331(f331(f248(x68911),f79(x68911)),f331(f331(f262(x68911),x68912),f331(a118,x68913))))
% 162.26/162.08 [6893]~P77(x68931)+~P24(f331(f331(f248(x68931),f331(f80(x68931),x68933)),f331(f80(x68931),x68932)))+P24(f331(f331(f248(x68931),x68932),x68933))
% 162.26/162.08 [6894]~P77(x68941)+~P24(f331(f331(f247(x68941),f331(f80(x68941),x68943)),f331(f80(x68941),x68942)))+P24(f331(f331(f247(x68941),x68942),x68943))
% 162.26/162.08 [6895]~P85(x68951)+~P24(f331(f331(f247(x68951),f331(f80(x68951),x68953)),f331(f80(x68951),x68952)))+P24(f331(f331(f247(x68951),x68952),x68953))
% 162.26/162.08 [6921]P24(f331(x69211,x69212))+~P24(f331(x69211,f413(x69211,x69213)))+~P24(f331(f331(f333(a883),x69212),f302(a883,f2(a883),x69213)))
% 162.26/162.08 [6940]~P63(x69401)+P24(f331(f331(f248(x69401),f481(x69403,x69402,x69401)),f79(x69401)))+P24(f331(f331(f247(x69401),x69402),x69403))
% 162.26/162.08 [6960]~E(f45(a883,x69603,x69602),f45(a883,x69601,x69602))+E(f331(f331(f81(a883),x69601),f331(f331(f82(a883),x69602),f718(x69601,x69602,x69603))),x69603)+~P24(f331(f331(f247(a883),x69601),x69603))
% 162.26/162.08 [6979]E(f331(x69791,f703(x69791,x69792,x69793)),f199(x69792))+~P24(f331(f62(x69793),f186(x69793,x69792,x69791)))+P24(f331(f62(x69793),f256(f891(x69793,a877))))
% 162.26/162.08 [7020]E(f331(f331(f9(x70201,a883),x70202),x70203),f79(a883))+~P24(f331(f62(x70201),x70203))+P24(f331(f331(f333(x70201),f380(x70202,x70203,x70201)),x70203))
% 162.26/162.08 [7021]E(f331(f331(f6(x70211,a883),x70212),x70213),f2(a883))+~P24(f331(f62(x70211),x70213))+P24(f331(f331(f333(x70211),f451(x70212,x70213,x70211)),x70213))
% 162.26/162.08 [7043]~P107(x70431)+~P24(f331(f331(f248(x70431),x70432),x70433))+P24(f331(f331(f248(f891(x70431,a877)),f331(f254(x70431),x70432)),f331(f254(x70431),x70433)))
% 162.26/162.08 [7044]~P108(x70441)+~P24(f331(f331(f247(x70441),x70442),x70443))+P24(f331(f331(f247(f891(x70441,a877)),f331(f300(x70441),x70442)),f331(f300(x70441),x70443)))
% 162.26/162.08 [7045]~P107(x70451)+~P24(f331(f331(f247(x70451),x70452),x70453))+P24(f331(f331(f247(f891(x70451,a877)),f331(f254(x70451),x70452)),f331(f254(x70451),x70453)))
% 162.26/162.08 [7046]~P108(x70461)+~P24(f331(f331(f247(x70461),x70463),x70462))+P24(f331(f331(f247(f891(x70461,a877)),f331(f255(x70461),x70462)),f331(f255(x70461),x70463)))
% 162.26/162.08 [7047]~P107(x70471)+~P24(f331(f331(f247(x70471),x70473),x70472))+P24(f331(f331(f247(f891(x70471,a877)),f331(f303(x70471),x70472)),f331(f303(x70471),x70473)))
% 162.26/162.08 [7055]~P27(x70551)+P24(f331(f331(f247(x70551),x70552),f41(x70551,x70553)))+P24(f331(f331(f333(x70551),f519(x70553,x70552,x70551)),x70553))
% 162.26/162.08 [7061]~P77(x70611)+P24(f331(f331(f248(x70611),f331(f331(f22(x70611),x70612),x70613)),f2(x70611)))+~P24(f331(f331(f248(x70611),x70612),x70613))
% 162.26/162.08 [7062]~P77(x70621)+P24(f331(f331(f247(x70621),f331(f331(f22(x70621),x70622),x70623)),f2(x70621)))+~P24(f331(f331(f247(x70621),x70622),x70623))
% 162.26/162.08 [7103]P24(f331(x71031,x71032))+P24(f331(f331(f247(a883),f413(x71031,x71033)),x71033))+~P24(f331(f331(f333(a883),x71032),f302(a883,f2(a883),x71033)))
% 162.26/162.08 [7143]~E(f331(f331(f6(x71431,a883),x71432),x71433),f79(a883))+~P24(f331(f62(x71431),x71433))+P24(f331(f331(f333(x71431),f450(x71432,x71433,x71431)),x71433))
% 162.26/162.08 [7144]~P24(f331(x71441,x71443))+P24(f331(f331(f247(a883),f412(x71441,x71442)),x71442))+~P24(f331(f331(f333(a883),x71443),f302(a883,f2(a883),x71442)))
% 162.26/162.08 [7184]~P27(x71841)+P24(f331(f331(f333(x71841),f527(x71843,x71842,x71841)),x71842))+P24(f331(f331(f247(x71841),f40(x71841,x71842)),x71843))
% 162.26/162.08 [7215]~E(f331(f331(f6(x72151,a883),x72152),x72153),f331(a118,f2(a883)))+~P24(f331(f62(x72151),x72153))+P24(f331(f331(f333(x72151),f452(x72152,x72153,x72151)),x72153))
% 162.26/162.08 [7226]E(x72261,f2(a883))+P24(f331(x72262,f45(a883,x72263,x72261)))+P24(f331(f331(f248(a883),f377(x72261,x72263,x72262)),x72261))
% 162.26/162.08 [7320]~P24(f331(x73201,x73202))+P24(f331(x73201,f45(a883,x73202,x73203)))+P24(f331(f331(f248(a883),f377(x73203,x73202,x73201)),x73203))
% 162.26/162.08 [7443]E(x74431,f119(x74432))+~P24(f331(f331(f333(f884(x74432)),x74431),f164(x74432,x74433)))+P24(f331(f331(f333(x74432),f655(x74433,x74431,x74432)),x74433))
% 162.26/162.08 [7465]~P107(x74651)+E(f331(f331(f107(f891(x74651,a877)),f331(f331(f309(x74651),x74652),f196(f891(x74651,a877)))),f305(x74651,x74652,x74653)),f331(f301(x74651,x74652),x74653))+~P24(f331(f331(f248(x74651),x74652),x74653))
% 162.26/162.08 [7488]~P107(x74881)+E(f331(f331(f107(f891(x74881,a877)),f331(f331(f309(x74881),x74882),f196(f891(x74881,a877)))),f304(x74881,x74882,x74883)),f302(x74881,x74882,x74883))+~P24(f331(f331(f247(x74881),x74882),x74883))
% 162.26/162.08 [7592]~P107(x75921)+P24(f331(f331(f248(x75921),x75922),x75923))+~P24(f331(f331(f248(f891(x75921,a877)),f331(f254(x75921),x75922)),f331(f254(x75921),x75923)))
% 162.26/162.08 [7593]~P107(x75931)+P24(f331(f331(f247(x75931),x75932),x75933))+~P24(f331(f331(f247(f891(x75931,a877)),f331(f303(x75931),x75933)),f331(f303(x75931),x75932)))
% 162.26/162.08 [7594]~P108(x75941)+P24(f331(f331(f247(x75941),x75942),x75943))+~P24(f331(f331(f247(f891(x75941,a877)),f331(f255(x75941),x75943)),f331(f255(x75941),x75942)))
% 162.26/162.08 [7595]~P107(x75951)+P24(f331(f331(f247(x75951),x75952),x75953))+~P24(f331(f331(f247(f891(x75951,a877)),f331(f254(x75951),x75952)),f331(f254(x75951),x75953)))
% 162.26/162.08 [7596]~P108(x75961)+P24(f331(f331(f247(x75961),x75962),x75963))+~P24(f331(f331(f247(f891(x75961,a877)),f331(f300(x75961),x75962)),f331(f300(x75961),x75963)))
% 162.26/162.08 [7619]~P77(x76191)+~P24(f331(f331(f248(x76191),f331(f331(f22(x76191),x76192),x76193)),f2(x76191)))+P24(f331(f331(f248(x76191),x76192),x76193))
% 162.26/162.08 [7620]~P77(x76201)+~P24(f331(f331(f247(x76201),f331(f331(f22(x76201),x76202),x76203)),f2(x76201)))+P24(f331(f331(f247(x76201),x76202),x76203))
% 162.26/162.08 [7778]E(x77781,f2(a883))+~E(f331(f145(a883,a883,f81(a883),x77782),x77783),f2(a883))+~P24(f331(f331(f333(a883),x77781),f331(f175(a883),x77783)))
% 162.26/162.08 [7782]~P27(x77821)+~P24(f331(f331(f247(x77821),f527(x77823,x77822,x77821)),x77823))+P24(f331(f331(f247(x77821),f40(x77821,x77822)),x77823))
% 162.26/162.08 [7928]P24(f331(f331(f247(a1),f2(a1)),f364(x79281,x79282,x79283)))+P24(f331(f331(x79282,f331(f331(f39(a1),x79281),x79283)),f45(a1,x79281,x79283)))+~P24(f331(f331(f248(a1),f2(a1)),x79283))
% 162.26/162.08 [8021]E(x80211,x80212)+~E(f331(f197(f884(x80213)),x80211),f331(f197(f884(x80213)),x80212))+~P24(f331(f331(f270(x80213,x80213,a877),a328),f608(x80213,x80211,x80212)))
% 162.26/162.08 [8094]~P38(x80942,x80943)+E(x80941,f196(f891(x80942,a877)))+~P24(f331(f331(f247(f891(x80942,a877)),x80941),f331(f285(x80942,x80942,x80943),x80941)))
% 162.26/162.08 [8165]P48(x81651,x81652,x81653)+P24(f331(f331(f333(x81651),f587(x81653,x81652,x81651)),x81652))+P24(f331(f331(f333(f890(x81651,x81651)),f588(x81653,x81652,x81651)),x81653))
% 162.26/162.08 [8188]P24(f331(f331(x81882,f331(f331(f39(a1),x81881),x81883)),f45(a1,x81881,x81883)))+~P24(f331(f331(f248(a1),f2(a1)),x81883))+P24(f331(f331(f248(a1),f364(x81881,x81882,x81883)),x81883))
% 162.26/162.08 [8211]E(f331(f310(a883,a883,f331(f331(f7(a883,a883,a883),f22(a883)),x82111)),f331(f301(a883,x82112),x82113)),f196(f891(a883,a877)))+P24(f331(f331(f248(a883),x82111),x82113))+P24(f331(f331(f248(a883),x82112),x82113))
% 162.26/162.08 [8316]E(f331(f310(a883,a883,f331(f331(f7(a883,a883,a883),f22(a883)),x83161)),f331(f301(a883,x83162),x83163)),f331(f331(f309(a883),f2(a883)),f196(f891(a883,a877))))+P24(f331(f331(f248(a883),x83161),x83163))+~P24(f331(f331(f248(a883),x83162),x83163))
% 162.26/162.08 [8330]~P107(x83301)+E(f152(x83301,x83301,f5(x83301),x83302,x83303),x83303)+~P24(f331(f331(f333(x83301),x83302),f331(f175(x83301),x83303)))
% 162.26/162.08 [8344]P21(x83441,x83441,x83442,x83443)+~P24(f331(f62(x83441),x83443))+~P24(f331(f331(f247(f891(x83441,a877)),x83443),f331(f310(x83441,x83441,x83442),x83443)))
% 162.26/162.08 [8367]E(f331(f331(f81(a1),f331(f331(f82(a1),x83671),f365(x83672,x83673,x83671))),f364(x83672,x83673,x83671)),x83672)+P24(f331(f331(x83673,f331(f331(f39(a1),x83672),x83671)),f45(a1,x83672,x83671)))+~P24(f331(f331(f248(a1),f2(a1)),x83671))
% 162.26/162.08 [8607]~P24(f331(f331(x86071,f365(x86072,x86071,x86073)),f364(x86072,x86071,x86073)))+P24(f331(f331(x86071,f331(f331(f39(a1),x86072),x86073)),f45(a1,x86072,x86073)))+~P24(f331(f331(f248(a1),f2(a1)),x86073))
% 162.26/162.08 [9463]~P24(f331(f62(x94631),x94632))+~P24(f331(f331(f333(x94631),x94633),x94632))+P24(f331(f331(f248(a883),f331(f38(x94631),f331(f331(f22(f891(x94631,a877)),x94632),f331(f331(f309(x94631),x94633),f196(f891(x94631,a877)))))),f331(f38(x94631),x94632)))
% 162.26/162.08 [10072]P48(x100721,x100722,x100723)+~P24(f331(f331(f270(x100721,x100721,a877),f331(f331(f7(x100721,f891(x100721,a877),f891(x100721,a877)),f331(f331(f8(f891(a877,a877),f891(f891(x100721,a877),f891(x100721,a877)),x100721),f8(a877,a877,x100721)),f331(f331(f8(a877,f891(a877,a877),x100721),a329),f331(f331(f7(x100721,f891(x100721,a877),a877),f333(x100721)),x100722)))),f331(f331(f7(x100721,f891(x100721,a877),a877),f333(x100721)),x100722))),f588(x100723,x100722,x100721)))+P24(f331(f331(f333(x100721),f587(x100723,x100722,x100721)),x100722))
% 162.26/162.08 [5501]~P119(x55012)+E(x55011,f2(x55012))+E(f331(f331(f289(x55012),x55013),f331(f80(x55012),x55011)),f331(f80(x55012),f331(f331(f289(x55012),x55013),x55011)))
% 162.26/162.08 [5633]~E(x56333,f196(f891(x56331,a877)))+~E(x56332,f196(f891(x56331,a877)))+E(f331(f331(f107(f891(x56331,a877)),x56332),x56333),f196(f891(x56331,a877)))
% 162.26/162.08 [5691]~E(x56913,f2(a883))+~P24(f331(x56911,f2(a883)))+P24(f331(x56911,f331(f331(f39(a883),x56912),x56913)))
% 162.26/162.08 [5832]~P64(x58322)+E(x58321,f2(x58322))+E(f331(f331(f289(x58322),f331(f76(x58322),x58323)),f331(f76(x58322),x58321)),f331(f76(x58322),f331(f331(f289(x58322),x58323),x58321)))
% 162.26/162.08 [5999]~P24(f331(f62(x59991),x59993))+E(f331(f38(x59991),f331(f331(f309(x59991),x59992),x59993)),f331(a118,f331(f38(x59991),x59993)))+P24(f331(f331(f333(x59991),x59992),x59993))
% 162.26/162.08 [6072]~E(x60722,f2(a883))+P24(f331(x60721,f2(a883)))+~P24(f331(x60721,f331(f331(f39(a883),x60723),x60722)))
% 162.26/162.08 [6091]~P24(f331(f62(x60911),x60913))+E(f331(f38(x60911),f331(f331(f309(x60911),x60912),x60913)),f331(f38(x60911),x60913))+~P24(f331(f331(f333(x60911),x60912),x60913))
% 162.26/162.08 [6125]~P24(f331(f62(x61251),x61253))+E(f331(f38(x61251),f331(f331(f309(x61251),x61252),x61253)),f331(f331(f81(a883),f79(a883)),f331(f38(x61251),x61253)))+P24(f331(f331(f333(x61251),x61252),x61253))
% 162.26/162.08 [6242]E(f331(f331(f81(a883),x62421),f769(x62421,x62422,x62423)),x62422)+~P24(f331(x62423,f2(a883)))+P24(f331(x62423,f331(f331(f22(a883),x62422),x62421)))
% 162.26/162.08 [6243]E(f331(f331(f81(a883),x62431),f784(x62431,x62432,x62433)),x62432)+~P24(f331(x62433,f2(a883)))+P24(f331(x62433,f331(f331(f22(a883),x62432),x62431)))
% 162.26/162.08 [6290]~P27(x62901)+~P24(f331(f62(x62901),x62903))+E(f331(f331(f65(x62901,x62901,f107(x62901)),x62902),x62903),f331(f331(f107(x62901),x62902),f40(x62901,x62903)))
% 162.26/162.08 [6291]~P27(x62911)+~P24(f331(f62(x62911),x62913))+E(f331(f331(f65(x62911,x62911,f108(x62911)),x62912),x62913),f331(f331(f108(x62911),x62912),f41(x62911,x62913)))
% 162.26/162.08 [6297]~P94(x62971)+~E(f331(f110(x62971),x62972),f331(f110(x62971),x62973))+P31(x62971,f331(f110(x62971),f331(f331(f81(a1),x62972),f331(f80(a1),x62973))))
% 162.26/162.08 [6303]~P138(x63031)+E(f331(f331(f22(x63031),f331(f106(x63031),x63032)),f331(f106(x63031),x63033)),f331(f106(x63031),f331(f331(f22(a883),x63032),x63033)))+~P24(f331(f331(f247(a883),x63033),x63032))
% 162.26/162.08 [6388]E(f331(f331(f81(a883),x63881),f769(x63881,x63882,x63883)),x63882)+P24(f331(f331(f248(a883),x63882),x63881))+P24(f331(x63883,f331(f331(f22(a883),x63882),x63881)))
% 162.26/162.08 [6389]E(f331(f331(f81(a883),x63891),f784(x63891,x63892,x63893)),x63892)+P24(f331(f331(f248(a883),x63892),x63891))+P24(f331(x63893,f331(f331(f22(a883),x63892),x63891)))
% 162.26/162.08 [6404]~P111(x64041)+E(f331(f331(f82(x64041),f331(f76(x64041),x64042)),x64043),f331(f76(x64041),f331(f331(f82(x64041),x64042),x64043)))+~P24(f331(f331(f247(x64041),f2(x64041)),x64043))
% 162.26/162.08 [6405]~P63(x64051)+E(f331(f331(f289(x64051),f331(f76(x64051),x64052)),x64053),f331(f76(x64051),f331(f331(f289(x64051),x64052),x64053)))+~P24(f331(f331(f248(x64051),f2(x64051)),x64053))
% 162.26/162.08 [6413]~P96(x64131)+~P24(f331(f62(x64131),x64133))+E(f331(f331(f65(x64131,x64131,f107(x64131)),x64132),x64133),f13(x64131,f331(f331(f309(x64131),x64132),x64133)))
% 162.26/162.08 [6414]~P107(x64141)+~P24(f331(f62(x64141),x64143))+E(f331(f331(f65(x64141,x64141,f251(x64141)),x64142),x64143),f14(x64141,f331(f331(f309(x64141),x64142),x64143)))
% 162.26/162.08 [6415]~P107(x64151)+~P24(f331(f62(x64151),x64153))+E(f331(f331(f65(x64151,x64151,f246(x64151)),x64152),x64153),f15(x64151,f331(f331(f309(x64151),x64152),x64153)))
% 162.26/162.08 [6416]~P96(x64161)+~P24(f331(f62(x64161),x64163))+E(f331(f331(f65(x64161,x64161,f108(x64161)),x64162),x64163),f10(x64161,f331(f331(f309(x64161),x64162),x64163)))
% 162.26/162.08 [6461]E(x64611,f119(x64612))+~E(f182(x64612,x64613),f119(f884(x64612)))+~P24(f331(f331(f333(f884(x64612)),x64611),f331(f175(f884(x64612)),x64613)))
% 162.26/162.08 [6502]~P24(f331(f140(x65021),x65023))+P24(f331(f331(f333(x65021),x65022),f331(f175(x65021),x65023)))+P24(f331(f140(x65021),f331(f331(f154(x65021),x65022),x65023)))
% 162.26/162.08 [6513]~P95(x65131)+~P24(f331(f62(x65131),x65133))+E(f331(f64(x65131,f82(x65131)),f331(f331(f309(x65131),x65132),x65133)),f331(f331(f65(x65131,x65131,f82(x65131)),x65132),x65133))
% 162.26/162.08 [6533]~P107(x65331)+~P24(f331(f62(x65331),x65333))+E(f11(x65331,f251(x65331),f331(f331(f309(x65331),x65332),x65333)),f331(f331(f65(x65331,x65331,f251(x65331)),x65332),x65333))
% 162.26/162.08 [6534]~P107(x65341)+~P24(f331(f62(x65341),x65343))+E(f12(x65341,f246(x65341),f331(f331(f309(x65341),x65342),x65343)),f331(f331(f65(x65341,x65341,f246(x65341)),x65342),x65343))
% 162.26/162.08 [6536]P24(f331(x65361,f2(a883)))+~P24(f331(f331(f248(a883),x65362),x65363))+~P24(f331(x65361,f331(f331(f22(a883),x65362),x65363)))
% 162.26/162.08 [6554]~P111(x65541)+P24(f331(f331(f248(x65541),x65542),x65543))+~P24(f331(f331(f248(x65541),f331(f76(x65541),x65542)),x65543))
% 162.26/162.08 [6556]~P83(x65561)+P24(f331(f331(f247(x65561),x65562),x65563))+~P24(f331(f331(f247(x65561),f331(f76(x65561),x65562)),x65563))
% 162.26/162.08 [6573]E(x65731,f119(x65732))+E(f331(f144(x65732),f331(f331(f141(x65732),x65733),x65731)),f331(f331(f168(x65732),x65731),x65733))+~P24(f331(f331(f248(a883),x65733),f331(f197(f884(x65732)),x65731)))
% 162.26/162.08 [6625]~P24(f331(x66251,x66253))+P24(f331(x66251,f441(x66251,x66252)))+~P24(f331(f331(f333(a883),x66253),f331(f301(a883,f2(a883)),x66252)))
% 162.26/162.08 [6647]P24(f331(x66471,x66472))+~P24(f331(f331(f248(a883),x66472),x66473))+P24(f331(f331(f333(a883),f440(x66471,x66473)),f331(f301(a883,f2(a883)),x66473)))
% 162.26/162.08 [6663]~P110(x66631)+~P24(f331(f331(f248(x66631),f2(x66631)),x66632))+P24(f331(f331(f248(x66631),f2(x66631)),f331(f331(f262(x66631),x66632),x66633)))
% 162.26/162.08 [6664]~P110(x66641)+~P24(f331(f331(f247(x66641),f79(x66641)),x66642))+P24(f331(f331(f247(x66641),f79(x66641)),f331(f331(f262(x66641),x66642),x66643)))
% 162.26/162.08 [6666]~P110(x66661)+~P24(f331(f331(f247(x66661),f2(x66661)),x66662))+P24(f331(f331(f247(x66661),f2(x66661)),f331(f331(f262(x66661),x66662),x66663)))
% 162.26/162.08 [6690]~P24(f331(x66901,x66903))+~P24(f331(f331(f248(a883),x66903),x66902))+P24(f331(f331(f333(a883),f414(x66901,x66902)),f331(f301(a883,f2(a883)),x66902)))
% 162.26/162.08 [6697]P24(f331(f62(x66971),x66972))+~P24(f331(f62(x66971),x66973))+~P24(f331(f331(f247(f891(x66971,a877)),x66972),x66973))
% 162.26/162.08 [6705]P24(f331(x67051,x67052))+~P24(f331(x67051,f442(x67051,x67053)))+~P24(f331(f331(f333(a883),x67052),f331(f301(a883,f2(a883)),x67053)))
% 162.26/162.08 [6716]E(x67161,f2(a883))+P24(f331(x67162,f375(x67161,x67163,x67162)))+~P24(f331(x67162,f331(f331(f39(a883),x67163),x67161)))
% 162.26/162.08 [6724]~P123(x67242)+E(x67241,f2(x67242))+~E(f331(f331(f81(x67242),f331(f331(f82(x67242),x67243),x67243)),f331(f331(f82(x67242),x67241),x67241)),f2(x67242))
% 162.26/162.08 [6725]~P123(x67252)+E(x67251,f2(x67252))+~E(f331(f331(f81(x67252),f331(f331(f82(x67252),x67251),x67251)),f331(f331(f82(x67252),x67253),x67253)),f2(x67252))
% 162.26/162.08 [6764]E(x67641,f2(a883))+~P24(f331(x67642,f376(x67641,x67643,x67642)))+P24(f331(x67642,f331(f331(f39(a883),x67643),x67641)))
% 162.26/162.08 [6769]~P107(x67691)+~P29(x67691,x67693)+P29(x67691,f331(f331(f151(x67691,x67691,f5(x67691)),x67692),x67693))
% 162.26/162.08 [6811]P24(f331(x68111,f375(x68112,x68113,x68111)))+P24(f331(x68111,f2(a883)))+~P24(f331(x68111,f331(f331(f39(a883),x68113),x68112)))
% 162.26/162.08 [6816]~P94(x68161)+E(f331(f110(x68161),x68162),f331(f110(x68161),x68163))+~P31(x68161,f331(f110(x68161),f331(f331(f81(a1),x68162),f331(f80(a1),x68163))))
% 162.26/162.08 [6880]E(x68801,f2(a1))+E(x68802,f2(a1))+~P24(f331(f49(x68802,x68802),f331(f331(f261(a1,a1),x68803),x68801)))
% 162.26/162.08 [6881]E(x68811,f79(a1))+E(x68812,f2(a1))+~P24(f331(f49(x68812,x68812),f331(f331(f261(a1,a1),x68811),x68813)))
% 162.26/162.08 [6892]P24(f331(x68921,x68922))+P24(f331(f331(f248(a883),f442(x68921,x68923)),x68923))+~P24(f331(f331(f333(a883),x68922),f331(f301(a883,f2(a883)),x68923)))
% 162.26/162.08 [6916]~P24(f331(x69161,f769(x69163,x69162,x69161)))+~P24(f331(x69161,f2(a883)))+P24(f331(x69161,f331(f331(f22(a883),x69162),x69163)))
% 162.26/162.08 [6917]~P24(f331(x69171,f784(x69173,x69172,x69171)))+~P24(f331(x69171,f2(a883)))+P24(f331(x69171,f331(f331(f22(a883),x69172),x69173)))
% 162.26/162.08 [6918]~P24(f331(x69181,f376(x69183,x69182,x69181)))+~P24(f331(x69181,f2(a883)))+P24(f331(x69181,f331(f331(f39(a883),x69182),x69183)))
% 162.26/162.08 [6936]~P24(f331(x69361,x69363))+P24(f331(f331(f248(a883),f441(x69361,x69362)),x69362))+~P24(f331(f331(f333(a883),x69363),f331(f301(a883,f2(a883)),x69362)))
% 162.26/162.08 [6937]E(f331(f331(f22(a883),f331(f331(f22(a883),x69371),x69372)),f331(f331(f22(a883),x69373),x69372)),f331(f331(f22(a883),x69371),x69373))+~P24(f331(f331(f247(a883),x69372),x69371))+~P24(f331(f331(f247(a883),x69372),x69373))
% 162.26/162.08 [6973]~P77(x69731)+~P24(f331(f331(f248(x69731),f331(f80(x69731),x69733)),x69732))+P24(f331(f331(f248(x69731),f331(f80(x69731),x69732)),x69733))
% 162.26/162.08 [6974]~P111(x69741)+~P24(f331(f331(f248(x69741),f331(f76(x69741),x69742)),x69743))+P24(f331(f331(f248(x69741),f331(f80(x69741),x69742)),x69743))
% 162.26/162.08 [6976]~P77(x69761)+~P24(f331(f331(f247(x69761),f331(f80(x69761),x69763)),x69762))+P24(f331(f331(f247(x69761),f331(f80(x69761),x69762)),x69763))
% 162.26/162.08 [6978]~P83(x69781)+~P24(f331(f331(f247(x69781),f331(f76(x69781),x69782)),x69783))+P24(f331(f331(f247(x69781),f331(f80(x69781),x69782)),x69783))
% 162.26/162.08 [7014]~P24(f331(x70143,f769(x70142,x70141,x70143)))+P24(f331(f331(f248(a883),x70141),x70142))+P24(f331(x70143,f331(f331(f22(a883),x70141),x70142)))
% 162.26/162.08 [7015]~P24(f331(x70153,f784(x70152,x70151,x70153)))+P24(f331(f331(f248(a883),x70151),x70152))+P24(f331(x70153,f331(f331(f22(a883),x70151),x70152)))
% 162.26/162.08 [7065]~E(f531(x70653,x70652,x70651),f532(x70653,x70652,x70651))+E(f331(f331(f108(f891(x70651,a877)),x70652),f40(f891(x70651,a877),x70653)),f196(f891(x70651,a877)))+P24(f331(f331(f333(f891(x70651,a877)),x70652),x70653))
% 162.26/162.08 [7073]~P24(f331(f62(x70731),x70733))+P24(f331(f62(x70731),f41(f891(x70731,a877),x70732)))+~P24(f331(f331(f333(f891(x70731,a877)),x70733),x70732))
% 162.26/162.08 [7132]~P107(x71321)+E(f331(f331(f107(f891(x71321,a877)),f331(f301(x71321,x71322),x71323)),f331(f331(f309(x71321),x71323),f196(f891(x71321,a877)))),f302(x71321,x71322,x71323))+~P24(f331(f331(f247(x71321),x71322),x71323))
% 162.26/162.08 [7133]E(x71331,f2(a883))+P24(f331(f331(f248(a883),f378(x71331,x71333,x71332)),x71331))+P24(f331(x71332,f331(f331(f39(a883),x71333),x71331)))
% 162.26/162.08 [7168]E(x71681,x71682)+~P24(f331(f331(f247(f891(x71683,a877)),x71681),x71682))+P24(f331(f331(f248(f891(x71683,a877)),x71681),x71682))
% 162.26/162.08 [7181]E(x71811,x71812)+~E(f331(f197(f884(x71813)),x71811),f331(f197(f884(x71813)),x71812))+P24(f331(f331(f248(a883),f607(x71813,x71811,x71812)),f331(f197(f884(x71813)),x71812)))
% 162.26/162.08 [7227]P6(x72271,x72272,x72273)+~E(f331(f259(x72271,x72271),x72273),x72272)+~E(f331(f331(f288(x72271,x72271,x72271),f331(f286(x72271,x72271),x72273)),x72273),x72273)
% 162.26/162.08 [7295]~P24(f331(x72951,f2(a883)))+P24(f331(f331(f248(a883),f378(x72953,x72952,x72951)),x72953))+P24(f331(x72951,f331(f331(f39(a883),x72952),x72953)))
% 162.26/162.08 [7304]~P107(x73041)+E(f331(f331(f107(f891(x73041,a877)),f305(x73041,x73042,x73043)),f331(f331(f309(x73041),x73043),f196(f891(x73041,a877)))),f304(x73041,x73042,x73043))+~P24(f331(f331(f248(x73041),x73042),x73043))
% 162.26/162.08 [7397]~P24(f331(f62(x73971),x73973))+P24(f331(f331(f248(a883),f331(f38(x73971),x73972)),f331(f38(x73971),x73973)))+~P24(f331(f331(f248(f891(x73971,a877)),x73972),x73973))
% 162.26/162.08 [7398]~P24(f331(f62(x73981),x73983))+P24(f331(f331(f247(a883),f331(f38(x73981),x73982)),f331(f38(x73981),x73983)))+~P24(f331(f331(f247(f891(x73981,a877)),x73982),x73983))
% 162.26/162.08 [7436]~P24(f331(x74363,x74362))+P24(f331(f331(f203(x74361),x74362),f593(x74362,x74361,x74363)))+~P24(f331(f331(f203(f33(x74363,x74361)),x74362),x74362))
% 162.26/162.08 [7533]E(x75331,x75332)+~P24(f331(f331(f247(f891(x75333,a877)),x75332),x75331))+~P24(f331(f331(f247(f891(x75333,a877)),x75331),x75332))
% 162.26/162.08 [7536]~P107(x75361)+P29(x75361,x75362)+~P29(x75361,f331(f331(f151(x75361,x75361,f5(x75361)),x75363),x75362))
% 162.26/162.08 [7599]~P24(f331(f331(f248(a883),x75993),x75992))+~P24(f331(f331(f248(a883),x75993),x75991))+P24(f331(f331(f248(a883),f331(f331(f22(a883),x75991),x75992)),f331(f331(f22(a883),x75991),x75993)))
% 162.26/162.08 [7600]~P24(f331(f331(f248(a883),x76001),x76003))+~P24(f331(f331(f247(a883),x76002),x76001))+P24(f331(f331(f248(a883),f331(f331(f22(a883),x76001),x76002)),f331(f331(f22(a883),x76003),x76002)))
% 162.26/162.08 [7617]~P24(f331(f331(f248(a1),x76172),f2(a1)))+~P24(f331(f331(f247(a1),x76173),x76171))+P24(f331(f331(f247(a1),f331(f331(f39(a1),x76171),x76172)),f331(f331(f39(a1),x76173),x76172)))
% 162.26/162.08 [7637]~P24(f331(f331(f248(a883),f2(a883)),x76372))+~P24(f331(f331(f248(a883),x76371),x76373))+P24(f331(f331(f248(a883),f331(f331(f82(a883),x76371),x76372)),f331(f331(f82(a883),x76373),x76372)))
% 162.26/162.08 [7638]~P24(f331(f331(f248(a883),f2(a883)),x76381))+~P24(f331(f331(f248(a883),x76382),x76383))+P24(f331(f331(f248(a883),f331(f331(f82(a883),x76381),x76382)),f331(f331(f82(a883),x76381),x76383)))
% 162.26/162.08 [7639]~P24(f331(f331(f248(a1),f2(a1)),x76391))+~P24(f331(f331(f248(a1),x76392),x76393))+P24(f331(f331(f248(a1),f331(f331(f82(a1),x76391),x76392)),f331(f331(f82(a1),x76391),x76393)))
% 162.26/162.08 [7641]~P24(f331(f331(f248(a883),f2(a883)),x76413))+~P24(f331(f331(f247(a883),x76413),x76412))+P24(f331(f331(f247(a883),f331(f331(f39(a883),x76411),x76412)),f331(f331(f39(a883),x76411),x76413)))
% 162.26/162.08 [7642]~P24(f331(f331(f248(a1),f2(a1)),x76422))+~P24(f331(f331(f247(a1),x76421),x76423))+P24(f331(f331(f247(a1),f331(f331(f39(a1),x76421),x76422)),f331(f331(f39(a1),x76423),x76422)))
% 162.26/162.08 [7690]E(x76901,f2(a883))+E(f331(f331(f81(a883),f331(f331(f82(a883),x76901),f376(x76901,x76902,x76903))),f378(x76901,x76902,x76903)),x76902)+P24(f331(x76903,f331(f331(f39(a883),x76902),x76901)))
% 162.26/162.08 [7750]E(f331(f331(f81(a883),f331(f331(f82(a883),x77501),f376(x77501,x77502,x77503))),f378(x77501,x77502,x77503)),x77502)+~P24(f331(x77503,f2(a883)))+P24(f331(x77503,f331(f331(f39(a883),x77502),x77501)))
% 162.26/162.08 [7769]~P24(f331(f62(x77691),x77693))+P24(f331(f331(f333(x77691),f383(x77692,x77693,x77691)),x77693))+P24(f331(f331(f248(a883),f2(a883)),f331(f331(f9(x77691,a883),x77692),x77693)))
% 162.26/162.08 [7770]~P24(f331(f62(x77701),x77703))+P24(f331(f331(f333(x77701),f536(x77702,x77703,x77701)),x77703))+P24(f331(f331(f248(a883),f2(a883)),f331(f331(f9(x77701,a883),x77702),x77703)))
% 162.26/162.08 [8060]E(x80601,f196(f891(x80602,a877)))+E(x80601,f331(f331(f309(x80602),x80603),f196(f891(x80602,a877))))+~P24(f331(f331(f247(f891(x80602,a877)),x80601),f331(f331(f309(x80602),x80603),f196(f891(x80602,a877)))))
% 162.26/162.08 [8076]~P60(x80761)+P8(x80761,x80762,x80763)+P24(f331(f331(f333(f884(x80761)),f682(x80763,x80762,x80761)),f331(f175(f884(x80761)),f55(x80761,x80763,f56(x80761)))))
% 162.26/162.08 [8096]~P24(f331(f331(f248(a883),f2(a883)),x80963))+P24(f331(f331(f248(a883),x80961),x80962))+~P24(f331(f331(f248(a883),f331(f331(f262(a883),x80963),x80961)),f331(f331(f262(a883),x80963),x80962)))
% 162.26/162.08 [8098]~P24(f331(f331(f248(a883),f2(a883)),x80983))+P24(f331(f331(f247(a883),x80981),x80982))+~P24(f331(f331(f247(a883),f331(f331(f82(a883),x80983),x80981)),f331(f331(f82(a883),x80983),x80982)))
% 162.26/162.08 [8099]~P24(f331(f331(f248(a883),f2(a883)),x80993))+P24(f331(f331(f247(a883),x80991),x80992))+~P24(f331(f331(f247(a883),f331(f331(f82(a883),x80991),x80993)),f331(f331(f82(a883),x80992),x80993)))
% 162.26/162.08 [8126]~P60(x81261)+~P7(x81261,x81263,x81262)+P24(f331(f331(f333(f884(x81261)),f681(x81262,x81263,x81261)),f331(f175(f884(x81261)),f55(x81261,x81262,f56(x81261)))))
% 162.26/162.08 [8134]~P24(f331(x81341,x81343))+P24(f331(f331(f203(f33(x81341,x81342)),f593(x81343,x81342,x81341)),x81343))+~P24(f331(f331(f203(f33(x81341,x81342)),x81343),x81343))
% 162.26/162.08 [8143]~E(f331(f331(f108(f891(x81431,a877)),f532(x81433,x81432,x81431)),f531(x81433,x81432,x81431)),f196(f891(x81431,a877)))+E(f331(f331(f108(f891(x81431,a877)),x81432),f40(f891(x81431,a877),x81433)),f196(f891(x81431,a877)))+P24(f331(f331(f333(f891(x81431,a877)),x81432),x81433))
% 162.26/162.08 [8160]E(x81601,f119(x81602))+~E(f331(f145(f884(x81602),f884(x81602),f137(x81602),f119(x81602)),x81603),f119(x81602))+~P24(f331(f331(f333(f884(x81602)),x81601),f331(f175(f884(x81602)),x81603)))
% 162.26/162.08 [8216]E(x82161,f196(f891(f891(x82162,a877),a877)))+P24(f331(f331(f333(f891(x82162,a877)),f529(x82163,x82161,x82162)),x82161))+P24(f331(f331(f247(f891(x82162,a877)),f41(f891(x82162,a877),x82161)),x82163))
% 162.26/162.08 [8222]~P73(x82221)+~P74(x82221)+E(f331(f331(f9(a1,x82221),f331(f331(f8(a883,x82221,a1),x82222),a111)),f331(f310(a883,a1,f106(a1)),x82223)),f331(f331(f9(a883,x82221),x82222),x82223))
% 162.26/162.08 [8223]~P73(x82231)+~P74(x82231)+E(f331(f331(f6(a1,x82231),f331(f331(f8(a883,x82231,a1),x82232),a111)),f331(f310(a883,a1,f106(a1)),x82233)),f331(f331(f6(a883,x82231),x82232),x82233))
% 162.26/162.08 [8262]~P24(f331(f62(x82621),x82623))+~P24(f331(f331(f248(a883),f2(a883)),f331(x82622,f383(x82622,x82623,x82621))))+P24(f331(f331(f248(a883),f2(a883)),f331(f331(f9(x82621,a883),x82622),x82623)))
% 162.26/162.08 [8263]~P24(f331(f62(x82631),x82633))+~P24(f331(f331(f248(a883),f2(a883)),f331(x82632,f536(x82632,x82633,x82631))))+P24(f331(f331(f248(a883),f2(a883)),f331(f331(f9(x82631,a883),x82632),x82633)))
% 162.26/162.08 [8298]~P62(x82982)+E(x82981,f79(x82982))+E(f331(f331(f289(x82982),f331(f331(f22(x82982),f331(f331(f262(x82982),x82981),x82983)),f79(x82982))),f331(f331(f22(x82982),x82981),f79(x82982))),f331(f331(f6(a883,x82982),f331(f262(x82982),x82981)),f331(f301(a883,f2(a883)),x82983)))
% 162.26/162.08 [8353]E(x83531,f2(a883))+~P24(f331(x83533,f331(f331(f39(a883),x83532),x83531)))+P24(f331(f331(f248(a883),x83532),f331(f331(f82(a883),x83531),f331(a118,f375(x83531,x83532,x83533)))))
% 162.26/162.08 [8371]P24(f331(x83711,f2(a883)))+~P24(f331(x83711,f331(f331(f39(a883),x83712),x83713)))+P24(f331(f331(f248(a883),x83712),f331(f331(f82(a883),x83713),f331(a118,f375(x83713,x83712,x83711)))))
% 162.26/162.08 [8409]E(x84091,f2(a883))+~P24(f331(x84093,f331(f331(f39(a883),x84092),x84091)))+P24(f331(f331(f247(a883),f331(f331(f82(a883),x84091),f375(x84091,x84092,x84093))),x84092))
% 162.26/162.08 [8451]P24(f331(x84511,f2(a883)))+~P24(f331(x84511,f331(f331(f39(a883),x84513),x84512)))+P24(f331(f331(f247(a883),f331(f331(f82(a883),x84512),f375(x84512,x84513,x84511))),x84513))
% 162.26/162.08 [8454]~P107(x84541)+E(f331(f331(f151(x84541,x84541,f5(x84541)),x84542),x84543),f152(x84541,x84541,f5(x84541),x84542,x84543))+P24(f331(f331(f333(x84541),x84542),f331(f175(x84541),x84543)))
% 162.26/162.08 [8490]~E(f331(x84903,f708(x84902,x84903,x84901)),f331(x84903,f710(x84902,x84903,x84901)))+~P57(x84901,f331(x84903,f709(x84902,x84903,x84901)))+P57(x84901,f331(f331(f42(x84902,f891(x84901,f891(x84901,a877))),f256(f891(x84902,a877))),x84903))
% 162.26/162.08 [8498]E(x84981,f196(f891(f891(x84982,a877),a877)))+~P24(f331(f331(f247(f891(x84982,a877)),f529(x84983,x84981,x84982)),x84983))+P24(f331(f331(f247(f891(x84982,a877)),f41(f891(x84982,a877),x84981)),x84983))
% 162.26/162.08 [8560]~P64(x85601)+~P24(f331(f331(f248(x85601),x85602),x85603))+P24(f331(f331(f248(x85601),x85602),f331(f331(f289(x85601),f331(f331(f81(x85601),x85602),x85603)),f331(f331(f81(x85601),f79(x85601)),f79(x85601)))))
% 162.26/162.08 [8615]~P24(f331(f331(x86151,f388(x86151,x86153,x86152)),f391(x86151,x86153,x86152)))+P24(f331(f331(x86151,x86152),x86153))+~P24(f331(f319(f890(a1,a1),a52),f331(f331(f261(a1,a1),x86152),x86153)))
% 162.26/162.08 [8616]~P24(f331(f331(x86161,f392(x86161,x86163,x86162)),f394(x86161,x86163,x86162)))+P24(f331(f331(x86161,x86162),x86163))+~P24(f331(f319(f890(a1,a1),a57),f331(f331(f261(a1,a1),x86162),x86163)))
% 162.26/162.08 [8617]~P24(f331(f331(x86171,f395(x86171,x86173,x86172)),f400(x86171,x86173,x86172)))+P24(f331(f331(x86171,x86172),x86173))+~P24(f331(f319(f890(a1,a1),a236),f331(f331(f261(a1,a1),x86172),x86173)))
% 162.26/162.08 [8618]~P24(f331(f331(x86181,f499(x86181,x86183,x86182)),f504(x86181,x86183,x86182)))+P24(f331(f331(x86181,x86182),x86183))+~P24(f331(f319(f890(a883,a883),a231),f331(f331(f261(a883,a883),x86182),x86183)))
% 162.26/162.08 [8619]~P24(f331(f331(x86191,f642(x86191,x86193,x86192)),f644(x86191,x86193,x86192)))+P24(f331(f331(x86191,x86192),x86193))+~P24(f331(f319(f890(a1,a1),a185),f331(f331(f261(a1,a1),x86192),x86193)))
% 162.26/162.08 [8620]~P24(f331(f331(x86201,f821(x86201,x86203,x86202)),f822(x86201,x86203,x86202)))+P24(f331(f331(x86201,x86202),x86203))+~P24(f331(f319(f890(a1,a1),a136),f331(f331(f261(a1,a1),x86202),x86203)))
% 162.26/162.08 [8866]P24(f331(f331(x88661,x88662),x88663))+P24(f331(f319(f890(a883,a883),a231),f331(f331(f261(a883,a883),f499(x88661,x88663,x88662)),f504(x88661,x88663,x88662))))+~P24(f331(f319(f890(a883,a883),a231),f331(f331(f261(a883,a883),x88662),x88663)))
% 162.26/162.08 [8867]P24(f331(f331(x88671,x88672),x88673))+P24(f331(f319(f890(a1,a1),a52),f331(f331(f261(a1,a1),f388(x88671,x88673,x88672)),f391(x88671,x88673,x88672))))+~P24(f331(f319(f890(a1,a1),a52),f331(f331(f261(a1,a1),x88672),x88673)))
% 162.26/162.08 [8868]P24(f331(f331(x88681,x88682),x88683))+P24(f331(f319(f890(a1,a1),a57),f331(f331(f261(a1,a1),f392(x88681,x88683,x88682)),f394(x88681,x88683,x88682))))+~P24(f331(f319(f890(a1,a1),a57),f331(f331(f261(a1,a1),x88682),x88683)))
% 162.26/162.08 [8869]P24(f331(f331(x88691,x88692),x88693))+P24(f331(f319(f890(a1,a1),a236),f331(f331(f261(a1,a1),f395(x88691,x88693,x88692)),f400(x88691,x88693,x88692))))+~P24(f331(f319(f890(a1,a1),a236),f331(f331(f261(a1,a1),x88692),x88693)))
% 162.26/162.08 [8870]P24(f331(f331(x88701,x88702),x88703))+P24(f331(f319(f890(a1,a1),a185),f331(f331(f261(a1,a1),f642(x88701,x88703,x88702)),f644(x88701,x88703,x88702))))+~P24(f331(f319(f890(a1,a1),a185),f331(f331(f261(a1,a1),x88702),x88703)))
% 162.26/162.08 [8871]P24(f331(f331(x88711,x88712),x88713))+P24(f331(f319(f890(a1,a1),a136),f331(f331(f261(a1,a1),f821(x88711,x88713,x88712)),f822(x88711,x88713,x88712))))+~P24(f331(f319(f890(a1,a1),a136),f331(f331(f261(a1,a1),x88712),x88713)))
% 162.26/162.08 [9211]~P24(f331(f62(x92111),x92113))+P24(f331(f331(f333(f890(f891(x92111,a877),f891(x92111,a877))),f331(f331(f261(f891(x92111,a877),f891(x92111,a877)),x92112),x92113)),f306(x92111)))+~P24(f331(f331(f248(f891(x92111,a877)),x92112),x92113))
% 162.26/162.08 [9219]~P23(a878,f196(f891(f882(a878),a877)),f331(f331(f309(f882(a878)),f331(f331(f331(f93(a878),x92191),x92192),x92193)),f196(f891(f882(a878),a877))))+P20(a878,f196(f891(f882(a878),a877)),f331(f331(f309(f882(a878)),f331(f331(f331(f93(a878),x92191),x92192),x92193)),f196(f891(f882(a878),a877))))+~P20(a878,f196(f891(f882(a878),a877)),f331(f331(f309(f882(a878)),f331(a94,x92192)),f196(f891(f882(a878),a877))))
% 162.26/162.08 [9291]~P57(x92911,f331(x92913,f709(x92912,x92913,x92911)))+P57(x92911,f331(f331(f42(x92912,f891(x92911,f891(x92911,a877))),f256(f891(x92912,a877))),x92913))+~E(f331(f331(f108(f891(x92911,a877)),f266(x92911,x92911,f331(x92913,f708(x92912,x92913,x92911)))),f267(x92911,x92911,f331(x92913,f710(x92912,x92913,x92911)))),f196(f891(x92911,a877)))
% 162.26/162.08 [9481]P48(x94811,x94812,x94813)+P24(f331(f331(f333(f890(x94811,x94811)),f588(x94813,x94812,x94811)),x94813))+~P24(f331(f331(f333(f890(x94811,x94811)),f331(f331(f261(x94811,x94811),f587(x94813,x94812,x94811)),f587(x94813,x94812,x94811))),x94813))
% 162.26/162.08 [10082]P48(x100821,x100822,x100823)+~P24(f331(f331(f270(x100821,x100821,a877),f331(f331(f7(x100821,f891(x100821,a877),f891(x100821,a877)),f331(f331(f8(f891(a877,a877),f891(f891(x100821,a877),f891(x100821,a877)),x100821),f8(a877,a877,x100821)),f331(f331(f8(a877,f891(a877,a877),x100821),a329),f331(f331(f7(x100821,f891(x100821,a877),a877),f333(x100821)),x100822)))),f331(f331(f7(x100821,f891(x100821,a877),a877),f333(x100821)),x100822))),f588(x100823,x100822,x100821)))+~P24(f331(f331(f333(f890(x100821,x100821)),f331(f331(f261(x100821,x100821),f587(x100823,x100822,x100821)),f587(x100823,x100822,x100821))),x100823))
% 162.26/162.08 [5672]~P58(x56722)+E(x56721,f2(x56722))+E(f331(f331(f39(x56722),f331(f331(f82(x56722),x56723),x56721)),x56721),x56723)
% 162.26/162.08 [5673]~P58(x56732)+E(x56731,f2(x56732))+E(f331(f331(f39(x56732),f331(f331(f82(x56732),x56731),x56733)),x56731),x56733)
% 162.26/162.08 [6460]~P74(x64601)+~E(f331(x64602,f2(a883)),f2(x64601))+E(f331(f331(f6(a883,x64601),x64602),f331(f301(a883,f331(a118,f2(a883))),x64603)),f331(f331(f6(a883,x64601),x64602),f331(f301(a883,f2(a883)),x64603)))
% 162.26/162.08 [6586]~P58(x65862)+E(x65861,f2(x65862))+E(f331(f331(f39(x65862),f331(f331(f81(x65862),x65863),x65861)),x65861),f331(f331(f81(x65862),f331(f331(f39(x65862),x65863),x65861)),f79(x65862)))
% 162.26/162.08 [6587]~P58(x65872)+E(x65871,f2(x65872))+E(f331(f331(f39(x65872),f331(f331(f81(x65872),x65871),x65873)),x65871),f331(f331(f81(x65872),f331(f331(f39(x65872),x65873),x65871)),f79(x65872)))
% 162.26/162.08 [6800]~P24(f331(x68003,f2(a1)))+P24(f331(f331(f247(a883),x68001),x68002))+P24(f331(x68003,f331(f106(a1),f331(f331(f22(a883),x68002),x68001))))
% 162.26/162.08 [6898]P24(f331(f331(f247(a883),x68982),x68981))+P24(f331(f331(f248(a883),x68981),x68982))+P24(f331(x68983,f331(f106(a1),f331(f331(f22(a883),x68981),x68982))))
% 162.26/162.08 [6971]E(f331(f331(f81(a883),f331(f110(a883),x69711)),f331(f331(f81(a883),f331(f110(a883),x69712)),x69713)),f331(f331(f81(a883),f331(f110(a883),x69711)),x69713))+P24(f331(a202,f331(f110(a1),x69711)))+~P24(f331(a202,f331(f110(a1),x69712)))
% 162.26/162.08 [7052]~E(x70522,f331(f331(f39(a883),x70523),x70521))+~P24(f331(f331(f248(a883),f2(a883)),x70521))+P24(f331(f331(f247(a883),f331(f331(f82(a883),x70521),x70522)),x70523))
% 162.26/162.08 [7166]~P24(f331(f62(x71661),x71663))+~P24(f331(f62(x71661),x71662))+P24(f331(f62(x71661),f331(f331(f107(f891(x71661,a877)),x71662),x71663)))
% 162.26/162.08 [7449]~P107(x74491)+~P24(f331(f62(x74491),x74492))+E(f142(x74491,f331(f331(f22(f891(x74491,a877)),x74492),f331(f331(f309(x74491),x74493),f196(f891(x74491,a877))))),f173(x74491,x74493,f142(x74491,x74492)))
% 162.26/162.08 [7512]P24(f331(x75121,f2(a1)))+~P24(f331(f331(f248(a883),x75122),x75123))+~P24(f331(x75121,f331(f106(a1),f331(f331(f22(a883),x75122),x75123))))
% 162.26/162.08 [7530]~P24(f331(f62(x75301),x75302))+E(f331(f38(x75301),f331(f331(f22(f891(x75301,a877)),x75302),f331(f331(f309(x75301),x75303),f196(f891(x75301,a877))))),f331(f38(x75301),x75302))+P24(f331(f331(f333(x75301),x75303),x75302))
% 162.26/162.08 [7657]~P110(x76571)+~P24(f331(f331(f248(x76571),f79(x76571)),x76572))+P24(f331(f331(f248(x76571),f79(x76571)),f331(f331(f82(x76571),x76572),f331(f331(f262(x76571),x76572),x76573))))
% 162.26/162.08 [7701]~P24(f331(f62(x77011),x77013))+E(f331(f331(f22(a883),f331(f38(x77011),x77012)),f331(f38(x77011),x77013)),f331(f38(x77011),f331(f331(f22(f891(x77011,a877)),x77012),x77013)))+~P24(f331(f331(f247(f891(x77011,a877)),x77013),x77012))
% 162.26/162.08 [7759]~P24(f331(f331(f247(a883),x77592),x77593))+~P24(f331(f331(f247(a883),x77591),f331(f331(f22(a883),x77593),x77592)))+P24(f331(f331(f247(a883),f331(f331(f81(a883),x77591),x77592)),x77593))
% 162.26/162.08 [7814]P24(f331(f62(x78141),x78142))+~P24(f331(f62(x78141),x78143))+~P24(f331(f62(x78141),f331(f331(f22(f891(x78141,a877)),x78142),x78143)))
% 162.26/162.08 [7820]~P24(f331(f62(x78201),x78202))+E(f331(f38(x78201),f331(f331(f22(f891(x78201,a877)),x78202),f331(f331(f309(x78201),x78203),f196(f891(x78201,a877))))),f331(f331(f22(a883),f331(f38(x78201),x78202)),f79(a883)))+~P24(f331(f331(f333(x78201),x78203),x78202))
% 162.26/162.08 [7891]P57(x78911,x78912)+~P57(x78911,x78913)+~P24(f331(f331(f247(f891(x78911,f891(x78911,a877))),x78912),x78913))
% 162.26/162.08 [7927]~P24(f331(f331(f247(a883),x79273),x79272))+P24(f331(f331(f247(a883),x79271),f331(f331(f22(a883),x79272),x79273)))+~P24(f331(f331(f247(a883),f331(f331(f81(a883),x79271),x79273)),x79272))
% 162.26/162.08 [7945]P38(x79451,x79452)+~P38(x79451,x79453)+~P24(f331(f331(f247(f891(f890(x79451,x79451),a877)),x79452),x79453))
% 162.26/162.08 [7946]P55(x79461,x79462)+~P55(x79461,x79463)+~P24(f331(f331(f247(f891(f890(x79461,x79461),a877)),x79462),x79463))
% 162.26/162.08 [8196]~P110(x81961)+~P24(f331(f331(f248(x81961),f79(x81961)),x81962))+P24(f331(f331(f248(x81961),f331(f331(f262(x81961),x81962),x81963)),f331(f331(f82(x81961),x81962),f331(f331(f262(x81961),x81962),x81963))))
% 162.26/162.08 [8282]~P24(f331(x82821,f2(a1)))+~P24(f331(x82821,f331(f331(f22(a1),f331(f106(a1),x82822)),f331(f106(a1),x82823))))+P24(f331(x82821,f331(f106(a1),f331(f331(f22(a883),x82822),x82823))))
% 162.26/162.08 [8295]~P24(f331(f331(f247(a883),x82953),x82952))+P24(f331(x82951,f331(f331(f22(a1),f331(f106(a1),x82952)),f331(f106(a1),x82953))))+~P24(f331(x82951,f331(f106(a1),f331(f331(f22(a883),x82952),x82953))))
% 162.26/162.08 [8313]P24(f331(f331(f248(a883),x83131),x83132))+~P24(f331(x83133,f331(f331(f22(a1),f331(f106(a1),x83131)),f331(f106(a1),x83132))))+P24(f331(x83133,f331(f106(a1),f331(f331(f22(a883),x83131),x83132))))
% 162.26/162.08 [8364]~P123(x83642)+E(x83641,f2(x83642))+P24(f331(f331(f248(x83642),f2(x83642)),f331(f331(f81(x83642),f331(f331(f82(x83642),x83643),x83643)),f331(f331(f82(x83642),x83641),x83641))))
% 162.26/162.08 [8365]~P123(x83652)+E(x83651,f2(x83652))+P24(f331(f331(f248(x83652),f2(x83652)),f331(f331(f81(x83652),f331(f331(f82(x83652),x83651),x83651)),f331(f331(f82(x83652),x83653),x83653))))
% 162.26/162.08 [8472]~P24(f331(f331(f248(a883),f2(a883)),x84721))+~P24(f331(f331(f248(a1),x84722),x84723))+P24(f331(f331(f248(a1),f331(f331(f82(a1),f331(f106(a1),x84721)),x84722)),f331(f331(f82(a1),f331(f106(a1),x84721)),x84723)))
% 162.26/162.08 [8530]E(f331(f331(f108(f891(x85301,a877)),x85302),f40(f891(x85301,a877),x85303)),f196(f891(x85301,a877)))+P24(f331(f331(f333(f891(x85301,a877)),x85302),x85303))+P24(f331(f331(f333(f891(x85301,a877)),f532(x85303,x85302,x85301)),f331(f331(f309(f891(x85301,a877)),x85302),x85303)))
% 162.26/162.08 [8531]E(f331(f331(f108(f891(x85311,a877)),x85312),f40(f891(x85311,a877),x85313)),f196(f891(x85311,a877)))+P24(f331(f331(f333(f891(x85311,a877)),x85312),x85313))+P24(f331(f331(f333(f891(x85311,a877)),f531(x85313,x85312,x85311)),f331(f331(f309(f891(x85311,a877)),x85312),x85313)))
% 162.26/162.08 [8559]E(x85591,x85592)+~E(f331(f197(f884(x85593)),x85591),f331(f197(f884(x85593)),x85592))+P24(f331(f331(f333(f890(x85593,x85593)),f608(x85593,x85591,x85592)),f331(f175(f890(x85593,x85593)),f331(f331(f184(x85593,x85593),x85592),x85591))))
% 162.26/162.08 [8781]E(f307(x87811,x87812),f307(x87811,x87813))+~P24(f331(f331(f247(f891(f890(x87811,x87811),a877)),x87813),f307(x87811,x87812)))+~P24(f331(f331(f247(f891(f890(x87811,x87811),a877)),x87812),x87813))
% 162.26/162.08 [8844]~P48(x88441,f256(f891(x88441,a877)),x88443)+P24(f331(f331(f247(f891(f890(f884(x88441),f884(x88441)),a877)),f160(x88441,x88442)),f161(x88441,x88443)))+~P24(f331(f331(f247(f891(f890(x88441,x88441),a877)),x88442),x88443))
% 162.26/162.08 [9044]P38(x90441,x90442)+~P24(f331(f331(f333(x90441),x90443),f783(x90442,x90441)))+P24(f331(f331(f333(f890(x90441,x90441)),f331(f331(f261(x90441,x90441),f799(x90442,x90441,x90443)),x90443)),x90442))
% 162.26/162.08 [9072]~P24(f331(f62(x90721),x90722))+P24(f331(f62(f891(x90721,a877)),f331(f331(f61(x90721),x90722),x90723)))+~P24(f331(f331(f247(f891(f890(x90721,x90721),a877)),x90723),f331(f331(f268(x90721,x90721),x90722),f331(f16(f891(x90721,a877),x90721),x90722))))
% 162.26/162.08 [9113]P48(x91131,x91132,x91133)+P24(f331(f331(f333(x91131),f550(x91133,x91132,x91131)),x91132))+~P24(f331(f331(f247(f891(f890(x91131,x91131),a877)),x91133),f331(f331(f268(x91131,x91131),x91132),f331(f16(f891(x91131,a877),x91131),x91132))))
% 162.26/162.08 [9114]P48(x91141,x91142,x91143)+P24(f331(f331(f333(x91141),f559(x91142,x91143,x91141)),x91142))+~P24(f331(f331(f247(f891(f890(x91141,x91141),a877)),x91143),f331(f331(f268(x91141,x91141),x91142),f331(f16(f891(x91141,a877),x91141),x91142))))
% 162.26/162.08 [9154]~P64(x91541)+~P24(f331(f331(f248(x91541),x91542),x91543))+P24(f331(f331(f248(x91541),f331(f331(f289(x91541),f331(f331(f81(x91541),x91542),x91543)),f331(f331(f81(x91541),f79(x91541)),f79(x91541)))),x91543))
% 162.26/162.08 [9183]~P63(x91831)+P24(f331(f331(f247(x91831),x91832),x91833))+~P24(f331(f331(f247(x91831),f331(f331(f82(x91831),f481(x91833,x91832,x91831)),x91832)),x91833))
% 162.26/162.08 [9321]E(f331(f197(f884(f884(x93211))),f331(f139(f884(x93211),f331(f331(f8(a883,a877,f884(x93211)),f331(f248(a883),x93212)),f197(f884(x93211)))),f182(x93211,x93213))),f331(f197(f884(x93211)),f331(f331(f168(f884(x93211)),x93213),x93212)))+~P29(a883,f331(f172(a883),f331(f331(f157(f884(x93211),a883),f197(f884(x93211))),x93213)))+~P24(f331(f331(f248(a883),x93212),f331(f197(f884(f884(x93211))),x93213)))
% 162.26/162.08 [9426]~P38(x94261,x94262)+P22(x94261,f331(f331(f261(f891(f890(x94261,x94261),a877),f891(f890(x94261,x94261),a877)),x94262),x94263))+~P24(f331(f331(f247(f891(f890(x94261,x94261),a877)),f331(f331(f288(x94261,x94261,x94261),x94262),x94263)),x94262))
% 162.26/162.08 [9433]E(f331(f331(f157(f884(x94331),x94331),f331(f331(f7(f884(x94331),a883,x94331),f168(x94331)),x94332)),f331(f139(f884(x94331),f331(f331(f8(a883,a877,f884(x94331)),f331(f248(a883),x94332)),f197(f884(x94331)))),f182(x94331,x94333))),f331(f331(f168(f884(x94331)),x94333),x94332))+~P29(a883,f331(f172(a883),f331(f331(f157(f884(x94331),a883),f197(f884(x94331))),x94333)))+~P24(f331(f331(f248(a883),x94332),f331(f197(f884(f884(x94331))),x94333)))
% 162.26/162.08 [9577]P48(x95771,x95772,x95773)+~P24(f331(f331(f333(f890(x95771,x95771)),f331(f331(f261(x95771,x95771),f550(x95773,x95772,x95771)),f550(x95773,x95772,x95771))),x95773))+~P24(f331(f331(f247(f891(f890(x95771,x95771),a877)),x95773),f331(f331(f268(x95771,x95771),x95772),f331(f16(f891(x95771,a877),x95771),x95772))))
% 162.26/162.08 [9578]P48(x95781,x95782,x95783)+~P24(f331(f331(f333(f890(x95781,x95781)),f331(f331(f261(x95781,x95781),f559(x95782,x95783,x95781)),f559(x95782,x95783,x95781))),x95783))+~P24(f331(f331(f247(f891(f890(x95781,x95781),a877)),x95783),f331(f331(f268(x95781,x95781),x95782),f331(f16(f891(x95781,a877),x95781),x95782))))
% 162.26/162.08 [9776]~P138(x97761)+~P122(x97761)+E(f331(f331(f289(x97761),f331(f109(x97761),f331(f331(f74(f890(a1,a1),a1,x97762,f260(a1,a1)),f224(x97762)),x97763))),f331(f109(x97761),f331(f331(f74(f890(a1,a1),a1,x97762,f269(a1,a1)),f224(x97762)),x97763))),f237(x97762,x97761,x97763))
% 162.26/162.08 [9957]~E(x99573,f2(a883))+~E(f331(f197(f884(x99571)),f331(f331(f168(f884(x99571)),x99572),f675(x99573,x99571,x99572))),x99573)+E(f331(f331(f157(a883,f884(x99571)),f331(f331(f7(a883,f884(a883),f884(x99571)),f331(f331(f8(f891(a883,x99571),f891(f884(a883),f884(x99571)),a883),f157(a883,x99571)),f331(f7(a883,a883,x99571),f331(f331(f8(f884(x99571),f891(a883,x99571),a883),f168(x99571)),f331(f168(f884(x99571)),x99572))))),f142(a883,f331(f301(a883,f2(a883)),f331(f197(f884(f884(x99571))),x99572))))),f142(a883,f331(f301(a883,f2(a883)),x99573))),f182(x99571,x99572))
% 162.26/162.08 [9958]E(x99581,f119(f884(x99582)))+~E(f331(f197(f884(x99582)),f331(f331(f168(f884(x99582)),x99581),f675(x99583,x99582,x99581))),x99583)+E(f331(f331(f157(a883,f884(x99582)),f331(f331(f7(a883,f884(a883),f884(x99582)),f331(f331(f8(f891(a883,x99582),f891(f884(a883),f884(x99582)),a883),f157(a883,x99582)),f331(f7(a883,a883,x99582),f331(f331(f8(f884(x99582),f891(a883,x99582),a883),f168(x99582)),f331(f168(f884(x99582)),x99581))))),f142(a883,f331(f301(a883,f2(a883)),f331(f197(f884(f884(x99582))),x99581))))),f142(a883,f331(f301(a883,f2(a883)),x99583))),f182(x99582,x99581))
% 162.26/162.08 [9959]~E(x99593,f2(a883))+E(f331(f331(f157(a883,f884(x99591)),f331(f331(f7(a883,f884(a883),f884(x99591)),f331(f331(f8(f891(a883,x99591),f891(f884(a883),f884(x99591)),a883),f157(a883,x99591)),f331(f7(a883,a883,x99591),f331(f331(f8(f884(x99591),f891(a883,x99591),a883),f168(x99591)),f331(f168(f884(x99591)),x99592))))),f142(a883,f331(f301(a883,f2(a883)),f331(f197(f884(f884(x99591))),x99592))))),f142(a883,f331(f301(a883,f2(a883)),x99593))),f182(x99591,x99592))+P24(f331(f331(f248(a883),f675(x99593,x99591,x99592)),f331(f197(f884(f884(x99591))),x99592)))
% 162.26/162.08 [9960]E(x99601,f119(f884(x99602)))+E(f331(f331(f157(a883,f884(x99602)),f331(f331(f7(a883,f884(a883),f884(x99602)),f331(f331(f8(f891(a883,x99602),f891(f884(a883),f884(x99602)),a883),f157(a883,x99602)),f331(f7(a883,a883,x99602),f331(f331(f8(f884(x99602),f891(a883,x99602),a883),f168(x99602)),f331(f168(f884(x99602)),x99601))))),f142(a883,f331(f301(a883,f2(a883)),f331(f197(f884(f884(x99602))),x99601))))),f142(a883,f331(f301(a883,f2(a883)),x99603))),f182(x99602,x99601))+P24(f331(f331(f248(a883),f675(x99603,x99602,x99601)),f331(f197(f884(f884(x99602))),x99601)))
% 162.26/162.08 [7698]E(f331(f331(f81(a883),f331(f110(a883),x76981)),f331(f331(f81(a883),f331(f110(a883),x76982)),x76983)),f331(f331(f81(a883),f331(f110(a883),f331(f331(f81(a1),x76981),x76982))),x76983))+P24(f331(a202,f331(f110(a1),x76981)))+P24(f331(a202,f331(f110(a1),x76982)))
% 162.26/162.08 [8463]~P24(f331(f62(x84631),x84632))+~P24(f331(f331(f333(x84631),x84633),x84632))+E(f331(a118,f331(f38(x84631),f331(f331(f22(f891(x84631,a877)),x84632),f331(f331(f309(x84631),x84633),f196(f891(x84631,a877)))))),f331(f38(x84631),x84632))
% 162.26/162.08 [8480]~P24(f331(f62(x84801),x84802))+~P24(f331(f331(f333(x84801),x84803),x84802))+E(f331(f331(f81(a883),f79(a883)),f331(f38(x84801),f331(f331(f22(f891(x84801,a877)),x84802),f331(f331(f309(x84801),x84803),f196(f891(x84801,a877)))))),f331(f38(x84801),x84802))
% 162.26/162.08 [8567]~P107(x85671)+~P24(f331(f62(x85671),x85673))+E(f331(f331(f151(x85671,x85671,f5(x85671)),x85672),f142(x85671,f331(f331(f22(f891(x85671,a877)),x85673),f331(f331(f309(x85671),x85672),f196(f891(x85671,a877)))))),f142(x85671,f331(f331(f309(x85671),x85672),x85673)))
% 162.26/162.08 [8711]~P24(f331(f62(x87111),x87113))+~P24(f331(f62(x87111),x87112))+E(f331(f331(f81(a883),f331(f38(x87111),f331(f331(f107(f891(x87111,a877)),x87112),x87113))),f331(f38(x87111),f331(f331(f108(f891(x87111,a877)),x87112),x87113))),f331(f331(f81(a883),f331(f38(x87111),x87112)),f331(f38(x87111),x87113)))
% 162.26/162.08 [9917]~P21(x99171,f891(f891(x99171,a877),a877),f331(f331(f7(x99171,f891(f890(x99171,x99171),a877),f891(f891(x99171,a877),a877)),f331(f331(f8(f891(x99171,a877),f891(f891(f890(x99171,x99171),a877),f891(f891(x99171,a877),a877)),x99171),f61(x99171)),f331(f331(f7(x99171,f891(x99171,a877),f891(x99171,a877)),f309(x99171)),f196(f891(x99171,a877))))),x99173),x99172)+~P24(f331(f62(x99171),x99172))+E(f331(f38(f891(x99171,a877)),f331(f331(f61(x99171),x99172),x99173)),f331(f38(x99171),x99172))
% 162.26/162.08 [8107]~P94(x81071)+P24(f331(f331(f247(a1),f2(a1)),f331(f110(a1),x81073)))+E(f331(f331(f262(x81071),x81072),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x81073)),x81073))),f79(x81071))
% 162.26/162.08 [9417]~P94(x94171)+~P24(f331(f331(f247(a1),f2(a1)),f331(f110(a1),x94173)))+E(f331(f331(f262(x94171),x94172),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x94173)),x94173))),f331(f331(f89(x94171,x94171),f331(f331(f262(x94171),x94172),f331(f110(a883),x94173))),f331(f331(f18(x94171,x94171,x94171),f331(f331(f8(x94171,f891(x94171,x94171),x94171),f82(x94171)),f331(f82(x94171),x94172))),f5(x94171))))
% 162.26/162.08 [9833]~P24(f331(f140(x98331),x98333))+~P24(f331(f331(f333(x98331),x98332),f331(f175(x98331),x98333)))+E(f331(f331(f141(x98331),f331(f197(f884(x98331)),f179(x98331,f331(f331(f8(a877,a877,x98331),a326),f331(f331(f7(x98331,x98331,a877),a328),x98332)),f331(f172(x98331),x98333)))),f331(f172(x98331),x98333)),f331(f331(f154(x98331),x98332),f331(f172(x98331),f179(x98331,f331(f331(f8(a877,a877,x98331),a326),f331(f331(f7(x98331,x98331,a877),a328),x98332)),x98333))))
% 162.26/162.08 [9900]P24(f331(f331(f247(f891(f890(x99001,x99001),a877)),f307(x99001,x99002)),x99003))+~P24(f331(f331(f247(f891(f890(x99001,x99001),a877)),f307(x99001,f196(f891(f890(x99001,x99001),a877)))),x99003))+~P24(f331(f331(f247(f891(f890(x99001,x99001),a877)),f331(f331(f288(x99001,x99001,x99001),f331(f331(f108(f891(f890(x99001,x99001),a877)),f307(x99001,x99002)),x99003)),x99002)),x99003))
% 162.26/162.08 [9740]~P24(f331(f62(x97401),f331(f253(x97401),x97403)))+~P24(f331(f62(x97401),f331(f253(x97401),x97402)))+P24(f331(f62(x97401),f331(f253(x97401),f331(f331(f18(x97401,a877,a877),f331(f331(f8(a877,f891(a877,a877),x97401),a330),x97402)),x97403))))
% 162.26/162.08 [10020]P24(f331(f331(f247(f891(f890(x100201,x100201),a877)),f331(f331(f288(x100201,x100201,x100201),x100202),f307(x100201,x100202))),x100203))+~P24(f331(f331(f247(f891(f890(x100201,x100201),a877)),x100202),x100203))+~P24(f331(f331(f247(f891(f890(x100201,x100201),a877)),f331(f331(f288(x100201,x100201,x100201),f331(f331(f108(f891(f890(x100201,x100201),a877)),f331(f331(f288(x100201,x100201,x100201),x100202),f307(x100201,x100202))),x100203)),x100202)),x100203))
% 162.26/162.08 [9979]~P24(f331(f140(x99791),x99793))+~P24(f331(f331(f333(x99791),x99792),f331(f175(x99791),x99793)))+E(f331(f172(x99791),f331(f174(x99791),f331(f331(f141(x99791),f331(f197(f884(x99791)),f179(x99791,f331(f331(f8(a877,a877,x99791),a326),f331(f331(f7(x99791,x99791,a877),a328),x99792)),x99793))),x99793))),f179(x99791,f331(f331(f8(a877,a877,x99791),a326),f331(f331(f7(x99791,x99791,a877),a328),x99792)),f331(f172(x99791),x99793)))
% 162.26/162.08 [10151]~P111(x101512)+E(x101511,f2(x101512))+~E(f331(f331(f81(x101512),f331(f331(f262(x101512),x101513),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f331(f331(f262(x101512),x101511),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f2(x101512))
% 162.26/162.08 [10152]~P111(x101522)+E(x101521,f2(x101522))+~E(f331(f331(f81(x101522),f331(f331(f262(x101522),x101521),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f331(f331(f262(x101522),x101523),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f2(x101522))
% 162.26/162.08 [10186]~P111(x101862)+E(x101861,f2(x101862))+P24(f331(f331(f248(x101862),f2(x101862)),f331(f331(f81(x101862),f331(f331(f262(x101862),x101863),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f331(f331(f262(x101862),x101861),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))))
% 162.26/162.08 [10187]~P111(x101872)+E(x101871,f2(x101872))+P24(f331(f331(f248(x101872),f2(x101872)),f331(f331(f81(x101872),f331(f331(f262(x101872),x101871),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f331(f331(f262(x101872),x101873),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))))
% 162.26/162.08 [10208]~P111(x102081)+P24(f331(f331(f247(x102081),f2(x102081)),x102082))+~P24(f331(f331(f247(x102081),f2(x102081)),f331(f331(f262(x102081),x102082),f331(a118,f331(f331(f82(a883),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),x102083)))))
% 162.26/162.08 [5513]~P20(x55131,x55134,x55133)+P20(x55131,x55132,x55133)+~P20(x55131,x55132,x55134)
% 162.26/162.08 [4975]~E(x49752,f91(x49753,x49751))+P24(f331(x49751,x49752))+~P24(f331(x49751,x49754))
% 162.26/162.08 [6717]~P38(x67172,x67174)+~P38(x67171,x67173)+P38(f890(x67171,x67172),f323(x67171,x67172,x67173,x67174))
% 162.26/162.08 [5153]~P5(x51534,x51531)+~E(f331(x51531,x51532),f331(x51531,x51533))+P24(f331(f331(x51531,x51532),x51533))
% 162.26/162.08 [5328]~P5(x53284,x53281)+E(f331(x53281,x53282),f331(x53281,x53283))+~P24(f331(f331(x53281,x53282),x53283))
% 162.26/162.08 [5421]~P14(x54213,x54214,x54211)+E(f331(x54211,x54212),f331(f64(x54213,x54214),x54212))+~P24(f331(f62(x54213),x54212))
% 162.26/162.08 [5422]~P3(x54223,x54224,x54221)+E(f331(x54221,x54222),f331(f64(x54223,x54224),x54222))+~P24(f331(f62(x54223),x54222))
% 162.26/162.08 [5546]~P5(x55464,x55461)+~P24(f331(f331(x55461,x55463),x55462))+P24(f331(f331(x55461,x55462),x55463))
% 162.26/162.08 [5615]E(x56151,x56152)+~E(f331(f260(x56153,x56154),x56151),f331(f260(x56153,x56154),x56152))+~E(f331(f269(x56153,x56154),x56151),f331(f269(x56153,x56154),x56152))
% 162.26/162.08 [5640]E(x56401,x56402)+~P24(f331(f48(x56403,x56404),x56402))+~P24(f331(f48(x56403,x56404),x56401))
% 162.26/162.08 [5831]~P74(x58312)+E(f238(x58311,x58312,x58313,x58314),f2(x58312))+P24(f331(f62(x58311),x58314))
% 162.26/162.08 [5967]~P24(f331(f319(x59671,x59672),x59674))+P24(f331(f319(x59671,x59672),x59673))+~P24(f331(f331(x59672,x59673),x59674))
% 162.26/162.08 [7886]~P107(x78862)+~P24(f331(f140(x78861),x78864))+P24(f331(f140(x78861),f153(x78861,x78862,x78863,x78864)))
% 162.26/162.08 [8114]~P24(f331(f62(x81142),x81144))+~P24(f331(f62(x81141),x81143))+P24(f331(f62(f889(x81141,x81142)),f318(x81141,x81142,x81143,x81144)))
% 162.26/162.08 [8115]~P24(f331(f140(x81152),x81154))+~P24(f331(f140(x81151),x81153))+P24(f331(f140(f890(x81151,x81152)),f60(x81151,x81152,x81153,x81154)))
% 162.26/162.08 [8119]P24(f331(f331(f333(f884(x81191)),f331(f331(f137(x81191),x81192),x81193)),f164(x81191,x81194)))+~P24(f331(f331(f333(f884(x81191)),x81193),f164(x81191,x81194)))+~P24(f331(f331(f333(f884(x81191)),x81192),f164(x81191,x81194)))
% 162.26/162.08 [8430]P24(f331(x84301,x84302))+~E(x84303,f331(f239(x84304),x84302))+~P24(f331(x84301,f834(x84302,x84301,x84303,x84304)))
% 162.26/162.08 [8442]~P107(x84423)+~P24(f331(f140(x84421),f153(x84421,x84423,x84424,x84422)))+P24(f331(f140(x84421),x84422))
% 162.26/162.08 [8702]~P24(f331(f331(f333(f890(x87021,x87021)),f331(f331(f261(x87021,x87021),x87022),x87024)),f307(x87021,x87023)))+P24(f331(f331(f333(x87021),x87022),f320(x87021,x87023)))+~P24(f331(f331(f333(x87021),x87024),f320(x87021,x87023)))
% 162.26/162.08 [8723]~E(x87234,f331(f239(x87233),x87232))+P24(f331(x87231,x87232))+P24(f331(f331(f333(x87233),f834(x87232,x87231,x87234,x87233)),f240(x87233,x87234)))
% 162.26/162.08 [5138]~P73(x51382)+E(f331(f331(f9(x51381,x51382),x51383),x51384),f79(x51382))+P24(f331(f62(x51381),x51384))
% 162.26/162.08 [5141]~P74(x51412)+E(f331(f331(f6(x51411,x51412),x51413),x51414),f2(x51412))+P24(f331(f62(x51411),x51414))
% 162.26/162.08 [5292]~P67(x52923)+E(x52921,x52922)+~E(f331(f331(f81(x52923),x52924),x52921),f331(f331(f81(x52923),x52924),x52922))
% 162.26/162.08 [5293]~P68(x52933)+E(x52931,x52932)+~E(f331(f331(f81(x52933),x52934),x52931),f331(f331(f81(x52933),x52934),x52932))
% 162.26/162.08 [5295]~P67(x52953)+E(x52951,x52952)+~E(f331(f331(f81(x52953),x52951),x52954),f331(f331(f81(x52953),x52952),x52954))
% 162.26/162.08 [5374]~E(x53742,f331(f331(f309(x53741),x53743),x53744))+~P24(f331(f62(x53741),x53744))+P24(f331(f62(x53741),x53742))
% 162.26/162.08 [5417]~P27(x54173)+E(x54171,f196(f891(x54172,a877)))+E(f331(f331(f42(x54172,x54173),x54171),f331(f16(x54173,x54172),x54174)),x54174)
% 162.26/162.08 [5418]~P27(x54183)+E(x54181,f196(f891(x54182,a877)))+E(f331(f331(f43(x54182,x54183),x54181),f331(f16(x54183,x54182),x54184)),x54184)
% 162.26/162.08 [5628]~P108(x56283)+E(x56281,x56282)+~E(f302(x56283,x56284,x56281),f331(f331(f309(x56283),x56282),f196(f891(x56283,a877))))
% 162.26/162.08 [5629]~P108(x56293)+E(x56291,x56292)+~E(f302(x56293,x56291,x56292),f331(f331(f309(x56293),x56294),f196(f891(x56293,a877))))
% 162.26/162.08 [5689]~P36(x56893,x56891,x56894)+P36(x56893,x56891,f331(f331(f154(x56893),x56892),x56894))+P24(f331(x56891,x56892))
% 162.26/162.08 [5791]~P32(x57911,x57912,x57914)+~P24(f331(x57912,x57913))+P32(x57911,x57912,f331(f331(f154(x57911),x57913),x57914))
% 162.26/162.08 [5924]P24(f331(x59241,x59242))+~P24(f331(f265(x59243,x59241),x59244))+~P24(f331(f331(f333(x59243),x59242),x59244))
% 162.26/162.08 [5933]~P32(x59331,x59332,x59334)+~P32(x59331,x59332,x59333)+P32(x59331,x59332,f331(f331(f137(x59331),x59333),x59334))
% 162.26/162.08 [5942]P34(x59421,x59422,x59423)+~P34(x59421,x59422,f331(f331(f154(x59421),x59424),x59423))+P24(f331(x59422,x59424))
% 162.26/162.08 [5943]P36(x59431,x59432,x59433)+~P36(x59431,x59432,f331(f331(f154(x59431),x59434),x59433))+P24(f331(x59432,x59434))
% 162.26/162.08 [5956]E(x59561,x59562)+~P24(f331(f331(f203(x59563),x59564),x59562))+~P24(f331(f331(f203(x59563),x59564),x59561))
% 162.26/162.08 [6022]P34(x60221,x60222,x60223)+P34(x60221,x60222,x60224)+~P34(x60221,x60222,f331(f331(f137(x60221),x60224),x60223))
% 162.26/162.08 [6041]~P74(x60411)+E(f331(f331(f6(a883,x60411),x60412),f331(f301(a883,x60413),f331(a118,x60414))),f2(x60411))+~P24(f331(f331(f248(a883),x60414),x60413))
% 162.26/162.08 [6046]~P59(x60461)+~E(f45(x60461,x60462,x60463),f45(x60461,x60464,x60463))+E(f45(x60461,f331(f80(x60461),x60462),x60463),f45(x60461,f331(f80(x60461),x60464),x60463))
% 162.26/162.08 [6114]P24(f331(x61141,x61142))+~E(f331(f139(x61143,x61141),x61144),x61144)+~P24(f331(f331(f333(x61143),x61142),f331(f175(x61143),x61144)))
% 162.26/162.08 [6133]~E(f331(f331(f81(a883),x61333),x61332),f331(f331(f81(a883),x61331),x61334))+~P24(f331(f331(f248(a883),x61333),x61334))+P24(f331(f331(f248(a883),x61331),x61332))
% 162.26/162.08 [6137]P34(x61371,x61372,x61373)+~P24(f331(x61372,x61374))+~P24(f331(f331(f333(x61371),x61374),f331(f175(x61371),x61373)))
% 162.26/162.08 [6175]~P32(x61753,x61751,x61754)+P24(f331(x61751,x61752))+~P24(f331(f331(f333(x61753),x61752),f331(f175(x61753),x61754)))
% 162.26/162.08 [6177]~E(f331(f139(x61771,x61772),x61773),f119(x61771))+~P24(f331(x61772,x61774))+~P24(f331(f331(f333(x61771),x61774),f331(f175(x61771),x61773)))
% 162.26/162.08 [6178]~E(f179(x61783,x61781,x61784),x61784)+P24(f331(x61781,x61782))+~P24(f331(f331(f333(x61783),x61782),f331(f175(x61783),x61784)))
% 162.26/162.08 [6208]~E(x62084,f196(f891(x62082,a877)))+~E(x62083,f196(f891(x62081,a877)))+E(f318(x62081,x62082,x62083,x62084),f196(f891(f889(x62081,x62082),a877)))
% 162.26/162.08 [6349]P24(f331(x63491,x63492))+~P24(f331(f163(x63493,x63491),x63494))+~P24(f331(f331(f333(x63493),x63492),f331(f175(x63493),x63494)))
% 162.26/162.08 [6615]~P74(x66151)+E(f331(f331(f6(a883,x66151),x66152),f302(a883,x66153,f331(a118,x66154))),f2(x66151))+~P24(f331(f331(f248(a883),f331(a118,x66154)),x66153))
% 162.26/162.08 [6756]~P107(x67561)+E(f331(f331(f22(f891(x67561,a877)),f331(f301(x67561,x67562),x67563)),f331(f301(x67561,x67562),x67564)),f331(f301(x67561,x67564),x67563))+~P24(f331(f331(f247(x67561),x67562),x67564))
% 162.26/162.08 [7097]~P24(f331(f331(f333(f884(x70971)),x70974),f164(x70971,x70973)))+P24(f331(f331(f333(x70971),x70972),x70973))+~P24(f331(f331(f333(x70971),x70972),f331(f175(x70971),x70974)))
% 162.26/162.08 [7104]~P38(x71041,x71042)+P24(f331(f331(f333(x71041),f795(x71042,x71041,x71043)),x71043))+~P24(f331(f331(f333(x71041),x71044),x71043))
% 162.26/162.08 [7160]~P73(x71601)+E(f331(f331(f331(f66(x71601,x71602,f82(x71601)),x71603),f79(x71601)),x71604),f331(f331(f9(x71602,x71601),x71603),x71604))+~P24(f331(f62(x71602),x71604))
% 162.26/162.08 [7162]~P74(x71621)+E(f331(f331(f331(f66(x71621,x71622,f81(x71621)),x71623),f2(x71621)),x71624),f331(f331(f6(x71622,x71621),x71623),x71624))+~P24(f331(f62(x71622),x71624))
% 162.26/162.08 [7190]P21(x71901,x71902,x71903,x71904)+~E(f331(f38(x71902),f331(f310(x71901,x71902,x71903),x71904)),f331(f38(x71901),x71904))+~P24(f331(f62(x71901),x71904))
% 162.26/162.08 [7364]~P74(x73641)+E(f331(f331(f81(x73641),f331(x73642,x73643)),f331(f331(f6(a883,x73641),x73642),f304(a883,x73643,x73644))),f331(f331(f6(a883,x73641),x73642),f302(a883,x73643,x73644)))+~P24(f331(f331(f247(a883),x73643),x73644))
% 162.26/162.08 [7374]~P73(x73741)+~P21(x73742,x73741,x73743,x73744)+E(f331(f331(f9(x73741,x73741),f35(x73741)),f331(f310(x73742,x73741,x73743),x73744)),f331(f331(f9(x73742,x73741),x73743),x73744))
% 162.26/162.08 [7375]~P74(x73751)+~P21(x73752,x73751,x73753,x73754)+E(f331(f331(f6(x73751,x73751),f35(x73751)),f331(f310(x73752,x73751,x73753),x73754)),f331(f331(f6(x73752,x73751),x73753),x73754))
% 162.26/162.08 [7429]E(f331(f38(f889(x74291,x74292)),f318(x74291,x74292,x74293,x74294)),f331(f331(f81(a883),f331(f38(x74291),x74293)),f331(f38(x74292),x74294)))+~P24(f331(f62(x74292),x74294))+~P24(f331(f62(x74291),x74293))
% 162.26/162.08 [7513]E(x75131,x75132)+P24(f331(f331(f333(x75133),x75131),f331(f175(x75133),f173(x75133,x75132,x75134))))+~P24(f331(f331(f333(x75133),x75131),f331(f175(x75133),x75134)))
% 162.26/162.08 [7734]~P74(x77341)+E(f331(f331(f81(x77341),f331(f331(f6(a883,x77341),x77342),f331(f301(a883,x77343),x77344))),f331(x77342,x77344)),f331(f331(f6(a883,x77341),x77342),f331(f301(a883,x77343),f331(a118,x77344))))+P24(f331(f331(f248(a883),x77344),x77343))
% 162.26/162.08 [7790]~P21(x77901,x77902,x77903,f256(f891(x77901,a877)))+~P24(f331(f62(x77902),x77904))+P24(f331(f62(x77901),f331(f311(x77901,x77902,x77903),x77904)))
% 162.26/162.08 [7899]P24(f331(f331(f333(f884(x78991)),f331(f331(f154(x78991),x78992),x78993)),f164(x78991,x78994)))+~P24(f331(f331(f333(f884(x78991)),x78993),f164(x78991,x78994)))+~P24(f331(f331(f333(x78991),x78992),x78994))
% 162.26/162.08 [7984]~E(f331(f310(x79843,x79841,x79844),f256(f891(x79843,a877))),f256(f891(x79841,a877)))+P24(f331(f62(x79841),x79842))+~P24(f331(f62(x79843),f331(f311(x79843,x79841,x79844),x79842)))
% 162.26/162.08 [8085]~P21(x80851,x80853,x80854,x80852)+P24(f331(f62(x80851),x80852))+~P24(f331(f62(x80853),f331(f310(x80851,x80853,x80854),x80852)))
% 162.26/162.08 [8106]~E(x81062,x81063)+P24(f331(f331(f333(f890(x81061,x81061)),f331(f331(f261(x81061,x81061),x81062),x81063)),f258(x81061,x81064)))+~P24(f331(f331(f333(x81061),x81062),x81064))
% 162.26/162.08 [8145]~P74(x81451)+E(f331(f331(f81(x81451),f331(f331(f6(a883,x81451),x81452),f302(a883,x81453,x81454))),f331(x81452,f331(a118,x81454))),f331(f331(f6(a883,x81451),x81452),f302(a883,x81453,f331(a118,x81454))))+P24(f331(f331(f248(a883),f331(a118,x81454)),x81453))
% 162.26/162.08 [8208]P24(f331(x82081,x82082))+~P24(f331(x82081,f331(f331(f168(x82083),x82084),f621(x82081,x82084,x82083))))+~P24(f331(f331(f333(x82083),x82082),f331(f175(x82083),x82084)))
% 162.26/162.08 [8343]~P24(f331(f331(f333(x83431),x83432),f320(x83431,x83434)))+P24(f331(f331(f333(f884(x83431)),f331(f331(f154(x83431),x83432),x83433)),f320(f884(x83431),f160(x83431,x83434))))+~P24(f331(f331(f333(f884(x83431)),x83433),f320(f884(x83431),f160(x83431,x83434))))
% 162.26/162.08 [8356]~P21(x83562,x83563,x83564,f530(x83564,x83563,x83562,x83561))+P21(x83562,x83563,x83564,f41(f891(x83562,a877),x83561))+E(x83561,f196(f891(f891(x83562,a877),a877)))
% 162.26/162.08 [8629]E(x86291,x86292)+~P24(f331(f331(f333(f890(x86293,x86293)),f331(f331(f261(x86293,x86293),x86291),x86292)),f307(x86293,x86294)))+P24(f331(f331(f333(x86293),x86291),f331(f259(x86293,x86293),x86294)))
% 162.26/162.08 [8905]P21(x89052,x89053,x89054,f41(f891(x89052,a877),x89051))+E(x89051,f196(f891(f891(x89052,a877),a877)))+P24(f331(f331(f333(f891(x89052,a877)),f530(x89054,x89053,x89052,x89051)),x89051))
% 162.26/162.08 [9037]P24(f331(f62(x90371),x90372))+~P24(f331(f62(x90374),f331(f310(x90371,x90374,x90373),x90372)))+P24(f331(f331(f333(x90371),f584(x90373,x90374,x90372,x90371)),x90372))
% 162.26/162.08 [9129]~P27(x91292)+E(f331(f331(f65(x91291,x91292,f331(f331(f8(x91292,f891(x91292,x91292),x91291),f107(x91292)),x91293)),f196(x91292)),x91294),f331(f331(f42(x91291,x91292),x91294),x91293))+~P24(f331(f62(x91291),x91294))
% 162.26/162.08 [9130]~P27(x91302)+E(f331(f331(f65(x91301,x91302,f331(f331(f8(x91302,f891(x91302,x91302),x91301),f108(x91302)),x91303)),f256(x91302)),x91304),f331(f331(f43(x91301,x91302),x91304),x91303))+~P24(f331(f62(x91301),x91304))
% 162.26/162.08 [9214]P24(f331(x92141,x92142))+~P24(f331(x92141,f331(f331(f168(x92143),x92144),f698(x92142,x92141,x92144,x92143))))+~P24(f331(f331(f333(x92143),x92142),f331(f175(x92143),x92144)))
% 162.26/162.08 [9235]E(x92351,x92352)+~P24(f331(f331(f333(f890(x92353,x92353)),f331(f331(f261(x92353,x92353),x92351),x92352)),f307(x92353,x92354)))+P24(f331(f331(f333(f890(x92353,x92353)),f331(f331(f261(x92353,x92353),x92351),x92352)),f331(f331(f288(x92353,x92353,x92353),x92354),f307(x92353,x92354))))
% 162.26/162.08 [9292]~E(f331(f197(f884(x92921)),x92922),f331(f197(f884(x92921)),x92923))+~P24(f331(f331(f333(f890(f884(x92921),f884(x92921))),f331(f331(f261(f884(x92921),f884(x92921)),x92922),x92923)),f150(x92921,x92924)))+P24(f331(f331(f333(f890(f884(x92921),f884(x92921))),f331(f331(f261(f884(x92921),f884(x92921)),x92922),x92923)),f148(x92921,x92924)))
% 162.26/162.08 [9526]P32(x95261,f331(f331(f18(x95261,a877,a877),f331(f331(f8(a877,f891(a877,a877),x95261),a330),f331(f331(f8(a877,a877,x95261),a326),x95262))),f331(a328,x95263)),x95264)+~P24(f331(x95262,x95263))+~P36(x95261,x95262,f331(f331(f154(x95261),x95263),x95264))
% 162.26/162.08 [9697]~P32(x96971,f331(f331(f18(x96971,a877,a877),f331(f331(f8(a877,f891(a877,a877),x96971),a330),f331(f331(f8(a877,a877,x96971),a326),x96972))),f331(a328,x96973)),x96974)+~P24(f331(x96972,x96973))+P36(x96971,x96972,f331(f331(f154(x96971),x96973),x96974))
% 162.26/162.08 [9701]~P36(x97011,x97012,x97014)+~P32(x97011,f331(f331(f18(x97011,a877,a877),f331(f331(f8(a877,f891(a877,a877),x97011),a330),f331(f331(f8(a877,a877,x97011),a326),x97012))),f331(a328,x97013)),x97014)+P36(x97011,x97012,f331(f331(f154(x97011),x97013),x97014))
% 162.26/162.08 [9743]~P70(x97431)+E(f331(f331(f6(a883,x97431),f331(f331(f18(a883,x97431,x97431),f331(f331(f8(x97431,f891(x97431,x97431),a883),f22(x97431)),x97432)),f331(f331(f8(a883,x97431,a883),x97432),f331(f331(f7(a883,a883,a883),f81(a883)),f79(a883))))),f302(a883,x97433,x97434)),f2(x97431))+P24(f331(f331(f247(a883),x97433),x97434))
% 162.26/162.08 [9973]~P38(x99732,x99734)+~P21(x99732,x99731,x99733,f256(f891(x99732,a877)))+P38(x99731,f331(f310(f890(x99732,x99732),f890(x99731,x99731),f271(x99732,x99731,x99732,x99731,x99733,x99733)),x99734))
% 162.26/162.08 [10164]~E(f331(f197(f884(x101641)),x101643),f331(f197(f884(x101641)),x101642))+P24(f331(f331(f333(f890(f884(x101641),f884(x101641))),f331(f331(f261(f884(x101641),f884(x101641)),x101642),x101643)),f161(x101641,x101644)))+~P24(f331(f331(f270(x101641,x101641,a877),f331(f331(f7(x101641,f891(f890(x101641,x101641),a877),f891(x101641,a877)),f331(f331(f8(f891(x101641,f891(f891(f890(x101641,x101641),a877),a877)),f891(f891(f890(x101641,x101641),a877),f891(x101641,a877)),x101641),f7(x101641,f891(f890(x101641,x101641),a877),a877)),f331(f331(f8(f891(x101641,f890(x101641,x101641)),f891(x101641,f891(f891(f890(x101641,x101641),a877),a877)),x101641),f331(f8(f890(x101641,x101641),f891(f891(f890(x101641,x101641),a877),a877),x101641),f333(f890(x101641,x101641)))),f261(x101641,x101641)))),x101644)),f615(x101644,x101643,x101642,x101641)))
% 162.26/162.08 [6006]~E(x60064,x60062)+P24(f331(x60061,x60062))+P24(f331(f331(f203(f33(x60061,x60063)),x60062),x60064))
% 162.26/162.08 [6098]~P58(x60981)+~E(x60982,f2(x60981))+E(f331(f331(f39(x60981),f331(f331(f82(x60981),x60982),x60983)),f331(f331(f82(x60981),x60982),x60984)),f2(x60981))
% 162.26/162.08 [6136]E(x61361,f119(x61362))+E(x61363,f331(f331(f22(a883),f331(f197(f884(x61362)),x61361)),f79(a883)))+E(f147(x61362,f331(f331(f162(x61362,x61361),x61363),x61364)),f147(x61362,x61361))
% 162.26/162.08 [6166]E(x61661,x61662)+P24(f331(x61663,x61662))+~P24(f331(f331(f331(f309(x61664),x61661),x61663),x61662))
% 162.26/162.08 [6182]~P74(x61821)+~P24(f331(f140(x61822),x61824))+E(f331(f169(x61821),f331(f331(f157(x61822,x61821),x61823),x61824)),f331(f331(f6(x61822,x61821),x61823),f331(f175(x61822),x61824)))
% 162.26/162.08 [6201]~P73(x62012)+~P24(f331(f62(x62011),x62014))+E(f331(f331(f9(x62011,x62012),f331(f16(x62012,x62011),x62013)),x62014),f331(f331(f262(x62012),x62013),f331(f38(x62011),x62014)))
% 162.26/162.08 [6255]~P58(x62552)+E(x62551,f2(x62552))+E(f331(f331(f39(x62552),f331(f331(f82(x62552),x62553),x62551)),f331(f331(f82(x62552),x62554),x62551)),f331(f331(f39(x62552),x62553),x62554))
% 162.26/162.08 [6257]~P61(x62572)+E(x62571,f2(x62572))+E(f331(f331(f289(x62572),f331(f331(f82(x62572),x62573),x62571)),f331(f331(f82(x62572),x62574),x62571)),f331(f331(f289(x62572),x62573),x62574))
% 162.26/162.08 [6258]~P61(x62582)+E(x62581,f2(x62582))+E(f331(f331(f289(x62582),f331(f331(f82(x62582),x62581),x62583)),f331(f331(f82(x62582),x62581),x62584)),f331(f331(f289(x62582),x62583),x62584))
% 162.26/162.08 [6259]~P58(x62592)+E(x62591,f2(x62592))+E(f331(f331(f39(x62592),f331(f331(f82(x62592),x62591),x62593)),f331(f331(f82(x62592),x62591),x62594)),f331(f331(f39(x62592),x62593),x62594))
% 162.26/162.08 [6321]P24(f331(x63211,x63212))+~E(x63213,f331(f331(f81(a883),x63214),x63212))+~P24(f331(x63211,f331(f331(f22(a883),x63213),x63214)))
% 162.26/162.08 [6401]P23(x64011,x64012,x64013)+P30(x64011,f591(x64013,x64012,x64011),x64014)+~P24(f331(f331(f333(f882(x64011)),x64014),x64012))
% 162.26/162.08 [6403]~P24(f331(x64032,x64033))+~P24(f331(f163(x64031,x64032),x64034))+P24(f331(f163(x64031,x64032),f331(f331(f154(x64031),x64033),x64034)))
% 162.26/162.08 [6443]E(x64431,f119(x64432))+~E(x64433,f331(f331(f22(a883),f331(f197(f884(x64432)),x64431)),f79(a883)))+E(f147(x64432,f331(f331(f162(x64432,x64431),x64433),x64434)),x64434)
% 162.26/162.08 [6465]~P101(x64651)+~P24(f331(f331(f248(x64651),x64652),x64654))+P24(f331(f331(f248(x64651),x64652),f331(f331(f107(x64651),x64653),x64654)))
% 162.26/162.08 [6466]~P101(x64661)+~P24(f331(f331(f248(x64661),x64662),x64663))+P24(f331(f331(f248(x64661),x64662),f331(f331(f107(x64661),x64663),x64664)))
% 162.26/162.08 [6468]~P107(x64681)+~P24(f331(f331(f248(x64681),x64682),x64684))+P24(f331(f331(f248(x64681),x64682),f331(f331(f246(x64681),x64683),x64684)))
% 162.26/162.08 [6470]~P107(x64701)+~P24(f331(f331(f248(x64701),x64702),x64703))+P24(f331(f331(f248(x64701),x64702),f331(f331(f246(x64701),x64703),x64704)))
% 162.26/162.08 [6471]~P101(x64711)+~P24(f331(f331(f247(x64711),x64712),x64714))+P24(f331(f331(f247(x64711),x64712),f331(f331(f107(x64711),x64713),x64714)))
% 162.26/162.08 [6472]~P101(x64721)+~P24(f331(f331(f247(x64721),x64722),x64723))+P24(f331(f331(f247(x64721),x64722),f331(f331(f107(x64721),x64723),x64724)))
% 162.26/162.08 [6474]~P107(x64741)+~P24(f331(f331(f247(x64741),x64742),x64744))+P24(f331(f331(f247(x64741),x64742),f331(f331(f246(x64741),x64743),x64744)))
% 162.26/162.08 [6476]~P107(x64761)+~P24(f331(f331(f247(x64761),x64762),x64763))+P24(f331(f331(f247(x64761),x64762),f331(f331(f246(x64761),x64763),x64764)))
% 162.26/162.08 [6560]~E(f331(f331(f168(x65601),x65602),x65603),x65604)+E(f331(f331(f162(x65601,x65602),x65603),x65604),x65602)+~P24(f331(f331(f248(a883),x65603),f331(f197(f884(x65601)),x65602)))
% 162.26/162.08 [6577]E(x65771,x65772)+P24(f331(x65773,x65771))+~P24(f331(f331(f203(f33(x65773,x65774)),x65771),x65772))
% 162.26/162.08 [6601]P24(f331(x66011,x66012))+~P24(f331(x66013,x66012))+~P24(f331(f331(f247(f891(x66014,a877)),x66013),x66011))
% 162.26/162.08 [6633]~E(f331(f331(f162(x66331,x66332),x66333),x66334),x66332)+E(f331(f331(f168(x66331),x66332),x66333),x66334)+~P24(f331(f331(f248(a883),x66333),f331(f197(f884(x66331)),x66332)))
% 162.26/162.08 [6648]~P24(f331(f163(x66481,x66482),x66484))+~P24(f331(f163(x66481,x66482),x66483))+P24(f331(f163(x66481,x66482),f331(f331(f137(x66481),x66483),x66484)))
% 162.26/162.08 [6744]P30(x67441,x67442,x67443)+~P30(x67441,f331(a118,x67442),f592(x67442,x67444,x67441))+~P24(f331(f331(f333(f882(x67441)),x67443),x67444))
% 162.26/162.08 [6753]E(x67531,f196(f891(x67532,a877)))+E(x67533,f196(f891(x67534,a877)))+~E(f331(f331(f268(x67534,x67532),x67533),f331(f16(f891(x67532,a877),x67534),x67531)),f196(f891(f890(x67534,x67532),a877)))
% 162.26/162.08 [6766]E(x67661,x67662)+P24(f331(f331(f333(x67663),x67661),x67664))+~P24(f331(f331(f333(x67663),x67661),f331(f331(f309(x67663),x67662),x67664)))
% 162.26/162.08 [6782]~P107(x67821)+P24(f331(f331(f248(x67821),x67822),x67823))+~P24(f331(f331(f248(x67821),x67822),f331(f331(f251(x67821),x67824),x67823)))
% 162.26/162.08 [6783]~P107(x67831)+P24(f331(f331(f248(x67831),x67832),x67833))+~P24(f331(f331(f248(x67831),x67832),f331(f331(f251(x67831),x67833),x67834)))
% 162.26/162.08 [6785]~P107(x67851)+P24(f331(f331(f247(x67851),x67852),x67853))+~P24(f331(f331(f247(x67851),x67852),f331(f331(f251(x67851),x67854),x67853)))
% 162.26/162.08 [6787]~P107(x67871)+P24(f331(f331(f247(x67871),x67872),x67873))+~P24(f331(f331(f247(x67871),x67872),f331(f331(f251(x67871),x67873),x67874)))
% 162.26/162.08 [6789]~P102(x67891)+P24(f331(f331(f247(x67891),x67892),x67893))+~P24(f331(f331(f247(x67891),x67892),f331(f331(f108(x67891),x67894),x67893)))
% 162.26/162.08 [6791]~P102(x67911)+P24(f331(f331(f247(x67911),x67912),x67913))+~P24(f331(f331(f247(x67911),x67912),f331(f331(f108(x67911),x67913),x67914)))
% 162.26/162.08 [6812]~E(f331(f331(f168(x68121),x68123),x68124),x68122)+P24(f331(f331(f333(x68121),x68122),f331(f175(x68121),x68123)))+~P24(f331(f331(f248(a883),x68124),f331(f197(f884(x68121)),x68123)))
% 162.26/162.08 [6822]~P107(x68221)+~P29(x68221,f331(f331(f154(x68221),x68222),f331(f331(f154(x68221),x68223),x68224)))+P24(f331(f331(f247(x68221),x68222),x68223))
% 162.26/162.08 [6961]~P32(x69612,x69611,x69613)+P24(f331(x69611,f331(f331(f168(x69612),x69613),x69614)))+~P24(f331(f331(f248(a883),x69614),f331(f197(f884(x69612)),x69613)))
% 162.26/162.08 [6980]E(x69801,f2(a1))+E(f331(f331(f39(a1),x69802),x69801),x69803)+~P24(f331(f49(x69802,x69801),f331(f331(f261(a1,a1),x69803),x69804)))
% 162.26/162.08 [7001]E(f45(a1,x70012,x70011),x70013)+E(x70011,f2(a1))+~P24(f331(f49(x70012,x70011),f331(f331(f261(a1,a1),x70014),x70013)))
% 162.26/162.08 [7118]P24(f331(f331(f333(x71181),x71182),x71183))+~P24(f331(f331(f333(x71181),x71182),x71184))+~P24(f331(f331(f248(f891(x71181,a877)),x71184),x71183))
% 162.26/162.08 [7122]P24(f331(f331(f333(x71221),x71222),x71223))+~P24(f331(f331(f333(x71221),x71222),x71224))+~P24(f331(f331(f247(f891(x71221,a877)),x71224),x71223))
% 162.26/162.08 [7230]P34(x72301,x72302,x72303)+~P24(f331(x72302,f331(f331(f168(x72301),x72303),x72304)))+~P24(f331(f331(f248(a883),x72304),f331(f197(f884(x72301)),x72303)))
% 162.26/162.08 [7330]~P109(x73302)+~P24(f331(f331(f248(f891(x73301,x73302)),x73303),x73304))+P24(f331(f331(f247(f891(x73301,x73302)),x73303),x73304))
% 162.26/162.08 [7417]~P20(x74171,x74172,x74174)+P20(x74171,x74172,f331(f331(f309(f882(x74171)),x74173),x74174))+~P20(x74171,x74172,f331(f331(f309(f882(x74171)),x74173),f196(f891(f882(x74171),a877))))
% 162.26/162.08 [7462]~P24(f331(f331(f333(x74621),x74622),x74624))+P24(f331(f331(f333(x74621),x74622),f40(f891(x74621,a877),x74623)))+~P24(f331(f331(f333(f891(x74621,a877)),x74624),x74623))
% 162.26/162.08 [7474]P30(x74741,x74742,x74743)+P24(f331(f331(f333(f882(x74741)),f592(x74742,x74744,x74741)),x74744))+~P24(f331(f331(f333(f882(x74741)),x74743),x74744))
% 162.26/162.08 [7491]~P81(x74911)+~P24(f331(f331(f248(x74911),x74913),x74914))+P24(f331(f331(f248(x74911),f331(f331(f81(x74911),x74912),x74913)),f331(f331(f81(x74911),x74912),x74914)))
% 162.26/162.08 [7492]~P84(x74921)+~P24(f331(f331(f248(x74921),x74923),x74924))+P24(f331(f331(f248(x74921),f331(f331(f81(x74921),x74922),x74923)),f331(f331(f81(x74921),x74922),x74924)))
% 162.26/162.08 [7493]~P81(x74931)+~P24(f331(f331(f248(x74931),x74932),x74934))+P24(f331(f331(f248(x74931),f331(f331(f81(x74931),x74932),x74933)),f331(f331(f81(x74931),x74934),x74933)))
% 162.26/162.08 [7494]~P84(x74941)+~P24(f331(f331(f248(x74941),x74942),x74944))+P24(f331(f331(f248(x74941),f331(f331(f81(x74941),x74942),x74943)),f331(f331(f81(x74941),x74944),x74943)))
% 162.26/162.08 [7495]~P81(x74951)+~P24(f331(f331(f247(x74951),x74953),x74954))+P24(f331(f331(f247(x74951),f331(f331(f81(x74951),x74952),x74953)),f331(f331(f81(x74951),x74952),x74954)))
% 162.26/162.08 [7496]~P82(x74961)+~P24(f331(f331(f247(x74961),x74963),x74964))+P24(f331(f331(f247(x74961),f331(f331(f81(x74961),x74962),x74963)),f331(f331(f81(x74961),x74962),x74964)))
% 162.26/162.08 [7497]~P81(x74971)+~P24(f331(f331(f247(x74971),x74972),x74974))+P24(f331(f331(f247(x74971),f331(f331(f81(x74971),x74972),x74973)),f331(f331(f81(x74971),x74974),x74973)))
% 162.26/162.08 [7498]~P82(x74981)+~P24(f331(f331(f247(x74981),x74982),x74984))+P24(f331(f331(f247(x74981),f331(f331(f81(x74981),x74982),x74983)),f331(f331(f81(x74981),x74984),x74983)))
% 162.26/162.08 [7507]~P125(x75071)+~P92(x75071)+E(f331(f331(f22(x75071),f331(f331(f82(x75071),x75072),f331(f110(x75071),x75073))),f331(f331(f82(x75071),x75074),f331(f110(x75071),x75073))),f331(f331(f82(x75071),f331(f331(f22(x75071),x75072),x75074)),f331(f110(x75071),x75073)))
% 162.26/162.08 [7508]~P139(x75081)+~P92(x75081)+E(f331(f331(f81(x75081),f331(f331(f82(x75081),x75082),f331(f110(x75081),x75083))),f331(f331(f82(x75081),x75084),f331(f110(x75081),x75083))),f331(f331(f82(x75081),f331(f331(f81(x75081),x75082),x75084)),f331(f110(x75081),x75083)))
% 162.26/162.08 [7544]~P74(x75441)+E(f331(f331(f81(x75441),f331(x75442,x75443)),f331(f331(f6(a883,x75441),x75442),f302(a883,f331(a118,x75443),x75444))),f331(f331(f6(a883,x75441),x75442),f302(a883,x75443,x75444)))+~P24(f331(f331(f247(a883),x75443),x75444))
% 162.26/162.08 [7554]~P21(x75542,x75541,x75543,f331(f175(x75542),x75544))+~P24(f331(f140(x75542),x75544))+P24(f331(f140(x75541),f331(f331(f157(x75542,x75541),x75543),x75544)))
% 162.26/162.08 [7601]~P24(f331(f331(f248(a883),x76012),x76014))+~P24(f331(f331(f248(a883),x76011),x76013))+P24(f331(f331(f248(a883),f331(f331(f81(a883),x76011),x76012)),f331(f331(f81(a883),x76013),x76014)))
% 162.26/162.08 [7602]~P24(f331(f331(f248(a1),x76021),x76023))+~P24(f331(f331(f247(a1),x76022),x76024))+P24(f331(f331(f248(a1),f331(f331(f81(a1),x76021),x76022)),f331(f331(f81(a1),x76023),x76024)))
% 162.26/162.08 [7603]~P24(f331(f331(f247(a883),x76032),x76034))+~P24(f331(f331(f247(a883),x76031),x76033))+P24(f331(f331(f247(a883),f331(f331(f81(a883),x76031),x76032)),f331(f331(f81(a883),x76033),x76034)))
% 162.26/162.08 [7604]~P24(f331(f331(f247(a883),x76042),x76044))+~P24(f331(f331(f247(a883),x76041),x76043))+P24(f331(f331(f247(a883),f331(f331(f82(a883),x76041),x76042)),f331(f331(f82(a883),x76043),x76044)))
% 162.26/162.08 [7652]P24(f331(f331(f333(x76521),x76522),x76523))+~P24(f331(f331(f333(x76521),x76522),f41(f891(x76521,a877),x76524)))+~P24(f331(f331(f333(f891(x76521,a877)),x76523),x76524))
% 162.26/162.08 [7667]~P24(f331(x76671,f620(x76671,x76673,x76672)))+P24(f331(x76671,f331(f331(f168(x76672),x76673),x76674)))+~P24(f331(f331(f248(a883),x76674),f331(f197(f884(x76672)),x76673)))
% 162.26/162.08 [7672]P24(f331(x76721,x76722))+~P24(f331(f331(f333(x76724),x76722),f331(f175(x76724),x76723)))+P24(f331(f331(f248(a883),f621(x76721,x76723,x76724)),f331(f197(f884(x76724)),x76723)))
% 162.26/162.08 [7691]~P24(f331(f331(f203(x76912),x76913),x76914))+~P24(f331(f331(f203(f33(x76911,x76912)),x76914),x76913))+P24(f331(f331(f203(f33(x76911,x76912)),x76913),x76913))
% 162.26/162.08 [7720]~P109(x77201)+~P24(f331(f331(f247(f891(x77202,x77201)),x77204),x77203))+~P24(f331(f331(f248(f891(x77202,x77201)),x77203),x77204))
% 162.26/162.08 [7767]~P24(f331(x77674,x77672))+~P24(f331(f331(f333(x77671),x77672),x77673))+P24(f331(f331(f333(x77671),x77672),f331(f331(f108(f891(x77671,a877)),x77673),f331(f253(x77671),x77674))))
% 162.26/162.08 [7908]~P24(f331(f331(f333(x79081),x79083),x79084))+~P24(f331(f331(f248(f891(x79081,a877)),x79082),x79084))+P24(f331(f331(f248(f891(x79081,a877)),x79082),f331(f331(f309(x79081),x79083),x79084)))
% 162.26/162.08 [7910]E(f331(f331(f108(f891(x79101,a877)),x79102),x79103),f196(f891(x79101,a877)))+~E(f331(f331(f108(f891(x79101,a877)),f40(f891(x79101,a877),x79104)),x79103),f196(f891(x79101,a877)))+~P24(f331(f331(f333(f891(x79101,a877)),x79102),x79104))
% 162.26/162.08 [7980]P24(f331(f331(f333(x79801),x79802),x79803))+~P24(f331(f331(f247(f891(x79801,a877)),x79803),f331(f331(f309(x79801),x79802),x79804)))+P24(f331(f331(f247(f891(x79801,a877)),x79803),x79804))
% 162.26/162.08 [8002]P24(f331(f331(f333(x80022),f620(x80021,x80023,x80022)),f331(f175(x80022),x80023)))+P24(f331(x80021,f331(f331(f168(x80022),x80023),x80024)))+~P24(f331(f331(f248(a883),x80024),f331(f197(f884(x80022)),x80023)))
% 162.26/162.08 [8010]~P24(f331(f331(f248(f891(x80101,a877)),x80102),x80104))+P24(f331(f331(f248(f891(x80101,a877)),x80102),x80103))+~P24(f331(f331(f248(f891(x80101,a877)),x80104),x80103))
% 162.26/162.08 [8011]~P24(f331(f331(f247(f891(x80111,a877)),x80112),x80114))+P24(f331(f331(f248(f891(x80111,a877)),x80112),x80113))+~P24(f331(f331(f248(f891(x80111,a877)),x80114),x80113))
% 162.26/162.08 [8012]~P24(f331(f331(f247(f891(x80121,a877)),x80124),x80123))+~P24(f331(f331(f248(f891(x80121,a877)),x80122),x80124))+P24(f331(f331(f248(f891(x80121,a877)),x80122),x80123))
% 162.26/162.08 [8013]~P24(f331(f331(f247(f891(x80131,a877)),x80132),x80134))+P24(f331(f331(f247(f891(x80131,a877)),x80132),x80133))+~P24(f331(f331(f247(f891(x80131,a877)),x80134),x80133))
% 162.26/162.08 [8059]~P24(f331(f331(f333(x80591),x80594),x80593))+~P24(f331(f331(f248(f891(x80591,a877)),x80592),f331(f331(f309(x80591),x80594),x80593)))+P24(f331(f331(f248(f891(x80591,a877)),x80592),x80593))
% 162.26/162.08 [8069]~P81(x80691)+P24(f331(f331(f248(x80691),x80692),x80693))+~P24(f331(f331(f248(x80691),f331(f331(f81(x80691),x80694),x80692)),f331(f331(f81(x80691),x80694),x80693)))
% 162.26/162.08 [8071]~P81(x80711)+P24(f331(f331(f248(x80711),x80712),x80713))+~P24(f331(f331(f248(x80711),f331(f331(f81(x80711),x80712),x80714)),f331(f331(f81(x80711),x80713),x80714)))
% 162.26/162.08 [8073]~P81(x80731)+P24(f331(f331(f247(x80731),x80732),x80733))+~P24(f331(f331(f247(x80731),f331(f331(f81(x80731),x80734),x80732)),f331(f331(f81(x80731),x80734),x80733)))
% 162.26/162.08 [8075]~P81(x80751)+P24(f331(f331(f247(x80751),x80752),x80753))+~P24(f331(f331(f247(x80751),f331(f331(f81(x80751),x80752),x80754)),f331(f331(f81(x80751),x80753),x80754)))
% 162.26/162.08 [8125]P24(f331(x81251,x81252))+~E(f331(f331(f141(x81253),f331(f197(f884(x81253)),f179(x81253,x81251,x81254))),x81254),f119(x81253))+~P24(f331(f331(f333(x81253),x81252),f331(f175(x81253),x81254)))
% 162.26/162.08 [8249]P24(f331(x82491,x82492))+~P24(f331(f331(f333(x82493),x82492),f331(f175(x82493),x82494)))+P24(f331(f331(f248(a883),f331(f197(f884(x82493)),f331(f139(x82493,x82491),x82494))),f331(f197(f884(x82493)),x82494)))
% 162.26/162.08 [8372]E(x83721,x83722)+P24(f331(f331(f203(x83723),x83721),f594(x83722,x83721,x83723,x83724)))+~P24(f331(f331(f203(f33(x83724,x83723)),x83721),x83722))
% 162.26/162.08 [8397]~P24(f331(x83974,x83972))+P24(f331(f331(f203(x83971),x83972),f594(x83973,x83972,x83971,x83974)))+~P24(f331(f331(f203(f33(x83974,x83971)),x83972),x83973))
% 162.26/162.08 [8713]~P24(f331(x87131,f742(x87131,x87133,x87132,x87134)))+P24(f331(x87131,f331(f331(f168(x87132),x87133),x87134)))+~P24(f331(f331(f248(a883),x87134),f331(f197(f884(x87132)),x87133)))
% 162.26/162.08 [8731]~P21(x87314,x87313,x87311,f256(f891(x87314,a877)))+E(f331(x87311,f500(x87312,x87311,x87313,x87314)),x87312)+~P24(f331(f331(f333(x87313),x87312),f331(f310(x87314,x87313,x87311),f256(f891(x87314,a877)))))
% 162.26/162.08 [8803]E(f179(x88031,x88032,x88033),f331(f331(f176(x88031),x88034),x88033))+P24(f331(f331(f248(a883),f689(x88032,x88033,x88031,x88034)),x88034))+P24(f331(f331(f248(a883),x88034),f331(f197(f884(x88031)),x88033)))
% 162.26/162.08 [8806]E(f179(x88061,x88062,x88063),f331(f331(f176(x88061),x88064),x88063))+P24(f331(f331(f248(a883),f689(x88062,x88063,x88061,x88064)),x88064))+P24(f331(x88062,f331(f331(f168(x88061),x88063),x88064)))
% 162.26/162.08 [8837]P24(f331(x88371,x88372))+~P24(f331(f331(f333(x88374),x88372),f331(f175(x88374),x88373)))+P24(f331(f331(f248(a883),f698(x88372,x88371,x88373,x88374)),f331(f197(f884(x88374)),x88373)))
% 162.26/162.08 [8840]E(f179(x88401,x88402,x88403),f331(f331(f176(x88401),x88404),x88403))+P24(f331(f331(f248(a883),x88404),f331(f197(f884(x88401)),x88403)))+P24(f331(f331(f248(a883),f689(x88402,x88403,x88401,x88404)),f331(f197(f884(x88401)),x88403)))
% 162.26/162.08 [8846]E(f179(x88461,x88462,x88463),f331(f331(f176(x88461),x88464),x88463))+P24(f331(x88462,f331(f331(f168(x88461),x88463),x88464)))+P24(f331(f331(f248(a883),f689(x88462,x88463,x88461,x88464)),f331(f197(f884(x88461)),x88463)))
% 162.26/162.08 [8874]~P110(x88744)+P24(f331(f331(f333(x88741),f804(x88742,x88743,x88741,x88744)),x88743))+P24(f331(f331(f248(x88744),f2(x88744)),f331(f331(f9(x88741,x88744),x88742),x88743)))
% 162.26/162.08 [8875]~P110(x88754)+P24(f331(f331(f333(x88751),f819(x88752,x88753,x88751,x88754)),x88753))+P24(f331(f331(f247(x88754),f2(x88754)),f331(f331(f9(x88751,x88754),x88752),x88753)))
% 162.26/162.08 [8907]~P24(f331(f62(x89071),x89074))+P24(f331(f331(f333(x89071),f546(x89072,x89073,x89074,x89071)),x89074))+P24(f331(f62(f890(x89071,x89073)),f331(f331(f268(x89071,x89073),x89074),x89072)))
% 162.26/162.08 [8941]P24(f331(f331(f333(x89412),f742(x89411,x89413,x89412,x89414)),f331(f175(x89412),x89413)))+P24(f331(x89411,f331(f331(f168(x89412),x89413),x89414)))+~P24(f331(f331(f248(a883),x89414),f331(f197(f884(x89412)),x89413)))
% 162.26/162.08 [8956]E(x89561,x89562)+P24(f331(f331(f203(f33(x89563,x89564)),f594(x89561,x89562,x89564,x89563)),x89561))+~P24(f331(f331(f203(f33(x89563,x89564)),x89562),x89561))
% 162.26/162.08 [8976]~P24(f331(x89761,x89764))+P24(f331(f331(f203(f33(x89761,x89762)),f594(x89763,x89764,x89762,x89761)),x89763))+~P24(f331(f331(f203(f33(x89761,x89762)),x89764),x89763))
% 162.26/162.08 [9058]P24(f331(f331(f247(a883),x90584),f331(f197(f884(x90582)),f179(x90582,x90583,x90581))))+P24(f331(f331(f248(a883),f690(x90581,x90582,x90583,x90584)),x90584))+~P24(f331(f331(f247(a883),x90584),f331(f197(f884(x90582)),x90581)))
% 162.26/162.08 [9173]~E(f331(f331(f180(x91731,x91732),x91733),f706(x91734,x91733,x91732,x91731)),f331(f331(f180(x91731,x91732),x91734),f706(x91734,x91733,x91732,x91731)))+E(f331(f180(x91731,x91732),x91733),f331(f180(x91731,x91732),x91734))+~E(f331(f175(x91731),f331(f331(f157(f890(x91731,x91732),x91731),f260(x91731,x91732)),x91733)),f331(f175(x91731),f331(f331(f157(f890(x91731,x91732),x91731),f260(x91731,x91732)),x91734)))
% 162.26/162.08 [9217]E(f179(x92171,x92172,x92173),f331(f331(f176(x92171),x92174),x92173))+~P24(f331(x92172,f331(f331(f168(x92171),x92173),f689(x92172,x92173,x92171,x92174))))+P24(f331(f331(f248(a883),x92174),f331(f197(f884(x92171)),x92173)))
% 162.26/162.08 [9222]E(f179(x92221,x92222,x92223),f331(f331(f176(x92221),x92224),x92223))+~P24(f331(x92222,f331(f331(f168(x92221),x92223),f689(x92222,x92223,x92221,x92224))))+P24(f331(x92222,f331(f331(f168(x92221),x92223),x92224)))
% 162.26/162.08 [9229]~P24(f331(f62(x92291),x92293))+~P24(f331(f62(x92292),f331(x92294,f546(x92294,x92292,x92293,x92291))))+P24(f331(f62(f890(x92291,x92292)),f331(f331(f268(x92291,x92292),x92293),x92294)))
% 162.26/162.08 [9237]~P110(x92371)+~P24(f331(f331(f248(x92371),f2(x92371)),f331(x92373,f804(x92373,x92374,x92372,x92371))))+P24(f331(f331(f248(x92371),f2(x92371)),f331(f331(f9(x92372,x92371),x92373),x92374)))
% 162.26/162.08 [9238]~P110(x92381)+~P24(f331(f331(f247(x92381),f2(x92381)),f331(x92383,f819(x92383,x92384,x92382,x92381))))+P24(f331(f331(f247(x92381),f2(x92381)),f331(f331(f9(x92382,x92381),x92383),x92384)))
% 162.26/162.08 [9244]~E(f331(f197(f884(x92444)),x92442),f331(f197(f884(x92444)),x92443))+P24(f331(f331(f333(f890(f884(x92444),f884(x92444))),f331(f331(f261(f884(x92444),f884(x92444)),x92443),x92442)),f161(x92444,x92441)))+P24(f331(f331(f248(a883),f626(x92441,x92442,x92443,x92444)),f331(f197(f884(x92444)),x92443)))
% 162.26/162.08 [9301]~P24(f331(x93013,f331(f331(f168(x93012),x93014),f690(x93014,x93012,x93013,x93011))))+P24(f331(f331(f247(a883),x93011),f331(f197(f884(x93012)),f179(x93012,x93013,x93014))))+~P24(f331(f331(f247(a883),x93011),f331(f197(f884(x93012)),x93014)))
% 162.26/162.08 [9382]E(f331(f331(f176(x93821),f627(x93822,x93823,x93824,x93821)),x93823),f331(f331(f176(x93821),f627(x93822,x93823,x93824,x93821)),x93824))+~P24(f331(f331(f333(f890(f884(x93821),f884(x93821))),f331(f331(f261(f884(x93821),f884(x93821)),x93824),x93823)),f150(x93821,x93822)))+P24(f331(f331(f248(a883),f331(f197(f884(x93821)),x93824)),f331(f197(f884(x93821)),x93823)))
% 162.26/162.08 [9429]~P24(f331(f331(f248(a883),f2(a883)),x94293))+~P24(f331(f331(f248(a883),x94294),x94291))+P24(f331(f331(f248(a883),f331(f331(f81(a883),f331(f331(f82(a883),x94291),f45(a883,x94292,x94293))),x94294)),f331(f331(f82(a883),x94291),x94293)))
% 162.26/162.08 [9644]~P109(x96442)+~P24(f331(f331(f247(x96442),f331(x96443,f691(x96444,x96443,x96441,x96442))),f331(x96444,f691(x96444,x96443,x96441,x96442))))+P24(f331(f331(f247(f891(x96441,x96442)),x96443),x96444))
% 162.26/162.08 [9750]~P70(x97501)+E(f331(f331(f6(a883,x97501),f331(f331(f18(a883,x97501,x97501),f331(f331(f8(x97501,f891(x97501,x97501),a883),f22(x97501)),x97502)),f331(f331(f8(a883,x97501,a883),x97502),f331(f331(f7(a883,a883,a883),f81(a883)),f79(a883))))),f302(a883,x97503,x97504)),f331(f331(f22(x97501),f331(x97502,x97503)),f331(x97502,f331(f331(f81(a883),x97504),f79(a883)))))+~P24(f331(f331(f247(a883),x97503),x97504))
% 162.26/162.08 [6815]E(f331(f331(f137(x68151),x68152),x68153),x68154)+~E(x68153,f331(f331(f141(x68151),f331(f197(f884(x68151)),x68152)),x68154))+~E(f331(f331(f176(x68151),f331(f197(f884(x68151)),x68152)),x68154),x68152)
% 162.26/162.08 [6869]~P62(x68692)+E(x68691,f2(x68692))+E(f331(f331(f289(x68692),f331(f331(f262(x68692),x68693),x68694)),f331(f331(f262(x68692),x68691),x68694)),f331(f331(f262(x68692),f331(f331(f289(x68692),x68693),x68691)),x68694))
% 162.26/162.08 [7003]~E(f331(f197(f884(x70031)),x70033),f331(f197(f884(x70032)),x70034))+~P24(f331(f140(x70031),x70033))+E(f186(x70031,x70032,f331(f180(x70031,x70032),f331(f331(f184(x70031,x70032),x70033),x70034))),f331(f175(x70031),x70033))
% 162.26/162.08 [7023]~P107(x70231)+~P24(f331(f331(f248(x70231),x70233),x70234))+P24(f331(f331(f248(x70231),f331(f331(f251(x70231),x70232),x70233)),x70234))
% 162.26/162.08 [7025]~P107(x70251)+~P24(f331(f331(f248(x70251),x70252),x70254))+P24(f331(f331(f248(x70251),f331(f331(f251(x70251),x70252),x70253)),x70254))
% 162.26/162.08 [7026]~P102(x70261)+~P24(f331(f331(f248(x70261),x70263),x70264))+P24(f331(f331(f248(x70261),f331(f331(f108(x70261),x70262),x70263)),x70264))
% 162.26/162.08 [7027]~P102(x70271)+~P24(f331(f331(f248(x70271),x70272),x70274))+P24(f331(f331(f248(x70271),f331(f331(f108(x70271),x70272),x70273)),x70274))
% 162.26/162.08 [7029]~P107(x70291)+~P24(f331(f331(f247(x70291),x70293),x70294))+P24(f331(f331(f247(x70291),f331(f331(f251(x70291),x70292),x70293)),x70294))
% 162.26/162.08 [7031]~P107(x70311)+~P24(f331(f331(f247(x70311),x70312),x70314))+P24(f331(f331(f247(x70311),f331(f331(f251(x70311),x70312),x70313)),x70314))
% 162.26/162.08 [7032]~P102(x70321)+~P24(f331(f331(f247(x70321),x70323),x70324))+P24(f331(f331(f247(x70321),f331(f331(f108(x70321),x70322),x70323)),x70324))
% 162.26/162.08 [7033]~P102(x70331)+~P24(f331(f331(f247(x70331),x70332),x70334))+P24(f331(f331(f247(x70331),f331(f331(f108(x70331),x70332),x70333)),x70334))
% 162.26/162.08 [7053]~P24(f331(x70533,x70534))+~P24(f331(x70532,x70534))+P24(f331(f331(f331(f108(f891(x70531,a877)),x70532),x70533),x70534))
% 162.26/162.08 [7176]P20(x71761,x71762,x71763)+~P20(x71761,x71764,x71763)+~P24(f331(f331(f247(f891(f882(x71761),a877)),x71764),x71762))
% 162.26/162.08 [7177]P20(x71771,x71772,x71773)+~P20(x71771,x71772,x71774)+~P24(f331(f331(f247(f891(f882(x71771),a877)),x71773),x71774))
% 162.26/162.08 [7534]~P74(x75341)+E(f331(f331(f81(x75341),f331(x75342,x75343)),f331(f331(f6(a883,x75341),x75342),f331(f301(a883,f331(a118,x75343)),x75344))),f331(f331(f6(a883,x75341),x75342),f331(f301(a883,x75343),x75344)))+~P24(f331(f331(f248(a883),x75343),x75344))
% 162.26/162.08 [7561]~P107(x75611)+P24(f331(f331(f248(x75611),x75612),x75613))+~P24(f331(f331(f248(x75611),f331(f331(f246(x75611),x75614),x75612)),x75613))
% 162.26/162.08 [7562]~P107(x75621)+P24(f331(f331(f248(x75621),x75622),x75623))+~P24(f331(f331(f248(x75621),f331(f331(f246(x75621),x75622),x75624)),x75623))
% 162.26/162.08 [7564]~P107(x75641)+P24(f331(f331(f247(x75641),x75642),x75643))+~P24(f331(f331(f247(x75641),f331(f331(f246(x75641),x75644),x75642)),x75643))
% 162.26/162.08 [7566]~P107(x75661)+P24(f331(f331(f247(x75661),x75662),x75663))+~P24(f331(f331(f247(x75661),f331(f331(f246(x75661),x75662),x75664)),x75663))
% 162.26/162.08 [7568]~P101(x75681)+P24(f331(f331(f247(x75681),x75682),x75683))+~P24(f331(f331(f247(x75681),f331(f331(f107(x75681),x75684),x75682)),x75683))
% 162.26/162.08 [7570]~P101(x75701)+P24(f331(f331(f247(x75701),x75702),x75703))+~P24(f331(f331(f247(x75701),f331(f331(f107(x75701),x75702),x75704)),x75703))
% 162.26/162.08 [7644]~P24(f331(f331(f333(x76441),x76442),x76444))+P24(f331(f331(f333(x76441),x76442),x76443))+P24(f331(f331(f333(x76441),x76442),f331(f331(f22(f891(x76441,a877)),x76444),x76443)))
% 162.26/162.08 [7726]P24(f331(x77261,x77262))+P24(f331(x77263,x77262))+~P24(f331(f331(f331(f107(f891(x77264,a877)),x77263),x77261),x77262))
% 162.26/162.08 [7736]~P24(f331(f331(f333(x77361),x77362),x77364))+~P24(f331(f331(f333(x77361),x77362),x77363))+P24(f331(f331(f333(x77361),x77362),f331(f331(f108(f891(x77361,a877)),x77363),x77364)))
% 162.26/162.08 [7791]~P101(x77911)+~P24(f331(f62(x77911),x77914))+E(f331(f331(f65(x77911,x77911,f107(x77911)),x77912),f331(f331(f309(x77911),x77913),x77914)),f331(f331(f107(x77911),x77913),f331(f331(f65(x77911,x77911,f107(x77911)),x77912),x77914)))
% 162.26/162.08 [7792]~P107(x77921)+~P24(f331(f62(x77921),x77924))+E(f331(f331(f65(x77921,x77921,f251(x77921)),x77922),f331(f331(f309(x77921),x77923),x77924)),f331(f331(f251(x77921),x77923),f331(f331(f65(x77921,x77921,f251(x77921)),x77922),x77924)))
% 162.26/162.08 [7793]~P107(x77931)+~P24(f331(f62(x77931),x77934))+E(f331(f331(f65(x77931,x77931,f246(x77931)),x77932),f331(f331(f309(x77931),x77933),x77934)),f331(f331(f246(x77931),x77933),f331(f331(f65(x77931,x77931,f246(x77931)),x77932),x77934)))
% 162.26/162.08 [7794]~P102(x77941)+~P24(f331(f62(x77941),x77944))+E(f331(f331(f65(x77941,x77941,f108(x77941)),x77942),f331(f331(f309(x77941),x77943),x77944)),f331(f331(f108(x77941),x77943),f331(f331(f65(x77941,x77941,f108(x77941)),x77942),x77944)))
% 162.26/162.08 [7795]~P125(x77951)+~P92(x77951)+E(f331(f331(f22(x77951),f331(f331(f82(x77951),f331(f110(x77951),x77952)),x77953)),f331(f331(f82(x77951),f331(f110(x77951),x77952)),x77954)),f331(f331(f82(x77951),f331(f110(x77951),x77952)),f331(f331(f22(x77951),x77953),x77954)))
% 162.26/162.08 [7796]~P139(x77961)+~P92(x77961)+E(f331(f331(f81(x77961),f331(f331(f82(x77961),f331(f110(x77961),x77962)),x77963)),f331(f331(f82(x77961),f331(f110(x77961),x77962)),x77964)),f331(f331(f82(x77961),f331(f110(x77961),x77962)),f331(f331(f81(x77961),x77963),x77964)))
% 162.26/162.08 [7906]E(x79061,x79062)+P24(f331(f331(f333(x79063),x79061),f331(f175(x79063),x79064)))+~P24(f331(f331(f333(x79063),x79061),f331(f175(x79063),f331(f331(f154(x79063),x79062),x79064))))
% 162.26/162.08 [7926]~P60(x79261)+~E(f331(f197(f884(x79262)),x79263),f331(f197(f884(x79261)),f56(x79261)))+E(f331(f331(f180(x79261,x79262),f331(f331(f184(x79261,x79262),f56(x79261)),x79263)),x79264),f331(f239(x79262),f687(x79264,x79263,x79262,x79261)))
% 162.26/162.08 [8082]P52(x80821,x80822,x80823)+~P52(x80821,x80822,x80824)+~P24(f331(f331(f247(f891(f890(x80821,x80822),a877)),x80823),x80824))
% 162.26/162.08 [8128]P24(f331(f331(f333(x81281),x81282),x81283))+P24(f331(f331(f333(x81281),x81282),x81284))+~P24(f331(f331(f333(x81281),x81282),f331(f331(f107(f891(x81281,a877)),x81284),x81283)))
% 162.26/162.08 [8139]~P48(x81391,x81394,x81393)+~P24(f331(f331(f333(x81391),x81392),x81394))+P24(f331(f331(f333(f890(x81391,x81391)),f331(f331(f261(x81391,x81391),x81392),x81392)),x81393))
% 162.26/162.08 [8154]~P24(f331(f62(x81542),x81544))+~P24(f331(f62(x81541),x81543))+P24(f331(f62(f890(x81541,x81542)),f331(f331(f268(x81541,x81542),x81543),f331(f16(f891(x81542,a877),x81541),x81544))))
% 162.26/162.08 [8155]~P24(f331(f331(f333(x81551),x81552),x81554))+~P24(f331(f331(f247(f891(x81551,a877)),x81553),x81554))+P24(f331(f331(f247(f891(x81551,a877)),f331(f331(f309(x81551),x81552),x81553)),x81554))
% 162.26/162.08 [8163]~P73(x81632)+~P143(x81632)+E(f331(f331(f9(x81631,x81632),f331(f331(f8(a883,x81632,x81631),f106(x81632)),x81633)),x81634),f331(f106(x81632),f331(f331(f9(x81631,a883),x81633),x81634)))
% 162.26/162.08 [8164]~P73(x81642)+~P138(x81642)+E(f331(f331(f9(x81641,x81642),f331(f331(f8(a1,x81642,x81641),f109(x81642)),x81643)),x81644),f331(f109(x81642),f331(f331(f9(x81641,a1),x81643),x81644)))
% 162.26/162.08 [8191]E(f331(f331(f22(f891(x81911,a877)),x81912),f331(f331(f22(f891(x81911,a877)),x81913),x81914)),x81914)+~P24(f331(f331(f247(f891(x81911,a877)),x81912),x81913))+~P24(f331(f331(f247(f891(x81911,a877)),x81914),x81912))
% 162.26/162.08 [8283]~P24(f331(f62(x82831),x82834))+E(f331(f331(f22(a883),f331(f331(f6(x82831,a883),x82832),x82833)),f331(f331(f6(x82831,a883),x82832),x82834)),f331(f331(f6(x82831,a883),x82832),f331(f331(f22(f891(x82831,a877)),x82833),x82834)))+~P24(f331(f331(f247(f891(x82831,a877)),x82834),x82833))
% 162.26/162.08 [8434]~P6(x84341,x84344,x84343)+~P24(f331(f331(f333(x84341),x84342),x84344))+P24(f331(f331(f333(x84341),x84342),f331(f285(x84341,x84341,x84343),f331(f331(f309(x84341),x84342),f196(f891(x84341,a877))))))
% 162.26/162.08 [8496]~P24(f331(f331(f247(f891(x84961,a877)),x84962),x84963))+~P24(f331(f331(f247(f891(x84961,a877)),x84962),x84964))+P24(f331(f331(f247(f891(x84961,a877)),x84962),f331(f331(f108(f891(x84961,a877)),x84963),x84964)))
% 162.26/162.08 [8595]E(x85951,f196(f891(x85952,a877)))+P24(f331(f62(x85953),x85954))+~P24(f331(f62(f890(x85953,x85952)),f331(f331(f268(x85953,x85952),x85954),f331(f16(f891(x85952,a877),x85953),x85951))))
% 162.26/162.08 [8596]E(x85961,f196(f891(x85962,a877)))+P24(f331(f62(x85963),x85964))+~P24(f331(f62(f890(x85962,x85963)),f331(f331(f268(x85962,x85963),x85961),f331(f16(f891(x85963,a877),x85962),x85964))))
% 162.26/162.08 [8658]P24(f331(f331(f333(x86581),x86582),f320(x86581,x86583)))+~P24(f331(f331(f333(x86581),x86584),f320(x86581,x86583)))+~P24(f331(f331(f333(f890(x86581,x86581)),f331(f331(f261(x86581,x86581),x86582),x86584)),x86583))
% 162.26/162.08 [8708]~P38(x87081,x87084)+P24(f331(f331(f333(f890(x87081,x87081)),f331(f331(f261(x87081,x87081),x87083),x87082)),f307(x87081,x87084)))+P38(x87081,f331(f331(f309(f890(x87081,x87081)),f331(f331(f261(x87081,x87081),x87082),x87083)),x87084))
% 162.26/162.08 [8709]~P55(x87091,x87094)+P24(f331(f331(f333(f890(x87091,x87091)),f331(f331(f261(x87091,x87091),x87093),x87092)),f307(x87091,x87094)))+P55(x87091,f331(f331(f309(f890(x87091,x87091)),f331(f331(f261(x87091,x87091),x87092),x87093)),x87094))
% 162.26/162.08 [8786]~E(x87862,x87863)+~P24(f331(f331(f333(x87861),x87862),f331(f175(x87861),x87864)))+P24(f331(f331(f333(f890(x87861,x87861)),f331(f331(f261(x87861,x87861),x87862),x87863)),f331(f175(f890(x87861,x87861)),f331(f331(f184(x87861,x87861),x87864),x87864))))
% 162.26/162.08 [8872]~E(x88723,x88724)+P24(f331(f331(f270(x88721,x88721,a877),a328),x88722))+~P24(f331(f331(f333(f890(x88721,x88721)),x88722),f331(f175(f890(x88721,x88721)),f331(f331(f184(x88721,x88721),x88723),x88724))))
% 162.26/162.08 [8899]~P24(f331(x88994,x88992))+P24(f331(f331(f331(f331(a205,x88991),x88992),x88993),f596(x88993,x88992,x88991,x88994)))+~P24(f331(f331(f331(f331(a205,f33(x88994,x88991)),x88992),x88993),x88992))
% 162.26/162.08 [8925]P24(f331(f331(f333(f890(f884(x89251),f884(x89251))),f331(f331(f261(f884(x89251),f884(x89251)),x89252),x89253)),f150(x89251,x89254)))+~E(f331(f331(f176(x89251),f331(f197(f884(x89251)),x89252)),x89253),x89252)+~P24(f331(f331(f248(a883),f331(f197(f884(x89251)),x89252)),f331(f197(f884(x89251)),x89253)))
% 162.26/162.08 [9023]~P24(f331(f62(x90231),x90234))+P24(f331(f331(f333(x90231),f345(x90232,x90233,x90234,x90231)),x90234))+P24(f331(f62(x90233),f331(f331(f42(x90231,f891(x90233,a877)),x90234),x90232)))
% 162.26/162.08 [9024]~P24(f331(f62(x90241),x90244))+P24(f331(f331(f333(x90241),f605(x90242,x90243,x90244,x90241)),x90244))+P24(f331(f62(x90243),f331(f331(f42(x90241,f891(x90243,a877)),x90244),x90242)))
% 162.26/162.08 [9097]P24(f331(f331(f333(f890(x90971,x90971)),x90972),f331(f331(f288(x90971,x90971,x90971),x90973),f307(x90971,x90973))))+~P24(f331(f331(f248(a883),f2(a883)),x90974))+~P24(f331(f331(f333(f890(x90971,x90971)),x90972),f331(f331(f191(f890(x90971,x90971),a877),x90974),x90973)))
% 162.26/162.08 [9106]~P38(x91061,x91062)+~P24(f331(f331(f333(f890(x91061,x91061)),f331(f331(f261(x91061,x91061),x91064),x91063)),x91062))+~P24(f331(f331(f333(f890(x91061,x91061)),f331(f331(f261(x91061,x91061),x91063),x91064)),x91062))
% 162.26/162.08 [9236]~P24(f331(f62(x92361),x92364))+E(f331(f331(f6(x92361,a883),f331(f331(f8(f891(x92362,a877),a883,x92361),f38(x92362)),x92363)),x92364),f331(f38(f890(x92361,x92362)),f331(f331(f268(x92361,x92362),x92364),x92363)))+P24(f331(f331(f333(x92361),f551(x92363,x92362,x92364,x92361)),x92364))
% 162.26/162.08 [9240]~P24(f331(f140(x92401),x92402))+P24(f331(f140(x92401),f331(f331(f162(x92401,x92402),x92403),x92404)))+P24(f331(f331(f333(x92401),x92404),f331(f331(f22(f891(x92401,a877)),f331(f175(x92401),x92402)),f331(f331(f309(x92401),f331(f331(f168(x92401),x92402),x92403)),f196(f891(x92401,a877))))))
% 162.26/162.08 [9256]~P24(f331(f62(x92562),x92563))+~P24(f331(f62(x92561),f331(x92564,f345(x92564,x92561,x92563,x92562))))+P24(f331(f62(x92561),f331(f331(f42(x92562,f891(x92561,a877)),x92563),x92564)))
% 162.26/162.08 [9257]~P24(f331(f62(x92572),x92573))+~P24(f331(f62(x92571),f331(x92574,f605(x92574,x92571,x92573,x92572))))+P24(f331(f62(x92571),f331(f331(f42(x92572,f891(x92571,a877)),x92573),x92574)))
% 162.26/162.08 [9339]~P24(f331(f331(f333(f890(x93391,x93391)),x93392),f331(f331(f288(x93391,x93391,x93391),x93394),f307(x93391,x93394))))+P24(f331(f331(f333(f890(x93391,x93391)),x93392),f331(f331(f288(x93391,x93391,x93391),x93393),f307(x93391,x93393))))+~P24(f331(f331(f247(f891(f890(x93391,x93391),a877)),x93394),x93393))
% 162.26/162.08 [9346]E(f331(f331(f176(x93461),f627(x93464,x93463,x93462,x93461)),x93463),f331(f331(f176(x93461),f627(x93464,x93463,x93462,x93461)),x93462))+~P24(f331(f331(f333(f890(f884(x93461),f884(x93461))),f331(f331(f261(f884(x93461),f884(x93461)),x93462),x93463)),f150(x93461,x93464)))+E(f331(f331(f176(x93461),f331(f197(f884(x93461)),x93462)),x93463),x93462)
% 162.26/162.08 [9366]~P24(f331(f62(x93661),x93664))+E(f331(f331(f6(x93661,a883),f331(f331(f8(f891(x93662,a877),a883,x93661),f38(x93662)),x93663)),x93664),f331(f38(f890(x93661,x93662)),f331(f331(f268(x93661,x93662),x93664),x93663)))+~P24(f331(f62(x93662),f331(x93663,f551(x93663,x93662,x93664,x93661))))
% 162.26/162.08 [9371]~E(f331(f197(f884(x93711)),x93713),f331(f197(f884(x93711)),x93712))+P24(f331(f331(f333(f890(f884(x93711),f884(x93711))),f331(f331(f261(f884(x93711),f884(x93711)),x93712),x93713)),f161(x93711,x93714)))+P24(f331(f331(f333(f890(x93711,x93711)),f615(x93714,x93713,x93712,x93711)),f331(f175(f890(x93711,x93711)),f331(f331(f184(x93711,x93711),x93712),x93713))))
% 162.26/162.08 [9439]~P24(f331(f331(f333(f890(f884(x94391),f884(x94391))),f331(f331(f261(f884(x94391),f884(x94391)),x94392),x94393)),f150(x94391,x94394)))+E(f331(f331(f176(x94391),f331(f197(f884(x94391)),x94392)),x94393),x94392)+P24(f331(f331(f248(a883),f627(x94394,x94393,x94392,x94391)),f331(f331(f251(a883),f331(f197(f884(x94391)),x94392)),f331(f197(f884(x94391)),x94393))))
% 162.26/162.08 [9440]E(f331(f180(x94401,x94402),x94403),f331(f180(x94401,x94402),x94404))+~E(f331(f175(x94401),f331(f331(f157(f890(x94401,x94402),x94401),f260(x94401,x94402)),x94403)),f331(f175(x94401),f331(f331(f157(f890(x94401,x94402),x94401),f260(x94401,x94402)),x94404)))+P24(f331(f331(f333(x94401),f706(x94403,x94404,x94402,x94401)),f331(f175(x94401),f331(f331(f157(f890(x94401,x94402),x94401),f260(x94401,x94402)),x94404))))
% 162.26/162.08 [9456]~P24(f331(x94561,x94564))+P24(f331(f331(f331(f331(a205,f33(x94561,x94562)),f596(x94563,x94564,x94562,x94561)),x94563),x94564))+~P24(f331(f331(f331(f331(a205,f33(x94561,x94562)),x94564),x94563),x94564))
% 162.26/162.08 [9461]~P24(f331(f331(f333(f890(f884(x94611),f884(x94611))),f331(f331(f261(f884(x94611),f884(x94611)),x94612),x94613)),f150(x94611,x94614)))+P24(f331(f331(f248(a883),f331(f197(f884(x94611)),x94612)),f331(f197(f884(x94611)),x94613)))+P24(f331(f331(f248(a883),f627(x94614,x94613,x94612,x94611)),f331(f331(f251(a883),f331(f197(f884(x94611)),x94612)),f331(f197(f884(x94611)),x94613))))
% 162.26/162.08 [9796]~P24(f331(f331(f331(x97961,f397(x97961,x97964,x97963,x97962)),f398(x97961,x97964,x97963,x97962)),f399(x97961,x97964,x97963,x97962)))+P24(f331(f331(f331(x97961,x97962),x97963),x97964))+~P24(f331(f319(f890(f891(a1,f887(f884(a327))),f890(a1,a1)),a317),f331(f331(f261(f891(a1,f887(f884(a327))),f890(a1,a1)),x97962),f331(f331(f261(a1,a1),x97963),x97964))))
% 162.26/162.08 [9867]P24(f331(f331(f331(x98671,x98672),x98673),x98674))+P24(f331(f319(f890(f891(a1,f887(f884(a327))),f890(a1,a1)),a317),f331(f331(f261(f891(a1,f887(f884(a327))),f890(a1,a1)),f397(x98671,x98674,x98673,x98672)),f331(f331(f261(a1,a1),f398(x98671,x98674,x98673,x98672)),f399(x98671,x98674,x98673,x98672)))))+~P24(f331(f319(f890(f891(a1,f887(f884(a327))),f890(a1,a1)),a317),f331(f331(f261(f891(a1,f887(f884(a327))),f890(a1,a1)),x98672),f331(f331(f261(a1,a1),x98673),x98674))))
% 162.26/162.08 [9905]~P24(f331(f331(f333(f890(f884(x99051),f884(x99051))),f331(f331(f261(f884(x99051),f884(x99051)),x99052),x99053)),f150(x99051,x99054)))+E(f331(f331(f176(x99051),f331(f197(f884(x99051)),x99052)),x99053),x99052)+P24(f331(f331(f333(f890(x99051,x99051)),f331(f331(f261(x99051,x99051),f331(f331(f168(x99051),x99052),f627(x99054,x99053,x99052,x99051))),f331(f331(f168(x99051),x99053),f627(x99054,x99053,x99052,x99051)))),x99054))
% 162.26/162.08 [9908]~P24(f331(f331(f333(f890(f884(x99081),f884(x99081))),f331(f331(f261(f884(x99081),f884(x99081)),x99082),x99083)),f150(x99081,x99084)))+P24(f331(f331(f248(a883),f331(f197(f884(x99081)),x99082)),f331(f197(f884(x99081)),x99083)))+P24(f331(f331(f333(f890(x99081,x99081)),f331(f331(f261(x99081,x99081),f331(f331(f168(x99081),x99082),f627(x99084,x99083,x99082,x99081))),f331(f331(f168(x99081),x99083),f627(x99084,x99083,x99082,x99081)))),x99084))
% 162.26/162.08 [9952]~E(f331(f197(f884(x99521)),x99522),f331(f197(f884(x99521)),x99523))+P24(f331(f331(f333(f890(f884(x99521),f884(x99521))),f331(f331(f261(f884(x99521),f884(x99521)),x99522),x99523)),f161(x99521,x99524)))+~P24(f331(f331(f333(f890(x99521,x99521)),f331(f331(f261(x99521,x99521),f331(f331(f168(x99521),x99522),f626(x99524,x99523,x99522,x99521))),f331(f331(f168(x99521),x99523),f626(x99524,x99523,x99522,x99521)))),x99524))
% 162.26/162.08 [10089]~P74(x100891)+~P24(f331(f62(x100892),x100894))+E(f331(f169(x100891),f331(f331(f157(x100892,x100891),x100893),f91(f884(x100892),f331(f331(f18(f884(x100892),a877,a877),f331(f331(f8(a877,f891(a877,a877),f884(x100892)),a329),f331(f331(f7(f884(x100892),f891(x100892,a877),a877),f331(f331(f8(f891(x100892,a877),f891(f891(x100892,a877),a877),f884(x100892)),a328),f175(x100892))),x100894))),f140(x100892))))),f238(x100892,x100891,x100893,x100894))
% 162.26/162.08 [7376]~P61(x73762)+E(x73761,f2(x73762))+E(f331(f331(f289(x73762),f331(f331(f81(x73762),x73763),f331(f331(f82(x73762),x73764),x73761))),x73761),f331(f331(f81(x73762),x73764),f331(f331(f289(x73762),x73763),x73761)))
% 162.26/162.08 [7377]~P58(x73772)+E(x73771,f2(x73772))+E(f331(f331(f39(x73772),f331(f331(f81(x73772),x73773),f331(f331(f82(x73772),x73774),x73771))),x73771),f331(f331(f81(x73772),x73774),f331(f331(f39(x73772),x73773),x73771)))
% 162.26/162.08 [7378]~P58(x73782)+E(x73781,f2(x73782))+E(f331(f331(f39(x73782),f331(f331(f81(x73782),x73783),f331(f331(f82(x73782),x73781),x73784))),x73781),f331(f331(f81(x73782),x73784),f331(f331(f39(x73782),x73783),x73781)))
% 162.26/162.08 [7607]~P62(x76072)+E(x76071,f2(x76072))+E(f331(f331(f289(x76072),f331(f331(f22(x76072),x76073),f331(f331(f82(x76072),x76071),x76074))),x76071),f331(f331(f22(x76072),f331(f331(f289(x76072),x76073),x76071)),x76074))
% 162.26/162.08 [7608]~P61(x76082)+E(x76081,f2(x76082))+E(f331(f331(f289(x76082),f331(f331(f81(x76082),x76083),f331(f331(f82(x76082),x76084),x76081))),x76081),f331(f331(f81(x76082),f331(f331(f289(x76082),x76083),x76081)),x76084))
% 162.26/162.08 [7609]~P62(x76092)+E(x76091,f2(x76092))+E(f331(f331(f289(x76092),f331(f331(f81(x76092),x76093),f331(f331(f82(x76092),x76091),x76094))),x76091),f331(f331(f81(x76092),f331(f331(f289(x76092),x76093),x76091)),x76094))
% 162.26/162.08 [8311]~P24(f331(f163(x83111,x83113),x83114))+~P24(f331(f163(x83111,x83112),x83114))+P24(f331(f163(x83111,f331(f331(f108(f891(x83111,a877)),x83112),x83113)),x83114))
% 162.26/162.08 [8670]~E(f331(f331(f288(x86701,x86701,x86701),x86702),x86704),f196(f891(f890(x86701,x86701),a877)))+~E(f331(f331(f288(x86701,x86701,x86701),x86702),x86703),f196(f891(f890(x86701,x86701),a877)))+E(f331(f331(f288(x86701,x86701,x86701),x86702),f331(f331(f107(f891(f890(x86701,x86701),a877)),x86703),x86704)),f196(f891(f890(x86701,x86701),a877)))
% 162.26/162.08 [8787]~P24(f331(f331(f247(f891(x87871,a877)),x87873),x87874))+~P24(f331(f331(f247(f891(x87871,a877)),x87872),x87874))+P24(f331(f331(f247(f891(x87871,a877)),f331(f331(f107(f891(x87871,a877)),x87872),x87873)),x87874))
% 162.26/162.08 [9167]~P24(f331(f62(x91671),x91674))+~P24(f331(f62(x91671),x91673))+E(f331(f331(f22(a883),f331(f331(f81(a883),f331(f331(f6(x91671,a883),x91672),x91673)),f331(f331(f6(x91671,a883),x91672),x91674))),f331(f331(f6(x91671,a883),x91672),f331(f331(f108(f891(x91671,a877)),x91673),x91674))),f331(f331(f6(x91671,a883),x91672),f331(f331(f107(f891(x91671,a877)),x91673),x91674)))
% 162.26/162.08 [9253]~P24(f331(f331(f333(x92531),x92533),x92532))+~P24(f331(f331(f247(f891(x92531,a877)),x92532),f331(f331(f309(x92531),x92533),x92534)))+P24(f331(f331(f247(f891(x92531,a877)),f331(f331(f22(f891(x92531,a877)),x92532),f331(f331(f309(x92531),x92533),f196(f891(x92531,a877))))),x92534))
% 162.26/162.08 [9411]~P24(f331(f331(f333(x94111),x94113),x94112))+P24(f331(f331(f247(f891(x94111,a877)),x94112),f331(f331(f309(x94111),x94113),x94114)))+~P24(f331(f331(f247(f891(x94111,a877)),f331(f331(f22(f891(x94111,a877)),x94112),f331(f331(f309(x94111),x94113),f196(f891(x94111,a877))))),x94114))
% 162.26/162.08 [9515]~P24(f331(f331(f248(a883),x95152),x95154))+~P24(f331(f331(f247(a883),x95151),x95153))+P24(f331(f331(f333(f890(f890(a883,a883),f890(a883,a883))),f331(f331(f261(f890(a883,a883),f890(a883,a883)),f331(f331(f261(a883,a883),x95151),x95152)),f331(f331(f261(a883,a883),x95153),x95154))),a36))
% 162.26/162.08 [9516]~P24(f331(f331(f247(a883),x95162),x95164))+~P24(f331(f331(f247(a883),x95161),x95163))+P24(f331(f331(f333(f890(f890(a883,a883),f890(a883,a883))),f331(f331(f261(f890(a883,a883),f890(a883,a883)),f331(f331(f261(a883,a883),x95161),x95162)),f331(f331(f261(a883,a883),x95163),x95164))),a71))
% 162.26/162.08 [9831]~P24(f331(f331(f333(f884(x98311)),x98314),f164(x98311,x98313)))+~P24(f331(f331(f333(f884(x98311)),x98314),f164(x98311,x98312)))+P24(f331(f163(x98311,f331(f331(f108(f891(x98311,a877)),f331(f331(f7(x98311,f891(x98311,a877),a877),f333(x98311)),x98312)),f331(f331(f7(x98311,f891(x98311,a877),a877),f333(x98311)),x98313))),x98314))
% 162.26/162.08 [9926]~P21(x99261,f891(f891(x99261,a877),a877),f331(f331(f7(x99261,f891(f890(x99261,x99261),a877),f891(f891(x99261,a877),a877)),f331(f331(f8(f891(x99261,a877),f891(f891(f890(x99261,x99261),a877),f891(f891(x99261,a877),a877)),x99261),f61(x99261)),f331(f331(f7(x99261,f891(x99261,a877),f891(x99261,a877)),f309(x99261)),f196(f891(x99261,a877))))),x99263),x99262)+~P24(f331(f331(f333(x99261),x99264),x99262))+E(f331(f331(f22(f891(f891(x99261,a877),a877)),f331(f331(f61(x99261),x99262),x99263)),f331(f331(f61(x99261),f331(f331(f309(x99261),x99264),f196(f891(x99261,a877)))),x99263)),f331(f331(f61(x99261),f331(f331(f22(f891(x99261,a877)),x99262),f331(f331(f309(x99261),x99264),f196(f891(x99261,a877))))),x99263))
% 162.26/162.08 [10046]~P48(x100461,x100462,x100464)+~P24(f331(f331(f333(f890(x100461,x100461)),x100463),x100464))+P24(f331(f331(f270(x100461,x100461,a877),f331(f331(f7(x100461,f891(x100461,a877),f891(x100461,a877)),f331(f331(f8(f891(a877,a877),f891(f891(x100461,a877),f891(x100461,a877)),x100461),f8(a877,a877,x100461)),f331(f331(f8(a877,f891(a877,a877),x100461),a329),f331(f331(f7(x100461,f891(x100461,a877),a877),f333(x100461)),x100462)))),f331(f331(f7(x100461,f891(x100461,a877),a877),f333(x100461)),x100462))),x100463))
% 162.26/162.08 [10058]P24(f331(f62(x100581),x100582))+~P24(f331(f62(x100583),f331(f310(x100581,x100583,x100584),x100582)))+~P24(f331(f62(x100581),f331(f253(x100581),f331(f331(f18(x100581,a877,a877),f331(f331(f8(a877,f891(a877,a877),x100581),a329),f331(f331(f7(x100581,f891(x100581,a877),a877),f333(x100581)),x100582))),f331(f331(f7(x100581,x100583,a877),f331(f331(f8(x100583,f891(x100583,a877),x100581),a328),x100584)),f331(x100584,f584(x100584,x100583,x100582,x100581)))))))
% 162.26/162.08 [8064]~P62(x80642)+E(x80641,f2(x80642))+E(f331(f331(f289(x80642),f331(f331(f22(x80642),f331(f331(f82(x80642),x80641),x80643)),x80644)),x80641),f331(f331(f22(x80642),x80643),f331(f331(f289(x80642),x80644),x80641)))
% 162.26/162.08 [8065]~P62(x80652)+E(x80651,f2(x80652))+E(f331(f331(f289(x80652),f331(f331(f81(x80652),f331(f331(f82(x80652),x80651),x80653)),x80654)),x80651),f331(f331(f81(x80652),x80653),f331(f331(f289(x80652),x80654),x80651)))
% 162.26/162.08 [8955]~E(f331(f331(f288(x89551,x89551,x89551),x89553),x89554),f196(f891(f890(x89551,x89551),a877)))+~E(f331(f331(f288(x89551,x89551,x89551),x89552),x89554),f196(f891(f890(x89551,x89551),a877)))+E(f331(f331(f288(x89551,x89551,x89551),f331(f331(f107(f891(f890(x89551,x89551),a877)),x89552),x89553)),x89554),f196(f891(f890(x89551,x89551),a877)))
% 162.26/162.08 [9991]~P145(x99911)+~P145(x99912)+E(f331(f331(f316(x99911),f331(f331(f7(x99911,a105,f887(f884(a327))),f331(f331(f8(f891(x99912,f887(f884(a327))),f891(a105,f887(f884(a327))),x99911),f316(x99912)),f331(f331(f8(f891(x99912,f890(x99911,x99912)),f891(x99912,f887(f884(a327))),x99911),f331(f8(f890(x99911,x99912),f887(f884(a327)),x99912),x99913)),f261(x99911,x99912)))),x99914)),x99914),f331(f331(f316(f890(x99911,x99912)),x99913),x99914))
% 162.26/162.08 [9730]~P24(f331(f163(x97301,x97303),x97304))+~P24(f331(f163(x97301,x97302),x97304))+P24(f331(f163(x97301,f331(f331(f18(x97301,a877,a877),f331(f331(f8(a877,f891(a877,a877),x97301),a329),x97302)),x97303)),x97304))
% 162.26/162.08 [9983]P24(f331(x99831,f571(x99832,x99833,x99831,x99834)))+~P24(f331(f62(x99834),f331(f253(x99834),x99831)))+P24(f331(f62(x99833),f331(f253(x99833),f331(f331(f8(f891(x99834,a877),a877,x99833),f87(x99834)),f331(f331(f8(f891(x99834,a877),f891(x99834,a877),x99833),f331(f18(x99834,a877,a877),f331(f331(f8(a877,f891(a877,a877),x99834),a329),x99831))),x99832)))))
% 162.26/162.08 [10005]~P24(f331(f62(x100052),f331(f253(x100052),x100053)))+~P24(f331(f62(x100051),f331(f253(x100051),f331(f331(f7(x100051,x100052,a877),x100054),f571(x100054,x100051,x100053,x100052)))))+P24(f331(f62(x100051),f331(f253(x100051),f331(f331(f8(f891(x100052,a877),a877,x100051),f87(x100052)),f331(f331(f8(f891(x100052,a877),f891(x100052,a877),x100051),f331(f18(x100052,a877,a877),f331(f331(f8(a877,f891(a877,a877),x100052),a329),x100053))),x100054)))))
% 162.26/162.08 [6541]E(x65411,x65412)+~E(f331(x65413,x65411),f331(x65413,x65412))+~P21(x65414,x65415,x65413,f256(f891(x65414,a877)))
% 162.26/162.08 [6701]~E(f331(x67013,x67015),f199(x67012))+~E(f331(x67014,x67015),f199(x67012))+E(f331(f187(x67011,x67012,x67013,x67014),x67015),f199(x67012))
% 162.26/162.08 [7412]E(x74121,x74122)+~P21(x74123,x74124,x74125,f256(f891(x74123,a877)))+~E(f331(f310(x74123,x74124,x74125),x74121),f331(f310(x74123,x74124,x74125),x74122))
% 162.26/162.08 [7661]P21(x76612,x76613,f482(x76614,x76613,x76612,x76611),x76611)+~E(f331(f310(x76613,x76612,x76615),x76614),x76611)+E(x76611,f196(f891(x76612,a877)))
% 162.26/162.08 [8202]~P24(f331(f331(x82023,x82022),x82025))+~P24(f331(f331(x82023,x82024),x82022))+P24(f331(f331(f333(x82021),x82022),f298(x82021,x82023,x82024,x82025)))
% 162.26/162.08 [8203]~P24(f331(f331(x82033,x82032),x82035))+~P24(f331(f331(x82033,x82034),x82032))+P24(f331(f331(f333(x82031),x82032),f295(x82031,x82033,x82034,x82035)))
% 162.26/162.08 [8746]~P21(x87461,x87463,x87465,f256(f891(x87461,a877)))+~P21(x87463,x87462,x87464,f256(f891(x87463,a877)))+P21(x87461,x87462,f331(f74(x87463,x87462,x87461,x87464),x87465),f256(f891(x87461,a877)))
% 162.26/162.08 [9315]P24(f331(f331(f333(f890(x93151,x93151)),f331(f331(f261(x93151,x93151),x93152),x93153)),f307(x93151,x93154)))+~P24(f331(f331(f333(f890(x93151,x93151)),f331(f331(f261(x93151,x93151),x93152),x93155)),f307(x93151,x93154)))+~P24(f331(f331(f333(f890(x93151,x93151)),f331(f331(f261(x93151,x93151),x93155),x93153)),f307(x93151,x93154)))
% 162.26/162.08 [9353]~P107(x93532)+~P24(f331(f140(x93531),x93535))+P24(f331(f140(x93531),f152(x93531,x93532,x93533,x93534,x93535)))
% 162.26/162.08 [5383]~E(x53832,f119(x53831))+E(f331(f331(f137(x53831),x53832),x53833),f331(f331(f154(x53831),x53834),x53835))+~E(x53833,f331(f331(f154(x53831),x53834),x53835))
% 162.26/162.08 [5384]~E(x53842,f119(x53841))+E(f331(f331(f137(x53841),x53842),x53843),f331(f331(f154(x53841),x53844),x53845))+~E(f331(f331(f154(x53841),x53844),x53845),x53843)
% 162.26/162.08 [6500]~E(f331(f197(f884(x65001)),x65005),f331(f197(f884(x65002)),x65004))+E(f331(f331(f157(f890(x65001,x65002),x65002),f269(x65001,x65002)),x65003),x65004)+~E(f331(f331(f184(x65001,x65002),x65005),x65004),x65003)
% 162.26/162.08 [6501]~E(f331(f197(f884(x65011)),x65014),f331(f197(f884(x65012)),x65015))+E(f331(f331(f157(f890(x65011,x65012),x65011),f260(x65011,x65012)),x65013),x65014)+~E(f331(f331(f184(x65011,x65012),x65014),x65015),x65013)
% 162.26/162.08 [6962]~P107(x69621)+~P29(x69621,f331(f331(f157(x69622,x69621),x69623),x69625))+P29(x69621,f331(f331(f157(x69622,x69621),x69623),f331(f139(x69622,x69624),x69625)))
% 162.26/162.08 [7009]~P24(f331(x70093,x70095))+~P24(f331(f331(x70092,x70094),x70095))+P24(f331(f331(f98(x70091,x70092,x70093),x70094),x70095))
% 162.26/162.08 [7105]~P107(x71051)+P29(x71051,f331(f331(f157(x71052,x71051),x71053),f173(x71052,x71054,x71055)))+~P29(x71051,f331(f331(f157(x71052,x71051),x71053),x71055))
% 162.26/162.08 [7128]~P52(x71283,x71282,x71285)+~P52(x71281,x71283,x71284)+P52(x71281,x71282,f331(f331(f288(x71281,x71283,x71282),x71284),x71285))
% 162.26/162.08 [7220]E(x72201,x72202)+~P21(x72203,x72204,x72205,f256(f891(x72203,a877)))+~E(f331(f331(f157(x72203,x72204),x72205),x72201),f331(f331(f157(x72203,x72204),x72205),x72202))
% 162.26/162.08 [7362]~P24(f331(f331(f248(a883),x73621),f331(x73623,x73625)))+P24(f331(f331(f248(a883),x73621),f158(x73622,x73623,x73624)))+~P24(f331(f331(f333(x73622),x73625),f331(f175(x73622),x73624)))
% 162.26/162.08 [7363]~P24(f331(f331(f247(a883),x73631),f331(x73633,x73635)))+P24(f331(f331(f247(a883),x73631),f158(x73632,x73633,x73634)))+~P24(f331(f331(f333(x73632),x73635),f331(f175(x73632),x73634)))
% 162.26/162.08 [7764]~P108(x77641)+P24(f331(f331(f247(f891(x77641,a877)),f302(x77641,x77642,x77643)),f302(x77641,x77644,x77645)))+P24(f331(f331(f247(x77641),x77642),x77643))
% 162.26/162.08 [7789]~P27(x77891)+P24(f331(f331(f247(x77891),f331(f331(f43(x77892,x77891),x77893),x77894)),f331(x77894,x77895)))+~P24(f331(f331(f333(x77892),x77895),x77893))
% 162.26/162.08 [7857]~P21(x78571,x78572,x78574,x78573)+E(f331(f78(x78571,x78572,x78573,x78574),f331(x78574,x78575)),x78575)+~P24(f331(f331(f333(x78571),x78575),x78573))
% 162.26/162.08 [8054]~P24(f331(x80541,x80545))+P24(f331(x80541,f837(x80541,x80542,x80543,x80544)))+~P24(f331(f331(f333(x80544),x80545),x80543))
% 162.26/162.08 [8055]~P24(f331(x80551,x80555))+P24(f331(x80551,f837(x80551,x80552,x80553,x80554)))+~P24(f331(f331(f333(x80554),x80555),x80552))
% 162.26/162.08 [8152]P24(f331(f62(x81521),x81522))+~P24(f331(f62(x81523),x81524))+~P24(f331(f331(f247(f891(x81521,a877)),x81522),f331(f310(x81523,x81521,x81525),x81524)))
% 162.26/162.08 [8315]E(x83151,x83152)+~P21(x83153,x83154,x83155,f331(f331(f107(f891(x83153,a877)),f331(f175(x83153),x83151)),f331(f175(x83153),x83152)))+~E(f331(f331(f157(x83153,x83154),x83155),x83151),f331(f331(f157(x83153,x83154),x83155),x83152))
% 162.26/162.08 [8366]~P108(x83661)+~P24(f331(f331(f248(f891(x83661,a877)),f302(x83661,x83664,x83665)),f302(x83661,x83662,x83663)))+P24(f331(f331(f247(x83661),x83662),x83663))
% 162.26/162.08 [8432]~P21(x84321,x84324,x84325,f256(f891(x84321,a877)))+~P24(f331(f331(f333(x84324),f331(x84325,x84322)),f331(f310(x84321,x84324,x84325),x84323)))+P24(f331(f331(f333(x84321),x84322),x84323))
% 162.26/162.08 [8508]P24(f331(x85081,x85082))+~P24(f331(x85081,f838(x85081,x85083,x85084,x85085)))+~P24(f331(f331(f333(x85085),x85082),x85084))
% 162.26/162.08 [8509]P24(f331(x85091,x85092))+~P24(f331(x85091,f838(x85091,x85093,x85094,x85095)))+~P24(f331(f331(f333(x85095),x85092),x85093))
% 162.26/162.08 [8784]~P21(x87842,x87843,x87841,x87844)+E(f331(x87841,f331(f78(x87842,x87843,x87844,x87841),x87845)),x87845)+~P24(f331(f331(f333(x87843),x87845),f331(f310(x87842,x87843,x87841),x87844)))
% 162.26/162.08 [8894]E(x88941,f119(x88942))+E(f331(f331(f154(x88942),x88943),f645(x88944,x88943,x88945,x88941,x88942)),x88941)+~E(f331(f331(f137(x88942),x88941),x88945),f331(f331(f154(x88942),x88943),x88944))
% 162.26/162.08 [8895]E(x88951,f119(x88952))+E(f331(f331(f154(x88952),x88953),f646(x88954,x88951,x88955,x88953,x88952)),x88951)+~E(f331(f331(f137(x88952),x88951),x88954),f331(f331(f154(x88952),x88953),x88955))
% 162.26/162.08 [8911]E(f331(f331(f154(x89112),x89113),f645(x89114,x89113,x89111,x89115,x89112)),x89115)+~E(f331(f331(f137(x89112),x89115),x89111),f331(f331(f154(x89112),x89113),x89114))+E(x89111,f331(f331(f154(x89112),x89113),x89114))
% 162.26/162.08 [8912]E(f331(f331(f154(x89121),x89122),f646(x89124,x89125,x89123,x89122,x89121)),x89125)+~E(f331(f331(f137(x89121),x89125),x89124),f331(f331(f154(x89121),x89122),x89123))+E(f331(f331(f154(x89121),x89122),x89123),x89124)
% 162.26/162.08 [8993]~E(f331(f310(x89933,x89932,x89934),f256(f891(x89933,a877))),f256(f891(x89932,a877)))+~E(f331(f310(x89931,x89933,x89935),f256(f891(x89931,a877))),f256(f891(x89933,a877)))+E(f331(f310(x89931,x89932,f331(f74(x89933,x89932,x89931,x89934),x89935)),f256(f891(x89931,a877))),f256(f891(x89932,a877)))
% 162.26/162.08 [9363]E(x93631,f119(x93632))+~E(f331(f331(f137(x93632),x93631),x93633),f331(f331(f154(x93632),x93635),x93634))+E(f331(f331(f137(x93632),f646(x93633,x93631,x93634,x93635,x93632)),x93633),x93634)
% 162.26/162.08 [9364]E(x93641,f119(x93642))+~E(f331(f331(f137(x93642),x93641),x93645),f331(f331(f154(x93642),x93644),x93643))+E(f331(f331(f137(x93642),f645(x93643,x93644,x93645,x93641,x93642)),x93645),x93643)
% 162.26/162.08 [9372]E(f331(f331(f137(x93722),f645(x93724,x93723,x93721,x93725,x93722)),x93721),x93724)+~E(f331(f331(f137(x93722),x93725),x93721),f331(f331(f154(x93722),x93723),x93724))+E(x93721,f331(f331(f154(x93722),x93723),x93724))
% 162.26/162.08 [9373]~E(f331(f331(f137(x93731),x93735),x93734),f331(f331(f154(x93731),x93732),x93733))+E(f331(f331(f137(x93731),f646(x93734,x93735,x93733,x93732,x93731)),x93734),x93733)+E(f331(f331(f154(x93731),x93732),x93733),x93734)
% 162.26/162.08 [9374]E(f331(f331(f137(x93741),x93745),f648(x93743,x93742,x93744,x93745,x93741)),x93742)+E(f331(f331(f137(x93741),x93742),f647(x93743,x93742,x93744,x93745,x93741)),x93745)+~E(f331(f331(f137(x93741),x93745),x93744),f331(f331(f137(x93741),x93742),x93743))
% 162.26/162.08 [9399]~P107(x93991)+P29(x93991,f331(f331(f157(x93992,x93991),x93993),f152(x93992,x93991,x93993,x93994,x93995)))+~P29(x93991,f331(f331(f157(x93992,x93991),x93993),x93995))
% 162.26/162.08 [9408]~P56(x94085,x94081,x94084,x94083)+P24(f331(f331(x94081,x94082),f523(x94083,x94084,x94081,x94085,x94082)))+~P24(f331(f331(f333(x94085),x94082),x94084))
% 162.26/162.08 [9527]~P24(f331(f331(f333(f890(x95271,x95271)),f331(f331(f261(x95271,x95271),x95275),x95273)),f307(x95271,x95274)))+P24(f331(f331(f333(f890(x95271,x95271)),f331(f331(f261(x95271,x95271),x95272),x95273)),f331(f331(f288(x95271,x95271,x95271),x95274),f307(x95271,x95274))))+~P24(f331(f331(f333(f890(x95271,x95271)),f331(f331(f261(x95271,x95271),x95272),x95275)),f331(f331(f288(x95271,x95271,x95271),x95274),f307(x95271,x95274))))
% 162.26/162.08 [9528]~P24(f331(f331(f333(f890(x95281,x95281)),f331(f331(f261(x95281,x95281),x95282),x95285)),f307(x95281,x95284)))+P24(f331(f331(f333(f890(x95281,x95281)),f331(f331(f261(x95281,x95281),x95282),x95283)),f331(f331(f288(x95281,x95281,x95281),x95284),f307(x95281,x95284))))+~P24(f331(f331(f333(f890(x95281,x95281)),f331(f331(f261(x95281,x95281),x95285),x95283)),f331(f331(f288(x95281,x95281,x95281),x95284),f307(x95281,x95284))))
% 162.26/162.08 [9531]P24(f331(f331(f333(f890(f884(x95311),f884(x95311))),f331(f331(f261(f884(x95311),f884(x95311)),x95312),x95313)),f161(x95311,f307(x95311,x95314))))+~P24(f331(f331(f333(f890(f884(x95311),f884(x95311))),f331(f331(f261(f884(x95311),f884(x95311)),x95312),x95315)),f161(x95311,f307(x95311,x95314))))+~P24(f331(f331(f333(f890(f884(x95311),f884(x95311))),f331(f331(f261(f884(x95311),f884(x95311)),x95315),x95313)),f161(x95311,f307(x95311,x95314))))
% 162.26/162.08 [9535]E(f331(f331(f137(x95351),x95352),f647(x95353,x95352,x95354,x95355,x95351)),x95355)+E(f331(f331(f137(x95351),f648(x95353,x95352,x95354,x95355,x95351)),x95353),x95354)+~E(f331(f331(f137(x95351),x95352),x95353),f331(f331(f137(x95351),x95355),x95354))
% 162.26/162.08 [9536]E(f331(f331(f137(x95361),x95362),f648(x95363,x95364,x95365,x95362,x95361)),x95364)+E(f331(f331(f137(x95361),f647(x95363,x95364,x95365,x95362,x95361)),x95365),x95363)+~E(f331(f331(f137(x95361),x95362),x95365),f331(f331(f137(x95361),x95364),x95363))
% 162.26/162.08 [9596]P24(f331(f331(f333(f890(x95961,x95961)),f331(f331(f261(x95961,x95961),x95962),x95963)),f331(f331(f288(x95961,x95961,x95961),x95964),f307(x95961,x95964))))+~P24(f331(f331(f333(f890(x95961,x95961)),f331(f331(f261(x95961,x95961),x95962),x95965)),f331(f331(f288(x95961,x95961,x95961),x95964),f307(x95961,x95964))))+~P24(f331(f331(f333(f890(x95961,x95961)),f331(f331(f261(x95961,x95961),x95965),x95963)),f331(f331(f288(x95961,x95961,x95961),x95964),f307(x95961,x95964))))
% 162.26/162.08 [9627]P35(x96271,x96272,x96273,x96274,x96275)+~E(f331(f197(f884(x96271)),x96274),f331(f197(f884(x96272)),x96275))+~P24(f331(f331(f270(x96271,x96272,a877),x96273),f692(x96275,x96274,x96273,x96272,x96271)))
% 162.26/162.08 [9628]P35(x96281,x96282,x96283,x96284,x96285)+~E(f331(f197(f884(x96281)),x96284),f331(f197(f884(x96282)),x96285))+~P24(f331(f331(f270(x96281,x96282,a877),x96283),f699(x96283,x96285,x96284,x96282,x96281)))
% 162.26/162.08 [9633]E(f331(f331(f137(x96331),f647(x96332,x96333,x96334,x96335,x96331)),x96334),x96332)+~E(f331(f331(f137(x96331),x96333),x96332),f331(f331(f137(x96331),x96335),x96334))+E(f331(f331(f137(x96331),f648(x96332,x96333,x96334,x96335,x96331)),x96332),x96334)
% 162.26/162.08 [9650]~P107(x96502)+E(f331(f331(f151(x96501,x96502,x96503),x96504),x96505),f331(f331(f154(x96501),x96504),x96505))+P24(f331(f331(f333(x96501),f721(x96504,x96503,x96505,x96501,x96502)),f331(f175(x96501),x96505)))
% 162.26/162.08 [9655]~P56(x96551,x96554,x96553,x96552)+~P24(f331(f331(f333(x96551),x96555),x96553))+P24(f331(f331(f333(x96551),f523(x96552,x96553,x96554,x96551,x96555)),x96552))
% 162.26/162.08 [9788]~P24(f331(f331(f333(f890(f891(x97881,a877),f891(x97881,a877))),f331(f331(f261(f891(x97881,a877),f891(x97881,a877)),x97884),x97883)),f322(x97881,x97882)))+~P24(f331(f331(f333(x97881),x97885),x97884))+P24(f331(f331(f333(x97881),f746(x97882,x97883,x97884,x97881,x97885)),x97883))
% 162.26/162.08 [9799]~P107(x97992)+E(f331(f331(f151(x97991,x97992,x97993),x97994),x97995),f331(f331(f154(x97991),x97994),x97995))+~P24(f331(f331(f247(x97992),f331(x97993,x97994)),f331(x97993,f721(x97994,x97993,x97995,x97991,x97992))))
% 162.26/162.08 [9967]P35(x99671,x99672,x99673,x99674,x99675)+~E(f331(f197(f884(x99671)),x99674),f331(f197(f884(x99672)),x99675))+~P24(f331(f331(x99673,f331(f331(f168(x99671),x99674),f700(x99675,x99674,x99673,x99672,x99671))),f331(f331(f168(x99672),x99675),f700(x99675,x99674,x99673,x99672,x99671))))
% 162.26/162.08 [9968]P35(x99681,x99682,x99683,x99684,x99685)+~E(f331(f197(f884(x99681)),x99684),f331(f197(f884(x99682)),x99685))+~P24(f331(f331(x99683,f331(f331(f168(x99681),x99684),f712(x99683,x99685,x99682,x99684,x99681))),f331(f331(f168(x99682),x99685),f712(x99683,x99685,x99682,x99684,x99681))))
% 162.26/162.08 [6569]~P13(x65692,x65695,x65691)+~P24(f331(f62(x65692),x65694))+E(f331(x65691,f331(f331(f309(x65692),x65693),x65694)),f331(f331(f65(x65692,x65692,x65695),x65693),x65694))
% 162.26/162.08 [6570]~E(x65703,x65704)+~E(x65702,x65705)+E(f331(f331(f309(x65701),x65702),f331(f331(f309(x65701),x65703),f196(f891(x65701,a877)))),f331(f331(f309(x65701),x65704),f331(f331(f309(x65701),x65705),f196(f891(x65701,a877)))))
% 162.26/162.08 [6581]P24(f331(x65812,x65815))+E(f179(x65811,x65812,f331(f331(f137(x65811),x65813),x65814)),f179(x65811,x65812,x65813))+~P24(f331(f331(f333(x65811),x65815),f331(f175(x65811),x65813)))
% 162.26/162.08 [6618]E(f331(x66181,x66182),f196(f891(x66183,a877)))+~E(f331(f331(f42(x66184,f891(x66183,a877)),x66185),x66181),f196(f891(x66183,a877)))+~P24(f331(f331(f333(x66184),x66182),x66185))
% 162.26/162.08 [6619]E(f331(x66191,x66192),f256(f891(x66193,a877)))+~E(f331(f331(f43(x66194,f891(x66193,a877)),x66195),x66191),f256(f891(x66193,a877)))+~P24(f331(f331(f333(x66194),x66192),x66195))
% 162.26/162.08 [6910]~P24(f331(f331(f203(x69101),x69103),x69105))+~P24(f331(f331(f203(x69102),x69105),x69104))+P24(f331(f331(f203(f34(x69101,x69102)),x69103),x69104))
% 162.26/162.08 [7115]~E(x71152,x71154)+~P141(x71151)+E(f331(f331(f81(x71151),f331(f331(f82(x71151),x71152),x71153)),f331(f331(f82(x71151),x71154),x71155)),f331(f331(f81(x71151),f331(f331(f82(x71151),x71152),x71155)),f331(f331(f82(x71151),x71154),x71153)))
% 162.26/162.08 [7175]~P27(x71751)+~P24(f331(f331(f333(x71754),x71753),x71755))+P24(f331(f331(f247(x71751),f331(x71752,x71753)),f331(f331(f42(x71754,x71751),x71755),x71752)))
% 162.26/162.08 [7225]~P109(x72251)+P24(f331(f331(f247(x72251),f331(x72252,x72253)),f331(x72254,x72253)))+~P24(f331(f331(f247(f891(x72255,x72251)),x72252),x72254))
% 162.26/162.08 [7331]E(x73311,x73312)+E(x73313,x73311)+~E(f331(f331(f309(x73314),x73311),f331(f331(f309(x73314),x73315),f196(f891(x73314,a877)))),f331(f331(f309(x73314),x73312),f331(f331(f309(x73314),x73313),f196(f891(x73314,a877)))))
% 162.26/162.08 [7332]E(x73321,x73322)+E(x73323,x73321)+~E(f331(f331(f309(x73324),x73323),f331(f331(f309(x73324),x73322),f196(f891(x73324,a877)))),f331(f331(f309(x73324),x73325),f331(f331(f309(x73324),x73321),f196(f891(x73324,a877)))))
% 162.26/162.08 [7333]E(x73331,x73332)+E(x73331,x73333)+~E(f331(f331(f309(x73334),x73333),f331(f331(f309(x73334),x73332),f196(f891(x73334,a877)))),f331(f331(f309(x73334),x73335),f331(f331(f309(x73334),x73331),f196(f891(x73334,a877)))))
% 162.26/162.08 [7334]E(x73341,x73342)+E(x73341,x73343)+~E(f331(f331(f309(x73344),x73341),f331(f331(f309(x73344),x73345),f196(f891(x73344,a877)))),f331(f331(f309(x73344),x73342),f331(f331(f309(x73344),x73343),f196(f891(x73344,a877)))))
% 162.26/162.08 [7862]P21(x78621,x78622,x78623,x78624)+~P21(x78621,x78622,x78623,x78625)+~P24(f331(f331(f247(f891(x78621,a877)),x78624),x78625))
% 162.26/162.08 [7869]~P24(f331(f331(f247(a883),x78695),x78693))+~P24(f331(f331(f331(f331(a205,x78691),x78692),x78695),x78694))+P24(f331(f331(f331(f331(a205,x78691),x78692),x78693),x78694))
% 162.26/162.08 [7960]P24(f331(x79601,x79602))+~P24(f331(f331(f203(x79604),x79602),x79605))+P24(f331(f331(f203(f31(x79601,x79603,x79604)),x79602),x79605))
% 162.26/162.08 [7987]~P24(f331(x79871,x79874))+~P24(f331(f331(f203(x79872),x79874),x79875))+P24(f331(f331(f203(f31(x79871,x79872,x79873)),x79874),x79875))
% 162.26/162.08 [8039]E(x80391,x80392)+~E(f331(f310(x80393,x80394,x80395),x80391),f331(f310(x80393,x80394,x80395),x80392))+~P21(x80393,x80394,x80395,f331(f331(f107(f891(x80393,a877)),x80391),x80392))
% 162.26/162.08 [8118]P24(f331(x81182,x81184))+E(f331(f331(f141(x81181),f331(f197(f884(x81181)),f179(x81181,x81182,x81183))),x81183),f331(f331(f154(x81181),x81184),x81185))+~E(f331(f331(f137(x81181),f179(x81181,x81182,x81183)),f331(f331(f154(x81181),x81184),x81185)),x81183)
% 162.26/162.08 [8149]~P21(x81491,x81492,x81493,x81495)+~P21(x81491,x81492,x81493,x81494)+P21(x81491,x81492,x81493,f331(f331(f108(f891(x81491,a877)),x81494),x81495))
% 162.26/162.08 [8256]~P74(x82561)+E(f331(f331(f81(x82561),f331(x82562,x82563)),f331(f169(x82561),f331(f331(f157(x82564,x82561),x82562),f173(x82564,x82563,x82565)))),f331(f169(x82561),f331(f331(f157(x82564,x82561),x82562),x82565)))+~P24(f331(f331(f333(x82564),x82563),f331(f175(x82564),x82565)))
% 162.26/162.08 [8342]~P107(x83421)+~P29(x83421,f331(f331(f157(x83422,x83421),x83423),x83425))+P29(x83421,f331(f331(f157(x83422,x83421),x83423),f331(f331(f151(x83422,x83421,x83423),x83424),x83425)))
% 162.26/162.08 [8416]P24(f331(x84161,x84162))+P24(f331(f331(f203(x84163),x84162),x84164))+~P24(f331(f331(f203(f31(x84161,x84165,x84163)),x84162),x84164))
% 162.26/162.08 [8427]~P27(x84271)+P24(f331(f331(f247(x84271),f331(f331(f42(x84272,x84271),x84273),x84274)),f331(f331(f42(x84272,x84271),x84275),x84274)))+~P24(f331(f331(f247(f891(x84272,a877)),x84273),x84275))
% 162.26/162.08 [8428]~P27(x84281)+P24(f331(f331(f247(x84281),f331(f331(f43(x84282,x84281),x84283),x84284)),f331(f331(f43(x84282,x84281),x84285),x84284)))+~P24(f331(f331(f247(f891(x84282,a877)),x84285),x84283))
% 162.26/162.08 [8441]~P24(f331(x84414,x84412))+P24(f331(f331(f203(x84411),x84412),x84413))+~P24(f331(f331(f203(f31(x84414,x84411,x84415)),x84412),x84413))
% 162.26/162.08 [8465]~P107(x84653)+P24(f331(f140(x84651),x84652))+~P24(f331(f140(x84651),f331(f331(f151(x84651,x84653,x84654),x84655),x84652)))
% 162.26/162.08 [8475]P24(f331(f331(f203(x84751),x84752),x84753))+P24(f331(f331(f203(x84754),x84752),x84753))+~P24(f331(f331(f203(f31(x84755,x84751,x84754)),x84752),x84753))
% 162.26/162.08 [8606]~P107(x86061)+~P24(f331(f331(f333(x86062),x86063),f331(f175(x86062),x86064)))+~P24(f331(f140(x86062),f331(f331(f151(x86062,x86061,x86065),x86063),x86064)))
% 162.26/162.08 [8680]~P107(x86801)+P29(x86801,f331(f331(f157(x86802,x86801),x86803),x86804))+~P29(x86801,f331(f331(f157(x86802,x86801),x86803),f331(f331(f151(x86802,x86801,x86803),x86805),x86804)))
% 162.26/162.08 [8772]~P107(x87722)+E(f331(f331(f151(x87721,x87722,x87723),x87724),x87725),f152(x87721,x87722,x87723,x87724,x87725))+P24(f331(f331(f333(x87722),f331(x87723,x87724)),f331(f310(x87721,x87722,x87723),f331(f175(x87721),x87725))))
% 162.26/162.08 [8849]~P107(x88492)+E(f152(x88491,x88492,x88493,x88494,x88495),x88495)+~P24(f331(f331(f333(x88492),f331(x88493,x88494)),f331(f310(x88491,x88492,x88493),f331(f175(x88491),x88495))))
% 162.26/162.08 [8865]~P21(x88652,x88651,x88653,x88655)+P24(f331(f331(f248(f891(x88651,a877)),f331(f310(x88652,x88651,x88653),x88654)),f331(f310(x88652,x88651,x88653),x88655)))+~P24(f331(f331(f248(f891(x88652,a877)),x88654),x88655))
% 162.26/162.08 [9030]~P21(x90301,x90302,x90303,f256(f891(x90301,a877)))+~P24(f331(f331(f247(f891(x90302,a877)),x90304),f331(f310(x90301,x90302,x90303),x90305)))+P24(f331(f331(f247(f891(x90301,a877)),f331(f311(x90301,x90302,x90303),x90304)),x90305))
% 162.26/162.08 [9048]~E(f331(f310(x90483,x90481,x90484),f256(f891(x90483,a877))),f256(f891(x90481,a877)))+P24(f331(f331(f247(f891(x90481,a877)),x90482),f331(f310(x90483,x90481,x90484),x90485)))+~P24(f331(f331(f247(f891(x90483,a877)),f331(f311(x90483,x90481,x90484),x90482)),x90485))
% 162.26/162.08 [9066]~E(f331(f239(x90662),x90664),f331(f331(f180(x90661,x90662),x90665),x90663))+~P24(f331(f140(x90661),f331(f331(f157(f890(x90661,x90662),x90661),f260(x90661,x90662)),x90665)))+P24(f331(f331(f333(f890(x90661,x90662)),f331(f331(f261(x90661,x90662),x90663),x90664)),f331(f175(f890(x90661,x90662)),x90665)))
% 162.26/162.08 [9159]~P21(x91591,x91594,x91595,f256(f891(x91591,a877)))+~P24(f331(f331(f247(f891(x91594,a877)),f331(f310(x91591,x91594,x91595),x91592)),f331(f310(x91591,x91594,x91595),x91593)))+P24(f331(f331(f247(f891(x91591,a877)),x91592),x91593))
% 162.26/162.08 [9223]E(f331(f239(x92231),x92232),f331(f331(f180(x92233,x92231),x92234),x92235))+~P24(f331(f140(x92233),f331(f331(f157(f890(x92233,x92231),x92233),f260(x92233,x92231)),x92234)))+~P24(f331(f331(f333(f890(x92233,x92231)),f331(f331(f261(x92233,x92231),x92235),x92232)),f331(f175(f890(x92233,x92231)),x92234)))
% 162.26/162.08 [9225]E(f331(f331(f180(x92251,x92252),x92253),x92254),f331(f239(x92252),x92255))+~P24(f331(f140(x92251),f331(f331(f157(f890(x92251,x92252),x92251),f260(x92251,x92252)),x92253)))+~P24(f331(f331(f333(f890(x92251,x92252)),f331(f331(f261(x92251,x92252),x92254),x92255)),f331(f175(f890(x92251,x92252)),x92253)))
% 162.26/162.08 [9283]~P80(x92831)+~E(f331(x92833,f679(x92833,x92834,x92835,x92832,x92831)),f2(x92831))+E(f331(f169(x92831),f331(f331(f157(x92832,x92831),x92833),f331(f139(x92832,x92834),x92835))),f331(f169(x92831),f331(f331(f157(x92832,x92831),x92833),x92835)))
% 162.26/162.08 [9455]~P12(x94551,x94552,x94553)+~P24(f331(f62(x94551),x94555))+P24(f331(f67(x94551,x94552,x94553,x94554,x94555),f331(f331(f65(x94551,x94552,x94553),x94554),x94555)))
% 162.26/162.08 [9548]P24(f331(x95481,f801(x95482,x95481,x95483,x95484,x95485)))+~P24(f331(f331(f247(f891(x95485,a877)),x95484),x95483))+P24(f331(f331(f247(f891(x95485,a877)),f331(f331(f108(f891(x95485,a877)),x95484),f331(f253(x95485),x95481))),f331(f331(f108(f891(x95485,a877)),x95483),f331(f253(x95485),x95482))))
% 162.26/162.08 [9562]~P80(x95621)+~P24(f331(x95624,f679(x95623,x95624,x95625,x95622,x95621)))+E(f331(f169(x95621),f331(f331(f157(x95622,x95621),x95623),f331(f139(x95622,x95624),x95625))),f331(f169(x95621),f331(f331(f157(x95622,x95621),x95623),x95625)))
% 162.26/162.08 [9653]~P27(x96535)+P24(f331(f331(f333(x96531),f508(x96532,x96533,x96531,x96534,x96535)),x96533))+P24(f331(f331(f247(x96535),x96534),f331(f331(f43(x96531,x96535),x96533),x96532)))
% 162.26/162.08 [9656]~P80(x96561)+E(f331(f169(x96561),f331(f331(f157(x96562,x96561),x96563),f331(f139(x96562,x96564),x96565))),f331(f169(x96561),f331(f331(f157(x96562,x96561),x96563),x96565)))+P24(f331(f331(f333(x96562),f679(x96563,x96564,x96565,x96562,x96561)),f331(f175(x96562),x96565)))
% 162.26/162.08 [9663]~P24(f331(x96635,f801(x96635,x96633,x96634,x96632,x96631)))+~P24(f331(f331(f247(f891(x96631,a877)),x96632),x96634))+P24(f331(f331(f247(f891(x96631,a877)),f331(f331(f108(f891(x96631,a877)),x96632),f331(f253(x96631),x96633))),f331(f331(f108(f891(x96631,a877)),x96634),f331(f253(x96631),x96635))))
% 162.26/162.08 [9698]P35(x96981,x96982,x96983,x96984,x96985)+~E(f331(f197(f884(x96982)),x96985),f331(f197(f884(x96981)),x96984))+P24(f331(f331(f248(a883),f700(x96985,x96984,x96983,x96982,x96981)),f331(f197(f884(x96981)),x96984)))
% 162.26/162.08 [9699]P35(x96991,x96992,x96993,x96994,x96995)+~E(f331(f197(f884(x96992)),x96995),f331(f197(f884(x96991)),x96994))+P24(f331(f331(f248(a883),f712(x96993,x96995,x96992,x96994,x96991)),f331(f197(f884(x96991)),x96994)))
% 162.26/162.08 [9732]P24(f331(f331(f333(x97321),f801(x97322,x97323,x97324,x97325,x97321)),x97325))+~P24(f331(f331(f247(f891(x97321,a877)),x97325),x97324))+P24(f331(f331(f247(f891(x97321,a877)),f331(f331(f108(f891(x97321,a877)),x97325),f331(f253(x97321),x97323))),f331(f331(f108(f891(x97321,a877)),x97324),f331(f253(x97321),x97322))))
% 162.26/162.08 [9800]~P27(x98001)+~P24(f331(f331(f247(x98001),x98002),f331(x98005,f508(x98005,x98004,x98003,x98002,x98001))))+P24(f331(f331(f247(x98001),x98002),f331(f331(f43(x98003,x98001),x98004),x98005)))
% 162.26/162.08 [9829]~P73(x98291)+~P24(f331(f62(x98292),x98295))+E(f331(f331(f331(f66(x98291,x98292,f82(x98291)),f331(f331(f18(x98292,x98291,x98291),f331(f331(f8(x98291,f891(x98291,x98291),x98292),f82(x98291)),x98293)),x98294)),f79(x98291)),x98295),f331(f331(f82(x98291),f331(f331(f331(f66(x98291,x98292,f82(x98291)),x98293),f79(x98291)),x98295)),f331(f331(f331(f66(x98291,x98292,f82(x98291)),x98294),f79(x98291)),x98295)))
% 162.26/162.08 [9889]~P24(f331(f331(f333(f890(f891(x98891,a877),f891(x98891,a877))),f331(f331(f261(f891(x98891,a877),f891(x98891,a877)),x98895),x98894)),f322(x98891,x98893)))+~P24(f331(f331(f333(x98891),x98892),x98895))+P24(f331(f331(f333(f890(x98891,x98891)),f331(f331(f261(x98891,x98891),x98892),f746(x98893,x98894,x98895,x98891,x98892))),x98893))
% 162.26/162.08 [10000]~P24(f331(f331(f333(f890(f884(x100001),f884(x100001))),f331(f331(f261(f884(x100001),f884(x100001)),f331(f331(f137(x100001),x100005),x100002)),f331(f331(f137(x100001),x100005),x100003))),f150(x100001,x100004)))+P24(f331(f331(f333(f890(f884(x100001),f884(x100001))),f331(f331(f261(f884(x100001),f884(x100001)),x100002),x100003)),f150(x100001,x100004)))+P24(f331(f331(f333(f890(x100001,x100001)),f331(f331(f261(x100001,x100001),f654(x100004,x100003,x100002,x100005,x100001)),f654(x100004,x100003,x100002,x100005,x100001))),x100004))
% 162.26/162.08 [7155]~E(f331(f197(f884(x71551)),x71553),f331(f197(f884(x71552)),x71554))+E(f331(f331(f180(x71551,x71552),f331(f331(f184(x71551,x71552),x71553),x71554)),x71555),f199(x71552))+P24(f331(f331(f333(x71551),x71555),f331(f175(x71551),x71553)))
% 162.26/162.08 [7228]~E(x72283,x72285)+E(f331(f331(f168(x72281),f331(f331(f162(x72281,x72282),x72283),x72284)),x72285),x72284)+~P24(f331(f331(f248(a883),x72283),f331(f197(f884(x72281)),x72282)))
% 162.26/162.08 [7326]~E(f331(f331(f137(x73261),x73262),x73264),f331(f331(f137(x73261),x73263),x73265))+E(f331(f331(f176(x73261),f331(f197(f884(x73261)),x73262)),x73263),x73262)+P24(f331(f331(f247(a883),f331(f197(f884(x73261)),x73263)),f331(f197(f884(x73261)),x73262)))
% 162.26/162.08 [7343]~E(x73435,x73432)+P24(f331(x73431,x73432))+P24(f331(f331(f331(f331(a205,f33(x73431,x73433)),x73432),x73434),x73435))
% 162.26/162.08 [7828]~E(f331(f331(f137(x78281),x78282),x78284),f331(f331(f137(x78281),x78283),x78285))+E(f331(f331(f176(x78281),f331(f197(f884(x78281)),x78282)),x78283),x78282)+~P24(f331(f331(f247(a883),f331(f197(f884(x78281)),x78282)),f331(f197(f884(x78281)),x78283)))
% 162.26/162.08 [7852]~P24(f331(f62(x78521),f331(x78524,x78525)))+~P24(f331(f331(f333(x78522),x78525),x78523))+P24(f331(f62(x78521),f331(f331(f43(x78522,f891(x78521,a877)),x78523),x78524)))
% 162.26/162.08 [7900]~E(f331(f197(f884(x79001)),x79002),f331(f197(f884(x79003)),x79004))+~E(f331(f331(f180(x79001,x79003),f331(f331(f184(x79001,x79003),x79002),x79004)),x79005),f199(x79003))+~P24(f331(f331(f333(x79001),x79005),f331(f175(x79001),x79002)))
% 162.26/162.08 [8023]~P48(x80231,x80233,x80235)+~P48(x80231,x80232,x80234)+P48(x80231,f331(f331(f107(f891(x80231,a877)),x80232),x80233),f331(f331(f107(f891(f890(x80231,x80231),a877)),x80234),x80235))
% 162.26/162.08 [8024]~P48(x80241,x80243,x80245)+~P48(x80241,x80242,x80244)+P48(x80241,f331(f331(f108(f891(x80241,a877)),x80242),x80243),f331(f331(f108(f891(f890(x80241,x80241),a877)),x80244),x80245))
% 162.26/162.08 [8112]E(x81121,x81122)+P24(f331(x81123,x81121))+~P24(f331(f331(f331(f331(a205,f33(x81123,x81124)),x81121),x81125),x81122))
% 162.26/162.08 [8380]E(f331(f331(f261(x83801,x83802),f331(f331(f168(x83801),x83803),x83804)),f331(f331(f168(x83802),x83805),x83804)),f331(f331(f168(f890(x83801,x83802)),f331(f331(f184(x83801,x83802),x83803),x83805)),x83804))+~P24(f331(f331(f248(a883),x83804),f331(f197(f884(x83801)),x83803)))+~P24(f331(f331(f248(a883),x83804),f331(f197(f884(x83802)),x83805)))
% 162.26/162.08 [8541]~P48(x85411,x85413,x85414)+P24(f331(f331(f333(x85411),x85412),x85413))+~P24(f331(f331(f333(f890(x85411,x85411)),f331(f331(f261(x85411,x85411),x85415),x85412)),x85414))
% 162.26/162.08 [8542]~P48(x85421,x85423,x85424)+P24(f331(f331(f333(x85421),x85422),x85423))+~P24(f331(f331(f333(f890(x85421,x85421)),f331(f331(f261(x85421,x85421),x85422),x85425)),x85424))
% 162.26/162.08 [8543]~P6(x85431,x85433,x85434)+P24(f331(f331(f333(x85431),x85432),x85433))+~P24(f331(f331(f333(f890(x85431,x85431)),f331(f331(f261(x85431,x85431),x85435),x85432)),x85434))
% 162.26/162.08 [8544]~P6(x85441,x85443,x85444)+P24(f331(f331(f333(x85441),x85442),x85443))+~P24(f331(f331(f333(f890(x85441,x85441)),f331(f331(f261(x85441,x85441),x85442),x85445)),x85444))
% 162.26/162.08 [8796]~P6(x87961,x87965,x87962)+E(f331(f285(x87961,x87961,x87962),f331(f331(f309(x87961),x87963),f196(f891(x87961,a877)))),f331(f285(x87961,x87961,x87962),f331(f331(f309(x87961),x87964),f196(f891(x87961,a877)))))+~P24(f331(f331(f333(f890(x87961,x87961)),f331(f331(f261(x87961,x87961),x87963),x87964)),x87962))
% 162.26/162.08 [8881]~P24(f331(f331(f331(f331(a205,x88812),x88813),x88814),x88815))+~P24(f331(f331(f331(f331(a205,f33(x88811,x88812)),x88815),x88814),x88813))+P24(f331(f331(f331(f331(a205,f33(x88811,x88812)),x88813),x88814),x88813))
% 162.26/162.08 [8990]P24(f331(x89901,x89902))+~P24(f331(f331(f333(x89903),x89902),x89905))+P24(f331(f331(f333(x89903),f838(x89901,x89904,x89905,x89903)),f331(f331(f107(f891(x89903,a877)),x89905),x89904)))
% 162.26/162.08 [8991]P24(f331(x89911,x89912))+~P24(f331(f331(f333(x89913),x89912),x89914))+P24(f331(f331(f333(x89913),f838(x89911,x89914,x89915,x89913)),f331(f331(f107(f891(x89913,a877)),x89915),x89914)))
% 162.26/162.08 [8999]~P24(f331(x89992,x89995))+~P24(f331(f331(f333(x89991),x89995),x89994))+P24(f331(f331(f333(x89991),f837(x89992,x89993,x89994,x89991)),f331(f331(f107(f891(x89991,a877)),x89994),x89993)))
% 162.26/162.08 [9000]~P24(f331(x90002,x90005))+~P24(f331(f331(f333(x90001),x90005),x90003))+P24(f331(f331(f333(x90001),f837(x90002,x90003,x90004,x90001)),f331(f331(f107(f891(x90001,a877)),x90004),x90003)))
% 162.26/162.08 [9015]~P24(f331(f331(f247(f891(x90151,a877)),x90155),x90153))+~P24(f331(f331(f247(f891(x90151,a877)),x90152),x90154))+P24(f331(f331(f247(f891(x90151,a877)),f331(f331(f22(f891(x90151,a877)),x90152),x90153)),f331(f331(f22(f891(x90151,a877)),x90154),x90155)))
% 162.26/162.08 [9016]~P24(f331(f331(f247(f891(x90161,a877)),x90163),x90165))+~P24(f331(f331(f247(f891(x90161,a877)),x90162),x90164))+P24(f331(f331(f247(f891(x90161,a877)),f331(f331(f107(f891(x90161,a877)),x90162),x90163)),f331(f331(f107(f891(x90161,a877)),x90164),x90165)))
% 162.26/162.08 [9017]~P24(f331(f331(f247(f891(x90171,a877)),x90173),x90175))+~P24(f331(f331(f247(f891(x90171,a877)),x90172),x90174))+P24(f331(f331(f247(f891(x90171,a877)),f331(f331(f108(f891(x90171,a877)),x90172),x90173)),f331(f331(f108(f891(x90171,a877)),x90174),x90175)))
% 162.26/162.08 [9096]~E(f331(f197(f884(x90961)),x90963),f331(f197(f884(x90962)),x90964))+E(f331(f331(f180(x90961,x90962),f331(f331(f184(x90961,x90962),x90963),x90964)),x90965),f331(f239(x90962),f613(x90965,x90964,x90962,x90963,x90961)))+~P24(f331(f331(f333(x90961),x90965),f331(f175(x90961),x90963)))
% 162.26/162.08 [9101]P24(f331(f331(f333(f890(x91011,x91011)),f331(f331(f261(x91011,x91011),x91012),x91013)),f325(x91011,x91014,x91015)))+~P24(f331(f331(f247(a883),f331(x91014,x91012)),f331(x91014,x91013)))+~P24(f331(f331(f333(f890(x91011,x91011)),f331(f331(f261(x91011,x91011),x91012),x91013)),x91015))
% 162.26/162.08 [9298]P24(f331(f331(f333(f890(x92981,x92981)),f331(f331(f261(x92981,x92981),x92982),x92983)),f307(x92981,x92984)))+~P24(f331(f331(f333(f890(x92981,x92981)),f331(f331(f261(x92981,x92981),x92982),x92985)),f307(x92981,x92984)))+~P24(f331(f331(f333(f890(x92981,x92981)),f331(f331(f261(x92981,x92981),x92985),x92983)),x92984))
% 162.26/162.08 [9299]P24(f331(f331(f333(f890(x92991,x92991)),f331(f331(f261(x92991,x92991),x92992),x92993)),f307(x92991,x92994)))+~P24(f331(f331(f333(f890(x92991,x92991)),f331(f331(f261(x92991,x92991),x92995),x92993)),f307(x92991,x92994)))+~P24(f331(f331(f333(f890(x92991,x92991)),f331(f331(f261(x92991,x92991),x92992),x92995)),x92994))
% 162.26/162.08 [9392]E(x93921,x93922)+E(f331(a118,f767(x93923,x93924,x93921,x93922,x93925)),x93924)+~P24(f331(f331(f333(f890(x93925,x93925)),f331(f331(f261(x93925,x93925),x93922),x93921)),f331(f331(f191(f890(x93925,x93925),a877),x93924),x93923)))
% 162.26/162.08 [9393]E(x93931,x93932)+E(f331(a118,f770(x93933,x93934,x93931,x93932,x93935)),x93934)+~P24(f331(f331(f333(f890(x93935,x93935)),f331(f331(f261(x93935,x93935),x93932),x93931)),f331(f331(f191(f890(x93935,x93935),a877),x93934),x93933)))
% 162.26/162.08 [9394]E(x93941,f2(a883))+E(f331(a118,f767(x93942,x93941,x93943,x93944,x93945)),x93941)+~P24(f331(f331(f333(f890(x93945,x93945)),f331(f331(f261(x93945,x93945),x93944),x93943)),f331(f331(f191(f890(x93945,x93945),a877),x93941),x93942)))
% 162.26/162.08 [9395]E(x93951,f2(a883))+E(f331(a118,f770(x93952,x93951,x93953,x93954,x93955)),x93951)+~P24(f331(f331(f333(f890(x93955,x93955)),f331(f331(f261(x93955,x93955),x93954),x93953)),f331(f331(f191(f890(x93955,x93955),a877),x93951),x93952)))
% 162.26/162.08 [9407]P24(f331(f331(f333(f890(x94071,x94071)),f331(f331(f261(x94071,x94071),x94072),x94073)),f331(f331(f288(x94071,x94071,x94071),x94074),f307(x94071,x94074))))+~P24(f331(f331(f333(f890(x94071,x94071)),f331(f331(f261(x94071,x94071),x94072),x94075)),x94074))+~P24(f331(f331(f333(f890(x94071,x94071)),f331(f331(f261(x94071,x94071),x94075),x94073)),x94074))
% 162.26/162.08 [9412]~P24(f331(f331(f333(f890(x94121,x94121)),f331(f331(f261(x94121,x94121),x94122),x94125)),f307(x94121,x94124)))+P24(f331(f331(f333(f890(x94121,x94121)),f331(f331(f261(x94121,x94121),x94122),x94123)),f331(f331(f288(x94121,x94121,x94121),x94124),f307(x94121,x94124))))+~P24(f331(f331(f333(f890(x94121,x94121)),f331(f331(f261(x94121,x94121),x94125),x94123)),x94124))
% 162.26/162.08 [9451]~P6(x94511,x94515,x94512)+~P24(f331(f331(f333(f890(x94511,x94511)),f331(f331(f261(x94511,x94511),x94513),x94514)),x94512))+P24(f331(f331(f247(f891(x94511,a877)),f331(f285(x94511,x94511,x94512),f331(f331(f309(x94511),x94513),f196(f891(x94511,a877))))),f331(f285(x94511,x94511,x94512),f331(f331(f309(x94511),x94514),f196(f891(x94511,a877))))))
% 162.26/162.08 [9477]E(x94771,x94772)+P24(f331(f331(f331(f331(a205,x94773),x94771),x94774),f597(x94772,x94774,x94771,x94773,x94775)))+~P24(f331(f331(f331(f331(a205,f33(x94775,x94773)),x94771),x94774),x94772))
% 162.26/162.08 [9480]~P24(f331(x94805,x94802))+P24(f331(f331(f331(f331(a205,x94801),x94802),x94803),f597(x94804,x94803,x94802,x94801,x94805)))+~P24(f331(f331(f331(f331(a205,f33(x94805,x94801)),x94802),x94803),x94804))
% 162.26/162.08 [9520]P24(f331(f331(f333(f890(x95201,x95201)),f331(f331(f261(x95201,x95201),x95202),x95203)),f331(f331(f288(x95201,x95201,x95201),x95204),f307(x95201,x95204))))+~P24(f331(f331(f333(f890(x95201,x95201)),f331(f331(f261(x95201,x95201),x95202),x95205)),f331(f331(f288(x95201,x95201,x95201),x95204),f307(x95201,x95204))))+~P24(f331(f331(f333(f890(x95201,x95201)),f331(f331(f261(x95201,x95201),x95205),x95203)),x95204))
% 162.26/162.08 [9521]P24(f331(f331(f333(f890(x95211,x95211)),f331(f331(f261(x95211,x95211),x95212),x95213)),f331(f331(f288(x95211,x95211,x95211),x95214),f307(x95211,x95214))))+~P24(f331(f331(f333(f890(x95211,x95211)),f331(f331(f261(x95211,x95211),x95215),x95213)),f331(f331(f288(x95211,x95211,x95211),x95214),f307(x95211,x95214))))+~P24(f331(f331(f333(f890(x95211,x95211)),f331(f331(f261(x95211,x95211),x95212),x95215)),x95214))
% 162.26/162.08 [9569]~P24(f331(f67(x95691,x95691,x95694,x95692,x95693),x95695))+P24(f331(f331(f333(x95691),x95692),x95693))+P24(f331(f63(x95691,x95694,f331(f331(f309(x95691),x95692),x95693)),x95695))
% 162.26/162.08 [9616]~E(f331(f310(x96163,x96162,x96165),x96164),x96161)+E(x96161,f196(f891(x96162,a877)))+P24(f331(f331(f247(f891(x96163,a877)),f331(f310(x96162,x96163,f482(x96164,x96163,x96162,x96161)),x96161)),x96164))
% 162.26/162.08 [9666]~P27(x96665)+P24(f331(f331(f333(x96661),f360(x96662,x96663,x96664,x96661,x96665)),x96664))+P24(f331(f331(f247(x96665),f331(f331(f42(x96661,x96665),x96664),x96663)),x96662))
% 162.26/162.08 [9718]P35(x97181,x97182,x97183,x97184,x97185)+~E(f331(f197(f884(x97181)),x97184),f331(f197(f884(x97182)),x97185))+P24(f331(f331(f333(f890(x97181,x97182)),f692(x97185,x97184,x97183,x97182,x97181)),f331(f175(f890(x97181,x97182)),f331(f331(f184(x97181,x97182),x97184),x97185))))
% 162.26/162.08 [9719]P35(x97191,x97192,x97193,x97194,x97195)+~E(f331(f197(f884(x97191)),x97194),f331(f197(f884(x97192)),x97195))+P24(f331(f331(f333(f890(x97191,x97192)),f699(x97193,x97195,x97194,x97192,x97191)),f331(f175(f890(x97191,x97192)),f331(f331(f184(x97191,x97192),x97194),x97195))))
% 162.26/162.08 [9856]E(x98561,x98562)+P24(f331(f331(f331(f331(a205,f33(x98563,x98564)),f597(x98561,x98565,x98562,x98564,x98563)),x98565),x98561))+~P24(f331(f331(f331(f331(a205,f33(x98563,x98564)),x98562),x98565),x98561))
% 162.26/162.08 [9858]~P24(f331(x98581,x98585))+P24(f331(f331(f331(f331(a205,f33(x98581,x98582)),f597(x98583,x98584,x98585,x98582,x98581)),x98584),x98583))+~P24(f331(f331(f331(f331(a205,f33(x98581,x98582)),x98585),x98584),x98583))
% 162.26/162.08 [9865]E(x98651,x98652)+P24(f331(f331(f333(f890(x98653,x98653)),f331(f331(f261(x98653,x98653),x98651),f771(x98654,x98655,x98652,x98651,x98653))),x98654))+~P24(f331(f331(f333(f890(x98653,x98653)),f331(f331(f261(x98653,x98653),x98651),x98652)),f331(f331(f191(f890(x98653,x98653),a877),x98655),x98654)))
% 162.26/162.08 [9866]E(x98661,f2(a883))+P24(f331(f331(f333(f890(x98662,x98662)),f331(f331(f261(x98662,x98662),x98663),f771(x98664,x98661,x98665,x98663,x98662))),x98664))+~P24(f331(f331(f333(f890(x98662,x98662)),f331(f331(f261(x98662,x98662),x98663),x98665)),f331(f331(f191(f890(x98662,x98662),a877),x98661),x98664)))
% 162.26/162.08 [9909]~P27(x99091)+~P24(f331(f331(f247(x99091),f331(x99094,f360(x99095,x99094,x99093,x99092,x99091))),x99095))+P24(f331(f331(f247(x99091),f331(f331(f42(x99092,x99091),x99093),x99094)),x99095))
% 162.26/162.08 [9934]E(x99341,x99342)+P24(f331(f331(f333(f890(x99343,x99343)),f331(f331(f261(x99343,x99343),f768(x99344,x99345,x99341,x99342,x99343)),x99341)),x99344))+~P24(f331(f331(f333(f890(x99343,x99343)),f331(f331(f261(x99343,x99343),x99342),x99341)),f331(f331(f191(f890(x99343,x99343),a877),x99345),x99344)))
% 162.26/162.08 [9935]E(x99351,f2(a883))+P24(f331(f331(f333(f890(x99352,x99352)),f331(f331(f261(x99352,x99352),f768(x99353,x99351,x99354,x99355,x99352)),x99354)),x99353))+~P24(f331(f331(f333(f890(x99352,x99352)),f331(f331(f261(x99352,x99352),x99355),x99354)),f331(f331(f191(f890(x99352,x99352),a877),x99351),x99353)))
% 162.26/162.08 [9945]E(x99451,x99452)+P24(f331(f331(f333(f890(x99453,x99453)),f331(f331(f261(x99453,x99453),x99451),f768(x99454,x99455,x99452,x99451,x99453))),f331(f331(f191(f890(x99453,x99453),a877),f767(x99454,x99455,x99452,x99451,x99453)),x99454)))+~P24(f331(f331(f333(f890(x99453,x99453)),f331(f331(f261(x99453,x99453),x99451),x99452)),f331(f331(f191(f890(x99453,x99453),a877),x99455),x99454)))
% 162.26/162.08 [9946]E(x99461,f2(a883))+P24(f331(f331(f333(f890(x99462,x99462)),f331(f331(f261(x99462,x99462),x99463),f768(x99464,x99461,x99465,x99463,x99462))),f331(f331(f191(f890(x99462,x99462),a877),f767(x99464,x99461,x99465,x99463,x99462)),x99464)))+~P24(f331(f331(f333(f890(x99462,x99462)),f331(f331(f261(x99462,x99462),x99463),x99465)),f331(f331(f191(f890(x99462,x99462),a877),x99461),x99464)))
% 162.26/162.08 [9992]E(x99921,x99922)+P24(f331(f331(f333(f890(x99923,x99923)),f331(f331(f261(x99923,x99923),f771(x99924,x99925,x99921,x99922,x99923)),x99921)),f331(f331(f191(f890(x99923,x99923),a877),f770(x99924,x99925,x99921,x99922,x99923)),x99924)))+~P24(f331(f331(f333(f890(x99923,x99923)),f331(f331(f261(x99923,x99923),x99922),x99921)),f331(f331(f191(f890(x99923,x99923),a877),x99925),x99924)))
% 162.26/162.08 [9993]E(x99931,f2(a883))+P24(f331(f331(f333(f890(x99932,x99932)),f331(f331(f261(x99932,x99932),f771(x99933,x99931,x99934,x99935,x99932)),x99934)),f331(f331(f191(f890(x99932,x99932),a877),f770(x99933,x99931,x99934,x99935,x99932)),x99933)))+~P24(f331(f331(f333(f890(x99932,x99932)),f331(f331(f261(x99932,x99932),x99935),x99934)),f331(f331(f191(f890(x99932,x99932),a877),x99931),x99933)))
% 162.26/162.08 [10029]~P74(x100292)+~P24(f331(f62(x100291),x100295))+E(f331(f331(f6(x100291,x100292),f331(f331(f7(x100291,x100292,x100292),f331(f331(f18(x100291,x100292,f891(x100292,x100292)),f331(f331(f8(a877,f891(x100292,f891(x100292,x100292)),x100291),f102(x100292)),f331(f331(f7(x100291,f891(x100291,a877),a877),f333(x100291)),x100293))),x100294)),f2(x100292))),x100295),f331(f331(f6(x100291,x100292),x100294),f331(f331(f108(f891(x100291,a877)),x100295),x100293)))
% 162.26/162.08 [8603]~P73(x86031)+~P24(f331(f62(x86034),x86035))+E(f331(f331(f82(x86031),f331(x86032,x86033)),f331(f331(f9(x86034,x86031),x86032),f331(f331(f22(f891(x86034,a877)),x86035),f331(f331(f309(x86034),x86033),f196(f891(x86034,a877)))))),f331(f331(f9(x86034,x86031),x86032),f331(f331(f309(x86034),x86033),x86035)))
% 162.26/162.08 [8604]~P74(x86041)+~P24(f331(f62(x86044),x86045))+E(f331(f331(f81(x86041),f331(x86042,x86043)),f331(f331(f6(x86044,x86041),x86042),f331(f331(f22(f891(x86044,a877)),x86045),f331(f331(f309(x86044),x86043),f196(f891(x86044,a877)))))),f331(f331(f6(x86044,x86041),x86042),f331(f331(f309(x86044),x86043),x86045)))
% 162.26/162.08 [8920]~P107(x89202)+~P29(x89202,f331(f172(x89202),f331(f331(f157(x89201,x89202),x89204),x89205)))+E(f331(f139(x89201,f331(f331(f8(x89202,a877,x89201),f331(f248(x89202),x89203)),x89204)),x89205),f179(x89201,f331(f331(f8(x89202,a877,x89201),f331(f248(x89202),x89203)),x89204),x89205))
% 162.26/162.08 [8945]~P74(x89451)+E(f331(f331(f81(x89451),f331(f331(f6(a883,x89451),x89452),f302(a883,x89453,x89454))),f331(f331(f6(a883,x89451),x89452),f302(a883,f331(f331(f81(a883),x89454),f79(a883)),f331(f331(f81(a883),x89454),x89455)))),f331(f331(f6(a883,x89451),x89452),f302(a883,x89453,f331(f331(f81(a883),x89454),x89455))))+~P24(f331(f331(f247(a883),x89453),f331(f331(f81(a883),x89454),f79(a883))))
% 162.26/162.08 [8946]~P24(f331(f331(f333(x89461),x89464),x89465))+~P24(f331(f331(f247(f891(x89461,a877)),f331(f175(x89461),x89462)),x89465))+P24(f331(f331(f247(f891(x89461,a877)),f331(f175(x89461),f331(f331(f162(x89461,x89462),x89463),x89464))),x89465))
% 162.26/162.08 [9169]~P27(x91692)+~P24(f331(f62(x91691),x91695))+E(f331(f331(f65(x91691,x91692,f331(f331(f8(x91692,f891(x91692,x91692),x91691),f107(x91692)),x91693)),x91694),x91695),f331(f331(f107(x91692),x91694),f331(f331(f42(x91691,x91692),x91695),x91693)))
% 162.26/162.08 [9170]~P27(x91702)+~P24(f331(f62(x91701),x91705))+E(f331(f331(f65(x91701,x91702,f331(f331(f8(x91702,f891(x91702,x91702),x91701),f108(x91702)),x91703)),x91704),x91705),f331(f331(f108(x91702),x91704),f331(f331(f43(x91701,x91702),x91705),x91703)))
% 162.26/162.08 [9215]E(f331(x92151,x92152),f331(x92151,x92153))+P24(f331(f331(f248(a883),f331(x92151,x92152)),f331(x92151,x92153)))+~P24(f331(f331(f333(f890(x92154,x92154)),f331(f331(f261(x92154,x92154),x92152),x92153)),f156(x92154,f331(f331(f154(f891(x92154,a883)),x92151),x92155))))
% 162.26/162.08 [9247]~E(f331(x92474,x92472),f331(x92474,x92473))+~P24(f331(f331(f333(f890(x92471,x92471)),f331(f331(f261(x92471,x92471),x92472),x92473)),f156(x92471,x92475)))+P24(f331(f331(f333(f890(x92471,x92471)),f331(f331(f261(x92471,x92471),x92472),x92473)),f156(x92471,f331(f331(f154(f891(x92471,a883)),x92474),x92475))))
% 162.26/162.08 [9269]~P21(x92691,x92692,x92693,x92695)+P21(x92691,x92692,x92693,f331(f331(f309(x92691),x92694),x92695))+P24(f331(f331(f333(x92692),f331(x92693,x92694)),f331(f310(x92691,x92692,x92693),f331(f331(f22(f891(x92691,a877)),x92695),f331(f331(f309(x92691),x92694),f196(f891(x92691,a877)))))))
% 162.26/162.08 [9275]P24(f331(x92752,x92755))+~P24(f331(f331(f333(x92751),x92755),f331(f175(x92751),x92753)))+E(f331(f331(f141(x92751),f331(f197(f884(x92751)),f179(x92751,x92752,f331(f331(f137(x92751),x92753),x92754)))),f331(f331(f137(x92751),x92753),x92754)),f331(f331(f137(x92751),f331(f331(f141(x92751),f331(f197(f884(x92751)),f179(x92751,x92752,x92753))),x92753)),x92754))
% 162.26/162.08 [9279]~P24(f331(f331(f333(f890(x92791,x92791)),f331(f331(f261(x92791,x92791),x92792),x92793)),f156(x92791,x92795)))+~P24(f331(f331(f247(a883),f331(x92794,x92792)),f331(x92794,x92793)))+P24(f331(f331(f333(f890(x92791,x92791)),f331(f331(f261(x92791,x92791),x92792),x92793)),f156(x92791,f331(f331(f154(f891(x92791,a883)),x92794),x92795))))
% 162.26/162.08 [9344]P24(f331(f331(f333(f890(x93444,x93444)),f331(f331(f261(x93444,x93444),x93442),x93443)),f156(x93444,x93445)))+P24(f331(f331(f248(a883),f331(x93441,x93442)),f331(x93441,x93443)))+~P24(f331(f331(f333(f890(x93444,x93444)),f331(f331(f261(x93444,x93444),x93442),x93443)),f156(x93444,f331(f331(f154(f891(x93444,a883)),x93441),x93445))))
% 162.26/162.08 [9483]~P24(f331(f331(f333(f890(f884(x94831),f884(x94831))),f331(f331(f261(f884(x94831),f884(x94831)),x94832),x94834)),f161(x94831,x94835)))+~P24(f331(f331(f248(a883),x94833),f331(f197(f884(x94831)),x94832)))+P24(f331(f331(f333(f890(x94831,x94831)),f331(f331(f261(x94831,x94831),f331(f331(f168(x94831),x94832),x94833)),f331(f331(f168(x94831),x94834),x94833))),x94835))
% 162.26/162.08 [9751]E(x97511,f2(a1))+~P24(f331(f49(x97513,x97511),f331(f331(f261(a1,a1),x97514),x97515)))+P24(f331(f49(f331(f331(f82(a1),x97512),x97513),x97511),f331(f331(f261(a1,a1),f331(f331(f81(a1),f331(f331(f82(a1),x97512),x97514)),f331(f331(f39(a1),f331(f331(f82(a1),x97512),x97515)),x97511))),f45(a1,f331(f331(f82(a1),x97512),x97515),x97511))))
% 162.26/162.08 [9760]~P24(f331(f331(f248(a883),f2(a883)),x97603))+~P24(f331(f48(x97602,x97603),f331(f331(f261(a883,a883),x97604),x97605)))+P24(f331(f48(f331(f331(f82(a883),x97601),x97602),x97603),f331(f331(f261(a883,a883),f331(f331(f81(a883),f331(f331(f82(a883),x97601),x97604)),f331(f331(f39(a883),f331(f331(f82(a883),x97601),x97605)),x97603))),f45(a883,f331(f331(f82(a883),x97601),x97605),x97603))))
% 162.26/162.08 [10047]~P74(x100472)+~P24(f331(f62(x100471),x100474))+E(f331(f331(f6(x100471,x100472),x100473),f331(f253(x100471),f331(f331(f18(x100471,a877,a877),f331(f331(f8(a877,f891(a877,a877),x100471),a329),f331(f331(f7(x100471,f891(x100471,a877),a877),f333(x100471)),x100474))),f331(f331(f7(x100471,f891(x100471,a877),a877),f333(x100471)),x100475)))),f331(f331(f6(x100471,x100472),f331(f331(f7(x100471,x100472,x100472),f331(f331(f18(x100471,x100472,f891(x100472,x100472)),f331(f331(f8(a877,f891(x100472,f891(x100472,x100472)),x100471),f102(x100472)),f331(f331(f7(x100471,f891(x100471,a877),a877),f333(x100471)),x100475))),x100473)),f2(x100472))),x100474))
% 162.26/162.08 [8238]~E(f331(f331(f137(x82381),x82382),x82385),f331(f331(f137(x82381),x82383),x82384))+E(f331(f331(f137(x82381),f331(f331(f141(x82381),f331(f197(f884(x82381)),x82382)),x82383)),x82384),x82385)+P24(f331(f331(f247(a883),f331(f197(f884(x82381)),x82383)),f331(f197(f884(x82381)),x82382)))
% 162.26/162.08 [8431]~E(f331(f331(f137(x84312),x84313),x84311),f331(f331(f137(x84312),x84314),x84315))+E(x84311,f331(f331(f137(x84312),f331(f331(f141(x84312),f331(f197(f884(x84312)),x84313)),x84314)),x84315))+~P24(f331(f331(f247(a883),f331(f197(f884(x84312)),x84313)),f331(f197(f884(x84312)),x84314)))
% 162.26/162.08 [8524]~E(f331(f331(f81(a883),f331(f331(f82(a883),x85243),x85244)),x85241),f331(f331(f81(a883),f331(f331(f82(a883),x85242),x85244)),x85245))+~P24(f331(f331(f247(a883),x85243),x85242))+E(x85241,f331(f331(f81(a883),f331(f331(f82(a883),f331(f331(f22(a883),x85242),x85243)),x85244)),x85245))
% 162.26/162.08 [8525]~E(f331(f331(f81(a883),f331(f331(f82(a883),x85251),x85253)),x85254),f331(f331(f81(a883),f331(f331(f82(a883),x85252),x85253)),x85255))+~P24(f331(f331(f247(a883),x85252),x85251))+E(f331(f331(f81(a883),f331(f331(f82(a883),f331(f331(f22(a883),x85251),x85252)),x85253)),x85254),x85255)
% 162.26/162.08 [8673]E(f331(f331(f81(a883),f331(f331(f82(a883),x86731),x86732)),x86733),f331(f331(f81(a883),f331(f331(f82(a883),x86734),x86732)),x86735))+~P24(f331(f331(f247(a883),x86734),x86731))+~E(x86735,f331(f331(f81(a883),f331(f331(f82(a883),f331(f331(f22(a883),x86731),x86734)),x86732)),x86733))
% 162.26/162.08 [8674]E(f331(f331(f81(a883),f331(f331(f82(a883),x86741),x86742)),x86743),f331(f331(f81(a883),f331(f331(f82(a883),x86744),x86742)),x86745))+~P24(f331(f331(f247(a883),x86744),x86741))+~E(f331(f331(f81(a883),f331(f331(f82(a883),f331(f331(f22(a883),x86741),x86744)),x86742)),x86743),x86745)
% 162.26/162.08 [9546]~P61(x95462)+~P24(f331(f62(x95461),x95465))+E(f331(f331(f9(x95461,x95462),f331(f331(f18(x95461,x95462,x95462),f331(f331(f8(x95462,f891(x95462,x95462),x95461),f289(x95462)),x95463)),x95464)),x95465),f331(f331(f289(x95462),f331(f331(f9(x95461,x95462),x95463),x95465)),f331(f331(f9(x95461,x95462),x95464),x95465)))
% 162.26/162.08 [9681]~E(f773(x96815,x96814,x96813,x96812,x96811),f774(x96815,x96814,x96813,x96812,x96811))+P24(f331(f331(f333(f890(x96811,x96811)),f331(f331(f261(x96811,x96811),x96812),x96813)),f307(x96811,x96814)))+~P24(f331(f331(f333(f890(x96811,x96811)),f331(f331(f261(x96811,x96811),x96812),x96813)),f307(x96811,f331(f331(f107(f891(f890(x96811,x96811),a877)),x96814),x96815))))
% 162.26/162.08 [9682]~E(f775(x96825,x96824,x96823,x96822,x96821),f776(x96825,x96824,x96823,x96822,x96821))+P24(f331(f331(f333(f890(x96821,x96821)),f331(f331(f261(x96821,x96821),x96822),x96823)),f307(x96821,x96824)))+~P24(f331(f331(f333(f890(x96821,x96821)),f331(f331(f261(x96821,x96821),x96822),x96823)),f307(x96821,f331(f331(f107(f891(f890(x96821,x96821),a877)),x96824),x96825))))
% 162.26/162.08 [9899]P24(f331(f331(f333(f890(x98991,x98991)),f331(f331(f261(x98991,x98991),x98992),f776(x98995,x98994,x98993,x98992,x98991))),f307(x98991,x98994)))+P24(f331(f331(f333(f890(x98991,x98991)),f331(f331(f261(x98991,x98991),x98992),x98993)),f307(x98991,x98994)))+~P24(f331(f331(f333(f890(x98991,x98991)),f331(f331(f261(x98991,x98991),x98992),x98993)),f307(x98991,f331(f331(f107(f891(f890(x98991,x98991),a877)),x98994),x98995))))
% 162.26/162.08 [9964]P24(f331(f331(f333(f890(x99641,x99641)),f331(f331(f261(x99641,x99641),f774(x99645,x99644,x99643,x99642,x99641)),x99643)),f307(x99641,x99644)))+P24(f331(f331(f333(f890(x99641,x99641)),f331(f331(f261(x99641,x99641),x99642),x99643)),f307(x99641,x99644)))+~P24(f331(f331(f333(f890(x99641,x99641)),f331(f331(f261(x99641,x99641),x99642),x99643)),f307(x99641,f331(f331(f107(f891(f890(x99641,x99641),a877)),x99644),x99645))))
% 162.26/162.08 [9998]P24(f331(f331(f333(f890(x99981,x99981)),f331(f331(f261(x99981,x99981),x99982),x99983)),f307(x99981,x99984)))+P24(f331(f331(f333(f890(x99981,x99981)),f331(f331(f261(x99981,x99981),f773(x99985,x99984,x99983,x99982,x99981)),f774(x99985,x99984,x99983,x99982,x99981))),x99985))+~P24(f331(f331(f333(f890(x99981,x99981)),f331(f331(f261(x99981,x99981),x99982),x99983)),f307(x99981,f331(f331(f107(f891(f890(x99981,x99981),a877)),x99984),x99985))))
% 162.26/162.08 [9999]P24(f331(f331(f333(f890(x99991,x99991)),f331(f331(f261(x99991,x99991),x99992),x99993)),f307(x99991,x99994)))+P24(f331(f331(f333(f890(x99991,x99991)),f331(f331(f261(x99991,x99991),f776(x99995,x99994,x99993,x99992,x99991)),f775(x99995,x99994,x99993,x99992,x99991))),x99995))+~P24(f331(f331(f333(f890(x99991,x99991)),f331(f331(f261(x99991,x99991),x99992),x99993)),f307(x99991,f331(f331(f107(f891(f890(x99991,x99991),a877)),x99994),x99995))))
% 162.26/162.08 [10150]~P24(f331(f331(f333(f890(f884(x101501),f884(x101501))),f331(f331(f261(f884(x101501),f884(x101501)),x101504),x101505)),f161(x101501,x101502)))+~P24(f331(f331(f333(f890(x101501,x101501)),x101503),f331(f175(f890(x101501,x101501)),f331(f331(f184(x101501,x101501),x101504),x101505))))+P24(f331(f331(f270(x101501,x101501,a877),f331(f331(f7(x101501,f891(f890(x101501,x101501),a877),f891(x101501,a877)),f331(f331(f8(f891(x101501,f891(f891(f890(x101501,x101501),a877),a877)),f891(f891(f890(x101501,x101501),a877),f891(x101501,a877)),x101501),f7(x101501,f891(f890(x101501,x101501),a877),a877)),f331(f331(f8(f891(x101501,f890(x101501,x101501)),f891(x101501,f891(f891(f890(x101501,x101501),a877),a877)),x101501),f331(f8(f890(x101501,x101501),f891(f891(f890(x101501,x101501),a877),a877),x101501),f333(f890(x101501,x101501)))),f261(x101501,x101501)))),x101502)),x101503))
% 162.26/162.08 [9573]~P24(f331(f331(f247(a883),x95733),x95732))+~P24(f331(f331(f248(a883),f331(f331(f81(a883),f331(f331(f82(a883),x95733),x95734)),x95731)),f331(f331(f81(a883),f331(f331(f82(a883),x95732),x95734)),x95735)))+P24(f331(f331(f248(a883),x95731),f331(f331(f81(a883),f331(f331(f82(a883),f331(f331(f22(a883),x95732),x95733)),x95734)),x95735)))
% 162.26/162.08 [9574]~P24(f331(f331(f247(a883),x95743),x95742))+~P24(f331(f331(f247(a883),f331(f331(f81(a883),f331(f331(f82(a883),x95743),x95744)),x95741)),f331(f331(f81(a883),f331(f331(f82(a883),x95742),x95744)),x95745)))+P24(f331(f331(f247(a883),x95741),f331(f331(f81(a883),f331(f331(f82(a883),f331(f331(f22(a883),x95742),x95743)),x95744)),x95745)))
% 162.26/162.08 [9600]~P24(f331(f331(f247(a883),x96001),x96004))+P24(f331(f331(f248(a883),f331(f331(f81(a883),f331(f331(f82(a883),x96001),x96002)),x96003)),f331(f331(f81(a883),f331(f331(f82(a883),x96004),x96002)),x96005)))+~P24(f331(f331(f248(a883),x96003),f331(f331(f81(a883),f331(f331(f82(a883),f331(f331(f22(a883),x96004),x96001)),x96002)),x96005)))
% 162.26/162.08 [9601]~P24(f331(f331(f247(a883),x96011),x96014))+P24(f331(f331(f247(a883),f331(f331(f81(a883),f331(f331(f82(a883),x96011),x96012)),x96013)),f331(f331(f81(a883),f331(f331(f82(a883),x96014),x96012)),x96015)))+~P24(f331(f331(f247(a883),x96013),f331(f331(f81(a883),f331(f331(f82(a883),f331(f331(f22(a883),x96014),x96011)),x96012)),x96015)))
% 162.26/162.08 [9716]~P24(f331(f331(f247(a883),x97162),x97161))+~P24(f331(f331(f248(a883),f331(f331(f81(a883),f331(f331(f82(a883),x97161),x97163)),x97164)),f331(f331(f81(a883),f331(f331(f82(a883),x97162),x97163)),x97165)))+P24(f331(f331(f248(a883),f331(f331(f81(a883),f331(f331(f82(a883),f331(f331(f22(a883),x97161),x97162)),x97163)),x97164)),x97165))
% 162.26/162.08 [9717]~P24(f331(f331(f247(a883),x97172),x97171))+~P24(f331(f331(f247(a883),f331(f331(f81(a883),f331(f331(f82(a883),x97171),x97173)),x97174)),f331(f331(f81(a883),f331(f331(f82(a883),x97172),x97173)),x97175)))+P24(f331(f331(f247(a883),f331(f331(f81(a883),f331(f331(f82(a883),f331(f331(f22(a883),x97171),x97172)),x97173)),x97174)),x97175))
% 162.26/162.08 [9785]~P24(f331(f331(f247(a883),x97854),x97851))+P24(f331(f331(f248(a883),f331(f331(f81(a883),f331(f331(f82(a883),x97851),x97852)),x97853)),f331(f331(f81(a883),f331(f331(f82(a883),x97854),x97852)),x97855)))+~P24(f331(f331(f248(a883),f331(f331(f81(a883),f331(f331(f82(a883),f331(f331(f22(a883),x97851),x97854)),x97852)),x97853)),x97855))
% 162.26/162.08 [9786]~P24(f331(f331(f247(a883),x97864),x97861))+P24(f331(f331(f247(a883),f331(f331(f81(a883),f331(f331(f82(a883),x97861),x97862)),x97863)),f331(f331(f81(a883),f331(f331(f82(a883),x97864),x97862)),x97865)))+~P24(f331(f331(f247(a883),f331(f331(f81(a883),f331(f331(f82(a883),f331(f331(f22(a883),x97861),x97864)),x97862)),x97863)),x97865))
% 162.26/162.08 [9984]~P9(x99841,x99842,x99845,x99843)+~P24(f331(f331(f333(f890(x99841,x99841)),x99844),x99845))+P24(f331(f331(f270(x99841,x99841,a877),f331(f331(f7(x99841,f891(x99841,x99842),f891(x99841,a877)),f331(f331(f8(f891(x99842,a877),f891(f891(x99841,x99842),f891(x99841,a877)),x99841),f8(x99842,a877,x99841)),f331(f331(f8(x99842,f891(x99842,a877),x99841),a328),x99843))),x99843)),x99844))
% 162.26/162.08 [6805]~E(f331(x68054,x68055),f199(x68052))+E(f331(f187(x68051,x68052,x68053,x68054),x68055),f331(f239(x68052),x68056))+~E(f331(x68053,x68055),f331(f239(x68052),x68056))
% 162.26/162.08 [6899]~E(f331(x68993,x68996),f199(x68991))+E(f331(f242(f887(x68991),x68992,f199(x68991),x68993),f331(x68994,x68995)),f199(x68991))+~E(f331(x68994,x68995),f331(f239(x68992),x68996))
% 162.26/162.08 [7473]E(f331(x74731,x74732),f199(x74733))+~E(f331(f187(x74735,x74733,x74736,x74731),x74732),f331(f239(x74733),x74734))+E(f331(x74731,x74732),f331(f239(x74733),x74734))
% 162.26/162.08 [7506]~E(f331(f187(x75066,x75063,x75065,x75061),x75062),f331(f239(x75063),x75064))+E(f331(x75061,x75062),f331(f239(x75063),x75064))+E(f331(x75065,x75062),f331(f239(x75063),x75064))
% 162.26/162.08 [8393]~P15(x83936,x83931,x83932,x83934)+E(f331(f74(x83931,x83931,x83931,f331(x83932,x83933)),f331(x83934,x83935)),f331(f74(x83931,x83931,x83931,f331(x83934,x83935)),f331(x83932,x83933)))+~P24(f331(f62(x83936),x83935))
% 162.26/162.08 [8808]~P21(x88081,x88083,x88085,x88086)+~P21(x88083,x88082,x88084,f331(f310(x88081,x88083,x88085),x88086))+P21(x88081,x88082,f331(f74(x88083,x88082,x88081,x88084),x88085),x88086)
% 162.26/162.08 [9380]~P24(f331(f331(x93803,x93802),x93806))+~P24(f331(f331(x93804,x93805),x93802))+P24(f331(f331(f333(x93801),x93802),f299(x93801,x93803,x93804,x93805,x93806)))
% 162.26/162.08 [9381]~P24(f331(f331(x93814,x93812),x93816))+~P24(f331(f331(x93813,x93815),x93812))+P24(f331(f331(f333(x93811),x93812),f296(x93811,x93813,x93814,x93815,x93816)))
% 162.26/162.08 [9484]E(x94841,x94842)+E(x94843,x94844)+~P24(f331(f331(f333(f890(f884(x94845),f884(x94845))),f331(f331(f261(f884(x94845),f884(x94845)),f331(f331(f154(x94845),x94843),x94841)),f331(f331(f154(x94845),x94844),x94842))),f160(x94845,x94846)))
% 162.26/162.08 [9498]~E(x94982,x94984)+P24(f331(f331(f333(f890(f884(x94981),f884(x94981))),f331(f331(f261(f884(x94981),f884(x94981)),f331(f331(f154(x94981),x94982),x94983)),f331(f331(f154(x94981),x94984),x94985))),f148(x94981,x94986)))+~P24(f331(f331(f333(f890(f884(x94981),f884(x94981))),f331(f331(f261(f884(x94981),f884(x94981)),x94983),x94985)),f148(x94981,x94986)))
% 162.26/162.08 [9499]~E(x94992,x94994)+P24(f331(f331(f333(f890(f884(x94991),f884(x94991))),f331(f331(f261(f884(x94991),f884(x94991)),f331(f331(f154(x94991),x94992),x94993)),f331(f331(f154(x94991),x94994),x94995))),f150(x94991,x94996)))+~P24(f331(f331(f333(f890(f884(x94991),f884(x94991))),f331(f331(f261(f884(x94991),f884(x94991)),x94993),x94995)),f150(x94991,x94996)))
% 162.26/162.08 [9500]~E(x95002,x95004)+P24(f331(f331(f333(f890(f884(x95001),f884(x95001))),f331(f331(f261(f884(x95001),f884(x95001)),f331(f331(f154(x95001),x95002),x95003)),f331(f331(f154(x95001),x95004),x95005))),f160(x95001,x95006)))+~P24(f331(f331(f333(f890(f884(x95001),f884(x95001))),f331(f331(f261(f884(x95001),f884(x95001)),x95003),x95005)),f160(x95001,x95006)))
% 162.26/162.08 [9501]~E(x95012,x95014)+P24(f331(f331(f333(f890(f884(x95011),f884(x95011))),f331(f331(f261(f884(x95011),f884(x95011)),f331(f331(f137(x95011),x95012),x95013)),f331(f331(f137(x95011),x95014),x95015))),f160(x95011,x95016)))+~P24(f331(f331(f333(f890(f884(x95011),f884(x95011))),f331(f331(f261(f884(x95011),f884(x95011)),x95013),x95015)),f160(x95011,x95016)))
% 162.26/162.08 [9502]~E(x95023,x95025)+P24(f331(f331(f333(f890(f884(x95021),f884(x95021))),f331(f331(f261(f884(x95021),f884(x95021)),f331(f331(f137(x95021),x95022),x95023)),f331(f331(f137(x95021),x95024),x95025))),f160(x95021,x95026)))+~P24(f331(f331(f333(f890(f884(x95021),f884(x95021))),f331(f331(f261(f884(x95021),f884(x95021)),x95022),x95024)),f160(x95021,x95026)))
% 162.26/162.08 [9563]E(x95631,x95632)+P24(f331(f331(f333(f890(f884(x95633),f884(x95633))),f331(f331(f261(f884(x95633),f884(x95633)),x95631),x95632)),f160(x95633,x95634)))+~P24(f331(f331(f333(f890(f884(x95633),f884(x95633))),f331(f331(f261(f884(x95633),f884(x95633)),f331(f331(f154(x95633),x95635),x95631)),f331(f331(f154(x95633),x95636),x95632))),f160(x95633,x95634)))
% 162.26/162.08 [9720]~E(x97203,x97205)+P24(f331(f331(f333(f890(f884(x97201),f884(x97201))),f331(f331(f261(f884(x97201),f884(x97201)),f331(f331(f137(x97201),x97202),f331(f331(f154(x97201),x97203),f119(x97201)))),f331(f331(f137(x97201),x97204),f331(f331(f154(x97201),x97205),f119(x97201))))),f160(x97201,x97206)))+~P24(f331(f331(f333(f890(f884(x97201),f884(x97201))),f331(f331(f261(f884(x97201),f884(x97201)),x97202),x97204)),f160(x97201,x97206)))
% 162.26/162.08 [9741]E(f331(x97411,x97412),f199(x97413))+~E(f331(f242(f887(x97416),x97413,f199(x97416),x97414),f331(x97411,x97412)),f199(x97416))+E(f331(x97414,f372(x97412,x97411,x97414,x97415,x97416,x97413)),f199(x97416))
% 162.26/162.08 [9742]E(f331(x97421,x97422),f199(x97423))+~E(f331(f242(f887(x97426),x97423,f199(x97426),x97424),f331(x97421,x97422)),f199(x97426))+E(f331(f239(x97423),f372(x97422,x97421,x97424,x97425,x97426,x97423)),f331(x97421,x97422))
% 162.26/162.08 [9789]E(x97891,x97892)+E(x97893,x97894)+~P24(f331(f331(f333(f890(f884(x97895),f884(x97895))),f331(f331(f261(f884(x97895),f884(x97895)),f331(f331(f137(x97895),x97893),f331(f331(f154(x97895),x97891),f119(x97895)))),f331(f331(f137(x97895),x97894),f331(f331(f154(x97895),x97892),f119(x97895))))),f160(x97895,x97896)))
% 162.26/162.08 [9810]E(x98101,x98102)+~P24(f331(f331(f333(f890(f884(x98103),f884(x98103))),f331(f331(f261(f884(x98103),f884(x98103)),f331(f331(f137(x98103),x98101),f331(f331(f154(x98103),x98105),f119(x98103)))),f331(f331(f137(x98103),x98102),f331(f331(f154(x98103),x98106),f119(x98103))))),f160(x98103,x98104)))+P24(f331(f331(f333(f890(f884(x98103),f884(x98103))),f331(f331(f261(f884(x98103),f884(x98103)),x98101),x98102)),f160(x98103,x98104)))
% 162.26/162.08 [9851]~P24(f331(f331(f333(f890(f891(x98511,a877),f891(x98511,a877))),f331(f331(f261(f891(x98511,a877),f891(x98511,a877)),x98512),x98514)),f322(x98511,x98516)))+~P24(f331(f331(f333(f890(f891(x98511,a877),f891(x98511,a877))),f331(f331(f261(f891(x98511,a877),f891(x98511,a877)),x98513),x98515)),f322(x98511,x98516)))+P24(f331(f331(f333(f890(f891(x98511,a877),f891(x98511,a877))),f331(f331(f261(f891(x98511,a877),f891(x98511,a877)),f331(f331(f107(f891(x98511,a877)),x98512),x98513)),f331(f331(f107(f891(x98511,a877)),x98514),x98515))),f322(x98511,x98516)))
% 162.26/162.08 [5266]~E(f331(x52663,x52666),x52665)+~E(x52664,f331(f239(x52661),x52666))+E(f331(f331(f210(x52661,x52662),x52663),x52664),f331(f239(x52662),x52665))
% 162.26/162.08 [5681]~E(f331(f331(f137(x56811),x56816),x56813),x56815)+E(f331(f331(f137(x56811),x56812),x56813),f331(f331(f154(x56811),x56814),x56815))+~E(x56812,f331(f331(f154(x56811),x56814),x56816))
% 162.26/162.08 [5682]~E(f331(f331(f137(x56821),x56826),x56823),x56825)+E(f331(f331(f137(x56821),x56822),x56823),f331(f331(f137(x56821),x56824),x56825))+~E(x56822,f331(f331(f137(x56821),x56824),x56826))
% 162.26/162.08 [5684]E(f331(f331(f137(x56841),x56842),x56843),f331(f331(f154(x56841),x56844),x56845))+~E(f331(f331(f154(x56841),x56844),x56846),x56842)+~E(x56845,f331(f331(f137(x56841),x56846),x56843))
% 162.26/162.08 [5686]~E(f331(f331(f137(x56861),x56862),x56866),x56864)+E(f331(f331(f137(x56861),x56862),x56863),f331(f331(f137(x56861),x56864),x56865))+~E(x56863,f331(f331(f137(x56861),x56866),x56865))
% 162.26/162.08 [6799]E(f331(x67991,x67992),f331(x67993,x67992))+~E(f331(f331(f157(x67994,x67995),x67991),x67996),f331(f331(f157(x67994,x67995),x67993),x67996))+~P24(f331(f331(f333(x67994),x67992),f331(f175(x67994),x67996)))
% 162.26/162.08 [7178]~P15(x71784,x71785,x71786,x71781)+E(f331(f331(x71781,x71782),x71783),f331(f331(f65(x71784,x71785,x71786),x71783),x71782))+~P24(f331(f62(x71784),x71782))
% 162.26/162.08 [7244]~E(x72442,f331(x72444,x72446))+~P24(f331(f331(f333(x72443),x72446),x72445))+P24(f331(f331(f333(x72441),x72442),f331(f310(x72443,x72441,x72444),x72445)))
% 162.26/162.08 [7245]~E(f331(x72454,x72452),x72456)+~P24(f331(f331(f333(x72453),x72456),x72455))+P24(f331(f331(f333(x72451),x72452),f331(f311(x72451,x72453,x72454),x72455)))
% 162.26/162.08 [7681]~P33(x76811,x76812,x76814,x76816)+P33(x76811,x76812,f331(f331(f154(x76811),x76813),x76814),f331(f331(f154(x76811),x76815),x76816))+~P24(f331(f331(x76812,x76813),x76815))
% 162.26/162.08 [8681]~P54(x86814,x86815,x86811,x86812,x86816)+E(f331(x86811,f331(x86812,x86813)),x86813)+~P24(f331(f331(f333(x86815),x86813),x86816))
% 162.26/162.08 [9487]E(x94871,x94872)+E(f331(f197(f884(x94873)),x94874),f331(f197(f884(x94873)),x94875))+~P24(f331(f331(f333(f890(f884(x94873),f884(x94873))),f331(f331(f261(f884(x94873),f884(x94873)),f331(f331(f154(x94873),x94871),x94874)),f331(f331(f154(x94873),x94872),x94875))),f148(x94873,x94876)))
% 162.26/162.08 [9559]~P12(x95591,x95592,x95593)+E(f331(f331(f65(x95591,x95592,x95593),x95594),x95595),x95596)+~P24(f331(f67(x95591,x95592,x95593,x95594,x95595),x95596))
% 162.26/162.08 [9564]E(f331(f197(f884(x95641)),x95642),f331(f197(f884(x95641)),x95643))+P24(f331(f331(f333(f890(f884(x95641),f884(x95641))),f331(f331(f261(f884(x95641),f884(x95641)),x95642),x95643)),f148(x95641,x95644)))+~P24(f331(f331(f333(f890(f884(x95641),f884(x95641))),f331(f331(f261(f884(x95641),f884(x95641)),f331(f331(f154(x95641),x95645),x95642)),f331(f331(f154(x95641),x95646),x95643))),f148(x95641,x95644)))
% 162.26/162.08 [9594]~P24(f331(f331(f333(f890(x95941,x95941)),f331(f331(f261(x95941,x95941),x95942),x95944)),f307(x95941,x95946)))+P24(f331(f331(f333(f890(f884(x95941),f884(x95941))),f331(f331(f261(f884(x95941),f884(x95941)),f331(f331(f154(x95941),x95942),x95943)),f331(f331(f154(x95941),x95944),x95945))),f307(f884(x95941),f160(x95941,x95946))))+~P24(f331(f331(f333(f890(f884(x95941),f884(x95941))),f331(f331(f261(f884(x95941),f884(x95941)),x95943),x95945)),f307(f884(x95941),f160(x95941,x95946))))
% 162.26/162.08 [9794]~P24(f331(x97942,x97946))+~E(f331(f139(x97941,x97942),x97943),f331(f331(f154(x97941),x97944),x97945))+~P24(f331(f331(f333(x97941),x97946),f331(f175(x97941),f733(x97945,x97944,x97943,x97942,x97941))))
% 162.26/162.08 [9795]~P24(f331(x97954,x97956))+~E(f331(f331(f154(x97951),x97952),x97953),f331(f139(x97951,x97954),x97955))+~P24(f331(f331(f333(x97951),x97956),f331(f175(x97951),f735(x97955,x97954,x97953,x97952,x97951))))
% 162.26/162.08 [10083]~P74(x100832)+E(f331(f331(f6(x100831,x100832),f331(f331(f8(f891(x100833,a877),x100832,x100831),f331(f6(x100833,x100832),x100834)),f331(f331(f8(f891(x100833,a877),f891(x100833,a877),x100831),f253(x100833)),f331(f331(f8(f891(x100833,a877),f891(x100833,a877),x100831),f331(f18(x100833,a877,a877),f331(f331(f8(a877,f891(a877,a877),x100833),a329),f331(f331(f7(x100833,f891(x100833,a877),a877),f333(x100833)),x100835)))),f331(f7(x100833,x100831,a877),f331(f331(f8(x100831,f891(x100831,a877),x100833),a328),x100836)))))),f331(f310(x100833,x100831,x100836),x100835)),f331(f331(f6(x100833,x100832),x100834),x100835))+~P24(f331(f62(x100833),x100835))
% 162.26/162.08 [6853]~P107(x68533)+P24(f331(x68532,x68535))+E(f331(f139(x68531,x68532),f331(f331(f151(x68531,x68533,x68534),x68535),x68536)),f331(f139(x68531,x68532),x68536))
% 162.26/162.08 [6855]P24(f331(x68551,x68552))+~E(f170(x68553,x68551,x68554),f331(f331(f261(f884(x68553),f884(x68553)),x68555),x68556))+~P24(f331(f331(f333(x68553),x68552),f331(f175(x68553),x68555)))
% 162.26/162.08 [6896]~P24(f331(x68962,x68966))+~E(f170(x68961,x68962,x68963),f331(f331(f261(f884(x68961),f884(x68961)),x68964),x68965))+~P24(f331(f331(f333(x68961),x68966),f331(f175(x68961),x68965)))
% 162.26/162.08 [7551]~P11(x75511,x75512,x75513)+~P24(f331(f62(x75511),x75516))+E(f331(f331(f65(x75511,x75512,x75513),x75514),f331(f331(f309(x75511),x75515),x75516)),f331(f331(f65(x75511,x75512,x75513),f331(f331(x75513,x75515),x75514)),x75516))
% 162.26/162.08 [7598]~P107(x75982)+~P24(f331(f331(f247(x75982),f331(x75983,x75984)),f331(x75983,x75985)))+E(f331(f331(f151(x75981,x75982,x75983),x75984),f331(f331(f154(x75981),x75985),x75986)),f331(f331(f154(x75981),x75984),f331(f331(f154(x75981),x75985),x75986)))
% 162.26/162.08 [7712]E(x77121,x77122)+~E(f331(f331(f268(x77123,x77124),x77121),f331(f16(f891(x77124,a877),x77123),x77125)),f331(f331(f268(x77123,x77124),x77122),f331(f16(f891(x77124,a877),x77123),x77125)))+~P24(f331(f331(f333(x77124),x77126),x77125))
% 162.26/162.08 [7779]~P11(x77791,x77792,x77793)+~P24(f331(f62(x77791),x77796))+E(f331(f331(f65(x77791,x77792,x77793),x77794),f331(f331(f309(x77791),x77795),x77796)),f331(f331(x77793,x77795),f331(f331(f65(x77791,x77792,x77793),x77794),x77796)))
% 162.26/162.08 [7892]~P12(x78921,x78922,x78923)+~P24(f331(f62(x78921),x78926))+E(f331(f331(f65(x78921,x78922,x78923),f331(f331(x78923,x78924),x78925)),x78926),f331(f331(x78923,x78924),f331(f331(f65(x78921,x78922,x78923),x78925),x78926)))
% 162.26/162.08 [7956]~P16(x79562,x79565,x79566,x79561)+~P24(f331(f62(x79562),x79564))+E(f331(x79561,f331(f331(f309(x79562),x79563),x79564)),f331(f74(x79565,x79565,x79565,f331(x79561,x79564)),f331(x79566,x79563)))
% 162.26/162.08 [7993]~P107(x79932)+P24(f331(f331(f247(x79932),f331(x79933,x79934)),f331(x79933,x79935)))+E(f331(f331(f151(x79931,x79932,x79933),x79934),f331(f331(f154(x79931),x79935),x79936)),f331(f331(f154(x79931),x79935),f331(f331(f151(x79931,x79932,x79933),x79934),x79936)))
% 162.26/162.08 [8141]~E(f331(f197(f884(x81411)),x81415),f331(f197(f884(x81412)),x81416))+~E(f331(f197(f884(x81411)),x81413),f331(f197(f884(x81412)),x81414))+E(f331(f331(f137(f890(x81411,x81412)),f331(f331(f184(x81411,x81412),x81413),x81414)),f331(f331(f184(x81411,x81412),x81415),x81416)),f331(f331(f184(x81411,x81412),f331(f331(f137(x81411),x81413),x81415)),f331(f331(f137(x81412),x81414),x81416)))
% 162.26/162.08 [8253]~E(x82532,f331(f310(x82533,x82531,x82534),x82536))+P24(f331(f331(f247(f891(x82531,a877)),x82532),f331(f310(x82533,x82531,x82534),x82535)))+~P24(f331(f331(f247(f891(x82533,a877)),x82536),x82535))
% 162.26/162.08 [8351]~P107(x83515)+E(f331(x83511,x83512),f331(x83511,x83513))+E(f331(f331(f151(x83514,x83515,x83511),x83512),f331(f331(f151(x83514,x83515,x83511),x83513),x83516)),f331(f331(f151(x83514,x83515,x83511),x83513),f331(f331(f151(x83514,x83515,x83511),x83512),x83516)))
% 162.26/162.08 [8387]~P21(x83873,x83871,x83874,x83875)+P21(x83873,x83871,f331(f331(f331(f73(x83873,x83871),x83874),x83876),x83872),x83875)+P24(f331(f331(f333(x83871),x83872),f331(f310(x83873,x83871,x83874),x83875)))
% 162.26/162.08 [8533]~P24(f331(f331(f333(x85332),x85334),f331(x85336,x85333)))+~P24(f331(f331(f333(x85331),x85333),x85335))+P24(f331(f331(f333(f890(x85331,x85332)),f331(f331(f261(x85331,x85332),x85333),x85334)),f331(f331(f268(x85331,x85332),x85335),x85336)))
% 162.26/162.08 [8988]~P73(x89882)+~P21(x89884,x89881,x89885,x89886)+E(f331(f331(f9(x89881,x89882),x89883),f331(f310(x89884,x89881,x89885),x89886)),f331(f331(f9(x89884,x89882),f331(f74(x89881,x89882,x89884,x89883),x89885)),x89886))
% 162.26/162.08 [8989]~P74(x89892)+~P21(x89894,x89891,x89895,x89896)+E(f331(f331(f6(x89891,x89892),x89893),f331(f310(x89894,x89891,x89895),x89896)),f331(f331(f6(x89894,x89892),f331(f74(x89891,x89892,x89894,x89893),x89895)),x89896))
% 162.26/162.08 [9032]~P35(x90322,x90325,x90321,x90323,x90326)+P24(f331(f331(x90321,f331(f331(f168(x90322),x90323),x90324)),f331(f331(f168(x90325),x90326),x90324)))+~P24(f331(f331(f248(a883),x90324),f331(f197(f884(x90325)),x90326)))
% 162.26/162.08 [9033]~P35(x90332,x90335,x90331,x90333,x90336)+P24(f331(f331(x90331,f331(f331(f168(x90332),x90333),x90334)),f331(f331(f168(x90335),x90336),x90334)))+~P24(f331(f331(f248(a883),x90334),f331(f197(f884(x90332)),x90333)))
% 162.26/162.08 [9243]~P15(x92433,x92431,x92436,x92432)+~P24(f331(f62(x92433),x92434))+E(f331(f74(x92431,x92431,x92431,f331(x92432,f331(f331(f22(f891(x92433,a877)),x92434),f331(f331(f309(x92433),x92435),f196(f891(x92433,a877)))))),f331(x92436,x92435)),f331(x92432,f331(f331(f309(x92433),x92435),x92434)))
% 162.26/162.08 [9880]~E(f331(f310(x98802,x98804,x98806),f256(f891(x98802,a877))),f256(f891(x98804,a877)))+~E(f331(f310(x98801,x98803,x98805),f256(f891(x98801,a877))),f256(f891(x98803,a877)))+E(f331(f310(f890(x98801,x98802),f890(x98803,x98804),f271(x98801,x98803,x98802,x98804,x98805,x98806)),f256(f891(f890(x98801,x98802),a877))),f256(f891(f890(x98803,x98804),a877)))
% 162.26/162.08 [9924]~P21(x99243,x99244,x99245,f331(x99246,f560(x99246,x99245,x99244,x99243,x99242,x99241)))+P21(x99243,x99244,x99245,f331(f331(f43(x99242,f891(x99243,a877)),x99241),x99246))+E(x99241,f196(f891(x99242,a877)))
% 162.26/162.08 [9972]P21(x99726,x99725,x99724,f331(f331(f43(x99722,f891(x99726,a877)),x99721),x99723))+E(x99721,f196(f891(x99722,a877)))+P24(f331(f331(f333(x99722),f560(x99723,x99724,x99725,x99726,x99722,x99721)),x99721))
% 162.26/162.08 [9976]P24(f331(f331(f333(x99761),f737(x99762,x99763,x99764,x99765,x99766,x99761)),x99766))+P24(f331(f331(f247(f891(f890(x99761,x99764),a877)),f331(f331(f268(x99761,x99764),x99766),x99763)),f331(f331(f268(x99761,x99764),x99765),x99762)))+~P24(f331(f331(f247(f891(x99761,a877)),x99766),x99765))
% 162.26/162.08 [10014]P20(x100146,x100145,f331(f331(f309(f882(x100146)),f331(f331(f331(f93(x100146),x100144),x100143),x100142)),f196(f891(f882(x100146),a877))))+~P20(x100146,x100145,f331(f331(f309(f882(x100146)),f331(f331(f331(f93(x100146),x100144),x100143),x100141)),f196(f891(f882(x100146),a877))))+P24(f331(f331(x100141,f871(x100142,x100141,x100143,x100144,x100145,x100146)),f876(x100142,x100141,x100143,x100144,x100145,x100146)))
% 162.26/162.08 [10015]P20(x100156,x100155,f331(f331(f309(f882(x100156)),f331(f331(f331(f93(x100156),x100151),x100153),x100152)),f196(f891(f882(x100156),a877))))+~P20(x100156,x100155,f331(f331(f309(f882(x100156)),f331(f331(f331(f93(x100156),x100154),x100153),x100152)),f196(f891(f882(x100156),a877))))+P24(f331(f331(x100151,f353(x100151,x100152,x100153,x100154,x100155,x100156)),f362(x100151,x100152,x100153,x100154,x100155,x100156)))
% 162.26/162.08 [10050]~P20(x100501,x100502,f331(f331(f309(f882(x100501)),f331(f331(f331(f93(x100501),x100503),x100504),x100506)),f196(f891(f882(x100501),a877))))+P20(x100501,x100502,f331(f331(f309(f882(x100501)),f331(f331(f331(f93(x100501),x100503),x100504),x100505)),f196(f891(f882(x100501),a877))))+~P24(f331(f331(x100505,f871(x100505,x100506,x100504,x100503,x100502,x100501)),f876(x100505,x100506,x100504,x100503,x100502,x100501)))
% 162.26/162.08 [10051]~P20(x100511,x100512,f331(f331(f309(f882(x100511)),f331(f331(f331(f93(x100511),x100516),x100514),x100515)),f196(f891(f882(x100511),a877))))+P20(x100511,x100512,f331(f331(f309(f882(x100511)),f331(f331(f331(f93(x100511),x100513),x100514),x100515)),f196(f891(f882(x100511),a877))))+~P24(f331(f331(x100516,f353(x100513,x100515,x100514,x100516,x100512,x100511)),f362(x100513,x100515,x100514,x100516,x100512,x100511)))
% 162.26/162.08 [10093]~P24(f331(f331(f247(f891(x100932,a877)),f331(x100934,f737(x100936,x100934,x100932,x100935,x100933,x100931))),f331(x100936,f737(x100936,x100934,x100932,x100935,x100933,x100931))))+~P24(f331(f331(f247(f891(x100931,a877)),x100933),x100935))+P24(f331(f331(f247(f891(f890(x100931,x100932),a877)),f331(f331(f268(x100931,x100932),x100933),x100934)),f331(f331(f268(x100931,x100932),x100935),x100936)))
% 162.26/162.08 [7731]~P24(f331(x77311,x77315))+~P24(f331(x77316,x77314))+P24(f331(x77311,f331(f269(x77312,x77313),f331(f331(f261(x77312,x77313),x77314),x77315))))
% 162.26/162.08 [7732]~P24(f331(x77321,x77324))+~P24(f331(x77326,x77325))+P24(f331(x77321,f331(f260(x77322,x77323),f331(f331(f261(x77322,x77323),x77324),x77325))))
% 162.26/162.08 [7755]~E(f331(f197(f884(x77551)),x77553),f331(f197(f884(x77554)),x77555))+~E(f331(f331(f180(x77551,x77554),f331(f331(f184(x77551,x77554),x77553),x77555)),x77552),f331(f239(x77554),x77556))+P24(f331(f331(f333(x77551),x77552),f331(f175(x77551),x77553)))
% 162.26/162.08 [7784]~P24(f331(f331(x77844,x77846),x77845))+~P24(f331(f331(f333(x77841),x77846),x77843))+P24(f331(f331(f331(f42(x77841,f891(x77842,a877)),x77843),x77844),x77845))
% 162.26/162.08 [8089]~P24(f331(f331(f333(x80891),x80892),f331(x80895,x80896)))+~P24(f331(f331(f333(x80893),x80896),x80894))+P24(f331(f331(f333(x80891),x80892),f331(f331(f42(x80893,f891(x80891,a877)),x80894),x80895)))
% 162.26/162.08 [8133]P24(f331(f331(x81331,x81332),x81333))+~P24(f331(f331(x81334,x81332),x81333))+~P24(f331(f331(f247(f891(x81335,f891(x81336,a877))),x81334),x81331))
% 162.26/162.08 [8277]P24(f331(f331(x82771,x82772),x82773))+~P24(f331(f331(f333(x82774),x82772),x82775))+~P24(f331(f331(f331(f43(x82774,f891(x82776,a877)),x82775),x82771),x82773))
% 162.26/162.08 [8406]P24(f331(f331(f333(x84061),x84062),f331(x84063,x84064)))+~P24(f331(f331(f333(x84065),x84064),x84066))+~P24(f331(f331(f333(x84061),x84062),f331(f331(f43(x84065,f891(x84061,a877)),x84066),x84063)))
% 162.26/162.08 [8600]~P24(f331(f331(f331(f331(a205,x86001),x86003),x86004),x86006))+~P24(f331(f331(f331(f331(a205,x86002),x86006),x86004),x86005))+P24(f331(f331(f331(f331(a205,f34(x86001,x86002)),x86003),x86004),x86005))
% 162.26/162.08 [8664]~P9(x86644,x86645,x86646,x86641)+E(f331(x86641,x86642),f331(x86641,x86643))+~P24(f331(f331(f333(f890(x86644,x86644)),f331(f331(f261(x86644,x86644),x86642),x86643)),x86646))
% 162.26/162.08 [8694]P24(f331(f331(f247(f891(x86941,a877)),x86942),f331(x86943,x86944)))+~P24(f331(f331(f333(x86945),x86944),x86946))+~P24(f331(f331(f247(f891(x86941,a877)),x86942),f331(f331(f43(x86945,f891(x86941,a877)),x86946),x86943)))
% 162.26/162.08 [8724]~P52(x87243,x87244,f331(f286(x87244,x87243),x87245))+E(x87241,f196(f891(x87242,a877)))+E(f331(f331(f43(x87242,f891(x87243,a877)),x87241),f331(f331(f8(f891(x87244,a877),f891(x87243,a877),x87242),f285(x87244,x87243,x87245)),x87246)),f331(f285(x87244,x87243,x87245),f331(f331(f43(x87242,f891(x87244,a877)),x87241),x87246)))
% 162.26/162.08 [8799]P24(f331(f331(f333(x87991),x87992),f331(f285(x87993,x87991,x87994),x87995)))+~P24(f331(f331(f333(x87993),x87996),x87995))+~P24(f331(f331(f333(f890(x87993,x87991)),f331(f331(f261(x87993,x87991),x87996),x87992)),x87994))
% 162.26/162.08 [8919]P24(f331(x89191,x89192))+~P24(f331(f331(f331(f331(a205,x89194),x89192),x89195),x89196))+P24(f331(f331(f331(f331(a205,f31(x89191,x89193,x89194)),x89192),x89195),x89196))
% 162.26/162.08 [8936]~P24(f331(x89361,x89364))+~P24(f331(f331(f331(f331(a205,x89362),x89364),x89365),x89366))+P24(f331(f331(f331(f331(a205,f31(x89361,x89362,x89363)),x89364),x89365),x89366))
% 162.26/162.08 [9103]P24(f331(f331(f247(f891(x91031,a877)),f331(f285(x91032,x91031,x91033),x91034)),f331(f285(x91032,x91031,x91035),x91036)))+~P24(f331(f331(f247(f891(x91032,a877)),x91034),x91036))+~P24(f331(f331(f247(f891(f890(x91032,x91031),a877)),x91033),x91035))
% 162.26/162.08 [9196]P24(f331(x91961,x91962))+P24(f331(f331(f331(f331(a205,x91963),x91962),x91964),x91965))+~P24(f331(f331(f331(f331(a205,f31(x91961,x91966,x91963)),x91962),x91964),x91965))
% 162.26/162.08 [9201]~P24(f331(x92015,x92012))+P24(f331(f331(f331(f331(a205,x92011),x92012),x92013),x92014))+~P24(f331(f331(f331(f331(a205,f31(x92015,x92011,x92016)),x92012),x92013),x92014))
% 162.26/162.08 [9250]P24(f331(f331(f331(f331(a205,x92501),x92502),x92503),x92504))+P24(f331(f331(f331(f331(a205,x92505),x92502),x92503),x92504))+~P24(f331(f331(f331(f331(a205,f31(x92506,x92501,x92505)),x92502),x92503),x92504))
% 162.26/162.08 [9300]~P24(f331(f331(f333(x93002),x93006),x93004))+~P24(f331(f331(f247(f891(x93001,a877)),x93003),x93005))+P24(f331(f331(f247(f891(f890(x93001,x93002),a877)),f331(f331(f268(x93001,x93002),x93003),f331(f16(f891(x93002,a877),x93001),x93004))),f331(f331(f268(x93001,x93002),x93005),f331(f16(f891(x93002,a877),x93001),x93004))))
% 162.26/162.08 [9308]~P35(x93081,x93082,x93083,x93085,x93086)+P24(f331(f331(f270(x93081,x93082,a877),x93083),x93084))+~P24(f331(f331(f333(f890(x93081,x93082)),x93084),f331(f175(f890(x93081,x93082)),f331(f331(f184(x93081,x93082),x93085),x93086))))
% 162.26/162.08 [9437]~E(x94373,x94375)+P24(f331(f331(f333(f890(f884(x94371),f884(x94371))),f331(f331(f261(f884(x94371),f884(x94371)),f331(f331(f154(x94371),x94372),x94373)),f331(f331(f154(x94371),x94374),x94375))),f160(x94371,x94376)))+~P24(f331(f331(f333(f890(x94371,x94371)),f331(f331(f261(x94371,x94371),x94372),x94374)),x94376))
% 162.26/162.08 [9443]~E(f331(f197(f884(x94431)),x94435),f331(f197(f884(x94432)),x94436))+E(f189(x94431,x94432,f190(x94431,x94432,x94433,f331(f331(f22(f891(x94431,a877)),x94434),f331(f175(x94431),x94435))),x94435,x94436),f190(x94431,x94432,f189(x94431,x94432,x94433,x94435,x94436),x94434))+~P24(f331(f331(f247(f891(x94431,a877)),f331(f175(x94431),x94435)),x94434))
% 162.26/162.08 [9444]~E(f331(f197(f884(x94441)),x94443),f331(f197(f884(x94441)),x94445))+P24(f331(f331(f333(f890(f884(x94441),f884(x94441))),f331(f331(f261(f884(x94441),f884(x94441)),f331(f331(f154(x94441),x94442),x94443)),f331(f331(f154(x94441),x94444),x94445))),f148(x94441,x94446)))+~P24(f331(f331(f333(f890(x94441,x94441)),f331(f331(f261(x94441,x94441),x94442),x94444)),x94446))
% 162.26/162.08 [9478]P24(f331(f331(f333(f890(x94781,x94781)),f331(f331(f261(x94781,x94781),x94782),x94783)),f331(f331(f191(f890(x94781,x94781),a877),f331(a118,x94784)),x94785)))+~P24(f331(f331(f333(f890(x94781,x94781)),f331(f331(f261(x94781,x94781),x94786),x94783)),x94785))+~P24(f331(f331(f333(f890(x94781,x94781)),f331(f331(f261(x94781,x94781),x94782),x94786)),f331(f331(f191(f890(x94781,x94781),a877),x94784),x94785)))
% 162.26/162.08 [9479]P24(f331(f331(f333(f890(x94791,x94791)),f331(f331(f261(x94791,x94791),x94792),x94793)),f331(f331(f191(f890(x94791,x94791),a877),f331(a118,x94794)),x94795)))+~P24(f331(f331(f333(f890(x94791,x94791)),f331(f331(f261(x94791,x94791),x94792),x94796)),x94795))+~P24(f331(f331(f333(f890(x94791,x94791)),f331(f331(f261(x94791,x94791),x94796),x94793)),f331(f331(f191(f890(x94791,x94791),a877),x94794),x94795)))
% 162.26/162.08 [9482]~P24(f331(f331(f333(x94824),x94825),x94826))+P24(f331(f331(f247(f891(x94821,a877)),x94822),x94823))+~P24(f331(f331(f247(f891(f890(x94821,x94824),a877)),f331(f331(f268(x94821,x94824),x94822),f331(f16(f891(x94824,a877),x94821),x94826))),f331(f331(f268(x94821,x94824),x94823),f331(f16(f891(x94824,a877),x94821),x94826))))
% 162.26/162.08 [9537]E(x95371,x95372)+~P24(f331(f331(f333(f890(f884(x95373),f884(x95373))),f331(f331(f261(f884(x95373),f884(x95373)),f331(f331(f154(x95373),x95371),x95375)),f331(f331(f154(x95373),x95372),x95376))),f148(x95373,x95374)))+P24(f331(f331(f333(f890(x95373,x95373)),f331(f331(f261(x95373,x95373),x95371),x95372)),x95374))
% 162.26/162.08 [9538]E(x95381,x95382)+~P24(f331(f331(f333(f890(f884(x95383),f884(x95383))),f331(f331(f261(f884(x95383),f884(x95383)),f331(f331(f154(x95383),x95381),x95385)),f331(f331(f154(x95383),x95382),x95386))),f150(x95383,x95384)))+P24(f331(f331(f333(f890(x95383,x95383)),f331(f331(f261(x95383,x95383),x95381),x95382)),x95384))
% 162.26/162.08 [9539]E(x95391,x95392)+~P24(f331(f331(f333(f890(f884(x95393),f884(x95393))),f331(f331(f261(f884(x95393),f884(x95393)),f331(f331(f154(x95393),x95391),x95395)),f331(f331(f154(x95393),x95392),x95396))),f160(x95393,x95394)))+P24(f331(f331(f333(f890(x95393,x95393)),f331(f331(f261(x95393,x95393),x95391),x95392)),x95394))
% 162.26/162.08 [9572]P24(f331(f331(f333(f890(f884(x95721),f884(x95721))),f331(f331(f261(f884(x95721),f884(x95721)),f331(f331(f154(x95721),x95722),x95723)),f331(f331(f154(x95721),x95724),x95725))),f161(x95721,x95726)))+~P24(f331(f331(f333(f890(f884(x95721),f884(x95721))),f331(f331(f261(f884(x95721),f884(x95721)),x95723),x95725)),f161(x95721,x95726)))+~P24(f331(f331(f333(f890(x95721,x95721)),f331(f331(f261(x95721,x95721),x95722),x95724)),x95726))
% 162.26/162.08 [9598]P24(f331(x95981,x95982))+~P24(f331(x95981,f355(x95981,x95983,x95984,x95985,x95986)))+~P24(f331(f331(f333(x95986),x95982),f331(f331(f42(x95985,f891(x95986,a877)),x95984),x95983)))
% 162.26/162.08 [9603]~P24(f331(f331(f333(f890(f884(x96031),f884(x96031))),f331(f331(f261(f884(x96031),f884(x96031)),f331(f331(f154(x96031),x96032),x96035)),f331(f331(f154(x96031),x96033),x96036))),f148(x96031,x96034)))+P24(f331(f331(f333(f890(f884(x96031),f884(x96031))),f331(f331(f261(f884(x96031),f884(x96031)),x96035),x96036)),f148(x96031,x96034)))+P24(f331(f331(f333(f890(x96031,x96031)),f331(f331(f261(x96031,x96031),x96032),x96033)),x96034))
% 162.26/162.08 [9604]~P24(f331(f331(f333(f890(f884(x96041),f884(x96041))),f331(f331(f261(f884(x96041),f884(x96041)),f331(f331(f154(x96041),x96042),x96045)),f331(f331(f154(x96041),x96043),x96046))),f150(x96041,x96044)))+P24(f331(f331(f333(f890(f884(x96041),f884(x96041))),f331(f331(f261(f884(x96041),f884(x96041)),x96045),x96046)),f150(x96041,x96044)))+P24(f331(f331(f333(f890(x96041,x96041)),f331(f331(f261(x96041,x96041),x96042),x96043)),x96044))
% 162.26/162.08 [9605]~P24(f331(f331(f333(f890(f884(x96051),f884(x96051))),f331(f331(f261(f884(x96051),f884(x96051)),f331(f331(f154(x96051),x96052),x96055)),f331(f331(f154(x96051),x96053),x96056))),f160(x96051,x96054)))+P24(f331(f331(f333(f890(f884(x96051),f884(x96051))),f331(f331(f261(f884(x96051),f884(x96051)),x96055),x96056)),f160(x96051,x96054)))+P24(f331(f331(f333(f890(x96051,x96051)),f331(f331(f261(x96051,x96051),x96052),x96053)),x96054))
% 162.26/162.08 [9692]P24(f331(x96921,x96922))+P24(f331(f331(f333(x96923),f356(x96921,x96924,x96925,x96923,x96926)),x96925))+~P24(f331(f331(f333(x96926),x96922),f331(f331(f42(x96923,f891(x96926,a877)),x96925),x96924)))
% 162.26/162.08 [9703]~E(x97032,x97034)+P24(f331(f331(f333(f890(f884(x97031),f884(x97031))),f331(f331(f261(f884(x97031),f884(x97031)),f331(f331(f137(x97031),x97032),f331(f331(f154(x97031),x97033),f119(x97031)))),f331(f331(f137(x97031),x97034),f331(f331(f154(x97031),x97035),f119(x97031))))),f160(x97031,x97036)))+~P24(f331(f331(f333(f890(x97031,x97031)),f331(f331(f261(x97031,x97031),x97033),x97035)),x97036))
% 162.26/162.08 [9804]E(x98041,x98042)+~P24(f331(f331(f333(f890(f884(x98043),f884(x98043))),f331(f331(f261(f884(x98043),f884(x98043)),f331(f331(f137(x98043),x98045),f331(f331(f154(x98043),x98041),f119(x98043)))),f331(f331(f137(x98043),x98046),f331(f331(f154(x98043),x98042),f119(x98043))))),f160(x98043,x98044)))+P24(f331(f331(f333(f890(x98043,x98043)),f331(f331(f261(x98043,x98043),x98041),x98042)),x98044))
% 162.26/162.08 [9828]~P24(f331(f331(f333(f890(f884(x98281),f884(x98281))),f331(f331(f261(f884(x98281),f884(x98281)),f331(f331(f137(x98281),x98285),f331(f331(f154(x98281),x98282),f119(x98281)))),f331(f331(f137(x98281),x98286),f331(f331(f154(x98281),x98283),f119(x98281))))),f160(x98281,x98284)))+P24(f331(f331(f333(f890(f884(x98281),f884(x98281))),f331(f331(f261(f884(x98281),f884(x98281)),x98285),x98286)),f160(x98281,x98284)))+P24(f331(f331(f333(f890(x98281,x98281)),f331(f331(f261(x98281,x98281),x98282),x98283)),x98284))
% 162.26/162.08 [9852]P24(f331(x98521,x98522))+P24(f331(f331(f333(x98523),f355(x98521,x98524,x98525,x98526,x98523)),f331(x98524,f356(x98521,x98524,x98525,x98526,x98523))))+~P24(f331(f331(f333(x98523),x98522),f331(f331(f42(x98526,f891(x98523,a877)),x98525),x98524)))
% 162.26/162.08 [8815]~P12(x88153,x88154,x88151)+~P24(f331(f62(x88153),x88156))+E(f331(f331(x88151,x88152),f331(f331(f65(x88153,x88154,x88151),x88155),f331(f331(f22(f891(x88153,a877)),x88156),f331(f331(f309(x88153),x88152),f196(f891(x88153,a877)))))),f331(f331(f65(x88153,x88154,x88151),x88155),f331(f331(f309(x88153),x88152),x88156)))
% 162.26/162.08 [8903]~E(f331(f331(f180(x89031,x89032),x89034),x89035),f331(f239(x89032),x89036))+~P24(f331(f331(x89033,x89035),x89036))+E(f331(f331(f180(x89031,x89032),f331(f139(f890(x89031,x89032),f331(f270(x89031,x89032,a877),x89033)),x89034)),x89035),f331(f239(x89032),x89036))
% 162.26/162.08 [9110]~P24(f331(f331(f333(x91105),x91103),x91106))+P24(f331(f331(f247(f891(x91101,a877)),f331(x91102,x91103)),x91104))+~P24(f331(f331(f247(f891(x91101,a877)),f331(f331(f42(x91105,f891(x91101,a877)),x91106),x91102)),x91104))
% 162.26/162.08 [9775]~P6(x97751,x97755,x97754)+P24(f331(f331(f333(f890(x97751,x97751)),f331(f331(f261(x97751,x97751),x97752),x97753)),x97754))+~P24(f331(f331(f333(x97751),x97756),f331(f331(f108(f891(x97751,a877)),f331(f285(x97751,x97751,x97754),f331(f331(f309(x97751),x97752),f196(f891(x97751,a877))))),f331(f285(x97751,x97751,x97754),f331(f331(f309(x97751),x97753),f196(f891(x97751,a877)))))))
% 162.26/162.08 [8568]~P125(x85682)+~E(f331(f331(f81(x85682),f331(f331(f82(x85682),x85684),x85685)),x85681),f331(f331(f81(x85682),f331(f331(f82(x85682),x85683),x85685)),x85686))+E(x85681,f331(f331(f81(x85682),f331(f331(f82(x85682),f331(f331(f22(x85682),x85683),x85684)),x85685)),x85686))
% 162.26/162.08 [8569]~P125(x85691)+~E(f331(f331(f81(x85691),f331(f331(f82(x85691),x85692),x85694)),x85695),f331(f331(f81(x85691),f331(f331(f82(x85691),x85693),x85694)),x85696))+E(f331(f331(f81(x85691),f331(f331(f82(x85691),f331(f331(f22(x85691),x85692),x85693)),x85694)),x85695),x85696)
% 162.26/162.08 [8727]~P125(x87271)+E(f331(f331(f81(x87271),f331(f331(f82(x87271),x87272),x87273)),x87274),f331(f331(f81(x87271),f331(f331(f82(x87271),x87275),x87273)),x87276))+~E(x87276,f331(f331(f81(x87271),f331(f331(f82(x87271),f331(f331(f22(x87271),x87272),x87275)),x87273)),x87274))
% 162.26/162.08 [8728]~P125(x87281)+E(f331(f331(f81(x87281),f331(f331(f82(x87281),x87282),x87283)),x87284),f331(f331(f81(x87281),f331(f331(f82(x87281),x87285),x87283)),x87286))+~E(f331(f331(f81(x87281),f331(f331(f82(x87281),f331(f331(f22(x87281),x87282),x87285)),x87283)),x87284),x87286)
% 162.26/162.08 [9050]~P24(f331(f331(x90504,x90505),x90506))+~P24(f331(f331(x90503,x90505),x90506))+P24(f331(f331(f331(f331(f108(f891(x90501,f891(x90502,a877))),x90503),x90504),x90505),x90506))
% 162.26/162.08 [9316]P24(f331(f331(x93161,x93162),x93163))+P24(f331(f331(x93164,x93162),x93163))+~P24(f331(f331(f331(f331(f107(f891(x93165,f891(x93166,a877))),x93164),x93161),x93162),x93163))
% 162.26/162.08 [9618]~P126(x96181)+~P24(f331(f331(f248(x96181),f331(f331(f81(x96181),f331(f331(f82(x96181),x96184),x96185)),x96182)),f331(f331(f81(x96181),f331(f331(f82(x96181),x96183),x96185)),x96186)))+P24(f331(f331(f248(x96181),x96182),f331(f331(f81(x96181),f331(f331(f82(x96181),f331(f331(f22(x96181),x96183),x96184)),x96185)),x96186)))
% 162.26/162.08 [9619]~P126(x96191)+~P24(f331(f331(f247(x96191),f331(f331(f81(x96191),f331(f331(f82(x96191),x96194),x96195)),x96192)),f331(f331(f81(x96191),f331(f331(f82(x96191),x96193),x96195)),x96196)))+P24(f331(f331(f247(x96191),x96192),f331(f331(f81(x96191),f331(f331(f82(x96191),f331(f331(f22(x96191),x96193),x96194)),x96195)),x96196)))
% 162.26/162.08 [9648]~P126(x96481)+P24(f331(f331(f248(x96481),f331(f331(f81(x96481),f331(f331(f82(x96481),x96482),x96483)),x96484)),f331(f331(f81(x96481),f331(f331(f82(x96481),x96485),x96483)),x96486)))+~P24(f331(f331(f248(x96481),x96484),f331(f331(f81(x96481),f331(f331(f82(x96481),f331(f331(f22(x96481),x96485),x96482)),x96483)),x96486)))
% 162.26/162.08 [9649]~P126(x96491)+P24(f331(f331(f247(x96491),f331(f331(f81(x96491),f331(f331(f82(x96491),x96492),x96493)),x96494)),f331(f331(f81(x96491),f331(f331(f82(x96491),x96495),x96493)),x96496)))+~P24(f331(f331(f247(x96491),x96494),f331(f331(f81(x96491),f331(f331(f82(x96491),f331(f331(f22(x96491),x96495),x96492)),x96493)),x96496)))
% 162.26/162.08 [9763]~P126(x97631)+~P24(f331(f331(f248(x97631),f331(f331(f81(x97631),f331(f331(f82(x97631),x97632),x97634)),x97635)),f331(f331(f81(x97631),f331(f331(f82(x97631),x97633),x97634)),x97636)))+P24(f331(f331(f248(x97631),f331(f331(f81(x97631),f331(f331(f82(x97631),f331(f331(f22(x97631),x97632),x97633)),x97634)),x97635)),x97636))
% 162.26/162.08 [9764]~P126(x97641)+~P24(f331(f331(f247(x97641),f331(f331(f81(x97641),f331(f331(f82(x97641),x97642),x97644)),x97645)),f331(f331(f81(x97641),f331(f331(f82(x97641),x97643),x97644)),x97646)))+P24(f331(f331(f247(x97641),f331(f331(f81(x97641),f331(f331(f82(x97641),f331(f331(f22(x97641),x97642),x97643)),x97644)),x97645)),x97646))
% 162.26/162.08 [9812]~P126(x98121)+P24(f331(f331(f248(x98121),f331(f331(f81(x98121),f331(f331(f82(x98121),x98122),x98123)),x98124)),f331(f331(f81(x98121),f331(f331(f82(x98121),x98125),x98123)),x98126)))+~P24(f331(f331(f248(x98121),f331(f331(f81(x98121),f331(f331(f82(x98121),f331(f331(f22(x98121),x98122),x98125)),x98123)),x98124)),x98126))
% 162.26/162.08 [9813]~P126(x98131)+P24(f331(f331(f247(x98131),f331(f331(f81(x98131),f331(f331(f82(x98131),x98132),x98133)),x98134)),f331(f331(f81(x98131),f331(f331(f82(x98131),x98135),x98133)),x98136)))+~P24(f331(f331(f247(x98131),f331(f331(f81(x98131),f331(f331(f82(x98131),f331(f331(f22(x98131),x98132),x98135)),x98133)),x98134)),x98136))
% 162.26/162.08 [9965]~P74(x99652)+~P24(f331(f62(x99651),x99656))+E(f331(f331(f6(x99651,x99652),f331(f331(f18(x99651,x99652,x99652),f331(f331(f18(x99651,x99652,f891(x99652,x99652)),f331(f331(f8(a877,f891(x99652,f891(x99652,x99652)),x99651),f102(x99652)),x99653)),x99654)),x99655)),x99656),f331(f331(f81(x99652),f331(f331(f6(x99651,x99652),x99654),f331(f331(f108(f891(x99651,a877)),x99656),f331(f253(x99651),x99653)))),f331(f331(f6(x99651,x99652),x99655),f331(f331(f108(f891(x99651,a877)),x99656),f331(f80(f891(x99651,a877)),f331(f253(x99651),x99653))))))
% 162.26/162.08 [10025]P24(f331(f331(f333(x100252),x100254),x100256))+P24(f331(f331(f333(x100252),x100255),x100256))+E(f331(f311(x100251,x100252,f331(f331(f7(x100251,x100252,x100252),f331(f331(f7(x100251,x100252,f891(x100252,x100252)),f331(f331(f8(a877,f891(x100252,f891(x100252,x100252)),x100251),f102(x100252)),f331(f331(f7(x100251,f891(x100251,a877),a877),f333(x100251)),x100253))),x100254)),x100255)),x100256),f196(f891(x100251,a877)))
% 162.26/162.08 [10026]P24(f331(f331(f333(x100262),x100265),x100266))+~P24(f331(f331(f333(x100262),x100264),x100266))+E(f331(f311(x100261,x100262,f331(f331(f7(x100261,x100262,x100262),f331(f331(f7(x100261,x100262,f891(x100262,x100262)),f331(f331(f8(a877,f891(x100262,f891(x100262,x100262)),x100261),f102(x100262)),f331(f331(f7(x100261,f891(x100261,a877),a877),f333(x100261)),x100263))),x100264)),x100265)),x100266),x100263)
% 162.26/162.08 [10027]P24(f331(f331(f333(x100272),x100274),x100276))+~P24(f331(f331(f333(x100272),x100275),x100276))+E(f331(f311(x100271,x100272,f331(f331(f7(x100271,x100272,x100272),f331(f331(f7(x100271,x100272,f891(x100272,x100272)),f331(f331(f8(a877,f891(x100272,f891(x100272,x100272)),x100271),f102(x100272)),f331(f331(f7(x100271,f891(x100271,a877),a877),f333(x100271)),x100273))),x100274)),x100275)),x100276),f331(f80(f891(x100271,a877)),x100273))
% 162.26/162.08 [10028]~P24(f331(f331(f333(x100282),x100284),x100286))+~P24(f331(f331(f333(x100282),x100285),x100286))+E(f331(f311(x100281,x100282,f331(f331(f7(x100281,x100282,x100282),f331(f331(f7(x100281,x100282,f891(x100282,x100282)),f331(f331(f8(a877,f891(x100282,f891(x100282,x100282)),x100281),f102(x100282)),f331(f331(f7(x100281,f891(x100281,a877),a877),f333(x100281)),x100283))),x100284)),x100285)),x100286),f256(f891(x100281,a877)))
% 162.26/162.08 [10195]P20(x101951,x101952,f331(f331(f309(f882(x101951)),f331(f331(f331(f93(x101951),f331(x101953,x101954)),f331(a28,x101954)),f331(x101955,x101954))),f196(f891(f882(x101951),a877))))+~P24(f331(f331(f333(a880),x101954),x101956))+~P20(x101951,f331(f331(f107(f891(f882(x101951),a877)),x101952),f331(f310(a880,f882(x101951),f331(f331(f18(a880,f891(x101951,f891(a878,a877)),f882(x101951)),f331(f331(f18(a880,a879,f891(f891(x101951,f891(a878,a877)),f882(x101951))),f331(f331(f8(f891(x101951,f891(a878,a877)),f891(a879,f891(f891(x101951,f891(a878,a877)),f882(x101951))),a880),f93(x101951)),x101953)),a28)),x101955)),x101956)),f331(f310(a880,f882(x101951),f331(f331(f18(a880,f891(x101951,f891(a878,a877)),f882(x101951)),f331(f331(f18(a880,a879,f891(f891(x101951,f891(a878,a877)),f882(x101951))),f331(f331(f8(f891(x101951,f891(a878,a877)),f891(a879,f891(f891(x101951,f891(a878,a877)),f882(x101951))),a880),f93(x101951)),x101953)),f331(f331(f8(f887(a879),a879,a880),f244(a879)),a26))),x101955)),x101956))
% 162.26/162.08 [8597]E(x85971,x85972)+~P54(x85974,x85975,x85973,x85976,x85977)+~E(f331(x85973,x85971),f331(x85973,x85972))
% 162.26/162.08 [7005]E(f331(f242(f887(x70051),x70052,f199(x70051),x70053),f331(x70054,x70055)),f331(f239(x70051),x70056))+~E(f331(x70054,x70055),f331(f239(x70052),x70057))+~E(f331(x70053,x70057),f331(f239(x70051),x70056))
% 162.26/162.08 [8627]~P4(x86276,x86275,x86277,x86274,x86271)+E(f331(f331(x86271,x86272),x86273),x86274)+P24(f331(f62(x86275),x86273))
% 162.26/162.08 [9464]P42(x94641,x94642,x94643,x94644,x94645,f331(f331(x94643,x94646),x94647))+~E(f331(f331(x94643,x94646),x94647),x94644)+~E(x94645,f196(f891(x94641,a877)))
% 162.26/162.08 [9667]~P24(f331(x96676,x96673))+~P24(f331(f331(f333(f890(x96672,x96672)),f331(f331(f261(x96672,x96672),x96674),x96675)),f331(x96677,x96673)))+P24(f331(f331(f333(f890(f890(x96671,x96672),f890(x96671,x96672))),f331(f331(f261(f890(x96671,x96672),f890(x96671,x96672)),f331(f331(f261(x96671,x96672),x96673),x96674)),f331(f331(f261(x96671,x96672),x96673),x96675))),f283(x96671,x96672,x96676,x96677)))
% 162.26/162.08 [10085]~P42(x100852,x100857,x100853,x100856,x100851,f331(f331(x100853,x100855),x100854))+E(f331(f331(x100853,f830(x100854,x100855,x100851,x100856,x100853,x100857,x100852)),f831(x100854,x100855,x100851,x100856,x100853,x100857,x100852)),f331(f331(x100853,x100855),x100854))+E(x100851,f196(f891(x100852,a877)))
% 162.26/162.08 [10086]~P42(x100867,x100866,x100861,x100864,x100865,f331(f331(x100861,x100862),x100863))+E(f331(f331(x100861,f830(x100863,x100862,x100865,x100864,x100861,x100866,x100867)),f831(x100863,x100862,x100865,x100864,x100861,x100866,x100867)),f331(f331(x100861,x100862),x100863))+E(f331(f331(x100861,x100862),x100863),x100864)
% 162.26/162.08 [9153]~P35(x91531,x91532,x91533,x91535,x91537)+P35(x91531,x91532,x91533,f331(f331(f154(x91531),x91534),x91535),f331(f331(f154(x91532),x91536),x91537))+~P24(f331(f331(x91533,x91534),x91536))
% 162.26/162.08 [9171]P35(x91711,x91712,x91713,x91714,x91715)+~P35(x91711,x91712,x91713,f331(f331(f137(x91711),x91716),x91714),f331(f331(f137(x91712),x91717),x91715))+~E(f331(f197(f884(x91711)),x91716),f331(f197(f884(x91712)),x91717))
% 162.26/162.08 [9172]P35(x91721,x91722,x91723,x91724,x91725)+~P35(x91721,x91722,x91723,f331(f331(f137(x91721),x91724),x91726),f331(f331(f137(x91722),x91725),x91727))+~E(f331(f197(f884(x91721)),x91724),f331(f197(f884(x91722)),x91725))
% 162.26/162.08 [9383]~P35(x93831,x93832,x93833,x93835,x93837)+~P35(x93831,x93832,x93833,x93834,x93836)+P35(x93831,x93832,x93833,f331(f331(f137(x93831),x93834),x93835),f331(f331(f137(x93832),x93836),x93837))
% 162.26/162.08 [9745]~P24(f331(f67(x97451,x97454,x97455,x97456,x97453),x97457))+P24(f331(f67(x97451,x97454,x97455,x97456,f331(f331(f309(x97451),x97452),x97453)),f331(f331(x97455,x97452),x97457)))+P24(f331(f331(f333(x97451),x97452),x97453))
% 162.26/162.08 [9878]~P21(x98783,x98781,x98784,f256(f891(x98783,a877)))+E(f331(f331(f180(x98781,x98782),f331(f331(f157(f890(x98783,x98782),f890(x98781,x98782)),f331(f270(x98783,x98782,f890(x98781,x98782)),f331(f331(f8(x98781,f891(x98782,f890(x98781,x98782)),x98783),f261(x98781,x98782)),x98784))),x98785)),f331(x98784,x98786)),f331(f239(x98782),x98787))+~E(f331(f331(f180(x98783,x98782),x98785),x98786),f331(f239(x98782),x98787))
% 162.26/162.08 [10106]~P42(x101062,x101067,x101066,x101065,x101061,f331(f331(x101066,x101064),x101063))+E(x101061,f196(f891(x101062,a877)))+P24(f331(f331(f333(x101062),f830(x101063,x101064,x101061,x101065,x101066,x101067,x101062)),x101061))
% 162.26/162.08 [10107]~P42(x101075,x101077,x101071,x101074,x101076,f331(f331(x101071,x101072),x101073))+E(f331(f331(x101071,x101072),x101073),x101074)+P24(f331(f331(f333(x101075),f830(x101073,x101072,x101076,x101074,x101071,x101077,x101075)),x101076))
% 162.26/162.08 [6798]~E(x67985,x67987)+~E(x67986,x67984)+E(f331(f331(f331(f331(f73(x67981,f887(x67982)),x67983),x67984),f331(f239(x67982),x67985)),x67986),f331(f239(x67982),x67987))
% 162.26/162.08 [6920]E(x69201,x69202)+~E(f331(x69205,x69201),f331(f239(x69204),x69207))+E(f331(f331(f331(f331(f73(x69203,f887(x69204)),x69205),x69202),f331(f239(x69204),x69206)),x69201),f331(f239(x69204),x69207))
% 162.26/162.08 [7623]E(x76231,x76232)+~E(x76233,x76234)+~E(f331(f331(f331(f331(f73(x76235,f887(x76236)),x76237),x76234),f331(f239(x76236),x76231)),x76233),f331(f239(x76236),x76232))
% 162.26/162.08 [7687]E(x76871,x76872)+E(f331(x76873,x76874),f331(f239(x76875),x76871))+~E(f331(f331(f331(f331(f73(x76876,f887(x76875)),x76873),x76877),f331(f239(x76875),x76872)),x76874),f331(f239(x76875),x76871))
% 162.26/162.08 [7688]E(x76881,x76882)+E(f331(x76883,x76881),f331(f239(x76884),x76885))+~E(f331(f331(f331(f331(f73(x76886,f887(x76884)),x76883),x76882),f331(f239(x76884),x76887)),x76881),f331(f239(x76884),x76885))
% 162.26/162.08 [8841]~P17(x88414,x88415,x88416,x88417,x88411)+~P24(f331(f62(x88415),x88413))+E(f331(f331(x88411,x88412),x88413),f331(f331(f331(f66(x88414,x88415,x88416),x88412),x88417),x88413))
% 162.26/162.08 [8842]~P4(x88424,x88425,x88426,x88427,x88421)+~P24(f331(f62(x88425),x88423))+E(f331(f331(x88421,x88422),x88423),f331(f331(f331(f66(x88424,x88425,x88426),x88422),x88427),x88423))
% 162.26/162.08 [9432]~P20(x94321,x94322,f331(f331(f309(f882(x94321)),f331(f331(f331(f93(x94321),x94323),x94324),x94327)),f196(f891(f882(x94321),a877))))+P20(x94321,x94322,f331(f331(f309(f882(x94321)),f331(f331(f331(f93(x94321),x94323),f34(x94324,x94325)),x94326)),f196(f891(f882(x94321),a877))))+~P20(x94321,x94322,f331(f331(f309(f882(x94321)),f331(f331(f331(f93(x94321),x94327),x94325),x94326)),f196(f891(f882(x94321),a877))))
% 162.26/162.08 [9643]~P19(x96433,x96434,x96435,x96437,x96436,x96431)+~P24(f331(f62(x96434),x96432))+E(f331(x96431,x96432),f331(f331(f331(f66(x96433,x96434,x96435),x96436),x96437),x96432))
% 162.26/162.08 [9808]P42(x98081,x98082,x98083,x98084,x98085,f331(f331(x98083,x98086),x98087))+~P42(x98081,x98082,x98083,x98084,f331(f331(f22(f891(x98081,a877)),x98085),f331(f331(f309(x98081),x98086),f196(f891(x98081,a877)))),x98087)+~P24(f331(f331(f333(x98081),x98086),x98085))
% 162.26/162.08 [10052]~P20(x100521,x100522,f331(f331(f309(f882(x100521)),f331(f331(f331(f93(x100521),f98(x100521,x100523,x100524)),x100525),x100527)),f196(f891(f882(x100521),a877))))+P20(x100521,x100522,f331(f331(f309(f882(x100521)),f331(f331(f331(f93(x100521),x100523),f31(x100524,x100525,x100526)),x100527)),f196(f891(f882(x100521),a877))))+~P20(x100521,x100522,f331(f331(f309(f882(x100521)),f331(f331(f331(f93(x100521),f98(x100521,x100523,f331(f74(a877,a877,a878,a326),x100524))),x100526),x100527)),f196(f891(f882(x100521),a877))))
% 162.26/162.08 [10146]P20(x101467,x101466,f331(f331(f309(f882(x101467)),f331(f331(f331(f93(x101467),x101461),x101464),x101462)),f196(f891(f882(x101467),a877))))+~P20(x101467,x101466,f331(f331(f309(f882(x101467)),f331(f331(f331(f93(x101467),x101465),x101464),x101463)),f196(f891(f882(x101467),a877))))+P24(f331(f331(x101461,f427(x101462,x101461,x101463,x101464,x101465,x101466,x101467)),f439(x101462,x101461,x101463,x101464,x101465,x101466,x101467)))
% 162.26/162.08 [10156]~P42(x101562,x101563,x101564,x101565,x101561,f331(f331(x101564,x101567),x101566))+P42(x101562,x101563,x101564,x101565,f331(f331(f22(f891(x101562,a877)),x101561),f331(f331(f309(x101562),f830(x101566,x101567,x101561,x101565,x101564,x101563,x101562)),f196(f891(x101562,a877)))),f831(x101566,x101567,x101561,x101565,x101564,x101563,x101562))+E(x101561,f196(f891(x101562,a877)))
% 162.26/162.08 [10157]~P42(x101575,x101576,x101571,x101574,x101577,f331(f331(x101571,x101572),x101573))+P42(x101575,x101576,x101571,x101574,f331(f331(f22(f891(x101575,a877)),x101577),f331(f331(f309(x101575),f830(x101573,x101572,x101577,x101574,x101571,x101576,x101575)),f196(f891(x101575,a877)))),f831(x101573,x101572,x101577,x101574,x101571,x101576,x101575))+E(f331(f331(x101571,x101572),x101573),x101574)
% 162.26/162.08 [10158]~P20(x101581,x101582,f331(f331(f309(f882(x101581)),f331(f331(f331(f93(x101581),x101587),x101584),x101586)),f196(f891(f882(x101581),a877))))+P20(x101581,x101582,f331(f331(f309(f882(x101581)),f331(f331(f331(f93(x101581),x101583),x101584),x101585)),f196(f891(f882(x101581),a877))))+~P24(f331(f331(x101585,f427(x101585,x101583,x101586,x101584,x101587,x101582,x101581)),f446(x101585,x101583,x101586,x101584,x101587,x101582,x101581)))
% 162.26/162.08 [9160]E(f189(x91601,x91602,x91603,x91604,f331(f331(f162(x91602,x91605),x91606),x91607)),f189(x91601,x91602,x91603,x91604,x91605))+~P24(f331(f331(f248(a883),x91606),f331(f197(f884(x91602)),x91605)))+~P24(f331(f331(f247(a883),f331(f197(f884(x91601)),x91604)),x91606))
% 162.26/162.08 [9452]P24(f331(f331(f247(f891(f890(x94521,x94522),a877)),f331(f331(f288(x94521,x94523,x94522),x94524),x94525)),f331(f331(f288(x94521,x94523,x94522),x94526),x94527)))+~P24(f331(f331(f247(f891(f890(x94523,x94522),a877)),x94525),x94527))+~P24(f331(f331(f247(f891(f890(x94521,x94523),a877)),x94524),x94526))
% 162.26/162.08 [9818]~P24(f331(f331(f333(x98181),x98186),x98185))+P24(f331(f67(x98181,x98182,x98183,x98184,x98185),f331(f331(x98183,x98186),x98187)))+~P24(f331(f67(x98181,x98182,x98183,x98184,f331(f331(f22(f891(x98181,a877)),x98185),f331(f331(f309(x98181),x98186),f196(f891(x98181,a877))))),x98187))
% 162.26/162.08 [10233]~P144(x102331)+~P21(f890(x102332,x102333),x102331,f331(f270(x102332,x102333,x102331),f331(f331(f7(x102332,f891(x102333,x102331),f891(x102333,x102331)),f331(f331(f8(f891(x102331,x102331),f891(f891(x102333,x102331),f891(x102333,x102331)),x102332),f8(x102331,x102331,x102333)),f331(f331(f8(x102331,f891(x102331,x102331),x102332),f82(x102331)),x102334))),x102335)),f331(f331(f268(x102332,x102333),x102336),f331(f16(f891(x102333,a877),x102332),x102337)))+E(f331(f331(f6(x102331,x102331),f35(x102331)),f331(f253(x102331),f331(f331(f8(f891(x102332,a877),a877,x102331),f87(x102332)),f331(f331(f8(f891(x102332,f891(x102333,a877)),f891(x102332,a877),x102331),f331(f8(f891(x102333,a877),a877,x102332),f87(x102333))),f331(f331(f7(x102331,f891(x102332,f891(x102333,a877)),f891(x102332,f891(x102333,a877))),f331(f331(f8(f891(x102332,f891(f891(x102333,a877),f891(x102333,a877))),f891(f891(x102332,f891(x102333,a877)),f891(x102332,f891(x102333,a877))),x102331),f18(x102332,f891(x102333,a877),f891(x102333,a877))),f331(f331(f8(f891(x102332,f891(x102333,f891(a877,a877))),f891(x102332,f891(f891(x102333,a877),f891(x102333,a877))),x102331),f331(f8(f891(x102333,f891(a877,a877)),f891(f891(x102333,a877),f891(x102333,a877)),x102332),f18(x102333,a877,a877))),f331(f331(f8(f891(x102332,f891(x102333,a877)),f891(x102332,f891(x102333,f891(a877,a877))),x102331),f331(f8(f891(x102333,a877),f891(x102333,f891(a877,a877)),x102332),f331(f8(a877,f891(a877,a877),x102333),a329))),f331(f331(f7(x102331,f891(x102332,f891(x102333,x102331)),f891(x102332,f891(x102333,a877))),f331(f331(f8(f891(f891(x102333,x102331),f891(x102333,a877)),f891(f891(x102332,f891(x102333,x102331)),f891(x102332,f891(x102333,a877))),x102331),f8(f891(x102333,x102331),f891(x102333,a877),x102332)),f331(f331(f8(f891(x102331,a877),f891(f891(x102333,x102331),f891(x102333,a877)),x102331),f8(x102331,a877,x102333)),a328))),f331(f331(f7(x102332,f891(x102333,x102331),f891(x102333,x102331)),f331(f331(f8(f891(x102331,x102331),f891(f891(x102333,x102331),f891(x102333,x102331)),x102332),f8(x102331,x102331,x102333)),f331(f331(f8(x102331,f891(x102331,x102331),x102332),f82(x102331)),x102334))),x102335)))))),f331(f331(f7(x102332,f891(x102333,a877),f891(x102333,a877)),f331(f331(f8(f891(a877,a877),f891(f891(x102333,a877),f891(x102333,a877)),x102332),f8(a877,a877,x102333)),f331(f331(f8(a877,f891(a877,a877),x102332),a329),f331(f331(f7(x102332,f891(x102332,a877),a877),f333(x102332)),x102336)))),f331(f331(f7(x102333,f891(x102333,a877),a877),f333(x102333)),x102337))))))),f331(f331(f82(x102331),f331(f331(f6(x102332,x102331),x102334),x102336)),f331(f331(f6(x102333,x102331),x102335),x102337)))
% 162.26/162.08 [9907]P51(x99071,x99072,x99073,x99074,x99075,x99076,x99077)+~P24(f331(f331(x99074,x99076),x99078))+~P24(f331(f331(x99075,x99078),x99077))
% 162.26/162.08 [9220]~P15(x92208,x92201,x92203,x92205)+~P24(f331(f62(x92208),x92206))+E(f331(f74(x92201,x92201,x92202,f331(x92203,x92204)),f331(f74(x92201,x92201,x92202,f331(x92205,x92206)),x92207)),f331(f74(x92201,x92201,x92202,f331(x92205,x92206)),f331(f74(x92201,x92201,x92202,f331(x92203,x92204)),x92207)))
% 162.26/162.08 [9629]~P18(x96297,x96292,x96295,x96298,x96296,x96291)+~P24(f331(f62(x96292),x96294))+E(f331(x96291,f331(f331(f309(x96292),x96293),x96294)),f331(f331(x96295,f331(x96296,x96293)),f331(x96291,x96294)))
% 162.26/162.08 [9761]~P21(x97612,x97614,x97616,x97618)+~P21(x97611,x97613,x97615,x97617)+P21(f890(x97611,x97612),f890(x97613,x97614),f271(x97611,x97613,x97612,x97614,x97615,x97616),f331(f331(f268(x97611,x97612),x97617),f331(f16(f891(x97612,a877),x97611),x97618)))
% 162.26/162.08 [9400]P24(f331(f331(f333(f890(x94001,x94002)),f331(f331(f261(x94001,x94002),x94003),x94004)),f331(f331(f288(x94001,x94005,x94002),x94006),x94007)))+~P24(f331(f331(f333(f890(x94001,x94005)),f331(f331(f261(x94001,x94005),x94003),x94008)),x94006))+~P24(f331(f331(f333(f890(x94005,x94002)),f331(f331(f261(x94005,x94002),x94008),x94004)),x94007))
% 162.26/162.08 [9606]~P24(f331(f331(f247(f891(f890(x96063,x96062),a877)),x96065),f331(f331(f268(x96063,x96062),x96068),f331(f16(f891(x96062,a877),x96063),x96067))))+~P24(f331(f331(f247(f891(f890(x96061,x96063),a877)),x96064),f331(f331(f268(x96061,x96063),x96066),f331(f16(f891(x96063,a877),x96061),x96068))))+P24(f331(f331(f247(f891(f890(x96061,x96062),a877)),f331(f331(f288(x96061,x96063,x96062),x96064),x96065)),f331(f331(f268(x96061,x96062),x96066),f331(f16(f891(x96062,a877),x96061),x96067))))
% 162.26/162.08 [9662]~E(x96623,x96625)+P24(f331(f331(f333(f890(f890(x96621,x96622),f890(x96621,x96622))),f331(f331(f261(f890(x96621,x96622),f890(x96621,x96622)),f331(f331(f261(x96621,x96622),x96623),x96624)),f331(f331(f261(x96621,x96622),x96625),x96626))),f323(x96621,x96622,x96627,x96628)))+~P24(f331(f331(f333(f890(x96622,x96622)),f331(f331(f261(x96622,x96622),x96624),x96626)),x96628))
% 162.26/162.08 [9787]E(x97871,x97872)+~P24(f331(f331(f333(f890(f890(x97873,x97875),f890(x97873,x97875))),f331(f331(f261(f890(x97873,x97875),f890(x97873,x97875)),f331(f331(f261(x97873,x97875),x97871),x97876)),f331(f331(f261(x97873,x97875),x97872),x97877))),f323(x97873,x97875,x97874,x97878)))+P24(f331(f331(f333(f890(x97873,x97873)),f331(f331(f261(x97873,x97873),x97871),x97872)),x97874))
% 162.26/162.08 [9803]~P24(f331(f331(f333(f890(f890(x98031,x98035),f890(x98031,x98035))),f331(f331(f261(f890(x98031,x98035),f890(x98031,x98035)),f331(f331(f261(x98031,x98035),x98032),x98036)),f331(f331(f261(x98031,x98035),x98033),x98037))),f323(x98031,x98035,x98034,x98038)))+P24(f331(f331(f333(f890(x98031,x98031)),f331(f331(f261(x98031,x98031),x98032),x98033)),x98034))+P24(f331(f331(f333(f890(x98035,x98035)),f331(f331(f261(x98035,x98035),x98036),x98037)),x98038))
% 162.26/162.08 [9693]~P19(x96937,x96935,x96931,x96938,x96932,x96934)+~P24(f331(f62(x96935),x96936))+E(f331(f331(x96931,f331(x96932,x96933)),f331(x96934,f331(f331(f22(f891(x96935,a877)),x96936),f331(f331(f309(x96935),x96933),f196(f891(x96935,a877)))))),f331(x96934,f331(f331(f309(x96935),x96933),x96936)))
% 162.26/162.08 [9179]~P24(f331(f331(f331(x91795,x91798),x91796),x91797))+~P24(f331(f331(f333(x91791),x91798),x91794))+P24(f331(f331(f331(f331(f42(x91791,f891(x91792,f891(x91793,a877))),x91794),x91795),x91796),x91797))
% 162.26/162.08 [9391]P24(f331(f331(f331(x93911,x93912),x93913),x93914))+~P24(f331(f331(f333(x93915),x93912),x93916))+~P24(f331(f331(f331(f331(f43(x93915,f891(x93917,f891(x93918,a877))),x93916),x93911),x93913),x93914))
% 162.26/162.08 [9599]~P17(x95993,x95992,x95994,x95998,x95991)+~P24(f331(f62(x95992),x95997))+E(f331(f331(x95991,f331(f331(f18(x95992,x95993,x95993),f331(f331(f8(x95993,f891(x95993,x95993),x95992),x95994),x95995)),x95996)),x95997),f331(f331(x95994,f331(f331(x95991,x95995),x95997)),f331(f331(x95991,x95996),x95997)))
% 162.26/162.08 [9886]~E(f331(f310(x98862,x98864,x98866),x98868),x988610)+~E(f331(f310(x98861,x98863,x98865),x98867),x98869)+E(f331(f310(f890(x98861,x98862),f890(x98863,x98864),f271(x98861,x98863,x98862,x98864,x98865,x98866)),f331(f331(f268(x98861,x98862),x98867),f331(f16(f891(x98862,a877),x98861),x98868))),f331(f331(f268(x98863,x98864),x98869),f331(f16(f891(x98864,a877),x98863),x988610)))
% 162.26/162.08 [9872]~P1(a5000)+~P2(a5000)+P20(a878,f331(f310(a880,f882(a878),f331(f331(f8(a879,f882(a878),a880),a94),a28)),f186(a880,a879,a26)),x98721)+~P24(f331(f331(f247(f891(f882(a878),a877)),x98721),f331(f310(a880,f882(a878),f331(f331(f8(a879,f882(a878),a880),a94),f331(f331(f8(f887(a879),a879,a880),f244(a879)),a26))),f186(a880,a879,a26))))
% 162.26/162.08 [6517]~P1(a5000)+~P2(a5000)+~P24(f331(a25,x65171))+P20(a878,f196(f891(f882(a878),a877)),f331(f331(f309(f882(a878)),f331(a94,x65171)),f196(f891(f882(a878),a877))))
% 162.26/162.08 [4860]~P107(x48602)+~P29(x48602,x48601)+P29(x48602,f120(x48602,x48601))+E(x48601,f119(x48602))
% 162.26/162.08 [4861]~P107(x48612)+~P29(x48612,x48611)+P29(x48612,f660(x48611,x48612))+E(x48611,f119(x48612))
% 162.26/162.08 [5093]~P27(x50932)+E(f10(x50932,x50931),f41(x50932,x50931))+E(x50931,f196(f891(x50932,a877)))+~P24(f331(f62(x50932),x50931))
% 162.26/162.08 [5094]~P27(x50942)+E(f13(x50942,x50941),f40(x50942,x50941))+E(x50941,f196(f891(x50942,a877)))+~P24(f331(f62(x50942),x50941))
% 162.26/162.08 [5254]~P107(x52542)+~P29(x52542,x52541)+E(x52541,f119(x52542))+E(f331(f331(f154(x52542),f695(x52541,x52542)),f660(x52541,x52542)),x52541)
% 162.26/162.08 [6050]~P96(x60502)+E(x60501,f196(f891(x60502,a877)))+P24(f331(f331(f247(x60502),f10(x60502,x60501)),f13(x60502,x60501)))+~P24(f331(f62(x60502),x60501))
% 162.26/162.08 [6062]~P40(x60622)+~P40(x60621)+E(x60621,x60622)+~E(f331(f310(a1,a883,a111),x60621),f331(f310(a1,a883,a111),x60622))
% 162.26/162.08 [9034]~P111(x90341)+~P24(f331(f331(f333(x90341),x90342),f116(x90341)))+P24(f331(f331(f248(x90341),f331(f331(f81(x90341),f331(f331(f81(x90341),f79(x90341)),x90342)),x90342)),f2(x90341)))+~P24(f331(f331(f248(x90341),x90342),f2(x90341)))
% 162.26/162.08 [9278]~P111(x92781)+~P24(f331(f331(f333(x92781),x92782),f116(x92781)))+~P24(f331(f331(f248(x92781),f331(f331(f81(x92781),f331(f331(f81(x92781),f79(x92781)),x92782)),x92782)),f2(x92781)))+P24(f331(f331(f248(x92781),x92782),f2(x92781)))
% 162.26/162.08 [4916]~P115(x49162)+~P144(x49162)+E(x49161,f2(a883))+E(f331(f331(f262(x49162),f2(x49162)),x49161),f2(x49162))
% 162.26/162.08 [4921]~P115(x49211)+~P144(x49211)+~E(x49212,f2(a883))+E(f331(f331(f262(x49211),f2(x49211)),x49212),f79(x49211))
% 162.26/162.08 [5080]~P137(x50802)+E(x50801,f79(x50802))+E(x50801,f331(f80(x50802),f79(x50802)))+~E(f331(f331(f82(x50802),x50801),x50801),f79(x50802))
% 162.26/162.08 [5337]~P88(x53372)+E(x53371,f2(x53372))+E(f83(x53372,x53371),f331(f80(x53372),f79(x53372)))+P24(f331(f331(f248(x53372),f2(x53372)),x53371))
% 162.26/162.08 [5571]~P88(x55712)+E(f83(x55712,x55711),f79(x55712))+E(x55711,f2(x55712))+~P24(f331(f331(f248(x55712),f2(x55712)),x55711))
% 162.26/162.08 [5580]E(x55801,x55802)+~E(f331(f110(a883),x55801),f331(f110(a883),x55802))+P24(f331(a202,f331(f110(a1),x55802)))+P24(f331(a202,f331(f110(a1),x55801)))
% 162.26/162.08 [5631]~P91(x56311)+~E(x56312,f2(x56311))+E(f331(f331(f81(x56311),x56312),x56312),f2(x56311))+~P24(f331(f331(f333(x56311),x56312),f116(x56311)))
% 162.26/162.08 [5669]E(x56691,f2(a1))+~E(f331(f331(f39(a1),x56692),x56691),f2(a1))+P24(f331(f331(f248(a1),x56691),x56692))+P24(f331(f331(f248(a1),x56692),x56691))
% 162.26/162.08 [5700]E(x57001,f2(a1))+~E(f331(f331(f39(a1),x57002),x57001),f2(a1))+P24(f331(f331(f247(a1),x57002),f2(a1)))+P24(f331(f331(f248(a1),x57002),x57001))
% 162.26/162.08 [5733]E(x57331,f2(a1))+~E(f331(f331(f39(a1),x57332),x57331),f2(a1))+P24(f331(f331(f247(a1),f2(a1)),x57332))+P24(f331(f331(f248(a1),x57331),x57332))
% 162.26/162.08 [5769]~P91(x57692)+E(x57691,f2(x57692))+~E(f331(f331(f81(x57692),x57691),x57691),f2(x57692))+~P24(f331(f331(f333(x57692),x57691),f116(x57692)))
% 162.26/162.08 [5829]E(f331(f110(a883),x58291),f331(f110(a883),x58292))+~E(f331(f110(a1),x58292),f2(a1))+P24(f331(a202,f331(f110(a1),x58292)))+~P24(f331(a202,f331(f110(a1),x58291)))
% 162.26/162.08 [5856]~E(f331(f110(a883),x58562),f331(f110(a883),x58561))+E(f331(f110(a1),x58561),f2(a1))+P24(f331(a202,f331(f110(a1),x58561)))+~P24(f331(a202,f331(f110(a1),x58562)))
% 162.26/162.08 [5865]~P107(x58652)+E(x58651,f196(f891(x58652,a877)))+~P24(f331(f62(x58652),x58651))+P24(f331(f331(f333(x58652),f14(x58652,x58651)),x58651))
% 162.26/162.08 [5866]~P107(x58662)+E(x58661,f196(f891(x58662,a877)))+~P24(f331(f62(x58662),x58661))+P24(f331(f331(f333(x58662),f15(x58662,x58661)),x58661))
% 162.26/162.08 [6030]~P111(x60301)+~P94(x60301)+P24(f331(f331(f248(x60301),f2(x60301)),f331(f110(x60301),x60302)))+~P24(f331(f331(f248(a1),a84),x60302))
% 162.26/162.08 [6031]~P111(x60311)+~P94(x60311)+P24(f331(f331(f247(x60311),f2(x60311)),f331(f110(x60311),x60312)))+~P24(f331(f331(f247(a1),a84),x60312))
% 162.26/162.08 [6049]~P111(x60491)+~P94(x60491)+E(f331(f76(x60491),f331(f110(x60491),x60492)),f331(f110(x60491),x60492))+P24(f331(f331(f248(x60491),f331(f110(x60491),x60492)),f2(x60491)))
% 162.26/162.08 [6089]E(x60891,x60892)+~E(f331(a111,x60891),f331(a111,x60892))+~P24(f331(f331(f247(a1),f2(a1)),x60892))+~P24(f331(f331(f247(a1),f2(a1)),x60891))
% 162.26/162.08 [6282]~P94(x62822)+~P111(x62822)+~P24(f331(f331(f248(x62822),f2(x62822)),f331(f110(x62822),x62821)))+P24(f331(f331(f248(a1),a84),x62821))
% 162.26/162.08 [6283]~P94(x62832)+~P111(x62832)+~P24(f331(f331(f247(x62832),f2(x62832)),f331(f110(x62832),x62831)))+P24(f331(f331(f247(a1),a84),x62831))
% 162.26/162.08 [6288]~P111(x62881)+~P94(x62881)+P24(f331(f331(f248(x62881),f331(f110(x62881),x62882)),f2(x62881)))+~P24(f331(f331(f248(a1),x62882),a84))
% 162.26/162.08 [6289]~P111(x62891)+~P94(x62891)+P24(f331(f331(f247(x62891),f331(f110(x62891),x62892)),f2(x62891)))+~P24(f331(f331(f247(a1),x62892),a84))
% 162.26/162.08 [6592]~P94(x65922)+~P111(x65922)+~P24(f331(f331(f248(x65922),f331(f110(x65922),x65921)),f2(x65922)))+P24(f331(f331(f248(a1),x65921),a84))
% 162.26/162.08 [6593]~P94(x65932)+~P111(x65932)+~P24(f331(f331(f247(x65932),f331(f110(x65932),x65931)),f2(x65932)))+P24(f331(f331(f247(a1),x65931),a84))
% 162.26/162.08 [6684]~P111(x66841)+~P94(x66841)+E(f331(f76(x66841),f331(f110(x66841),x66842)),f331(f80(x66841),f331(f110(x66841),x66842)))+~P24(f331(f331(f248(x66841),f331(f110(x66841),x66842)),f2(x66841)))
% 162.26/162.08 [6702]E(f331(f110(a883),x67021),f331(f110(a883),x67022))+~E(f331(f110(a1),x67022),f2(a1))+~P24(f331(f331(f247(a1),f331(f110(a1),x67021)),f2(a1)))+~P24(f331(a202,f331(f110(a1),x67021)))
% 162.26/162.08 [7556]~P107(x75562)+E(x75561,f196(f891(x75562,a877)))+~P24(f331(f62(x75562),x75561))+P24(f331(f331(f247(x75562),f11(x75562,f251(x75562),x75561)),f12(x75562,f246(x75562),x75561)))
% 162.26/162.08 [7868]~P40(x78682)+~P28(x78681)+P24(f331(f331(f333(a1),x78681),x78682))+~P24(f331(f331(f333(a883),f331(a111,x78681)),f331(f310(a1,a883,a111),x78682)))
% 162.26/162.08 [8144]~P60(x81442)+P24(f331(x81441,f199(x81442)))+~P24(f331(f58(f887(x81442)),x81441))+P24(f331(f58(x81442),f331(f331(f8(f887(x81442),a877,x81442),x81441),f239(x81442))))
% 162.26/162.08 [8605]~P60(x86051)+~P24(f331(x86052,f199(x86051)))+P24(f331(f59(f887(x86051)),x86052))+~P24(f331(f59(x86051),f331(f331(f8(f887(x86051),a877,x86051),x86052),f239(x86051))))
% 162.26/162.08 [5862]~P138(x58622)+E(x58621,f2(a1))+E(f331(f80(x58622),f331(f109(x58622),f331(f80(a1),x58621))),f331(f109(x58622),x58621))+~P24(f331(f331(f248(a1),x58621),f2(a1)))
% 162.26/162.08 [6270]~P75(x62702)+E(x62701,f196(f891(x62702,a877)))+E(f15(x62702,f331(f310(x62702,x62702,f80(x62702)),x62701)),f331(f80(x62702),f14(x62702,x62701)))+~P24(f331(f62(x62702),x62701))
% 162.26/162.08 [6271]~P75(x62712)+E(x62711,f196(f891(x62712,a877)))+E(f14(x62712,f331(f310(x62712,x62712,f80(x62712)),x62711)),f331(f80(x62712),f15(x62712,x62711)))+~P24(f331(f62(x62712),x62711))
% 162.26/162.08 [6390]E(x63901,f2(a1))+E(f331(a51,f50(f331(f80(a1),x63901),f331(f80(a1),x63902))),f46(x63901,x63902))+P24(f331(f331(f247(a1),f2(a1)),x63902))+~P24(f331(f331(f247(a1),f2(a1)),x63901))
% 162.26/162.08 [7382]~P1(a5000)+~P24(f331(a25,x73821))+P20(a878,x73822,f331(f331(f309(f882(a878)),f331(a94,x73821)),f196(f891(f882(a878),a877))))+P24(f331(f331(f333(a880),f673(x73821,x73822)),f186(a880,a879,a26)))
% 162.26/162.08 [8638]~P1(a5000)+~P24(f331(a25,x86382))+P20(a878,x86381,f331(f331(f309(f882(a878)),f331(a94,x86382)),f196(f891(f882(a878),a877))))+~P20(a878,x86381,f331(f331(f309(f882(a878)),f331(a94,f331(a28,f673(x86382,x86381)))),f196(f891(f882(a878),a877))))
% 162.26/162.08 [8645]~P40(x86452)+~P40(x86451)+P24(f331(f331(f248(f891(a883,a877)),f331(f310(a1,a883,a111),x86451)),f331(f310(a1,a883,a111),x86452)))+~P24(f331(f331(f248(f891(a1,a877)),x86451),x86452))
% 162.26/162.08 [8859]~E(f705(x88592,x88591),f701(x88592,x88591))+~P24(f331(f140(x88591),f702(x88592,x88591)))+~P24(f331(f140(f884(x88591)),x88592))+P24(f331(f140(x88591),f331(f145(f884(x88591),f884(x88591),f137(x88591),f119(x88591)),x88592)))
% 162.26/162.08 [8957]~P40(x89572)+~P40(x89571)+~P24(f331(f331(f248(f891(a883,a877)),f331(f310(a1,a883,a111),x89571)),f331(f310(a1,a883,a111),x89572)))+P24(f331(f331(f248(f891(a1,a877)),x89571),x89572))
% 162.26/162.08 [8958]~P40(x89582)+~P40(x89581)+~P24(f331(f331(f247(f891(a883,a877)),f331(f310(a1,a883,a111),x89581)),f331(f310(a1,a883,a111),x89582)))+P24(f331(f331(f247(f891(a1,a877)),x89581),x89582))
% 162.26/162.08 [8964]~E(f705(x89642,x89641),f701(x89642,x89641))+~P24(f331(f140(f884(x89641)),x89642))+P24(f331(f140(x89641),f331(f145(f884(x89641),f884(x89641),f137(x89641),f119(x89641)),x89642)))+P24(f331(f331(f333(f884(x89641)),f702(x89642,x89641)),f331(f175(f884(x89641)),x89642)))
% 162.26/162.08 [9006]~P24(f331(f140(x90061),f702(x90062,x90061)))+~P24(f331(f140(f884(x90061)),x90062))+P24(f331(f140(x90061),f331(f145(f884(x90061),f884(x90061),f137(x90061),f119(x90061)),x90062)))+P24(f331(f331(f333(f884(x90061)),f701(x90062,x90061)),f331(f175(f884(x90061)),x90062)))
% 162.26/162.08 [9007]~P24(f331(f140(x90071),f702(x90072,x90071)))+~P24(f331(f140(f884(x90071)),x90072))+P24(f331(f140(x90071),f331(f145(f884(x90071),f884(x90071),f137(x90071),f119(x90071)),x90072)))+P24(f331(f331(f333(f884(x90071)),f705(x90072,x90071)),f331(f175(f884(x90071)),x90072)))
% 162.26/162.08 [9069]~P24(f331(f140(f884(x90691)),x90692))+P24(f331(f140(x90691),f331(f145(f884(x90691),f884(x90691),f137(x90691),f119(x90691)),x90692)))+P24(f331(f331(f333(f884(x90691)),f701(x90692,x90691)),f331(f175(f884(x90691)),x90692)))+P24(f331(f331(f333(f884(x90691)),f702(x90692,x90691)),f331(f175(f884(x90691)),x90692)))
% 162.26/162.08 [9070]~P24(f331(f140(f884(x90701)),x90702))+P24(f331(f140(x90701),f331(f145(f884(x90701),f884(x90701),f137(x90701),f119(x90701)),x90702)))+P24(f331(f331(f333(f884(x90701)),f705(x90702,x90701)),f331(f175(f884(x90701)),x90702)))+P24(f331(f331(f333(f884(x90701)),f702(x90702,x90701)),f331(f175(f884(x90701)),x90702)))
% 162.26/162.08 [9083]~E(f331(f331(f108(f891(x90831,a877)),f331(f175(x90831),f701(x90832,x90831))),f331(f175(x90831),f705(x90832,x90831))),f196(f891(x90831,a877)))+~P24(f331(f140(x90831),f702(x90832,x90831)))+~P24(f331(f140(f884(x90831)),x90832))+P24(f331(f140(x90831),f331(f145(f884(x90831),f884(x90831),f137(x90831),f119(x90831)),x90832)))
% 162.26/162.08 [9156]~E(f331(f331(f108(f891(x91561,a877)),f331(f175(x91561),f701(x91562,x91561))),f331(f175(x91561),f705(x91562,x91561))),f196(f891(x91561,a877)))+~P24(f331(f140(f884(x91561)),x91562))+P24(f331(f140(x91561),f331(f145(f884(x91561),f884(x91561),f137(x91561),f119(x91561)),x91562)))+P24(f331(f331(f333(f884(x91561)),f702(x91562,x91561)),f331(f175(f884(x91561)),x91562)))
% 162.26/162.08 [9424]E(x94241,f2(a1))+E(x94242,f2(a1))+E(f331(f331(f89(a1,f890(a1,a1)),f331(f331(a229,x94242),x94241)),f331(f331(f18(a1,a1,f890(a1,a1)),f331(f331(f8(a1,f891(a1,f890(a1,a1)),a1),f261(a1,a1)),f331(f39(a1),x94242))),f331(f39(a1),x94241))),f227(x94242,x94241))+P24(f331(f331(f248(a1),x94241),f2(a1)))
% 162.26/162.08 [8326]~P94(x83262)+~P111(x83262)+~P24(f331(f331(f248(x83262),f331(f110(x83262),x83261)),f79(x83262)))+P24(f331(f331(f248(a1),x83261),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)))
% 162.26/162.08 [8327]~P94(x83272)+~P111(x83272)+~P24(f331(f331(f247(x83272),f331(f110(x83272),x83271)),f79(x83272)))+P24(f331(f331(f247(a1),x83271),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)))
% 162.26/162.08 [8608]~P111(x86081)+~P94(x86081)+P24(f331(f331(f248(x86081),f331(f110(x86081),x86082)),f79(x86081)))+~P24(f331(f331(f248(a1),x86082),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)))
% 162.26/162.08 [8609]~P111(x86091)+~P94(x86091)+P24(f331(f331(f247(x86091),f331(f110(x86091),x86092)),f79(x86091)))+~P24(f331(f331(f247(a1),x86092),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)))
% 162.26/162.08 [8793]~P94(x87932)+~P111(x87932)+~P24(f331(f331(f248(x87932),f79(x87932)),f331(f110(x87932),x87931)))+P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)),x87931))
% 162.26/162.08 [8794]~P94(x87942)+~P111(x87942)+~P24(f331(f331(f247(x87942),f79(x87942)),f331(f110(x87942),x87941)))+P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)),x87941))
% 162.26/162.08 [9146]~P111(x91461)+~P94(x91461)+P24(f331(f331(f248(x91461),f79(x91461)),f331(f110(x91461),x91462)))+~P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)),x91462))
% 162.26/162.08 [9147]~P111(x91471)+~P94(x91471)+P24(f331(f331(f247(x91471),f79(x91471)),f331(f110(x91471),x91472)))+~P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84)),x91472))
% 162.26/162.08 [9276]~P91(x92761)+~P94(x92761)+~P31(x92761,f331(f110(x92761),x92762))+P31(x92761,f331(f110(x92761),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x92762)),x92762)),a103)))
% 162.26/162.08 [9491]~P91(x94911)+~P94(x94911)+P31(x94911,f331(f110(x94911),x94912))+~P31(x94911,f331(f110(x94911),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),x94912)),x94912)),a103)))
% 162.26/162.08 [10002]~P137(x100022)+E(x100021,f79(x100022))+E(x100021,f331(f80(x100022),f79(x100022)))+~E(f331(f331(f262(x100022),x100021),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f79(x100022))
% 162.26/162.08 [10080]~P94(x100801)+~P63(x100801)+~P24(f331(f331(f248(x100801),f2(x100801)),x100802))+P24(f331(f331(f248(x100801),f2(x100801)),f331(f331(f289(x100801),x100802),f331(f110(x100801),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))))
% 162.26/162.08 [10115]~P94(x101151)+~P63(x101151)+P24(f331(f331(f248(x101151),f2(x101151)),x101152))+~P24(f331(f331(f248(x101151),f2(x101151)),f331(f331(f289(x101151),x101152),f331(f110(x101151),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))))
% 162.26/162.08 [10194]~P138(x101942)+E(x101941,f2(a1))+P24(f331(f331(f248(a1),x101941),f2(a1)))+E(f331(f331(f270(a1,a1,x101942),f331(f331(f7(a1,f891(a1,f891(x101942,x101942)),f891(a1,x101942)),f331(f331(f8(f891(f891(x101942,x101942),x101942),f891(f891(a1,f891(x101942,x101942)),f891(a1,x101942)),a1),f8(f891(x101942,x101942),x101942,a1)),f331(f331(f8(x101942,f891(f891(x101942,x101942),x101942),a1),f89(x101942,x101942)),f109(x101942)))),f331(f331(f7(a1,f891(x101942,x101942),f891(x101942,x101942)),f331(f331(f8(f891(x101942,f891(x101942,x101942)),f891(f891(x101942,x101942),f891(x101942,x101942)),a1),f18(x101942,x101942,x101942)),f331(f331(f7(a1,f891(x101942,x101942),f891(x101942,f891(x101942,x101942))),f331(f331(f8(f891(x101942,f891(x101942,x101942)),f891(f891(x101942,x101942),f891(x101942,f891(x101942,x101942))),a1),f8(x101942,f891(x101942,x101942),x101942)),f331(f331(f8(a877,f891(x101942,f891(x101942,x101942)),a1),f102(x101942)),f331(f331(f7(a1,a1,a877),a328),f2(a1))))),f331(f331(f18(x101942,x101942,x101942),f81(x101942)),f5(x101942))))),f331(f331(f7(x101942,x101942,x101942),f331(f331(f8(x101942,f891(x101942,x101942),x101942),f81(x101942)),f331(f331(f18(x101942,x101942,x101942),f81(x101942)),f5(x101942)))),f79(x101942))))),f46(x101941,f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f331(f109(x101942),x101941))
% 162.26/162.08 [5249]~P60(x52493)+~P36(x52493,x52492,f56(x52493))+E(x52491,f780(x52492,x52493))+~P24(f331(x52492,x52491))
% 162.26/162.08 [5409]~P60(x54091)+P36(x54091,x54092,f56(x54091))+~E(f781(x54092,x54091,x54093),x54093)+~P24(f331(x54092,x54093))
% 162.26/162.08 [4887]~P91(x48873)+~P94(x48873)+E(x48871,x48872)+~E(f331(f110(x48873),x48871),f331(f110(x48873),x48872))
% 162.26/162.08 [6029]~P60(x60291)+P36(x60291,x60292,f56(x60291))+~P24(f331(x60292,x60293))+P24(f331(x60292,f781(x60292,x60291,x60293)))
% 162.26/162.08 [6039]~P24(f331(x60391,x60392))+~P24(f331(x60391,x60393))+~P24(f331(f331(f247(a883),x60393),f828(x60392,x60391)))+P24(f331(x60391,f2(a883)))
% 162.26/162.08 [6453]P147(x64532,x64531,x64533)+E(x64531,f2(a1))+P24(f331(f331(f247(a1),f2(a1)),f814(x64533,x64531,x64532)))+P24(f331(f331(f248(a1),x64531),f2(a1)))
% 162.26/162.08 [6454]P146(x64542,x64541,x64543)+E(x64541,f2(a1))+P24(f331(f331(f247(a1),f2(a1)),f825(x64543,x64541,x64542)))+P24(f331(f331(f248(a1),x64541),f2(a1)))
% 162.26/162.08 [6571]P146(x65711,x65712,x65713)+~P24(f331(x65711,x65713))+P24(f331(f331(f247(a1),f2(a1)),f825(x65713,x65712,x65711)))+P24(f331(f331(f248(a1),x65712),f2(a1)))
% 162.26/162.08 [6598]P147(x65981,x65982,x65983)+P24(f331(f331(f247(a1),f2(a1)),f814(x65983,x65982,x65981)))+~P24(f331(x65981,f2(a1)))+P24(f331(f331(f248(a1),x65982),f2(a1)))
% 162.26/162.08 [6626]P147(x66262,x66261,x66263)+E(x66261,f2(a1))+~P24(f331(x66262,f815(x66263,x66261,x66262)))+P24(f331(f331(f248(a1),x66261),f2(a1)))
% 162.26/162.08 [6627]P146(x66272,x66271,x66273)+E(x66271,f2(a1))+~P24(f331(x66272,f825(x66273,x66271,x66272)))+P24(f331(f331(f248(a1),x66271),f2(a1)))
% 162.26/162.08 [6727]~P107(x67271)+~P27(x67271)+~P24(f331(f331(f248(x67271),x67272),f40(x67271,x67273)))+P24(f331(f331(f248(x67271),x67272),f525(x67273,x67272,x67271)))
% 162.26/162.08 [6736]P146(x67361,x67362,x67363)+~P24(f331(x67361,x67363))+~P24(f331(x67361,f825(x67363,x67362,x67361)))+P24(f331(f331(f248(a1),x67362),f2(a1)))
% 162.26/162.08 [6762]P147(x67621,x67622,x67623)+~P24(f331(x67621,f815(x67623,x67622,x67621)))+~P24(f331(x67621,f2(a1)))+P24(f331(f331(f248(a1),x67622),f2(a1)))
% 162.26/162.08 [7010]P147(x70102,x70101,x70103)+E(x70101,f2(a1))+P24(f331(f331(f247(a1),f2(a1)),f814(x70103,x70101,x70102)))+P24(f331(f331(f248(a1),x70101),f813(x70103,x70101,x70102)))
% 162.26/162.08 [7011]P146(x70112,x70111,x70113)+E(x70111,f2(a1))+P24(f331(f331(f247(a1),f2(a1)),f825(x70113,x70111,x70112)))+P24(f331(f331(f248(a1),x70111),f824(x70113,x70111,x70112)))
% 162.26/162.08 [7127]P146(x71271,x71272,x71273)+~P24(f331(x71271,x71273))+P24(f331(f331(f247(a1),f2(a1)),f825(x71273,x71272,x71271)))+P24(f331(f331(f248(a1),x71272),f824(x71273,x71272,x71271)))
% 162.26/162.08 [7146]P147(x71461,x71462,x71463)+P24(f331(f331(f247(a1),f2(a1)),f814(x71463,x71462,x71461)))+P24(f331(f331(f248(a1),x71462),f813(x71463,x71462,x71461)))+~P24(f331(x71461,f2(a1)))
% 162.26/162.08 [7179]P147(x71792,x71791,x71793)+E(x71791,f2(a1))+~P24(f331(x71792,f815(x71793,x71791,x71792)))+P24(f331(f331(f248(a1),x71791),f813(x71793,x71791,x71792)))
% 162.26/162.08 [7180]P146(x71802,x71801,x71803)+E(x71801,f2(a1))+~P24(f331(x71802,f825(x71803,x71801,x71802)))+P24(f331(f331(f248(a1),x71801),f824(x71803,x71801,x71802)))
% 162.26/162.08 [7221]P147(x72212,x72211,x72213)+E(x72211,f2(a1))+P24(f331(f331(f247(a1),f2(a1)),f814(x72213,x72211,x72212)))+~P24(f331(x72212,f823(x72213,x72211,x72212)))
% 162.26/162.08 [7222]P146(x72222,x72221,x72223)+E(x72221,f2(a1))+P24(f331(f331(f247(a1),f2(a1)),f825(x72223,x72221,x72222)))+~P24(f331(x72222,f824(x72223,x72221,x72222)))
% 162.26/162.08 [7306]P146(x73061,x73062,x73063)+~P24(f331(x73061,x73063))+~P24(f331(x73061,f825(x73063,x73062,x73061)))+P24(f331(f331(f248(a1),x73062),f824(x73063,x73062,x73061)))
% 162.26/162.08 [7315]P147(x73151,x73152,x73153)+~P24(f331(x73151,f815(x73153,x73152,x73151)))+P24(f331(f331(f248(a1),x73152),f813(x73153,x73152,x73151)))+~P24(f331(x73151,f2(a1)))
% 162.26/162.08 [7319]P146(x73191,x73192,x73193)+~P24(f331(x73191,x73193))+P24(f331(f331(f247(a1),f2(a1)),f825(x73193,x73192,x73191)))+~P24(f331(x73191,f824(x73193,x73192,x73191)))
% 162.26/162.08 [7337]P147(x73371,x73372,x73373)+P24(f331(f331(f247(a1),f2(a1)),f814(x73373,x73372,x73371)))+~P24(f331(x73371,f823(x73373,x73372,x73371)))+~P24(f331(x73371,f2(a1)))
% 162.26/162.08 [7360]P147(x73602,x73601,x73603)+E(x73601,f2(a1))+~P24(f331(x73602,f815(x73603,x73601,x73602)))+~P24(f331(x73602,f823(x73603,x73601,x73602)))
% 162.26/162.08 [7361]P146(x73612,x73611,x73613)+E(x73611,f2(a1))+~P24(f331(x73612,f825(x73613,x73611,x73612)))+~P24(f331(x73612,f824(x73613,x73611,x73612)))
% 162.26/162.08 [7454]P146(x74541,x74542,x74543)+~P24(f331(x74541,x74543))+~P24(f331(x74541,f825(x74543,x74542,x74541)))+~P24(f331(x74541,f824(x74543,x74542,x74541)))
% 162.26/162.08 [7471]P147(x74711,x74712,x74713)+~P24(f331(x74711,f815(x74713,x74712,x74711)))+~P24(f331(x74711,f823(x74713,x74712,x74711)))+~P24(f331(x74711,f2(a1)))
% 162.26/162.08 [7517]P147(x75172,x75171,x75173)+E(x75171,f2(a1))+P24(f331(f331(f247(a1),f2(a1)),f814(x75173,x75171,x75172)))+P24(f331(f331(f247(a1),f813(x75173,x75171,x75172)),f2(a1)))
% 162.26/162.08 [7518]P146(x75182,x75181,x75183)+E(x75181,f2(a1))+P24(f331(f331(f247(a1),f2(a1)),f825(x75183,x75181,x75182)))+P24(f331(f331(f247(a1),f824(x75183,x75181,x75182)),f2(a1)))
% 162.26/162.08 [7519]~P138(x75191)+~P24(f331(f331(f333(x75191),x75193),f116(x75191)))+~P24(f331(f331(f333(x75191),x75192),f116(x75191)))+P24(f331(f331(f333(x75191),f331(f331(f22(x75191),x75192),x75193)),f116(x75191)))
% 162.26/162.08 [7520]~P138(x75201)+~P24(f331(f331(f333(x75201),x75203),f116(x75201)))+~P24(f331(f331(f333(x75201),x75202),f116(x75201)))+P24(f331(f331(f333(x75201),f331(f331(f81(x75201),x75202),x75203)),f116(x75201)))
% 162.26/162.08 [7521]~P143(x75211)+~P24(f331(f331(f333(x75211),x75213),f194(x75211)))+~P24(f331(f331(f333(x75211),x75212),f194(x75211)))+P24(f331(f331(f333(x75211),f331(f331(f81(x75211),x75212),x75213)),f194(x75211)))
% 162.26/162.08 [7522]~P138(x75221)+~P24(f331(f331(f333(x75221),x75223),f116(x75221)))+~P24(f331(f331(f333(x75221),x75222),f116(x75221)))+P24(f331(f331(f333(x75221),f331(f331(f82(x75221),x75222),x75223)),f116(x75221)))
% 162.26/162.08 [7523]~P143(x75231)+~P24(f331(f331(f333(x75231),x75233),f194(x75231)))+~P24(f331(f331(f333(x75231),x75232),f194(x75231)))+P24(f331(f331(f333(x75231),f331(f331(f82(x75231),x75232),x75233)),f194(x75231)))
% 162.26/162.08 [7524]~P87(x75241)+~P24(f331(f331(f248(x75241),x75243),f2(x75241)))+~P24(f331(f331(f248(x75241),x75242),f2(x75241)))+P24(f331(f331(f248(x75241),f331(f331(f81(x75241),x75242),x75243)),f2(x75241)))
% 162.26/162.08 [7525]~P87(x75251)+~P24(f331(f331(f247(x75251),x75252),f2(x75251)))+~P24(f331(f331(f248(x75251),x75253),f2(x75251)))+P24(f331(f331(f248(x75251),f331(f331(f81(x75251),x75252),x75253)),f2(x75251)))
% 162.26/162.08 [7526]~P87(x75261)+~P24(f331(f331(f247(x75261),x75263),f2(x75261)))+~P24(f331(f331(f248(x75261),x75262),f2(x75261)))+P24(f331(f331(f248(x75261),f331(f331(f81(x75261),x75262),x75263)),f2(x75261)))
% 162.26/162.08 [7527]~P87(x75271)+~P24(f331(f331(f247(x75271),x75273),f2(x75271)))+~P24(f331(f331(f247(x75271),x75272),f2(x75271)))+P24(f331(f331(f247(x75271),f331(f331(f81(x75271),x75272),x75273)),f2(x75271)))
% 162.26/162.08 [7552]P147(x75523,x75521,x75522)+E(x75521,f2(a1))+E(f331(f331(f81(a1),f331(f331(f82(a1),x75521),f815(x75522,x75521,x75523))),f814(x75522,x75521,x75523)),x75522)+P24(f331(f331(f248(a1),x75521),f2(a1)))
% 162.26/162.08 [7553]P146(x75533,x75531,x75532)+E(x75531,f2(a1))+E(f331(f331(f81(a1),f331(f331(f82(a1),x75531),f826(x75532,x75531,x75533))),f825(x75532,x75531,x75533)),x75532)+P24(f331(f331(f248(a1),x75531),f2(a1)))
% 162.26/162.08 [7633]P146(x76331,x76332,x76333)+~P24(f331(x76331,x76333))+P24(f331(f331(f247(a1),f2(a1)),f825(x76333,x76332,x76331)))+P24(f331(f331(f247(a1),f824(x76333,x76332,x76331)),f2(a1)))
% 162.26/162.08 [7662]P147(x76621,x76622,x76623)+P24(f331(f331(f247(a1),f2(a1)),f814(x76623,x76622,x76621)))+~P24(f331(x76621,f2(a1)))+P24(f331(f331(f247(a1),f813(x76623,x76622,x76621)),f2(a1)))
% 162.26/162.08 [7671]P146(x76713,x76711,x76712)+~P24(f331(x76713,x76712))+E(f331(f331(f81(a1),f331(f331(f82(a1),x76711),f826(x76712,x76711,x76713))),f825(x76712,x76711,x76713)),x76712)+P24(f331(f331(f248(a1),x76711),f2(a1)))
% 162.26/162.08 [7677]P147(x76772,x76771,x76773)+E(x76771,f2(a1))+~P24(f331(x76772,f815(x76773,x76771,x76772)))+P24(f331(f331(f247(a1),f813(x76773,x76771,x76772)),f2(a1)))
% 162.26/162.08 [7678]P146(x76782,x76781,x76783)+E(x76781,f2(a1))+~P24(f331(x76782,f825(x76783,x76781,x76782)))+P24(f331(f331(f247(a1),f824(x76783,x76781,x76782)),f2(a1)))
% 162.26/162.08 [7682]P147(x76823,x76821,x76822)+E(f331(f331(f81(a1),f331(f331(f82(a1),x76821),f815(x76822,x76821,x76823))),f814(x76822,x76821,x76823)),x76822)+~P24(f331(x76823,f2(a1)))+P24(f331(f331(f248(a1),x76821),f2(a1)))
% 162.26/162.08 [7737]P146(x77371,x77372,x77373)+~P24(f331(x77371,x77373))+~P24(f331(x77371,f825(x77373,x77372,x77371)))+P24(f331(f331(f247(a1),f824(x77373,x77372,x77371)),f2(a1)))
% 162.26/162.08 [7742]P147(x77421,x77422,x77423)+~P24(f331(x77421,f815(x77423,x77422,x77421)))+~P24(f331(x77421,f2(a1)))+P24(f331(f331(f247(a1),f813(x77423,x77422,x77421)),f2(a1)))
% 162.26/162.08 [7815]~P63(x78151)+~P24(f331(f331(f248(x78151),f331(f331(f289(x78151),x78153),x78152)),f2(x78151)))+P24(f331(f331(f248(x78151),x78152),f2(x78151)))+P24(f331(f331(f248(x78151),x78153),f2(x78151)))
% 162.26/162.08 [7816]~P123(x78161)+~P24(f331(f331(f247(x78161),f331(f331(f82(x78161),x78163),x78162)),f2(x78161)))+P24(f331(f331(f247(x78161),x78162),f2(x78161)))+P24(f331(f331(f247(x78161),x78163),f2(x78161)))
% 162.26/162.08 [7817]~P63(x78171)+~P24(f331(f331(f247(x78171),f331(f331(f289(x78171),x78173),x78172)),f2(x78171)))+P24(f331(f331(f247(x78171),x78172),f2(x78171)))+P24(f331(f331(f247(x78171),x78173),f2(x78171)))
% 162.26/162.08 [7921]P147(x79213,x79211,x79212)+E(x79211,f2(a1))+E(f331(f331(f81(a1),f331(f331(f82(a1),x79211),f815(x79212,x79211,x79213))),f814(x79212,x79211,x79213)),x79212)+P24(f331(f331(f248(a1),x79211),f813(x79212,x79211,x79213)))
% 162.26/162.08 [7922]P146(x79223,x79221,x79222)+E(x79221,f2(a1))+E(f331(f331(f81(a1),f331(f331(f82(a1),x79221),f826(x79222,x79221,x79223))),f825(x79222,x79221,x79223)),x79222)+P24(f331(f331(f248(a1),x79221),f824(x79222,x79221,x79223)))
% 162.26/162.08 [7934]P147(x79343,x79341,x79342)+E(x79341,f2(a1))+E(f331(f331(f81(a1),f331(f331(f82(a1),x79341),f823(x79342,x79341,x79343))),f813(x79342,x79341,x79343)),x79342)+P24(f331(f331(f247(a1),f2(a1)),f814(x79342,x79341,x79343)))
% 162.26/162.08 [7935]P146(x79353,x79351,x79352)+E(x79351,f2(a1))+E(f331(f331(f81(a1),f331(f331(f82(a1),x79351),f827(x79352,x79351,x79353))),f824(x79352,x79351,x79353)),x79352)+P24(f331(f331(f247(a1),f2(a1)),f825(x79352,x79351,x79353)))
% 162.26/162.08 [7978]P146(x79783,x79781,x79782)+~P24(f331(x79783,x79782))+E(f331(f331(f81(a1),f331(f331(f82(a1),x79781),f826(x79782,x79781,x79783))),f825(x79782,x79781,x79783)),x79782)+P24(f331(f331(f248(a1),x79781),f824(x79782,x79781,x79783)))
% 162.26/162.08 [7990]P147(x79903,x79901,x79902)+E(f331(f331(f81(a1),f331(f331(f82(a1),x79901),f815(x79902,x79901,x79903))),f814(x79902,x79901,x79903)),x79902)+P24(f331(f331(f248(a1),x79901),f813(x79902,x79901,x79903)))+~P24(f331(x79903,f2(a1)))
% 162.26/162.08 [7996]P146(x79963,x79961,x79962)+~P24(f331(x79963,x79962))+E(f331(f331(f81(a1),f331(f331(f82(a1),x79961),f827(x79962,x79961,x79963))),f824(x79962,x79961,x79963)),x79962)+P24(f331(f331(f247(a1),f2(a1)),f825(x79962,x79961,x79963)))
% 162.26/162.08 [8004]P147(x80043,x80041,x80042)+E(f331(f331(f81(a1),f331(f331(f82(a1),x80041),f823(x80042,x80041,x80043))),f813(x80042,x80041,x80043)),x80042)+P24(f331(f331(f247(a1),f2(a1)),f814(x80042,x80041,x80043)))+~P24(f331(x80043,f2(a1)))
% 162.26/162.08 [8015]P147(x80153,x80151,x80152)+E(x80151,f2(a1))+E(f331(f331(f81(a1),f331(f331(f82(a1),x80151),f815(x80152,x80151,x80153))),f814(x80152,x80151,x80153)),x80152)+~P24(f331(x80153,f823(x80152,x80151,x80153)))
% 162.26/162.08 [8016]P146(x80163,x80161,x80162)+E(x80161,f2(a1))+E(f331(f331(f81(a1),f331(f331(f82(a1),x80161),f826(x80162,x80161,x80163))),f825(x80162,x80161,x80163)),x80162)+~P24(f331(x80163,f824(x80162,x80161,x80163)))
% 162.26/162.08 [8017]P147(x80173,x80171,x80172)+E(x80171,f2(a1))+E(f331(f331(f81(a1),f331(f331(f82(a1),x80171),f823(x80172,x80171,x80173))),f813(x80172,x80171,x80173)),x80172)+~P24(f331(x80173,f815(x80172,x80171,x80173)))
% 162.26/162.08 [8018]P146(x80183,x80181,x80182)+E(x80181,f2(a1))+E(f331(f331(f81(a1),f331(f331(f82(a1),x80181),f827(x80182,x80181,x80183))),f824(x80182,x80181,x80183)),x80182)+~P24(f331(x80183,f825(x80182,x80181,x80183)))
% 162.26/162.08 [8080]P146(x80803,x80801,x80802)+~P24(f331(x80803,x80802))+E(f331(f331(f81(a1),f331(f331(f82(a1),x80801),f826(x80802,x80801,x80803))),f825(x80802,x80801,x80803)),x80802)+~P24(f331(x80803,f824(x80802,x80801,x80803)))
% 162.26/162.08 [8081]P146(x80813,x80811,x80812)+~P24(f331(x80813,x80812))+E(f331(f331(f81(a1),f331(f331(f82(a1),x80811),f827(x80812,x80811,x80813))),f824(x80812,x80811,x80813)),x80812)+~P24(f331(x80813,f825(x80812,x80811,x80813)))
% 162.26/162.08 [8092]P147(x80923,x80921,x80922)+E(f331(f331(f81(a1),f331(f331(f82(a1),x80921),f815(x80922,x80921,x80923))),f814(x80922,x80921,x80923)),x80922)+~P24(f331(x80923,f823(x80922,x80921,x80923)))+~P24(f331(x80923,f2(a1)))
% 162.26/162.08 [8093]P147(x80933,x80931,x80932)+E(f331(f331(f81(a1),f331(f331(f82(a1),x80931),f823(x80932,x80931,x80933))),f813(x80932,x80931,x80933)),x80932)+~P24(f331(x80933,f815(x80932,x80931,x80933)))+~P24(f331(x80933,f2(a1)))
% 162.26/162.08 [8199]P147(x81993,x81991,x81992)+E(x81991,f2(a1))+E(f331(f331(f81(a1),f331(f331(f82(a1),x81991),f815(x81992,x81991,x81993))),f814(x81992,x81991,x81993)),x81992)+P24(f331(f331(f247(a1),f813(x81992,x81991,x81993)),f2(a1)))
% 162.26/162.08 [8200]P146(x82003,x82001,x82002)+E(x82001,f2(a1))+E(f331(f331(f81(a1),f331(f331(f82(a1),x82001),f826(x82002,x82001,x82003))),f825(x82002,x82001,x82003)),x82002)+P24(f331(f331(f247(a1),f824(x82002,x82001,x82003)),f2(a1)))
% 162.26/162.08 [8237]P146(x82373,x82371,x82372)+~P24(f331(x82373,x82372))+E(f331(f331(f81(a1),f331(f331(f82(a1),x82371),f826(x82372,x82371,x82373))),f825(x82372,x82371,x82373)),x82372)+P24(f331(f331(f247(a1),f824(x82372,x82371,x82373)),f2(a1)))
% 162.26/162.08 [8242]P147(x82423,x82421,x82422)+E(f331(f331(f81(a1),f331(f331(f82(a1),x82421),f815(x82422,x82421,x82423))),f814(x82422,x82421,x82423)),x82422)+~P24(f331(x82423,f2(a1)))+P24(f331(f331(f247(a1),f813(x82422,x82421,x82423)),f2(a1)))
% 162.26/162.08 [8368]P147(x83683,x83681,x83682)+E(x83681,f2(a1))+E(f331(f331(f81(a1),f331(f331(f82(a1),x83681),f823(x83682,x83681,x83683))),f813(x83682,x83681,x83683)),x83682)+E(f331(f331(f81(a1),f331(f331(f82(a1),x83681),f815(x83682,x83681,x83683))),f814(x83682,x83681,x83683)),x83682)
% 162.26/162.08 [8369]P146(x83693,x83691,x83692)+E(x83691,f2(a1))+E(f331(f331(f81(a1),f331(f331(f82(a1),x83691),f827(x83692,x83691,x83693))),f824(x83692,x83691,x83693)),x83692)+E(f331(f331(f81(a1),f331(f331(f82(a1),x83691),f826(x83692,x83691,x83693))),f825(x83692,x83691,x83693)),x83692)
% 162.26/162.08 [8392]P146(x83923,x83921,x83922)+~P24(f331(x83923,x83922))+E(f331(f331(f81(a1),f331(f331(f82(a1),x83921),f827(x83922,x83921,x83923))),f824(x83922,x83921,x83923)),x83922)+E(f331(f331(f81(a1),f331(f331(f82(a1),x83921),f826(x83922,x83921,x83923))),f825(x83922,x83921,x83923)),x83922)
% 162.26/162.08 [8399]P147(x83993,x83991,x83992)+E(f331(f331(f81(a1),f331(f331(f82(a1),x83991),f823(x83992,x83991,x83993))),f813(x83992,x83991,x83993)),x83992)+E(f331(f331(f81(a1),f331(f331(f82(a1),x83991),f815(x83992,x83991,x83993))),f814(x83992,x83991,x83993)),x83992)+~P24(f331(x83993,f2(a1)))
% 162.26/162.08 [9043]~P123(x90431)+~E(x90433,f2(x90431))+~E(x90432,f2(x90431))+P24(f331(f331(f247(x90431),f331(f331(f81(x90431),f331(f331(f82(x90431),x90432),x90432)),f331(f331(f82(x90431),x90433),x90433))),f2(x90431)))
% 162.26/162.08 [10207]~P111(x102071)+~E(x102073,f2(x102071))+~E(x102072,f2(x102071))+P24(f331(f331(f247(x102071),f331(f331(f81(x102071),f331(f331(f262(x102071),x102072),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f331(f331(f262(x102071),x102073),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))),f2(x102071)))
% 162.26/162.08 [4837]~E(x48373,x48371)+~P119(x48372)+E(x48371,f2(x48372))+E(f331(f331(f289(x48372),x48373),x48371),f79(x48372))
% 162.26/162.08 [4888]~P97(x48881)+~E(x48883,f196(x48881))+~E(x48882,f196(x48881))+E(f331(f331(f107(x48881),x48882),x48883),f196(x48881))
% 162.26/162.08 [4889]~P100(x48891)+~E(x48893,f256(x48891))+~E(x48892,f256(x48891))+E(f331(f331(f108(x48891),x48892),x48893),f256(x48891))
% 162.26/162.08 [4976]~P119(x49763)+E(x49761,x49762)+E(x49762,f2(x49763))+~E(f331(f331(f289(x49763),x49761),x49762),f79(x49763))
% 162.26/162.08 [4995]~P130(x49952)+E(x49951,f2(x49952))+E(x49953,f2(x49952))+~E(f331(f331(f82(x49952),x49953),x49951),f2(x49952))
% 162.26/162.08 [4996]~P140(x49962)+E(x49961,f2(x49962))+E(x49963,f2(x49962))+~E(f331(f331(f82(x49962),x49963),x49961),f2(x49962))
% 162.26/162.08 [5376]~P112(x53763)+E(x53761,x53762)+E(x53761,f331(f80(x53763),x53762))+~E(f331(f331(f82(x53763),x53761),x53761),f331(f331(f82(x53763),x53762),x53762))
% 162.26/162.08 [5416]~P85(x54161)+E(f331(f80(x54161),x54162),x54163)+~E(f331(f331(f107(x54161),x54162),x54163),f256(x54161))+~E(f331(f331(f108(x54161),x54162),x54163),f196(x54161))
% 162.26/162.08 [5495]~P111(x54953)+E(x54951,x54952)+P24(f331(f331(f248(x54953),x54952),x54951))+P24(f331(f331(f248(x54953),x54951),x54952))
% 162.26/162.08 [5496]~P107(x54963)+E(x54961,x54962)+P24(f331(f331(f248(x54963),x54962),x54961))+P24(f331(f331(f248(x54963),x54961),x54962))
% 162.26/162.08 [5497]~E(x54972,x54973)+~P107(x54971)+P24(f331(f331(f247(x54971),x54972),x54973))+P24(f331(f331(f248(x54971),x54972),x54973))
% 162.26/162.08 [5749]~P108(x57493)+E(x57491,x57492)+~P24(f331(f331(f247(x57493),x57492),x57491))+P24(f331(f331(f248(x57493),x57492),x57491))
% 162.26/162.08 [5751]~P107(x57513)+E(x57511,x57512)+~P24(f331(f331(f247(x57513),x57511),x57512))+P24(f331(f331(f248(x57513),x57511),x57512))
% 162.26/162.08 [5757]~P108(x57573)+E(x57571,x57572)+~P24(f331(f331(f247(x57573),x57571),x57572))+P24(f331(f331(f248(x57573),x57571),x57572))
% 162.26/162.08 [5859]P146(x58591,x58592,x58593)+~P24(f331(x58591,x58593))+P24(f331(f331(f248(a1),x58592),f2(a1)))+P24(f331(f331(f248(a1),f2(a1)),x58592))
% 162.26/162.08 [5906]P147(x59061,x59062,x59063)+~P24(f331(x59061,f2(a1)))+P24(f331(f331(f248(a1),x59062),f2(a1)))+P24(f331(f331(f248(a1),f2(a1)),x59062))
% 162.26/162.08 [5910]~P96(x59101)+E(f331(f331(f107(x59101),x59102),f10(x59101,x59103)),x59102)+~P24(f331(f62(x59101),x59103))+~P24(f331(f331(f333(x59101),x59102),x59103))
% 162.26/162.08 [5911]~P96(x59111)+E(f331(f331(f108(x59111),x59112),f13(x59111,x59113)),x59112)+~P24(f331(f62(x59111),x59113))+~P24(f331(f331(f333(x59111),x59112),x59113))
% 162.26/162.08 [5946]~P96(x59461)+E(f331(f331(f107(x59461),x59462),f13(x59461,x59463)),f13(x59461,x59463))+~P24(f331(f62(x59461),x59463))+~P24(f331(f331(f333(x59461),x59462),x59463))
% 162.26/162.08 [5947]~P107(x59471)+E(f331(f331(f251(x59471),x59472),f14(x59471,x59473)),f14(x59471,x59473))+~P24(f331(f62(x59471),x59473))+~P24(f331(f331(f333(x59471),x59472),x59473))
% 162.26/162.08 [5948]~P107(x59481)+E(f331(f331(f246(x59481),x59482),f15(x59481,x59483)),f15(x59481,x59483))+~P24(f331(f62(x59481),x59483))+~P24(f331(f331(f333(x59481),x59482),x59483))
% 162.26/162.08 [5949]~P96(x59491)+E(f331(f331(f108(x59491),x59492),f10(x59491,x59493)),f10(x59491,x59493))+~P24(f331(f62(x59491),x59493))+~P24(f331(f331(f333(x59491),x59492),x59493))
% 162.26/162.08 [5994]E(x59941,x59942)+~P108(x59943)+~P24(f331(f331(f247(x59943),x59942),x59941))+~P24(f331(f331(f247(x59943),x59941),x59942))
% 162.26/162.08 [6134]~P106(x61341)+P24(f331(f331(f247(x61341),x61343),x61342))+~P24(f331(f331(f247(x61341),x61342),x61343))+P24(f331(f331(f248(x61341),x61342),x61343))
% 162.26/162.08 [6157]~P107(x61571)+~P24(f331(f62(x61571),x61573))+P24(f331(f331(f247(x61571),x61572),f15(x61571,x61573)))+~P24(f331(f331(f333(x61571),x61572),x61573))
% 162.26/162.08 [6206]~P107(x62061)+E(f331(f331(f251(x62061),x62062),f12(x62061,f246(x62061),x62063)),x62062)+~P24(f331(f62(x62061),x62063))+~P24(f331(f331(f333(x62061),x62062),x62063))
% 162.26/162.08 [6207]~P107(x62071)+E(f331(f331(f246(x62071),x62072),f11(x62071,f251(x62071),x62073)),x62072)+~P24(f331(f62(x62071),x62073))+~P24(f331(f331(f333(x62071),x62072),x62073))
% 162.26/162.08 [6341]E(x63411,x63412)+~E(f331(f331(f22(a883),x63411),x63413),f331(f331(f22(a883),x63412),x63413))+~P24(f331(f331(f247(a883),x63413),x63411))+~P24(f331(f331(f247(a883),x63413),x63412))
% 162.26/162.08 [6370]~P107(x63701)+~P24(f331(f62(x63701),x63702))+~P24(f331(f331(f333(x63701),x63703),x63702))+P24(f331(f331(f247(x63701),f14(x63701,x63702)),x63703))
% 162.26/162.08 [6432]P147(x64322,x64321,x64323)+E(x64321,f2(a1))+P24(f331(f331(f248(a1),x64321),f813(x64323,x64321,x64322)))+P24(f331(f331(f248(a1),f2(a1)),x64321))
% 162.26/162.08 [6433]P146(x64332,x64331,x64333)+E(x64331,f2(a1))+P24(f331(f331(f248(a1),x64331),f824(x64333,x64331,x64332)))+P24(f331(f331(f248(a1),f2(a1)),x64331))
% 162.26/162.08 [6434]~P107(x64341)+E(f331(f331(f251(x64341),x64342),f11(x64341,f251(x64341),x64343)),f11(x64341,f251(x64341),x64343))+~P24(f331(f62(x64341),x64343))+~P24(f331(f331(f333(x64341),x64342),x64343))
% 162.26/162.08 [6435]~P107(x64351)+E(f331(f331(f246(x64351),x64352),f12(x64351,f246(x64351),x64353)),f12(x64351,f246(x64351),x64353))+~P24(f331(f62(x64351),x64353))+~P24(f331(f331(f333(x64351),x64352),x64353))
% 162.26/162.08 [6441]~P24(f331(x64411,x64412))+P24(f331(x64411,f729(x64412,x64411,x64413)))+P24(f331(x64411,f2(a883)))+~P24(f331(f331(f248(a883),x64412),x64413))
% 162.26/162.08 [6495]~P24(f331(x64951,x64952))+~P24(f331(f62(x64953),x64952))+P24(f331(x64951,f518(x64951,x64952,x64953)))+P24(f331(x64951,f196(f891(x64953,a877))))
% 162.26/162.08 [6508]~P111(x65081)+~P94(x65081)+P24(f331(f331(f248(x65081),f331(f110(x65081),x65082)),f331(f110(x65081),x65083)))+~P24(f331(f331(f248(a1),x65082),x65083))
% 162.26/162.08 [6509]~P111(x65091)+~P94(x65091)+P24(f331(f331(f247(x65091),f331(f110(x65091),x65092)),f331(f110(x65091),x65093)))+~P24(f331(f331(f247(a1),x65092),x65093))
% 162.26/162.08 [6512]~P24(f331(x65121,x65123))+~P24(f331(f62(x65122),x65123))+P24(f331(f62(x65122),f518(x65121,x65123,x65122)))+P24(f331(x65121,f196(f891(x65122,a877))))
% 162.26/162.08 [6543]P146(x65431,x65432,x65433)+~P24(f331(x65431,x65433))+P24(f331(f331(f248(a1),x65432),f824(x65433,x65432,x65431)))+P24(f331(f331(f248(a1),f2(a1)),x65432))
% 162.26/162.08 [6578]P147(x65781,x65782,x65783)+P24(f331(f331(f248(a1),x65782),f813(x65783,x65782,x65781)))+~P24(f331(x65781,f2(a1)))+P24(f331(f331(f248(a1),f2(a1)),x65782))
% 162.26/162.08 [6609]~P109(x66091)+~P92(x66091)+E(f331(f331(f251(x66091),f331(f110(x66091),x66092)),f331(f110(x66091),x66093)),f331(f110(x66091),x66093))+P24(f331(f331(f247(x66091),f331(f110(x66091),x66092)),f331(f110(x66091),x66093)))
% 162.26/162.08 [6610]~P109(x66101)+~P92(x66101)+E(f331(f331(f246(x66101),f331(f110(x66101),x66102)),f331(f110(x66101),x66103)),f331(f110(x66101),x66102))+P24(f331(f331(f247(x66101),f331(f110(x66101),x66102)),f331(f110(x66101),x66103)))
% 162.26/162.08 [6668]P147(x66682,x66681,x66683)+E(x66681,f2(a1))+~P24(f331(x66682,f823(x66683,x66681,x66682)))+P24(f331(f331(f248(a1),f2(a1)),x66681))
% 162.26/162.08 [6669]P146(x66692,x66691,x66693)+E(x66691,f2(a1))+~P24(f331(x66692,f824(x66693,x66691,x66692)))+P24(f331(f331(f248(a1),f2(a1)),x66691))
% 162.26/162.08 [6673]P24(f331(x66731,x66732))+~P24(f331(f62(x66733),x66732))+P24(f331(x66731,f683(x66731,x66732,x66733)))+~P24(f331(x66731,f196(f891(x66733,a877))))
% 162.26/162.08 [6692]P24(f331(x66921,x66922))+P24(f331(f62(x66923),f683(x66921,x66922,x66923)))+~P24(f331(f62(x66923),x66922))+~P24(f331(x66921,f196(f891(x66923,a877))))
% 162.26/162.08 [6757]P146(x67571,x67572,x67573)+~P24(f331(x67571,x67573))+~P24(f331(x67571,f824(x67573,x67572,x67571)))+P24(f331(f331(f248(a1),f2(a1)),x67572))
% 162.26/162.08 [6781]P147(x67811,x67812,x67813)+~P24(f331(x67811,f823(x67813,x67812,x67811)))+~P24(f331(x67811,f2(a1)))+P24(f331(f331(f248(a1),f2(a1)),x67812))
% 162.26/162.08 [6885]~P94(x68853)+~P111(x68853)+~P24(f331(f331(f248(x68853),f331(f110(x68853),x68851)),f331(f110(x68853),x68852)))+P24(f331(f331(f248(a1),x68851),x68852))
% 162.26/162.08 [6886]~P94(x68863)+~P111(x68863)+~P24(f331(f331(f247(x68863),f331(f110(x68863),x68861)),f331(f110(x68863),x68862)))+P24(f331(f331(f247(a1),x68861),x68862))
% 162.26/162.08 [6912]~P107(x69121)+~P29(x69121,x69123)+P29(x69121,f331(f331(f154(x69121),x69122),x69123))+~P24(f331(f331(f247(x69121),x69122),f665(x69123,x69122,x69121)))
% 162.26/162.08 [6913]~P107(x69131)+~P29(x69131,x69133)+P29(x69131,f331(f331(f154(x69131),x69132),x69133))+~P24(f331(f331(f247(x69131),x69132),f666(x69133,x69132,x69131)))
% 162.26/162.08 [6914]~P107(x69141)+~P29(x69141,x69143)+P29(x69141,f331(f331(f154(x69141),x69142),x69143))+~P24(f331(f331(f247(x69141),x69142),f747(x69142,x69143,x69141)))
% 162.26/162.08 [6999]P147(x69992,x69991,x69993)+E(x69991,f2(a1))+P24(f331(f331(f248(a1),x69991),f2(a1)))+P24(f331(f331(f248(a1),f814(x69993,x69991,x69992)),x69991))
% 162.26/162.08 [7000]P146(x70002,x70001,x70003)+E(x70001,f2(a1))+P24(f331(f331(f248(a1),x70001),f2(a1)))+P24(f331(f331(f248(a1),f825(x70003,x70001,x70002)),x70001))
% 162.26/162.08 [7041]P147(x70412,x70411,x70413)+E(x70411,f2(a1))+P24(f331(f331(f247(a1),f813(x70413,x70411,x70412)),f2(a1)))+P24(f331(f331(f248(a1),f2(a1)),x70411))
% 162.26/162.08 [7042]P146(x70422,x70421,x70423)+E(x70421,f2(a1))+P24(f331(f331(f247(a1),f824(x70423,x70421,x70422)),f2(a1)))+P24(f331(f331(f248(a1),f2(a1)),x70421))
% 162.26/162.08 [7064]~P107(x70641)+~P29(x70641,x70643)+E(f331(f331(f151(x70641,x70641,f5(x70641)),x70642),f173(x70641,x70642,x70643)),x70643)+~P24(f331(f331(f333(x70641),x70642),f331(f175(x70641),x70643)))
% 162.26/162.08 [7110]P146(x71101,x71102,x71103)+~P24(f331(x71101,x71103))+P24(f331(f331(f248(a1),x71102),f2(a1)))+P24(f331(f331(f248(a1),f825(x71103,x71102,x71101)),x71102))
% 162.26/162.08 [7116]~P109(x71161)+~P92(x71161)+E(f331(f331(f251(x71161),f331(f110(x71161),x71162)),f331(f110(x71161),x71163)),f331(f110(x71161),x71162))+~P24(f331(f331(f247(x71161),f331(f110(x71161),x71162)),f331(f110(x71161),x71163)))
% 162.26/162.08 [7117]~P109(x71171)+~P92(x71171)+E(f331(f331(f246(x71171),f331(f110(x71171),x71172)),f331(f110(x71171),x71173)),f331(f110(x71171),x71173))+~P24(f331(f331(f247(x71171),f331(f110(x71171),x71172)),f331(f110(x71171),x71173)))
% 162.26/162.08 [7131]P147(x71311,x71312,x71313)+~P24(f331(x71311,f2(a1)))+P24(f331(f331(f248(a1),x71312),f2(a1)))+P24(f331(f331(f248(a1),f814(x71313,x71312,x71311)),x71312))
% 162.26/162.08 [7139]P146(x71391,x71392,x71393)+~P24(f331(x71391,x71393))+P24(f331(f331(f247(a1),f824(x71393,x71392,x71391)),f2(a1)))+P24(f331(f331(f248(a1),f2(a1)),x71392))
% 162.26/162.08 [7163]P147(x71631,x71632,x71633)+~P24(f331(x71631,f2(a1)))+P24(f331(f331(f247(a1),f813(x71633,x71632,x71631)),f2(a1)))+P24(f331(f331(f248(a1),f2(a1)),x71632))
% 162.26/162.08 [7191]~P24(f331(x71911,x71912))+P24(f331(x71911,f2(a883)))+~P24(f331(f331(f248(a883),x71912),x71913))+P24(f331(f331(f248(a883),f729(x71912,x71911,x71913)),x71913))
% 162.26/162.08 [7208]~P107(x72081)+~P29(x72081,x72083)+P29(x72081,f331(f331(f154(x72081),x72082),x72083))+P24(f331(f331(f333(x72081),f665(x72083,x72082,x72081)),f331(f175(x72081),x72083)))
% 162.26/162.08 [7209]~P107(x72091)+~P29(x72091,x72093)+P29(x72091,f331(f331(f154(x72091),x72092),x72093))+P24(f331(f331(f333(x72091),f666(x72093,x72092,x72091)),f331(f175(x72091),x72093)))
% 162.26/162.08 [7210]~P107(x72101)+~P29(x72101,x72103)+P29(x72101,f331(f331(f154(x72101),x72102),x72103))+P24(f331(f331(f333(x72101),f747(x72102,x72103,x72101)),f331(f175(x72101),x72103)))
% 162.26/162.08 [7310]~P107(x73101)+~P27(x73101)+~P24(f331(f331(f248(x73101),x73103),f40(x73101,x73102)))+P24(f331(f331(f333(x73101),f525(x73102,x73103,x73101)),x73102))
% 162.26/162.08 [7469]~P107(x74691)+~P27(x74691)+~P24(f331(f331(f248(x74691),f41(x74691,x74693)),x74692))+P24(f331(f331(f333(x74691),f520(x74692,x74693,x74691)),x74693))
% 162.26/162.08 [7470]~P107(x74701)+~P27(x74701)+~P24(f331(f331(f248(x74701),f41(x74701,x74703)),x74702))+P24(f331(f331(f248(x74701),f520(x74702,x74703,x74701)),x74702))
% 162.26/162.08 [7482]P147(x74822,x74821,x74823)+E(x74821,f2(a1))+P24(f331(f331(f248(a1),x74821),f813(x74823,x74821,x74822)))+P24(f331(f331(f248(a1),f814(x74823,x74821,x74822)),x74821))
% 162.26/162.08 [7483]P146(x74832,x74831,x74833)+E(x74831,f2(a1))+P24(f331(f331(f248(a1),x74831),f824(x74833,x74831,x74832)))+P24(f331(f331(f248(a1),f825(x74833,x74831,x74832)),x74831))
% 162.26/162.08 [7571]P147(x75713,x75711,x75712)+E(x75711,f2(a1))+E(f331(f331(f81(a1),f331(f331(f82(a1),x75711),f823(x75712,x75711,x75713))),f813(x75712,x75711,x75713)),x75712)+P24(f331(f331(f248(a1),f2(a1)),x75711))
% 162.26/162.08 [7572]P146(x75723,x75721,x75722)+E(x75721,f2(a1))+E(f331(f331(f81(a1),f331(f331(f82(a1),x75721),f827(x75722,x75721,x75723))),f824(x75722,x75721,x75723)),x75722)+P24(f331(f331(f248(a1),f2(a1)),x75721))
% 162.26/162.08 [7574]~P132(x75741)+~P24(f331(f331(f248(x75741),x75743),f2(x75741)))+P24(f331(f331(f248(x75741),f331(f331(f82(x75741),x75742),x75743)),f2(x75741)))+~P24(f331(f331(f248(x75741),f2(x75741)),x75742))
% 162.26/162.08 [7575]~P132(x75751)+~P24(f331(f331(f248(x75751),x75752),f2(x75751)))+P24(f331(f331(f248(x75751),f331(f331(f82(x75751),x75752),x75753)),f2(x75751)))+~P24(f331(f331(f248(x75751),f2(x75751)),x75753))
% 162.26/162.08 [7576]~P63(x75761)+~P24(f331(f331(f248(x75761),x75763),f2(x75761)))+P24(f331(f331(f248(x75761),f331(f331(f289(x75761),x75762),x75763)),f2(x75761)))+~P24(f331(f331(f248(x75761),f2(x75761)),x75762))
% 162.26/162.08 [7577]~P63(x75771)+~P24(f331(f331(f248(x75771),x75772),f2(x75771)))+P24(f331(f331(f248(x75771),f331(f331(f289(x75771),x75772),x75773)),f2(x75771)))+~P24(f331(f331(f248(x75771),f2(x75771)),x75773))
% 162.26/162.08 [7578]~P64(x75781)+~P24(f331(f331(f248(x75781),x75783),f2(x75781)))+P24(f331(f331(f248(x75781),f331(f331(f289(x75781),x75782),x75783)),f2(x75781)))+~P24(f331(f331(f248(x75781),f2(x75781)),x75782))
% 162.26/162.08 [7579]~P64(x75791)+~P24(f331(f331(f248(x75791),x75792),f2(x75791)))+P24(f331(f331(f248(x75791),f331(f331(f289(x75791),x75792),x75793)),f2(x75791)))+~P24(f331(f331(f248(x75791),f2(x75791)),x75793))
% 162.26/162.08 [7582]~P133(x75821)+~P24(f331(f331(f247(x75821),x75823),f2(x75821)))+P24(f331(f331(f247(x75821),f331(f331(f82(x75821),x75822),x75823)),f2(x75821)))+~P24(f331(f331(f247(x75821),f2(x75821)),x75822))
% 162.26/162.08 [7584]~P133(x75841)+~P24(f331(f331(f247(x75841),x75842),f2(x75841)))+P24(f331(f331(f247(x75841),f331(f331(f82(x75841),x75842),x75843)),f2(x75841)))+~P24(f331(f331(f247(x75841),f2(x75841)),x75843))
% 162.26/162.08 [7585]~P123(x75851)+~P24(f331(f331(f247(x75851),x75853),f2(x75851)))+P24(f331(f331(f247(x75851),f331(f331(f82(x75851),x75852),x75853)),f2(x75851)))+~P24(f331(f331(f247(x75851),f2(x75851)),x75852))
% 162.26/162.08 [7586]~P123(x75861)+~P24(f331(f331(f247(x75861),x75862),f2(x75861)))+P24(f331(f331(f247(x75861),f331(f331(f82(x75861),x75862),x75863)),f2(x75861)))+~P24(f331(f331(f247(x75861),f2(x75861)),x75863))
% 162.26/162.08 [7587]~P63(x75871)+~P24(f331(f331(f247(x75871),x75873),f2(x75871)))+P24(f331(f331(f247(x75871),f331(f331(f289(x75871),x75872),x75873)),f2(x75871)))+~P24(f331(f331(f247(x75871),f2(x75871)),x75872))
% 162.26/162.08 [7588]~P63(x75881)+~P24(f331(f331(f247(x75881),x75882),f2(x75881)))+P24(f331(f331(f247(x75881),f331(f331(f289(x75881),x75882),x75883)),f2(x75881)))+~P24(f331(f331(f247(x75881),f2(x75881)),x75883))
% 162.26/162.08 [7589]~P64(x75891)+~P24(f331(f331(f248(x75891),x75893),f2(x75891)))+P24(f331(f331(f247(x75891),f331(f331(f289(x75891),x75892),x75893)),f2(x75891)))+~P24(f331(f331(f247(x75891),f2(x75891)),x75892))
% 162.26/162.08 [7590]~P64(x75901)+~P24(f331(f331(f247(x75901),x75902),f2(x75901)))+P24(f331(f331(f247(x75901),f331(f331(f289(x75901),x75902),x75903)),f2(x75901)))+~P24(f331(f331(f248(x75901),f2(x75901)),x75903))
% 162.26/162.08 [7605]P146(x76051,x76052,x76053)+~P24(f331(x76051,x76053))+P24(f331(f331(f248(a1),x76052),f824(x76053,x76052,x76051)))+P24(f331(f331(f248(a1),f825(x76053,x76052,x76051)),x76052))
% 162.26/162.08 [7618]P147(x76181,x76182,x76183)+P24(f331(f331(f248(a1),x76182),f813(x76183,x76182,x76181)))+~P24(f331(x76181,f2(a1)))+P24(f331(f331(f248(a1),f814(x76183,x76182,x76181)),x76182))
% 162.26/162.08 [7668]P147(x76682,x76681,x76683)+E(x76681,f2(a1))+~P24(f331(x76682,f823(x76683,x76681,x76682)))+P24(f331(f331(f248(a1),f814(x76683,x76681,x76682)),x76681))
% 162.26/162.08 [7669]P146(x76692,x76691,x76693)+E(x76691,f2(a1))+~P24(f331(x76692,f824(x76693,x76691,x76692)))+P24(f331(f331(f248(a1),f825(x76693,x76691,x76692)),x76691))
% 162.26/162.08 [7679]P146(x76793,x76791,x76792)+~P24(f331(x76793,x76792))+E(f331(f331(f81(a1),f331(f331(f82(a1),x76791),f827(x76792,x76791,x76793))),f824(x76792,x76791,x76793)),x76792)+P24(f331(f331(f248(a1),f2(a1)),x76791))
% 162.26/162.08 [7697]P147(x76973,x76971,x76972)+E(f331(f331(f81(a1),f331(f331(f82(a1),x76971),f823(x76972,x76971,x76973))),f813(x76972,x76971,x76973)),x76972)+~P24(f331(x76973,f2(a1)))+P24(f331(f331(f248(a1),f2(a1)),x76971))
% 162.26/162.08 [7722]~P24(f331(x77221,x77223))+~P24(f331(f62(x77222),x77223))+P24(f331(f331(f333(x77222),f497(x77221,x77223,x77222)),f518(x77221,x77223,x77222)))+P24(f331(x77221,f196(f891(x77222,a877))))
% 162.26/162.08 [7733]P146(x77331,x77332,x77333)+~P24(f331(x77331,x77333))+~P24(f331(x77331,f824(x77333,x77332,x77331)))+P24(f331(f331(f248(a1),f825(x77333,x77332,x77331)),x77332))
% 162.26/162.08 [7738]P147(x77381,x77382,x77383)+~P24(f331(x77381,f823(x77383,x77382,x77381)))+~P24(f331(x77381,f2(a1)))+P24(f331(f331(f248(a1),f814(x77383,x77382,x77381)),x77382))
% 162.26/162.08 [7846]~P63(x78461)+~P24(f331(f331(f248(x78461),f331(f331(f289(x78461),x78463),x78462)),f2(x78461)))+P24(f331(f331(f248(x78461),x78462),f2(x78461)))+P24(f331(f331(f248(x78461),f2(x78461)),x78462))
% 162.26/162.08 [7847]~P63(x78471)+~P24(f331(f331(f248(x78471),f331(f331(f289(x78471),x78472),x78473)),f2(x78471)))+P24(f331(f331(f248(x78471),x78472),f2(x78471)))+P24(f331(f331(f248(x78471),f2(x78471)),x78472))
% 162.26/162.08 [7848]~P123(x78481)+~P24(f331(f331(f247(x78481),f331(f331(f82(x78481),x78483),x78482)),f2(x78481)))+P24(f331(f331(f247(x78481),x78482),f2(x78481)))+P24(f331(f331(f247(x78481),f2(x78481)),x78482))
% 162.26/162.08 [7849]~P123(x78491)+~P24(f331(f331(f247(x78491),f331(f331(f82(x78491),x78492),x78493)),f2(x78491)))+P24(f331(f331(f247(x78491),x78492),f2(x78491)))+P24(f331(f331(f247(x78491),f2(x78491)),x78492))
% 162.26/162.08 [7850]~P63(x78501)+~P24(f331(f331(f247(x78501),f331(f331(f289(x78501),x78503),x78502)),f2(x78501)))+P24(f331(f331(f247(x78501),x78502),f2(x78501)))+P24(f331(f331(f247(x78501),f2(x78501)),x78502))
% 162.26/162.08 [7851]~P63(x78511)+~P24(f331(f331(f247(x78511),f331(f331(f289(x78511),x78512),x78513)),f2(x78511)))+P24(f331(f331(f247(x78511),x78512),f2(x78511)))+P24(f331(f331(f247(x78511),f2(x78511)),x78512))
% 162.26/162.08 [7870]~P63(x78701)+~P24(f331(f331(f248(x78701),f331(f331(f289(x78701),x78702),x78703)),f2(x78701)))+P24(f331(f331(f248(x78701),f2(x78701)),x78702))+P24(f331(f331(f248(x78701),f2(x78701)),x78703))
% 162.26/162.08 [7871]~P123(x78711)+~P24(f331(f331(f247(x78711),f331(f331(f82(x78711),x78712),x78713)),f2(x78711)))+P24(f331(f331(f247(x78711),f2(x78711)),x78712))+P24(f331(f331(f247(x78711),f2(x78711)),x78713))
% 162.26/162.08 [7872]~P63(x78721)+~P24(f331(f331(f247(x78721),f331(f331(f289(x78721),x78722),x78723)),f2(x78721)))+P24(f331(f331(f247(x78721),f2(x78721)),x78722))+P24(f331(f331(f247(x78721),f2(x78721)),x78723))
% 162.26/162.08 [7893]P147(x78932,x78931,x78933)+E(x78931,f2(a1))+P24(f331(f331(f247(a1),f813(x78933,x78931,x78932)),f2(a1)))+P24(f331(f331(f248(a1),f814(x78933,x78931,x78932)),x78931))
% 162.26/162.08 [7894]P146(x78942,x78941,x78943)+E(x78941,f2(a1))+P24(f331(f331(f247(a1),f824(x78943,x78941,x78942)),f2(a1)))+P24(f331(f331(f248(a1),f825(x78943,x78941,x78942)),x78941))
% 162.26/162.08 [7901]~P110(x79011)+~P24(f331(f331(f248(x79011),x79012),f79(x79011)))+P24(f331(f331(f248(x79011),f331(f331(f262(x79011),x79012),f331(a118,x79013))),f79(x79011)))+~P24(f331(f331(f248(x79011),f2(x79011)),x79012))
% 162.26/162.08 [7950]~P107(x79501)+~E(x79503,f119(x79501))+~P29(x79501,f331(f172(x79501),x79503))+E(f331(f145(x79501,x79501,f331(f7(x79501,x79501,x79501),f246(x79501)),x79502),f331(f172(x79501),x79503)),x79502)
% 162.26/162.08 [7953]P146(x79531,x79532,x79533)+~P24(f331(x79531,x79533))+P24(f331(f331(f247(a1),f824(x79533,x79532,x79531)),f2(a1)))+P24(f331(f331(f248(a1),f825(x79533,x79532,x79531)),x79532))
% 162.26/162.08 [7962]P147(x79621,x79622,x79623)+~P24(f331(x79621,f2(a1)))+P24(f331(f331(f247(a1),f813(x79623,x79622,x79621)),f2(a1)))+P24(f331(f331(f248(a1),f814(x79623,x79622,x79621)),x79622))
% 162.26/162.08 [8194]P147(x81943,x81941,x81942)+E(x81941,f2(a1))+E(f331(f331(f81(a1),f331(f331(f82(a1),x81941),f823(x81942,x81941,x81943))),f813(x81942,x81941,x81943)),x81942)+P24(f331(f331(f248(a1),f814(x81942,x81941,x81943)),x81941))
% 162.26/162.08 [8195]P146(x81953,x81951,x81952)+E(x81951,f2(a1))+E(f331(f331(f81(a1),f331(f331(f82(a1),x81951),f827(x81952,x81951,x81953))),f824(x81952,x81951,x81953)),x81952)+P24(f331(f331(f248(a1),f825(x81952,x81951,x81953)),x81951))
% 162.26/162.08 [8228]P146(x82283,x82281,x82282)+~P24(f331(x82283,x82282))+E(f331(f331(f81(a1),f331(f331(f82(a1),x82281),f827(x82282,x82281,x82283))),f824(x82282,x82281,x82283)),x82282)+P24(f331(f331(f248(a1),f825(x82282,x82281,x82283)),x82281))
% 162.26/162.08 [8229]~P73(x82291)+~P74(x82291)+~P40(x82293)+E(f331(f331(f9(a883,x82291),f331(f331(f8(a1,x82291,a883),x82292),f106(a1))),f331(f310(a1,a883,a111),x82293)),f331(f331(f9(a1,x82291),x82292),x82293))
% 162.26/162.08 [8230]~P73(x82301)+~P74(x82301)+~P40(x82303)+E(f331(f331(f6(a883,x82301),f331(f331(f8(a1,x82301,a883),x82302),f106(a1))),f331(f310(a1,a883,a111),x82303)),f331(f331(f6(a1,x82301),x82302),x82303))
% 162.26/162.08 [8239]P147(x82393,x82391,x82392)+E(f331(f331(f81(a1),f331(f331(f82(a1),x82391),f823(x82392,x82391,x82393))),f813(x82392,x82391,x82393)),x82392)+~P24(f331(x82393,f2(a1)))+P24(f331(f331(f248(a1),f814(x82392,x82391,x82393)),x82391))
% 162.26/162.08 [8258]~E(x82582,f2(a883))+~E(f331(f260(a883,a883),x82583),f2(a883))+~E(x82581,f331(f331(f81(a883),f331(f331(f82(a883),f331(f260(a883,a883),x82583)),x82582)),f331(f269(a883,a883),x82583)))+P24(f331(f48(x82581,x82582),x82583))
% 162.26/162.08 [8312]P24(f331(x83121,x83122))+~P24(f331(f331(f333(x83123),f674(x83121,x83122,x83123)),f683(x83121,x83122,x83123)))+~P24(f331(f62(x83123),x83122))+~P24(f331(x83121,f196(f891(x83123,a877))))
% 162.26/162.08 [8921]P24(f331(x89211,x89212))+~P24(f331(f62(x89213),x89212))+~P24(f331(x89211,f331(f331(f309(x89213),f674(x89211,x89212,x89213)),f683(x89211,x89212,x89213))))+~P24(f331(x89211,f196(f891(x89213,a877))))
% 162.26/162.08 [9152]P24(f331(f331(f247(a1),x91521),f2(a1)))+~P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f82(a1),x91522),x91521)),x91523)),f2(a1)))+~P24(f331(f331(f248(a1),f2(a1)),x91522))+~P24(f331(f331(f247(a1),f2(a1)),x91523))
% 162.26/162.08 [5820]~P96(x58202)+E(x58201,f196(f891(x58202,a877)))+~P24(f331(f62(x58202),x58201))+E(f13(x58202,f331(f331(f309(x58202),x58203),x58201)),f331(f331(f107(x58202),x58203),f13(x58202,x58201)))
% 162.26/162.08 [5821]~P107(x58212)+E(x58211,f196(f891(x58212,a877)))+~P24(f331(f62(x58212),x58211))+E(f14(x58212,f331(f331(f309(x58212),x58213),x58211)),f331(f331(f251(x58212),x58213),f14(x58212,x58211)))
% 162.26/162.09 [5822]~P107(x58222)+E(x58221,f196(f891(x58222,a877)))+~P24(f331(f62(x58222),x58221))+E(f15(x58222,f331(f331(f309(x58222),x58223),x58221)),f331(f331(f246(x58222),x58223),f15(x58222,x58221)))
% 162.26/162.09 [5823]~P96(x58232)+E(x58231,f196(f891(x58232,a877)))+~P24(f331(f62(x58232),x58231))+E(f10(x58232,f331(f331(f309(x58232),x58233),x58231)),f331(f331(f108(x58232),x58233),f10(x58232,x58231)))
% 162.26/162.09 [6131]~P123(x61311)+~E(x61313,f2(x61311))+~E(x61312,f2(x61311))+E(f331(f331(f81(x61311),f331(f331(f82(x61311),x61312),x61312)),f331(f331(f82(x61311),x61313),x61313)),f2(x61311))
% 162.26/162.09 [6199]~P95(x61992)+E(x61991,f196(f891(x61992,a877)))+~P24(f331(f62(x61992),x61991))+E(f331(f64(x61992,f82(x61992)),f331(f331(f309(x61992),x61993),x61991)),f331(f331(f82(x61992),x61993),f331(f64(x61992,f82(x61992)),x61991)))
% 162.26/162.09 [6322]~P107(x63222)+E(x63221,f196(f891(x63222,a877)))+~P24(f331(f62(x63222),x63221))+E(f11(x63222,f251(x63222),f331(f331(f309(x63222),x63223),x63221)),f331(f331(f251(x63222),x63223),f11(x63222,f251(x63222),x63221)))
% 162.26/162.09 [6323]~P107(x63232)+E(x63231,f196(f891(x63232,a877)))+~P24(f331(f62(x63232),x63231))+E(f12(x63232,f246(x63232),f331(f331(f309(x63232),x63233),x63231)),f331(f331(f246(x63232),x63233),f12(x63232,f246(x63232),x63231)))
% 162.26/162.09 [6814]~P71(x68141)+~P24(f331(f62(x68141),x68143))+E(f331(f64(x68141,f82(x68141)),f331(f331(f309(x68141),x68142),x68143)),f331(f331(f65(x68141,x68141,f82(x68141)),x68142),x68143))+P24(f331(f331(f333(x68141),x68142),x68143))
% 162.26/162.09 [6890]~E(f331(f331(f81(a1),x68902),f331(f331(f82(a1),x68903),x68901)),x68903)+~P24(f331(f331(f248(a1),f2(a1)),x68903))+P24(f331(f331(f247(a1),f79(a1)),x68901))+~P24(f331(f331(f248(a1),x68902),x68903))
% 162.26/162.09 [6919]~E(f331(f331(f81(a1),x69192),f331(f331(f82(a1),x69193),x69191)),x69193)+P24(f331(f331(f247(a1),x69191),f79(a1)))+~P24(f331(f331(f248(a1),f2(a1)),x69193))+~P24(f331(f331(f247(a1),f2(a1)),x69192))
% 162.26/162.09 [6935]E(x69351,f2(a883))+~P24(f331(f48(x69353,x69351),x69352))+~P24(f331(f331(f248(a883),f2(a883)),x69351))+P24(f331(f331(f248(a883),f331(f269(a883,a883),x69352)),x69351))
% 162.26/162.09 [6966]~P136(x69661)+~P24(f331(f331(f247(x69661),x69662),f2(x69661)))+~P24(f331(f331(f247(x69661),x69663),f2(x69661)))+E(f331(f331(f82(x69661),f331(f76(x69661),x69662)),f331(f76(x69661),x69663)),f331(f76(x69661),f331(f331(f82(x69661),x69662),x69663)))
% 162.26/162.09 [7018]~P136(x70181)+~P24(f331(f331(f247(x70181),x70182),f2(x70181)))+E(f331(f331(f82(x70181),f331(f76(x70181),x70182)),f331(f76(x70181),x70183)),f331(f76(x70181),f331(f331(f82(x70181),x70182),x70183)))+~P24(f331(f331(f247(x70181),f2(x70181)),x70183))
% 162.26/162.09 [7019]~P136(x70191)+~P24(f331(f331(f247(x70191),x70193),f2(x70191)))+E(f331(f331(f82(x70191),f331(f76(x70191),x70192)),f331(f76(x70191),x70193)),f331(f76(x70191),f331(f331(f82(x70191),x70192),x70193)))+~P24(f331(f331(f247(x70191),f2(x70191)),x70192))
% 162.26/162.09 [7072]~P136(x70721)+E(f331(f331(f82(x70721),f331(f76(x70721),x70722)),f331(f76(x70721),x70723)),f331(f76(x70721),f331(f331(f82(x70721),x70722),x70723)))+~P24(f331(f331(f247(x70721),f2(x70721)),x70722))+~P24(f331(f331(f247(x70721),f2(x70721)),x70723))
% 162.26/162.09 [7088]~P123(x70881)+~P24(f331(f331(f248(x70881),x70883),f2(x70881)))+~P24(f331(f331(f248(x70881),x70882),f2(x70881)))+P24(f331(f331(f248(x70881),f2(x70881)),f331(f331(f82(x70881),x70882),x70883)))
% 162.26/162.09 [7089]~P63(x70891)+~P24(f331(f331(f248(x70891),x70893),f2(x70891)))+~P24(f331(f331(f248(x70891),x70892),f2(x70891)))+P24(f331(f331(f248(x70891),f2(x70891)),f331(f331(f289(x70891),x70892),x70893)))
% 162.26/162.09 [7090]~P64(x70901)+~P24(f331(f331(f248(x70901),x70903),f2(x70901)))+~P24(f331(f331(f248(x70901),x70902),f2(x70901)))+P24(f331(f331(f248(x70901),f2(x70901)),f331(f331(f289(x70901),x70902),x70903)))
% 162.26/162.09 [7092]~P126(x70921)+~P24(f331(f331(f247(x70921),x70923),f2(x70921)))+~P24(f331(f331(f247(x70921),x70922),f2(x70921)))+P24(f331(f331(f247(x70921),f2(x70921)),f331(f331(f82(x70921),x70922),x70923)))
% 162.26/162.09 [7093]~P123(x70931)+~P24(f331(f331(f247(x70931),x70933),f2(x70931)))+~P24(f331(f331(f247(x70931),x70932),f2(x70931)))+P24(f331(f331(f247(x70931),f2(x70931)),f331(f331(f82(x70931),x70932),x70933)))
% 162.26/162.09 [7094]~P63(x70941)+~P24(f331(f331(f247(x70941),x70943),f2(x70941)))+~P24(f331(f331(f247(x70941),x70942),f2(x70941)))+P24(f331(f331(f247(x70941),f2(x70941)),f331(f331(f289(x70941),x70942),x70943)))
% 162.26/162.09 [7095]~P64(x70951)+~P24(f331(f331(f248(x70951),x70953),f2(x70951)))+~P24(f331(f331(f247(x70951),x70952),f2(x70951)))+P24(f331(f331(f247(x70951),f2(x70951)),f331(f331(f289(x70951),x70952),x70953)))
% 162.26/162.09 [7096]~P110(x70961)+~P24(f331(f331(f248(a883),f2(a883)),x70963))+~P24(f331(f331(f248(x70961),f79(x70961)),x70962))+P24(f331(f331(f248(x70961),f79(x70961)),f331(f331(f262(x70961),x70962),x70963)))
% 162.26/162.09 [7192]~P110(x71921)+~P24(f331(f331(f248(x71921),f79(x71921)),x71923))+~P24(f331(f331(f248(x71921),f79(x71921)),x71922))+P24(f331(f331(f248(x71921),f79(x71921)),f331(f331(f82(x71921),x71922),x71923)))
% 162.26/162.09 [7193]~P87(x71931)+~P24(f331(f331(f248(x71931),f2(x71931)),x71933))+~P24(f331(f331(f248(x71931),f2(x71931)),x71932))+P24(f331(f331(f248(x71931),f2(x71931)),f331(f331(f81(x71931),x71932),x71933)))
% 162.26/162.09 [7196]~P132(x71961)+~P24(f331(f331(f248(x71961),f2(x71961)),x71963))+~P24(f331(f331(f248(x71961),f2(x71961)),x71962))+P24(f331(f331(f248(x71961),f2(x71961)),f331(f331(f82(x71961),x71962),x71963)))
% 162.26/162.09 [7197]~P63(x71971)+~P24(f331(f331(f248(x71971),f2(x71971)),x71973))+~P24(f331(f331(f248(x71971),f2(x71971)),x71972))+P24(f331(f331(f248(x71971),f2(x71971)),f331(f331(f289(x71971),x71972),x71973)))
% 162.26/162.09 [7198]~P64(x71981)+~P24(f331(f331(f248(x71981),f2(x71981)),x71983))+~P24(f331(f331(f248(x71981),f2(x71981)),x71982))+P24(f331(f331(f248(x71981),f2(x71981)),f331(f331(f289(x71981),x71982),x71983)))
% 162.26/162.09 [7200]~P126(x72001)+~P24(f331(f331(f247(x72001),f2(x72001)),x72003))+~P24(f331(f331(f247(x72001),f2(x72001)),x72002))+P24(f331(f331(f247(x72001),f2(x72001)),f331(f331(f82(x72001),x72002),x72003)))
% 162.26/162.09 [7201]~P133(x72011)+~P24(f331(f331(f247(x72011),f2(x72011)),x72013))+~P24(f331(f331(f247(x72011),f2(x72011)),x72012))+P24(f331(f331(f247(x72011),f2(x72011)),f331(f331(f82(x72011),x72012),x72013)))
% 162.26/162.09 [7202]~P123(x72021)+~P24(f331(f331(f247(x72021),f2(x72021)),x72023))+~P24(f331(f331(f247(x72021),f2(x72021)),x72022))+P24(f331(f331(f247(x72021),f2(x72021)),f331(f331(f82(x72021),x72022),x72023)))
% 162.26/162.09 [7203]~P63(x72031)+~P24(f331(f331(f247(x72031),f2(x72031)),x72033))+~P24(f331(f331(f247(x72031),f2(x72031)),x72032))+P24(f331(f331(f247(x72031),f2(x72031)),f331(f331(f289(x72031),x72032),x72033)))
% 162.26/162.09 [7204]~P64(x72041)+~P24(f331(f331(f248(x72041),f2(x72041)),x72043))+~P24(f331(f331(f247(x72041),f2(x72041)),x72042))+P24(f331(f331(f247(x72041),f2(x72041)),f331(f331(f289(x72041),x72042),x72043)))
% 162.26/162.09 [7270]~P96(x72701)+~P24(f331(f62(x72701),x72703))+E(f13(x72701,f331(f331(f309(x72701),x72702),x72703)),x72702)+~E(f331(f331(f22(f891(x72701,a877)),x72703),f331(f331(f309(x72701),x72702),f196(f891(x72701,a877)))),f196(f891(x72701,a877)))
% 162.26/162.09 [7271]~P107(x72711)+~P24(f331(f62(x72711),x72713))+E(f14(x72711,f331(f331(f309(x72711),x72712),x72713)),x72712)+~E(f331(f331(f22(f891(x72711,a877)),x72713),f331(f331(f309(x72711),x72712),f196(f891(x72711,a877)))),f196(f891(x72711,a877)))
% 162.26/162.09 [7272]~P107(x72721)+~P24(f331(f62(x72721),x72723))+E(f15(x72721,f331(f331(f309(x72721),x72722),x72723)),x72722)+~E(f331(f331(f22(f891(x72721,a877)),x72723),f331(f331(f309(x72721),x72722),f196(f891(x72721,a877)))),f196(f891(x72721,a877)))
% 162.26/162.09 [7273]~P96(x72731)+~P24(f331(f62(x72731),x72733))+E(f10(x72731,f331(f331(f309(x72731),x72732),x72733)),x72732)+~E(f331(f331(f22(f891(x72731,a877)),x72733),f331(f331(f309(x72731),x72732),f196(f891(x72731,a877)))),f196(f891(x72731,a877)))
% 162.26/162.09 [7274]~P63(x72741)+P24(f331(f331(f248(x72741),x72742),f2(x72741)))+P24(f331(f331(f248(x72741),f2(x72741)),x72743))+~P24(f331(f331(f248(x72741),f2(x72741)),f331(f331(f289(x72741),x72743),x72742)))
% 162.26/162.09 [7275]~P63(x72751)+P24(f331(f331(f248(x72751),x72752),f2(x72751)))+P24(f331(f331(f248(x72751),f2(x72751)),x72753))+~P24(f331(f331(f248(x72751),f2(x72751)),f331(f331(f289(x72751),x72752),x72753)))
% 162.26/162.09 [7276]~P63(x72761)+P24(f331(f331(f248(x72761),x72762),f2(x72761)))+P24(f331(f331(f248(x72761),f2(x72761)),x72762))+~P24(f331(f331(f248(x72761),f2(x72761)),f331(f331(f289(x72761),x72763),x72762)))
% 162.26/162.09 [7277]~P63(x72771)+P24(f331(f331(f248(x72771),x72772),f2(x72771)))+P24(f331(f331(f248(x72771),f2(x72771)),x72772))+~P24(f331(f331(f248(x72771),f2(x72771)),f331(f331(f289(x72771),x72772),x72773)))
% 162.26/162.09 [7278]~P123(x72781)+P24(f331(f331(f247(x72781),x72782),f2(x72781)))+P24(f331(f331(f247(x72781),f2(x72781)),x72783))+~P24(f331(f331(f247(x72781),f2(x72781)),f331(f331(f82(x72781),x72783),x72782)))
% 162.26/162.09 [7279]~P123(x72791)+P24(f331(f331(f247(x72791),x72792),f2(x72791)))+P24(f331(f331(f247(x72791),f2(x72791)),x72793))+~P24(f331(f331(f247(x72791),f2(x72791)),f331(f331(f82(x72791),x72792),x72793)))
% 162.26/162.09 [7280]~P63(x72801)+P24(f331(f331(f247(x72801),x72802),f2(x72801)))+P24(f331(f331(f247(x72801),f2(x72801)),x72803))+~P24(f331(f331(f247(x72801),f2(x72801)),f331(f331(f289(x72801),x72803),x72802)))
% 162.26/162.09 [7281]~P63(x72811)+P24(f331(f331(f247(x72811),x72812),f2(x72811)))+P24(f331(f331(f247(x72811),f2(x72811)),x72813))+~P24(f331(f331(f247(x72811),f2(x72811)),f331(f331(f289(x72811),x72812),x72813)))
% 162.26/162.09 [7282]~P123(x72821)+P24(f331(f331(f247(x72821),x72822),f2(x72821)))+P24(f331(f331(f247(x72821),f2(x72821)),x72822))+~P24(f331(f331(f247(x72821),f2(x72821)),f331(f331(f82(x72821),x72823),x72822)))
% 162.26/162.09 [7283]~P123(x72831)+P24(f331(f331(f247(x72831),x72832),f2(x72831)))+P24(f331(f331(f247(x72831),f2(x72831)),x72832))+~P24(f331(f331(f247(x72831),f2(x72831)),f331(f331(f82(x72831),x72832),x72833)))
% 162.26/162.09 [7284]~P63(x72841)+P24(f331(f331(f247(x72841),x72842),f2(x72841)))+P24(f331(f331(f247(x72841),f2(x72841)),x72842))+~P24(f331(f331(f247(x72841),f2(x72841)),f331(f331(f289(x72841),x72843),x72842)))
% 162.26/162.09 [7285]~P63(x72851)+P24(f331(f331(f247(x72851),x72852),f2(x72851)))+P24(f331(f331(f247(x72851),f2(x72851)),x72852))+~P24(f331(f331(f247(x72851),f2(x72851)),f331(f331(f289(x72851),x72852),x72853)))
% 162.26/162.09 [7368]~E(f331(f331(f108(f891(x73681,a877)),f331(f175(x73681),x73682)),f331(f175(x73681),x73683)),f196(f891(x73681,a877)))+~P24(f331(f140(x73681),x73683))+~P24(f331(f140(x73681),x73682))+P24(f331(f140(x73681),f331(f331(f137(x73681),x73682),x73683)))
% 162.26/162.09 [7369]~P107(x73691)+~P24(f331(f62(x73691),x73693))+E(f11(x73691,f251(x73691),f331(f331(f309(x73691),x73692),x73693)),x73692)+~E(f331(f331(f22(f891(x73691,a877)),x73693),f331(f331(f309(x73691),x73692),f196(f891(x73691,a877)))),f196(f891(x73691,a877)))
% 162.26/162.09 [7370]~P107(x73701)+~P24(f331(f62(x73701),x73703))+E(f12(x73701,f246(x73701),f331(f331(f309(x73701),x73702),x73703)),x73702)+~E(f331(f331(f22(f891(x73701,a877)),x73703),f331(f331(f309(x73701),x73702),f196(f891(x73701,a877)))),f196(f891(x73701,a877)))
% 162.26/162.09 [7386]~P111(x73861)+~P24(f331(f331(f248(x73861),x73862),x73863))+~P24(f331(f331(f248(x73861),f331(f80(x73861),x73862)),x73863))+P24(f331(f331(f248(x73861),f331(f76(x73861),x73862)),x73863))
% 162.26/162.09 [7388]~P83(x73881)+~P24(f331(f331(f247(x73881),x73882),x73883))+~P24(f331(f331(f247(x73881),f331(f80(x73881),x73882)),x73883))+P24(f331(f331(f247(x73881),f331(f76(x73881),x73882)),x73883))
% 162.26/162.09 [7459]~P132(x74591)+P24(f331(f331(f248(x74591),f2(x74591)),x74592))+~P24(f331(f331(f248(x74591),f2(x74591)),x74593))+~P24(f331(f331(f248(x74591),f2(x74591)),f331(f331(f82(x74591),x74593),x74592)))
% 162.26/162.09 [7460]~P132(x74601)+P24(f331(f331(f248(x74601),f2(x74601)),x74602))+~P24(f331(f331(f248(x74601),f2(x74601)),x74603))+~P24(f331(f331(f248(x74601),f2(x74601)),f331(f331(f82(x74601),x74602),x74603)))
% 162.26/162.09 [7757]E(x77571,x77572)+~P24(f331(f62(x77573),x77571))+~P24(f331(f331(f247(a883),f331(f38(x77573),x77571)),f331(f38(x77573),x77572)))+~P24(f331(f331(f247(f891(x77573,a877)),x77572),x77571))
% 162.26/162.09 [7897]~P24(f331(f331(f248(a1),x78971),f2(a1)))+~P24(f331(f331(f248(a1),f2(a1)),x78972))+~P24(f331(f331(f247(a1),x78972),x78973))+P24(f331(f331(f247(a1),f331(f331(f39(a1),x78971),x78972)),f331(f331(f39(a1),x78971),x78973)))
% 162.26/162.09 [7909]~P24(f331(f331(f248(a1),f2(a1)),x79093))+~P24(f331(f331(f247(a1),f2(a1)),x79091))+~P24(f331(f331(f247(a1),x79093),x79092))+P24(f331(f331(f247(a1),f331(f331(f39(a1),x79091),x79092)),f331(f331(f39(a1),x79091),x79093)))
% 162.26/162.09 [8044]E(f331(x80441,f539(x80442,x80441,x80443)),x80442)+~P24(f331(f331(f247(a1),x80442),f331(x80441,x80443)))+P24(f331(f331(f248(a883),f540(x80442,x80441,x80443)),x80443))+~P24(f331(f331(f247(a1),f331(x80441,f2(a883))),x80442))
% 162.26/162.09 [8045]E(f331(x80451,f541(x80452,x80451,x80453)),x80452)+~P24(f331(f331(f247(a1),x80452),f331(x80451,x80453)))+P24(f331(f331(f248(a883),f542(x80452,x80451,x80453)),x80453))+~P24(f331(f331(f247(a1),f331(x80451,f2(a883))),x80452))
% 162.26/162.09 [8153]~P24(f331(f62(x81531),x81533))+~P24(f331(f331(f248(a883),f331(f38(x81531),x81532)),f331(f38(x81531),x81533)))+~P24(f331(f331(f247(f891(x81531,a877)),x81532),x81533))+P24(f331(f331(f248(f891(x81531,a877)),x81532),x81533))
% 162.26/162.09 [8182]E(f331(f331(f81(a1),f405(x81823,x81821,x81822)),f406(x81823,x81821,x81822)),x81821)+E(f331(f331(f22(a1),x81821),x81822),x81821)+~P24(f331(f331(f248(a1),f2(a1)),x81822))+~P24(f331(f331(f333(a1),f331(f331(f22(a1),x81821),f79(a1))),x81823))
% 162.26/162.09 [8183]E(f331(f331(f22(a1),f416(x81833,x81831,x81832)),f417(x81833,x81831,x81832)),x81831)+E(f331(f331(f81(a1),x81831),x81832),x81831)+~P24(f331(f331(f248(a1),f2(a1)),x81832))+~P24(f331(f331(f333(a1),f331(f331(f81(a1),x81831),f79(a1))),x81833))
% 162.26/162.09 [8234]~P24(f331(f331(f247(a883),x82343),x82341))+P24(f331(f331(f248(a883),x82341),x82342))+~P24(f331(f331(f247(a883),x82343),x82342))+~P24(f331(f331(f248(a883),f331(f331(f22(a883),x82341),x82343)),f331(f331(f22(a883),x82342),x82343)))
% 162.26/162.09 [8235]~P24(f331(f331(f247(a883),x82353),x82351))+P24(f331(f331(f247(a883),x82351),x82352))+~P24(f331(f331(f247(a883),x82353),x82352))+~P24(f331(f331(f247(a883),f331(f331(f22(a883),x82351),x82353)),f331(f331(f22(a883),x82352),x82353)))
% 162.26/162.09 [8251]~P107(x82512)+E(x82511,f119(x82512))+~P29(x82512,f331(f172(x82512),x82511))+E(f331(f145(x82512,x82512,f331(f7(x82512,x82512,x82512),f246(x82512)),x82513),f331(f172(x82512),x82511)),f331(f331(f246(x82512),f331(f331(f168(x82512),x82511),f2(a883))),x82513))
% 162.26/162.09 [8317]E(f331(f331(f22(a1),x83171),x83172),x83171)+~P24(f331(f331(f248(a1),f2(a1)),x83172))+P24(f331(f331(f333(a1),f405(x83173,x83171,x83172)),x83173))+~P24(f331(f331(f333(a1),f331(f331(f22(a1),x83171),f79(a1))),x83173))
% 162.26/162.09 [8318]E(f331(f331(f81(a1),x83181),x83182),x83181)+~P24(f331(f331(f248(a1),f2(a1)),x83182))+P24(f331(f331(f333(a1),f416(x83183,x83181,x83182)),x83183))+~P24(f331(f331(f333(a1),f331(f331(f81(a1),x83181),f79(a1))),x83183))
% 162.26/162.09 [8390]~P24(f331(f331(f247(a1),x83901),f331(x83902,x83903)))+P24(f331(f331(f247(a883),f539(x83901,x83902,x83903)),x83903))+P24(f331(f331(f248(a883),f540(x83901,x83902,x83903)),x83903))+~P24(f331(f331(f247(a1),f331(x83902,f2(a883))),x83901))
% 162.26/162.09 [8391]~P24(f331(f331(f247(a1),x83911),f331(x83912,x83913)))+P24(f331(f331(f247(a883),f541(x83911,x83912,x83913)),x83913))+P24(f331(f331(f248(a883),f542(x83911,x83912,x83913)),x83913))+~P24(f331(f331(f247(a1),f331(x83912,f2(a883))),x83911))
% 162.26/162.09 [8468]E(f331(f331(f22(a1),x84681),x84682),x84681)+~P24(f331(f331(f248(a1),f2(a1)),x84682))+P24(f331(f331(f333(a1),f406(x84683,x84681,x84682)),f302(a1,f79(a1),x84682)))+~P24(f331(f331(f333(a1),f331(f331(f22(a1),x84681),f79(a1))),x84683))
% 162.26/162.09 [8469]E(f331(f331(f81(a1),x84691),x84692),x84691)+~P24(f331(f331(f248(a1),f2(a1)),x84692))+P24(f331(f331(f333(a1),f417(x84693,x84691,x84692)),f302(a1,f79(a1),x84692)))+~P24(f331(f331(f333(a1),f331(f331(f81(a1),x84691),f79(a1))),x84693))
% 162.26/162.09 [8598]~P110(x85981)+~P24(f331(f331(f248(x85981),x85982),f79(x85981)))+~P24(f331(f331(f248(x85981),f2(x85981)),x85982))+P24(f331(f331(f248(x85981),f331(f331(f82(x85981),x85982),f331(f331(f262(x85981),x85982),x85983))),f331(f331(f262(x85981),x85982),x85983)))
% 162.26/162.09 [8675]~P24(f331(x86751,x86752))+P24(f331(x86751,f2(a883)))+~P24(f331(f331(f248(a883),x86752),x86753))+~P24(f331(x86751,f45(a883,f331(a118,f729(x86752,x86751,x86753)),x86753)))
% 162.26/162.09 [8816]E(f504(x88161,x88162,x88163),f2(a883))+P24(f331(f331(x88161,x88163),x88162))+P24(f331(f331(x88161,f504(x88161,x88162,x88163)),f45(a883,f499(x88161,x88162,x88163),f504(x88161,x88162,x88163))))+~P24(f331(f319(f890(a883,a883),a231),f331(f331(f261(a883,a883),x88163),x88162)))
% 162.26/162.09 [8854]~P21(x88541,x88541,x88542,x88543)+E(f331(f310(x88541,x88541,x88542),x88543),x88543)+~P24(f331(f62(x88541),x88543))+~P24(f331(f331(f247(f891(x88541,a877)),f331(f310(x88541,x88541,x88542),x88543)),x88543))
% 162.26/162.09 [9065]P24(f331(f331(x90651,x90652),x90653))+P24(f331(f331(f248(a1),f821(x90651,x90653,x90652)),f822(x90651,x90653,x90652)))+P24(f331(f331(x90651,f821(x90651,x90653,x90652)),f331(f331(f81(a1),f822(x90651,x90653,x90652)),f79(a1))))+~P24(f331(f319(f890(a1,a1),a136),f331(f331(f261(a1,a1),x90652),x90653)))
% 162.26/162.09 [9082]P24(f331(f331(x90821,x90822),x90823))+~P24(f331(f331(f248(a1),f400(x90821,x90823,x90822)),f2(a1)))+P24(f331(f331(x90821,f331(f80(a1),f395(x90821,x90823,x90822))),f331(f80(a1),f400(x90821,x90823,x90822))))+~P24(f331(f319(f890(a1,a1),a236),f331(f331(f261(a1,a1),x90822),x90823)))
% 162.26/162.09 [9282]P24(f331(f331(x92821,x92822),x92823))+P24(f331(f331(x92821,f331(f331(f81(a1),f642(x92821,x92823,x92822)),f79(a1))),f644(x92821,x92823,x92822)))+~P24(f331(f331(f247(a1),f642(x92821,x92823,x92822)),f644(x92821,x92823,x92822)))+~P24(f331(f319(f890(a1,a1),a185),f331(f331(f261(a1,a1),x92822),x92823)))
% 162.26/162.09 [9725]~P60(x97252)+~P60(x97251)+~P24(f331(f59(f890(x97251,x97252)),x97253))+P24(f331(f59(x97251),f331(f331(f8(f891(x97252,a877),a877,x97251),f59(x97252)),f331(f331(f8(f891(x97252,f890(x97251,x97252)),f891(x97252,a877),x97251),f331(f8(f890(x97251,x97252),a877,x97252),x97253)),f261(x97251,x97252)))))
% 162.26/162.09 [9726]~P60(x97262)+~P60(x97261)+~P24(f331(f58(f890(x97261,x97262)),x97263))+P24(f331(f58(x97261),f331(f331(f8(f891(x97262,a877),a877,x97261),f58(x97262)),f331(f331(f8(f891(x97262,f890(x97261,x97262)),f891(x97262,a877),x97261),f331(f8(f890(x97261,x97262),a877,x97262),x97263)),f261(x97261,x97262)))))
% 162.26/162.09 [9838]~P60(x98382)+~P60(x98381)+P24(f331(f59(f890(x98381,x98382)),x98383))+~P24(f331(f59(x98381),f331(f331(f8(f891(x98382,a877),a877,x98381),f59(x98382)),f331(f331(f8(f891(x98382,f890(x98381,x98382)),f891(x98382,a877),x98381),f331(f8(f890(x98381,x98382),a877,x98382),x98383)),f261(x98381,x98382)))))
% 162.26/162.09 [9839]~P60(x98392)+~P60(x98391)+P24(f331(f58(f890(x98391,x98392)),x98393))+~P24(f331(f58(x98391),f331(f331(f8(f891(x98392,a877),a877,x98391),f58(x98392)),f331(f331(f8(f891(x98392,f890(x98391,x98392)),f891(x98392,a877),x98391),f331(f8(f890(x98391,x98392),a877,x98392),x98393)),f261(x98391,x98392)))))
% 162.26/162.09 [9989]E(f331(x99891,f539(x99892,x99891,x99893)),x99892)+~P24(f331(f331(f247(a1),x99892),f331(x99891,x99893)))+~P24(f331(f331(f247(a1),f331(f76(a1),f331(f331(f22(a1),f331(x99891,f331(f331(f81(a883),f540(x99892,x99891,x99893)),f79(a883)))),f331(x99891,f540(x99892,x99891,x99893))))),f79(a1)))+~P24(f331(f331(f247(a1),f331(x99891,f2(a883))),x99892))
% 162.26/162.09 [9990]E(f331(x99901,f541(x99902,x99901,x99903)),x99902)+~P24(f331(f331(f247(a1),x99902),f331(x99901,x99903)))+~P24(f331(f331(f247(a1),f331(f76(a1),f331(f331(f22(a1),f331(x99901,f331(f331(f81(a883),f542(x99902,x99901,x99903)),f79(a883)))),f331(x99901,f542(x99902,x99901,x99903))))),f79(a1)))+~P24(f331(f331(f247(a1),f331(x99901,f2(a883))),x99902))
% 162.26/162.09 [9994]~P24(f331(f331(f247(a1),x99941),f331(x99942,x99943)))+~P24(f331(f331(f247(a1),f331(f76(a1),f331(f331(f22(a1),f331(x99942,f331(f331(f81(a883),f540(x99941,x99942,x99943)),f79(a883)))),f331(x99942,f540(x99941,x99942,x99943))))),f79(a1)))+P24(f331(f331(f247(a883),f539(x99941,x99942,x99943)),x99943))+~P24(f331(f331(f247(a1),f331(x99942,f2(a883))),x99941))
% 162.26/162.09 [9995]~P24(f331(f331(f247(a1),x99951),f331(x99952,x99953)))+~P24(f331(f331(f247(a1),f331(f76(a1),f331(f331(f22(a1),f331(x99952,f331(f331(f81(a883),f542(x99951,x99952,x99953)),f79(a883)))),f331(x99952,f542(x99951,x99952,x99953))))),f79(a1)))+P24(f331(f331(f247(a883),f541(x99951,x99952,x99953)),x99953))+~P24(f331(f331(f247(a1),f331(x99952,f2(a883))),x99951))
% 162.26/162.09 [10048]E(x100481,x100482)+~E(f331(f145(f884(x100483),f884(x100483),f137(x100483),f119(x100483)),x100481),f331(f145(f884(x100483),f884(x100483),f137(x100483),f119(x100483)),x100482))+~E(f331(f197(f884(f884(x100483))),x100481),f331(f197(f884(f884(x100483))),x100482))+~P24(f331(f331(f270(f884(x100483),f884(x100483),a877),f331(f331(f7(f884(x100483),f891(f884(x100483),a883),f891(f884(x100483),a877)),f331(f331(f8(f891(a883,a877),f891(f891(f884(x100483),a883),f891(f884(x100483),a877)),f884(x100483)),f8(a883,a877,f884(x100483))),f331(f331(f8(a883,f891(a883,a877),f884(x100483)),a328),f197(f884(x100483))))),f197(f884(x100483)))),f676(x100481,x100482,x100483)))
% 162.26/162.09 [10049]E(x100491,x100492)+~E(f331(f145(f884(x100493),f884(x100493),f137(x100493),f119(x100493)),x100491),f331(f145(f884(x100493),f884(x100493),f137(x100493),f119(x100493)),x100492))+~E(f331(f197(f884(f884(x100493))),x100491),f331(f197(f884(f884(x100493))),x100492))+~P24(f331(f331(f270(f884(x100493),f884(x100493),a877),f331(f331(f7(f884(x100493),f891(f884(x100493),a883),f891(f884(x100493),a877)),f331(f331(f8(f891(a883,a877),f891(f891(f884(x100493),a883),f891(f884(x100493),a877)),f884(x100493)),f8(a883,a877,f884(x100493))),f331(f331(f8(a883,f891(a883,a877),f884(x100493)),a328),f197(f884(x100493))))),f197(f884(x100493)))),f677(x100492,x100491,x100493)))
% 162.26/162.09 [6803]~E(f79(a883),f2(a883))+~P24(f331(f62(x68031),x68033))+~P24(f331(f62(x68031),x68032))+E(f331(f331(f81(a883),f331(f38(x68031),x68032)),f331(f38(x68031),x68033)),f331(f38(x68031),f331(f331(f107(f891(x68031,a877)),x68032),x68033)))
% 162.26/162.09 [7211]~P107(x72111)+~P24(f331(f62(x72111),x72112))+~P24(f331(f331(f333(x72111),x72113),x72112))+P24(f331(f331(f247(x72111),f331(f64(x72111,f251(x72111)),x72112)),x72113))
% 162.26/162.09 [7212]~P102(x72121)+~P24(f331(f62(x72121),x72122))+~P24(f331(f331(f333(x72121),x72123),x72122))+P24(f331(f331(f247(x72121),f331(f64(x72121,f108(x72121)),x72122)),x72123))
% 162.26/162.09 [7453]~P24(f331(f62(x74531),x74533))+~P24(f331(f62(x74531),x74532))+~E(f331(f331(f108(f891(x74531,a877)),x74532),x74533),f196(f891(x74531,a877)))+E(f331(f331(f81(a883),f331(f38(x74531),x74532)),f331(f38(x74531),x74533)),f331(f38(x74531),f331(f331(f107(f891(x74531,a877)),x74532),x74533)))
% 162.26/162.09 [8240]~P38(x82401,x82403)+~P38(x82401,x82402)+~E(f331(f331(f108(f891(x82401,a877)),f331(f259(x82401,x82401),x82402)),f331(f257(x82401,x82401),x82403)),f196(f891(x82401,a877)))+P38(x82401,f331(f331(f107(f891(f890(x82401,x82401),a877)),x82402),x82403))
% 162.26/162.09 [8329]E(x83291,f331(f331(f39(a883),x83292),x83293))+~P24(f331(f331(f248(a883),f2(a883)),x83293))+~P24(f331(f331(f248(a883),x83292),f331(f331(f82(a883),x83293),f331(a118,x83291))))+~P24(f331(f331(f247(a883),f331(f331(f82(a883),x83293),x83291)),x83292))
% 162.26/162.09 [8466]~P24(f331(f62(x84661),x84662))+~P24(f331(f62(x84661),x84663))+E(f331(f331(f81(a883),f331(f38(x84661),x84662)),f331(f38(x84661),x84663)),f331(f38(x84661),f331(f331(f107(f891(x84661,a877)),x84662),x84663)))+P24(f331(f331(f333(x84661),f472(x84663,x84662,x84661)),f331(f331(f108(f891(x84661,a877)),x84662),x84663)))
% 162.26/162.09 [8829]~P123(x88292)+~E(x88291,f2(x88292))+~E(x88293,f2(x88292))+~P24(f331(f331(f248(x88292),f2(x88292)),f331(f331(f81(x88292),f331(f331(f82(x88292),x88293),x88293)),f331(f331(f82(x88292),x88291),x88291))))
% 162.26/162.09 [9365]~P38(x93651,x93653)+~P38(x93651,x93652)+P38(x93651,f331(f331(f107(f891(f890(x93651,x93651),a877)),x93652),x93653))+~P24(f331(f331(f247(f891(f890(x93651,x93651),a877)),f331(f331(f288(x93651,x93651,x93651),x93652),x93653)),x93652))
% 162.26/162.09 [9485]~P24(f331(x94851,x94853))+~P24(f331(f62(x94852),x94853))+P24(f331(x94851,f196(f891(x94852,a877))))+~P24(f331(x94851,f331(f331(f22(f891(x94852,a877)),f518(x94851,x94853,x94852)),f331(f331(f309(x94852),f497(x94851,x94853,x94852)),f196(f891(x94852,a877))))))
% 162.26/162.09 [9767]~P60(x97671)+~P60(x97672)+P8(x97671,f331(f331(f8(f891(x97672,x97671),a877,f884(x97671)),x97673),f331(f331(f8(f891(x97672,f887(x97671)),f891(x97672,x97671),f884(x97671)),f74(f887(x97671),x97671,x97672,f244(x97671))),f331(f331(f8(f884(f890(x97672,x97671)),f891(x97672,f887(x97671)),f884(x97671)),f180(x97672,x97671)),f331(f184(x97672,x97671),f56(x97672))))),f331(f197(f884(x97672)),f56(x97672)))+~P24(f331(f59(f891(x97672,x97671)),x97673))
% 162.26/162.09 [9768]~P60(x97681)+~P60(x97682)+P7(x97681,f331(f331(f8(f891(x97682,x97681),a877,f884(x97681)),x97683),f331(f331(f8(f891(x97682,f887(x97681)),f891(x97682,x97681),f884(x97681)),f74(f887(x97681),x97681,x97682,f244(x97681))),f331(f331(f8(f884(f890(x97682,x97681)),f891(x97682,f887(x97681)),f884(x97681)),f180(x97682,x97681)),f331(f184(x97682,x97681),f56(x97682))))),f331(f197(f884(x97682)),f56(x97682)))+~P24(f331(f58(f891(x97682,x97681)),x97683))
% 162.26/162.09 [9859]~P60(x98591)+~P60(x98592)+~P8(x98592,f331(f331(f8(f891(x98591,x98592),a877,f884(x98592)),x98593),f331(f331(f8(f891(x98591,f887(x98592)),f891(x98591,x98592),f884(x98592)),f74(f887(x98592),x98592,x98591,f244(x98592))),f331(f331(f8(f884(f890(x98591,x98592)),f891(x98591,f887(x98592)),f884(x98592)),f180(x98591,x98592)),f331(f184(x98591,x98592),f56(x98591))))),f331(f197(f884(x98591)),f56(x98591)))+P24(f331(f59(f891(x98591,x98592)),x98593))
% 162.26/162.09 [9860]~P60(x98601)+~P60(x98602)+~P7(x98602,f331(f331(f8(f891(x98601,x98602),a877,f884(x98602)),x98603),f331(f331(f8(f891(x98601,f887(x98602)),f891(x98601,x98602),f884(x98602)),f74(f887(x98602),x98602,x98601,f244(x98602))),f331(f331(f8(f884(f890(x98601,x98602)),f891(x98601,f887(x98602)),f884(x98602)),f180(x98601,x98602)),f331(f184(x98601,x98602),f56(x98601))))),f331(f197(f884(x98601)),f56(x98601)))+P24(f331(f58(f891(x98601,x98602)),x98603))
% 162.26/162.09 [8635]~P24(f331(f331(f248(a1),f2(a1)),x86353))+P24(f331(f331(f247(a1),f2(a1)),x86351))+~P24(f331(f331(f248(a1),x86352),x86353))+~P24(f331(f331(f247(a1),f2(a1)),f331(f331(f81(a1),f331(f331(f82(a1),x86353),x86351)),x86352)))
% 162.26/162.09 [8651]~P96(x86511)+~P24(f331(f62(x86511),x86512))+E(f331(f331(f22(f891(x86511,a877)),x86512),f331(f331(f309(x86511),x86513),f196(f891(x86511,a877)))),f196(f891(x86511,a877)))+E(f331(f331(f107(x86511),x86513),f13(x86511,f331(f331(f22(f891(x86511,a877)),x86512),f331(f331(f309(x86511),x86513),f196(f891(x86511,a877)))))),f13(x86511,f331(f331(f309(x86511),x86513),x86512)))
% 162.26/162.09 [8652]~P107(x86521)+~P24(f331(f62(x86521),x86522))+E(f331(f331(f22(f891(x86521,a877)),x86522),f331(f331(f309(x86521),x86523),f196(f891(x86521,a877)))),f196(f891(x86521,a877)))+E(f331(f331(f251(x86521),x86523),f14(x86521,f331(f331(f22(f891(x86521,a877)),x86522),f331(f331(f309(x86521),x86523),f196(f891(x86521,a877)))))),f14(x86521,f331(f331(f309(x86521),x86523),x86522)))
% 162.26/162.09 [8653]~P107(x86531)+~P24(f331(f62(x86531),x86532))+E(f331(f331(f22(f891(x86531,a877)),x86532),f331(f331(f309(x86531),x86533),f196(f891(x86531,a877)))),f196(f891(x86531,a877)))+E(f331(f331(f246(x86531),x86533),f15(x86531,f331(f331(f22(f891(x86531,a877)),x86532),f331(f331(f309(x86531),x86533),f196(f891(x86531,a877)))))),f15(x86531,f331(f331(f309(x86531),x86533),x86532)))
% 162.26/162.09 [8654]~P96(x86541)+~P24(f331(f62(x86541),x86542))+E(f331(f331(f22(f891(x86541,a877)),x86542),f331(f331(f309(x86541),x86543),f196(f891(x86541,a877)))),f196(f891(x86541,a877)))+E(f331(f331(f108(x86541),x86543),f10(x86541,f331(f331(f22(f891(x86541,a877)),x86542),f331(f331(f309(x86541),x86543),f196(f891(x86541,a877)))))),f10(x86541,f331(f331(f309(x86541),x86543),x86542)))
% 162.26/162.09 [8716]~P107(x87161)+~P24(f331(f62(x87161),x87162))+E(f331(f331(f22(f891(x87161,a877)),x87162),f331(f331(f309(x87161),x87163),f196(f891(x87161,a877)))),f196(f891(x87161,a877)))+E(f331(f331(f251(x87161),x87163),f11(x87161,f251(x87161),f331(f331(f22(f891(x87161,a877)),x87162),f331(f331(f309(x87161),x87163),f196(f891(x87161,a877)))))),f11(x87161,f251(x87161),f331(f331(f309(x87161),x87163),x87162)))
% 162.26/162.09 [8717]~P107(x87171)+~P24(f331(f62(x87171),x87172))+E(f331(f331(f22(f891(x87171,a877)),x87172),f331(f331(f309(x87171),x87173),f196(f891(x87171,a877)))),f196(f891(x87171,a877)))+E(f331(f331(f246(x87171),x87173),f12(x87171,f246(x87171),f331(f331(f22(f891(x87171,a877)),x87172),f331(f331(f309(x87171),x87173),f196(f891(x87171,a877)))))),f12(x87171,f246(x87171),f331(f331(f309(x87171),x87173),x87172)))
% 162.26/162.09 [9302]E(x93021,x93022)+~E(f331(f145(f884(x93023),f884(x93023),f137(x93023),f119(x93023)),x93021),f331(f145(f884(x93023),f884(x93023),f137(x93023),f119(x93023)),x93022))+~E(f331(f197(f884(f884(x93023))),x93021),f331(f197(f884(f884(x93023))),x93022))+P24(f331(f331(f333(f890(f884(x93023),f884(x93023))),f676(x93021,x93022,x93023)),f331(f175(f890(f884(x93023),f884(x93023))),f331(f331(f184(f884(x93023),f884(x93023)),x93022),x93021))))
% 162.26/162.09 [9303]E(x93031,x93032)+~E(f331(f145(f884(x93033),f884(x93033),f137(x93033),f119(x93033)),x93031),f331(f145(f884(x93033),f884(x93033),f137(x93033),f119(x93033)),x93032))+~E(f331(f197(f884(f884(x93033))),x93031),f331(f197(f884(f884(x93033))),x93032))+P24(f331(f331(f333(f890(f884(x93033),f884(x93033))),f677(x93032,x93031,x93033)),f331(f175(f890(f884(x93033),f884(x93033))),f331(f331(f184(f884(x93033),f884(x93033)),x93031),x93032))))
% 162.26/162.09 [10169]~P76(x101692)+E(x101691,f196(f891(x101692,a877)))+~P24(f331(f62(x101692),x101691))+E(f14(x101692,f331(f253(x101692),f331(f331(f8(f891(x101692,a877),a877,x101692),f87(x101692)),f331(f331(f7(x101692,f891(x101692,a877),f891(x101692,a877)),f331(f331(f8(f891(x101692,f891(a877,a877)),f891(f891(x101692,a877),f891(x101692,a877)),x101692),f18(x101692,a877,a877)),f331(f331(f8(f891(x101692,a877),f891(x101692,f891(a877,a877)),x101692),f331(f8(a877,f891(a877,a877),x101692),a329)),f331(f331(f7(x101692,f891(x101692,x101692),f891(x101692,a877)),f331(f331(f8(f891(x101692,a877),f891(f891(x101692,x101692),f891(x101692,a877)),x101692),f8(x101692,a877,x101692)),a328)),f331(f81(x101692),x101693))))),f331(f331(f7(x101692,f891(x101692,a877),a877),f333(x101692)),x101691))))),f331(f331(f81(x101692),x101693),f14(x101692,x101691)))
% 162.26/162.09 [10170]~P76(x101702)+E(x101701,f196(f891(x101702,a877)))+~P24(f331(f62(x101702),x101701))+E(f15(x101702,f331(f253(x101702),f331(f331(f8(f891(x101702,a877),a877,x101702),f87(x101702)),f331(f331(f7(x101702,f891(x101702,a877),f891(x101702,a877)),f331(f331(f8(f891(x101702,f891(a877,a877)),f891(f891(x101702,a877),f891(x101702,a877)),x101702),f18(x101702,a877,a877)),f331(f331(f8(f891(x101702,a877),f891(x101702,f891(a877,a877)),x101702),f331(f8(a877,f891(a877,a877),x101702),a329)),f331(f331(f7(x101702,f891(x101702,x101702),f891(x101702,a877)),f331(f331(f8(f891(x101702,a877),f891(f891(x101702,x101702),f891(x101702,a877)),x101702),f8(x101702,a877,x101702)),a328)),f331(f81(x101702),x101703))))),f331(f331(f7(x101702,f891(x101702,a877),a877),f333(x101702)),x101701))))),f331(f331(f81(x101702),x101703),f15(x101702,x101701)))
% 162.26/162.09 [10171]~P99(x101712)+E(x101711,f196(f891(x101712,a877)))+~P24(f331(f62(x101712),x101711))+E(f10(x101712,f331(f253(x101712),f331(f331(f8(f891(x101712,a877),a877,x101712),f87(x101712)),f331(f331(f7(x101712,f891(x101712,a877),f891(x101712,a877)),f331(f331(f8(f891(x101712,f891(a877,a877)),f891(f891(x101712,a877),f891(x101712,a877)),x101712),f18(x101712,a877,a877)),f331(f331(f8(f891(x101712,a877),f891(x101712,f891(a877,a877)),x101712),f331(f8(a877,f891(a877,a877),x101712),a329)),f331(f331(f7(x101712,f891(x101712,x101712),f891(x101712,a877)),f331(f331(f8(f891(x101712,a877),f891(f891(x101712,x101712),f891(x101712,a877)),x101712),f8(x101712,a877,x101712)),a328)),f331(f107(x101712),x101713))))),f331(f331(f7(x101712,f891(x101712,a877),a877),f333(x101712)),x101711))))),f331(f331(f107(x101712),x101713),f10(x101712,x101711)))
% 162.26/162.09 [10172]~P99(x101722)+E(x101721,f196(f891(x101722,a877)))+~P24(f331(f62(x101722),x101721))+E(f13(x101722,f331(f253(x101722),f331(f331(f8(f891(x101722,a877),a877,x101722),f87(x101722)),f331(f331(f7(x101722,f891(x101722,a877),f891(x101722,a877)),f331(f331(f8(f891(x101722,f891(a877,a877)),f891(f891(x101722,a877),f891(x101722,a877)),x101722),f18(x101722,a877,a877)),f331(f331(f8(f891(x101722,a877),f891(x101722,f891(a877,a877)),x101722),f331(f8(a877,f891(a877,a877),x101722),a329)),f331(f331(f7(x101722,f891(x101722,x101722),f891(x101722,a877)),f331(f331(f8(f891(x101722,a877),f891(f891(x101722,x101722),f891(x101722,a877)),x101722),f8(x101722,a877,x101722)),a328)),f331(f108(x101722),x101723))))),f331(f331(f7(x101722,f891(x101722,a877),a877),f333(x101722)),x101721))))),f331(f331(f108(x101722),x101723),f13(x101722,x101721)))
% 162.26/162.09 [10173]~P107(x101732)+E(x101731,f196(f891(x101732,a877)))+~P24(f331(f62(x101732),x101731))+E(f12(x101732,f246(x101732),f331(f253(x101732),f331(f331(f8(f891(x101732,a877),a877,x101732),f87(x101732)),f331(f331(f7(x101732,f891(x101732,a877),f891(x101732,a877)),f331(f331(f8(f891(x101732,f891(a877,a877)),f891(f891(x101732,a877),f891(x101732,a877)),x101732),f18(x101732,a877,a877)),f331(f331(f8(f891(x101732,a877),f891(x101732,f891(a877,a877)),x101732),f331(f8(a877,f891(a877,a877),x101732),a329)),f331(f331(f7(x101732,f891(x101732,x101732),f891(x101732,a877)),f331(f331(f8(f891(x101732,a877),f891(f891(x101732,x101732),f891(x101732,a877)),x101732),f8(x101732,a877,x101732)),a328)),f331(f251(x101732),x101733))))),f331(f331(f7(x101732,f891(x101732,a877),a877),f333(x101732)),x101731))))),f331(f331(f251(x101732),x101733),f12(x101732,f246(x101732),x101731)))
% 162.26/162.09 [10174]~P107(x101742)+E(x101741,f196(f891(x101742,a877)))+~P24(f331(f62(x101742),x101741))+E(f11(x101742,f251(x101742),f331(f253(x101742),f331(f331(f8(f891(x101742,a877),a877,x101742),f87(x101742)),f331(f331(f7(x101742,f891(x101742,a877),f891(x101742,a877)),f331(f331(f8(f891(x101742,f891(a877,a877)),f891(f891(x101742,a877),f891(x101742,a877)),x101742),f18(x101742,a877,a877)),f331(f331(f8(f891(x101742,a877),f891(x101742,f891(a877,a877)),x101742),f331(f8(a877,f891(a877,a877),x101742),a329)),f331(f331(f7(x101742,f891(x101742,x101742),f891(x101742,a877)),f331(f331(f8(f891(x101742,a877),f891(f891(x101742,x101742),f891(x101742,a877)),x101742),f8(x101742,a877,x101742)),a328)),f331(f246(x101742),x101743))))),f331(f331(f7(x101742,f891(x101742,a877),a877),f333(x101742)),x101741))))),f331(f331(f246(x101742),x101743),f11(x101742,f251(x101742),x101741)))
% 162.26/162.09 [10111]~P111(x101111)+~E(x101113,f2(x101111))+~E(x101112,f2(x101111))+E(f331(f331(f81(x101111),f331(f331(f262(x101111),x101112),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f331(f331(f262(x101111),x101113),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f2(x101111))
% 162.26/162.09 [10178]~P110(x101781)+~P24(f331(f331(f247(x101781),f2(x101781)),x101783))+P24(f331(f331(f247(x101781),x101782),x101783))+~P24(f331(f331(f247(x101781),f331(f331(f262(x101781),x101782),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f331(f331(f262(x101781),x101783),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))))
% 162.26/162.09 [10201]~P111(x102012)+~E(x102011,f2(x102012))+~E(x102013,f2(x102012))+~P24(f331(f331(f248(x102012),f2(x102012)),f331(f331(f81(x102012),f331(f331(f262(x102012),x102013),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103)))),f331(f331(f262(x102012),x102011),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))))
% 162.26/162.09 [9261]E(x92611,x92612)+~E(f629(x92611,x92612,x92614,x92613),f633(x92611,x92612,x92614,x92613))+P24(f331(f331(f333(f890(f884(x92613),f884(x92613))),f331(f331(f261(f884(x92613),f884(x92613)),x92612),x92611)),f150(x92613,x92614)))+P24(f331(f331(f333(f890(f884(x92613),f884(x92613))),f331(f331(f261(f884(x92613),f884(x92613)),x92611),x92612)),f150(x92613,x92614)))
% 162.26/162.09 [4874]~P61(x48742)+~E(x48744,f2(x48742))+~E(x48741,f2(x48742))+E(x48741,f331(f331(f289(x48742),x48743),x48744))
% 162.26/162.09 [4875]~P61(x48751)+~E(x48753,f2(x48751))+~E(x48754,f2(x48751))+E(f331(f331(f289(x48751),x48752),x48753),x48754)
% 162.26/162.09 [4985]~P61(x49852)+E(x49851,f2(x49852))+~E(x49853,f2(x49852))+~E(x49851,f331(f331(f289(x49852),x49854),x49853))
% 162.26/162.09 [4986]~P61(x49862)+E(x49861,f2(x49862))+~E(x49863,f2(x49862))+~E(f331(f331(f289(x49862),x49864),x49863),x49861)
% 162.26/162.09 [5160]~P119(x51602)+E(x51601,f2(x51602))+~E(f331(f331(f289(x51602),x51603),x51601),x51604)+E(x51603,f331(f331(f82(x51602),x51604),x51601))
% 162.26/162.09 [5162]~P119(x51622)+E(x51621,f2(x51622))+~E(f331(f331(f82(x51622),x51623),x51621),x51624)+E(x51623,f331(f331(f289(x51622),x51624),x51621))
% 162.26/162.09 [5163]~P61(x51632)+E(x51631,f2(x51632))+~E(f331(f331(f289(x51632),x51633),x51631),x51634)+E(x51633,f331(f331(f82(x51632),x51634),x51631))
% 162.26/162.09 [5164]~P61(x51642)+E(x51641,f2(x51642))+~E(f331(f331(f82(x51642),x51643),x51641),x51644)+E(x51643,f331(f331(f289(x51642),x51644),x51641))
% 162.26/162.09 [5165]~P119(x51652)+E(x51651,f2(x51652))+~E(x51653,f331(f331(f289(x51652),x51654),x51651))+E(f331(f331(f82(x51652),x51653),x51651),x51654)
% 162.26/162.09 [5167]~P119(x51672)+E(x51671,f2(x51672))+~E(x51673,f331(f331(f82(x51672),x51674),x51671))+E(f331(f331(f289(x51672),x51673),x51671),x51674)
% 162.26/162.09 [5168]~P61(x51682)+E(x51681,f2(x51682))+~E(x51683,f331(f331(f289(x51682),x51684),x51681))+E(f331(f331(f82(x51682),x51683),x51681),x51684)
% 162.26/162.09 [5169]~P61(x51692)+E(x51691,f2(x51692))+~E(x51693,f331(f331(f82(x51692),x51694),x51691))+E(f331(f331(f289(x51692),x51693),x51691),x51694)
% 162.26/162.09 [5202]~P61(x52022)+~E(x52021,f2(x52022))+~E(f331(f331(f82(x52022),x52021),x52024),x52023)+E(x52021,f331(f331(f289(x52022),x52023),x52024))
% 162.26/162.09 [5203]~P61(x52031)+~E(x52034,f2(x52031))+~E(x52032,f331(f331(f82(x52031),x52034),x52033))+E(f331(f331(f289(x52031),x52032),x52033),x52034)
% 162.26/162.09 [5277]~E(x52773,x52774)+~E(x52772,x52773)+~P108(x52771)+E(f302(x52771,x52772,x52773),f331(f331(f309(x52771),x52774),f196(f891(x52771,a877))))
% 162.26/162.09 [5485]~E(f120(x54852,x54851),x54853)+~E(f147(x54852,x54851),x54854)+E(x54851,f119(x54852))+E(f331(f331(f137(x54852),x54853),f331(f331(f154(x54852),x54854),f119(x54852))),x54851)
% 162.26/162.09 [6099]~P110(x60993)+E(x60991,x60992)+~E(f331(f331(f262(x60993),x60994),x60991),f331(f331(f262(x60993),x60994),x60992))+~P24(f331(f331(f248(x60993),f79(x60993)),x60994))
% 162.26/162.09 [6100]E(x61001,x61002)+~E(f331(f331(f309(x61003),x61004),x61001),f331(f331(f309(x61003),x61004),x61002))+P24(f331(f331(f333(x61003),x61004),x61002))+P24(f331(f331(f333(x61003),x61004),x61001))
% 162.26/162.09 [6138]E(f331(x61381,x61382),f79(a883))+~E(f331(f331(f9(x61383,a883),x61381),x61384),f79(a883))+~P24(f331(f62(x61383),x61384))+~P24(f331(f331(f333(x61383),x61382),x61384))
% 162.26/162.09 [6139]E(f331(x61391,x61392),f2(a883))+~E(f331(f331(f6(x61393,a883),x61391),x61394),f2(a883))+~P24(f331(f62(x61393),x61394))+~P24(f331(f331(f333(x61393),x61392),x61394))
% 162.26/162.09 [6353]~P108(x63531)+~P24(f331(f331(f248(x63531),x63534),x63533))+P24(f331(f331(f248(x63531),x63532),x63533))+~P24(f331(f331(f248(x63531),x63532),x63534))
% 162.26/162.09 [6354]~P108(x63541)+~P24(f331(f331(f247(x63541),x63544),x63543))+P24(f331(f331(f248(x63541),x63542),x63543))+~P24(f331(f331(f248(x63541),x63542),x63544))
% 162.26/162.09 [6355]~P108(x63551)+~P24(f331(f331(f247(x63551),x63552),x63554))+P24(f331(f331(f248(x63551),x63552),x63553))+~P24(f331(f331(f248(x63551),x63554),x63553))
% 162.26/162.09 [6356]~P106(x63561)+~P24(f331(f331(f248(x63561),x63562),x63564))+P24(f331(f331(f248(x63561),x63562),x63563))+~P24(f331(f331(f248(x63561),x63564),x63563))
% 162.26/162.09 [6357]~P106(x63571)+~P24(f331(f331(f247(x63571),x63572),x63574))+P24(f331(f331(f248(x63571),x63572),x63573))+~P24(f331(f331(f248(x63571),x63574),x63573))
% 162.26/162.09 [6358]~P106(x63581)+~P24(f331(f331(f247(x63581),x63584),x63583))+P24(f331(f331(f248(x63581),x63582),x63583))+~P24(f331(f331(f248(x63581),x63582),x63584))
% 162.26/162.09 [6359]~P108(x63591)+~P24(f331(f331(f247(x63591),x63594),x63593))+P24(f331(f331(f247(x63591),x63592),x63593))+~P24(f331(f331(f247(x63591),x63592),x63594))
% 162.26/162.09 [6360]~P106(x63601)+~P24(f331(f331(f247(x63601),x63602),x63604))+P24(f331(f331(f247(x63601),x63602),x63603))+~P24(f331(f331(f247(x63601),x63604),x63603))
% 162.26/162.09 [6442]~P36(x64424,x64423,x64422)+E(x64421,f811(x64422,x64423,x64424))+~P24(f331(x64423,x64421))+~P24(f331(f331(f333(x64424),x64421),f331(f175(x64424),x64422)))
% 162.26/162.09 [6584]~P27(x65841)+~P24(f331(f331(f247(x65841),x65842),f41(x65841,x65844)))+P24(f331(f331(f247(x65841),x65842),x65843))+~P24(f331(f331(f333(x65841),x65843),x65844))
% 162.26/162.09 [6730]~P107(x67301)+~P29(x67301,f331(f331(f154(x67301),x67302),x67304))+~P24(f331(f331(f333(x67301),x67303),f331(f175(x67301),x67304)))+P24(f331(f331(f247(x67301),x67302),x67303))
% 162.26/162.09 [6813]~P27(x68131)+~P24(f331(f331(f247(x68131),f40(x68131,x68134)),x68133))+P24(f331(f331(f247(x68131),x68132),x68133))+~P24(f331(f331(f333(x68131),x68132),x68134))
% 162.26/162.09 [7214]~P107(x72141)+E(f331(f331(f107(f891(x72141,a877)),f331(f301(x72141,x72142),x72143)),f331(f301(x72141,x72143),x72144)),f331(f301(x72141,x72142),x72144))+~P24(f331(f331(f247(x72141),x72143),x72144))+~P24(f331(f331(f247(x72141),x72142),x72143))
% 162.26/162.09 [7251]P36(x72511,x72512,x72513)+~E(f816(x72513,x72512,x72511,x72514),x72514)+~P24(f331(x72512,x72514))+~P24(f331(f331(f333(x72511),x72514),f331(f175(x72511),x72513)))
% 162.26/162.09 [7314]~P107(x73141)+E(f331(f331(f107(f891(x73141,a877)),f331(f301(x73141,x73142),x73143)),f302(x73141,x73143,x73144)),f302(x73141,x73142,x73144))+~P24(f331(f331(f247(x73141),x73143),x73144))+~P24(f331(f331(f247(x73141),x73142),x73143))
% 162.26/162.09 [7379]~P107(x73791)+E(f331(f331(f107(f891(x73791,a877)),f305(x73791,x73792,x73793)),f331(f301(x73791,x73793),x73794)),f305(x73791,x73792,x73794))+~P24(f331(f331(f248(x73791),x73792),x73793))+~P24(f331(f331(f247(x73791),x73793),x73794))
% 162.26/162.09 [7400]~P107(x74001)+E(f331(f331(f107(f891(x74001,a877)),f302(x74001,x74002,x74003)),f305(x74001,x74003,x74004)),f331(f301(x74001,x74002),x74004))+~P24(f331(f331(f248(x74001),x74003),x74004))+~P24(f331(f331(f247(x74001),x74002),x74003))
% 162.26/162.09 [7432]~P107(x74321)+E(f331(f331(f107(f891(x74321,a877)),f305(x74321,x74322,x74323)),f302(x74321,x74323,x74324)),f304(x74321,x74322,x74324))+~P24(f331(f331(f248(x74321),x74322),x74323))+~P24(f331(f331(f247(x74321),x74323),x74324))
% 162.26/162.09 [7433]~P107(x74331)+E(f331(f331(f107(f891(x74331,a877)),f304(x74331,x74332,x74333)),f305(x74331,x74333,x74334)),f305(x74331,x74332,x74334))+~P24(f331(f331(f248(x74331),x74333),x74334))+~P24(f331(f331(f247(x74331),x74332),x74333))
% 162.26/162.09 [7434]~P107(x74341)+E(f331(f331(f107(f891(x74341,a877)),f304(x74341,x74342,x74343)),f304(x74341,x74343,x74344)),f304(x74341,x74342,x74344))+~P24(f331(f331(f247(x74341),x74343),x74344))+~P24(f331(f331(f247(x74341),x74342),x74343))
% 162.26/162.09 [7435]~P107(x74351)+E(f331(f331(f107(f891(x74351,a877)),f302(x74351,x74352,x74353)),f304(x74351,x74353,x74354)),f302(x74351,x74352,x74354))+~P24(f331(f331(f247(x74351),x74353),x74354))+~P24(f331(f331(f247(x74351),x74352),x74353))
% 162.26/162.09 [8224]P21(x82241,x82242,f484(x82243,x82242,x82244,x82241),x82244)+~P24(f331(f62(x82242),x82243))+~P24(f331(f62(x82241),x82244))+~P24(f331(f331(f247(a883),f331(f38(x82241),x82244)),f331(f38(x82242),x82243)))
% 162.26/162.09 [8245]P36(x82451,x82452,x82453)+~P24(f331(x82452,x82454))+P24(f331(x82452,f816(x82453,x82452,x82451,x82454)))+~P24(f331(f331(f333(x82451),x82454),f331(f175(x82451),x82453)))
% 162.26/162.09 [8296]~P73(x82961)+~E(f331(x82963,f741(x82963,x82964,x82962,x82961)),f79(x82961))+E(f331(f331(f331(f66(x82961,x82962,f82(x82961)),x82963),f79(x82961)),x82964),f79(x82961))+~P24(f331(f62(x82962),x82964))
% 162.26/162.09 [8566]~P110(x85661)+~P24(f331(f331(f247(x85661),f2(x85661)),x85663))+P24(f331(f331(f247(x85661),x85662),x85663))+~P24(f331(f331(f247(x85661),f331(f331(f262(x85661),x85662),f331(a118,x85664))),f331(f331(f262(x85661),x85663),f331(a118,x85664))))
% 162.26/162.09 [8855]P36(x88551,x88552,x88553)+~P24(f331(x88552,x88554))+~P24(f331(f331(f333(x88551),x88554),f331(f175(x88551),x88553)))+P24(f331(f331(f333(x88551),f816(x88553,x88552,x88551,x88554)),f331(f175(x88551),x88553)))
% 162.26/162.09 [8942]~P73(x89421)+E(f331(f331(f331(f66(x89421,x89422,f82(x89421)),x89423),f79(x89421)),x89424),f79(x89421))+~P24(f331(f62(x89422),x89424))+P24(f331(f331(f333(x89422),f741(x89423,x89424,x89422,x89421)),x89424))
% 162.26/162.09 [9425]~P24(f331(f331(f247(a1),x94254),f2(a1)))+P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f82(a1),x94251),f45(a1,x94252,x94253))),x94254)),f2(a1)))+~P24(f331(f331(f248(a1),f2(a1)),x94253))+~P24(f331(f331(f248(a1),x94251),x94254))
% 162.26/162.09 [9901]~P24(f331(f62(x99011),x99012))+~P24(f331(f331(f333(x99011),x99014),x99012))+~P24(f331(f331(f333(x99011),x99013),x99012))+P24(f331(f331(f248(a883),f331(f38(x99011),f331(f331(f22(f891(x99011,a877)),f331(f331(f22(f891(x99011,a877)),x99012),f331(f331(f309(x99011),x99013),f196(f891(x99011,a877))))),f331(f331(f309(x99011),x99014),f196(f891(x99011,a877)))))),f331(f38(x99011),x99012)))
% 162.26/162.09 [6922]~P107(x69221)+~P24(f331(f331(f248(x69221),x69222),x69224))+~P24(f331(f331(f248(x69221),x69222),x69223))+P24(f331(f331(f248(x69221),x69222),f331(f331(f251(x69221),x69223),x69224)))
% 162.26/162.09 [6925]~P107(x69251)+~P24(f331(f331(f247(x69251),x69252),x69254))+~P24(f331(f331(f247(x69251),x69252),x69253))+P24(f331(f331(f247(x69251),x69252),f331(f331(f251(x69251),x69253),x69254)))
% 162.26/162.09 [6928]~P102(x69281)+~P24(f331(f331(f247(x69281),x69282),x69284))+~P24(f331(f331(f247(x69281),x69282),x69283))+P24(f331(f331(f247(x69281),x69282),f331(f331(f108(x69281),x69283),x69284)))
% 162.26/162.09 [6947]~P62(x69472)+E(x69471,f2(x69472))+E(f331(f331(f289(x69472),f331(f331(f262(x69472),x69471),x69473)),f331(f331(f262(x69472),x69471),x69474)),f331(f331(f262(x69472),x69471),f331(f331(f22(a883),x69473),x69474)))+~P24(f331(f331(f247(a883),x69474),x69473))
% 162.26/162.09 [6993]~P107(x69931)+~P29(x69931,f331(f331(f154(x69931),x69933),x69934))+P29(x69931,f331(f331(f154(x69931),x69932),f331(f331(f154(x69931),x69933),x69934)))+~P24(f331(f331(f247(x69931),x69932),x69933))
% 162.26/162.09 [7034]~P110(x70341)+~P24(f331(f331(f248(x70341),f2(x70341)),x70343))+~P24(f331(f331(f248(x70341),x70342),x70344))+P24(f331(f331(f248(x70341),x70342),f331(f331(f81(x70341),x70343),x70344)))
% 162.26/162.09 [7035]~P87(x70351)+~P24(f331(f331(f247(x70351),f2(x70351)),x70353))+~P24(f331(f331(f248(x70351),x70352),x70354))+P24(f331(f331(f248(x70351),x70352),f331(f331(f81(x70351),x70353),x70354)))
% 162.26/162.09 [7036]~P87(x70361)+~P24(f331(f331(f247(x70361),x70362),x70364))+~P24(f331(f331(f248(x70361),f2(x70361)),x70363))+P24(f331(f331(f248(x70361),x70362),f331(f331(f81(x70361),x70363),x70364)))
% 162.26/162.09 [7037]~P87(x70371)+~P24(f331(f331(f247(x70371),f2(x70371)),x70374))+~P24(f331(f331(f247(x70371),x70372),x70373))+P24(f331(f331(f247(x70371),x70372),f331(f331(f81(x70371),x70373),x70374)))
% 162.26/162.09 [7038]~P87(x70381)+~P24(f331(f331(f247(x70381),f2(x70381)),x70383))+~P24(f331(f331(f247(x70381),x70382),x70384))+P24(f331(f331(f247(x70381),x70382),f331(f331(f81(x70381),x70383),x70384)))
% 162.26/162.09 [7076]~P107(x70761)+P24(f331(f331(f248(x70761),x70762),x70763))+P24(f331(f331(f248(x70761),x70762),x70764))+~P24(f331(f331(f248(x70761),x70762),f331(f331(f246(x70761),x70764),x70763)))
% 162.26/162.09 [7077]~P107(x70771)+P24(f331(f331(f247(x70771),x70772),x70773))+P24(f331(f331(f247(x70771),x70772),x70774))+~P24(f331(f331(f247(x70771),x70772),f331(f331(f246(x70771),x70774),x70773)))
% 162.26/162.09 [7353]~P108(x73532)+~P60(x73531)+~P24(f331(f331(f248(f891(x73531,x73532)),x73533),x73534))+P24(f331(f331(f247(f891(x73531,x73532)),x73533),x73534))
% 162.26/162.09 [7716]~P64(x77161)+~P24(f331(f331(f248(x77161),x77164),f2(x77161)))+~P24(f331(f331(f248(x77161),x77163),f331(f331(f289(x77161),x77162),x77164)))+P24(f331(f331(f248(x77161),x77162),f331(f331(f82(x77161),x77163),x77164)))
% 162.26/162.09 [7717]~P64(x77171)+~P24(f331(f331(f248(x77171),x77174),f2(x77171)))+~P24(f331(f331(f248(x77171),x77173),f331(f331(f82(x77171),x77172),x77174)))+P24(f331(f331(f248(x77171),x77172),f331(f331(f289(x77171),x77173),x77174)))
% 162.26/162.09 [7718]~P64(x77181)+~P24(f331(f331(f248(x77181),x77184),f2(x77181)))+~P24(f331(f331(f247(x77181),x77183),f331(f331(f289(x77181),x77182),x77184)))+P24(f331(f331(f247(x77181),x77182),f331(f331(f82(x77181),x77183),x77184)))
% 162.26/162.09 [7719]~P64(x77191)+~P24(f331(f331(f248(x77191),x77194),f2(x77191)))+~P24(f331(f331(f247(x77191),x77193),f331(f331(f82(x77191),x77192),x77194)))+P24(f331(f331(f247(x77191),x77192),f331(f331(f289(x77191),x77193),x77194)))
% 162.26/162.09 [7832]~P123(x78321)+~P24(f331(f331(f248(x78321),x78323),f2(x78321)))+~P24(f331(f331(f248(x78321),x78324),x78322))+P24(f331(f331(f248(x78321),f331(f331(f82(x78321),x78322),x78323)),f331(f331(f82(x78321),x78324),x78323)))
% 162.26/162.09 [7833]~P123(x78331)+~P24(f331(f331(f248(x78331),x78332),f2(x78331)))+~P24(f331(f331(f248(x78331),x78334),x78333))+P24(f331(f331(f248(x78331),f331(f331(f82(x78331),x78332),x78333)),f331(f331(f82(x78331),x78332),x78334)))
% 162.26/162.09 [7834]~P64(x78341)+~P24(f331(f331(f248(x78341),x78343),f2(x78341)))+~P24(f331(f331(f248(x78341),x78344),x78342))+P24(f331(f331(f248(x78341),f331(f331(f289(x78341),x78342),x78343)),f331(f331(f289(x78341),x78344),x78343)))
% 162.26/162.09 [7835]~P126(x78351)+~P24(f331(f331(f247(x78351),x78352),f2(x78351)))+~P24(f331(f331(f247(x78351),x78354),x78353))+P24(f331(f331(f247(x78351),f331(f331(f82(x78351),x78352),x78353)),f331(f331(f82(x78351),x78352),x78354)))
% 162.26/162.09 [7836]~P123(x78361)+~P24(f331(f331(f248(x78361),x78362),f2(x78361)))+~P24(f331(f331(f247(x78361),x78364),x78363))+P24(f331(f331(f247(x78361),f331(f331(f82(x78361),x78362),x78363)),f331(f331(f82(x78361),x78362),x78364)))
% 162.26/162.09 [7837]~P126(x78371)+~P24(f331(f331(f247(x78371),x78373),f2(x78371)))+~P24(f331(f331(f247(x78371),x78374),x78372))+P24(f331(f331(f247(x78371),f331(f331(f82(x78371),x78372),x78373)),f331(f331(f82(x78371),x78374),x78373)))
% 162.26/162.09 [7838]~P63(x78381)+~P24(f331(f331(f247(x78381),x78383),f2(x78381)))+~P24(f331(f331(f247(x78381),x78384),x78382))+P24(f331(f331(f247(x78381),f331(f331(f289(x78381),x78382),x78383)),f331(f331(f289(x78381),x78384),x78383)))
% 162.26/162.09 [7840]~P110(x78401)+~P24(f331(f331(f248(x78401),f79(x78401)),x78402))+~P24(f331(f331(f248(a883),x78403),x78404))+P24(f331(f331(f248(x78401),f331(f331(f262(x78401),x78402),x78403)),f331(f331(f262(x78401),x78402),x78404)))
% 162.26/162.09 [7841]~P110(x78411)+~P24(f331(f331(f248(x78411),f79(x78411)),x78412))+~P24(f331(f331(f247(a883),x78413),x78414))+P24(f331(f331(f247(x78411),f331(f331(f262(x78411),x78412),x78413)),f331(f331(f262(x78411),x78412),x78414)))
% 162.26/162.09 [7842]~P110(x78421)+~P24(f331(f331(f247(x78421),f79(x78421)),x78422))+~P24(f331(f331(f247(a883),x78423),x78424))+P24(f331(f331(f247(x78421),f331(f331(f262(x78421),x78422),x78423)),f331(f331(f262(x78421),x78422),x78424)))
% 162.26/162.09 [7864]P24(f331(f331(f248(a883),f2(a883)),f331(x78641,x78642)))+~P24(f331(f62(x78643),x78644))+~P24(f331(f331(f333(x78643),x78642),x78644))+~P24(f331(f331(f248(a883),f2(a883)),f331(f331(f9(x78643,a883),x78641),x78644)))
% 162.26/162.09 [7874]~P132(x78741)+~P24(f331(f331(f248(x78741),x78743),x78744))+~P24(f331(f331(f248(x78741),f2(x78741)),x78742))+P24(f331(f331(f248(x78741),f331(f331(f82(x78741),x78742),x78743)),f331(f331(f82(x78741),x78742),x78744)))
% 162.26/162.09 [7875]~P121(x78751)+~P24(f331(f331(f248(x78751),x78753),x78754))+~P24(f331(f331(f248(x78751),f2(x78751)),x78752))+P24(f331(f331(f248(x78751),f331(f331(f82(x78751),x78752),x78753)),f331(f331(f82(x78751),x78752),x78754)))
% 162.26/162.09 [7876]~P123(x78761)+~P24(f331(f331(f248(x78761),x78762),x78764))+~P24(f331(f331(f248(x78761),f2(x78761)),x78763))+P24(f331(f331(f248(x78761),f331(f331(f82(x78761),x78762),x78763)),f331(f331(f82(x78761),x78764),x78763)))
% 162.26/162.09 [7877]~P132(x78771)+~P24(f331(f331(f248(x78771),x78772),x78774))+~P24(f331(f331(f248(x78771),f2(x78771)),x78773))+P24(f331(f331(f248(x78771),f331(f331(f82(x78771),x78772),x78773)),f331(f331(f82(x78771),x78774),x78773)))
% 162.26/162.09 [7878]~P123(x78781)+~P24(f331(f331(f248(x78781),x78783),x78784))+~P24(f331(f331(f248(x78781),f2(x78781)),x78782))+P24(f331(f331(f248(x78781),f331(f331(f82(x78781),x78782),x78783)),f331(f331(f82(x78781),x78782),x78784)))
% 162.26/162.09 [7879]~P64(x78791)+~P24(f331(f331(f248(x78791),x78792),x78794))+~P24(f331(f331(f248(x78791),f2(x78791)),x78793))+P24(f331(f331(f248(x78791),f331(f331(f289(x78791),x78792),x78793)),f331(f331(f289(x78791),x78794),x78793)))
% 162.26/162.09 [7880]~P135(x78801)+~P24(f331(f331(f247(x78801),x78803),x78804))+~P24(f331(f331(f247(x78801),f2(x78801)),x78802))+P24(f331(f331(f247(x78801),f331(f331(f82(x78801),x78802),x78803)),f331(f331(f82(x78801),x78802),x78804)))
% 162.26/162.09 [7881]~P134(x78811)+~P24(f331(f331(f247(x78811),x78813),x78814))+~P24(f331(f331(f247(x78811),f2(x78811)),x78812))+P24(f331(f331(f247(x78811),f331(f331(f82(x78811),x78812),x78813)),f331(f331(f82(x78811),x78812),x78814)))
% 162.26/162.09 [7882]~P123(x78821)+~P24(f331(f331(f248(x78821),f2(x78821)),x78822))+~P24(f331(f331(f247(x78821),x78823),x78824))+P24(f331(f331(f247(x78821),f331(f331(f82(x78821),x78822),x78823)),f331(f331(f82(x78821),x78822),x78824)))
% 162.26/162.09 [7883]~P135(x78831)+~P24(f331(f331(f247(x78831),x78832),x78834))+~P24(f331(f331(f247(x78831),f2(x78831)),x78833))+P24(f331(f331(f247(x78831),f331(f331(f82(x78831),x78832),x78833)),f331(f331(f82(x78831),x78834),x78833)))
% 162.26/162.09 [7884]~P110(x78841)+~P24(f331(f331(f247(x78841),x78842),x78844))+~P24(f331(f331(f247(x78841),f2(x78841)),x78842))+P24(f331(f331(f247(x78841),f331(f331(f262(x78841),x78842),x78843)),f331(f331(f262(x78841),x78844),x78843)))
% 162.26/162.09 [7885]~P63(x78851)+~P24(f331(f331(f247(x78851),x78852),x78854))+~P24(f331(f331(f247(x78851),f2(x78851)),x78853))+P24(f331(f331(f247(x78851),f331(f331(f289(x78851),x78852),x78853)),f331(f331(f289(x78851),x78854),x78853)))
% 162.26/162.09 [7923]~P109(x79232)+P24(f331(f331(f247(f891(x79231,x79232)),x79234),x79233))+~P24(f331(f331(f247(f891(x79231,x79232)),x79233),x79234))+P24(f331(f331(f248(f891(x79231,x79232)),x79233),x79234))
% 162.26/162.09 [7964]P24(f331(f331(f333(x79641),x79642),x79643))+P24(f331(f331(f333(x79641),x79642),x79644))+~P24(f331(f331(f247(f891(x79641,a877)),x79644),x79643))+P24(f331(f331(f248(f891(x79641,a877)),x79644),f331(f331(f309(x79641),x79642),x79643)))
% 162.26/162.09 [8131]P24(f331(f331(f333(x81311),x81312),x81313))+P24(f331(f331(f333(x81311),x81312),x81314))+~P24(f331(f331(f248(f891(x81311,a877)),x81314),f331(f331(f309(x81311),x81312),x81313)))+P24(f331(f331(f247(f891(x81311,a877)),x81314),x81313))
% 162.26/162.09 [8140]~P60(x81401)+P7(x81401,x81402,x81403)+~P24(f331(x81402,x81404))+~P24(f331(f331(f333(f884(x81401)),x81404),f331(f175(f884(x81401)),f55(x81401,x81403,f56(x81401)))))
% 162.26/162.09 [8150]~P8(x81503,x81501,x81504)+~P60(x81503)+P24(f331(x81501,x81502))+~P24(f331(f331(f333(f884(x81503)),x81502),f331(f175(f884(x81503)),f55(x81503,x81504,f56(x81503)))))
% 162.26/162.09 [8204]~P123(x82041)+P24(f331(f331(f248(x82041),x82043),x82042))+P24(f331(f331(f248(x82041),x82042),x82043))+~P24(f331(f331(f248(x82041),f331(f331(f82(x82041),x82044),x82042)),f331(f331(f82(x82041),x82044),x82043)))
% 162.26/162.09 [8205]~P123(x82051)+P24(f331(f331(f248(x82051),x82053),x82052))+P24(f331(f331(f248(x82051),x82052),x82053))+~P24(f331(f331(f248(x82051),f331(f331(f82(x82051),x82052),x82054)),f331(f331(f82(x82051),x82053),x82054)))
% 162.26/162.09 [8214]~P123(x82141)+P24(f331(f331(f248(x82141),x82144),f2(x82141)))+P24(f331(f331(f248(x82141),x82142),x82143))+~P24(f331(f331(f248(x82141),f331(f331(f82(x82141),x82142),x82144)),f331(f331(f82(x82141),x82143),x82144)))
% 162.26/162.09 [8215]~P123(x82151)+P24(f331(f331(f248(x82151),x82154),f2(x82151)))+P24(f331(f331(f248(x82151),x82152),x82153))+~P24(f331(f331(f248(x82151),f331(f331(f82(x82151),x82154),x82152)),f331(f331(f82(x82151),x82154),x82153)))
% 162.26/162.09 [8219]~P123(x82191)+P24(f331(f331(f248(x82191),x82192),x82193))+P24(f331(f331(f248(x82191),f2(x82191)),x82194))+~P24(f331(f331(f248(x82191),f331(f331(f82(x82191),x82194),x82193)),f331(f331(f82(x82191),x82194),x82192)))
% 162.26/162.09 [8220]~P123(x82201)+P24(f331(f331(f248(x82201),x82202),x82203))+P24(f331(f331(f248(x82201),f2(x82201)),x82204))+~P24(f331(f331(f248(x82201),f331(f331(f82(x82201),x82203),x82204)),f331(f331(f82(x82201),x82202),x82204)))
% 162.26/162.09 [8232]~P123(x82321)+P24(f331(f331(f248(x82321),x82322),f2(x82321)))+P24(f331(f331(f248(x82321),f2(x82321)),x82322))+~P24(f331(f331(f248(x82321),f331(f331(f82(x82321),x82323),x82322)),f331(f331(f82(x82321),x82324),x82322)))
% 162.26/162.09 [8233]~P123(x82331)+P24(f331(f331(f248(x82331),x82332),f2(x82331)))+P24(f331(f331(f248(x82331),f2(x82331)),x82332))+~P24(f331(f331(f248(x82331),f331(f331(f82(x82331),x82332),x82333)),f331(f331(f82(x82331),x82332),x82334)))
% 162.26/162.09 [8259]~P123(x82591)+~P24(f331(f331(f248(x82591),x82594),f2(x82591)))+P24(f331(f331(f248(x82591),x82592),x82593))+~P24(f331(f331(f248(x82591),f331(f331(f82(x82591),x82594),x82593)),f331(f331(f82(x82591),x82594),x82592)))
% 162.26/162.09 [8260]~P123(x82601)+~P24(f331(f331(f248(x82601),x82604),f2(x82601)))+P24(f331(f331(f247(x82601),x82602),x82603))+~P24(f331(f331(f247(x82601),f331(f331(f82(x82601),x82604),x82603)),f331(f331(f82(x82601),x82604),x82602)))
% 162.26/162.09 [8272]~P110(x82723)+~P24(f331(f331(f248(x82723),f79(x82723)),x82724))+P24(f331(f331(f248(a883),x82721),x82722))+~P24(f331(f331(f248(x82723),f331(f331(f262(x82723),x82724),x82721)),f331(f331(f262(x82723),x82724),x82722)))
% 162.26/162.09 [8274]~P110(x82743)+~P24(f331(f331(f248(x82743),f79(x82743)),x82744))+P24(f331(f331(f247(a883),x82741),x82742))+~P24(f331(f331(f247(x82743),f331(f331(f262(x82743),x82744),x82741)),f331(f331(f262(x82743),x82744),x82742)))
% 162.26/162.09 [8284]~P123(x82841)+P24(f331(f331(f248(x82841),x82842),x82843))+~P24(f331(f331(f248(x82841),f2(x82841)),x82844))+~P24(f331(f331(f248(x82841),f331(f331(f82(x82841),x82844),x82842)),f331(f331(f82(x82841),x82844),x82843)))
% 162.26/162.09 [8285]~P132(x82851)+P24(f331(f331(f248(x82851),x82852),x82853))+~P24(f331(f331(f247(x82851),f2(x82851)),x82854))+~P24(f331(f331(f248(x82851),f331(f331(f82(x82851),x82854),x82852)),f331(f331(f82(x82851),x82854),x82853)))
% 162.26/162.09 [8286]~P128(x82861)+P24(f331(f331(f248(x82861),x82862),x82863))+~P24(f331(f331(f247(x82861),f2(x82861)),x82864))+~P24(f331(f331(f248(x82861),f331(f331(f82(x82861),x82864),x82862)),f331(f331(f82(x82861),x82864),x82863)))
% 162.26/162.09 [8287]~P110(x82871)+~P24(f331(f331(f247(x82871),f2(x82871)),x82873))+P24(f331(f331(f248(x82871),x82872),x82873))+~P24(f331(f331(f248(x82871),f331(f331(f262(x82871),x82872),x82874)),f331(f331(f262(x82871),x82873),x82874)))
% 162.26/162.09 [8288]~P132(x82881)+P24(f331(f331(f248(x82881),x82882),x82883))+~P24(f331(f331(f247(x82881),f2(x82881)),x82884))+~P24(f331(f331(f248(x82881),f331(f331(f82(x82881),x82882),x82884)),f331(f331(f82(x82881),x82883),x82884)))
% 162.26/162.09 [8289]~P128(x82891)+P24(f331(f331(f248(x82891),x82892),x82893))+~P24(f331(f331(f247(x82891),f2(x82891)),x82894))+~P24(f331(f331(f248(x82891),f331(f331(f82(x82891),x82892),x82894)),f331(f331(f82(x82891),x82893),x82894)))
% 162.26/162.09 [8290]~P123(x82901)+P24(f331(f331(f247(x82901),x82902),x82903))+~P24(f331(f331(f248(x82901),f2(x82901)),x82904))+~P24(f331(f331(f247(x82901),f331(f331(f82(x82901),x82904),x82902)),f331(f331(f82(x82901),x82904),x82903)))
% 162.26/162.09 [8291]~P132(x82911)+P24(f331(f331(f247(x82911),x82912),x82913))+~P24(f331(f331(f248(x82911),f2(x82911)),x82914))+~P24(f331(f331(f247(x82911),f331(f331(f82(x82911),x82914),x82912)),f331(f331(f82(x82911),x82914),x82913)))
% 162.26/162.09 [8292]~P132(x82921)+P24(f331(f331(f247(x82921),x82922),x82923))+~P24(f331(f331(f248(x82921),f2(x82921)),x82924))+~P24(f331(f331(f247(x82921),f331(f331(f82(x82921),x82922),x82924)),f331(f331(f82(x82921),x82923),x82924)))
% 162.26/162.09 [8332]P24(f331(f331(f333(x83321),x83322),x83323))+~P24(f331(f331(f247(f891(x83321,a877)),x83323),x83324))+~P24(f331(f331(f248(f891(x83321,a877)),x83323),x83324))+P24(f331(f331(f248(f891(x83321,a877)),x83323),f331(f331(f309(x83321),x83322),x83324)))
% 162.26/162.09 [8589]~P60(x85891)+~P93(x85892)+~E(f331(x85893,f818(x85894,x85893,x85891,x85892)),f331(x85894,f818(x85894,x85893,x85891,x85892)))+P24(f331(f331(f92(f891(x85891,x85892)),x85893),x85894))
% 162.26/162.09 [8696]E(f331(f331(f22(a1),f428(x86961,x86962,x86963,x86964)),f429(x86961,x86962,x86963,x86964)),x86964)+~P24(f331(f331(f248(a1),f2(a1)),x86963))+~P24(f331(f331(f247(a1),x86961),x86964))+P24(f331(f331(f247(a1),x86961),f331(f331(f81(a1),x86964),x86963)))
% 162.26/162.09 [8697]E(f331(f331(f22(a1),f435(x86971,x86972,x86973,x86974)),f436(x86971,x86972,x86973,x86974)),x86974)+~P24(f331(f331(f248(a1),f2(a1)),x86973))+~P24(f331(f331(f248(a1),x86971),x86974))+P24(f331(f331(f248(a1),x86971),f331(f331(f81(a1),x86974),x86973)))
% 162.26/162.09 [8836]~E(f331(f331(f168(x88361),x88363),f643(x88364,x88363,x88361,x88362)),f331(f331(f168(x88361),x88364),f643(x88364,x88363,x88361,x88362)))+E(f331(f331(f176(x88361),x88362),x88363),f331(f331(f176(x88361),x88362),x88364))+~P24(f331(f331(f247(a883),x88362),f331(f197(f884(x88361)),x88363)))+~P24(f331(f331(f247(a883),x88362),f331(f197(f884(x88361)),x88364)))
% 162.26/162.09 [8908]~P24(f331(f331(f248(a1),f2(a1)),x89083))+~P24(f331(f331(f247(a1),x89081),x89084))+P24(f331(f331(f333(a1),f428(x89081,x89082,x89083,x89084)),x89082))+P24(f331(f331(f247(a1),x89081),f331(f331(f81(a1),x89084),x89083)))
% 162.26/162.09 [8909]~P24(f331(f331(f248(a1),f2(a1)),x89093))+~P24(f331(f331(f248(a1),x89091),x89094))+P24(f331(f331(f333(a1),f435(x89091,x89092,x89093,x89094)),x89092))+P24(f331(f331(f248(a1),x89091),f331(f331(f81(a1),x89094),x89093)))
% 162.26/162.09 [8951]~P107(x89511)+~P24(f331(f62(x89511),x89513))+~P24(f331(f331(f333(x89511),x89514),x89513))+P24(f331(f331(f247(x89511),f331(f331(f65(x89511,x89511,f251(x89511)),x89512),x89513)),f331(f331(f251(x89511),x89514),x89512)))
% 162.26/162.09 [8952]~P102(x89521)+~P24(f331(f62(x89521),x89523))+~P24(f331(f331(f333(x89521),x89524),x89523))+P24(f331(f331(f247(x89521),f331(f331(f65(x89521,x89521,f108(x89521)),x89522),x89523)),f331(f331(f108(x89521),x89524),x89522)))
% 162.26/162.09 [8998]E(f331(f331(f176(x89981),x89982),x89983),f331(f331(f176(x89981),x89982),x89984))+P24(f331(f331(f248(a883),f643(x89983,x89984,x89981,x89982)),x89982))+~P24(f331(f331(f247(a883),x89982),f331(f197(f884(x89981)),x89983)))+~P24(f331(f331(f247(a883),x89982),f331(f197(f884(x89981)),x89984)))
% 162.26/162.09 [9003]~P24(f331(f331(f248(a1),f2(a1)),x90033))+~P24(f331(f331(f248(a1),x90031),x90032))+P24(f331(f331(f333(a1),f436(x90031,x90034,x90033,x90032)),f302(a1,f79(a1),x90033)))+P24(f331(f331(f248(a1),x90031),f331(f331(f81(a1),x90032),x90033)))
% 162.26/162.09 [9004]~P24(f331(f331(f248(a1),f2(a1)),x90043))+~P24(f331(f331(f247(a1),x90041),x90042))+P24(f331(f331(f333(a1),f429(x90041,x90044,x90043,x90042)),f302(a1,f79(a1),x90043)))+P24(f331(f331(f247(a1),x90041),f331(f331(f81(a1),x90042),x90043)))
% 162.26/162.09 [9165]~E(f331(f180(x91651,x91652),x91653),f331(f180(x91651,x91652),x91654))+E(f331(f175(f890(x91651,x91652)),x91653),f331(f175(f890(x91651,x91652)),x91654))+~P24(f331(f140(x91651),f331(f331(f157(f890(x91651,x91652),x91651),f260(x91651,x91652)),x91654)))+~P24(f331(f140(x91651),f331(f331(f157(f890(x91651,x91652),x91651),f260(x91651,x91652)),x91653)))
% 162.26/162.09 [9177]E(f331(f180(x91771,x91772),x91773),f331(f180(x91771,x91772),x91774))+~E(f331(f175(f890(x91771,x91772)),x91773),f331(f175(f890(x91771,x91772)),x91774))+~P24(f331(f140(x91771),f331(f331(f157(f890(x91771,x91772),x91771),f260(x91771,x91772)),x91774)))+~P24(f331(f140(x91771),f331(f331(f157(f890(x91771,x91772),x91771),f260(x91771,x91772)),x91773)))
% 162.26/162.09 [9322]~P107(x93221)+~P24(f331(f62(x93221),x93224))+P24(f331(f331(f333(x93221),f744(x93222,x93223,x93224,x93221)),x93224))+P24(f331(f331(f247(x93221),f331(f331(f65(x93221,x93221,f246(x93221)),x93222),x93224)),f331(f331(f246(x93221),x93223),x93222)))
% 162.26/162.09 [9323]~P101(x93231)+~P24(f331(f62(x93231),x93234))+P24(f331(f331(f333(x93231),f755(x93232,x93233,x93234,x93231)),x93234))+P24(f331(f331(f247(x93231),f331(f331(f65(x93231,x93231,f107(x93231)),x93232),x93234)),f331(f331(f107(x93231),x93233),x93232)))
% 162.26/162.09 [9441]~P101(x94411)+~P24(f331(f62(x94411),x94413))+~P24(f331(f331(f247(x94411),f755(x94412,x94414,x94413,x94411)),x94414))+P24(f331(f331(f247(x94411),f331(f331(f65(x94411,x94411,f107(x94411)),x94412),x94413)),f331(f331(f107(x94411),x94414),x94412)))
% 162.26/162.09 [9442]~P107(x94421)+~P24(f331(f62(x94421),x94423))+~P24(f331(f331(f247(x94421),f744(x94422,x94424,x94423,x94421)),x94424))+P24(f331(f331(f247(x94421),f331(f331(f65(x94421,x94421,f246(x94421)),x94422),x94423)),f331(f331(f246(x94421),x94424),x94422)))
% 162.26/162.09 [9445]~P24(f331(f331(f248(a1),f2(a1)),x94453))+~P24(f331(f331(f247(a1),f2(a1)),x94454))+~P24(f331(f331(f248(a1),x94454),x94451))+P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f82(a1),x94451),f45(a1,x94452,x94453))),x94454)),f331(f331(f82(a1),x94451),x94453)))
% 162.26/162.09 [9870]E(x98701,x98702)+P24(f331(f331(f333(f890(f884(x98703),f884(x98703))),f331(f331(f261(f884(x98703),f884(x98703)),x98702),x98701)),f150(x98703,x98704)))+P24(f331(f331(f333(f890(f884(x98703),f884(x98703))),f331(f331(f261(f884(x98703),f884(x98703)),x98701),x98702)),f150(x98703,x98704)))+~P24(f331(f331(f333(f890(x98703,x98703)),f331(f331(f261(x98703,x98703),f629(x98701,x98702,x98704,x98703)),f633(x98701,x98702,x98704,x98703))),x98704))
% 162.26/162.09 [9871]E(x98711,x98712)+P24(f331(f331(f333(f890(f884(x98713),f884(x98713))),f331(f331(f261(f884(x98713),f884(x98713)),x98712),x98711)),f150(x98713,x98714)))+P24(f331(f331(f333(f890(f884(x98713),f884(x98713))),f331(f331(f261(f884(x98713),f884(x98713)),x98711),x98712)),f150(x98713,x98714)))+~P24(f331(f331(f333(f890(x98713,x98713)),f331(f331(f261(x98713,x98713),f633(x98711,x98712,x98714,x98713)),f629(x98711,x98712,x98714,x98713))),x98714))
% 162.26/162.09 [7420]~P107(x74201)+~P24(f331(f331(f248(x74201),x74203),x74204))+~P24(f331(f331(f248(x74201),x74202),x74204))+P24(f331(f331(f248(x74201),f331(f331(f246(x74201),x74202),x74203)),x74204))
% 162.26/162.09 [7423]~P101(x74231)+~P24(f331(f331(f247(x74231),x74233),x74234))+~P24(f331(f331(f247(x74231),x74232),x74234))+P24(f331(f331(f247(x74231),f331(f331(f107(x74231),x74232),x74233)),x74234))
% 162.26/162.09 [7426]~P107(x74261)+~P24(f331(f331(f247(x74261),x74263),x74264))+~P24(f331(f331(f247(x74261),x74262),x74264))+P24(f331(f331(f247(x74261),f331(f331(f246(x74261),x74262),x74263)),x74264))
% 162.26/162.09 [7739]~E(x77391,x77393)+E(f142(a883,f331(f301(a883,x77391),x77392)),f331(f331(f154(a883),x77393),x77394))+~E(f142(a883,f331(f301(a883,f331(f331(f81(a883),x77391),f79(a883))),x77392)),x77394)+~P24(f331(f331(f248(a883),x77391),x77392))
% 162.26/162.09 [7751]~P107(x77511)+P24(f331(f331(f248(x77511),x77512),x77513))+P24(f331(f331(f248(x77511),x77514),x77513))+~P24(f331(f331(f248(x77511),f331(f331(f251(x77511),x77514),x77512)),x77513))
% 162.26/162.09 [7752]~P107(x77521)+P24(f331(f331(f247(x77521),x77522),x77523))+P24(f331(f331(f247(x77521),x77524),x77523))+~P24(f331(f331(f247(x77521),f331(f331(f251(x77521),x77524),x77522)),x77523))
% 162.26/162.09 [8025]~P63(x80251)+~P24(f331(f331(f248(x80251),f2(x80251)),x80253))+~P24(f331(f331(f248(x80251),x80252),f331(f331(f289(x80251),x80254),x80253)))+P24(f331(f331(f248(x80251),f331(f331(f82(x80251),x80252),x80253)),x80254))
% 162.26/162.09 [8026]~P64(x80261)+~P24(f331(f331(f248(x80261),f2(x80261)),x80263))+~P24(f331(f331(f248(x80261),x80262),f331(f331(f289(x80261),x80264),x80263)))+P24(f331(f331(f248(x80261),f331(f331(f82(x80261),x80262),x80263)),x80264))
% 162.26/162.09 [8027]~P63(x80271)+~P24(f331(f331(f248(x80271),f2(x80271)),x80273))+~P24(f331(f331(f248(x80271),x80272),f331(f331(f82(x80271),x80274),x80273)))+P24(f331(f331(f248(x80271),f331(f331(f289(x80271),x80272),x80273)),x80274))
% 162.26/162.09 [8029]~P64(x80291)+~P24(f331(f331(f248(x80291),f2(x80291)),x80293))+~P24(f331(f331(f248(x80291),x80292),f331(f331(f82(x80291),x80294),x80293)))+P24(f331(f331(f248(x80291),f331(f331(f289(x80291),x80292),x80293)),x80294))
% 162.26/162.09 [8030]~P63(x80301)+~P24(f331(f331(f248(x80301),f2(x80301)),x80303))+~P24(f331(f331(f247(x80301),x80302),f331(f331(f289(x80301),x80304),x80303)))+P24(f331(f331(f247(x80301),f331(f331(f82(x80301),x80302),x80303)),x80304))
% 162.26/162.09 [8031]~P64(x80311)+~P24(f331(f331(f248(x80311),f2(x80311)),x80313))+~P24(f331(f331(f247(x80311),x80312),f331(f331(f289(x80311),x80314),x80313)))+P24(f331(f331(f247(x80311),f331(f331(f82(x80311),x80312),x80313)),x80314))
% 162.26/162.09 [8032]~P63(x80321)+~P24(f331(f331(f248(x80321),f2(x80321)),x80323))+~P24(f331(f331(f247(x80321),x80322),f331(f331(f82(x80321),x80324),x80323)))+P24(f331(f331(f247(x80321),f331(f331(f289(x80321),x80322),x80323)),x80324))
% 162.26/162.09 [8034]~P64(x80341)+~P24(f331(f331(f248(x80341),f2(x80341)),x80343))+~P24(f331(f331(f247(x80341),x80342),f331(f331(f82(x80341),x80344),x80343)))+P24(f331(f331(f247(x80341),f331(f331(f289(x80341),x80342),x80343)),x80344))
% 162.26/162.09 [8172]~P63(x81721)+~P24(f331(f331(f248(x81721),f2(x81721)),x81724))+P24(f331(f331(f248(x81721),x81722),f331(f331(f82(x81721),x81723),x81724)))+~P24(f331(f331(f248(x81721),f331(f331(f289(x81721),x81722),x81724)),x81723))
% 162.26/162.09 [8173]~P63(x81731)+~P24(f331(f331(f248(x81731),f2(x81731)),x81734))+P24(f331(f331(f248(x81731),x81732),f331(f331(f289(x81731),x81733),x81734)))+~P24(f331(f331(f248(x81731),f331(f331(f82(x81731),x81732),x81734)),x81733))
% 162.26/162.09 [8175]~P64(x81751)+~P24(f331(f331(f248(x81751),f2(x81751)),x81754))+P24(f331(f331(f248(x81751),x81752),f331(f331(f82(x81751),x81753),x81754)))+~P24(f331(f331(f248(x81751),f331(f331(f289(x81751),x81752),x81754)),x81753))
% 162.26/162.09 [8176]~P64(x81761)+~P24(f331(f331(f248(x81761),f2(x81761)),x81764))+P24(f331(f331(f248(x81761),x81762),f331(f331(f289(x81761),x81763),x81764)))+~P24(f331(f331(f248(x81761),f331(f331(f82(x81761),x81762),x81764)),x81763))
% 162.26/162.09 [8177]~P63(x81771)+~P24(f331(f331(f248(x81771),f2(x81771)),x81774))+P24(f331(f331(f247(x81771),x81772),f331(f331(f82(x81771),x81773),x81774)))+~P24(f331(f331(f247(x81771),f331(f331(f289(x81771),x81772),x81774)),x81773))
% 162.26/162.09 [8178]~P63(x81781)+~P24(f331(f331(f248(x81781),f2(x81781)),x81784))+P24(f331(f331(f247(x81781),x81782),f331(f331(f289(x81781),x81783),x81784)))+~P24(f331(f331(f247(x81781),f331(f331(f82(x81781),x81782),x81784)),x81783))
% 162.26/162.09 [8180]~P64(x81801)+~P24(f331(f331(f248(x81801),f2(x81801)),x81804))+P24(f331(f331(f247(x81801),x81802),f331(f331(f82(x81801),x81803),x81804)))+~P24(f331(f331(f247(x81801),f331(f331(f289(x81801),x81802),x81804)),x81803))
% 162.26/162.09 [8181]~P64(x81811)+~P24(f331(f331(f248(x81811),f2(x81811)),x81814))+P24(f331(f331(f247(x81811),x81812),f331(f331(f289(x81811),x81813),x81814)))+~P24(f331(f331(f247(x81811),f331(f331(f82(x81811),x81812),x81814)),x81813))
% 162.26/162.09 [8336]~P64(x83361)+~P24(f331(f331(f248(x83361),x83363),f2(x83361)))+~P24(f331(f331(f248(x83361),f331(f331(f289(x83361),x83364),x83363)),x83362))+P24(f331(f331(f248(x83361),f331(f331(f82(x83361),x83362),x83363)),x83364))
% 162.26/162.09 [8337]~P64(x83371)+~P24(f331(f331(f248(x83371),x83373),f2(x83371)))+~P24(f331(f331(f248(x83371),f331(f331(f82(x83371),x83374),x83373)),x83372))+P24(f331(f331(f248(x83371),f331(f331(f289(x83371),x83372),x83373)),x83374))
% 162.26/162.09 [8338]~P64(x83381)+~P24(f331(f331(f248(x83381),x83383),f2(x83381)))+~P24(f331(f331(f247(x83381),f331(f331(f289(x83381),x83384),x83383)),x83382))+P24(f331(f331(f247(x83381),f331(f331(f82(x83381),x83382),x83383)),x83384))
% 162.26/162.09 [8339]~P64(x83391)+~P24(f331(f331(f248(x83391),x83393),f2(x83391)))+~P24(f331(f331(f247(x83391),f331(f331(f82(x83391),x83394),x83393)),x83392))+P24(f331(f331(f247(x83391),f331(f331(f289(x83391),x83392),x83393)),x83394))
% 162.26/162.09 [8349]~P24(f331(x83491,x83494))+~P24(f331(f331(f248(a883),x83492),f331(f331(f82(a883),x83493),f331(a118,x83494))))+P24(f331(x83491,f331(f331(f39(a883),x83492),x83493)))+~P24(f331(f331(f247(a883),f331(f331(f82(a883),x83493),x83494)),x83492))
% 162.26/162.09 [8563]~P101(x85631)+~P24(f331(f62(x85631),x85634))+~P24(f331(f331(f333(x85631),x85632),x85634))+P24(f331(f331(f247(x85631),f331(f331(f107(x85631),x85632),x85633)),f331(f331(f65(x85631,x85631,f107(x85631)),x85633),x85634)))
% 162.26/162.09 [8564]~P107(x85641)+~P24(f331(f62(x85641),x85644))+~P24(f331(f331(f333(x85641),x85642),x85644))+P24(f331(f331(f247(x85641),f331(f331(f246(x85641),x85642),x85643)),f331(f331(f65(x85641,x85641,f246(x85641)),x85643),x85644)))
% 162.26/162.09 [8698]~P24(f331(f62(x86981),x86982))+E(f331(f38(x86981),f331(f331(f22(f891(x86981,a877)),x86982),f331(f331(f309(x86981),x86983),x86984))),f331(f331(f22(a883),f331(f38(x86981),f331(f331(f22(f891(x86981,a877)),x86982),x86984))),f79(a883)))+P24(f331(f331(f333(x86981),x86983),x86984))+~P24(f331(f331(f333(x86981),x86983),x86982))
% 162.26/162.09 [8768]E(f331(f331(f81(a1),f430(x87681,x87682,x87683,x87684)),f431(x87681,x87682,x87683,x87684)),x87684)+~P24(f331(f331(f248(a1),f2(a1)),x87683))+~P24(f331(f331(f247(a1),x87684),x87681))+P24(f331(f331(f247(a1),f331(f331(f22(a1),x87684),x87683)),x87681))
% 162.26/162.09 [8769]E(f331(f331(f81(a1),f437(x87691,x87692,x87693,x87694)),f438(x87691,x87692,x87693,x87694)),x87694)+~P24(f331(f331(f248(a1),f2(a1)),x87693))+~P24(f331(f331(f248(a1),x87694),x87691))+P24(f331(f331(f248(a1),f331(f331(f22(a1),x87694),x87693)),x87691))
% 162.26/162.09 [8983]~P24(f331(f331(f248(a1),f2(a1)),x89833))+~P24(f331(f331(f247(a1),x89834),x89831))+P24(f331(f331(f333(a1),f430(x89831,x89832,x89833,x89834)),x89832))+P24(f331(f331(f247(a1),f331(f331(f22(a1),x89834),x89833)),x89831))
% 162.26/162.09 [8984]~P24(f331(f331(f248(a1),f2(a1)),x89843))+~P24(f331(f331(f248(a1),x89844),x89841))+P24(f331(f331(f333(a1),f437(x89841,x89842,x89843,x89844)),x89842))+P24(f331(f331(f248(a1),f331(f331(f22(a1),x89844),x89843)),x89841))
% 162.26/162.09 [9056]~P24(f331(f331(f248(a1),f2(a1)),x90562))+~P24(f331(f331(f248(a1),x90561),x90563))+P24(f331(f331(f333(a1),f438(x90563,x90564,x90562,x90561)),f302(a1,f79(a1),x90562)))+P24(f331(f331(f248(a1),f331(f331(f22(a1),x90561),x90562)),x90563))
% 162.26/162.09 [9057]~P24(f331(f331(f248(a1),f2(a1)),x90572))+~P24(f331(f331(f247(a1),x90571),x90573))+P24(f331(f331(f333(a1),f431(x90573,x90574,x90572,x90571)),f302(a1,f79(a1),x90572)))+P24(f331(f331(f247(a1),f331(f331(f22(a1),x90571),x90572)),x90573))
% 162.26/162.09 [9073]~P24(f331(f331(f248(a1),f2(a1)),x90733))+~P24(f331(f331(f247(a1),f2(a1)),x90734))+~P24(f331(f331(f248(a1),x90734),x90731))+P24(f331(f331(f247(a1),f2(a1)),f331(f331(f81(a1),f331(f331(f82(a1),x90731),f45(a1,x90732,x90733))),x90734)))
% 162.26/162.09 [9148]~P107(x91481)+~P24(f331(f62(x91481),x91484))+~P24(f331(f331(f247(x91481),x91482),f743(x91483,x91482,x91484,x91481)))+P24(f331(f331(f247(x91481),f331(f331(f251(x91481),x91482),x91483)),f331(f331(f65(x91481,x91481,f251(x91481)),x91483),x91484)))
% 162.26/162.09 [9149]~P102(x91491)+~P24(f331(f62(x91491),x91494))+~P24(f331(f331(f247(x91491),x91492),f754(x91493,x91492,x91494,x91491)))+P24(f331(f331(f247(x91491),f331(f331(f108(x91491),x91492),x91493)),f331(f331(f65(x91491,x91491,f108(x91491)),x91493),x91494)))
% 162.26/162.09 [9164]~P24(f331(f331(f247(a1),x91644),f2(a1)))+~P24(f331(f331(f248(a1),f2(a1)),x91642))+~P24(f331(f331(f248(a1),x91641),x91644))+P24(f331(f331(f248(a1),f331(f331(f82(a1),x91641),x91642)),f331(f331(f81(a1),f331(f331(f82(a1),x91641),f45(a1,x91643,x91642))),x91644)))
% 162.26/162.09 [9186]P24(f331(f62(x91861),x91862))+~P24(f331(f62(x91861),x91863))+~P24(f331(f331(f333(f891(x91861,a877)),x91862),f331(f331(f61(x91861),x91863),x91864)))+~P24(f331(f331(f247(f891(f890(x91861,x91861),a877)),x91864),f331(f331(f268(x91861,x91861),x91863),f331(f16(f891(x91861,a877),x91861),x91863))))
% 162.26/162.09 [9212]~P107(x92121)+~P24(f331(f62(x92121),x92124))+P24(f331(f331(f333(x92121),f743(x92122,x92123,x92124,x92121)),x92124))+P24(f331(f331(f247(x92121),f331(f331(f251(x92121),x92123),x92122)),f331(f331(f65(x92121,x92121,f251(x92121)),x92122),x92124)))
% 162.26/162.09 [9213]~P102(x92131)+~P24(f331(f62(x92131),x92134))+P24(f331(f331(f333(x92131),f754(x92132,x92133,x92134,x92131)),x92134))+P24(f331(f331(f247(x92131),f331(f331(f108(x92131),x92133),x92132)),f331(f331(f65(x92131,x92131,f108(x92131)),x92132),x92134)))
% 162.26/162.09 [9631]~P24(f331(f62(x96312),x96314))+~P24(f331(f62(x96311),x96313))+~P24(f331(f331(f247(a883),f331(f38(x96312),x96314)),f331(f38(x96311),x96313)))+P24(f331(f331(f247(f891(x96311,a877)),f331(f310(x96312,x96311,f484(x96313,x96311,x96314,x96312)),x96314)),x96313))
% 162.26/162.09 [9260]~P24(f331(f331(f333(x92601),x92602),x92604))+P24(f331(f331(f333(x92601),x92602),x92603))+~P24(f331(f331(f248(f891(x92601,a877)),x92604),f331(f331(f309(x92601),x92602),x92603)))+P24(f331(f331(f248(f891(x92601,a877)),f331(f331(f22(f891(x92601,a877)),x92604),f331(f331(f309(x92601),x92602),f196(f891(x92601,a877))))),x92603))
% 162.26/162.09 [9421]~P24(f331(f331(f333(x94211),x94212),x94214))+P24(f331(f331(f333(x94211),x94212),x94213))+P24(f331(f331(f248(f891(x94211,a877)),x94214),f331(f331(f309(x94211),x94212),x94213)))+~P24(f331(f331(f248(f891(x94211,a877)),f331(f331(f22(f891(x94211,a877)),x94214),f331(f331(f309(x94211),x94212),f196(f891(x94211,a877))))),x94213))
% 162.26/162.09 [9448]P24(f331(f331(f333(x94481),x94482),x94483))+~P24(f331(f331(f247(f891(x94481,a877)),x94484),x94483))+P24(f331(f331(f248(f891(x94481,a877)),x94484),f331(f331(f309(x94481),x94482),x94483)))+~P24(f331(f331(f248(f891(x94481,a877)),f331(f331(f22(f891(x94481,a877)),x94484),f331(f331(f309(x94481),x94482),f196(f891(x94481,a877))))),x94483))
% 162.26/162.09 [9453]~P24(f331(f331(f333(x94531),x94533),x94532))+~P24(f331(f331(f248(f891(x94531,a877)),x94532),x94534))+P24(f331(f331(f248(f891(x94531,a877)),x94532),f331(f331(f309(x94531),x94533),x94534)))+~P24(f331(f331(f248(f891(x94531,a877)),f331(f331(f22(f891(x94531,a877)),x94532),f331(f331(f309(x94531),x94533),f196(f891(x94531,a877))))),x94534))
% 162.26/162.09 [9466]~P24(f331(f331(f247(f891(x94661,a877)),x94662),x94664))+~P24(f331(f331(f248(f891(x94661,a877)),x94662),x94664))+P24(f331(f331(f248(f891(x94661,a877)),x94662),f331(f331(f309(x94661),x94663),x94664)))+~P24(f331(f331(f248(f891(x94661,a877)),f331(f331(f22(f891(x94661,a877)),x94662),f331(f331(f309(x94661),x94663),f196(f891(x94661,a877))))),x94664))
% 162.26/162.09 [9524]~P108(x95242)+~P60(x95241)+~P24(f331(f331(f247(f891(x95241,x95242)),x95243),x95244))+P24(f331(f59(x95241),f331(f331(f18(x95241,x95242,a877),f331(f331(f8(x95242,f891(x95242,a877),x95241),f247(x95242)),x95243)),x95244)))
% 162.26/162.09 [9677]~P108(x96772)+~P60(x96771)+P24(f331(f331(f247(f891(x96771,x96772)),x96773),x96774))+~P24(f331(f59(x96771),f331(f331(f18(x96771,x96772,a877),f331(f331(f8(x96772,f891(x96772,a877),x96771),f247(x96772)),x96773)),x96774)))
% 162.26/162.09 [9855]E(f331(f331(f168(x98551),f331(f331(f168(f884(x98551)),f182(x98551,x98552)),x98553)),x98554),f331(f331(f168(x98551),f331(f331(f168(f884(x98551)),x98552),x98554)),x98553))+~P24(f331(f331(f248(a883),x98553),f331(f197(f884(f884(x98551))),f182(x98551,x98552))))+~P29(a883,f331(f172(a883),f331(f331(f157(f884(x98551),a883),f197(f884(x98551))),x98552)))+~P24(f331(f331(f248(a883),x98554),f331(f197(f884(f884(x98551))),f331(f139(f884(x98551),f331(f331(f8(a883,a877,f884(x98551)),f331(f248(a883),x98553)),f197(f884(x98551)))),x98552))))
% 162.26/162.09 [9884]~P24(f331(f331(f333(f890(a883,a883)),x98844),x98841))+~P24(f331(f331(f333(f890(f890(a883,a883),f890(a883,a883))),f331(f331(f261(f890(a883,a883),f890(a883,a883)),x98844),x98842)),a36))+~P24(f331(f331(f333(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877))),f331(f331(f261(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),x98841),x98843)),a69))+P24(f331(f331(f333(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877))),f331(f331(f261(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),x98841),f331(f331(f309(f890(a883,a883)),x98842),x98843))),a69))
% 162.26/162.09 [9885]~P24(f331(f331(f333(f890(a883,a883)),x98854),x98851))+~P24(f331(f331(f333(f890(f890(a883,a883),f890(a883,a883))),f331(f331(f261(f890(a883,a883),f890(a883,a883)),x98854),x98852)),a71))+~P24(f331(f331(f333(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877))),f331(f331(f261(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),x98851),x98853)),a72))+P24(f331(f331(f333(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877))),f331(f331(f261(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),x98851),f331(f331(f309(f890(a883,a883)),x98852),x98853))),a72))
% 162.26/162.09 [9774]~P108(x97742)+~P60(x97741)+~P24(f331(f331(f248(f891(x97741,x97742)),x97743),x97744))+P24(f331(f58(x97741),f331(f331(f8(a877,a877,x97741),a326),f331(f331(f18(x97741,x97742,a877),f331(f331(f8(x97742,f891(x97742,a877),x97741),a328),x97743)),x97744))))
% 162.26/162.09 [9897]~P24(f331(f331(f333(f890(a883,a883)),x98974),x98973))+~P24(f331(f331(f333(f890(f890(a883,a883),f890(a883,a883))),f331(f331(f261(f890(a883,a883),f890(a883,a883)),x98971),x98974)),a36))+~P24(f331(f331(f333(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877))),f331(f331(f261(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),x98972),x98973)),a37))+P24(f331(f331(f333(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877))),f331(f331(f261(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),f331(f331(f309(f890(a883,a883)),x98971),x98972)),x98973)),a37))
% 162.26/162.09 [9898]~P24(f331(f331(f333(f890(a883,a883)),x98984),x98983))+~P24(f331(f331(f333(f890(f890(a883,a883),f890(a883,a883))),f331(f331(f261(f890(a883,a883),f890(a883,a883)),x98981),x98984)),a71))+~P24(f331(f331(f333(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877))),f331(f331(f261(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),x98982),x98983)),a70))+P24(f331(f331(f333(f890(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877))),f331(f331(f261(f891(f890(a883,a883),a877),f891(f890(a883,a883),a877)),f331(f331(f309(f890(a883,a883)),x98981),x98982)),x98983)),a70))
% 162.26/162.09 [6048]~P5(x60484,x60481)+~P24(f331(f331(x60481,x60482),x60485))+P24(f331(f331(x60481,x60482),x60483))+~P24(f331(f331(x60481,x60485),x60483))
% 162.26/162.09 [5311]~P70(x53115)+E(x53111,x53112)+~E(x53113,x53114)+~E(f331(f331(f22(x53115),x53113),x53114),f331(f331(f22(x53115),x53111),x53112))
% 162.26/162.09 [6158]~P13(x61585,x61581,x61583)+E(f331(f331(x61581,x61582),f331(x61583,x61584)),f331(x61583,x61584))+~P24(f331(f62(x61585),x61584))+~P24(f331(f331(f333(x61585),x61582),x61584))
% 162.26/162.09 [6344]~P77(x63441)+~E(f331(f331(f22(x63441),x63444),x63445),f331(f331(f22(x63441),x63442),x63443))+~P24(f331(f331(f248(x63441),x63444),x63445))+P24(f331(f331(f248(x63441),x63442),x63443))
% 162.26/162.09 [6346]~P77(x63461)+~E(f331(f331(f22(x63461),x63464),x63465),f331(f331(f22(x63461),x63462),x63463))+~P24(f331(f331(f247(x63461),x63464),x63465))+P24(f331(f331(f247(x63461),x63462),x63463))
% 162.26/162.09 [7287]~E(x72872,f331(f331(f154(x72871),x72874),x72875))+P24(f331(f331(f333(f884(x72871)),x72872),f164(x72871,x72873)))+~P24(f331(f331(f333(f884(x72871)),x72875),f164(x72871,x72873)))+~P24(f331(f331(f333(x72871),x72874),x72873))
% 162.26/162.09 [7692]~E(f331(f197(f884(x76921)),x76923),f331(f197(f884(x76922)),x76924))+~E(f331(f331(f157(f890(x76921,x76922),x76922),f269(x76921,x76922)),x76925),x76924)+~E(f331(f331(f157(f890(x76921,x76922),x76921),f260(x76921,x76922)),x76925),x76923)+E(f331(f331(f184(x76921,x76922),x76923),x76924),x76925)
% 162.26/162.09 [8022]~P108(x80221)+P24(f331(f331(f248(f891(x80221,a877)),f302(x80221,x80222,x80223)),f302(x80221,x80224,x80225)))+~P24(f331(f331(f247(x80221),x80224),x80225))+P24(f331(f331(f247(x80221),x80222),x80223))
% 162.26/162.09 [8124]~P108(x81241)+P24(f331(f331(f247(f891(x81241,a877)),f302(x81241,x81242,x81243)),f302(x81241,x81244,x81245)))+~P24(f331(f331(f247(x81241),x81243),x81245))+~P24(f331(f331(f247(x81241),x81244),x81242))
% 162.26/162.09 [8247]~P107(x82471)+P24(f331(f331(f247(x82471),x82472),x82473))+P24(f331(f331(f247(x82471),x82474),x82473))+~P24(f331(f331(f247(f891(x82471,a877)),f331(f301(x82471,x82473),x82472)),f331(f301(x82471,x82474),x82475)))
% 162.26/162.09 [8248]~P107(x82481)+P24(f331(f331(f247(x82481),x82482),x82483))+P24(f331(f331(f247(x82481),x82482),x82484))+~P24(f331(f331(f247(f891(x82481,a877)),f331(f301(x82481,x82483),x82482)),f331(f301(x82481,x82485),x82484)))
% 162.26/162.09 [8481]~P108(x84811)+~P24(f331(f331(f248(f891(x84811,a877)),f302(x84811,x84814,x84812)),f302(x84811,x84815,x84813)))+P24(f331(f331(f247(x84811),x84812),x84813))+~P24(f331(f331(f247(x84811),x84814),x84812))
% 162.26/162.09 [8482]~P108(x84821)+~P24(f331(f331(f247(f891(x84821,a877)),f302(x84821,x84824,x84822)),f302(x84821,x84825,x84823)))+P24(f331(f331(f247(x84821),x84822),x84823))+~P24(f331(f331(f247(x84821),x84824),x84822))
% 162.26/162.09 [8483]~P108(x84831)+~P24(f331(f331(f248(f891(x84831,a877)),f302(x84831,x84833,x84834)),f302(x84831,x84832,x84835)))+P24(f331(f331(f247(x84831),x84832),x84833))+~P24(f331(f331(f247(x84831),x84833),x84834))
% 162.26/162.09 [8484]~P108(x84841)+~P24(f331(f331(f247(f891(x84841,a877)),f302(x84841,x84843,x84844)),f302(x84841,x84842,x84845)))+P24(f331(f331(f247(x84841),x84842),x84843))+~P24(f331(f331(f247(x84841),x84843),x84844))
% 162.26/162.09 [6047]~P13(x60472,x60475,x60473)+E(x60471,f196(f891(x60472,a877)))+~P24(f331(f62(x60472),x60471))+E(f331(x60473,f331(f331(f309(x60472),x60474),x60471)),f331(f331(x60475,x60474),f331(x60473,x60471)))
% 162.26/162.09 [6801]~E(x68011,x68012)+~E(f331(f331(f108(f891(x68013,a877)),x68014),x68015),f196(f891(x68013,a877)))+~P24(f331(f331(f333(x68013),x68012),x68015))+~P24(f331(f331(f333(x68013),x68011),x68014))
% 162.26/162.09 [6879]~P14(x68792,x68795,x68791)+~P24(f331(f62(x68792),x68794))+E(f331(x68791,f331(f331(f309(x68792),x68793),x68794)),f331(f331(f65(x68792,x68792,x68795),x68793),x68794))+P24(f331(f331(f333(x68792),x68793),x68794))
% 162.26/162.09 [6943]~P73(x69432)+~P24(f331(f62(x69431),x69435))+E(f331(f331(f9(x69431,x69432),x69433),f331(f331(f309(x69431),x69434),x69435)),f331(f331(f82(x69432),f331(x69433,x69434)),f331(f331(f9(x69431,x69432),x69433),x69435)))+P24(f331(f331(f333(x69431),x69434),x69435))
% 162.26/162.09 [6945]~P74(x69452)+~P24(f331(f62(x69451),x69455))+E(f331(f331(f6(x69451,x69452),x69453),f331(f331(f309(x69451),x69454),x69455)),f331(f331(f81(x69452),f331(x69453,x69454)),f331(f331(f6(x69451,x69452),x69453),x69455)))+P24(f331(f331(f333(x69451),x69454),x69455))
% 162.26/162.09 [7438]~P14(x74382,x74385,x74381)+~P24(f331(f62(x74382),x74384))+E(f331(x74381,f331(f331(f309(x74382),x74383),x74384)),x74383)+~E(f331(f331(f22(f891(x74382,a877)),x74384),f331(f331(f309(x74382),x74383),f196(f891(x74382,a877)))),f196(f891(x74382,a877)))
% 162.26/162.09 [7744]~P24(f331(x77441,x77443))+~P24(f331(f331(f203(x77442),x77443),x77445))+~P24(f331(f331(f203(f33(x77441,x77442)),x77445),x77444))+P24(f331(f331(f203(f33(x77441,x77442)),x77443),x77444))
% 162.26/162.09 [7798]~P84(x77981)+~P24(f331(f331(f248(x77981),x77983),x77985))+~P24(f331(f331(f248(x77981),x77982),x77984))+P24(f331(f331(f248(x77981),f331(f331(f81(x77981),x77982),x77983)),f331(f331(f81(x77981),x77984),x77985)))
% 162.26/162.09 [7799]~P84(x77991)+~P24(f331(f331(f247(x77991),x77992),x77994))+~P24(f331(f331(f248(x77991),x77993),x77995))+P24(f331(f331(f248(x77991),f331(f331(f81(x77991),x77992),x77993)),f331(f331(f81(x77991),x77994),x77995)))
% 162.26/162.09 [7800]~P84(x78001)+~P24(f331(f331(f247(x78001),x78003),x78005))+~P24(f331(f331(f248(x78001),x78002),x78004))+P24(f331(f331(f248(x78001),f331(f331(f81(x78001),x78002),x78003)),f331(f331(f81(x78001),x78004),x78005)))
% 162.26/162.09 [7801]~P82(x78011)+~P24(f331(f331(f247(x78011),x78013),x78015))+~P24(f331(f331(f247(x78011),x78012),x78014))+P24(f331(f331(f247(x78011),f331(f331(f81(x78011),x78012),x78013)),f331(f331(f81(x78011),x78014),x78015)))
% 162.26/162.09 [7802]~P101(x78021)+~P24(f331(f331(f247(x78021),x78023),x78025))+~P24(f331(f331(f247(x78021),x78022),x78024))+P24(f331(f331(f247(x78021),f331(f331(f107(x78021),x78022),x78023)),f331(f331(f107(x78021),x78024),x78025)))
% 162.26/162.09 [7803]~P107(x78031)+~P24(f331(f331(f247(x78031),x78033),x78035))+~P24(f331(f331(f247(x78031),x78032),x78034))+P24(f331(f331(f247(x78031),f331(f331(f251(x78031),x78032),x78033)),f331(f331(f251(x78031),x78034),x78035)))
% 162.26/162.09 [7804]~P107(x78041)+~P24(f331(f331(f247(x78041),x78043),x78045))+~P24(f331(f331(f247(x78041),x78042),x78044))+P24(f331(f331(f247(x78041),f331(f331(f246(x78041),x78042),x78043)),f331(f331(f246(x78041),x78044),x78045)))
% 162.26/162.09 [7805]~P102(x78051)+~P24(f331(f331(f247(x78051),x78053),x78055))+~P24(f331(f331(f247(x78051),x78052),x78054))+P24(f331(f331(f247(x78051),f331(f331(f108(x78051),x78052),x78053)),f331(f331(f108(x78051),x78054),x78055)))
% 162.26/162.09 [7933]~P141(x79335)+E(x79331,x79332)+E(x79333,x79334)+~E(f331(f331(f81(x79335),f331(f331(f82(x79335),x79333),x79331)),f331(f331(f82(x79335),x79334),x79332)),f331(f331(f81(x79335),f331(f331(f82(x79335),x79333),x79332)),f331(f331(f82(x79335),x79334),x79331)))
% 162.26/162.09 [8077]P30(x80771,x80772,x80773)+~P23(x80771,x80774,x80775)+~P30(x80771,x80772,f598(x80775,x80774,x80771,x80772))+~P24(f331(f331(f333(f882(x80771)),x80773),x80775))
% 162.26/162.09 [8147]~P107(x81474)+~P24(f331(f140(x81471),x81473))+P24(f331(f331(f333(x81471),x81472),f331(f175(x81471),x81473)))+P24(f331(f140(x81471),f331(f331(f151(x81471,x81474,x81475),x81472),x81473)))
% 162.26/162.09 [8293]~P70(x82931)+E(f331(f331(f22(x82931),f331(f331(f6(a883,x82931),x82932),f331(f301(a883,x82933),x82934))),f331(f331(f6(a883,x82931),x82932),f331(f301(a883,x82933),x82935))),f331(f331(f6(a883,x82931),x82932),f331(f301(a883,x82935),x82934)))+~P24(f331(f331(f247(a883),x82935),x82934))+~P24(f331(f331(f247(a883),x82933),x82935))
% 162.26/162.09 [8294]~P74(x82941)+E(f331(f331(f81(x82941),f331(f331(f6(a883,x82941),x82942),f331(f301(a883,x82943),x82944))),f331(f331(f6(a883,x82941),x82942),f331(f301(a883,x82944),x82945))),f331(f331(f6(a883,x82941),x82942),f331(f301(a883,x82943),x82945)))+~P24(f331(f331(f247(a883),x82944),x82945))+~P24(f331(f331(f247(a883),x82943),x82944))
% 162.26/162.09 [8621]~P62(x86212)+E(x86211,f2(x86212))+E(x86213,f2(x86212))+E(f331(f331(f289(x86212),f331(f331(f22(x86212),f331(f331(f82(x86212),x86214),x86211)),f331(f331(f82(x86212),x86215),x86213))),f331(f331(f82(x86212),x86213),x86211)),f331(f331(f22(x86212),f331(f331(f289(x86212),x86214),x86213)),f331(f331(f289(x86212),x86215),x86211)))
% 162.26/162.09 [8622]~P62(x86222)+E(x86221,f2(x86222))+E(x86223,f2(x86222))+E(f331(f331(f289(x86222),f331(f331(f81(x86222),f331(f331(f82(x86222),x86224),x86221)),f331(f331(f82(x86222),x86225),x86223))),f331(f331(f82(x86222),x86223),x86221)),f331(f331(f81(x86222),f331(f331(f289(x86222),x86224),x86223)),f331(f331(f289(x86222),x86225),x86221)))
% 162.26/162.09 [8631]~E(x86312,f331(x86313,x86311))+E(x86311,f500(x86312,x86313,x86314,x86315))+~P21(x86315,x86314,x86313,f256(f891(x86315,a877)))+~P24(f331(f331(f333(x86314),x86312),f331(f310(x86315,x86314,x86313),f256(f891(x86315,a877)))))
% 162.26/162.09 [8820]~P111(x88201)+~P24(f331(f331(f248(x88201),f331(f76(x88201),x88202)),x88204))+P24(f331(f331(f248(x88201),f331(f331(f82(x88201),f331(f76(x88201),x88202)),f331(f76(x88201),x88203))),f331(f331(f82(x88201),x88204),x88205)))+~P24(f331(f331(f248(x88201),f331(f76(x88201),x88203)),x88205))
% 162.26/162.09 [8838]~P23(x88381,x88385,x88384)+P30(x88381,x88382,x88383)+P24(f331(f331(f333(f882(x88381)),f598(x88384,x88385,x88381,x88382)),x88385))+~P24(f331(f331(f333(f882(x88381)),x88383),x88384))
% 162.26/162.09 [8943]~P21(x89431,x89433,x89435,x89432)+~P24(f331(f62(x89433),x89434))+P24(f331(f331(f247(a883),f331(f38(x89431),x89432)),f331(f38(x89433),x89434)))+~P24(f331(f331(f247(f891(x89433,a877)),f331(f310(x89431,x89433,x89435),x89432)),x89434))
% 162.26/162.09 [9012]~P73(x90122)+~P21(x90121,x90121,x90124,x90125)+~P24(f331(f62(x90121),x90125))+E(f331(f331(f9(x90121,x90122),f331(f74(x90121,x90122,x90121,x90123),x90124)),x90125),f331(f331(f9(x90121,x90122),x90123),f331(f310(x90121,x90121,x90124),x90125)))
% 162.26/162.09 [9013]~P74(x90132)+~P21(x90131,x90131,x90134,x90135)+~P24(f331(f62(x90131),x90135))+E(f331(f331(f6(x90131,x90132),f331(f74(x90131,x90132,x90131,x90133),x90134)),x90135),f331(f331(f6(x90131,x90132),x90133),f331(f310(x90131,x90131,x90134),x90135)))
% 162.26/162.09 [9116]~P38(x91161,x91162)+~P24(f331(f331(f333(x91161),x91163),x91164))+~P24(f331(f331(f333(x91161),x91165),x91164))+~P24(f331(f331(f333(f890(x91161,x91161)),f331(f331(f261(x91161,x91161),x91165),f795(x91162,x91161,x91164))),x91162))
% 162.26/162.09 [9163]~P21(x91632,x91633,x91635,x91631)+E(x91631,f196(f891(x91632,a877)))+E(f331(f310(x91633,x91632,f485(x91634,x91633,x91632,x91631)),x91634),x91631)+~P24(f331(f331(f247(f891(x91633,a877)),f331(f310(x91632,x91633,x91635),x91631)),x91634))
% 162.26/162.09 [9659]~P107(x96595)+~P27(x96595)+P24(f331(f331(f333(x96591),f359(x96592,x96593,x96591,x96594,x96595)),x96593))+~P24(f331(f331(f248(x96595),x96594),f331(f331(f42(x96591,x96595),x96593),x96592)))
% 162.26/162.09 [9664]~P107(x96641)+~P27(x96641)+P24(f331(f331(f248(x96641),x96642),f331(x96643,f359(x96643,x96644,x96645,x96642,x96641))))+~P24(f331(f331(f248(x96641),x96642),f331(f331(f42(x96645,x96641),x96644),x96643)))
% 162.26/162.09 [9747]~P71(x97471)+~P24(f331(f67(x97471,x97471,f82(x97471),x97472,x97473),x97475))+P24(f331(f331(f333(x97471),x97472),x97473))+P24(f331(f67(x97471,x97471,f82(x97471),x97474,f331(f331(f309(x97471),x97472),x97473)),f331(f331(f82(x97471),x97474),x97475)))
% 162.26/162.09 [9953]~P73(x99532)+~P24(f331(f62(x99531),x99535))+E(f331(f331(f9(x99531,x99532),f331(f331(f7(x99531,x99532,x99532),f331(f331(f18(x99531,x99532,f891(x99532,x99532)),f331(f331(f8(a877,f891(x99532,f891(x99532,x99532)),x99531),f102(x99532)),f331(a328,x99533))),x99534)),f79(x99532))),x99535),f79(x99532))+P24(f331(f331(f333(x99531),x99533),x99535))
% 162.26/162.09 [9954]~P74(x99542)+~P24(f331(f62(x99541),x99545))+E(f331(f331(f6(x99541,x99542),f331(f331(f7(x99541,x99542,x99542),f331(f331(f18(x99541,x99542,f891(x99542,x99542)),f331(f331(f8(a877,f891(x99542,f891(x99542,x99542)),x99541),f102(x99542)),f331(a328,x99543))),x99544)),f2(x99542))),x99545),f2(x99542))+P24(f331(f331(f333(x99541),x99543),x99545))
% 162.26/162.09 [9955]~P73(x99552)+~P24(f331(f62(x99551),x99555))+E(f331(f331(f9(x99551,x99552),f331(f331(f7(x99551,x99552,x99552),f331(f331(f18(x99551,x99552,f891(x99552,x99552)),f331(f331(f8(a877,f891(x99552,f891(x99552,x99552)),x99551),f102(x99552)),f331(a328,x99553))),x99554)),f79(x99552))),x99555),f331(x99554,x99553))+~P24(f331(f331(f333(x99551),x99553),x99555))
% 162.26/162.09 [9956]~P74(x99562)+~P24(f331(f62(x99561),x99565))+E(f331(f331(f6(x99561,x99562),f331(f331(f7(x99561,x99562,x99562),f331(f331(f18(x99561,x99562,f891(x99562,x99562)),f331(f331(f8(a877,f891(x99562,f891(x99562,x99562)),x99561),f102(x99562)),f331(a328,x99563))),x99564)),f2(x99562))),x99565),f331(x99564,x99563))+~P24(f331(f331(f333(x99561),x99563),x99565))
% 162.26/162.09 [10009]~P73(x100092)+~P24(f331(f62(x100091),x100095))+E(f331(f331(f9(x100091,x100092),f331(f331(f7(x100091,x100092,x100092),f331(f331(f18(x100091,x100092,f891(x100092,x100092)),f331(f331(f8(a877,f891(x100092,f891(x100092,x100092)),x100091),f102(x100092)),f331(f331(f7(x100091,x100091,a877),a328),x100093))),x100094)),f79(x100092))),x100095),f79(x100092))+P24(f331(f331(f333(x100091),x100093),x100095))
% 162.26/162.09 [10010]~P74(x100102)+~P24(f331(f62(x100101),x100105))+E(f331(f331(f6(x100101,x100102),f331(f331(f7(x100101,x100102,x100102),f331(f331(f18(x100101,x100102,f891(x100102,x100102)),f331(f331(f8(a877,f891(x100102,f891(x100102,x100102)),x100101),f102(x100102)),f331(f331(f7(x100101,x100101,a877),a328),x100103))),x100104)),f2(x100102))),x100105),f2(x100102))+P24(f331(f331(f333(x100101),x100103),x100105))
% 162.26/162.09 [10012]~P73(x100122)+~P24(f331(f62(x100121),x100125))+E(f331(f331(f9(x100121,x100122),f331(f331(f7(x100121,x100122,x100122),f331(f331(f18(x100121,x100122,f891(x100122,x100122)),f331(f331(f8(a877,f891(x100122,f891(x100122,x100122)),x100121),f102(x100122)),f331(f331(f7(x100121,x100121,a877),a328),x100123))),x100124)),f79(x100122))),x100125),f331(x100124,x100123))+~P24(f331(f331(f333(x100121),x100123),x100125))
% 162.26/162.09 [10013]~P74(x100132)+~P24(f331(f62(x100131),x100135))+E(f331(f331(f6(x100131,x100132),f331(f331(f7(x100131,x100132,x100132),f331(f331(f18(x100131,x100132,f891(x100132,x100132)),f331(f331(f8(a877,f891(x100132,f891(x100132,x100132)),x100131),f102(x100132)),f331(f331(f7(x100131,x100131,a877),a328),x100133))),x100134)),f2(x100132))),x100135),f331(x100134,x100133))+~P24(f331(f331(f333(x100131),x100133),x100135))
% 162.26/162.09 [7797]~P70(x77972)+~P24(f331(f62(x77971),x77974))+E(f331(f331(f6(x77971,x77972),x77973),f331(f331(f22(f891(x77971,a877)),x77974),f331(f331(f309(x77971),x77975),f196(f891(x77971,a877))))),f331(f331(f6(x77971,x77972),x77973),x77974))+P24(f331(f331(f333(x77971),x77975),x77974))
% 162.26/162.09 [8299]~P125(x82992)+~P24(f331(f62(x82991),x82994))+E(f331(f331(f6(x82991,x82992),x82993),f331(f331(f22(f891(x82991,a877)),x82994),f331(f331(f309(x82991),x82995),f196(f891(x82991,a877))))),f331(f331(f22(x82992),f331(f331(f6(x82991,x82992),x82993),x82994)),f331(x82993,x82995)))+~P24(f331(f331(f333(x82991),x82995),x82994))
% 162.26/162.09 [8300]~P70(x83002)+~P24(f331(f62(x83001),x83004))+E(f331(f331(f6(x83001,x83002),x83003),f331(f331(f22(f891(x83001,a877)),x83004),f331(f331(f309(x83001),x83005),f196(f891(x83001,a877))))),f331(f331(f22(x83002),f331(f331(f6(x83001,x83002),x83003),x83004)),f331(x83003,x83005)))+~P24(f331(f331(f333(x83001),x83005),x83004))
% 162.26/162.09 [8328]~P70(x83281)+~P24(f331(f62(x83282),x83284))+E(f331(f331(f22(x83281),f331(f331(f6(x83282,x83281),x83283),x83284)),f331(f331(f6(x83282,x83281),x83283),x83285)),f331(f331(f6(x83282,x83281),x83283),f331(f331(f22(f891(x83282,a877)),x83284),x83285)))+~P24(f331(f331(f247(f891(x83282,a877)),x83285),x83284))
% 162.26/162.09 [8348]P24(f331(f62(x83481),f331(x83482,x83483)))+~P24(f331(f62(x83484),x83485))+~P24(f331(f331(f333(x83484),x83483),x83485))+~P24(f331(f62(x83481),f331(f331(f42(x83484,f891(x83481,a877)),x83485),x83482)))
% 162.26/162.09 [8780]~P6(x87801,x87805,x87804)+~E(f331(f285(x87801,x87801,x87804),f331(f331(f309(x87801),x87802),f196(f891(x87801,a877)))),f331(f285(x87801,x87801,x87804),f331(f331(f309(x87801),x87803),f196(f891(x87801,a877)))))+~P24(f331(f331(f333(x87801),x87803),x87805))+P24(f331(f331(f333(f890(x87801,x87801)),f331(f331(f261(x87801,x87801),x87802),x87803)),x87804))
% 162.26/162.09 [9071]~P24(f331(x90711,x90715))+P24(f331(x90711,f843(x90711,x90712,x90713,x90714)))+P24(f331(x90711,f840(x90711,x90712,x90713,x90714)))+~P24(f331(f331(f333(x90714),x90715),f331(f331(f107(f891(x90714,a877)),x90713),x90712)))
% 162.26/162.09 [9265]~P24(f331(x92651,x92655))+P24(f331(x92651,f840(x92651,x92652,x92653,x92654)))+P24(f331(f331(f333(x92654),f843(x92651,x92652,x92653,x92654)),x92652))+~P24(f331(f331(f333(x92654),x92655),f331(f331(f107(f891(x92654,a877)),x92653),x92652)))
% 162.26/162.09 [9266]~P24(f331(x92661,x92665))+P24(f331(x92661,f843(x92661,x92662,x92663,x92664)))+P24(f331(f331(f333(x92664),f840(x92661,x92662,x92663,x92664)),x92663))+~P24(f331(f331(f333(x92664),x92665),f331(f331(f107(f891(x92664,a877)),x92663),x92662)))
% 162.26/162.09 [9274]P24(f331(x92741,x92742))+~P24(f331(x92741,f842(x92741,x92743,x92744,x92745)))+~P24(f331(x92741,f841(x92741,x92743,x92744,x92745)))+~P24(f331(f331(f333(x92745),x92742),f331(f331(f107(f891(x92745,a877)),x92744),x92743)))
% 162.26/162.09 [9317]E(x93171,x93172)+~P24(f331(f331(f333(f890(x93173,x93173)),f331(f331(f261(x93173,x93173),x93171),x93172)),f307(x93173,x93175)))+P24(f331(f331(f333(x93173),x93171),x93174))+~P24(f331(f331(f247(f891(f890(x93173,x93173),a877)),x93175),f331(f331(f268(x93173,x93173),x93174),f331(f16(f891(x93173,a877),x93173),x93174))))
% 162.26/162.09 [9336]P24(f331(x93361,x93362))+~P24(f331(x93361,f841(x93361,x93364,x93365,x93363)))+P24(f331(f331(f333(x93363),f842(x93361,x93364,x93365,x93363)),x93364))+~P24(f331(f331(f333(x93363),x93362),f331(f331(f107(f891(x93363,a877)),x93365),x93364)))
% 162.26/162.09 [9337]P24(f331(x93371,x93372))+~P24(f331(x93371,f842(x93371,x93374,x93375,x93373)))+P24(f331(f331(f333(x93373),f841(x93371,x93374,x93375,x93373)),x93375))+~P24(f331(f331(f333(x93373),x93372),f331(f331(f107(f891(x93373,a877)),x93375),x93374)))
% 162.26/162.09 [9396]P24(f331(x93961,x93962))+P24(f331(f331(f333(x93963),f842(x93961,x93964,x93965,x93963)),x93964))+P24(f331(f331(f333(x93963),f841(x93961,x93964,x93965,x93963)),x93965))+~P24(f331(f331(f333(x93963),x93962),f331(f331(f107(f891(x93963,a877)),x93965),x93964)))
% 162.26/162.09 [9397]~P24(f331(x93972,x93975))+P24(f331(f331(f333(x93971),f843(x93972,x93973,x93974,x93971)),x93973))+P24(f331(f331(f333(x93971),f840(x93972,x93973,x93974,x93971)),x93974))+~P24(f331(f331(f333(x93971),x93975),f331(f331(f107(f891(x93971,a877)),x93974),x93973)))
% 162.26/162.09 [9557]~P6(x95571,x95575,x95574)+~P24(f331(f331(f333(x95571),x95573),x95575))+P24(f331(f331(f333(f890(x95571,x95571)),f331(f331(f261(x95571,x95571),x95572),x95573)),x95574))+~P24(f331(f331(f247(f891(x95571,a877)),f331(f285(x95571,x95571,x95574),f331(f331(f309(x95571),x95573),f196(f891(x95571,a877))))),f331(f285(x95571,x95571,x95574),f331(f331(f309(x95571),x95572),f196(f891(x95571,a877))))))
% 162.26/162.09 [9690]~P107(x96905)+~P27(x96905)+P24(f331(f331(f333(x96901),f511(x96902,x96903,x96904,x96901,x96905)),x96904))+~P24(f331(f331(f248(x96905),f331(f331(f43(x96901,x96905),x96904),x96903)),x96902))
% 162.26/162.09 [9722]~P82(x97225)+~P80(x97225)+P24(f331(f331(f333(x97221),f638(x97222,x97223,x97224,x97221,x97225)),f331(f175(x97221),x97224)))+P24(f331(f331(f247(x97225),f331(f169(x97225),f331(f331(f157(x97221,x97225),x97223),x97224))),f331(f169(x97225),f331(f331(f157(x97221,x97225),x97222),x97224))))
% 162.26/162.09 [9853]~P107(x98531)+~P27(x98531)+P24(f331(f331(f248(x98531),f331(x98532,f511(x98533,x98532,x98534,x98535,x98531))),x98533))+~P24(f331(f331(f248(x98531),f331(f331(f43(x98535,x98531),x98534),x98532)),x98533))
% 162.26/162.09 [9970]~P82(x99701)+~P80(x99701)+~P24(f331(f331(f247(x99701),f331(x99703,f638(x99705,x99703,x99704,x99702,x99701))),f331(x99705,f638(x99705,x99703,x99704,x99702,x99701))))+P24(f331(f331(f247(x99701),f331(f169(x99701),f331(f331(f157(x99702,x99701),x99703),x99704))),f331(f169(x99701),f331(f331(f157(x99702,x99701),x99705),x99704))))
% 162.26/162.09 [8639]~P73(x86391)+~P24(f331(f62(x86394),x86395))+~P24(f331(f331(f333(x86394),x86393),x86395))+E(f331(f331(f82(x86391),f331(x86392,x86393)),f331(f331(f9(x86394,x86391),x86392),f331(f331(f22(f891(x86394,a877)),x86395),f331(f331(f309(x86394),x86393),f196(f891(x86394,a877)))))),f331(f331(f9(x86394,x86391),x86392),x86395))
% 162.26/162.09 [8641]~P74(x86411)+~P24(f331(f62(x86414),x86415))+~P24(f331(f331(f333(x86414),x86413),x86415))+E(f331(f331(f81(x86411),f331(x86412,x86413)),f331(f331(f6(x86414,x86411),x86412),f331(f331(f22(f891(x86414,a877)),x86415),f331(f331(f309(x86414),x86413),f196(f891(x86414,a877)))))),f331(f331(f6(x86414,x86411),x86412),x86415))
% 162.26/162.09 [8687]~P14(x86871,x86874,x86875)+~P24(f331(f62(x86871),x86872))+E(f331(f331(f22(f891(x86871,a877)),x86872),f331(f331(f309(x86871),x86873),f196(f891(x86871,a877)))),f196(f891(x86871,a877)))+E(f331(f331(x86874,x86873),f331(x86875,f331(f331(f22(f891(x86871,a877)),x86872),f331(f331(f309(x86871),x86873),f196(f891(x86871,a877)))))),f331(x86875,f331(f331(f309(x86871),x86873),x86872)))
% 162.26/162.09 [9051]~P74(x90511)+~P24(f331(f62(x90512),x90515))+~P24(f331(f62(x90512),x90514))+E(f331(f331(f81(x90511),f331(f331(f6(x90512,x90511),x90513),f331(f331(f107(f891(x90512,a877)),x90514),x90515))),f331(f331(f6(x90512,x90511),x90513),f331(f331(f108(f891(x90512,a877)),x90514),x90515))),f331(f331(f81(x90511),f331(f331(f6(x90512,x90511),x90513),x90514)),f331(f331(f6(x90512,x90511),x90513),x90515)))
% 162.26/162.09 [9053]~P73(x90531)+~P24(f331(f62(x90532),x90535))+~P24(f331(f62(x90532),x90534))+E(f331(f331(f82(x90531),f331(f331(f9(x90532,x90531),x90533),f331(f331(f107(f891(x90532,a877)),x90534),x90535))),f331(f331(f9(x90532,x90531),x90533),f331(f331(f108(f891(x90532,a877)),x90534),x90535))),f331(f331(f82(x90531),f331(f331(f9(x90532,x90531),x90533),x90534)),f331(f331(f9(x90532,x90531),x90533),x90535)))
% 162.26/162.09 [9203]~P70(x92031)+~P24(f331(f62(x92032),x92035))+~P24(f331(f62(x92032),x92034))+E(f331(f331(f22(x92031),f331(f331(f81(x92031),f331(f331(f6(x92032,x92031),x92033),x92034)),f331(f331(f6(x92032,x92031),x92033),x92035))),f331(f331(f6(x92032,x92031),x92033),f331(f331(f108(f891(x92032,a877)),x92034),x92035))),f331(f331(f6(x92032,x92031),x92033),f331(f331(f107(f891(x92032,a877)),x92034),x92035)))
% 162.26/162.09 [9406]~P21(x94061,x94062,x94063,x94065)+~P21(x94061,x94062,x94063,x94064)+P21(x94061,x94062,x94063,f331(f331(f107(f891(x94061,a877)),x94064),x94065))+~E(f331(f331(f108(f891(x94062,a877)),f331(f310(x94061,x94062,x94063),f331(f331(f22(f891(x94061,a877)),x94064),x94065))),f331(f310(x94061,x94062,x94063),f331(f331(f22(f891(x94061,a877)),x94065),x94064))),f196(f891(x94062,a877)))
% 162.26/162.09 [9532]E(x95321,f2(a1))+~P24(f331(f331(f248(a1),f2(a1)),x95323))+~P24(f331(f49(x95322,x95321),f331(f331(f261(a1,a1),x95324),x95325)))+P24(f331(f49(x95322,f331(f331(f82(a1),x95321),x95323)),f331(f331(f261(a1,a1),f331(f331(f39(a1),x95324),x95323)),f331(f331(f81(a1),f331(f331(f82(a1),x95321),f45(a1,x95324,x95323))),x95325))))
% 162.26/162.09 [9540]~P24(f331(f331(f248(a883),f2(a883)),x95403))+~P24(f331(f331(f248(a883),f2(a883)),x95402))+~P24(f331(f48(x95401,x95402),f331(f331(f261(a883,a883),x95404),x95405)))+P24(f331(f48(x95401,f331(f331(f82(a883),x95402),x95403)),f331(f331(f261(a883,a883),f331(f331(f39(a883),x95404),x95403)),f331(f331(f81(a883),f331(f331(f82(a883),x95402),f45(a883,x95404,x95403))),x95405))))
% 162.26/162.09 [9595]~P73(x95951)+~P24(f331(f62(x95952),x95955))+~P24(f331(f62(x95952),x95954))+E(f331(f331(f82(x95951),f331(f331(f331(f66(x95951,x95952,f82(x95951)),x95953),f79(x95951)),f331(f331(f107(f891(x95952,a877)),x95954),x95955))),f331(f331(f331(f66(x95951,x95952,f82(x95951)),x95953),f79(x95951)),f331(f331(f108(f891(x95952,a877)),x95954),x95955))),f331(f331(f82(x95951),f331(f331(f331(f66(x95951,x95952,f82(x95951)),x95953),f79(x95951)),x95954)),f331(f331(f331(f66(x95951,x95952,f82(x95951)),x95953),f79(x95951)),x95955)))
% 162.26/162.09 [9597]~E(f331(f331(f176(x95971),x95975),x95972),f331(f331(f176(x95971),x95975),x95973))+P24(f331(f331(f333(f890(f884(x95971),f884(x95971))),f331(f331(f261(f884(x95971),f884(x95971)),x95972),x95973)),f150(x95971,x95974)))+~P24(f331(f331(f248(a883),x95975),f331(f331(f251(a883),f331(f197(f884(x95971)),x95972)),f331(f197(f884(x95971)),x95973))))+~P24(f331(f331(f333(f890(x95971,x95971)),f331(f331(f261(x95971,x95971),f331(f331(f168(x95971),x95972),x95975)),f331(f331(f168(x95971),x95973),x95975))),x95974))
% 162.26/162.09 [9710]~P82(x97105)+~P143(x97105)+P24(f331(f331(f333(x97101),f458(x97102,x97103,x97104,x97101,x97105)),x97104))+P24(f331(f331(f247(x97105),f331(f331(f6(x97101,x97105),x97103),x97104)),f331(f331(f82(x97105),f331(f106(x97105),f331(f38(x97101),x97104))),x97102)))
% 162.26/162.09 [9911]~P82(x99111)+~P143(x99111)+~P24(f331(f331(f247(x99111),f331(x99113,f458(x99115,x99113,x99114,x99112,x99111))),x99115))+P24(f331(f331(f247(x99111),f331(f331(f6(x99112,x99111),x99113),x99114)),f331(f331(f82(x99111),f331(f106(x99111),f331(f38(x99112),x99114))),x99115)))
% 162.26/162.09 [8661]E(f331(f331(f137(x86611),x86612),x86613),f331(f331(f137(x86611),x86614),x86615))+~E(f331(f331(f176(x86611),f331(f197(f884(x86611)),x86612)),x86614),x86612)+~E(f331(f331(f137(x86611),f331(f331(f141(x86611),f331(f197(f884(x86611)),x86612)),x86614)),x86615),x86613)+P24(f331(f331(f247(a883),f331(f197(f884(x86611)),x86614)),f331(f197(f884(x86611)),x86612)))
% 162.26/162.09 [8779]E(f331(f331(f137(x87791),x87792),x87793),f331(f331(f137(x87791),x87794),x87795))+~E(f331(f331(f176(x87791),f331(f197(f884(x87791)),x87792)),x87794),x87792)+~E(x87793,f331(f331(f137(x87791),f331(f331(f141(x87791),f331(f197(f884(x87791)),x87792)),x87794)),x87795))+~P24(f331(f331(f247(a883),f331(f197(f884(x87791)),x87792)),f331(f197(f884(x87791)),x87794)))
% 162.26/162.09 [10033]~P24(f331(x100335,x100334))+~P24(f331(f62(x100332),f331(f253(x100332),x100335)))+P24(f331(f62(x100331),f331(f253(x100331),f331(f331(f7(x100331,x100332,a877),x100333),x100334))))+~P24(f331(f62(x100331),f331(f253(x100331),f331(f331(f8(f891(x100332,a877),a877,x100331),f87(x100332)),f331(f331(f8(f891(x100332,a877),f891(x100332,a877),x100331),f331(f18(x100332,a877,a877),f331(f331(f8(a877,f891(a877,a877),x100332),a329),x100335))),x100333)))))
% 162.26/162.09 [8461]~P15(x84615,x84611,x84616,x84612)+E(f331(f74(x84611,x84611,x84611,f331(x84612,x84613)),f331(x84612,x84614)),f331(f74(x84611,x84611,x84611,f331(x84612,x84614)),f331(x84612,x84613)))+~P24(f331(f62(x84615),x84614))+~P24(f331(f62(x84615),x84613))
% 162.26/162.09 [7854]~P21(x78541,x78542,x78544,x78543)+~E(f331(x78544,x78546),x78545)+E(f331(f78(x78541,x78542,x78543,x78544),x78545),x78546)+~P24(f331(f331(f333(x78541),x78546),x78543))
% 162.26/162.09 [8043]~P16(x80436,x80431,x80434,x80432)+E(f331(f74(x80431,x80431,x80431,f331(x80432,x80433)),f331(x80434,x80435)),f331(x80432,x80433))+~P24(f331(f62(x80436),x80433))+~P24(f331(f331(f333(x80436),x80435),x80433))
% 162.26/162.09 [9251]~P15(x92513,x92511,x92516,x92512)+E(f331(f74(x92511,x92511,x92511,f331(x92512,f331(f331(f22(f891(x92513,a877)),x92514),f331(f331(f309(x92513),x92515),f196(f891(x92513,a877)))))),f331(x92516,x92515)),f331(x92512,x92514))+~P24(f331(f62(x92513),x92514))+~P24(f331(f331(f333(x92513),x92515),x92514))
% 162.26/162.09 [6949]~P59(x69491)+~E(f45(x69491,x69493,x69494),f45(x69491,x69496,x69494))+~E(f45(x69491,x69492,x69494),f45(x69491,x69495,x69494))+E(f45(x69491,f331(f331(f22(x69491),x69492),x69493),x69494),f45(x69491,f331(f331(f22(x69491),x69495),x69496),x69494))
% 162.26/162.09 [6950]~P58(x69501)+~E(f45(x69501,x69503,x69504),f45(x69501,x69506,x69504))+~E(f45(x69501,x69502,x69504),f45(x69501,x69505,x69504))+E(f45(x69501,f331(f331(f81(x69501),x69502),x69503),x69504),f45(x69501,f331(f331(f81(x69501),x69505),x69506),x69504))
% 162.26/162.09 [6951]~P58(x69511)+~E(f45(x69511,x69513,x69514),f45(x69511,x69516,x69514))+~E(f45(x69511,x69512,x69514),f45(x69511,x69515,x69514))+E(f45(x69511,f331(f331(f82(x69511),x69512),x69513),x69514),f45(x69511,f331(f331(f82(x69511),x69515),x69516),x69514))
% 162.26/162.09 [7746]~P12(x77461,x77462,x77463)+~P24(f331(f62(x77461),x77466))+E(f331(f331(f65(x77461,x77462,x77463),x77464),f331(f331(f309(x77461),x77465),x77466)),f331(f331(f65(x77461,x77462,x77463),f331(f331(x77463,x77465),x77464)),x77466))+P24(f331(f331(f333(x77461),x77465),x77466))
% 162.26/162.09 [7811]~P27(x78111)+P24(f331(f331(f247(x78111),x78112),f331(x78113,x78114)))+~P24(f331(f331(f333(x78115),x78114),x78116))+~P24(f331(f331(f247(x78111),x78112),f331(f331(f43(x78115,x78111),x78116),x78113)))
% 162.26/162.09 [7961]~P12(x79611,x79612,x79613)+~P24(f331(f62(x79611),x79616))+E(f331(f331(f65(x79611,x79612,x79613),x79614),f331(f331(f309(x79611),x79615),x79616)),f331(f331(x79613,x79615),f331(f331(f65(x79611,x79612,x79613),x79614),x79616)))+P24(f331(f331(f333(x79611),x79615),x79616))
% 162.26/162.09 [8062]~P107(x80623)+~P24(f331(x80622,x80625))+~P29(x80623,f331(f331(f157(x80621,x80623),x80624),x80626))+E(f331(f139(x80621,x80622),f331(f331(f151(x80621,x80623,x80624),x80625),x80626)),f331(f331(f151(x80621,x80623,x80624),x80625),f331(f139(x80621,x80622),x80626)))
% 162.26/162.09 [8086]E(x80861,x80862)+E(x80863,f2(a1))+~P24(f331(f49(x80864,x80863),f331(f331(f261(a1,a1),x80865),x80862)))+~P24(f331(f49(x80864,x80863),f331(f331(f261(a1,a1),x80866),x80861)))
% 162.26/162.09 [8087]E(x80871,x80872)+E(x80873,f2(a1))+~P24(f331(f49(x80874,x80873),f331(f331(f261(a1,a1),x80872),x80875)))+~P24(f331(f49(x80874,x80873),f331(f331(f261(a1,a1),x80871),x80876)))
% 162.26/162.09 [8108]~P15(x81082,x81085,x81086,x81081)+~P24(f331(f62(x81082),x81084))+E(f331(x81081,f331(f331(f309(x81082),x81083),x81084)),f331(f74(x81085,x81085,x81085,f331(x81081,x81084)),f331(x81086,x81083)))+P24(f331(f331(f333(x81082),x81083),x81084))
% 162.26/162.09 [8331]~P16(x83315,x83311,x83316,x83312)+E(f331(f74(x83311,x83311,x83311,f331(x83312,x83313)),f331(x83312,x83314)),f331(x83312,x83313))+~P24(f331(f62(x83315),x83313))+~P24(f331(f331(f247(f891(x83315,a877)),x83314),x83313))
% 162.26/162.09 [9450]~P21(x94501,x94502,x94504,x94503)+~P24(f331(f331(f333(x94502),x94505),f331(f310(x94501,x94502,x94504),x94503)))+P24(f331(f331(f333(x94501),f331(f78(x94501,x94502,x94503,x94504),x94505)),x94506))+~P24(f331(f331(f247(f891(x94501,a877)),x94503),x94506))
% 162.26/162.09 [9857]~P74(x98572)+~E(f610(x98571,x98573,x98575,x98576,x98574,x98572),f611(x98571,x98573,x98575,x98576,x98574,x98572))+~P24(f331(f62(x98574),x98576))+E(f331(f331(f6(x98571,x98572),x98573),f331(f310(x98574,x98571,x98575),x98576)),f331(f331(f6(x98574,x98572),f331(f74(x98571,x98572,x98574,x98573),x98575)),x98576))
% 162.26/162.09 [9893]~P74(x98936)+E(f331(x98931,f610(x98932,x98933,x98931,x98934,x98935,x98936)),f331(x98931,f611(x98932,x98933,x98931,x98934,x98935,x98936)))+E(f331(f331(f6(x98932,x98936),x98933),f331(f310(x98935,x98932,x98931),x98934)),f331(f331(f6(x98935,x98936),f331(f74(x98932,x98936,x98935,x98933),x98931)),x98934))+~P24(f331(f62(x98935),x98934))
% 162.26/162.09 [9929]~P74(x99292)+~E(f331(x99293,f331(x99295,f611(x99291,x99293,x99295,x99296,x99294,x99292))),f2(x99292))+~P24(f331(f62(x99294),x99296))+E(f331(f331(f6(x99291,x99292),x99293),f331(f310(x99294,x99291,x99295),x99296)),f331(f331(f6(x99294,x99292),f331(f74(x99291,x99292,x99294,x99293),x99295)),x99296))
% 162.26/162.09 [9977]~P74(x99772)+~P24(f331(f62(x99774),x99776))+E(f331(f331(f6(x99771,x99772),x99773),f331(f310(x99774,x99771,x99775),x99776)),f331(f331(f6(x99774,x99772),f331(f74(x99771,x99772,x99774,x99773),x99775)),x99776))+P24(f331(f331(f333(x99774),f611(x99771,x99773,x99775,x99776,x99774,x99772)),x99776))
% 162.26/162.09 [9978]~P74(x99782)+~P24(f331(f62(x99784),x99786))+E(f331(f331(f6(x99781,x99782),x99783),f331(f310(x99784,x99781,x99785),x99786)),f331(f331(f6(x99784,x99782),f331(f74(x99781,x99782,x99784,x99783),x99785)),x99786))+P24(f331(f331(f333(x99784),f610(x99781,x99783,x99785,x99786,x99784,x99782)),x99786))
% 162.26/162.09 [10094]~P73(x100941)+~P24(f331(f62(x100942),x100946))+E(f331(f331(f331(f66(x100941,x100942,f82(x100941)),f331(f331(f18(x100942,f891(x100943,a877),x100941),f331(f331(f7(x100942,x100941,f891(f891(x100943,a877),x100941)),f331(f331(f8(f891(x100943,x100941),f891(x100941,f891(f891(x100943,a877),x100941)),x100942),f66(x100941,x100943,f82(x100941))),x100944)),f79(x100941))),x100945)),f79(x100941)),x100946),f331(f331(f331(f66(x100941,f890(x100942,x100943),f82(x100941)),f331(f270(x100942,x100943,x100941),x100944)),f79(x100941)),f331(f331(f268(x100942,x100943),x100946),x100945)))+P24(f331(f331(f333(x100942),f548(x100944,x100945,x100943,x100946,x100942,x100941)),x100946))
% 162.26/162.09 [10112]~P73(x101121)+~P24(f331(f62(x101122),x101126))+E(f331(f331(f331(f66(x101121,x101122,f82(x101121)),f331(f331(f18(x101122,f891(x101123,a877),x101121),f331(f331(f7(x101122,x101121,f891(f891(x101123,a877),x101121)),f331(f331(f8(f891(x101123,x101121),f891(x101121,f891(f891(x101123,a877),x101121)),x101122),f66(x101121,x101123,f82(x101121))),x101124)),f79(x101121))),x101125)),f79(x101121)),x101126),f331(f331(f331(f66(x101121,f890(x101122,x101123),f82(x101121)),f331(f270(x101122,x101123,x101121),x101124)),f79(x101121)),f331(f331(f268(x101122,x101123),x101126),x101125)))+~P24(f331(f62(x101123),f331(x101125,f548(x101124,x101125,x101123,x101126,x101122,x101121))))
% 162.26/162.09 [8246]~P16(x82462,x82465,x82466,x82461)+~P24(f331(f62(x82462),x82464))+~P24(f331(f62(x82462),x82463))+E(f331(x82461,f331(f331(f107(f891(x82462,a877)),x82463),x82464)),f331(f74(x82465,x82465,x82465,f331(x82461,x82463)),f331(x82461,x82464)))
% 162.26/162.09 [8462]~P27(x84621)+P24(f331(f331(f247(x84621),f331(x84622,x84623)),x84624))+~P24(f331(f331(f333(x84625),x84623),x84626))+~P24(f331(f331(f247(x84621),f331(f331(f42(x84625,x84621),x84626),x84622)),x84624))
% 162.26/162.09 [8862]~P21(x88622,x88621,x88623,x88626)+E(f331(f331(f22(f891(x88621,a877)),f331(f310(x88622,x88621,x88623),x88624)),f331(f310(x88622,x88621,x88623),x88625)),f331(f310(x88622,x88621,x88623),f331(f331(f22(f891(x88622,a877)),x88624),x88625)))+~P24(f331(f331(f247(f891(x88622,a877)),x88625),x88626))+~P24(f331(f331(f247(f891(x88622,a877)),x88624),x88626))
% 162.26/162.09 [8863]~P21(x88632,x88631,x88633,x88636)+E(f331(f331(f108(f891(x88631,a877)),f331(f310(x88632,x88631,x88633),x88634)),f331(f310(x88632,x88631,x88633),x88635)),f331(f310(x88632,x88631,x88633),f331(f331(f108(f891(x88632,a877)),x88634),x88635)))+~P24(f331(f331(f247(f891(x88632,a877)),x88635),x88636))+~P24(f331(f331(f247(f891(x88632,a877)),x88634),x88636))
% 162.26/162.09 [8902]~P24(f331(x89021,x89023))+~P24(f331(f331(f331(f331(a205,x89022),x89023),x89024),x89026))+~P24(f331(f331(f331(f331(a205,f33(x89021,x89022)),x89026),x89024),x89025))+P24(f331(f331(f331(f331(a205,f33(x89021,x89022)),x89023),x89024),x89025))
% 162.26/162.09 [9118]E(x91181,x91182)+~P52(x91183,x91184,x91185)+~P24(f331(f331(f333(f890(x91183,x91184)),f331(f331(f261(x91183,x91184),x91186),x91182)),x91185))+~P24(f331(f331(f333(f890(x91183,x91184)),f331(f331(f261(x91183,x91184),x91186),x91181)),x91185))
% 162.26/162.09 [9925]~P71(x99251)+~E(f331(x99253,f751(x99254,x99256,x99253,x99255,x99252,x99251)),f331(x99256,f751(x99254,x99256,x99253,x99255,x99252,x99251)))+~P24(f331(f62(x99252),x99255))+E(f331(f331(f331(f66(x99251,x99252,f82(x99251)),x99253),x99254),x99255),f331(f331(f331(f66(x99251,x99252,f82(x99251)),x99256),x99254),x99255))
% 162.26/162.09 [9975]~P71(x99751)+~P24(f331(f62(x99752),x99755))+E(f331(f331(f331(f66(x99751,x99752,f82(x99751)),x99753),x99754),x99755),f331(f331(f331(f66(x99751,x99752,f82(x99751)),x99756),x99754),x99755))+P24(f331(f331(f333(x99752),f751(x99754,x99753,x99756,x99755,x99752,x99751)),x99755))
% 162.26/162.09 [8672]~P71(x86721)+~P24(f331(f62(x86722),x86726))+P24(f331(f331(f333(x86722),x86725),x86726))+E(f331(f331(f331(f66(x86721,x86722,f82(x86721)),x86723),x86724),f331(f331(f309(x86722),x86725),x86726)),f331(f331(f82(x86721),f331(x86723,x86725)),f331(f331(f331(f66(x86721,x86722,f82(x86721)),x86723),x86724),x86726)))
% 162.26/162.09 [8718]~P6(x87181,x87186,x87183)+~P9(x87181,f891(x87182,a877),x87183,x87185)+~P24(f331(f331(f333(x87181),x87184),x87186))+E(f331(f331(f42(x87181,f891(x87182,a877)),f331(f285(x87181,x87181,x87183),f331(f331(f309(x87181),x87184),f196(f891(x87181,a877))))),x87185),f331(x87185,x87184))
% 162.26/162.09 [8839]~P12(x88393,x88394,x88391)+~P24(f331(f62(x88393),x88396))+~P24(f331(f331(f333(x88393),x88392),x88396))+E(f331(f331(x88391,x88392),f331(f331(f65(x88393,x88394,x88391),x88395),f331(f331(f22(f891(x88393,a877)),x88396),f331(f331(f309(x88393),x88392),f196(f891(x88393,a877)))))),f331(f331(f65(x88393,x88394,x88391),x88395),x88396))
% 162.26/162.09 [9138]~P15(x91383,x91381,x91386,x91382)+~P24(f331(f62(x91383),x91385))+~P24(f331(f62(x91383),x91384))+E(f331(f74(x91381,x91381,x91381,f331(x91382,f331(f331(f107(f891(x91383,a877)),x91384),x91385))),f331(x91382,f331(f331(f108(f891(x91383,a877)),x91384),x91385))),f331(f74(x91381,x91381,x91381,f331(x91382,x91384)),f331(x91382,x91385)))
% 162.26/162.09 [9470]~E(x94703,f331(f331(f162(x94701,x94702),x94705),x94706))+P24(f331(f331(f333(f890(f884(x94701),f884(x94701))),f331(f331(f261(f884(x94701),f884(x94701)),x94702),x94703)),f160(x94701,x94704)))+~P24(f331(f331(f248(a883),x94705),f331(f197(f884(x94701)),x94702)))+~P24(f331(f331(f333(f890(x94701,x94701)),f331(f331(f261(x94701,x94701),f331(f331(f168(x94701),x94702),x94705)),x94706)),x94704))
% 162.26/162.09 [9987]~P73(x99872)+~P24(f331(f62(x99871),x99876))+P24(f331(f331(f333(x99871),f552(x99874,x99875,x99873,x99876,x99871,x99872)),x99876))+E(f331(f331(f9(x99871,x99872),f331(f331(f18(x99871,f891(x99873,a877),x99872),f331(f331(f8(f891(x99873,x99872),f891(f891(x99873,a877),x99872),x99871),f9(x99873,x99872)),x99874)),x99875)),x99876),f331(f331(f9(f890(x99871,x99873),x99872),f331(f270(x99871,x99873,x99872),x99874)),f331(f331(f268(x99871,x99873),x99876),x99875)))
% 162.26/162.09 [9988]~P74(x99882)+~P24(f331(f62(x99881),x99886))+P24(f331(f331(f333(x99881),f553(x99884,x99885,x99883,x99886,x99881,x99882)),x99886))+E(f331(f331(f6(x99881,x99882),f331(f331(f18(x99881,f891(x99883,a877),x99882),f331(f331(f8(f891(x99883,x99882),f891(f891(x99883,a877),x99882),x99881),f6(x99883,x99882)),x99884)),x99885)),x99886),f331(f331(f6(f890(x99881,x99883),x99882),f331(f270(x99881,x99883,x99882),x99884)),f331(f331(f268(x99881,x99883),x99886),x99885)))
% 162.26/162.09 [10030]~P73(x100302)+~P24(f331(f62(x100301),x100306))+~P24(f331(f62(x100303),f331(x100305,f552(x100304,x100305,x100303,x100306,x100301,x100302))))+E(f331(f331(f9(x100301,x100302),f331(f331(f18(x100301,f891(x100303,a877),x100302),f331(f331(f8(f891(x100303,x100302),f891(f891(x100303,a877),x100302),x100301),f9(x100303,x100302)),x100304)),x100305)),x100306),f331(f331(f9(f890(x100301,x100303),x100302),f331(f270(x100301,x100303,x100302),x100304)),f331(f331(f268(x100301,x100303),x100306),x100305)))
% 162.26/162.09 [10031]~P74(x100312)+~P24(f331(f62(x100311),x100316))+~P24(f331(f62(x100313),f331(x100315,f553(x100314,x100315,x100313,x100316,x100311,x100312))))+E(f331(f331(f6(x100311,x100312),f331(f331(f18(x100311,f891(x100313,a877),x100312),f331(f331(f8(f891(x100313,x100312),f891(f891(x100313,a877),x100312),x100311),f6(x100313,x100312)),x100314)),x100315)),x100316),f331(f331(f6(f890(x100311,x100313),x100312),f331(f270(x100311,x100313,x100312),x100314)),f331(f331(f268(x100311,x100313),x100316),x100315)))
% 162.26/162.09 [10011]~P73(x100112)+~P24(f331(f62(x100111),x100116))+P24(f331(f331(f333(x100111),x100113),x100116))+E(f331(f331(f9(x100111,x100112),f331(f331(f7(x100111,x100112,x100112),f331(f331(f18(x100111,x100112,f891(x100112,x100112)),f331(f331(f8(a877,f891(x100112,f891(x100112,x100112)),x100111),f102(x100112)),f331(f331(f7(x100111,x100111,a877),a328),x100113))),x100114)),x100115)),x100116),f331(f331(f262(x100112),x100115),f331(f38(x100111),x100116)))
% 162.26/162.09 [10016]~P73(x100162)+~P24(f331(f62(x100161),x100166))+~P24(f331(f331(f333(x100161),x100163),x100166))+E(f331(f331(f9(x100161,x100162),f331(f331(f7(x100161,x100162,x100162),f331(f331(f18(x100161,x100162,f891(x100162,x100162)),f331(f331(f8(a877,f891(x100162,f891(x100162,x100162)),x100161),f102(x100162)),f331(f331(f7(x100161,x100161,a877),a328),x100163))),x100164)),x100165)),x100166),f331(f331(f82(x100162),f331(x100164,x100163)),f331(f331(f262(x100162),x100165),f331(f331(f22(a883),f331(f38(x100161),x100166)),f79(a883)))))
% 162.26/162.09 [10087]~P24(f331(f62(x100871),x100875))+~P24(f331(f62(x100872),x100873))+P24(f331(f331(f333(x100872),f572(x100876,x100874,x100873,x100872,x100875,x100871)),x100873))+E(f331(f331(f6(x100871,a883),f331(f331(f8(f891(x100872,a877),a883,x100871),f38(x100872)),f331(f331(f8(f891(x100872,a877),f891(x100872,a877),x100871),f253(x100872)),f331(f331(f8(f891(x100872,a877),f891(x100872,a877),x100871),f331(f18(x100872,a877,a877),f331(f331(f8(a877,f891(a877,a877),x100872),a329),f331(f331(f7(x100872,f891(x100872,a877),a877),f333(x100872)),x100873)))),x100874)))),x100875),f331(f331(f82(a883),x100876),f331(f38(x100872),x100873)))
% 162.26/162.09 [10088]~P24(f331(f62(x100881),x100885))+~P24(f331(f62(x100882),x100883))+P24(f331(f331(f333(x100882),f573(x100886,x100884,x100883,x100882,x100885,x100881)),x100883))+E(f331(f331(f6(x100881,a883),f331(f331(f8(f891(x100882,a877),a883,x100881),f38(x100882)),f331(f331(f8(f891(x100882,a877),f891(x100882,a877),x100881),f253(x100882)),f331(f331(f8(f891(x100882,a877),f891(x100882,a877),x100881),f331(f18(x100882,a877,a877),f331(f331(f8(a877,f891(a877,a877),x100882),a329),f331(f331(f7(x100882,f891(x100882,a877),a877),f333(x100882)),x100883)))),x100884)))),x100885),f331(f331(f6(x100882,a883),x100886),x100883))
% 162.26/162.09 [10123]~P24(f331(f62(x101232),x101233))+~P24(f331(f62(x101231),x101235))+~E(f331(f38(x101231),f331(f253(x101231),f331(f331(f18(x101231,a877,a877),f331(f331(f8(a877,f891(a877,a877),x101231),a329),f331(f331(f7(x101231,f891(x101231,a877),a877),f333(x101231)),x101235))),f331(f331(f7(x101231,x101232,a877),x101234),f572(x101236,x101234,x101233,x101232,x101235,x101231))))),x101236)+E(f331(f331(f6(x101231,a883),f331(f331(f8(f891(x101232,a877),a883,x101231),f38(x101232)),f331(f331(f8(f891(x101232,a877),f891(x101232,a877),x101231),f253(x101232)),f331(f331(f8(f891(x101232,a877),f891(x101232,a877),x101231),f331(f18(x101232,a877,a877),f331(f331(f8(a877,f891(a877,a877),x101232),a329),f331(f331(f7(x101232,f891(x101232,a877),a877),f333(x101232)),x101233)))),x101234)))),x101235),f331(f331(f82(a883),x101236),f331(f38(x101232),x101233)))
% 162.26/162.09 [10142]~P24(f331(f62(x101422),x101423))+~P24(f331(f62(x101421),x101425))+~E(f331(f38(x101421),f331(f253(x101421),f331(f331(f18(x101421,a877,a877),f331(f331(f8(a877,f891(a877,a877),x101421),a329),f331(f331(f7(x101421,f891(x101421,a877),a877),f333(x101421)),x101425))),f331(f331(f7(x101421,x101422,a877),x101424),f573(x101426,x101424,x101423,x101422,x101425,x101421))))),f331(x101426,f573(x101426,x101424,x101423,x101422,x101425,x101421)))+E(f331(f331(f6(x101421,a883),f331(f331(f8(f891(x101422,a877),a883,x101421),f38(x101422)),f331(f331(f8(f891(x101422,a877),f891(x101422,a877),x101421),f253(x101422)),f331(f331(f8(f891(x101422,a877),f891(x101422,a877),x101421),f331(f18(x101422,a877,a877),f331(f331(f8(a877,f891(a877,a877),x101422),a329),f331(f331(f7(x101422,f891(x101422,a877),a877),f333(x101422)),x101423)))),x101424)))),x101425),f331(f331(f6(x101422,a883),x101426),x101423))
% 162.26/162.09 [9792]E(x97921,x97922)+~P12(x97923,x97924,x97925)+~P24(f331(f67(x97923,x97924,x97925,x97926,x97927),x97922))+~P24(f331(f67(x97923,x97924,x97925,x97926,x97927),x97921))
% 162.26/162.09 [9560]P24(f331(x95601,x95602))+~P24(f331(f331(f333(x95607),x95602),f331(x95606,x95604)))+~P24(f331(x95601,f351(x95601,x95606,x95605,x95603,x95607)))+~P24(f331(f331(f333(x95603),x95604),x95605))
% 162.26/162.09 [10003]~P12(x100037,x100036,x100031)+E(f331(f331(x100031,x100032),f849(x100032,x100033,x100034,x100035,x100031,x100036,x100037)),x100033)+~P24(f331(f67(x100037,x100036,x100031,x100035,x100034),x100033))+~P24(f331(f331(f333(x100037),x100032),x100034))
% 162.26/162.09 [10062]~P12(x100621,x100622,x100623)+~P24(f331(f67(x100621,x100622,x100623,x100624,x100625),x100627))+P24(f331(f67(x100621,x100622,x100623,x100624,f331(f331(f22(f891(x100621,a877)),x100625),f331(f331(f309(x100621),x100626),f196(f891(x100621,a877))))),f849(x100626,x100627,x100625,x100624,x100623,x100622,x100621)))+~P24(f331(f331(f333(x100621),x100626),x100625))
% 162.26/162.09 [9446]~P71(x94461)+~P21(x94465,x94462,x94466,x94467)+~P24(f331(f62(x94465),x94467))+E(f331(f331(f331(f66(x94461,x94462,f82(x94461)),x94463),x94464),f331(f310(x94465,x94462,x94466),x94467)),f331(f331(f331(f66(x94461,x94465,f82(x94461)),f331(f74(x94462,x94461,x94465,x94463),x94466)),x94464),x94467))
% 162.26/162.09 [9582]~E(f331(f331(f309(x95821),x95825),x95826),f331(f331(f309(x95821),x95822),x95823))+~P24(f331(f67(x95821,x95821,x95824,x95822,x95823),x95827))+P24(f331(f331(f333(x95821),x95822),x95823))+P24(f331(f63(x95821,x95824,f331(f331(f309(x95821),x95825),x95826)),x95827))
% 162.26/162.09 [9676]P24(f331(x96761,x96762))+~P24(f331(f331(f333(x96763),x96762),f331(x96764,x96767)))+~P24(f331(f331(f333(x96766),x96767),x96765))+P24(f331(f331(f333(x96763),f351(x96761,x96764,x96765,x96766,x96763)),f331(f331(f42(x96766,f891(x96763,a877)),x96765),x96764)))
% 162.26/162.09 [9691]~P21(x96912,x96911,x96915,x96914)+~P21(x96911,x96913,x96916,f331(f310(x96912,x96911,x96915),x96914))+E(f331(f331(f74(x96911,x96912,x96913,f78(x96912,x96911,x96914,x96915)),f78(x96911,x96913,f331(f310(x96912,x96911,x96915),x96914),x96916)),x96917),f331(f78(x96912,x96913,x96914,f331(f74(x96911,x96913,x96912,x96916),x96915)),x96917))+~P24(f331(f331(f333(x96913),x96917),f331(f310(x96911,x96913,x96916),f331(f310(x96912,x96911,x96915),x96914))))
% 162.26/162.09 [10004]~P12(x100047,x100046,x100041)+E(f331(f331(x100041,x100042),f562(x100043,x100044,x100042,x100045,x100041,x100046,x100047)),x100043)+P24(f331(f331(f333(x100047),x100042),x100044))+~P24(f331(f67(x100047,x100046,x100041,x100045,f331(f331(f309(x100047),x100042),x100044)),x100043))
% 162.26/162.09 [10061]~P12(x100611,x100614,x100615)+P24(f331(f67(x100611,x100614,x100615,x100616,x100613),f562(x100617,x100613,x100612,x100616,x100615,x100614,x100611)))+P24(f331(f331(f333(x100611),x100612),x100613))+~P24(f331(f67(x100611,x100614,x100615,x100616,f331(f331(f309(x100611),x100612),x100613)),x100617))
% 162.26/162.09 [9771]E(x97711,f2(a1))+~P24(f331(f49(x97713,x97711),f331(f331(f261(a1,a1),x97715),x97717)))+~P24(f331(f49(x97712,x97711),f331(f331(f261(a1,a1),x97714),x97716)))+P24(f331(f49(f331(f331(f81(a1),x97712),x97713),x97711),f331(f331(f261(a1,a1),f331(f331(f81(a1),f331(f331(f81(a1),x97714),x97715)),f331(f331(f39(a1),f331(f331(f81(a1),x97716),x97717)),x97711))),f45(a1,f331(f331(f81(a1),x97716),x97717),x97711))))
% 162.26/162.09 [9773]~P24(f331(f331(f248(a883),f2(a883)),x97733))+~P24(f331(f48(x97732,x97733),f331(f331(f261(a883,a883),x97735),x97737)))+~P24(f331(f48(x97731,x97733),f331(f331(f261(a883,a883),x97734),x97736)))+P24(f331(f48(f331(f331(f81(a883),x97731),x97732),x97733),f331(f331(f261(a883,a883),f331(f331(f81(a883),f331(f331(f81(a883),x97734),x97735)),f331(f331(f39(a883),f331(f331(f81(a883),x97736),x97737)),x97733))),f45(a883,f331(f331(f81(a883),x97736),x97737),x97733))))
% 162.26/162.09 [10122]~P74(x101222)+~P24(f331(f62(x101223),x101225))+~P24(f331(f62(x101221),x101227))+E(f331(f331(f6(x101221,x101222),f331(f331(f18(x101221,f891(x101223,a877),x101222),f331(f331(f8(f891(x101223,x101222),f891(f891(x101223,a877),x101222),x101221),f6(x101223,x101222)),x101224)),f331(f331(f8(f891(x101223,a877),f891(x101223,a877),x101221),f253(x101223)),f331(f331(f8(f891(x101223,a877),f891(x101223,a877),x101221),f331(f18(x101223,a877,a877),f331(f331(f8(a877,f891(a877,a877),x101223),a329),f331(f331(f7(x101223,f891(x101223,a877),a877),f333(x101223)),x101225)))),x101226)))),x101227),f331(f331(f6(x101223,x101222),f331(f331(f18(x101223,f891(x101221,a877),x101222),f331(f331(f8(f891(x101221,x101222),f891(f891(x101221,a877),x101222),x101223),f6(x101221,x101222)),f331(f7(x101221,x101223,x101222),x101224))),f331(f331(f8(f891(x101221,a877),f891(x101221,a877),x101223),f253(x101221)),f331(f331(f8(f891(x101221,a877),f891(x101221,a877),x101223),f331(f18(x101221,a877,a877),f331(f331(f8(a877,f891(a877,a877),x101221),a329),f331(f331(f7(x101221,f891(x101221,a877),a877),f333(x101221)),x101227)))),f331(f7(x101221,x101223,a877),x101226))))),x101225))
% 162.26/162.09 [9630]~P18(x96307,x96306,x96301,x96308,x96302,x96304)+E(f331(f331(x96301,f331(x96302,x96303)),f331(x96304,x96305)),f331(x96304,x96305))+~P24(f331(f62(x96306),x96305))+~P24(f331(f331(f333(x96306),x96303),x96305))
% 162.26/162.09 [9634]~P10(x96346,x96341,x96342,x96348,x96343,x96344)+~P6(x96346,x96347,x96348)+P9(x96341,x96342,x96343,f331(x96344,x96345))+~P24(f331(f331(f333(x96346),x96345),x96347))
% 162.26/162.09 [8063]~P30(x80638,x80637,f331(f331(f331(f93(x80638),x80634),x80636),x80631))+P24(f331(f331(x80631,x80632),x80633))+~P24(f331(f331(x80634,x80632),x80635))+~P24(f331(f331(f331(f331(a205,x80636),x80635),x80637),x80633))
% 162.26/162.09 [9233]~P15(x92337,x92331,x92338,x92333)+~P24(f331(f62(x92337),x92335))+~P24(f331(f62(x92337),x92334))+E(f331(f74(x92331,x92331,x92332,f331(x92333,x92334)),f331(f74(x92331,x92331,x92332,f331(x92333,x92335)),x92336)),f331(f74(x92331,x92331,x92332,f331(x92333,x92335)),f331(f74(x92331,x92331,x92332,f331(x92333,x92334)),x92336)))
% 162.26/162.09 [9241]~P35(x92411,x92412,x92413,x92414,x92417)+P35(x92411,x92412,x92413,f331(f331(f162(x92411,x92414),x92415),x92416),f331(f331(f162(x92412,x92417),x92415),x92418))+~P24(f331(f331(x92413,x92416),x92418))+~P24(f331(f331(f248(a883),x92415),f331(f197(f884(x92411)),x92414)))
% 162.26/162.09 [9242]~P35(x92421,x92422,x92423,x92424,x92427)+P35(x92421,x92422,x92423,f331(f331(f162(x92421,x92424),x92425),x92426),f331(f331(f162(x92422,x92427),x92425),x92428))+~P24(f331(f331(x92423,x92426),x92428))+~P24(f331(f331(f248(a883),x92425),f331(f197(f884(x92422)),x92427)))
% 162.26/162.09 [9324]~P21(x93242,x93242,x93245,x93246)+~P17(x93243,x93242,x93247,x93248,x93241)+~P24(f331(f62(x93242),x93246))+E(f331(f331(x93241,f331(f74(x93242,x93243,x93242,x93244),x93245)),x93246),f331(f331(x93241,x93244),f331(f310(x93242,x93242,x93245),x93246)))
% 162.26/162.09 [9632]~P19(x96327,x96322,x96325,x96328,x96326,x96321)+~P24(f331(f62(x96322),x96324))+E(f331(x96321,f331(f331(f309(x96322),x96323),x96324)),f331(f331(x96325,f331(x96326,x96323)),f331(x96321,x96324)))+P24(f331(f331(f333(x96322),x96323),x96324))
% 162.26/162.09 [9645]~P18(x96456,x96455,x96451,x96457,x96458,x96452)+E(f331(f331(x96451,f331(x96452,x96453)),f331(x96452,x96454)),f331(x96452,x96454))+~P24(f331(f62(x96455),x96454))+~P24(f331(f331(f247(f891(x96455,a877)),x96453),x96454))
% 162.26/162.09 [10118]P20(x101188,x101187,f331(f331(f309(f882(x101188)),f331(f331(f331(f93(x101188),x101184),x101185),x101183)),f196(f891(f882(x101188),a877))))+~P20(x101188,x101187,f331(f331(f309(f882(x101188)),f331(f331(f331(f93(x101188),x101186),x101185),x101181)),f196(f891(f882(x101188),a877))))+~P24(f331(f331(x101186,x101182),f439(x101183,x101184,x101181,x101185,x101186,x101187,x101188)))+P24(f331(f331(x101181,x101182),f446(x101183,x101184,x101181,x101185,x101186,x101187,x101188)))
% 162.26/162.09 [9218]P24(f331(f331(f333(f890(f884(x92181),f884(x92181))),f331(f331(f261(f884(x92181),f884(x92181)),x92182),x92183)),f160(x92181,x92184)))+~E(x92183,f331(f331(f137(x92181),x92185),f331(f331(f154(x92181),x92186),x92187)))+~E(x92182,f331(f331(f137(x92181),x92185),f331(f331(f154(x92181),x92188),x92187)))+~P24(f331(f331(f333(f890(x92181,x92181)),f331(f331(f261(x92181,x92181),x92188),x92186)),x92184))
% 162.26/162.09 [9641]~P18(x96416,x96412,x96415,x96417,x96418,x96411)+~P24(f331(f62(x96412),x96414))+~P24(f331(f62(x96412),x96413))+E(f331(x96411,f331(f331(f107(f891(x96412,a877)),x96413),x96414)),f331(f331(x96415,f331(x96411,x96413)),f331(x96411,x96414)))
% 162.26/162.09 [10192]~P21(x101924,x101922,x101925,x101928)+E(f331(f331(f43(x101921,f891(x101922,a877)),x101923),f331(f331(f8(f891(x101924,a877),f891(x101922,a877),x101921),f310(x101924,x101922,x101925)),x101926)),f331(f310(x101924,x101922,x101925),f331(f331(f43(x101921,f891(x101924,a877)),x101923),x101926)))+~P24(f331(f331(f333(x101921),x101927),x101923))+P24(f331(f331(f333(x101921),f516(x101927,x101926,x101923,x101921,x101928,x101925,x101922,x101924)),x101923))
% 162.26/162.09 [10222]~P21(x102224,x102222,x102225,x102227)+E(f331(f331(f43(x102221,f891(x102222,a877)),x102223),f331(f331(f8(f891(x102224,a877),f891(x102222,a877),x102221),f310(x102224,x102222,x102225)),x102226)),f331(f310(x102224,x102222,x102225),f331(f331(f43(x102221,f891(x102224,a877)),x102223),x102226)))+~P24(f331(f331(f333(x102221),x102228),x102223))+~P24(f331(f331(f247(f891(x102224,a877)),f331(x102226,f516(x102228,x102226,x102223,x102221,x102227,x102225,x102222,x102224))),x102227))
% 162.26/162.09 [9700]~P19(x97007,x97005,x97001,x97008,x97002,x97004)+~P24(f331(f62(x97005),x97006))+~P24(f331(f331(f333(x97005),x97003),x97006))+E(f331(f331(x97001,f331(x97002,x97003)),f331(x97004,f331(f331(f22(f891(x97005,a877)),x97006),f331(f331(f309(x97005),x97003),f196(f891(x97005,a877)))))),f331(x97004,x97006))
% 162.26/162.09 [9708]~P19(x97086,x97083,x97081,x97087,x97088,x97082)+~P24(f331(f62(x97083),x97085))+~P24(f331(f62(x97083),x97084))+E(f331(f331(x97081,f331(x97082,f331(f331(f107(f891(x97083,a877)),x97084),x97085))),f331(x97082,f331(f331(f108(f891(x97083,a877)),x97084),x97085))),f331(f331(x97081,f331(x97082,x97084)),f331(x97082,x97085)))
% 162.26/162.09 [9811]P42(x98111,x98112,x98113,x98114,x98115,f331(f331(x98113,x98116),x98117))+~P42(x98111,x98112,x98113,x98114,f331(f331(f22(f891(x98111,a877)),x98115),f331(f331(f309(x98111),x98118),f196(f891(x98111,a877)))),x98119)+~E(f331(f331(x98113,x98116),x98117),f331(f331(x98113,x98118),x98119))+~P24(f331(f331(f333(x98111),x98118),x98115))
% 162.26/162.09 [10237]P20(x102371,x102372,f331(f331(f309(f882(x102371)),f331(f331(f331(f93(x102371),f331(x102373,f850(x102374,x102375,x102376,x102377,x102373,x102372,x102371,x102378,x102379))),f331(x102377,f850(x102374,x102375,x102376,x102377,x102373,x102372,x102371,x102378,x102379))),f331(x102376,f850(x102374,x102375,x102376,x102377,x102373,x102372,x102371,x102378,x102379)))),f196(f891(f882(x102371),a877))))+~P24(f331(f62(x102379),x102378))+~P20(x102371,x102372,f331(f310(x102379,f882(x102371),f331(f331(f18(x102379,f891(x102371,f891(a878,a877)),f882(x102371)),f331(f331(f18(x102379,a879,f891(f891(x102371,f891(a878,a877)),f882(x102371))),f331(f331(f8(f891(x102371,f891(a878,a877)),f891(a879,f891(f891(x102371,f891(a878,a877)),f882(x102371))),x102379),f93(x102371)),x102373)),x102377)),x102376)),x102378))+P20(x102371,x102372,f331(f310(x102379,f882(x102371),f331(f331(f18(x102379,f891(x102371,f891(a878,a877)),f882(x102371)),f331(f331(f18(x102379,a879,f891(f891(x102371,f891(a878,a877)),f882(x102371))),f331(f331(f8(f891(x102371,f891(a878,a877)),f891(a879,f891(f891(x102371,f891(a878,a877)),f882(x102371))),x102379),f93(x102371)),x102375)),x102377)),x102374)),x102378))
% 162.26/162.09 [10238]~P20(x102381,x102382,f331(f331(f309(f882(x102381)),f331(f331(f331(f93(x102381),f331(x102384,f850(x102386,x102384,x102388,x102385,x102389,x102382,x102381,x102387,x102383))),f331(x102385,f850(x102386,x102384,x102388,x102385,x102389,x102382,x102381,x102387,x102383))),f331(x102386,f850(x102386,x102384,x102388,x102385,x102389,x102382,x102381,x102387,x102383)))),f196(f891(f882(x102381),a877))))+~P24(f331(f62(x102383),x102387))+~P20(x102381,x102382,f331(f310(x102383,f882(x102381),f331(f331(f18(x102383,f891(x102381,f891(a878,a877)),f882(x102381)),f331(f331(f18(x102383,a879,f891(f891(x102381,f891(a878,a877)),f882(x102381))),f331(f331(f8(f891(x102381,f891(a878,a877)),f891(a879,f891(f891(x102381,f891(a878,a877)),f882(x102381))),x102383),f93(x102381)),x102389)),x102385)),x102388)),x102387))+P20(x102381,x102382,f331(f310(x102383,f882(x102381),f331(f331(f18(x102383,f891(x102381,f891(a878,a877)),f882(x102381)),f331(f331(f18(x102383,a879,f891(f891(x102381,f891(a878,a877)),f882(x102381))),f331(f331(f8(f891(x102381,f891(a878,a877)),f891(a879,f891(f891(x102381,f891(a878,a877)),f882(x102381))),x102383),f93(x102381)),x102384)),x102385)),x102386)),x102387))
% 162.26/162.09 [9734]~P10(x97346,x97347,x97348,x97349,x973410,x97341)+E(f331(f331(x97341,x97342),x97343),f331(f331(x97341,x97344),x97345))+~P24(f331(f331(f333(f890(x97347,x97347)),f331(f331(f261(x97347,x97347),x97343),x97345)),x973410))+~P24(f331(f331(f333(f890(x97346,x97346)),f331(f331(f261(x97346,x97346),x97342),x97344)),x97349))
% 162.26/162.09 [9326]~P96(x93262)+E(x93261,f196(f891(x93262,a877)))+~P24(f331(f62(x93262),x93261))+P24(f331(f331(f333(x93262),f13(x93262,x93261)),x93261))+~P24(f331(f331(f333(x93262),f331(f331(f107(x93262),f848(x93261,x93262)),f851(x93261,x93262))),f331(f331(f309(x93262),f848(x93261,x93262)),f331(f331(f309(x93262),f851(x93261,x93262)),f196(f891(x93262,a877))))))
% 162.26/162.09 [9329]~P96(x93292)+E(x93291,f196(f891(x93292,a877)))+~P24(f331(f62(x93292),x93291))+P24(f331(f331(f333(x93292),f10(x93292,x93291)),x93291))+~P24(f331(f331(f333(x93292),f331(f331(f108(x93292),f474(x93291,x93292)),f480(x93291,x93292))),f331(f331(f309(x93292),f474(x93291,x93292)),f331(f331(f309(x93292),f480(x93291,x93292)),f196(f891(x93292,a877))))))
% 162.26/162.09 [9362]~P71(x93622)+E(x93621,f196(f891(x93622,a877)))+~P24(f331(f62(x93622),x93621))+P24(f331(f331(f333(x93622),f331(f64(x93622,f82(x93622)),x93621)),x93621))+~P24(f331(f331(f333(x93622),f331(f331(f82(x93622),f805(x93621,x93622)),f817(x93621,x93622))),f331(f331(f309(x93622),f805(x93621,x93622)),f331(f331(f309(x93622),f817(x93621,x93622)),f196(f891(x93622,a877))))))
% 162.26/162.09 [9368]~P107(x93682)+E(x93681,f196(f891(x93682,a877)))+~P24(f331(f62(x93682),x93681))+P24(f331(f331(f333(x93682),f11(x93682,f251(x93682),x93681)),x93681))+~P24(f331(f331(f333(x93682),f331(f331(f251(x93682),f863(x93681,x93682)),f864(x93681,x93682))),f331(f331(f309(x93682),f863(x93681,x93682)),f331(f331(f309(x93682),f864(x93681,x93682)),f196(f891(x93682,a877))))))
% 162.26/162.09 [9369]~P107(x93692)+E(x93691,f196(f891(x93692,a877)))+~P24(f331(f62(x93692),x93691))+P24(f331(f331(f333(x93692),f12(x93692,f246(x93692),x93691)),x93691))+~P24(f331(f331(f333(x93692),f331(f331(f246(x93692),f869(x93691,x93692)),f870(x93691,x93692))),f331(f331(f309(x93692),f869(x93691,x93692)),f331(f331(f309(x93692),f870(x93691,x93692)),f196(f891(x93692,a877))))))
% 162.26/162.09 [6527]~P87(x65272)+E(x65271,f2(x65272))+~E(f331(f331(f81(x65272),x65273),x65271),f2(x65272))+~P24(f331(f331(f247(x65272),f2(x65272)),x65273))+~P24(f331(f331(f247(x65272),f2(x65272)),x65271))
% 162.26/162.09 [6528]~P87(x65282)+E(x65281,f2(x65282))+~E(f331(f331(f81(x65282),x65281),x65283),f2(x65282))+~P24(f331(f331(f247(x65282),f2(x65282)),x65283))+~P24(f331(f331(f247(x65282),f2(x65282)),x65281))
% 162.26/162.09 [7051]~P107(x70512)+~P29(x70512,x70511)+E(x70511,f119(x70512))+~P24(f331(f331(f333(x70512),x70513),f331(f175(x70512),f660(x70511,x70512))))+P24(f331(f331(f247(x70512),f695(x70511,x70512)),x70513))
% 162.26/162.09 [7216]~P107(x72161)+E(f14(x72161,x72162),x72163)+~P24(f331(f62(x72161),x72162))+~P24(f331(f331(f247(x72161),x72163),f750(x72163,x72162,x72161)))+~P24(f331(f331(f333(x72161),x72163),x72162))
% 162.26/162.09 [7247]~P107(x72471)+~P29(x72471,x72472)+~P29(x72471,x72473)+P29(x72471,f331(f331(f137(x72471),x72472),x72473))+P24(f331(f331(f333(x72471),f667(x72473,x72472,x72471)),f331(f175(x72471),x72472)))
% 162.26/162.09 [7248]~P107(x72481)+~P29(x72481,x72482)+~P29(x72481,x72483)+P29(x72481,f331(f331(f137(x72481),x72482),x72483))+P24(f331(f331(f333(x72481),f668(x72483,x72482,x72481)),f331(f175(x72481),x72483)))
% 162.26/162.09 [7300]~P107(x73001)+E(f14(x73001,x73002),x73003)+~P24(f331(f62(x73001),x73002))+P24(f331(f331(f333(x73001),f750(x73003,x73002,x73001)),x73002))+~P24(f331(f331(f333(x73001),x73003),x73002))
% 162.26/162.09 [7301]~P107(x73011)+E(f15(x73011,x73012),x73013)+~P24(f331(f62(x73011),x73012))+P24(f331(f331(f333(x73011),f752(x73013,x73012,x73011)),x73012))+~P24(f331(f331(f333(x73011),x73013),x73012))
% 162.26/162.09 [7867]~P107(x78671)+E(f15(x78671,x78672),x78673)+~P24(f331(f62(x78671),x78672))+~P24(f331(f331(f333(x78671),x78673),x78672))+~P24(f331(f331(f247(x78671),f752(x78673,x78672,x78671)),x78673))
% 162.26/162.09 [8197]~P107(x81971)+~P29(x81971,x81972)+~P29(x81971,x81973)+P29(x81971,f331(f331(f137(x81971),x81972),x81973))+~P24(f331(f331(f247(x81971),f667(x81973,x81972,x81971)),f668(x81973,x81972,x81971)))
% 162.26/162.09 [8967]~P96(x89672)+E(x89671,f196(f891(x89672,a877)))+~E(f331(f331(f107(x89672),f331(x89673,f858(x89671,x89673,x89672))),f331(x89673,f344(x89671,x89673,x89672))),f331(x89673,f331(f331(f107(x89672),f858(x89671,x89673,x89672)),f344(x89671,x89673,x89672))))+E(f13(x89672,f331(f310(x89672,x89672,x89673),x89671)),f331(x89673,f13(x89672,x89671)))+~P24(f331(f62(x89672),x89671))
% 162.26/162.09 [8968]~P107(x89682)+E(x89681,f196(f891(x89682,a877)))+~E(f331(f331(f251(x89682),f331(x89683,f859(x89681,x89683,x89682))),f331(x89683,f875(x89681,x89683,x89682))),f331(x89683,f331(f331(f251(x89682),f859(x89681,x89683,x89682)),f875(x89681,x89683,x89682))))+E(f14(x89682,f331(f310(x89682,x89682,x89683),x89681)),f331(x89683,f14(x89682,x89681)))+~P24(f331(f62(x89682),x89681))
% 162.26/162.09 [8969]~P107(x89692)+E(x89691,f196(f891(x89692,a877)))+~E(f331(f331(f246(x89692),f331(x89693,f860(x89691,x89693,x89692))),f331(x89693,f874(x89691,x89693,x89692))),f331(x89693,f331(f331(f246(x89692),f860(x89691,x89693,x89692)),f874(x89691,x89693,x89692))))+E(f15(x89692,f331(f310(x89692,x89692,x89693),x89691)),f331(x89693,f15(x89692,x89691)))+~P24(f331(f62(x89692),x89691))
% 162.26/162.09 [8970]~P96(x89702)+E(x89701,f196(f891(x89702,a877)))+~E(f331(f331(f108(x89702),f331(x89703,f486(x89701,x89703,x89702))),f331(x89703,f489(x89701,x89703,x89702))),f331(x89703,f331(f331(f108(x89702),f486(x89701,x89703,x89702)),f489(x89701,x89703,x89702))))+E(f10(x89702,f331(f310(x89702,x89702,x89703),x89701)),f331(x89703,f10(x89702,x89701)))+~P24(f331(f62(x89702),x89701))
% 162.26/162.09 [9035]~P107(x90352)+E(x90351,f196(f891(x90352,a877)))+~E(f331(f331(f251(x90352),f331(x90353,f861(x90351,x90353,x90352))),f331(x90353,f866(x90351,x90353,x90352))),f331(x90353,f331(f331(f251(x90352),f861(x90351,x90353,x90352)),f866(x90351,x90353,x90352))))+E(f11(x90352,f251(x90352),f331(f310(x90352,x90352,x90353),x90351)),f331(x90353,f11(x90352,f251(x90352),x90351)))+~P24(f331(f62(x90352),x90351))
% 162.26/162.09 [9036]~P107(x90362)+E(x90361,f196(f891(x90362,a877)))+~E(f331(f331(f246(x90362),f331(x90363,f867(x90361,x90363,x90362))),f331(x90363,f873(x90361,x90363,x90362))),f331(x90363,f331(f331(f246(x90362),f867(x90361,x90363,x90362)),f873(x90361,x90363,x90362))))+E(f12(x90362,f246(x90362),f331(f310(x90362,x90362,x90363),x90361)),f331(x90363,f12(x90362,f246(x90362),x90361)))+~P24(f331(f62(x90362),x90361))
% 162.26/162.09 [6545]~P71(x65452)+E(x65451,f196(f891(x65452,a877)))+~P24(f331(f62(x65452),x65451))+E(f331(f64(x65452,f82(x65452)),f331(f331(f309(x65452),x65453),x65451)),f331(f331(f82(x65452),x65453),f331(f64(x65452,f82(x65452)),x65451)))+P24(f331(f331(f333(x65452),x65453),x65451))
% 162.26/162.09 [7057]~P96(x70572)+E(f331(f331(f107(x70572),f13(x70572,x70571)),f13(x70572,x70573)),f13(x70572,x70573))+E(x70571,f196(f891(x70572,a877)))+~P24(f331(f62(x70572),x70573))+~P24(f331(f331(f247(f891(x70572,a877)),x70571),x70573))
% 162.26/162.09 [7058]~P107(x70582)+E(f331(f331(f251(x70582),f14(x70582,x70581)),f14(x70582,x70583)),f14(x70582,x70583))+E(x70581,f196(f891(x70582,a877)))+~P24(f331(f62(x70582),x70583))+~P24(f331(f331(f247(f891(x70582,a877)),x70581),x70583))
% 162.26/162.09 [7059]~P107(x70592)+E(f331(f331(f246(x70592),f15(x70592,x70591)),f15(x70592,x70593)),f15(x70592,x70593))+E(x70591,f196(f891(x70592,a877)))+~P24(f331(f62(x70592),x70593))+~P24(f331(f331(f247(f891(x70592,a877)),x70591),x70593))
% 162.26/162.09 [7060]~P96(x70602)+E(f331(f331(f108(x70602),f10(x70602,x70601)),f10(x70602,x70603)),f10(x70602,x70603))+E(x70601,f196(f891(x70602,a877)))+~P24(f331(f62(x70602),x70603))+~P24(f331(f331(f247(f891(x70602,a877)),x70601),x70603))
% 162.26/162.09 [7345]~P107(x73452)+E(x73451,f196(f891(x73452,a877)))+~P24(f331(f62(x73452),x73453))+P24(f331(f331(f247(x73452),f14(x73452,x73453)),f14(x73452,x73451)))+~P24(f331(f331(f247(f891(x73452,a877)),x73451),x73453))
% 162.26/162.09 [7346]~P107(x73462)+E(x73461,f196(f891(x73462,a877)))+~P24(f331(f62(x73462),x73463))+P24(f331(f331(f247(x73462),f15(x73462,x73461)),f15(x73462,x73463)))+~P24(f331(f331(f247(f891(x73462,a877)),x73461),x73463))
% 162.26/162.09 [7404]~P96(x74041)+E(f13(x74041,x74042),x74043)+~P24(f331(f62(x74041),x74042))+~E(f331(f331(f22(f891(x74041,a877)),x74042),f331(f331(f309(x74041),x74043),f196(f891(x74041,a877)))),f196(f891(x74041,a877)))+~P24(f331(f331(f333(x74041),x74043),x74042))
% 162.26/162.09 [7405]~P107(x74051)+E(f14(x74051,x74052),x74053)+~P24(f331(f62(x74051),x74052))+~E(f331(f331(f22(f891(x74051,a877)),x74052),f331(f331(f309(x74051),x74053),f196(f891(x74051,a877)))),f196(f891(x74051,a877)))+~P24(f331(f331(f333(x74051),x74053),x74052))
% 162.26/162.09 [7406]~P107(x74061)+E(f15(x74061,x74062),x74063)+~P24(f331(f62(x74061),x74062))+~E(f331(f331(f22(f891(x74061,a877)),x74062),f331(f331(f309(x74061),x74063),f196(f891(x74061,a877)))),f196(f891(x74061,a877)))+~P24(f331(f331(f333(x74061),x74063),x74062))
% 162.26/162.09 [7407]~P96(x74071)+E(f10(x74071,x74072),x74073)+~P24(f331(f62(x74071),x74072))+~E(f331(f331(f22(f891(x74071,a877)),x74072),f331(f331(f309(x74071),x74073),f196(f891(x74071,a877)))),f196(f891(x74071,a877)))+~P24(f331(f331(f333(x74071),x74073),x74072))
% 162.26/162.09 [7503]~P107(x75031)+E(f11(x75031,f251(x75031),x75032),x75033)+~P24(f331(f62(x75031),x75032))+~E(f331(f331(f22(f891(x75031,a877)),x75032),f331(f331(f309(x75031),x75033),f196(f891(x75031,a877)))),f196(f891(x75031,a877)))+~P24(f331(f331(f333(x75031),x75033),x75032))
% 162.26/162.09 [7504]~P107(x75041)+E(f12(x75041,f246(x75041),x75042),x75043)+~P24(f331(f62(x75041),x75042))+~E(f331(f331(f22(f891(x75041,a877)),x75042),f331(f331(f309(x75041),x75043),f196(f891(x75041,a877)))),f196(f891(x75041,a877)))+~P24(f331(f331(f333(x75041),x75043),x75042))
% 162.26/162.09 [7541]~P107(x75412)+E(x75411,f196(f891(x75412,a877)))+~P24(f331(f62(x75412),x75411))+~P24(f331(f331(f248(x75412),x75413),f855(x75413,x75411,x75412)))+P24(f331(f331(f248(x75412),x75413),f331(f64(x75412,f251(x75412)),x75411)))
% 162.26/162.09 [7542]~P107(x75422)+E(x75421,f196(f891(x75422,a877)))+~P24(f331(f62(x75422),x75421))+~P24(f331(f331(f247(x75422),x75423),f853(x75423,x75421,x75422)))+P24(f331(f331(f247(x75422),x75423),f331(f64(x75422,f251(x75422)),x75421)))
% 162.26/162.09 [7543]~P102(x75432)+E(x75431,f196(f891(x75432,a877)))+~P24(f331(f62(x75432),x75431))+~P24(f331(f331(f247(x75432),x75433),f465(x75433,x75431,x75432)))+P24(f331(f331(f247(x75432),x75433),f331(f64(x75432,f108(x75432)),x75431)))
% 162.26/162.09 [7625]~P107(x76252)+E(x76251,f196(f891(x76252,a877)))+~P24(f331(f62(x76252),x76251))+P24(f331(f331(f333(x76252),f853(x76253,x76251,x76252)),x76251))+P24(f331(f331(f247(x76252),x76253),f331(f64(x76252,f251(x76252)),x76251)))
% 162.26/162.09 [7626]~P107(x76262)+E(x76261,f196(f891(x76262,a877)))+~P24(f331(f62(x76262),x76261))+P24(f331(f331(f333(x76262),f855(x76263,x76261,x76262)),x76261))+P24(f331(f331(f248(x76262),x76263),f331(f64(x76262,f251(x76262)),x76261)))
% 162.26/162.09 [7627]~P102(x76272)+E(x76271,f196(f891(x76272,a877)))+~P24(f331(f62(x76272),x76271))+P24(f331(f331(f333(x76272),f465(x76273,x76271,x76272)),x76271))+P24(f331(f331(f247(x76272),x76273),f331(f64(x76272,f108(x76272)),x76271)))
% 162.26/162.09 [7748]~P107(x77482)+E(x77481,f196(f891(x77482,a877)))+E(f331(f331(f251(x77482),f11(x77482,f251(x77482),x77481)),f11(x77482,f251(x77482),x77483)),f11(x77482,f251(x77482),x77483))+~P24(f331(f62(x77482),x77483))+~P24(f331(f331(f247(f891(x77482,a877)),x77481),x77483))
% 162.26/162.09 [7749]~P107(x77492)+E(x77491,f196(f891(x77492,a877)))+E(f331(f331(f246(x77492),f12(x77492,f246(x77492),x77491)),f12(x77492,f246(x77492),x77493)),f12(x77492,f246(x77492),x77493))+~P24(f331(f62(x77492),x77493))+~P24(f331(f331(f247(f891(x77492,a877)),x77491),x77493))
% 162.26/162.09 [7941]~E(f537(x79411,x79413,x79412),f538(x79411,x79413,x79412))+~E(f331(f38(x79412),f534(x79411,x79413,x79412)),x79411)+E(f331(f331(f82(a883),x79411),f331(f38(f891(x79412,a877)),x79413)),f331(f38(x79412),f40(f891(x79412,a877),x79413)))+~P24(f331(f62(x79412),f40(f891(x79412,a877),x79413)))+~P24(f331(f62(f891(x79412,a877)),x79413))
% 162.26/162.09 [8129]~P107(x81292)+E(x81291,f196(f891(x81292,a877)))+~P24(f331(f62(x81292),x81293))+P24(f331(f331(f247(x81292),f331(f64(x81292,f251(x81292)),x81293)),f331(f64(x81292,f251(x81292)),x81291)))+~P24(f331(f331(f247(f891(x81292,a877)),x81291),x81293))
% 162.26/162.09 [8429]~E(f537(x84291,x84293,x84292),f538(x84291,x84293,x84292))+E(f331(f331(f82(a883),x84291),f331(f38(f891(x84292,a877)),x84293)),f331(f38(x84292),f40(f891(x84292,a877),x84293)))+P24(f331(f331(f333(f891(x84292,a877)),f534(x84291,x84293,x84292)),x84293))+~P24(f331(f62(x84292),f40(f891(x84292,a877),x84293)))+~P24(f331(f62(f891(x84292,a877)),x84293))
% 162.26/162.09 [8458]~E(f331(f38(x84582),f534(x84581,x84583,x84582)),x84581)+E(f331(f331(f82(a883),x84581),f331(f38(f891(x84582,a877)),x84583)),f331(f38(x84582),f40(f891(x84582,a877),x84583)))+P24(f331(f331(f333(f891(x84582,a877)),f538(x84581,x84583,x84582)),x84583))+~P24(f331(f62(x84582),f40(f891(x84582,a877),x84583)))+~P24(f331(f62(f891(x84582,a877)),x84583))
% 162.26/162.09 [8459]~E(f331(f38(x84592),f534(x84591,x84593,x84592)),x84591)+E(f331(f331(f82(a883),x84591),f331(f38(f891(x84592,a877)),x84593)),f331(f38(x84592),f40(f891(x84592,a877),x84593)))+P24(f331(f331(f333(f891(x84592,a877)),f537(x84591,x84593,x84592)),x84593))+~P24(f331(f62(x84592),f40(f891(x84592,a877),x84593)))+~P24(f331(f62(f891(x84592,a877)),x84593))
% 162.26/162.09 [8485]~E(f331(f38(x84852),f534(x84851,x84853,x84852)),x84851)+~E(f331(f331(f108(f891(x84852,a877)),f538(x84851,x84853,x84852)),f537(x84851,x84853,x84852)),f196(f891(x84852,a877)))+E(f331(f331(f82(a883),x84851),f331(f38(f891(x84852,a877)),x84853)),f331(f38(x84852),f40(f891(x84852,a877),x84853)))+~P24(f331(f62(f891(x84852,a877)),x84853))+~P24(f331(f62(x84852),f40(f891(x84852,a877),x84853)))
% 162.26/162.09 [8725]E(f331(f331(f82(a883),x87251),f331(f38(f891(x87252,a877)),x87253)),f331(f38(x87252),f40(f891(x87252,a877),x87253)))+P24(f331(f331(f333(f891(x87252,a877)),f534(x87251,x87253,x87252)),x87253))+P24(f331(f331(f333(f891(x87252,a877)),f538(x87251,x87253,x87252)),x87253))+~P24(f331(f62(f891(x87252,a877)),x87253))+~P24(f331(f62(x87252),f40(f891(x87252,a877),x87253)))
% 162.26/162.09 [8726]E(f331(f331(f82(a883),x87261),f331(f38(f891(x87262,a877)),x87263)),f331(f38(x87262),f40(f891(x87262,a877),x87263)))+P24(f331(f331(f333(f891(x87262,a877)),f534(x87261,x87263,x87262)),x87263))+P24(f331(f331(f333(f891(x87262,a877)),f537(x87261,x87263,x87262)),x87263))+~P24(f331(f62(f891(x87262,a877)),x87263))+~P24(f331(f62(x87262),f40(f891(x87262,a877),x87263)))
% 162.26/162.09 [8751]~E(f331(f331(f108(f891(x87512,a877)),f538(x87511,x87513,x87512)),f537(x87511,x87513,x87512)),f196(f891(x87512,a877)))+E(f331(f331(f82(a883),x87511),f331(f38(f891(x87512,a877)),x87513)),f331(f38(x87512),f40(f891(x87512,a877),x87513)))+~P24(f331(f62(f891(x87512,a877)),x87513))+P24(f331(f331(f333(f891(x87512,a877)),f534(x87511,x87513,x87512)),x87513))+~P24(f331(f62(x87512),f40(f891(x87512,a877),x87513)))
% 162.26/162.09 [9014]~P95(x90142)+E(x90141,f196(f891(x90142,a877)))+~E(f331(f331(f82(x90142),f331(x90143,f829(x90141,x90143,x90142))),f331(x90143,f832(x90141,x90143,x90142))),f331(x90143,f331(f331(f82(x90142),f829(x90141,x90143,x90142)),f832(x90141,x90143,x90142))))+~P24(f331(f62(x90142),x90141))+E(f331(f64(x90142,f82(x90142)),f331(f310(x90142,x90142,x90143),x90141)),f331(x90143,f331(f64(x90142,f82(x90142)),x90141)))
% 162.26/162.09 [10139]P24(f331(f331(x101391,x101392),x101393))+P24(f331(f331(f248(a1),f392(x101391,x101393,x101392)),f394(x101391,x101393,x101392)))+P24(f331(f331(f247(a1),f394(x101391,x101393,x101392)),f2(a1)))+P24(f331(f331(x101391,f392(x101391,x101393,x101392)),f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f394(x101391,x101393,x101392))))+~P24(f331(f319(f890(a1,a1),a57),f331(f331(f261(a1,a1),x101392),x101393)))
% 162.26/162.09 [10140]P24(f331(f331(x101401,x101402),x101403))+P24(f331(f331(f247(a1),f391(x101401,x101403,x101402)),f2(a1)))+P24(f331(f331(x101401,f388(x101401,x101403,x101402)),f331(f331(f82(a1),f331(f110(a1),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f391(x101401,x101403,x101402))))+P24(f331(f331(f247(a1),f2(a1)),f331(f331(f81(a1),f388(x101401,x101403,x101402)),f391(x101401,x101403,x101402))))+~P24(f331(f319(f890(a1,a1),a52),f331(f331(f261(a1,a1),x101402),x101403)))
% 162.26/162.09 [7912]~P111(x79121)+~P24(f331(f331(f247(x79121),x79122),f79(x79121)))+~P24(f331(f331(f247(x79121),f2(x79121)),x79122))+~P24(f331(f331(f247(x79121),f2(x79121)),x79123))+P24(f331(f331(f247(x79121),f331(f331(f82(x79121),x79122),x79123)),x79123))
% 162.26/162.09 [7913]~P111(x79131)+~P24(f331(f331(f247(x79131),x79133),f79(x79131)))+~P24(f331(f331(f247(x79131),f2(x79131)),x79133))+~P24(f331(f331(f247(x79131),f2(x79131)),x79132))+P24(f331(f331(f247(x79131),f331(f331(f82(x79131),x79132),x79133)),x79132))
% 162.26/162.09 [8278]~P107(x82782)+E(x82781,f196(f891(x82782,a877)))+~P24(f331(f62(x82782),x82781))+P24(f331(f331(f333(x82782),f854(x82783,x82781,x82782)),x82781))+~P24(f331(f331(f247(x82782),f331(f64(x82782,f251(x82782)),x82781)),x82783))
% 162.26/162.09 [8279]~P107(x82792)+E(x82791,f196(f891(x82792,a877)))+~P24(f331(f62(x82792),x82791))+P24(f331(f331(f333(x82792),f857(x82793,x82791,x82792)),x82791))+~P24(f331(f331(f248(x82792),f331(f64(x82792,f251(x82792)),x82791)),x82793))
% 162.26/162.09 [8280]~P107(x82802)+E(x82801,f196(f891(x82802,a877)))+~P24(f331(f62(x82802),x82801))+P24(f331(f331(f248(x82802),f857(x82803,x82801,x82802)),x82803))+~P24(f331(f331(f248(x82802),f331(f64(x82802,f251(x82802)),x82801)),x82803))
% 162.26/162.09 [8281]~P107(x82812)+E(x82811,f196(f891(x82812,a877)))+~P24(f331(f62(x82812),x82811))+P24(f331(f331(f247(x82812),f854(x82813,x82811,x82812)),x82813))+~P24(f331(f331(f247(x82812),f331(f64(x82812,f251(x82812)),x82811)),x82813))
% 162.26/162.09 [8362]~P24(f331(x83621,x83623))+P24(f331(x83621,f432(x83621,x83622)))+P24(f331(x83621,f420(x83621,x83622)))+~P24(f331(f331(f248(a1),f2(a1)),x83622))+P24(f331(x83621,f331(f331(f22(a1),f420(x83621,x83622)),f331(f331(f82(a1),f433(x83621,x83622)),x83622))))
% 162.26/162.09 [8583]~P24(f331(x85831,x85833))+P24(f331(x85831,f420(x85831,x85832)))+~P24(f331(f331(f248(a1),f2(a1)),x85832))+P24(f331(f331(f333(a1),f432(x85831,x85832)),f302(a1,f79(a1),x85832)))+P24(f331(x85831,f331(f331(f22(a1),f420(x85831,x85832)),f331(f331(f82(a1),f433(x85831,x85832)),x85832))))
% 162.26/162.09 [8771]~P24(f331(x87711,x87713))+~P24(f331(x87711,f420(x87711,x87712)))+P24(f331(x87711,f432(x87711,x87712)))+~P24(f331(f331(f248(a1),f2(a1)),x87712))+~P24(f331(x87711,f331(f331(f22(a1),f420(x87711,x87712)),f331(f331(f82(a1),f433(x87711,x87712)),x87712))))
% 162.26/162.09 [8900]~P24(f331(x89001,x89003))+~P24(f331(x89001,f420(x89001,x89002)))+~P24(f331(f331(f248(a1),f2(a1)),x89002))+P24(f331(f331(f333(a1),f432(x89001,x89002)),f302(a1,f79(a1),x89002)))+~P24(f331(x89001,f331(f331(f22(a1),f420(x89001,x89002)),f331(f331(f82(a1),f433(x89001,x89002)),x89002))))
% 162.26/162.09 [8683]~P96(x86831)+~P24(f331(f62(x86831),x86832))+E(f331(f331(f22(f891(x86831,a877)),x86832),f331(f331(f309(x86831),x86833),f196(f891(x86831,a877)))),f196(f891(x86831,a877)))+~P24(f331(f331(f333(x86831),x86833),x86832))+E(f331(f331(f107(x86831),x86833),f13(x86831,f331(f331(f22(f891(x86831,a877)),x86832),f331(f331(f309(x86831),x86833),f196(f891(x86831,a877)))))),f13(x86831,x86832))
% 162.26/162.09 [8684]~P107(x86841)+~P24(f331(f62(x86841),x86842))+E(f331(f331(f22(f891(x86841,a877)),x86842),f331(f331(f309(x86841),x86843),f196(f891(x86841,a877)))),f196(f891(x86841,a877)))+~P24(f331(f331(f333(x86841),x86843),x86842))+E(f331(f331(f251(x86841),x86843),f14(x86841,f331(f331(f22(f891(x86841,a877)),x86842),f331(f331(f309(x86841),x86843),f196(f891(x86841,a877)))))),f14(x86841,x86842))
% 162.26/162.09 [8685]~P107(x86851)+~P24(f331(f62(x86851),x86852))+E(f331(f331(f22(f891(x86851,a877)),x86852),f331(f331(f309(x86851),x86853),f196(f891(x86851,a877)))),f196(f891(x86851,a877)))+~P24(f331(f331(f333(x86851),x86853),x86852))+E(f331(f331(f246(x86851),x86853),f15(x86851,f331(f331(f22(f891(x86851,a877)),x86852),f331(f331(f309(x86851),x86853),f196(f891(x86851,a877)))))),f15(x86851,x86852))
% 162.26/162.09 [8686]~P96(x86861)+~P24(f331(f62(x86861),x86862))+E(f331(f331(f22(f891(x86861,a877)),x86862),f331(f331(f309(x86861),x86863),f196(f891(x86861,a877)))),f196(f891(x86861,a877)))+~P24(f331(f331(f333(x86861),x86863),x86862))+E(f331(f331(f108(x86861),x86863),f10(x86861,f331(f331(f22(f891(x86861,a877)),x86862),f331(f331(f309(x86861),x86863),f196(f891(x86861,a877)))))),f10(x86861,x86862))
% 162.26/162.09 [8743]~P107(x87431)+~P24(f331(f62(x87431),x87432))+E(f331(f331(f22(f891(x87431,a877)),x87432),f331(f331(f309(x87431),x87433),f196(f891(x87431,a877)))),f196(f891(x87431,a877)))+~P24(f331(f331(f333(x87431),x87433),x87432))+E(f331(f331(f251(x87431),x87433),f11(x87431,f251(x87431),f331(f331(f22(f891(x87431,a877)),x87432),f331(f331(f309(x87431),x87433),f196(f891(x87431,a877)))))),f11(x87431,f251(x87431),x87432))
% 162.26/162.09 [8744]~P107(x87441)+~P24(f331(f62(x87441),x87442))+E(f331(f331(f22(f891(x87441,a877)),x87442),f331(f331(f309(x87441),x87443),f196(f891(x87441,a877)))),f196(f891(x87441,a877)))+~P24(f331(f331(f333(x87441),x87443),x87442))+E(f331(f331(f246(x87441),x87443),f12(x87441,f246(x87441),f331(f331(f22(f891(x87441,a877)),x87442),f331(f331(f309(x87441),x87443),f196(f891(x87441,a877)))))),f12(x87441,f246(x87441),x87442))
% 162.26/162.09 [8758]~P96(x87581)+~P24(f331(f62(x87581),x87583))+~P24(f331(f62(x87581),x87582))+E(f331(f331(f108(f891(x87581,a877)),x87582),x87583),f196(f891(x87581,a877)))+E(f331(f331(f107(x87581),f13(x87581,f331(f331(f107(f891(x87581,a877)),x87582),x87583))),f13(x87581,f331(f331(f108(f891(x87581,a877)),x87582),x87583))),f331(f331(f107(x87581),f13(x87581,x87582)),f13(x87581,x87583)))
% 162.26/162.09 [8759]~P107(x87591)+~P24(f331(f62(x87591),x87593))+~P24(f331(f62(x87591),x87592))+E(f331(f331(f108(f891(x87591,a877)),x87592),x87593),f196(f891(x87591,a877)))+E(f331(f331(f251(x87591),f14(x87591,f331(f331(f107(f891(x87591,a877)),x87592),x87593))),f14(x87591,f331(f331(f108(f891(x87591,a877)),x87592),x87593))),f331(f331(f251(x87591),f14(x87591,x87592)),f14(x87591,x87593)))
% 162.26/162.09 [8760]~P107(x87601)+~P24(f331(f62(x87601),x87603))+~P24(f331(f62(x87601),x87602))+E(f331(f331(f108(f891(x87601,a877)),x87602),x87603),f196(f891(x87601,a877)))+E(f331(f331(f246(x87601),f15(x87601,f331(f331(f107(f891(x87601,a877)),x87602),x87603))),f15(x87601,f331(f331(f108(f891(x87601,a877)),x87602),x87603))),f331(f331(f246(x87601),f15(x87601,x87602)),f15(x87601,x87603)))
% 162.26/162.09 [8761]~P96(x87611)+~P24(f331(f62(x87611),x87613))+~P24(f331(f62(x87611),x87612))+E(f331(f331(f108(f891(x87611,a877)),x87612),x87613),f196(f891(x87611,a877)))+E(f331(f331(f108(x87611),f10(x87611,f331(f331(f107(f891(x87611,a877)),x87612),x87613))),f10(x87611,f331(f331(f108(f891(x87611,a877)),x87612),x87613))),f331(f331(f108(x87611),f10(x87611,x87612)),f10(x87611,x87613)))
% 162.26/162.09 [8986]~P107(x89861)+~P24(f331(f62(x89861),x89863))+~P24(f331(f62(x89861),x89862))+E(f331(f331(f108(f891(x89861,a877)),x89862),x89863),f196(f891(x89861,a877)))+E(f331(f331(f251(x89861),f11(x89861,f251(x89861),f331(f331(f107(f891(x89861,a877)),x89862),x89863))),f11(x89861,f251(x89861),f331(f331(f108(f891(x89861,a877)),x89862),x89863))),f331(f331(f251(x89861),f11(x89861,f251(x89861),x89862)),f11(x89861,f251(x89861),x89863)))
% 162.26/162.09 [8987]~P107(x89871)+~P24(f331(f62(x89871),x89873))+~P24(f331(f62(x89871),x89872))+E(f331(f331(f108(f891(x89871,a877)),x89872),x89873),f196(f891(x89871,a877)))+E(f331(f331(f246(x89871),f12(x89871,f246(x89871),f331(f331(f107(f891(x89871,a877)),x89872),x89873))),f12(x89871,f246(x89871),f331(f331(f108(f891(x89871,a877)),x89872),x89873))),f331(f331(f246(x89871),f12(x89871,f246(x89871),x89872)),f12(x89871,f246(x89871),x89873)))
% 162.26/162.09 [10064]~P110(x100643)+E(x100641,x100642)+~P24(f331(f331(f247(x100643),f2(x100643)),x100642))+~P24(f331(f331(f247(x100643),f2(x100643)),x100641))+~E(f331(f331(f262(x100643),x100641),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))),f331(f331(f262(x100643),x100642),f331(f110(a883),f331(f331(f81(a1),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),f331(f331(f81(a1),f331(f331(f81(a1),f79(a1)),a84)),a84))),a103))))
% 162.26/162.09 [6348]E(f450(x63481,x63482,x63483),x63484)+E(f331(x63481,x63484),f2(a883))+~E(f331(f331(f6(x63483,a883),x63481),x63482),f79(a883))+~P24(f331(f62(x63483),x63482))+~P24(f331(f331(f333(x63483),x63484),x63482))
% 162.26/162.09 [6411]E(f452(x64111,x64112,x64113),x64114)+E(f331(x64111,x64114),f2(a883))+~E(f331(f331(f6(x64113,a883),x64111),x64112),f331(a118,f2(a883)))+~P24(f331(f62(x64113),x64112))+~P24(f331(f331(f333(x64113),x64114),x64112))
% 162.26/162.09 [6516]~P107(x65161)+~P27(x65161)+P24(f331(f331(f248(x65161),x65162),f40(x65161,x65163)))+~P24(f331(f331(f248(x65161),x65162),x65164))+~P24(f331(f331(f333(x65161),x65164),x65163))
% 162.26/162.09 [6687]~P107(x66871)+~P27(x66871)+~P24(f331(f331(f248(x66871),x66874),x66873))+P24(f331(f331(f248(x66871),f41(x66871,x66872)),x66873))+~P24(f331(f331(f333(x66871),x66874),x66872))
% 162.26/162.09 [6934]~P110(x69343)+E(x69341,x69342)+~E(f331(f331(f262(x69343),x69341),f331(a118,x69344)),f331(f331(f262(x69343),x69342),f331(a118,x69344)))+~P24(f331(f331(f247(x69343),f2(x69343)),x69342))+~P24(f331(f331(f247(x69343),f2(x69343)),x69341))
% 162.26/162.09 [7145]~E(f454(x71452,x71453,x71451,x71454),x71454)+~E(f331(x71452,x71454),f79(a883))+E(f331(f331(f6(x71451,a883),x71452),x71453),f79(a883))+~P24(f331(f62(x71451),x71453))+~P24(f331(f331(f333(x71451),x71454),x71453))
% 162.26/162.09 [7152]~P118(x71524)+~P130(x71524)+E(f331(x71521,f381(x71521,x71522,x71523,x71524)),f2(x71524))+~E(f331(f331(f9(x71523,x71524),x71521),x71522),f2(x71524))+~P24(f331(f62(x71523),x71522))
% 162.26/162.09 [7238]~E(f453(x72382,x72383,x72381,x72384),x72384)+~E(f331(x72382,x72384),f331(a118,f2(a883)))+E(f331(f331(f6(x72381,a883),x72382),x72383),f331(a118,f2(a883)))+~P24(f331(f62(x72381),x72383))+~P24(f331(f331(f333(x72381),x72384),x72383))
% 162.26/162.09 [7952]~E(f331(x79522,x79524),f79(a883))+~E(f331(x79522,f454(x79522,x79523,x79521,x79524)),f2(a883))+E(f331(f331(f6(x79521,a883),x79522),x79523),f79(a883))+~P24(f331(f62(x79521),x79523))+~P24(f331(f331(f333(x79521),x79524),x79523))
% 162.26/162.09 [7995]~E(f331(x79952,x79954),f331(a118,f2(a883)))+~E(f331(x79952,f453(x79952,x79953,x79951,x79954)),f2(a883))+E(f331(f331(f6(x79951,a883),x79952),x79953),f331(a118,f2(a883)))+~P24(f331(f62(x79951),x79953))+~P24(f331(f331(f333(x79951),x79954),x79953))
% 162.26/162.09 [8554]~P107(x85541)+~P29(x85541,x85544)+P29(x85541,x85542)+~E(x85542,f331(f331(f154(x85541),x85543),x85544))+~P24(f331(f331(f247(x85541),x85543),f697(x85542,x85541,x85544,x85543)))
% 162.26/162.09 [8587]E(x85871,x85872)+E(f331(f331(f22(a1),f418(x85873,x85872,x85874,x85871)),f419(x85873,x85872,x85874,x85871)),x85871)+~E(f331(f331(f81(a1),x85871),x85874),x85872)+~P24(f331(f331(f248(a1),f2(a1)),x85874))+~P24(f331(f331(f333(a1),x85872),x85873))
% 162.26/162.09 [8588]E(x85881,x85882)+E(f331(f331(f81(a1),f421(x85883,x85882,x85884,x85881)),f422(x85883,x85882,x85884,x85881)),x85881)+~E(f331(f331(f22(a1),x85881),x85884),x85882)+~P24(f331(f331(f248(a1),f2(a1)),x85884))+~P24(f331(f331(f333(a1),x85882),x85883))
% 162.26/162.09 [8756]E(f331(x87561,f788(x87562,x87561,x87563,x87564)),x87562)+P24(f331(f331(f247(a883),x87564),f789(x87562,x87561,x87563,x87564)))+~P24(f331(f331(f247(a1),x87562),f331(x87561,x87563)))+~P24(f331(f331(f248(a883),x87564),x87563))+~P24(f331(f331(f247(a1),f331(x87561,x87564)),x87562))
% 162.26/162.09 [8757]~P107(x87571)+~P29(x87571,x87573)+P29(x87571,x87572)+~E(x87572,f331(f331(f154(x87571),x87574),x87573))+P24(f331(f331(f333(x87571),f697(x87572,x87571,x87573,x87574)),f331(f175(x87571),x87573)))
% 162.26/162.09 [8775]~P118(x87754)+~P130(x87754)+~E(f331(f331(f9(x87751,x87754),x87752),x87753),f2(x87754))+~P24(f331(f62(x87751),x87753))+P24(f331(f331(f333(x87751),f381(x87752,x87753,x87751,x87754)),x87753))
% 162.26/162.09 [8811]~E(f331(x88112,x88114),f79(a883))+E(f331(f331(f6(x88111,a883),x88112),x88113),f79(a883))+~P24(f331(f62(x88111),x88113))+~P24(f331(f331(f333(x88111),x88114),x88113))+P24(f331(f331(f333(x88111),f454(x88112,x88113,x88111,x88114)),x88113))
% 162.26/162.09 [8821]E(x88211,x88212)+~E(f331(f331(f81(a1),x88212),x88214),x88211)+~P24(f331(f331(f248(a1),f2(a1)),x88214))+~P24(f331(f331(f333(a1),x88211),x88213))+P24(f331(f331(f333(a1),f418(x88213,x88211,x88214,x88212)),x88213))
% 162.26/162.09 [8822]E(x88221,x88222)+~E(f331(f331(f22(a1),x88222),x88224),x88221)+~P24(f331(f331(f248(a1),f2(a1)),x88224))+~P24(f331(f331(f333(a1),x88221),x88223))+P24(f331(f331(f333(a1),f421(x88223,x88221,x88224,x88222)),x88223))
% 162.26/162.09 [8824]~E(f331(x88242,x88244),f331(a118,f2(a883)))+E(f331(f331(f6(x88241,a883),x88242),x88243),f331(a118,f2(a883)))+~P24(f331(f62(x88241),x88243))+~P24(f331(f331(f333(x88241),x88244),x88243))+P24(f331(f331(f333(x88241),f453(x88242,x88243,x88241,x88244)),x88243))
% 162.26/162.09 [8830]P56(x88302,x88303,x88304,x88301)+E(x88301,f196(f891(x88302,a877)))+~P24(f331(f62(x88302),x88304))+~P24(f331(f62(x88302),x88301))+P24(f331(f331(f333(x88302),f522(x88301,x88304,x88303,x88302)),x88304))
% 162.26/162.09 [8913]E(x89131,x89132)+~E(f331(f331(f81(a1),x89132),x89134),x89131)+~P24(f331(f331(f248(a1),f2(a1)),x89134))+~P24(f331(f331(f333(a1),x89131),x89133))+P24(f331(f331(f333(a1),f419(x89133,x89131,x89134,x89132)),f302(a1,f79(a1),x89134)))
% 162.26/162.09 [8914]E(x89141,x89142)+~E(f331(f331(f22(a1),x89142),x89144),x89141)+~P24(f331(f331(f248(a1),f2(a1)),x89144))+~P24(f331(f331(f333(a1),x89141),x89143))+P24(f331(f331(f333(a1),f422(x89143,x89141,x89144,x89142)),f302(a1,f79(a1),x89144)))
% 162.26/162.09 [8992]P24(f331(f331(f247(a883),x89921),f788(x89922,x89923,x89924,x89921)))+~P24(f331(f331(f247(a1),x89922),f331(x89923,x89924)))+P24(f331(f331(f247(a883),x89921),f789(x89922,x89923,x89924,x89921)))+~P24(f331(f331(f248(a883),x89921),x89924))+~P24(f331(f331(f247(a1),f331(x89923,x89921)),x89922))
% 162.26/162.09 [9094]E(f331(x90941,f788(x90942,x90941,x90943,x90944)),x90942)+~P24(f331(f331(f247(a1),x90942),f331(x90941,x90943)))+P24(f331(f331(f248(a883),f789(x90942,x90941,x90943,x90944)),x90943))+~P24(f331(f331(f248(a883),x90944),x90943))+~P24(f331(f331(f247(a1),f331(x90941,x90944)),x90942))
% 162.26/162.09 [9230]~P24(f331(f331(f247(a1),x92302),f331(x92303,x92304)))+P24(f331(f331(f247(a883),x92301),f789(x92302,x92303,x92304,x92301)))+P24(f331(f331(f247(a883),f788(x92302,x92303,x92304,x92301)),x92304))+~P24(f331(f331(f248(a883),x92301),x92304))+~P24(f331(f331(f247(a1),f331(x92303,x92301)),x92302))
% 162.26/162.09 [9231]~P24(f331(f331(f247(a1),x92312),f331(x92313,x92314)))+P24(f331(f331(f247(a883),x92311),f788(x92312,x92313,x92314,x92311)))+P24(f331(f331(f248(a883),f789(x92312,x92313,x92314,x92311)),x92314))+~P24(f331(f331(f248(a883),x92311),x92314))+~P24(f331(f331(f247(a1),f331(x92313,x92311)),x92312))
% 162.26/162.09 [9341]~P24(f331(f331(f247(a1),x93411),f331(x93412,x93413)))+P24(f331(f331(f247(a883),f788(x93411,x93412,x93413,x93414)),x93413))+~P24(f331(f331(f248(a883),x93414),x93413))+~P24(f331(f331(f247(a1),f331(x93412,x93414)),x93411))+P24(f331(f331(f248(a883),f789(x93411,x93412,x93413,x93414)),x93413))
% 162.26/162.09 [9414]E(x94141,f196(f891(x94142,a877)))+~P24(f331(f62(x94142),x94144))+~P24(f331(f62(x94142),x94141))+P24(f331(f331(f333(f890(f891(x94142,a877),f891(x94142,a877))),f331(f331(f261(f891(x94142,a877),f891(x94142,a877)),x94144),x94141)),f322(x94142,x94143)))+P24(f331(f331(f333(x94142),f526(x94143,x94141,x94144,x94142)),x94144))
% 162.26/162.09 [9415]E(x94151,f196(f891(x94152,a877)))+~P24(f331(f62(x94152),x94154))+~P24(f331(f62(x94152),x94151))+P24(f331(f331(f333(f890(f891(x94152,a877),f891(x94152,a877))),f331(f331(f261(f891(x94152,a877),f891(x94152,a877)),x94154),x94151)),f322(x94152,x94153)))+P24(f331(f331(f333(x94152),f745(x94153,x94151,x94154,x94152)),x94154))
% 162.26/162.09 [10095]E(f331(x100951,f788(x100952,x100951,x100953,x100954)),x100952)+~P24(f331(f331(f247(a1),x100952),f331(x100951,x100953)))+~P24(f331(f331(f247(a1),f331(f76(a1),f331(f331(f22(a1),f331(x100951,f331(f331(f81(a883),f789(x100952,x100951,x100953,x100954)),f79(a883)))),f331(x100951,f789(x100952,x100951,x100953,x100954))))),f79(a1)))+~P24(f331(f331(f248(a883),x100954),x100953))+~P24(f331(f331(f247(a1),f331(x100951,x100954)),x100952))
% 162.26/162.09 [10096]~P24(f331(f331(f247(a1),x100962),f331(x100963,x100964)))+P24(f331(f331(f247(a883),x100961),f788(x100962,x100963,x100964,x100961)))+~P24(f331(f331(f247(a1),f331(f76(a1),f331(f331(f22(a1),f331(x100963,f331(f331(f81(a883),f789(x100962,x100963,x100964,x100961)),f79(a883)))),f331(x100963,f789(x100962,x100963,x100964,x100961))))),f79(a1)))+~P24(f331(f331(f248(a883),x100961),x100964))+~P24(f331(f331(f247(a1),f331(x100963,x100961)),x100962))
% 162.26/162.09 [10097]~P24(f331(f331(f247(a1),x100971),f331(x100972,x100973)))+~P24(f331(f331(f247(a1),f331(f76(a1),f331(f331(f22(a1),f331(x100972,f331(f331(f81(a883),f789(x100971,x100972,x100973,x100974)),f79(a883)))),f331(x100972,f789(x100971,x100972,x100973,x100974))))),f79(a1)))+~P24(f331(f331(f248(a883),x100974),x100973))+~P24(f331(f331(f247(a1),f331(x100972,x100974)),x100971))+P24(f331(f331(f247(a883),f788(x100971,x100972,x100973,x100974)),x100973))
% 162.26/162.09 [7205]~P63(x72051)+P24(f331(f331(f248(x72051),x72052),f2(x72051)))+~P24(f331(f331(f248(x72051),x72053),f2(x72051)))+P24(f331(f331(f248(x72051),f2(x72051)),x72052))+P24(f331(f331(f248(x72051),x72053),f331(f331(f289(x72051),x72054),x72052)))
% 162.26/162.09 [7206]~P63(x72061)+P24(f331(f331(f248(x72061),x72062),f2(x72061)))+~P24(f331(f331(f247(x72061),x72063),f2(x72061)))+P24(f331(f331(f248(x72061),f2(x72061)),x72062))+P24(f331(f331(f247(x72061),x72063),f331(f331(f289(x72061),x72064),x72062)))
% 162.26/162.09 [7444]~P63(x74441)+P24(f331(f331(f248(x74441),x74442),f2(x74441)))+P24(f331(f331(f248(x74441),x74443),f2(x74441)))+P24(f331(f331(f248(x74441),f2(x74441)),x74443))+~P24(f331(f331(f248(x74441),x74442),f331(f331(f289(x74441),x74444),x74443)))
% 162.26/162.09 [7445]~P63(x74451)+P24(f331(f331(f248(x74451),x74452),f2(x74451)))+P24(f331(f331(f247(x74451),x74453),f2(x74451)))+P24(f331(f331(f248(x74451),f2(x74451)),x74452))+~P24(f331(f331(f247(x74451),x74453),f331(f331(f289(x74451),x74454),x74452)))
% 162.26/162.09 [7560]E(x75601,x75602)+~E(f331(f331(f168(x75603),x75604),x75601),f331(f331(f168(x75603),x75604),x75602))+~P24(f331(f140(x75603),x75604))+~P24(f331(f331(f248(a883),x75602),f331(f197(f884(x75603)),x75604)))+~P24(f331(f331(f248(a883),x75601),f331(f197(f884(x75603)),x75604)))
% 162.26/162.09 [7914]~P63(x79141)+~P24(f331(f331(f248(x79141),x79143),f2(x79141)))+P24(f331(f331(f248(x79141),f2(x79141)),x79142))+~P24(f331(f331(f248(x79141),x79144),f331(f331(f82(x79141),x79143),x79142)))+P24(f331(f331(f248(x79141),x79143),f331(f331(f289(x79141),x79144),x79142)))
% 162.26/162.09 [7915]~P63(x79151)+~P24(f331(f331(f247(x79151),x79153),f2(x79151)))+P24(f331(f331(f248(x79151),f2(x79151)),x79152))+~P24(f331(f331(f247(x79151),x79154),f331(f331(f82(x79151),x79153),x79152)))+P24(f331(f331(f247(x79151),x79153),f331(f331(f289(x79151),x79154),x79152)))
% 162.26/162.09 [7916]~P63(x79161)+~P24(f331(f331(f248(x79161),x79162),f2(x79161)))+P24(f331(f331(f248(x79161),f2(x79161)),x79162))+~P24(f331(f331(f248(x79161),x79164),f331(f331(f82(x79161),x79163),x79162)))+P24(f331(f331(f248(x79161),x79163),f331(f331(f289(x79161),x79164),x79162)))
% 162.26/162.09 [7917]~P63(x79171)+~P24(f331(f331(f248(x79171),x79172),f2(x79171)))+P24(f331(f331(f248(x79171),f2(x79171)),x79172))+~P24(f331(f331(f248(x79171),x79174),f331(f331(f289(x79171),x79173),x79172)))+P24(f331(f331(f248(x79171),x79173),f331(f331(f82(x79171),x79174),x79172)))
% 162.26/162.09 [7918]~P63(x79181)+~P24(f331(f331(f248(x79181),x79182),f2(x79181)))+P24(f331(f331(f248(x79181),f2(x79181)),x79182))+~P24(f331(f331(f247(x79181),x79184),f331(f331(f82(x79181),x79183),x79182)))+P24(f331(f331(f247(x79181),x79183),f331(f331(f289(x79181),x79184),x79182)))
% 162.26/162.09 [7919]~P63(x79191)+~P24(f331(f331(f248(x79191),x79192),f2(x79191)))+P24(f331(f331(f248(x79191),f2(x79191)),x79192))+~P24(f331(f331(f247(x79191),x79194),f331(f331(f289(x79191),x79193),x79192)))+P24(f331(f331(f247(x79191),x79193),f331(f331(f82(x79191),x79194),x79192)))
% 162.26/162.09 [8067]~P107(x80671)+~P29(x80671,x80672)+~P24(f331(f331(f247(a883),x80673),x80674))+P24(f331(f331(f247(x80671),f331(f331(f168(x80671),x80672),x80673)),f331(f331(f168(x80671),x80672),x80674)))+~P24(f331(f331(f248(a883),x80674),f331(f197(f884(x80671)),x80672)))
% 162.26/162.09 [8120]~P110(x81201)+~P24(f331(f331(f248(x81201),x81202),f79(x81201)))+~P24(f331(f331(f248(x81201),f2(x81201)),x81202))+~P24(f331(f331(f248(a883),x81204),x81203))+P24(f331(f331(f248(x81201),f331(f331(f262(x81201),x81202),x81203)),f331(f331(f262(x81201),x81202),x81204)))
% 162.26/162.09 [8121]~P110(x81211)+~P24(f331(f331(f247(x81211),x81212),f79(x81211)))+~P24(f331(f331(f247(x81211),f2(x81211)),x81212))+~P24(f331(f331(f247(a883),x81214),x81213))+P24(f331(f331(f247(x81211),f331(f331(f262(x81211),x81212),x81213)),f331(f331(f262(x81211),x81212),x81214)))
% 162.26/162.09 [8122]~P110(x81221)+~P24(f331(f331(f247(x81221),f2(x81221)),x81222))+~P24(f331(f331(f248(a883),f2(a883)),x81223))+~P24(f331(f331(f248(x81221),x81222),x81224))+P24(f331(f331(f248(x81221),f331(f331(f262(x81221),x81222),x81223)),f331(f331(f262(x81221),x81224),x81223)))
% 162.26/162.09 [8142]~P107(x81421)+~P29(x81421,f331(f172(x81421),x81422))+~P24(f331(f331(f247(a883),x81424),x81423))+P24(f331(f331(f247(x81421),f331(f331(f168(x81421),x81422),x81423)),f331(f331(f168(x81421),x81422),x81424)))+~P24(f331(f331(f248(a883),x81423),f331(f197(f884(x81421)),x81422)))
% 162.26/162.09 [8384]~P64(x83841)+~P24(f331(f331(f248(x83841),x83842),f2(x83841)))+~P24(f331(f331(f248(x83841),x83843),x83844))+~P24(f331(f331(f248(x83841),f2(x83841)),f331(f331(f82(x83841),x83843),x83844)))+P24(f331(f331(f248(x83841),f331(f331(f289(x83841),x83842),x83843)),f331(f331(f289(x83841),x83842),x83844)))
% 162.26/162.09 [8385]~P63(x83851)+~P24(f331(f331(f247(x83851),x83852),f2(x83851)))+~P24(f331(f331(f247(x83851),x83853),x83854))+~P24(f331(f331(f248(x83851),f2(x83851)),f331(f331(f82(x83851),x83853),x83854)))+P24(f331(f331(f247(x83851),f331(f331(f289(x83851),x83852),x83853)),f331(f331(f289(x83851),x83852),x83854)))
% 162.26/162.09 [8395]~P64(x83951)+~P24(f331(f331(f248(x83951),x83954),x83953))+~P24(f331(f331(f248(x83951),f2(x83951)),x83952))+~P24(f331(f331(f248(x83951),f2(x83951)),f331(f331(f82(x83951),x83953),x83954)))+P24(f331(f331(f248(x83951),f331(f331(f289(x83951),x83952),x83953)),f331(f331(f289(x83951),x83952),x83954)))
% 162.26/162.09 [8396]~P64(x83961)+~P24(f331(f331(f247(x83961),x83964),x83963))+~P24(f331(f331(f247(x83961),f2(x83961)),x83962))+~P24(f331(f331(f248(x83961),f2(x83961)),f331(f331(f82(x83961),x83963),x83964)))+P24(f331(f331(f247(x83961),f331(f331(f289(x83961),x83962),x83963)),f331(f331(f289(x83961),x83962),x83964)))
% 162.26/162.09 [8499]P24(f331(x84991,x84992))+~P24(f331(f62(x84994),x84992))+P24(f331(x84991,f731(x84991,x84993,x84992,x84994)))+~P24(f331(x84991,f196(f891(x84994,a877))))+~P24(f331(f331(f247(f891(x84994,a877)),x84992),x84993))
% 162.26/162.09 [8507]P24(f331(x85071,x85072))+P24(f331(f62(x85073),f731(x85071,x85074,x85072,x85073)))+~P24(f331(f62(x85073),x85072))+~P24(f331(x85071,f196(f891(x85073,a877))))+~P24(f331(f331(f247(f891(x85073,a877)),x85072),x85074))
% 162.26/162.09 [8752]E(f331(f331(f81(a1),f423(x87521,x87522,x87523,x87524)),f424(x87521,x87522,x87523,x87524)),x87524)+~P24(f331(f331(f248(a1),f2(a1)),x87523))+~P24(f331(f331(f248(a1),x87522),x87524))+~P24(f331(f331(f333(a1),x87522),x87521))+P24(f331(f331(f248(a1),x87522),f331(f331(f22(a1),x87524),x87523)))
% 162.26/162.09 [8973]~P24(f331(f331(f248(a1),f2(a1)),x89733))+~P24(f331(f331(f248(a1),x89732),x89734))+~P24(f331(f331(f333(a1),x89732),x89731))+P24(f331(f331(f333(a1),f423(x89731,x89732,x89733,x89734)),x89731))+P24(f331(f331(f248(a1),x89732),f331(f331(f22(a1),x89734),x89733)))
% 162.26/162.09 [8985]P24(f331(x89851,x89852))+~P24(f331(f62(x89853),x89852))+P24(f331(f331(f333(x89853),f713(x89851,x89854,x89852,x89853)),x89854))+~P24(f331(x89851,f196(f891(x89853,a877))))+~P24(f331(f331(f247(f891(x89853,a877)),x89852),x89854))
% 162.26/162.09 [9002]E(f331(f331(f81(a1),f408(x90021,x90022,x90023,x90024)),f409(x90021,x90022,x90023,x90024)),x90024)+~P24(f331(f331(f248(a1),f2(a1)),x90023))+~P24(f331(f331(f247(a1),x90022),x90024))+P24(f331(f331(f247(a1),x90022),f331(f331(f22(a1),x90024),x90023)))+~P24(f331(f331(f333(a1),f331(f331(f22(a1),x90022),f79(a1))),x90021))
% 162.26/162.09 [9047]~P24(f331(f331(f248(a1),f2(a1)),x90473))+~P24(f331(f331(f248(a1),x90471),x90472))+~P24(f331(f331(f333(a1),x90471),x90474))+P24(f331(f331(f333(a1),f424(x90474,x90471,x90473,x90472)),f302(a1,f79(a1),x90473)))+P24(f331(f331(f248(a1),x90471),f331(f331(f22(a1),x90472),x90473)))
% 162.26/162.09 [9145]~P24(f331(f331(f248(a1),f2(a1)),x91453))+~P24(f331(f331(f247(a1),x91452),x91454))+P24(f331(f331(f333(a1),f408(x91451,x91452,x91453,x91454)),x91451))+P24(f331(f331(f247(a1),x91452),f331(f331(f22(a1),x91454),x91453)))+~P24(f331(f331(f333(a1),f331(f331(f22(a1),x91452),f79(a1))),x91451))
% 162.26/162.09 [9187]~P24(f331(f331(f248(a1),f2(a1)),x91873))+~P24(f331(f331(f247(a1),x91871),x91872))+P24(f331(f331(f333(a1),f409(x91874,x91871,x91873,x91872)),f302(a1,f79(a1),x91873)))+P24(f331(f331(f247(a1),x91871),f331(f331(f22(a1),x91872),x91873)))+~P24(f331(f331(f333(a1),f331(f331(f22(a1),x91871),f79(a1))),x91874))
% 162.26/162.09 [9418]P24(f331(x94181,x94182))+~P24(f331(f331(f333(x94183),f713(x94181,x94184,x94182,x94183)),f731(x94181,x94184,x94182,x94183)))+~P24(f331(f62(x94183),x94182))+~P24(f331(x94181,f196(f891(x94183,a877))))+~P24(f331(f331(f247(f891(x94183,a877)),x94182),x94184))
% 162.26/162.09 [9658]P24(f331(x96581,x96582))+~P24(f331(f62(x96583),x96582))+~P24(f331(x96581,f331(f331(f309(x96583),f713(x96581,x96584,x96582,x96583)),f731(x96581,x96584,x96582,x96583))))+~P24(f331(x96581,f196(f891(x96583,a877))))+~P24(f331(f331(f247(f891(x96583,a877)),x96582),x96584))
% 162.26/162.09 [7693]~P63(x76931)+P24(f331(f331(f248(x76931),x76932),f2(x76931)))+P24(f331(f331(f248(x76931),f2(x76931)),x76932))+~P24(f331(f331(f248(x76931),f2(x76931)),x76934))+P24(f331(f331(f248(x76931),f331(f331(f289(x76931),x76933),x76932)),x76934))
% 162.26/162.09 [7694]~P63(x76941)+P24(f331(f331(f248(x76941),x76942),f2(x76941)))+~P24(f331(f331(f247(x76941),f2(x76941)),x76944))+P24(f331(f331(f248(x76941),f2(x76941)),x76942))+P24(f331(f331(f247(x76941),f331(f331(f289(x76941),x76943),x76942)),x76944))
% 162.26/162.09 [7967]~P24(f331(f331(f247(a1),x79674),f2(a1)))+~E(x79672,f331(f331(f81(a1),f331(f331(f82(a1),x79671),x79673)),x79674))+P24(f331(f331(f248(a1),f2(a1)),x79671))+~P24(f331(f331(f248(a1),x79671),x79674))+P24(f331(f49(x79672,x79671),f331(f331(f261(a1,a1),x79673),x79674)))
% 162.26/162.09 [8006]~P24(f331(x80061,x80064))+P24(f331(x80061,f856(x80062,x80061,x80063)))+~P24(f331(f331(f248(a1),f2(a1)),x80063))+~P24(f331(f331(f247(a1),f2(a1)),x80062))+P24(f331(x80061,f331(f331(f22(a1),x80064),f331(f331(f82(a1),x80062),x80063))))
% 162.26/162.09 [8007]~P24(f331(x80071,x80074))+P24(f331(x80071,f343(x80072,x80071,x80073)))+~P24(f331(f331(f248(a1),f2(a1)),x80073))+~P24(f331(f331(f247(a1),f2(a1)),x80072))+P24(f331(x80071,f331(f331(f81(a1),x80074),f331(f331(f82(a1),x80072),x80073))))
% 162.26/162.09 [8008]~P63(x80081)+P24(f331(f331(f248(x80081),x80082),f2(x80081)))+P24(f331(f331(f248(x80081),f2(x80081)),x80082))+P24(f331(f331(f248(x80081),f2(x80081)),x80083))+~P24(f331(f331(f248(x80081),f331(f331(f289(x80081),x80084),x80082)),x80083))
% 162.26/162.09 [8009]~P63(x80091)+P24(f331(f331(f248(x80091),x80092),f2(x80091)))+P24(f331(f331(f248(x80091),f2(x80091)),x80092))+P24(f331(f331(f247(x80091),f2(x80091)),x80093))+~P24(f331(f331(f247(x80091),f331(f331(f289(x80091),x80094),x80092)),x80093))
% 162.26/162.09 [8061]~E(x80611,f331(f331(f81(a1),f331(f331(f82(a1),x80612),x80613)),x80614))+~P24(f331(f331(f248(a1),f2(a1)),x80612))+~P24(f331(f331(f247(a1),f2(a1)),x80614))+~P24(f331(f331(f248(a1),x80614),x80612))+P24(f331(f49(x80611,x80612),f331(f331(f261(a1,a1),x80613),x80614)))
% 162.26/162.09 [8186]~P63(x81861)+P24(f331(f331(f248(x81861),x81862),f2(x81861)))+~P24(f331(f331(f248(x81861),f2(x81861)),x81864))+~P24(f331(f331(f248(x81861),x81863),f331(f331(f82(x81861),x81864),x81862)))+P24(f331(f331(f248(x81861),f331(f331(f289(x81861),x81863),x81862)),x81864))
% 162.26/162.09 [8187]~P63(x81871)+P24(f331(f331(f248(x81871),x81872),f2(x81871)))+~P24(f331(f331(f247(x81871),f2(x81871)),x81874))+~P24(f331(f331(f247(x81871),x81873),f331(f331(f82(x81871),x81874),x81872)))+P24(f331(f331(f247(x81871),f331(f331(f289(x81871),x81873),x81872)),x81874))
% 162.26/162.09 [8266]~P63(x82661)+P24(f331(f331(f248(x82661),x82662),f2(x82661)))+~P24(f331(f331(f248(x82661),x82663),f2(x82661)))+P24(f331(f331(f248(x82661),x82663),f331(f331(f289(x82661),x82664),x82662)))+~P24(f331(f331(f248(x82661),f331(f331(f82(x82661),x82663),x82662)),x82664))
% 162.26/162.09 [8267]~P63(x82671)+P24(f331(f331(f248(x82671),x82672),f2(x82671)))+~P24(f331(f331(f247(x82671),x82673),f2(x82671)))+P24(f331(f331(f247(x82671),x82673),f331(f331(f289(x82671),x82674),x82672)))+~P24(f331(f331(f247(x82671),f331(f331(f82(x82671),x82673),x82672)),x82674))
% 162.26/162.09 [8418]~P63(x84181)+~P24(f331(f331(f248(x84181),x84182),f2(x84181)))+P24(f331(f331(f248(x84181),f2(x84181)),x84182))+~P24(f331(f331(f248(x84181),f331(f331(f289(x84181),x84184),x84182)),x84183))+P24(f331(f331(f248(x84181),f331(f331(f82(x84181),x84183),x84182)),x84184))
% 162.26/162.09 [8419]~P63(x84191)+~P24(f331(f331(f248(x84191),x84192),f2(x84191)))+P24(f331(f331(f248(x84191),f2(x84191)),x84192))+~P24(f331(f331(f248(x84191),f331(f331(f82(x84191),x84194),x84192)),x84193))+P24(f331(f331(f248(x84191),f331(f331(f289(x84191),x84193),x84192)),x84194))
% 162.26/162.09 [8420]~P63(x84201)+~P24(f331(f331(f248(x84201),x84202),f2(x84201)))+P24(f331(f331(f248(x84201),f2(x84201)),x84202))+~P24(f331(f331(f247(x84201),f331(f331(f289(x84201),x84204),x84202)),x84203))+P24(f331(f331(f247(x84201),f331(f331(f82(x84201),x84203),x84202)),x84204))
% 162.26/162.09 [8421]~P63(x84211)+~P24(f331(f331(f248(x84211),x84212),f2(x84211)))+P24(f331(f331(f248(x84211),f2(x84211)),x84212))+~P24(f331(f331(f247(x84211),f331(f331(f82(x84211),x84214),x84212)),x84213))+P24(f331(f331(f247(x84211),f331(f331(f289(x84211),x84213),x84212)),x84214))
% 162.26/162.09 [8445]~P63(x84451)+~P24(f331(f331(f248(x84451),f2(x84451)),x84454))+P24(f331(f331(f248(x84451),f2(x84451)),x84452))+~P24(f331(f331(f248(x84451),f331(f331(f82(x84451),x84454),x84452)),x84453))+P24(f331(f331(f248(x84451),f331(f331(f289(x84451),x84453),x84452)),x84454))
% 162.26/162.09 [8446]~P63(x84461)+~P24(f331(f331(f247(x84461),f2(x84461)),x84464))+P24(f331(f331(f248(x84461),f2(x84461)),x84462))+~P24(f331(f331(f247(x84461),f331(f331(f82(x84461),x84464),x84462)),x84463))+P24(f331(f331(f247(x84461),f331(f331(f289(x84461),x84463),x84462)),x84464))
% 162.26/162.09 [8520]~P63(x85201)+~P24(f331(f331(f248(x85201),x85204),f2(x85201)))+~P24(f331(f331(f248(x85201),x85203),f331(f331(f82(x85201),x85202),x85204)))+P24(f331(f331(f248(x85201),x85202),f331(f331(f289(x85201),x85203),x85204)))+~P24(f331(f331(f248(x85201),f331(f331(f82(x85201),x85202),x85204)),x85203))
% 162.26/162.09 [8521]~P63(x85211)+~P24(f331(f331(f248(x85211),x85212),f2(x85211)))+~P24(f331(f331(f248(x85211),x85213),f331(f331(f82(x85211),x85212),x85214)))+P24(f331(f331(f248(x85211),x85212),f331(f331(f289(x85211),x85213),x85214)))+~P24(f331(f331(f248(x85211),f331(f331(f82(x85211),x85212),x85214)),x85213))
% 162.26/162.09 [8522]~P63(x85221)+~P24(f331(f331(f248(x85221),x85224),f2(x85221)))+~P24(f331(f331(f247(x85221),x85223),f331(f331(f82(x85221),x85222),x85224)))+P24(f331(f331(f247(x85221),x85222),f331(f331(f289(x85221),x85223),x85224)))+~P24(f331(f331(f247(x85221),f331(f331(f82(x85221),x85222),x85224)),x85223))
% 162.26/162.09 [8523]~P63(x85231)+~P24(f331(f331(f247(x85231),x85232),f2(x85231)))+~P24(f331(f331(f247(x85231),x85233),f331(f331(f82(x85231),x85232),x85234)))+P24(f331(f331(f247(x85231),x85232),f331(f331(f289(x85231),x85233),x85234)))+~P24(f331(f331(f247(x85231),f331(f331(f82(x85231),x85232),x85234)),x85233))
% 162.26/162.09 [8636]~P63(x86361)+~P24(f331(f331(f248(x86361),x86363),f2(x86361)))+~P24(f331(f331(f248(x86361),x86362),f331(f331(f82(x86361),x86364),x86363)))+~P24(f331(f331(f248(x86361),f331(f331(f82(x86361),x86364),x86363)),x86362))+P24(f331(f331(f248(x86361),f331(f331(f289(x86361),x86362),x86363)),x86364))
% 162.26/162.09 [8637]~P63(x86371)+~P24(f331(f331(f248(x86371),x86373),f2(x86371)))+~P24(f331(f331(f247(x86371),x86372),f331(f331(f82(x86371),x86374),x86373)))+~P24(f331(f331(f247(x86371),f331(f331(f82(x86371),x86374),x86373)),x86372))+P24(f331(f331(f247(x86371),f331(f331(f289(x86371),x86372),x86373)),x86374))
% 162.26/162.09 [8647]~P63(x86471)+~P24(f331(f331(f248(x86471),f2(x86471)),x86474))+~P24(f331(f331(f248(x86471),x86472),f331(f331(f82(x86471),x86474),x86473)))+~P24(f331(f331(f248(x86471),f331(f331(f82(x86471),x86474),x86473)),x86472))+P24(f331(f331(f248(x86471),f331(f331(f289(x86471),x86472),x86473)),x86474))
% 162.26/162.09 [8648]~P63(x86481)+~P24(f331(f331(f247(x86481),f2(x86481)),x86484))+~P24(f331(f331(f247(x86481),x86482),f331(f331(f82(x86481),x86484),x86483)))+~P24(f331(f331(f247(x86481),f331(f331(f82(x86481),x86484),x86483)),x86482))+P24(f331(f331(f247(x86481),f331(f331(f289(x86481),x86482),x86483)),x86484))
% 162.26/162.09 [8814]E(f331(f331(f22(a1),f425(x88141,x88142,x88143,x88144)),f426(x88141,x88142,x88143,x88144)),x88144)+~P24(f331(f331(f248(a1),f2(a1)),x88143))+~P24(f331(f331(f333(a1),x88142),x88141))+~P24(f331(f331(f248(a1),x88144),x88142))+P24(f331(f331(f248(a1),f331(f331(f81(a1),x88144),x88143)),x88142))
% 162.26/162.09 [8896]~P24(f331(x88961,x88962))+~P24(f331(f331(f248(a1),f2(a1)),x88964))+~P24(f331(f331(f247(a1),f2(a1)),x88963))+~P24(f331(x88961,f331(f331(f22(a1),f856(x88963,x88961,x88964)),x88964)))+P24(f331(x88961,f331(f331(f22(a1),x88962),f331(f331(f82(a1),x88963),x88964))))
% 162.26/162.09 [8897]~P24(f331(x88971,x88972))+~P24(f331(f331(f248(a1),f2(a1)),x88974))+~P24(f331(f331(f247(a1),f2(a1)),x88973))+~P24(f331(x88971,f331(f331(f81(a1),f343(x88973,x88971,x88974)),x88974)))+P24(f331(x88971,f331(f331(f81(a1),x88972),f331(f331(f82(a1),x88973),x88974))))
% 162.26/162.09 [9041]~P24(f331(f331(f248(a1),f2(a1)),x90413))+~P24(f331(f331(f333(a1),x90412),x90411))+~P24(f331(f331(f248(a1),x90414),x90412))+P24(f331(f331(f333(a1),f425(x90411,x90412,x90413,x90414)),x90411))+P24(f331(f331(f248(a1),f331(f331(f81(a1),x90414),x90413)),x90412))
% 162.26/162.09 [9055]E(f331(f331(f22(a1),f410(x90551,x90552,x90553,x90554)),f411(x90551,x90552,x90553,x90554)),x90554)+~P24(f331(f331(f248(a1),f2(a1)),x90553))+~P24(f331(f331(f247(a1),x90554),x90552))+~P24(f331(f331(f333(a1),f331(f331(f81(a1),x90552),f79(a1))),x90551))+P24(f331(f331(f247(a1),f331(f331(f81(a1),x90554),x90553)),x90552))
% 162.26/162.09 [9081]~P24(f331(f331(f248(a1),f2(a1)),x90812))+~P24(f331(f331(f333(a1),x90813),x90814))+~P24(f331(f331(f248(a1),x90811),x90813))+P24(f331(f331(f333(a1),f426(x90814,x90813,x90812,x90811)),f302(a1,f79(a1),x90812)))+P24(f331(f331(f248(a1),f331(f331(f81(a1),x90811),x90812)),x90813))
% 162.26/162.09 [9182]~P24(f331(f331(f248(a1),f2(a1)),x91823))+~P24(f331(f331(f247(a1),x91824),x91822))+P24(f331(f331(f333(a1),f410(x91821,x91822,x91823,x91824)),x91821))+~P24(f331(f331(f333(a1),f331(f331(f81(a1),x91822),f79(a1))),x91821))+P24(f331(f331(f247(a1),f331(f331(f81(a1),x91824),x91823)),x91822))
% 162.26/162.09 [9226]~P24(f331(f331(f248(a1),f2(a1)),x92262))+~P24(f331(f331(f247(a1),x92261),x92263))+P24(f331(f331(f333(a1),f411(x92264,x92263,x92262,x92261)),f302(a1,f79(a1),x92262)))+~P24(f331(f331(f333(a1),f331(f331(f81(a1),x92263),f79(a1))),x92264))+P24(f331(f331(f247(a1),f331(f331(f81(a1),x92261),x92262)),x92263))
% 162.26/162.09 [9523]~P38(x95231,x95233)+~P22(x95231,x95234)+P38(x95231,f331(f331(f107(f891(f890(x95231,x95231),a877)),x95232),x95233))+~P24(f331(f331(f247(f891(f890(x95231,x95231),a877)),x95232),f331(f260(f891(f890(x95231,x95231),a877),f891(f890(x95231,x95231),a877)),x95234)))+~P24(f331(f331(f247(f891(f890(x95231,x95231),a877)),x95233),f331(f269(f891(f890(x95231,x95231),a877),f891(f890(x95231,x95231),a877)),x95234)))
% 162.26/162.09 [9835]~E(f331(f397(x98351,x98354,x98353,x98352),f399(x98351,x98354,x98353,x98352)),f199(f884(a327)))+P24(f331(f331(f248(a1),f398(x98351,x98354,x98353,x98352)),f399(x98351,x98354,x98353,x98352)))+P24(f331(f331(f331(x98351,x98352),x98353),x98354))+P24(f331(f331(f331(x98351,f397(x98351,x98354,x98353,x98352)),f398(x98351,x98354,x98353,x98352)),f331(f331(f81(a1),f399(x98351,x98354,x98353,x98352)),f79(a1))))+~P24(f331(f319(f890(f891(a1,f887(f884(a327))),f890(a1,a1)),a317),f331(f331(f261(f891(a1,f887(f884(a327))),f890(a1,a1)),x98352),f331(f331(f261(a1,a1),x98353),x98354))))
% 162.26/162.09 [9928]~P14(x99282,x99284,x99283)+E(x99281,f196(f891(x99282,a877)))+~P24(f331(f62(x99282),x99281))+P24(f331(f331(f333(x99282),f331(x99283,x99281)),x99281))+~P24(f331(f331(f333(x99282),f331(f331(x99284,f493(x99281,x99283,x99284,x99282)),f505(x99281,x99283,x99284,x99282))),f331(f331(f309(x99282),f493(x99281,x99283,x99284,x99282)),f331(f331(f309(x99282),f505(x99281,x99283,x99284,x99282)),f196(f891(x99282,a877))))))
% 162.26/162.09 [9864]~P108(x98642)+~P60(x98641)+~P24(f331(f331(f247(f891(x98641,x98642)),x98643),x98644))+P24(f331(f331(f248(f891(x98641,x98642)),x98643),x98644))+~P24(f331(f58(x98641),f331(f331(f8(a877,a877,x98641),a326),f331(f331(f18(x98641,x98642,a877),f331(f331(f8(x98642,f891(x98642,a877),x98641),a328),x98643)),x98644))))
% 162.26/162.09 [9427]~P52(x94271,x94271,x94274)+P24(f331(f331(f333(f890(x94271,x94271)),f331(f331(f261(x94271,x94271),x94272),x94273)),f307(x94271,x94274)))+P24(f331(f331(f333(f890(x94271,x94271)),f331(f331(f261(x94271,x94271),x94273),x94272)),f307(x94271,x94274)))+~P24(f331(f331(f333(f890(x94271,x94271)),f331(f331(f261(x94271,x94271),x94275),x94272)),f307(x94271,x94274)))+~P24(f331(f331(f333(f890(x94271,x94271)),f331(f331(f261(x94271,x94271),x94275),x94273)),f307(x94271,x94274)))
% 162.26/162.09 [5638]E(x56381,f2(a883))+~E(f331(f38(x56382),x56385),x56381)+E(f331(f38(x56382),x56383),f331(a118,x56381))+~E(x56383,f331(f331(f309(x56382),x56384),x56385))+P24(f331(f331(f333(x56382),x56384),x56385))
% 162.26/162.09 [5763]~P62(x57632)+E(x57631,f2(x57632))+E(x57633,f2(x57632))+~E(f331(f331(f289(x57632),x57634),x57633),f331(f331(f289(x57632),x57635),x57631))+E(f331(f331(f82(x57632),x57634),x57631),f331(f331(f82(x57632),x57635),x57633))
% 162.26/162.09 [5764]~P62(x57642)+E(x57641,f2(x57642))+E(x57643,f2(x57642))+~E(f331(f331(f82(x57642),x57644),x57643),f331(f331(f82(x57642),x57645),x57641))+E(f331(f331(f289(x57642),x57644),x57641),f331(f331(f289(x57642),x57645),x57643))
% 162.26/162.09 [5830]~E(f331(f38(x58301),x58305),x58303)+~E(x58305,f196(f891(x58301,a877)))+E(f331(f38(x58301),x58302),f331(a118,x58303))+~E(x58302,f331(f331(f309(x58301),x58304),x58305))+P24(f331(f331(f333(x58301),x58304),x58305))
% 162.26/162.09 [6057]~P118(x60572)+~E(f331(x60573,x60575),f2(x60572))+E(f331(f331(f9(x60571,x60572),x60573),x60574),f2(x60572))+~P24(f331(f62(x60571),x60574))+~P24(f331(f331(f333(x60571),x60575),x60574))
% 162.26/162.09 [6424]~P107(x64243)+E(x64241,x64242)+~E(f331(f301(x64243,x64244),x64241),f331(f301(x64243,x64245),x64242))+~P24(f331(f331(f248(x64243),x64245),x64242))+~P24(f331(f331(f248(x64243),x64244),x64241))
% 162.26/162.09 [6425]~P107(x64253)+E(x64251,x64252)+~E(f331(f301(x64253,x64251),x64254),f331(f301(x64253,x64252),x64255))+~P24(f331(f331(f248(x64253),x64252),x64255))+~P24(f331(f331(f248(x64253),x64251),x64254))
% 162.26/162.09 [7461]~P107(x74611)+~P29(x74611,f331(f331(f137(x74611),x74614),x74615))+~P24(f331(f331(f333(x74611),x74613),f331(f175(x74611),x74615)))+~P24(f331(f331(f333(x74611),x74612),f331(f175(x74611),x74614)))+P24(f331(f331(f247(x74611),x74612),x74613))
% 162.26/162.09 [8556]~P108(x85561)+~P24(f331(f331(f248(f891(x85561,a877)),f302(x85561,x85565,x85562)),f302(x85561,x85564,x85563)))+~P24(f331(f331(f247(x85561),x85565),x85562))+P24(f331(f331(f248(x85561),x85562),x85563))+P24(f331(f331(f248(x85561),x85564),x85565))
% 162.26/162.09 [9961]~P13(x99612,x99615,x99613)+E(x99611,f196(f891(x99612,a877)))+~E(f331(f331(x99615,f331(x99614,f835(x99611,x99614,x99613,x99615,x99612))),f331(x99614,f836(x99611,x99614,x99613,x99615,x99612))),f331(x99614,f331(f331(x99615,f835(x99611,x99614,x99613,x99615,x99612)),f836(x99611,x99614,x99613,x99615,x99612))))+E(f331(x99613,f331(f310(x99612,x99612,x99614),x99611)),f331(x99614,f331(x99613,x99611)))+~P24(f331(f62(x99612),x99611))
% 162.26/162.09 [6421]~P14(x64212,x64215,x64213)+E(x64211,f196(f891(x64212,a877)))+~P24(f331(f62(x64212),x64211))+E(f331(x64213,f331(f331(f309(x64212),x64214),x64211)),f331(f331(x64215,x64214),f331(x64213,x64211)))+P24(f331(f331(f333(x64212),x64214),x64211))
% 162.26/162.09 [7229]~P13(x72292,x72293,x72294)+E(f331(f331(x72293,f331(x72294,x72291)),f331(x72294,x72295)),f331(x72294,x72295))+E(x72291,f196(f891(x72292,a877)))+~P24(f331(f62(x72292),x72295))+~P24(f331(f331(f247(f891(x72292,a877)),x72291),x72295))
% 162.26/162.09 [7437]~P60(x74374)+~P93(x74375)+E(f331(x74371,x74372),f331(x74373,x74372))+~P24(f331(f331(f333(x74374),x74372),f331(f175(x74374),f56(x74374))))+~P24(f331(f331(f92(f891(x74374,x74375)),x74371),x74373))
% 162.26/162.09 [7591]~P14(x75914,x75915,x75911)+E(f331(x75911,x75912),x75913)+~P24(f331(f62(x75914),x75912))+~E(f331(f331(f22(f891(x75914,a877)),x75912),f331(f331(f309(x75914),x75913),f196(f891(x75914,a877)))),f196(f891(x75914,a877)))+~P24(f331(f331(f333(x75914),x75913),x75912))
% 162.26/162.09 [7676]E(x76761,x76762)+~E(f331(f197(f884(x76763)),x76762),f331(f197(f884(x76764)),x76765))+~E(f331(f197(f884(x76763)),x76761),f331(f197(f884(x76764)),x76765))+~E(f331(f180(x76764,x76763),f331(f331(f184(x76764,x76763),x76765),x76761)),f331(f180(x76764,x76763),f331(f331(f184(x76764,x76763),x76765),x76762)))+~P24(f331(f140(x76764),x76765))
% 162.26/162.09 [8527]E(x85271,x85272)+~P6(x85273,x85274,x85275)+E(f331(f331(f108(f891(x85273,a877)),x85271),x85272),f196(f891(x85273,a877)))+~P24(f331(f331(f333(f891(x85273,a877)),x85272),f331(f331(f61(x85273),x85274),x85275)))+~P24(f331(f331(f333(f891(x85273,a877)),x85271),f331(f331(f61(x85273),x85274),x85275)))
% 162.26/162.09 [9311]~P73(x93112)+~E(f331(x93113,f401(x93113,x93114,x93115,x93111,x93112)),f79(x93112))+E(f331(f331(f9(x93111,x93112),x93113),x93114),f331(f331(f9(x93111,x93112),x93113),x93115))+~P24(f331(f62(x93111),x93115))+~P24(f331(f331(f247(f891(x93111,a877)),x93114),x93115))
% 162.26/162.09 [9312]~P73(x93122)+~E(f331(x93123,f402(x93123,x93124,x93125,x93121,x93122)),f79(x93122))+E(f331(f331(f9(x93121,x93122),x93123),x93124),f331(f331(f9(x93121,x93122),x93123),x93125))+~P24(f331(f62(x93121),x93125))+~P24(f331(f331(f247(f891(x93121,a877)),x93124),x93125))
% 162.26/162.09 [9313]~P74(x93132)+~E(f331(x93133,f490(x93133,x93134,x93135,x93131,x93132)),f2(x93132))+E(f331(f331(f6(x93131,x93132),x93133),x93134),f331(f331(f6(x93131,x93132),x93133),x93135))+~P24(f331(f62(x93131),x93135))+~P24(f331(f331(f247(f891(x93131,a877)),x93134),x93135))
% 162.26/162.09 [9314]~P74(x93142)+~E(f331(x93143,f492(x93143,x93144,x93145,x93141,x93142)),f2(x93142))+E(f331(f331(f6(x93141,x93142),x93143),x93144),f331(f331(f6(x93141,x93142),x93143),x93145))+~P24(f331(f62(x93141),x93145))+~P24(f331(f331(f247(f891(x93141,a877)),x93144),x93145))
% 162.26/162.09 [9816]~P87(x98161)+~P24(f331(f62(x98162),x98165))+~P24(f331(f331(f247(x98161),f2(x98161)),f331(x98163,f459(x98163,x98164,x98165,x98162,x98161))))+P24(f331(f331(f247(x98161),f331(f331(f6(x98162,x98161),x98163),x98164)),f331(f331(f6(x98162,x98161),x98163),x98165)))+~P24(f331(f331(f247(f891(x98162,a877)),x98164),x98165))
% 162.26/162.09 [7458]E(x74581,f2(a883))+P24(f331(x74582,x74583))+~E(x74584,f331(f331(f81(a883),f331(f331(f82(a883),x74581),x74583)),x74585))+~P24(f331(f331(f248(a883),x74585),x74581))+~P24(f331(x74582,f331(f331(f39(a883),x74584),x74581)))
% 162.26/162.09 [7535]E(x75351,f2(a883))+P24(f331(x75352,x75353))+~P24(f331(x75352,f45(a883,x75354,x75351)))+~E(x75354,f331(f331(f81(a883),f331(f331(f82(a883),x75351),x75355)),x75353))+~P24(f331(f331(f248(a883),x75353),x75351))
% 162.26/162.09 [7825]~P62(x78253)+E(f331(x78251,x78252),f2(x78253))+~P24(f331(f62(x78254),x78255))+E(f331(f331(f9(x78254,x78253),x78251),f331(f331(f22(f891(x78254,a877)),x78255),f331(f331(f309(x78254),x78252),f196(f891(x78254,a877))))),f331(f331(f9(x78254,x78253),x78251),x78255))+P24(f331(f331(f333(x78254),x78252),x78255))
% 162.26/162.09 [8226]~P73(x82261)+~P24(f331(f62(x82262),x82265))+~P24(f331(f62(x82262),x82264))+~E(f331(f331(f108(f891(x82262,a877)),x82264),x82265),f196(f891(x82262,a877)))+E(f331(f331(f82(x82261),f331(f331(f9(x82262,x82261),x82263),x82264)),f331(f331(f9(x82262,x82261),x82263),x82265)),f331(f331(f9(x82262,x82261),x82263),f331(f331(f107(f891(x82262,a877)),x82264),x82265)))
% 162.26/162.09 [8227]~P74(x82271)+~P24(f331(f62(x82272),x82275))+~P24(f331(f62(x82272),x82274))+~E(f331(f331(f108(f891(x82272,a877)),x82274),x82275),f196(f891(x82272,a877)))+E(f331(f331(f81(x82271),f331(f331(f6(x82272,x82271),x82273),x82274)),f331(f331(f6(x82272,x82271),x82273),x82275)),f331(f331(f6(x82272,x82271),x82273),f331(f331(f107(f891(x82272,a877)),x82274),x82275)))
% 162.26/162.09 [8320]~P62(x83203)+E(f331(x83201,x83202),f2(x83203))+~P24(f331(f62(x83204),x83205))+E(f331(f331(f9(x83204,x83203),x83201),f331(f331(f22(f891(x83204,a877)),x83205),f331(f331(f309(x83204),x83202),f196(f891(x83204,a877))))),f331(f331(f289(x83203),f331(f331(f9(x83204,x83203),x83201),x83205)),f331(x83201,x83202)))+~P24(f331(f331(f333(x83204),x83202),x83205))
% 162.26/162.09 [9027]~P6(x90271,x90275,x90274)+~E(f331(f331(f61(x90271),f331(f331(f309(x90271),x90272),f196(f891(x90271,a877)))),x90274),f331(f331(f61(x90271),f331(f331(f309(x90271),x90273),f196(f891(x90271,a877)))),x90274))+~P24(f331(f331(f333(x90271),x90273),x90275))+~P24(f331(f331(f333(x90271),x90272),x90275))+P24(f331(f331(f333(f890(x90271,x90271)),f331(f331(f261(x90271,x90271),x90272),x90273)),x90274))
% 162.26/162.09 [9040]~P6(x90401,x90405,x90403)+E(f331(f331(f61(x90401),f331(f331(f309(x90401),x90402),f196(f891(x90401,a877)))),x90403),f331(f331(f61(x90401),f331(f331(f309(x90401),x90404),f196(f891(x90401,a877)))),x90403))+~P24(f331(f331(f333(x90401),x90404),x90405))+~P24(f331(f331(f333(x90401),x90402),x90405))+~P24(f331(f331(f333(f890(x90401,x90401)),f331(f331(f261(x90401,x90401),x90402),x90404)),x90403))
% 162.26/162.09 [9340]~P73(x93401)+~P24(f331(f62(x93402),x93405))+~P24(f331(f62(x93402),x93404))+~E(f331(f331(f108(f891(x93402,a877)),x93404),x93405),f196(f891(x93402,a877)))+E(f331(f331(f82(x93401),f331(f331(f331(f66(x93401,x93402,f82(x93401)),x93403),f79(x93401)),x93404)),f331(f331(f331(f66(x93401,x93402,f82(x93401)),x93403),f79(x93401)),x93405)),f331(f331(f331(f66(x93401,x93402,f82(x93401)),x93403),f79(x93401)),f331(f331(f107(f891(x93402,a877)),x93404),x93405)))
% 162.26/162.09 [9349]~P73(x93491)+~E(f331(x93493,f475(x93493,x93495,x93494,x93492,x93491)),f79(x93491))+~P24(f331(f62(x93492),x93494))+~P24(f331(f62(x93492),x93495))+E(f331(f331(f82(x93491),f331(f331(f9(x93492,x93491),x93493),x93494)),f331(f331(f9(x93492,x93491),x93493),x93495)),f331(f331(f9(x93492,x93491),x93493),f331(f331(f107(f891(x93492,a877)),x93494),x93495)))
% 162.26/162.09 [9350]~P73(x93501)+~E(f331(x93503,f477(x93503,x93505,x93504,x93502,x93501)),f79(x93501))+~P24(f331(f62(x93502),x93504))+~P24(f331(f62(x93502),x93505))+E(f331(f331(f82(x93501),f331(f331(f9(x93502,x93501),x93503),x93504)),f331(f331(f9(x93502,x93501),x93503),x93505)),f331(f331(f9(x93502,x93501),x93503),f331(f331(f107(f891(x93502,a877)),x93504),x93505)))
% 162.26/162.09 [9351]~P74(x93511)+~E(f331(x93513,f478(x93513,x93515,x93514,x93512,x93511)),f2(x93511))+~P24(f331(f62(x93512),x93514))+~P24(f331(f62(x93512),x93515))+E(f331(f331(f81(x93511),f331(f331(f6(x93512,x93511),x93513),x93514)),f331(f331(f6(x93512,x93511),x93513),x93515)),f331(f331(f6(x93512,x93511),x93513),f331(f331(f107(f891(x93512,a877)),x93514),x93515)))
% 162.26/162.09 [9352]~P74(x93521)+~E(f331(x93523,f479(x93523,x93525,x93524,x93522,x93521)),f2(x93521))+~P24(f331(f62(x93522),x93524))+~P24(f331(f62(x93522),x93525))+E(f331(f331(f81(x93521),f331(f331(f6(x93522,x93521),x93523),x93524)),f331(f331(f6(x93522,x93521),x93523),x93525)),f331(f331(f6(x93522,x93521),x93523),f331(f331(f107(f891(x93522,a877)),x93524),x93525)))
% 162.26/162.09 [9565]~P73(x95651)+~E(f331(x95653,f487(x95653,x95655,x95654,x95652,x95651)),f79(x95651))+~P24(f331(f62(x95652),x95654))+~P24(f331(f62(x95652),x95655))+E(f331(f331(f82(x95651),f331(f331(f331(f66(x95651,x95652,f82(x95651)),x95653),f79(x95651)),x95654)),f331(f331(f331(f66(x95651,x95652,f82(x95651)),x95653),f79(x95651)),x95655)),f331(f331(f331(f66(x95651,x95652,f82(x95651)),x95653),f79(x95651)),f331(f331(f107(f891(x95652,a877)),x95654),x95655)))
% 162.26/162.09 [9683]~P73(x96832)+E(f331(f331(f9(x96831,x96832),x96833),x96834),f331(f331(f9(x96831,x96832),x96833),x96835))+~P24(f331(f62(x96831),x96835))+~P24(f331(f331(f247(f891(x96831,a877)),x96834),x96835))+P24(f331(f331(f333(x96831),f401(x96833,x96834,x96835,x96831,x96832)),f331(f331(f22(f891(x96831,a877)),x96835),x96834)))
% 162.26/162.09 [9684]~P73(x96842)+E(f331(f331(f9(x96841,x96842),x96843),x96844),f331(f331(f9(x96841,x96842),x96843),x96845))+~P24(f331(f62(x96841),x96845))+~P24(f331(f331(f247(f891(x96841,a877)),x96844),x96845))+P24(f331(f331(f333(x96841),f402(x96843,x96844,x96845,x96841,x96842)),f331(f331(f22(f891(x96841,a877)),x96845),x96844)))
% 162.26/162.09 [9685]~P74(x96852)+E(f331(f331(f6(x96851,x96852),x96853),x96854),f331(f331(f6(x96851,x96852),x96853),x96855))+~P24(f331(f62(x96851),x96855))+~P24(f331(f331(f247(f891(x96851,a877)),x96854),x96855))+P24(f331(f331(f333(x96851),f490(x96853,x96854,x96855,x96851,x96852)),f331(f331(f22(f891(x96851,a877)),x96855),x96854)))
% 162.26/162.09 [9686]~P74(x96862)+E(f331(f331(f6(x96861,x96862),x96863),x96864),f331(f331(f6(x96861,x96862),x96863),x96865))+~P24(f331(f62(x96861),x96865))+~P24(f331(f331(f247(f891(x96861,a877)),x96864),x96865))+P24(f331(f331(f333(x96861),f492(x96863,x96864,x96865,x96861,x96862)),f331(f331(f22(f891(x96861,a877)),x96865),x96864)))
% 162.26/162.09 [9704]~P73(x97041)+~P24(f331(f62(x97042),x97044))+~P24(f331(f62(x97042),x97045))+E(f331(f331(f82(x97041),f331(f331(f9(x97042,x97041),x97043),x97044)),f331(f331(f9(x97042,x97041),x97043),x97045)),f331(f331(f9(x97042,x97041),x97043),f331(f331(f107(f891(x97042,a877)),x97044),x97045)))+P24(f331(f331(f333(x97042),f475(x97043,x97045,x97044,x97042,x97041)),f331(f331(f108(f891(x97042,a877)),x97044),x97045)))
% 162.26/162.09 [9705]~P73(x97051)+~P24(f331(f62(x97052),x97054))+~P24(f331(f62(x97052),x97055))+E(f331(f331(f82(x97051),f331(f331(f9(x97052,x97051),x97053),x97054)),f331(f331(f9(x97052,x97051),x97053),x97055)),f331(f331(f9(x97052,x97051),x97053),f331(f331(f107(f891(x97052,a877)),x97054),x97055)))+P24(f331(f331(f333(x97052),f477(x97053,x97055,x97054,x97052,x97051)),f331(f331(f108(f891(x97052,a877)),x97054),x97055)))
% 162.26/162.09 [9706]~P74(x97061)+~P24(f331(f62(x97062),x97064))+~P24(f331(f62(x97062),x97065))+E(f331(f331(f81(x97061),f331(f331(f6(x97062,x97061),x97063),x97064)),f331(f331(f6(x97062,x97061),x97063),x97065)),f331(f331(f6(x97062,x97061),x97063),f331(f331(f107(f891(x97062,a877)),x97064),x97065)))+P24(f331(f331(f333(x97062),f478(x97063,x97065,x97064,x97062,x97061)),f331(f331(f108(f891(x97062,a877)),x97064),x97065)))
% 162.26/162.09 [9707]~P74(x97071)+~P24(f331(f62(x97072),x97074))+~P24(f331(f62(x97072),x97075))+E(f331(f331(f81(x97071),f331(f331(f6(x97072,x97071),x97073),x97074)),f331(f331(f6(x97072,x97071),x97073),x97075)),f331(f331(f6(x97072,x97071),x97073),f331(f331(f107(f891(x97072,a877)),x97074),x97075)))+P24(f331(f331(f333(x97072),f479(x97073,x97075,x97074,x97072,x97071)),f331(f331(f108(f891(x97072,a877)),x97074),x97075)))
% 162.26/162.09 [9714]~P87(x97145)+~P24(f331(f62(x97141),x97144))+P24(f331(f331(f247(x97145),f331(f331(f6(x97141,x97145),x97142),x97143)),f331(f331(f6(x97141,x97145),x97142),x97144)))+~P24(f331(f331(f247(f891(x97141,a877)),x97143),x97144))+P24(f331(f331(f333(x97141),f459(x97142,x97143,x97144,x97141,x97145)),f331(f331(f22(f891(x97141,a877)),x97144),x97143)))
% 162.26/162.09 [9779]~P73(x97791)+~P24(f331(f62(x97792),x97794))+~P24(f331(f62(x97792),x97795))+E(f331(f331(f82(x97791),f331(f331(f331(f66(x97791,x97792,f82(x97791)),x97793),f79(x97791)),x97794)),f331(f331(f331(f66(x97791,x97792,f82(x97791)),x97793),f79(x97791)),x97795)),f331(f331(f331(f66(x97791,x97792,f82(x97791)),x97793),f79(x97791)),f331(f331(f107(f891(x97792,a877)),x97794),x97795)))+P24(f331(f331(f333(x97792),f487(x97793,x97795,x97794,x97792,x97791)),f331(f331(f108(f891(x97792,a877)),x97794),x97795)))
% 162.26/162.09 [8712]~P14(x87121,x87124,x87125)+~P24(f331(f62(x87121),x87122))+E(f331(f331(f22(f891(x87121,a877)),x87122),f331(f331(f309(x87121),x87123),f196(f891(x87121,a877)))),f196(f891(x87121,a877)))+~P24(f331(f331(f333(x87121),x87123),x87122))+E(f331(f331(x87124,x87123),f331(x87125,f331(f331(f22(f891(x87121,a877)),x87122),f331(f331(f309(x87121),x87123),f196(f891(x87121,a877)))))),f331(x87125,x87122))
% 162.26/162.09 [8785]~P14(x87851,x87854,x87855)+~P24(f331(f62(x87851),x87853))+~P24(f331(f62(x87851),x87852))+E(f331(f331(f108(f891(x87851,a877)),x87852),x87853),f196(f891(x87851,a877)))+E(f331(f331(x87854,f331(x87855,f331(f331(f107(f891(x87851,a877)),x87852),x87853))),f331(x87855,f331(f331(f108(f891(x87851,a877)),x87852),x87853))),f331(f331(x87854,f331(x87855,x87852)),f331(x87855,x87853)))
% 162.26/162.09 [9354]~P24(f331(f331(f247(a1),x93544),f2(a1)))+~P24(f331(f331(f248(a1),x93543),x93545))+P24(f331(f331(f247(a1),x93541),x93542))+~P24(f331(f331(f248(a1),x93543),x93544))+~P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f82(a1),x93543),x93542)),x93545)),f331(f331(f81(a1),f331(f331(f82(a1),x93543),x93541)),x93544)))
% 162.26/162.09 [9361]~P24(f331(f331(f247(a1),f2(a1)),x93615))+P24(f331(f331(f247(a1),x93611),x93612))+~P24(f331(f331(f248(a1),x93613),x93614))+~P24(f331(f331(f248(a1),x93615),x93614))+~P24(f331(f331(f247(a1),f331(f331(f81(a1),f331(f331(f82(a1),x93614),x93611)),x93615)),f331(f331(f81(a1),f331(f331(f82(a1),x93614),x93612)),x93613)))
% 162.26/162.09 [9462]~P62(x94625)+E(f331(x94621,f476(x94621,x94622,x94623,x94624,x94625)),f2(x94625))+~P24(f331(f62(x94624),x94623))+~P24(f331(f62(x94624),x94622))+E(f331(f331(f289(x94625),f331(f331(f82(x94625),f331(f331(f9(x94624,x94625),x94621),x94623)),f331(f331(f9(x94624,x94625),x94621),x94622))),f331(f331(f9(x94624,x94625),x94621),f331(f331(f108(f891(x94624,a877)),x94623),x94622))),f331(f331(f9(x94624,x94625),x94621),f331(f331(f107(f891(x94624,a877)),x94623),x94622)))
% 162.26/162.09 [9772]~P62(x97721)+~P24(f331(f62(x97722),x97724))+~P24(f331(f62(x97722),x97725))+E(f331(f331(f289(x97721),f331(f331(f82(x97721),f331(f331(f9(x97722,x97721),x97723),x97724)),f331(f331(f9(x97722,x97721),x97723),x97725))),f331(f331(f9(x97722,x97721),x97723),f331(f331(f108(f891(x97722,a877)),x97724),x97725))),f331(f331(f9(x97722,x97721),x97723),f331(f331(f107(f891(x97722,a877)),x97724),x97725)))+P24(f331(f331(f333(x97722),f476(x97723,x97725,x97724,x97722,x97721)),f331(f331(f108(f891(x97722,a877)),x97724),x97725)))
% 162.26/162.09 [9054]E(f331(f331(f137(x90541),x90542),x90543),f331(f331(f137(x90541),x90544),x90545))+~E(f331(f331(f176(x90541),f331(f197(f884(x90541)),x90544)),x90542),x90544)+~E(f331(f331(f176(x90541),f331(f197(f884(x90541)),x90542)),x90544),x90542)+~E(x90545,f331(f331(f137(x90541),f331(f331(f141(x90541),f331(f197(f884(x90541)),x90544)),x90542)),x90543))+~E(f331(f331(f137(x90541),f331(f331(f141(x90541),f331(f197(f884(x90541)),x90542)),x90544)),x90545),x90543)
% 162.26/162.09 [9460]~P107(x94602)+E(f331(f331(f151(x94601,x94602,x94603),x94604),f173(x94601,x94604,x94605)),x94605)+~P29(x94602,f331(f331(f157(x94601,x94602),x94603),x94605))+~P24(f331(f331(f333(x94601),x94604),f331(f175(x94601),x94605)))+~E(f331(f144(x94601),f331(f139(x94601,f331(f331(f8(x94602,a877,x94601),f331(a328,f331(x94603,x94604))),x94603)),x94605)),x94604)
% 162.26/162.09 [9832]~P71(x98321)+~P24(f331(f67(x98321,x98321,f82(x98321),x98322,x98323),x98325))+~P24(f331(f331(f333(x98321),x98324),x98323))+P24(f331(f331(f333(x98321),x98322),x98323))+P24(f331(f67(x98321,x98321,f82(x98321),x98324,f331(f331(f309(x98321),x98322),f331(f331(f22(f891(x98321,a877)),x98323),f331(f331(f309(x98321),x98324),f196(f891(x98321,a877)))))),x98325))
% 162.26/162.09 [7237]E(x72371,x72372)+~P21(x72374,x72375,x72373,x72376)+~E(f331(x72373,x72371),f331(x72373,x72372))+~P24(f331(f331(f333(x72374),x72372),x72376))+~P24(f331(f331(f333(x72374),x72371),x72376))
% 162.26/162.09 [6511]~P141(x65114)+E(x65111,x65112)+~E(x65115,x65116)+E(x65113,f2(x65114))+~E(f331(f331(f81(x65114),x65115),f331(f331(f82(x65114),x65113),x65111)),f331(f331(f81(x65114),x65116),f331(f331(f82(x65114),x65113),x65112)))
% 162.26/162.09 [7515]~P107(x75151)+~P27(x75151)+~P24(f331(f331(f248(x75151),x75152),f331(x75155,x75156)))+~P24(f331(f331(f333(x75153),x75156),x75154))+P24(f331(f331(f248(x75151),x75152),f331(f331(f42(x75153,x75151),x75154),x75155)))
% 162.26/162.09 [8198]~P107(x81981)+~P27(x81981)+~P24(f331(f331(f248(x81981),f331(x81984,x81986)),x81985))+~P24(f331(f331(f333(x81982),x81986),x81983))+P24(f331(f331(f248(x81981),f331(f331(f43(x81982,x81981),x81983),x81984)),x81985))
% 162.26/162.09 [8452]~P15(x84522,x84525,x84526,x84521)+~P24(f331(f62(x84522),x84524))+~P24(f331(f62(x84522),x84523))+~E(f331(f331(f108(f891(x84522,a877)),x84523),x84524),f196(f891(x84522,a877)))+E(f331(x84521,f331(f331(f107(f891(x84522,a877)),x84523),x84524)),f331(f74(x84525,x84525,x84525,f331(x84521,x84523)),f331(x84521,x84524)))
% 162.26/162.09 [8755]E(x87551,x87552)+~P54(x87554,x87555,x87556,x87553,x87557)+~E(f331(x87553,x87551),f331(x87553,x87552))+~P24(f331(f331(f333(x87555),x87552),x87557))+~P24(f331(f331(f333(x87555),x87551),x87557))
% 162.26/162.09 [10056]~P24(f331(x100562,x100564))+~E(x100565,f331(f139(x100561,x100562),x100567))+E(f331(f139(x100561,x100562),x100563),f331(f331(f154(x100561),x100564),x100565))+~E(x100563,f331(f331(f137(x100561),x100566),f331(f331(f154(x100561),x100564),x100567)))+P24(f331(x100562,f736(x100565,x100564,x100563,x100562,x100561,x100566,x100567)))
% 162.26/162.09 [10057]~P24(f331(x100574,x100572))+~E(x100573,f331(f139(x100571,x100574),x100577))+E(f331(f331(f154(x100571),x100572),x100573),f331(f139(x100571,x100574),x100575))+~E(x100575,f331(f331(f137(x100571),x100576),f331(f331(f154(x100571),x100572),x100577)))+P24(f331(x100574,f738(x100575,x100574,x100573,x100572,x100571,x100576,x100577)))
% 162.26/162.09 [10098]~P24(f331(x100982,x100984))+~E(x100985,f331(f139(x100981,x100982),x100987))+E(f331(f139(x100981,x100982),x100983),f331(f331(f154(x100981),x100984),x100985))+~E(x100983,f331(f331(f137(x100981),x100986),f331(f331(f154(x100981),x100984),x100987)))+P24(f331(f331(f333(x100981),f736(x100985,x100984,x100983,x100982,x100981,x100986,x100987)),f331(f175(x100981),x100986)))
% 162.26/162.09 [10099]~P24(f331(x100994,x100992))+~E(x100993,f331(f139(x100991,x100994),x100997))+E(f331(f331(f154(x100991),x100992),x100993),f331(f139(x100991,x100994),x100995))+~E(x100995,f331(f331(f137(x100991),x100996),f331(f331(f154(x100991),x100992),x100997)))+P24(f331(f331(f333(x100991),f738(x100995,x100994,x100993,x100992,x100991,x100996,x100997)),f331(f175(x100991),x100996)))
% 162.26/162.09 [10103]~P6(x101031,x101037,x101036)+~P9(x101031,f891(x101035,a877),x101036,x101034)+P24(f331(f331(f333(x101031),f473(x101032,x101033,x101034,x101035,x101036,x101037,x101031)),x101037))+~P24(f331(f331(f333(f891(x101031,a877)),x101033),f331(f331(f61(x101031),x101037),x101036)))+P24(f331(f331(f333(f891(x101035,a877)),f331(f331(f42(x101031,f891(x101035,a877)),x101033),x101034)),x101032))
% 162.26/162.09 [10176]~P6(x101762,x101766,x101767)+~P9(x101762,f891(x101761,a877),x101767,x101764)+~P24(f331(f331(f333(f891(x101762,a877)),x101763),f331(f331(f61(x101762),x101766),x101767)))+~P24(f331(f331(f333(f891(x101761,a877)),f331(x101764,f473(x101765,x101763,x101764,x101761,x101767,x101766,x101762))),x101765))+P24(f331(f331(f333(f891(x101761,a877)),f331(f331(f42(x101762,f891(x101761,a877)),x101763),x101764)),x101765))
% 162.26/162.09 [8361]~P73(x83612)+~P21(x83611,x83615,x83618,x83614)+~E(x83613,f331(f74(x83615,x83612,x83611,x83616),x83618))+~E(x83617,f331(f310(x83611,x83615,x83618),x83614))+E(f331(f331(f9(x83611,x83612),x83613),x83614),f331(f331(f9(x83615,x83612),x83616),x83617))
% 162.26/162.09 [10184]~P73(x101842)+~P21(x101845,x101841,x101848,x101847)+~E(f331(x101846,f612(x101843,x101846,x101844,x101847,x101848,x101841,x101845,x101842)),f331(f331(f74(x101841,x101842,x101845,x101843),x101848),f612(x101843,x101846,x101844,x101847,x101848,x101841,x101845,x101842)))+~E(x101844,f331(f310(x101845,x101841,x101848),x101847))+E(f331(f331(f9(x101841,x101842),x101843),x101844),f331(f331(f9(x101845,x101842),x101846),x101847))
% 162.26/162.09 [10190]~P73(x101902)+~P21(x101901,x101905,x101908,x101904)+~E(x101907,f331(f310(x101901,x101905,x101908),x101904))+E(f331(f331(f9(x101901,x101902),x101903),x101904),f331(f331(f9(x101905,x101902),x101906),x101907))+P24(f331(f331(f333(x101901),f612(x101906,x101903,x101907,x101904,x101908,x101905,x101901,x101902)),x101904))
% 162.26/162.09 [10191]~P74(x101912)+~P21(x101911,x101915,x101918,x101914)+~E(x101917,f331(f310(x101911,x101915,x101918),x101914))+E(f331(f331(f6(x101911,x101912),x101913),x101914),f331(f331(f6(x101915,x101912),x101916),x101917))+P24(f331(f331(f333(x101911),f759(x101916,x101913,x101917,x101914,x101918,x101915,x101911,x101912)),x101914))
% 162.26/162.09 [10196]~P74(x101962)+~P21(x101965,x101961,x101968,x101967)+~E(x101964,f331(f310(x101965,x101961,x101968),x101967))+~E(f331(x101966,f759(x101963,x101966,x101964,x101967,x101968,x101961,x101965,x101962)),f331(x101963,f331(x101968,f759(x101963,x101966,x101964,x101967,x101968,x101961,x101965,x101962))))+E(f331(f331(f6(x101961,x101962),x101963),x101964),f331(f331(f6(x101965,x101962),x101966),x101967))
% 162.26/162.09 [9529]~E(f331(f197(f884(x95292)),x95295),f331(f197(f884(x95291)),x95293))+~E(f331(f197(f884(x95292)),x95294),f331(f197(f884(x95291)),x95293))+~E(f331(f331(f331(f73(x95291,f887(x95292)),f331(f180(x95291,x95292),f331(f331(f184(x95291,x95292),x95293),x95294))),x95296),f331(f239(x95292),x95297)),f331(f331(f331(f73(x95291,f887(x95292)),f331(f180(x95291,x95292),f331(f331(f184(x95291,x95292),x95293),x95295))),x95296),f331(f239(x95292),x95298)))+E(f331(f180(x95291,x95292),f331(f331(f184(x95291,x95292),x95293),x95294)),f331(f180(x95291,x95292),f331(f331(f184(x95291,x95292),x95293),x95295)))+P24(f331(f331(f333(x95291),x95296),f331(f175(x95291),x95293)))
% 162.26/162.09 [9654]~P19(x96546,x96542,x96545,x96547,x96548,x96541)+~P24(f331(f62(x96542),x96544))+~P24(f331(f62(x96542),x96543))+~E(f331(f331(f108(f891(x96542,a877)),x96543),x96544),f196(f891(x96542,a877)))+E(f331(x96541,f331(f331(f107(f891(x96542,a877)),x96543),x96544)),f331(f331(x96545,f331(x96541,x96543)),f331(x96541,x96544)))
% 162.26/162.09 [10045]~P19(x100458,x100452,x100455,x100457,x100456,x100451)+~E(f331(x100456,f561(x100454,x100453,x100451,x100456,x100457,x100455,x100452)),x100457)+~P24(f331(f62(x100452),x100453))+~P24(f331(f62(x100452),x100454))+E(f331(x100451,f331(f331(f107(f891(x100452,a877)),x100453),x100454)),f331(f331(x100455,f331(x100451,x100453)),f331(x100451,x100454)))
% 162.26/162.09 [10108]~P19(x101088,x101082,x101085,x101087,x101086,x101081)+~P24(f331(f62(x101082),x101083))+~P24(f331(f62(x101082),x101084))+E(f331(x101081,f331(f331(f107(f891(x101082,a877)),x101083),x101084)),f331(f331(x101085,f331(x101081,x101083)),f331(x101081,x101084)))+P24(f331(f331(f333(x101082),f561(x101084,x101083,x101081,x101086,x101087,x101085,x101082)),f331(f331(f108(f891(x101082,a877)),x101083),x101084)))
% 162.26/162.09 [9821]~P6(x98214,x98218,x98215)+~P6(x98211,x98219,x98213)+~P10(x98211,x98214,f891(x98212,a877),x98213,x98215,x98217)+P9(x98211,f891(x98212,a877),x98213,f331(f331(f8(f891(x98214,f891(x98212,a877)),f891(x98212,a877),x98211),f331(f42(x98214,f891(x98212,a877)),f331(f285(x98214,x98214,x98215),f331(f331(f309(x98214),x98216),f196(f891(x98214,a877)))))),x98217))+~P24(f331(f331(f333(x98214),x98216),x98218))
% 162.26/162.09 [5445]~P107(x54453)+~P29(x54453,x54451)+E(x54451,f694(x54452,x54453))+~E(f331(f175(x54453),x54451),x54452)+~P24(f331(f62(x54453),x54452))+~P24(f331(f140(x54453),x54451))
% 162.26/162.09 [5065]~P130(x50652)+~P131(x50652)+~P142(x50652)+~P115(x50652)+E(x50651,f2(x50652))+~E(f331(f331(f262(x50652),x50651),x50653),f2(x50652))
% 162.26/162.09 [5066]~P130(x50662)+~P131(x50662)+~P142(x50662)+~P115(x50662)+~E(x50661,f2(a883))+~E(f331(f331(f262(x50662),x50663),x50661),f2(x50662))
% 162.26/162.09 [6493]~P87(x64931)+~E(x64933,f2(x64931))+~E(x64932,f2(x64931))+E(f331(f331(f81(x64931),x64932),x64933),f2(x64931))+~P24(f331(f331(f247(x64931),f2(x64931)),x64933))+~P24(f331(f331(f247(x64931),f2(x64931)),x64932))
% 162.26/162.09 [8819]~E(f331(f260(a883,a883),x88193),f2(a883))+~E(x88191,f331(f331(f81(a883),f331(f331(f82(a883),f331(f260(a883,a883),x88193)),x88192)),f331(f269(a883,a883),x88193)))+P24(f331(f48(x88191,x88192),x88193))+~P24(f331(f331(f247(a883),f331(f269(a883,a883),x88193)),f2(a883)))+P24(f331(f331(f248(a883),f2(a883)),x88192))+~P24(f331(f331(f248(a883),x88192),f331(f269(a883,a883),x88193)))
% 162.26/162.09 [8827]E(x88271,f2(a883))+~E(x88272,f331(f331(f81(a883),f331(f331(f82(a883),f331(f260(a883,a883),x88273)),x88271)),f331(f269(a883,a883),x88273)))+P24(f331(f48(x88272,x88271),x88273))+~P24(f331(f331(f248(a883),f2(a883)),x88271))+~P24(f331(f331(f247(a883),f2(a883)),f331(f269(a883,a883),x88273)))+~P24(f331(f331(f248(a883),f331(f269(a883,a883),x88273)),x88271))
% 162.26/162.09 [8845]~E(f331(f260(a883,a883),x88453),f2(a883))+~E(x88451,f331(f331(f81(a883),f331(f331(f82(a883),f331(f260(a883,a883),x88453)),x88452)),f331(f269(a883,a883),x88453)))+P24(f331(f48(x88451,x88452),x88453))+~P24(f331(f331(f248(a883),f2(a883)),x88452))+~P24(f331(f331(f247(a883),f2(a883)),f331(f269(a883,a883),x88453)))+~P24(f331(f331(f248(a883),f331(f269(a883,a883),x88453)),x88452))
% 162.26/162.09 [6863]~P96(x68632)+E(x68631,f196(f891(x68632,a877)))+E(x68633,f196(f891(x68632,a877)))+~P24(f331(f62(x68632),x68631))+~P24(f331(f62(x68632),x68633))+E(f13(x68632,f331(f331(f107(f891(x68632,a877)),x68633),x68631)),f331(f331(f107(x68632),f13(x68632,x68633)),f13(x68632,x68631)))
% 162.26/162.09 [6864]~P107(x68642)+E(x68641,f196(f891(x68642,a877)))+E(x68643,f196(f891(x68642,a877)))+~P24(f331(f62(x68642),x68641))+~P24(f331(f62(x68642),x68643))+E(f14(x68642,f331(f331(f107(f891(x68642,a877)),x68643),x68641)),f331(f331(f251(x68642),f14(x68642,x68643)),f14(x68642,x68641)))
% 162.26/162.09 [6865]~P107(x68652)+E(x68651,f196(f891(x68652,a877)))+E(x68653,f196(f891(x68652,a877)))+~P24(f331(f62(x68652),x68651))+~P24(f331(f62(x68652),x68653))+E(f15(x68652,f331(f331(f107(f891(x68652,a877)),x68653),x68651)),f331(f331(f246(x68652),f15(x68652,x68653)),f15(x68652,x68651)))
% 162.26/162.09 [6866]~P96(x68662)+E(x68661,f196(f891(x68662,a877)))+E(x68663,f196(f891(x68662,a877)))+~P24(f331(f62(x68662),x68661))+~P24(f331(f62(x68662),x68663))+E(f10(x68662,f331(f331(f107(f891(x68662,a877)),x68663),x68661)),f331(f331(f108(x68662),f10(x68662,x68663)),f10(x68662,x68661)))
% 162.26/162.09 [7490]~P95(x74902)+E(x74901,f196(f891(x74902,a877)))+E(x74903,f196(f891(x74902,a877)))+~P24(f331(f62(x74902),x74901))+~P24(f331(f62(x74902),x74903))+E(f331(f331(f82(x74902),f331(f64(x74902,f82(x74902)),x74903)),f331(f64(x74902,f82(x74902)),x74901)),f331(f64(x74902,f82(x74902)),f331(f331(f107(f891(x74902,a877)),x74903),x74901)))
% 162.26/162.09 [7645]~P107(x76452)+E(x76451,f196(f891(x76452,a877)))+E(x76453,f196(f891(x76452,a877)))+~P24(f331(f62(x76452),x76451))+~P24(f331(f62(x76452),x76453))+E(f331(f331(f251(x76452),f11(x76452,f251(x76452),x76453)),f11(x76452,f251(x76452),x76451)),f11(x76452,f251(x76452),f331(f331(f107(f891(x76452,a877)),x76453),x76451)))
% 162.26/162.09 [7646]~P107(x76462)+E(x76461,f196(f891(x76462,a877)))+E(x76463,f196(f891(x76462,a877)))+~P24(f331(f62(x76462),x76461))+~P24(f331(f62(x76462),x76463))+E(f331(f331(f246(x76462),f12(x76462,f246(x76462),x76463)),f12(x76462,f246(x76462),x76461)),f12(x76462,f246(x76462),f331(f331(f107(f891(x76462,a877)),x76463),x76461)))
% 162.26/162.09 [8666]~P24(f331(x86661,x86663))+P24(f331(x86661,f434(x86661,x86662)))+P24(f331(x86661,f420(x86661,x86662)))+~P24(f331(f331(f248(a1),f2(a1)),x86662))+~P24(f331(f331(f333(a1),x86663),f302(a1,f79(a1),x86662)))+P24(f331(x86661,f331(f331(f22(a1),f420(x86661,x86662)),f331(f331(f82(a1),f433(x86661,x86662)),x86662))))
% 162.26/162.09 [8966]~P24(f331(x89661,x89663))+~P24(f331(x89661,f420(x89661,x89662)))+P24(f331(x89661,f434(x89661,x89662)))+~P24(f331(f331(f248(a1),f2(a1)),x89662))+~P24(f331(f331(f333(a1),x89663),f302(a1,f79(a1),x89662)))+~P24(f331(x89661,f331(f331(f22(a1),f420(x89661,x89662)),f331(f331(f82(a1),f433(x89661,x89662)),x89662))))
% 162.26/162.09 [10228]~P99(x102282)+E(x102281,f196(f891(x102282,a877)))+E(x102283,f196(f891(x102282,a877)))+~P24(f331(f62(x102282),x102281))+~P24(f331(f62(x102282),x102283))+E(f10(x102282,f331(f253(x102282),f331(f331(f8(f891(x102282,a877),a877,x102282),f87(x102282)),f331(f331(f8(f891(x102282,f891(x102282,a877)),f891(x102282,a877),x102282),f331(f8(f891(x102282,a877),a877,x102282),f87(x102282))),f331(f331(f7(x102282,f891(x102282,f891(x102282,a877)),f891(x102282,f891(x102282,a877))),f331(f331(f8(f891(x102282,f891(f891(x102282,a877),f891(x102282,a877))),f891(f891(x102282,f891(x102282,a877)),f891(x102282,f891(x102282,a877))),x102282),f18(x102282,f891(x102282,a877),f891(x102282,a877))),f331(f331(f8(f891(x102282,f891(x102282,f891(a877,a877))),f891(x102282,f891(f891(x102282,a877),f891(x102282,a877))),x102282),f331(f8(f891(x102282,f891(a877,a877)),f891(f891(x102282,a877),f891(x102282,a877)),x102282),f18(x102282,a877,a877))),f331(f331(f8(f891(x102282,f891(x102282,a877)),f891(x102282,f891(x102282,f891(a877,a877))),x102282),f331(f8(f891(x102282,a877),f891(x102282,f891(a877,a877)),x102282),f331(f8(a877,f891(a877,a877),x102282),a329))),f331(f331(f7(x102282,f891(x102282,f891(x102282,x102282)),f891(x102282,f891(x102282,a877))),f331(f331(f8(f891(f891(x102282,x102282),f891(x102282,a877)),f891(f891(x102282,f891(x102282,x102282)),f891(x102282,f891(x102282,a877))),x102282),f8(f891(x102282,x102282),f891(x102282,a877),x102282)),f331(f331(f8(f891(x102282,a877),f891(f891(x102282,x102282),f891(x102282,a877)),x102282),f8(x102282,a877,x102282)),a328))),f107(x102282)))))),f331(f331(f7(x102282,f891(x102282,a877),f891(x102282,a877)),f331(f331(f8(f891(a877,a877),f891(f891(x102282,a877),f891(x102282,a877)),x102282),f8(a877,a877,x102282)),f331(f331(f8(a877,f891(a877,a877),x102282),a329),f331(f331(f7(x102282,f891(x102282,a877),a877),f333(x102282)),x102283)))),f331(f331(f7(x102282,f891(x102282,a877),a877),f333(x102282)),x102281))))))),f331(f331(f107(x102282),f10(x102282,x102283)),f10(x102282,x102281)))
% 162.26/162.09 [10229]~P99(x102292)+E(x102291,f196(f891(x102292,a877)))+E(x102293,f196(f891(x102292,a877)))+~P24(f331(f62(x102292),x102291))+~P24(f331(f62(x102292),x102293))+E(f13(x102292,f331(f253(x102292),f331(f331(f8(f891(x102292,a877),a877,x102292),f87(x102292)),f331(f331(f8(f891(x102292,f891(x102292,a877)),f891(x102292,a877),x102292),f331(f8(f891(x102292,a877),a877,x102292),f87(x102292))),f331(f331(f7(x102292,f891(x102292,f891(x102292,a877)),f891(x102292,f891(x102292,a877))),f331(f331(f8(f891(x102292,f891(f891(x102292,a877),f891(x102292,a877))),f891(f891(x102292,f891(x102292,a877)),f891(x102292,f891(x102292,a877))),x102292),f18(x102292,f891(x102292,a877),f891(x102292,a877))),f331(f331(f8(f891(x102292,f891(x102292,f891(a877,a877))),f891(x102292,f891(f891(x102292,a877),f891(x102292,a877))),x102292),f331(f8(f891(x102292,f891(a877,a877)),f891(f891(x102292,a877),f891(x102292,a877)),x102292),f18(x102292,a877,a877))),f331(f331(f8(f891(x102292,f891(x102292,a877)),f891(x102292,f891(x102292,f891(a877,a877))),x102292),f331(f8(f891(x102292,a877),f891(x102292,f891(a877,a877)),x102292),f331(f8(a877,f891(a877,a877),x102292),a329))),f331(f331(f7(x102292,f891(x102292,f891(x102292,x102292)),f891(x102292,f891(x102292,a877))),f331(f331(f8(f891(f891(x102292,x102292),f891(x102292,a877)),f891(f891(x102292,f891(x102292,x102292)),f891(x102292,f891(x102292,a877))),x102292),f8(f891(x102292,x102292),f891(x102292,a877),x102292)),f331(f331(f8(f891(x102292,a877),f891(f891(x102292,x102292),f891(x102292,a877)),x102292),f8(x102292,a877,x102292)),a328))),f108(x102292)))))),f331(f331(f7(x102292,f891(x102292,a877),f891(x102292,a877)),f331(f331(f8(f891(a877,a877),f891(f891(x102292,a877),f891(x102292,a877)),x102292),f8(a877,a877,x102292)),f331(f331(f8(a877,f891(a877,a877),x102292),a329),f331(f331(f7(x102292,f891(x102292,a877),a877),f333(x102292)),x102293)))),f331(f331(f7(x102292,f891(x102292,a877),a877),f333(x102292)),x102291))))))),f331(f331(f108(x102292),f13(x102292,x102293)),f13(x102292,x102291)))
% 162.26/162.09 [10230]~P107(x102302)+E(x102301,f196(f891(x102302,a877)))+E(x102303,f196(f891(x102302,a877)))+~P24(f331(f62(x102302),x102301))+~P24(f331(f62(x102302),x102303))+E(f12(x102302,f246(x102302),f331(f253(x102302),f331(f331(f8(f891(x102302,a877),a877,x102302),f87(x102302)),f331(f331(f8(f891(x102302,f891(x102302,a877)),f891(x102302,a877),x102302),f331(f8(f891(x102302,a877),a877,x102302),f87(x102302))),f331(f331(f7(x102302,f891(x102302,f891(x102302,a877)),f891(x102302,f891(x102302,a877))),f331(f331(f8(f891(x102302,f891(f891(x102302,a877),f891(x102302,a877))),f891(f891(x102302,f891(x102302,a877)),f891(x102302,f891(x102302,a877))),x102302),f18(x102302,f891(x102302,a877),f891(x102302,a877))),f331(f331(f8(f891(x102302,f891(x102302,f891(a877,a877))),f891(x102302,f891(f891(x102302,a877),f891(x102302,a877))),x102302),f331(f8(f891(x102302,f891(a877,a877)),f891(f891(x102302,a877),f891(x102302,a877)),x102302),f18(x102302,a877,a877))),f331(f331(f8(f891(x102302,f891(x102302,a877)),f891(x102302,f891(x102302,f891(a877,a877))),x102302),f331(f8(f891(x102302,a877),f891(x102302,f891(a877,a877)),x102302),f331(f8(a877,f891(a877,a877),x102302),a329))),f331(f331(f7(x102302,f891(x102302,f891(x102302,x102302)),f891(x102302,f891(x102302,a877))),f331(f331(f8(f891(f891(x102302,x102302),f891(x102302,a877)),f891(f891(x102302,f891(x102302,x102302)),f891(x102302,f891(x102302,a877))),x102302),f8(f891(x102302,x102302),f891(x102302,a877),x102302)),f331(f331(f8(f891(x102302,a877),f891(f891(x102302,x102302),f891(x102302,a877)),x102302),f8(x102302,a877,x102302)),a328))),f251(x102302)))))),f331(f331(f7(x102302,f891(x102302,a877),f891(x102302,a877)),f331(f331(f8(f891(a877,a877),f891(f891(x102302,a877),f891(x102302,a877)),x102302),f8(a877,a877,x102302)),f331(f331(f8(a877,f891(a877,a877),x102302),a329),f331(f331(f7(x102302,f891(x102302,a877),a877),f333(x102302)),x102303)))),f331(f331(f7(x102302,f891(x102302,a877),a877),f333(x102302)),x102301))))))),f331(f331(f251(x102302),f12(x102302,f246(x102302),x102303)),f12(x102302,f246(x102302),x102301)))
% 162.26/162.09 [10231]~P107(x102312)+E(x102311,f196(f891(x102312,a877)))+E(x102313,f196(f891(x102312,a877)))+~P24(f331(f62(x102312),x102311))+~P24(f331(f62(x102312),x102313))+E(f11(x102312,f251(x102312),f331(f253(x102312),f331(f331(f8(f891(x102312,a877),a877,x102312),f87(x102312)),f331(f331(f8(f891(x102312,f891(x102312,a877)),f891(x102312,a877),x102312),f331(f8(f891(x102312,a877),a877,x102312),f87(x102312))),f331(f331(f7(x102312,f891(x102312,f891(x102312,a877)),f891(x102312,f891(x102312,a877))),f331(f331(f8(f891(x102312,f891(f891(x102312,a877),f891(x102312,a877))),f891(f891(x102312,f891(x102312,a877)),f891(x102312,f891(x102312,a877))),x102312),f18(x102312,f891(x102312,a877),f891(x102312,a877))),f331(f331(f8(f891(x102312,f891(x102312,f891(a877,a877))),f891(x102312,f891(f891(x102312,a877),f891(x102312,a877))),x102312),f331(f8(f891(x102312,f891(a877,a877)),f891(f891(x102312,a877),f891(x102312,a877)),x102312),f18(x102312,a877,a877))),f331(f331(f8(f891(x102312,f891(x102312,a877)),f891(x102312,f891(x102312,f891(a877,a877))),x102312),f331(f8(f891(x102312,a877),f891(x102312,f891(a877,a877)),x102312),f331(f8(a877,f891(a877,a877),x102312),a329))),f331(f331(f7(x102312,f891(x102312,f891(x102312,x102312)),f891(x102312,f891(x102312,a877))),f331(f331(f8(f891(f891(x102312,x102312),f891(x102312,a877)),f891(f891(x102312,f891(x102312,x102312)),f891(x102312,f891(x102312,a877))),x102312),f8(f891(x102312,x102312),f891(x102312,a877),x102312)),f331(f331(f8(f891(x102312,a877),f891(f891(x102312,x102312),f891(x102312,a877)),x102312),f8(x102312,a877,x102312)),a328))),f246(x102312)))))),f331(f331(f7(x102312,f891(x102312,a877),f891(x102312,a877)),f331(f331(f8(f891(a877,a877),f891(f891(x102312,a877),f891(x102312,a877)),x102312),f8(a877,a877,x102312)),f331(f331(f8(a877,f891(a877,a877),x102312),a329),f331(f331(f7(x102312,f891(x102312,a877),a877),f333(x102312)),x102313)))),f331(f331(f7(x102312,f891(x102312,a877),a877),f333(x102312)),x102311))))))),f331(f331(f246(x102312),f11(x102312,f251(x102312),x102313)),f11(x102312,f251(x102312),x102311)))
% 162.26/162.09 [7188]~P110(x71883)+E(x71881,x71882)+~E(f331(f331(f262(x71883),x71881),x71884),f331(f331(f262(x71883),x71882),x71884))+~P24(f331(f331(f247(x71883),f2(x71883)),x71882))+~P24(f331(f331(f247(x71883),f2(x71883)),x71881))+~P24(f331(f331(f248(a883),f2(a883)),x71884))
% 162.26/162.09 [7450]~P107(x74502)+E(x74501,f196(f891(x74502,a877)))+~P24(f331(f62(x74502),x74501))+~P24(f331(f331(f333(x74502),x74504),x74501))+P24(f331(f331(f248(x74502),x74503),x74504))+~P24(f331(f331(f248(x74502),x74503),f331(f64(x74502,f251(x74502)),x74501)))
% 162.26/162.09 [7451]~P107(x74512)+E(x74511,f196(f891(x74512,a877)))+~P24(f331(f62(x74512),x74511))+~P24(f331(f331(f333(x74512),x74514),x74511))+P24(f331(f331(f247(x74512),x74513),x74514))+~P24(f331(f331(f247(x74512),x74513),f331(f64(x74512,f251(x74512)),x74511)))
% 162.26/162.09 [7452]~P102(x74522)+E(x74521,f196(f891(x74522,a877)))+~P24(f331(f62(x74522),x74521))+~P24(f331(f331(f333(x74522),x74524),x74521))+P24(f331(f331(f247(x74522),x74523),x74524))+~P24(f331(f331(f247(x74522),x74523),f331(f64(x74522,f108(x74522)),x74521)))
% 162.26/162.09 [7351]E(x73511,f2(a1))+E(f331(f331(f39(a1),x73512),x73511),x73513)+~P24(f331(f331(f247(a1),x73514),f2(a1)))+~E(x73512,f331(f331(f81(a1),f331(f331(f82(a1),x73511),x73513)),x73514))+P24(f331(f331(f248(a1),f2(a1)),x73511))+~P24(f331(f331(f248(a1),x73511),x73514))
% 162.26/162.09 [7365]E(f45(a1,x73652,x73651),x73653)+E(x73651,f2(a1))+~P24(f331(f331(f247(a1),x73653),f2(a1)))+~E(x73652,f331(f331(f81(a1),f331(f331(f82(a1),x73651),x73654)),x73653))+P24(f331(f331(f248(a1),f2(a1)),x73651))+~P24(f331(f331(f248(a1),x73651),x73653))
% 162.26/162.09 [7489]E(x74891,f2(a1))+E(f331(f331(f39(a1),x74892),x74891),x74893)+~E(x74892,f331(f331(f81(a1),f331(f331(f82(a1),x74891),x74893)),x74894))+~P24(f331(f331(f248(a1),f2(a1)),x74891))+~P24(f331(f331(f247(a1),f2(a1)),x74894))+~P24(f331(f331(f248(a1),x74894),x74891))
% 162.26/162.09 [7511]E(f45(a1,x75112,x75111),x75113)+E(x75111,f2(a1))+~E(x75112,f331(f331(f81(a1),f331(f331(f82(a1),x75111),x75114)),x75113))+~P24(f331(f331(f248(a1),f2(a1)),x75111))+~P24(f331(f331(f247(a1),f2(a1)),x75113))+~P24(f331(f331(f248(a1),x75113),x75111))
% 162.26/162.09 [7649]~P107(x76492)+E(x76491,f196(f891(x76492,a877)))+~P24(f331(f62(x76492),x76491))+~P24(f331(f331(f248(x76492),x76494),x76493))+~P24(f331(f331(f333(x76492),x76494),x76491))+P24(f331(f331(f248(x76492),f331(f64(x76492,f251(x76492)),x76491)),x76493))
% 162.26/162.09 [7650]~P107(x76502)+E(x76501,f196(f891(x76502,a877)))+~P24(f331(f62(x76502),x76501))+~P24(f331(f331(f247(x76502),x76504),x76503))+~P24(f331(f331(f333(x76502),x76504),x76501))+P24(f331(f331(f247(x76502),f331(f64(x76502,f251(x76502)),x76501)),x76503))
% 162.26/162.09 [8221]~P24(f331(f331(f247(a1),x82214),f2(a1)))+~E(x82211,f331(f331(f81(a1),f331(f331(f82(a1),x82212),x82213)),x82214))+~P24(f331(f331(f247(a1),f2(a1)),x82214))+~P24(f331(f331(f248(a1),x82214),x82212))+~P24(f331(f331(f248(a1),x82212),x82214))+P24(f331(f49(x82211,x82212),f331(f331(f261(a1,a1),x82213),x82214)))
% 162.26/162.09 [9157]~P60(x91573)+~P60(x91574)+E(x91571,x91572)+~E(f331(f197(f884(x91573)),x91572),f331(f197(f884(x91574)),f56(x91574)))+~E(f331(f197(f884(x91573)),x91571),f331(f197(f884(x91574)),f56(x91574)))+~E(f331(f74(f887(x91573),x91573,x91574,f244(x91573)),f331(f180(x91574,x91573),f331(f331(f184(x91574,x91573),f56(x91574)),x91571))),f331(f74(f887(x91573),x91573,x91574,f244(x91573)),f331(f180(x91574,x91573),f331(f331(f184(x91574,x91573),f56(x91574)),x91572))))
% 162.26/162.09 [8381]~P108(x83811)+P24(f331(f331(f248(f891(x83811,a877)),f302(x83811,x83812,x83813)),f302(x83811,x83814,x83815)))+~P24(f331(f331(f248(x83811),x83813),x83815))+~P24(f331(f331(f247(x83811),x83814),x83812))+~P24(f331(f331(f247(x83811),x83814),x83815))+~P24(f331(f331(f247(x83811),x83813),x83815))
% 162.26/162.09 [8382]~P108(x83821)+P24(f331(f331(f248(f891(x83821,a877)),f302(x83821,x83822,x83823)),f302(x83821,x83824,x83825)))+~P24(f331(f331(f248(x83821),x83824),x83822))+~P24(f331(f331(f247(x83821),x83823),x83825))+~P24(f331(f331(f247(x83821),x83824),x83825))+~P24(f331(f331(f247(x83821),x83824),x83822))
% 162.26/162.09 [9221]P56(x92212,x92213,x92214,x92211)+E(x92211,f196(f891(x92212,a877)))+~P24(f331(f62(x92212),x92214))+~P24(f331(f62(x92212),x92211))+~P24(f331(f331(x92213,f522(x92211,x92214,x92213,x92212)),x92215))+~P24(f331(f331(f333(x92212),x92215),x92211))
% 162.26/162.09 [9377]~E(x93773,x93775)+~P73(x93771)+~P74(x93771)+~P40(x93773)+E(f331(f331(f9(a1,x93771),x93772),x93773),f331(f331(f9(a1,x93771),x93774),x93775))+P24(f331(f331(f247(a1),f2(a1)),f501(x93772,x93774,x93773,x93775,x93771)))
% 162.26/162.09 [9378]~E(x93783,x93785)+~P73(x93781)+~P74(x93781)+~P40(x93783)+E(f331(f331(f6(a1,x93781),x93782),x93783),f331(f331(f6(a1,x93781),x93784),x93785))+P24(f331(f331(f247(a1),f2(a1)),f502(x93782,x93784,x93783,x93785,x93781)))
% 162.26/162.09 [9550]~E(x95505,x95503)+~P73(x95501)+~P74(x95501)+~P40(x95505)+~E(f331(x95502,f501(x95504,x95502,x95505,x95503,x95501)),f331(x95504,f501(x95504,x95502,x95505,x95503,x95501)))+E(f331(f331(f9(a1,x95501),x95502),x95503),f331(f331(f9(a1,x95501),x95504),x95505))
% 162.26/162.09 [9551]~E(x95515,x95513)+~P73(x95511)+~P74(x95511)+~P40(x95515)+~E(f331(x95512,f502(x95514,x95512,x95515,x95513,x95511)),f331(x95514,f502(x95514,x95512,x95515,x95513,x95511)))+E(f331(f331(f6(a1,x95511),x95512),x95513),f331(f331(f6(a1,x95511),x95514),x95515))
% 162.26/162.09 [9651]~P77(x96513)+E(f331(x96511,x96512),f2(x96513))+~E(f331(f331(f6(x96514,x96513),x96511),x96515),f2(x96513))+~P24(f331(f62(x96514),x96515))+P24(f331(f331(f333(x96514),f463(x96512,x96511,x96515,x96514,x96513)),x96515))+~P24(f331(f331(f333(x96514),x96512),x96515))
% 162.26/162.09 [9798]~P77(x97983)+E(f331(x97981,x97982),f2(x97983))+~E(f331(f331(f6(x97984,x97983),x97981),x97985),f2(x97983))+~P24(f331(f62(x97984),x97985))+~P24(f331(f331(f333(x97984),x97982),x97985))+~P24(f331(f331(f247(x97983),f2(x97983)),f331(x97981,f463(x97982,x97981,x97985,x97984,x97983))))
% 162.26/162.09 [8301]~P132(x83011)+~P24(f331(f331(f247(x83011),f2(x83011)),x83013))+~P24(f331(f331(f248(x83011),x83013),x83015))+~P24(f331(f331(f248(x83011),x83012),x83014))+~P24(f331(f331(f248(x83011),f2(x83011)),x83014))+P24(f331(f331(f248(x83011),f331(f331(f82(x83011),x83012),x83013)),f331(f331(f82(x83011),x83014),x83015)))
% 162.26/162.09 [8302]~P132(x83021)+~P24(f331(f331(f247(x83021),f2(x83021)),x83023))+~P24(f331(f331(f247(x83021),f2(x83021)),x83022))+~P24(f331(f331(f248(x83021),x83023),x83025))+~P24(f331(f331(f248(x83021),x83022),x83024))+P24(f331(f331(f248(x83021),f331(f331(f82(x83021),x83022),x83023)),f331(f331(f82(x83021),x83024),x83025)))
% 162.26/162.09 [8303]~P132(x83031)+~P24(f331(f331(f247(x83031),x83032),x83034))+~P24(f331(f331(f247(x83031),f2(x83031)),x83033))+~P24(f331(f331(f248(x83031),x83033),x83035))+~P24(f331(f331(f248(x83031),f2(x83031)),x83032))+P24(f331(f331(f248(x83031),f331(f331(f82(x83031),x83032),x83033)),f331(f331(f82(x83031),x83034),x83035)))
% 162.26/162.09 [8304]~P132(x83041)+~P24(f331(f331(f247(x83041),x83043),x83045))+~P24(f331(f331(f247(x83041),f2(x83041)),x83042))+~P24(f331(f331(f248(x83041),x83042),x83044))+~P24(f331(f331(f248(x83041),f2(x83041)),x83043))+P24(f331(f331(f248(x83041),f331(f331(f82(x83041),x83042),x83043)),f331(f331(f82(x83041),x83044),x83045)))
% 162.26/162.09 [8305]~P64(x83051)+~P24(f331(f331(f247(x83051),x83052),x83054))+~P24(f331(f331(f248(x83051),x83055),x83053))+~P24(f331(f331(f248(x83051),f2(x83051)),x83055))+~P24(f331(f331(f248(x83051),f2(x83051)),x83052))+P24(f331(f331(f248(x83051),f331(f331(f289(x83051),x83052),x83053)),f331(f331(f289(x83051),x83054),x83055)))
% 162.26/162.09 [8306]~P64(x83061)+~P24(f331(f331(f247(x83061),x83065),x83063))+~P24(f331(f331(f247(x83061),f2(x83061)),x83062))+~P24(f331(f331(f248(x83061),x83062),x83064))+~P24(f331(f331(f248(x83061),f2(x83061)),x83065))+P24(f331(f331(f248(x83061),f331(f331(f289(x83061),x83062),x83063)),f331(f331(f289(x83061),x83064),x83065)))
% 162.26/162.09 [8307]~P135(x83071)+~P24(f331(f331(f247(x83071),x83073),x83075))+~P24(f331(f331(f247(x83071),x83072),x83074))+~P24(f331(f331(f247(x83071),f2(x83071)),x83073))+~P24(f331(f331(f247(x83071),f2(x83071)),x83074))+P24(f331(f331(f247(x83071),f331(f331(f82(x83071),x83072),x83073)),f331(f331(f82(x83071),x83074),x83075)))
% 162.26/162.09 [8308]~P135(x83081)+~P24(f331(f331(f247(x83081),x83083),x83085))+~P24(f331(f331(f247(x83081),x83082),x83084))+~P24(f331(f331(f247(x83081),f2(x83081)),x83083))+~P24(f331(f331(f247(x83081),f2(x83081)),x83082))+P24(f331(f331(f247(x83081),f331(f331(f82(x83081),x83082),x83083)),f331(f331(f82(x83081),x83084),x83085)))
% 162.26/162.09 [8309]~P64(x83091)+~P24(f331(f331(f248(x83091),f2(x83091)),x83095))+~P24(f331(f331(f247(x83091),x83095),x83093))+~P24(f331(f331(f247(x83091),x83092),x83094))+~P24(f331(f331(f247(x83091),f2(x83091)),x83092))+P24(f331(f331(f247(x83091),f331(f331(f289(x83091),x83092),x83093)),f331(f331(f289(x83091),x83094),x83095)))
% 162.26/162.09 [9688]~P84(x96885)+~P74(x96885)+E(x96881,f196(f891(x96882,a877)))+~P24(f331(f62(x96882),x96881))+P24(f331(f331(f333(x96882),f494(x96883,x96884,x96881,x96882,x96885)),x96881))+P24(f331(f331(f248(x96885),f331(f331(f6(x96882,x96885),x96884),x96881)),f331(f331(f6(x96882,x96885),x96883),x96881)))
% 162.26/162.09 [9817]~P82(x98171)+~P74(x98171)+~P24(f331(f62(x98172),x98175))+~P24(f331(f331(f247(x98171),f2(x98171)),f331(x98173,f460(x98173,x98174,x98175,x98172,x98171))))+P24(f331(f331(f247(x98171),f331(f331(f6(x98172,x98171),x98173),x98174)),f331(f331(f6(x98172,x98171),x98173),x98175)))+~P24(f331(f331(f247(f891(x98172,a877)),x98174),x98175))
% 162.26/162.09 [9966]~P84(x99663)+~P74(x99663)+E(x99661,f196(f891(x99662,a877)))+~P24(f331(f62(x99662),x99661))+~P24(f331(f331(f248(x99663),f331(x99664,f494(x99665,x99664,x99661,x99662,x99663))),f331(x99665,f494(x99665,x99664,x99661,x99662,x99663))))+P24(f331(f331(f248(x99663),f331(f331(f6(x99662,x99663),x99664),x99661)),f331(f331(f6(x99662,x99663),x99665),x99661)))
% 162.26/162.09 [7048]~P13(x70482,x70485,x70484)+E(x70481,f196(f891(x70482,a877)))+E(x70483,f196(f891(x70482,a877)))+~P24(f331(f62(x70482),x70481))+~P24(f331(f62(x70482),x70483))+E(f331(x70484,f331(f331(f107(f891(x70482,a877)),x70483),x70481)),f331(f331(x70485,f331(x70484,x70483)),f331(x70484,x70481)))
% 162.26/162.09 [7615]~P147(x76151,x76154,x76153)+P24(f331(x76151,x76152))+~P24(f331(f331(f248(a1),x76154),f2(a1)))+~P24(f331(f331(f247(a1),x76155),f2(a1)))+~E(x76153,f331(f331(f81(a1),f331(f331(f82(a1),x76154),x76152)),x76155))+~P24(f331(f331(f248(a1),x76154),x76155))
% 162.26/162.09 [7616]~P146(x76161,x76164,x76163)+P24(f331(x76161,x76162))+~P24(f331(f331(f248(a1),x76164),f2(a1)))+~P24(f331(f331(f247(a1),x76162),f2(a1)))+~E(x76163,f331(f331(f81(a1),f331(f331(f82(a1),x76164),x76165)),x76162))+~P24(f331(f331(f248(a1),x76164),x76162))
% 162.26/162.09 [7658]~P147(x76581,x76584,x76583)+P24(f331(x76581,x76582))+~E(x76583,f331(f331(f81(a1),f331(f331(f82(a1),x76584),x76582)),x76585))+~P24(f331(f331(f248(a1),f2(a1)),x76584))+~P24(f331(f331(f247(a1),f2(a1)),x76585))+~P24(f331(f331(f248(a1),x76585),x76584))
% 162.26/162.09 [7659]~P146(x76591,x76594,x76593)+P24(f331(x76591,x76592))+~E(x76593,f331(f331(f81(a1),f331(f331(f82(a1),x76594),x76595)),x76592))+~P24(f331(f331(f248(a1),f2(a1)),x76594))+~P24(f331(f331(f247(a1),f2(a1)),x76592))+~P24(f331(f331(f248(a1),x76592),x76594))
% 162.26/162.09 [8593]P24(f331(f331(x85931,x85932),x85933))+~P24(f331(f331(x85931,f331(f331(f39(a1),x85934),x85935)),f45(a1,x85934,x85935)))+~P24(f331(f331(f248(a1),x85935),f2(a1)))+~P24(f331(f331(f247(a1),x85933),f2(a1)))+~E(x85934,f331(f331(f81(a1),f331(f331(f82(a1),x85935),x85932)),x85933))+~P24(f331(f331(f248(a1),x85935),x85933))
% 162.26/162.09 [8602]P24(f331(f331(x86021,x86022),x86023))+~P24(f331(f331(x86021,f331(f331(f39(a1),x86024),x86025)),f45(a1,x86024,x86025)))+~E(x86024,f331(f331(f81(a1),f331(f331(f82(a1),x86025),x86022)),x86023))+~P24(f331(f331(f248(a1),f2(a1)),x86025))+~P24(f331(f331(f247(a1),f2(a1)),x86023))+~P24(f331(f331(f248(a1),x86023),x86025))
% 162.26/162.09 [8834]E(x88341,x88342)+~P53(x88343,x88345,x88344)+~P24(f331(f331(f333(x88343),x88342),x88345))+~P24(f331(f331(f333(x88343),x88341),x88345))+P24(f331(f331(f333(f890(x88343,x88343)),f331(f331(f261(x88343,x88343),x88341),x88342)),x88344))+P24(f331(f331(f333(f890(x88343,x88343)),f331(f331(f261(x88343,x88343),x88342),x88341)),x88344))
% 162.26/162.09 [9715]~P82(x97155)+~P74(x97155)+~P24(f331(f62(x97151),x97154))+P24(f331(f331(f247(x97155),f331(f331(f6(x97151,x97155),x97152),x97153)),f331(f331(f6(x97151,x97155),x97152),x97154)))+~P24(f331(f331(f247(f891(x97151,a877)),x97153),x97154))+P24(f331(f331(f333(x97151),f460(x97152,x97153,x97154,x97151,x97155)),f331(f331(f22(f891(x97151,a877)),x97154),x97153)))
% 162.26/162.09 [9824]E(x98241,f196(f891(x98242,a877)))+~P24(f331(f62(x98242),x98243))+~P24(f331(f62(x98242),x98241))+P24(f331(f331(f333(f890(f891(x98242,a877),f891(x98242,a877))),f331(f331(f261(f891(x98242,a877),f891(x98242,a877)),x98243),x98241)),f322(x98242,x98244)))+~P24(f331(f331(f333(x98242),x98245),x98241))+~P24(f331(f331(f333(f890(x98242,x98242)),f331(f331(f261(x98242,x98242),f526(x98244,x98241,x98243,x98242)),x98245)),x98244))
% 162.26/162.09 [9825]E(x98251,f196(f891(x98252,a877)))+~P24(f331(f62(x98252),x98253))+~P24(f331(f62(x98252),x98251))+P24(f331(f331(f333(f890(f891(x98252,a877),f891(x98252,a877))),f331(f331(f261(f891(x98252,a877),f891(x98252,a877)),x98253),x98251)),f322(x98252,x98254)))+~P24(f331(f331(f333(x98252),x98255),x98251))+~P24(f331(f331(f333(f890(x98252,x98252)),f331(f331(f261(x98252,x98252),f745(x98254,x98251,x98253,x98252)),x98255)),x98254))
% 162.26/162.09 [9971]~P77(x99711)+~E(f331(f331(f6(x99715,x99711),x99712),x99716),x99714)+~P24(f331(f62(x99715),x99716))+P24(f331(f331(f333(x99715),f461(x99713,x99714,x99712,x99716,x99715,x99711)),x99716))+P24(f331(f331(f247(x99711),f331(x99712,x99713)),x99714))+~P24(f331(f331(f333(x99715),x99713),x99716))
% 162.26/162.09 [10017]~P77(x100171)+~E(f331(f331(f6(x100175,x100171),x100172),x100176),x100174)+~P24(f331(f62(x100175),x100176))+~P24(f331(f331(f333(x100175),x100173),x100176))+~P24(f331(f331(f247(x100171),f2(x100171)),f331(x100172,f461(x100173,x100174,x100172,x100176,x100175,x100171))))+P24(f331(f331(f247(x100171),f331(x100172,x100173)),x100174))
% 162.26/162.09 [10160]~E(x101605,x101608)+~E(x101604,x101607)+~P109(x101601)+~P74(x101602)+E(f331(f331(f6(x101601,x101602),x101603),f331(f301(x101601,x101604),x101605)),f331(f331(f6(x101601,x101602),x101606),f331(f301(x101601,x101607),x101608)))+P24(f331(f331(f247(x101601),x101604),f758(x101603,x101606,x101605,x101608,x101604,x101607,x101601,x101602)))
% 162.26/162.09 [10183]~E(x101837,x101834)+~E(x101838,x101835)+~P109(x101831)+~P74(x101832)+~E(f331(x101833,f758(x101836,x101833,x101838,x101835,x101837,x101834,x101831,x101832)),f331(x101836,f758(x101836,x101833,x101838,x101835,x101837,x101834,x101831,x101832)))+E(f331(f331(f6(x101831,x101832),x101833),f331(f301(x101831,x101834),x101835)),f331(f331(f6(x101831,x101832),x101836),f331(f301(x101831,x101837),x101838)))
% 162.26/162.09 [10189]~E(x101894,x101897)+~E(x101895,x101898)+~P109(x101891)+~P74(x101892)+E(f331(f331(f6(x101891,x101892),x101893),f331(f301(x101891,x101894),x101895)),f331(f331(f6(x101891,x101892),x101896),f331(f301(x101891,x101897),x101898)))+P24(f331(f331(f248(x101891),f758(x101893,x101896,x101895,x101898,x101894,x101897,x101891,x101892)),x101895))
% 162.26/162.09 [9830]~P6(x98305,x98309,x98306)+~P6(x98301,x983010,x98303)+~P10(x98301,x98305,f891(x98302,a877),x98303,x98306,x98308)+~P24(f331(f331(f333(x98305),x98307),x98309))+~P24(f331(f331(f333(x98301),x98304),x983010))+E(f331(f331(f42(x98301,f891(x98302,a877)),f331(f285(x98301,x98301,x98303),f331(f331(f309(x98301),x98304),f196(f891(x98301,a877))))),f331(f331(f8(f891(x98305,f891(x98302,a877)),f891(x98302,a877),x98301),f331(f42(x98305,f891(x98302,a877)),f331(f285(x98305,x98305,x98306),f331(f331(f309(x98305),x98307),f196(f891(x98305,a877)))))),x98308)),f331(f331(x98308,x98304),x98307))
% 162.26/162.09 [5609]~P107(x56093)+~P29(x56093,x56092)+~P29(x56093,x56091)+E(x56091,x56092)+~E(f331(f175(x56093),x56091),f331(f175(x56093),x56092))+~P24(f331(f140(x56093),x56092))+~P24(f331(f140(x56093),x56091))
% 162.26/162.09 [4948]~P130(x49482)+~P131(x49482)+~P142(x49482)+~P115(x49482)+~E(x49483,f2(x49482))+E(x49481,f2(a883))+E(f331(f331(f262(x49482),x49483),x49481),f2(x49482))
% 162.26/162.09 [9087]E(x90871,f2(a883))+~E(x90872,f331(f331(f81(a883),f331(f331(f82(a883),f331(f260(a883,a883),x90873)),x90871)),f331(f269(a883,a883),x90873)))+P24(f331(f48(x90872,x90871),x90873))+~P24(f331(f331(f247(a883),f331(f269(a883,a883),x90873)),f2(a883)))+~P24(f331(f331(f247(a883),f2(a883)),f331(f269(a883,a883),x90873)))+~P24(f331(f331(f248(a883),x90871),f331(f269(a883,a883),x90873)))+~P24(f331(f331(f248(a883),f331(f269(a883,a883),x90873)),x90871))
% 162.26/162.09 [9102]~E(f331(f260(a883,a883),x91023),f2(a883))+~E(x91021,f331(f331(f81(a883),f331(f331(f82(a883),f331(f260(a883,a883),x91023)),x91022)),f331(f269(a883,a883),x91023)))+P24(f331(f48(x91021,x91022),x91023))+~P24(f331(f331(f247(a883),f331(f269(a883,a883),x91023)),f2(a883)))+~P24(f331(f331(f247(a883),f2(a883)),f331(f269(a883,a883),x91023)))+~P24(f331(f331(f248(a883),x91022),f331(f269(a883,a883),x91023)))+~P24(f331(f331(f248(a883),f331(f269(a883,a883),x91023)),x91022))
% 162.26/162.09 [7963]~P71(x79632)+E(x79631,f196(f891(x79632,a877)))+E(x79633,f196(f891(x79632,a877)))+~P24(f331(f62(x79632),x79631))+~P24(f331(f62(x79632),x79633))+~E(f331(f331(f108(f891(x79632,a877)),x79633),x79631),f196(f891(x79632,a877)))+E(f331(f331(f82(x79632),f331(f64(x79632,f82(x79632)),x79633)),f331(f64(x79632,f82(x79632)),x79631)),f331(f64(x79632,f82(x79632)),f331(f331(f107(f891(x79632,a877)),x79633),x79631)))
% 162.26/162.09 [7754]E(x77541,f2(a1))+E(f331(f331(f39(a1),x77542),x77541),x77543)+~P24(f331(f331(f247(a1),x77544),f2(a1)))+~E(x77542,f331(f331(f81(a1),f331(f331(f82(a1),x77541),x77543)),x77544))+~P24(f331(f331(f247(a1),f2(a1)),x77544))+~P24(f331(f331(f248(a1),x77544),x77541))+~P24(f331(f331(f248(a1),x77541),x77544))
% 162.26/162.09 [7761]E(f45(a1,x77612,x77611),x77613)+E(x77611,f2(a1))+~P24(f331(f331(f247(a1),x77613),f2(a1)))+~E(x77612,f331(f331(f81(a1),f331(f331(f82(a1),x77611),x77614)),x77613))+~P24(f331(f331(f247(a1),f2(a1)),x77613))+~P24(f331(f331(f248(a1),x77613),x77611))+~P24(f331(f331(f248(a1),x77611),x77613))
% 162.26/162.09 [7666]~P14(x76662,x76665,x76664)+E(x76661,f196(f891(x76662,a877)))+E(x76663,f196(f891(x76662,a877)))+~P24(f331(f62(x76662),x76661))+~P24(f331(f62(x76662),x76663))+~E(f331(f331(f108(f891(x76662,a877)),x76663),x76661),f196(f891(x76662,a877)))+E(f331(x76664,f331(f331(f107(f891(x76662,a877)),x76663),x76661)),f331(f331(x76665,f331(x76664,x76663)),f331(x76664,x76661)))
% 162.26/162.09 [9345]~P21(x93453,x93451,x93455,x93454)+~P21(x93451,x93453,x93456,x93452)+E(f331(f38(x93451),x93452),f331(f38(x93453),x93454))+~P24(f331(f62(x93453),x93454))+~P24(f331(f62(x93451),x93452))+~P24(f331(f331(f247(f891(x93453,a877)),f331(f310(x93451,x93453,x93456),x93452)),x93454))+~P24(f331(f331(f247(f891(x93451,a877)),f331(f310(x93453,x93451,x93455),x93454)),x93452))
% 162.26/162.09 [9294]~P24(f331(f331(f248(a1),f331(f331(f81(a1),f331(f331(f82(a1),x92945),x92941)),x92946)),f2(a1)))+~E(f331(f331(f81(a1),f331(f331(f82(a1),x92943),x92942)),x92944),f331(f331(f81(a1),f331(f331(f82(a1),x92945),x92941)),x92946))+~P24(f331(f331(f248(a1),f2(a1)),x92945))+~P24(f331(f331(f247(a1),f2(a1)),x92946))+~P24(f331(f331(f248(a1),x92944),x92943))+~P24(f331(f331(f247(a1),x92945),x92943))+P24(f331(f331(f247(a1),x92941),x92942))
% 162.26/162.09 [9046]~E(f331(f331(f81(a1),f331(f331(f82(a1),x90463),x90461)),x90464),f331(f331(f81(a1),f331(f331(f82(a1),x90465),x90462)),x90466))+~P24(f331(f331(f248(a1),f2(a1)),x90465))+~P24(f331(f331(f247(a1),f2(a1)),x90464))+~P24(f331(f331(f248(a1),x90466),x90465))+~P24(f331(f331(f247(a1),x90465),x90463))+P24(f331(f331(f247(a1),x90461),x90462))+~P24(f331(f331(f247(a1),f2(a1)),f331(f331(f81(a1),f331(f331(f82(a1),x90465),x90462)),x90466)))
% 162.26/162.09 [9227]~P127(x92271)+~E(f331(f331(f81(x92271),x92272),x92274),f79(x92271))+~P24(f331(f331(f247(x92271),f2(x92271)),x92274))+~P24(f331(f331(f247(x92271),f2(x92271)),x92272))+~P24(f331(f331(f248(x92271),x92275),x92276))+~P24(f331(f331(f248(x92271),x92273),x92276))+P24(f331(f331(f248(x92271),f331(f331(f81(x92271),f331(f331(f82(x92271),x92272),x92273)),f331(f331(f82(x92271),x92274),x92275))),x92276))
% 162.26/162.09 [9228]~P129(x92281)+~E(f331(f331(f81(x92281),x92282),x92284),f79(x92281))+~P24(f331(f331(f247(x92281),x92285),x92286))+~P24(f331(f331(f247(x92281),x92283),x92286))+~P24(f331(f331(f247(x92281),f2(x92281)),x92284))+~P24(f331(f331(f247(x92281),f2(x92281)),x92282))+P24(f331(f331(f247(x92281),f331(f331(f81(x92281),f331(f331(f82(x92281),x92282),x92283)),f331(f331(f82(x92281),x92284),x92285))),x92286))
% 162.26/162.09 [10059]~P6(x100597,x100596,x100595)+E(x100591,x100592)+~P9(x100597,f891(x100594,a877),x100595,x100593)+E(f331(x100593,f466(x100591,x100592,x100593,x100594,x100595,x100596,x100597)),f331(x100593,f467(x100591,x100592,x100593,x100594,x100595,x100596,x100597)))+~E(f331(f331(f42(x100597,f891(x100594,a877)),x100591),x100593),f331(f331(f42(x100597,f891(x100594,a877)),x100592),x100593))+~P24(f331(f331(f333(f891(x100597,a877)),x100592),f331(f331(f61(x100597),x100596),x100595)))+~P24(f331(f331(f333(f891(x100597,a877)),x100591),f331(f331(f61(x100597),x100596),x100595)))
% 162.26/162.09 [10101]~P6(x101013,x101017,x101016)+E(x101011,x101012)+~P9(x101013,f891(x101015,a877),x101016,x101014)+~E(f331(f331(f42(x101013,f891(x101015,a877)),x101011),x101014),f331(f331(f42(x101013,f891(x101015,a877)),x101012),x101014))+P24(f331(f331(f333(x101013),f467(x101011,x101012,x101014,x101015,x101016,x101017,x101013)),x101017))+~P24(f331(f331(f333(f891(x101013,a877)),x101012),f331(f331(f61(x101013),x101017),x101016)))+~P24(f331(f331(f333(f891(x101013,a877)),x101011),f331(f331(f61(x101013),x101017),x101016)))
% 162.26/162.09 [10102]~P6(x101023,x101027,x101026)+E(x101021,x101022)+~P9(x101023,f891(x101025,a877),x101026,x101024)+~E(f331(f331(f42(x101023,f891(x101025,a877)),x101021),x101024),f331(f331(f42(x101023,f891(x101025,a877)),x101022),x101024))+P24(f331(f331(f333(x101023),f466(x101021,x101022,x101024,x101025,x101026,x101027,x101023)),x101027))+~P24(f331(f331(f333(f891(x101023,a877)),x101022),f331(f331(f61(x101023),x101027),x101026)))+~P24(f331(f331(f333(f891(x101023,a877)),x101021),f331(f331(f61(x101023),x101027),x101026)))
% 162.26/162.09 [10209]E(x102091,x102092)+~P6(x102093,x102096,x102097)+~P9(x102093,f891(x102094,a877),x102097,x102095)+~E(f331(f331(f42(x102093,f891(x102094,a877)),x102091),x102095),f331(f331(f42(x102093,f891(x102094,a877)),x102092),x102095))+~P24(f331(f331(f333(f890(x102093,x102093)),f331(f331(f261(x102093,x102093),f467(x102091,x102092,x102095,x102094,x102097,x102096,x102093)),f466(x102091,x102092,x102095,x102094,x102097,x102096,x102093))),x102097))+~P24(f331(f331(f333(f891(x102093,a877)),x102092),f331(f331(f61(x102093),x102096),x102097)))+~P24(f331(f331(f333(f891(x102093,a877)),x102091),f331(f331(f61(x102093),x102096),x102097)))
% 162.26/162.09 [9045]~P6(x90451,x90457,x90454)+~E(x90455,x90456)+~P24(f331(f331(f333(x90451),x90453),x90456))+~P24(f331(f331(f333(x90451),x90452),x90455))+~P24(f331(f331(f333(f891(x90451,a877)),x90456),f331(f331(f61(x90451),x90457),x90454)))+~P24(f331(f331(f333(f891(x90451,a877)),x90455),f331(f331(f61(x90451),x90457),x90454)))+P24(f331(f331(f333(f890(x90451,x90451)),f331(f331(f261(x90451,x90451),x90452),x90453)),x90454))
% 162.26/162.09 [9185]E(x91851,x91852)+~P6(x91853,x91854,x91855)+~P24(f331(f331(f333(x91853),x91856),x91852))+~P24(f331(f331(f333(x91853),x91857),x91851))+~P24(f331(f331(f333(f891(x91853,a877)),x91852),f331(f331(f61(x91853),x91854),x91855)))+~P24(f331(f331(f333(f891(x91853,a877)),x91851),f331(f331(f61(x91853),x91854),x91855)))+~P24(f331(f331(f333(f890(x91853,x91853)),f331(f331(f261(x91853,x91853),x91857),x91856)),x91855))
% 162.26/162.09 [10235]~P6(x102359,x102358,x102357)+~P6(x102351,x1023511,x1023510)+~P10(x102351,x102359,f891(x102356,a877),x1023510,x102357,x102355)+P24(f331(f331(f333(x102351),f468(x102352,x102353,x102354,x102355,x102356,x102357,x102358,x102359,x1023510,x1023511,x102351)),x1023511))+~P24(f331(f331(f333(f891(x102359,a877)),x102353),f331(f331(f61(x102359),x102358),x102357)))+~P24(f331(f331(f333(f891(x102351,a877)),x102354),f331(f331(f61(x102351),x1023511),x1023510)))+P24(f331(f331(f333(f891(x102356,a877)),f331(f331(f42(x102351,f891(x102356,a877)),x102354),f331(f331(f8(f891(x102359,f891(x102356,a877)),f891(x102356,a877),x102351),f331(f42(x102359,f891(x102356,a877)),x102353)),x102355))),x102352))
% 162.26/162.09 [10236]~P6(x1023611,x1023610,x102369)+~P6(x102361,x102368,x102367)+~P10(x1023611,x102361,f891(x102366,a877),x102369,x102367,x102365)+P24(f331(f331(f333(x102361),f469(x102362,x102363,x102364,x102365,x102366,x102367,x102368,x102361,x102369,x1023610,x1023611)),x102368))+~P24(f331(f331(f333(f891(x1023611,a877)),x102364),f331(f331(f61(x1023611),x1023610),x102369)))+~P24(f331(f331(f333(f891(x102361,a877)),x102363),f331(f331(f61(x102361),x102368),x102367)))+P24(f331(f331(f333(f891(x102366,a877)),f331(f331(f42(x1023611,f891(x102366,a877)),x102364),f331(f331(f8(f891(x102361,f891(x102366,a877)),f891(x102366,a877),x1023611),f331(f42(x102361,f891(x102366,a877)),x102363)),x102365))),x102362))
% 162.26/162.09 [10239]~P6(x102392,x102398,x102399)+~P6(x102394,x1023910,x1023911)+~P10(x102392,x102394,f891(x102391,a877),x102399,x1023911,x102396)+~P24(f331(f331(f333(f891(x102392,a877)),x102393),f331(f331(f61(x102392),x102398),x102399)))+~P24(f331(f331(f333(f891(x102394,a877)),x102395),f331(f331(f61(x102394),x1023910),x1023911)))+~P24(f331(f331(f333(f891(x102391,a877)),f331(f331(x102396,f468(x102397,x102395,x102393,x102396,x102391,x1023911,x1023910,x102394,x102399,x102398,x102392)),f469(x102397,x102395,x102393,x102396,x102391,x1023911,x1023910,x102394,x102399,x102398,x102392))),x102397))+P24(f331(f331(f333(f891(x102391,a877)),f331(f331(f42(x102392,f891(x102391,a877)),x102393),f331(f331(f8(f891(x102394,f891(x102391,a877)),f891(x102391,a877),x102392),f331(f42(x102394,f891(x102391,a877)),x102395)),x102396))),x102397))
% 162.26/162.09 [9074]E(x90741,x90742)+~P107(x90744)+~P21(x90743,x90744,x90745,f331(f331(f107(f891(x90743,a877)),f331(f175(x90743),x90741)),f331(f175(x90743),x90742)))+~E(f331(f175(x90743),x90741),f331(f175(x90743),x90742))+~P29(x90744,f331(f331(f157(x90743,x90744),x90745),x90742))+~P29(x90744,f331(f331(f157(x90743,x90744),x90745),x90741))+~P24(f331(f140(x90744),f331(f331(f157(x90743,x90744),x90745),x90742)))+~P24(f331(f140(x90744),f331(f331(f157(x90743,x90744),x90745),x90741)))
% 162.26/162.09 %EqnAxiom
% 162.26/162.09 [1]E(x11,x11)
% 162.26/162.09 [2]E(x22,x21)+~E(x21,x22)
% 162.26/162.09 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 162.26/162.09 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 162.26/162.09 [5]~E(x51,x52)+E(f106(x51),f106(x52))
% 162.26/162.09 [6]~E(x61,x62)+E(f22(x61),f22(x62))
% 162.26/162.09 [7]~E(x71,x72)+E(f196(x71),f196(x72))
% 162.26/162.09 [8]~E(x81,x82)+E(f331(x81,x83),f331(x82,x83))
% 162.26/162.09 [9]~E(x91,x92)+E(f331(x93,x91),f331(x93,x92))
% 162.26/162.09 [10]~E(x101,x102)+E(f32(x101),f32(x102))
% 162.26/162.09 [11]~E(x111,x112)+E(f79(x111),f79(x112))
% 162.26/162.09 [12]~E(x121,x122)+E(f85(x121),f85(x122))
% 162.26/162.09 [13]~E(x131,x132)+E(f81(x131),f81(x132))
% 162.26/162.09 [14]~E(x141,x142)+E(f121(x141),f121(x142))
% 162.26/162.09 [15]~E(x151,x152)+E(f469(x151,x153,x154,x155,x156,x157,x158,x159,x1510,x1511,x1512),f469(x152,x153,x154,x155,x156,x157,x158,x159,x1510,x1511,x1512))
% 162.26/162.09 [16]~E(x161,x162)+E(f469(x163,x161,x164,x165,x166,x167,x168,x169,x1610,x1611,x1612),f469(x163,x162,x164,x165,x166,x167,x168,x169,x1610,x1611,x1612))
% 162.26/162.09 [17]~E(x171,x172)+E(f469(x173,x174,x171,x175,x176,x177,x178,x179,x1710,x1711,x1712),f469(x173,x174,x172,x175,x176,x177,x178,x179,x1710,x1711,x1712))
% 162.26/162.09 [18]~E(x181,x182)+E(f469(x183,x184,x185,x181,x186,x187,x188,x189,x1810,x1811,x1812),f469(x183,x184,x185,x182,x186,x187,x188,x189,x1810,x1811,x1812))
% 162.26/162.09 [19]~E(x191,x192)+E(f469(x193,x194,x195,x196,x191,x197,x198,x199,x1910,x1911,x1912),f469(x193,x194,x195,x196,x192,x197,x198,x199,x1910,x1911,x1912))
% 162.26/162.09 [20]~E(x201,x202)+E(f469(x203,x204,x205,x206,x207,x201,x208,x209,x2010,x2011,x2012),f469(x203,x204,x205,x206,x207,x202,x208,x209,x2010,x2011,x2012))
% 162.26/162.09 [21]~E(x211,x212)+E(f469(x213,x214,x215,x216,x217,x218,x211,x219,x2110,x2111,x2112),f469(x213,x214,x215,x216,x217,x218,x212,x219,x2110,x2111,x2112))
% 162.26/162.09 [22]~E(x221,x222)+E(f469(x223,x224,x225,x226,x227,x228,x229,x221,x2210,x2211,x2212),f469(x223,x224,x225,x226,x227,x228,x229,x222,x2210,x2211,x2212))
% 162.26/162.09 [23]~E(x231,x232)+E(f469(x233,x234,x235,x236,x237,x238,x239,x2310,x231,x2311,x2312),f469(x233,x234,x235,x236,x237,x238,x239,x2310,x232,x2311,x2312))
% 162.26/162.09 [24]~E(x241,x242)+E(f469(x243,x244,x245,x246,x247,x248,x249,x2410,x2411,x241,x2412),f469(x243,x244,x245,x246,x247,x248,x249,x2410,x2411,x242,x2412))
% 162.26/162.09 [25]~E(x251,x252)+E(f469(x253,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512,x251),f469(x253,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512,x252))
% 162.26/162.09 [26]~E(x261,x262)+E(f107(x261),f107(x262))
% 162.26/162.09 [27]~E(x271,x272)+E(f246(x271),f246(x272))
% 162.26/162.09 [28]~E(x281,x282)+E(f251(x281),f251(x282))
% 162.26/162.09 [29]~E(x291,x292)+E(f108(x291),f108(x292))
% 162.26/162.09 [30]~E(x301,x302)+E(f109(x301),f109(x302))
% 162.26/162.09 [31]~E(x311,x312)+E(f35(x311),f35(x312))
% 162.26/162.09 [32]~E(x321,x322)+E(f66(x321,x323,x324),f66(x322,x323,x324))
% 162.26/162.09 [33]~E(x331,x332)+E(f66(x333,x331,x334),f66(x333,x332,x334))
% 162.26/162.09 [34]~E(x341,x342)+E(f66(x343,x344,x341),f66(x343,x344,x342))
% 162.26/162.09 [35]~E(x351,x352)+E(f128(x351,x353),f128(x352,x353))
% 162.26/162.09 [36]~E(x361,x362)+E(f128(x363,x361),f128(x363,x362))
% 162.26/162.09 [37]~E(x371,x372)+E(f468(x371,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712),f468(x372,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712))
% 162.26/162.09 [38]~E(x381,x382)+E(f468(x383,x381,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812),f468(x383,x382,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812))
% 162.26/162.09 [39]~E(x391,x392)+E(f468(x393,x394,x391,x395,x396,x397,x398,x399,x3910,x3911,x3912),f468(x393,x394,x392,x395,x396,x397,x398,x399,x3910,x3911,x3912))
% 162.26/162.09 [40]~E(x401,x402)+E(f468(x403,x404,x405,x401,x406,x407,x408,x409,x4010,x4011,x4012),f468(x403,x404,x405,x402,x406,x407,x408,x409,x4010,x4011,x4012))
% 162.26/162.09 [41]~E(x411,x412)+E(f468(x413,x414,x415,x416,x411,x417,x418,x419,x4110,x4111,x4112),f468(x413,x414,x415,x416,x412,x417,x418,x419,x4110,x4111,x4112))
% 162.26/162.09 [42]~E(x421,x422)+E(f468(x423,x424,x425,x426,x427,x421,x428,x429,x4210,x4211,x4212),f468(x423,x424,x425,x426,x427,x422,x428,x429,x4210,x4211,x4212))
% 162.26/162.09 [43]~E(x431,x432)+E(f468(x433,x434,x435,x436,x437,x438,x431,x439,x4310,x4311,x4312),f468(x433,x434,x435,x436,x437,x438,x432,x439,x4310,x4311,x4312))
% 162.26/162.09 [44]~E(x441,x442)+E(f468(x443,x444,x445,x446,x447,x448,x449,x441,x4410,x4411,x4412),f468(x443,x444,x445,x446,x447,x448,x449,x442,x4410,x4411,x4412))
% 162.26/162.09 [45]~E(x451,x452)+E(f468(x453,x454,x455,x456,x457,x458,x459,x4510,x451,x4511,x4512),f468(x453,x454,x455,x456,x457,x458,x459,x4510,x452,x4511,x4512))
% 162.26/162.09 [46]~E(x461,x462)+E(f468(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x461,x4612),f468(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x462,x4612))
% 162.26/162.09 [47]~E(x471,x472)+E(f468(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x471),f468(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x472))
% 162.26/162.09 [48]~E(x481,x482)+E(f117(x481),f117(x482))
% 162.26/162.09 [49]~E(x491,x492)+E(f333(x491),f333(x492))
% 162.26/162.09 [50]~E(x501,x502)+E(f891(x501,x503),f891(x502,x503))
% 162.26/162.09 [51]~E(x511,x512)+E(f891(x513,x511),f891(x513,x512))
% 162.26/162.09 [52]~E(x521,x522)+E(f4(x521),f4(x522))
% 162.26/162.09 [53]~E(x531,x532)+E(f248(x531),f248(x532))
% 162.26/162.09 [54]~E(x541,x542)+E(f882(x541),f882(x542))
% 162.26/162.09 [55]~E(x551,x552)+E(f887(x551),f887(x552))
% 162.26/162.09 [56]~E(x561,x562)+E(f884(x561),f884(x562))
% 162.26/162.09 [57]~E(x571,x572)+E(f885(x571),f885(x572))
% 162.26/162.09 [58]~E(x581,x582)+E(f303(x581),f303(x582))
% 162.26/162.09 [59]~E(x591,x592)+E(f247(x591),f247(x592))
% 162.26/162.09 [60]~E(x601,x602)+E(f139(x601,x603),f139(x602,x603))
% 162.26/162.09 [61]~E(x611,x612)+E(f139(x613,x611),f139(x613,x612))
% 162.26/162.09 [62]~E(x621,x622)+E(f39(x621),f39(x622))
% 162.26/162.09 [63]~E(x631,x632)+E(f80(x631),f80(x632))
% 162.26/162.09 [64]~E(x641,x642)+E(f890(x641,x643),f890(x642,x643))
% 162.26/162.09 [65]~E(x651,x652)+E(f890(x653,x651),f890(x653,x652))
% 162.26/162.09 [66]~E(x661,x662)+E(f197(x661),f197(x662))
% 162.26/162.09 [67]~E(x671,x672)+E(f154(x671),f154(x672))
% 162.26/162.09 [68]~E(x681,x682)+E(f110(x681),f110(x682))
% 162.26/162.09 [69]~E(x691,x692)+E(f151(x691,x693,x694),f151(x692,x693,x694))
% 162.26/162.09 [70]~E(x701,x702)+E(f151(x703,x701,x704),f151(x703,x702,x704))
% 162.26/162.09 [71]~E(x711,x712)+E(f151(x713,x714,x711),f151(x713,x714,x712))
% 162.26/162.09 [72]~E(x721,x722)+E(f160(x721,x723),f160(x722,x723))
% 162.26/162.09 [73]~E(x731,x732)+E(f160(x733,x731),f160(x733,x732))
% 162.26/162.09 [74]~E(x741,x742)+E(f82(x741),f82(x742))
% 162.26/162.09 [75]~E(x751,x752)+E(f271(x751,x753,x754,x755,x756,x757),f271(x752,x753,x754,x755,x756,x757))
% 162.26/162.09 [76]~E(x761,x762)+E(f271(x763,x761,x764,x765,x766,x767),f271(x763,x762,x764,x765,x766,x767))
% 162.26/162.09 [77]~E(x771,x772)+E(f271(x773,x774,x771,x775,x776,x777),f271(x773,x774,x772,x775,x776,x777))
% 162.26/162.09 [78]~E(x781,x782)+E(f271(x783,x784,x785,x781,x786,x787),f271(x783,x784,x785,x782,x786,x787))
% 162.26/162.09 [79]~E(x791,x792)+E(f271(x793,x794,x795,x796,x791,x797),f271(x793,x794,x795,x796,x792,x797))
% 162.26/162.09 [80]~E(x801,x802)+E(f271(x803,x804,x805,x806,x807,x801),f271(x803,x804,x805,x806,x807,x802))
% 162.26/162.09 [81]~E(x811,x812)+E(f62(x811),f62(x812))
% 162.26/162.09 [82]~E(x821,x822)+E(f45(x821,x823,x824),f45(x822,x823,x824))
% 162.26/162.09 [83]~E(x831,x832)+E(f45(x833,x831,x834),f45(x833,x832,x834))
% 162.26/162.09 [84]~E(x841,x842)+E(f45(x843,x844,x841),f45(x843,x844,x842))
% 162.26/162.09 [85]~E(x851,x852)+E(f38(x851),f38(x852))
% 162.26/162.09 [86]~E(x861,x862)+E(f268(x861,x863),f268(x862,x863))
% 162.26/162.09 [87]~E(x871,x872)+E(f268(x873,x871),f268(x873,x872))
% 162.26/162.09 [88]~E(x881,x882)+E(f277(x881,x883),f277(x882,x883))
% 162.26/162.09 [89]~E(x891,x892)+E(f277(x893,x891),f277(x893,x892))
% 162.26/162.09 [90]~E(x901,x902)+E(f8(x901,x903,x904),f8(x902,x903,x904))
% 162.26/162.09 [91]~E(x911,x912)+E(f8(x913,x911,x914),f8(x913,x912,x914))
% 162.26/162.09 [92]~E(x921,x922)+E(f8(x923,x924,x921),f8(x923,x924,x922))
% 162.26/162.09 [93]~E(x931,x932)+E(f269(x931,x933),f269(x932,x933))
% 162.26/162.09 [94]~E(x941,x942)+E(f269(x943,x941),f269(x943,x942))
% 162.26/162.09 [95]~E(x951,x952)+E(f140(x951),f140(x952))
% 162.26/162.09 [96]~E(x961,x962)+E(f61(x961),f61(x962))
% 162.26/162.09 [97]~E(x971,x972)+E(f261(x971,x973),f261(x972,x973))
% 162.26/162.09 [98]~E(x981,x982)+E(f261(x983,x981),f261(x983,x982))
% 162.26/162.09 [99]~E(x991,x992)+E(f49(x991,x993),f49(x992,x993))
% 162.26/162.09 [100]~E(x1001,x1002)+E(f49(x1003,x1001),f49(x1003,x1002))
% 162.26/162.09 [101]~E(x1011,x1012)+E(f74(x1011,x1013,x1014,x1015),f74(x1012,x1013,x1014,x1015))
% 162.26/162.09 [102]~E(x1021,x1022)+E(f74(x1023,x1021,x1024,x1025),f74(x1023,x1022,x1024,x1025))
% 162.26/162.09 [103]~E(x1031,x1032)+E(f74(x1033,x1034,x1031,x1035),f74(x1033,x1034,x1032,x1035))
% 162.26/162.09 [104]~E(x1041,x1042)+E(f74(x1043,x1044,x1045,x1041),f74(x1043,x1044,x1045,x1042))
% 162.26/162.09 [105]~E(x1051,x1052)+E(f42(x1051,x1053),f42(x1052,x1053))
% 162.26/162.09 [106]~E(x1061,x1062)+E(f42(x1063,x1061),f42(x1063,x1062))
% 162.26/162.09 [107]~E(x1071,x1072)+E(f168(x1071),f168(x1072))
% 162.26/162.09 [108]~E(x1081,x1082)+E(f47(x1081,x1083),f47(x1082,x1083))
% 162.26/162.09 [109]~E(x1091,x1092)+E(f47(x1093,x1091),f47(x1093,x1092))
% 162.26/162.09 [110]~E(x1101,x1102)+E(f239(x1101),f239(x1102))
% 162.26/162.09 [111]~E(x1111,x1112)+E(f260(x1111,x1113),f260(x1112,x1113))
% 162.26/162.09 [112]~E(x1121,x1122)+E(f260(x1123,x1121),f260(x1123,x1122))
% 162.26/162.09 [113]~E(x1131,x1132)+E(f420(x1131,x1133),f420(x1132,x1133))
% 162.26/162.09 [114]~E(x1141,x1142)+E(f420(x1143,x1141),f420(x1143,x1142))
% 162.26/162.09 [115]~E(x1151,x1152)+E(f825(x1151,x1153,x1154),f825(x1152,x1153,x1154))
% 162.26/162.09 [116]~E(x1161,x1162)+E(f825(x1163,x1161,x1164),f825(x1163,x1162,x1164))
% 162.26/162.09 [117]~E(x1171,x1172)+E(f825(x1173,x1174,x1171),f825(x1173,x1174,x1172))
% 162.26/162.09 [118]~E(x1181,x1182)+E(f137(x1181),f137(x1182))
% 162.26/162.09 [119]~E(x1191,x1192)+E(f199(x1191),f199(x1192))
% 162.26/162.09 [120]~E(x1201,x1202)+E(f169(x1201),f169(x1202))
% 162.26/162.09 [121]~E(x1211,x1212)+E(f175(x1211),f175(x1212))
% 162.26/162.09 [122]~E(x1221,x1222)+E(f13(x1221,x1223),f13(x1222,x1223))
% 162.26/162.09 [123]~E(x1231,x1232)+E(f13(x1233,x1231),f13(x1233,x1232))
% 162.26/162.09 [124]~E(x1241,x1242)+E(f83(x1241,x1243),f83(x1242,x1243))
% 162.26/162.09 [125]~E(x1251,x1252)+E(f83(x1253,x1251),f83(x1253,x1252))
% 162.26/162.09 [126]~E(x1261,x1262)+E(f310(x1261,x1263,x1264),f310(x1262,x1263,x1264))
% 162.26/162.09 [127]~E(x1271,x1272)+E(f310(x1273,x1271,x1274),f310(x1273,x1272,x1274))
% 162.26/162.09 [128]~E(x1281,x1282)+E(f310(x1283,x1284,x1281),f310(x1283,x1284,x1282))
% 162.26/162.09 [129]~E(x1291,x1292)+E(f73(x1291,x1293),f73(x1292,x1293))
% 162.26/162.09 [130]~E(x1301,x1302)+E(f73(x1303,x1301),f73(x1303,x1302))
% 162.26/162.09 [131]~E(x1311,x1312)+E(f256(x1311),f256(x1312))
% 162.26/162.09 [132]~E(x1321,x1322)+E(f43(x1321,x1323),f43(x1322,x1323))
% 162.26/162.09 [133]~E(x1331,x1332)+E(f43(x1333,x1331),f43(x1333,x1332))
% 162.26/162.09 [134]~E(x1341,x1342)+E(f9(x1341,x1343),f9(x1342,x1343))
% 162.26/162.09 [135]~E(x1351,x1352)+E(f9(x1353,x1351),f9(x1353,x1352))
% 162.26/162.09 [136]~E(x1361,x1362)+E(f307(x1361,x1363),f307(x1362,x1363))
% 162.26/162.09 [137]~E(x1371,x1372)+E(f307(x1373,x1371),f307(x1373,x1372))
% 162.26/162.09 [138]~E(x1381,x1382)+E(f16(x1381,x1383),f16(x1382,x1383))
% 162.26/162.09 [139]~E(x1391,x1392)+E(f16(x1393,x1391),f16(x1393,x1392))
% 162.26/162.09 [140]~E(x1401,x1402)+E(f31(x1401,x1403,x1404),f31(x1402,x1403,x1404))
% 162.26/162.09 [141]~E(x1411,x1412)+E(f31(x1413,x1411,x1414),f31(x1413,x1412,x1414))
% 162.26/162.09 [142]~E(x1421,x1422)+E(f31(x1423,x1424,x1421),f31(x1423,x1424,x1422))
% 162.26/162.09 [143]~E(x1431,x1432)+E(f189(x1431,x1433,x1434,x1435,x1436),f189(x1432,x1433,x1434,x1435,x1436))
% 162.26/162.09 [144]~E(x1441,x1442)+E(f189(x1443,x1441,x1444,x1445,x1446),f189(x1443,x1442,x1444,x1445,x1446))
% 162.26/162.09 [145]~E(x1451,x1452)+E(f189(x1453,x1454,x1451,x1455,x1456),f189(x1453,x1454,x1452,x1455,x1456))
% 162.26/162.09 [146]~E(x1461,x1462)+E(f189(x1463,x1464,x1465,x1461,x1466),f189(x1463,x1464,x1465,x1462,x1466))
% 162.26/162.09 [147]~E(x1471,x1472)+E(f189(x1473,x1474,x1475,x1476,x1471),f189(x1473,x1474,x1475,x1476,x1472))
% 162.26/162.09 [148]~E(x1481,x1482)+E(f285(x1481,x1483,x1484),f285(x1482,x1483,x1484))
% 162.26/162.09 [149]~E(x1491,x1492)+E(f285(x1493,x1491,x1494),f285(x1493,x1492,x1494))
% 162.26/162.09 [150]~E(x1501,x1502)+E(f285(x1503,x1504,x1501),f285(x1503,x1504,x1502))
% 162.26/162.09 [151]~E(x1511,x1512)+E(f172(x1511),f172(x1512))
% 162.26/162.09 [152]~E(x1521,x1522)+E(f112(x1521),f112(x1522))
% 162.26/162.09 [153]~E(x1531,x1532)+E(f114(x1531),f114(x1532))
% 162.26/162.09 [154]~E(x1541,x1542)+E(f332(x1541),f332(x1542))
% 162.26/162.09 [155]~E(x1551,x1552)+E(f157(x1551,x1553),f157(x1552,x1553))
% 162.26/162.09 [156]~E(x1561,x1562)+E(f157(x1563,x1561),f157(x1563,x1562))
% 162.26/162.09 [157]~E(x1571,x1572)+E(f40(x1571,x1573),f40(x1572,x1573))
% 162.26/162.09 [158]~E(x1581,x1582)+E(f40(x1583,x1581),f40(x1583,x1582))
% 162.26/162.09 [159]~E(x1591,x1592)+E(f7(x1591,x1593,x1594),f7(x1592,x1593,x1594))
% 162.26/162.09 [160]~E(x1601,x1602)+E(f7(x1603,x1601,x1604),f7(x1603,x1602,x1604))
% 162.26/162.09 [161]~E(x1611,x1612)+E(f7(x1613,x1614,x1611),f7(x1613,x1614,x1612))
% 162.26/162.09 [162]~E(x1621,x1622)+E(f119(x1621),f119(x1622))
% 162.26/162.09 [163]~E(x1631,x1632)+E(f11(x1631,x1633,x1634),f11(x1632,x1633,x1634))
% 162.26/162.09 [164]~E(x1641,x1642)+E(f11(x1643,x1641,x1644),f11(x1643,x1642,x1644))
% 162.26/162.09 [165]~E(x1651,x1652)+E(f11(x1653,x1654,x1651),f11(x1653,x1654,x1652))
% 162.26/162.09 [166]~E(x1661,x1662)+E(f5(x1661),f5(x1662))
% 162.26/162.09 [167]~E(x1671,x1672)+E(f163(x1671,x1673),f163(x1672,x1673))
% 162.26/162.09 [168]~E(x1681,x1682)+E(f163(x1683,x1681),f163(x1683,x1682))
% 162.26/162.09 [169]~E(x1691,x1692)+E(f253(x1691),f253(x1692))
% 162.26/162.09 [170]~E(x1701,x1702)+E(f593(x1701,x1703,x1704),f593(x1702,x1703,x1704))
% 162.26/162.09 [171]~E(x1711,x1712)+E(f593(x1713,x1711,x1714),f593(x1713,x1712,x1714))
% 162.26/162.09 [172]~E(x1721,x1722)+E(f593(x1723,x1724,x1721),f593(x1723,x1724,x1722))
% 162.26/162.09 [173]~E(x1731,x1732)+E(f382(x1731,x1733,x1734),f382(x1732,x1733,x1734))
% 162.26/162.09 [174]~E(x1741,x1742)+E(f382(x1743,x1741,x1744),f382(x1743,x1742,x1744))
% 162.26/162.09 [175]~E(x1751,x1752)+E(f382(x1753,x1754,x1751),f382(x1753,x1754,x1752))
% 162.26/162.09 [176]~E(x1761,x1762)+E(f6(x1761,x1763),f6(x1762,x1763))
% 162.26/162.09 [177]~E(x1771,x1772)+E(f6(x1773,x1771),f6(x1773,x1772))
% 162.26/162.09 [178]~E(x1781,x1782)+E(f12(x1781,x1783,x1784),f12(x1782,x1783,x1784))
% 162.26/162.09 [179]~E(x1791,x1792)+E(f12(x1793,x1791,x1794),f12(x1793,x1792,x1794))
% 162.26/162.09 [180]~E(x1801,x1802)+E(f12(x1803,x1804,x1801),f12(x1803,x1804,x1802))
% 162.26/162.09 [181]~E(x1811,x1812)+E(f145(x1811,x1813,x1814,x1815),f145(x1812,x1813,x1814,x1815))
% 162.26/162.09 [182]~E(x1821,x1822)+E(f145(x1823,x1821,x1824,x1825),f145(x1823,x1822,x1824,x1825))
% 162.26/162.09 [183]~E(x1831,x1832)+E(f145(x1833,x1834,x1831,x1835),f145(x1833,x1834,x1832,x1835))
% 162.26/162.09 [184]~E(x1841,x1842)+E(f145(x1843,x1844,x1845,x1841),f145(x1843,x1844,x1845,x1842))
% 162.26/162.09 [185]~E(x1851,x1852)+E(f142(x1851,x1853),f142(x1852,x1853))
% 162.26/162.09 [186]~E(x1861,x1862)+E(f142(x1863,x1861),f142(x1863,x1862))
% 162.26/162.09 [187]~E(x1871,x1872)+E(f455(x1871,x1873,x1874),f455(x1872,x1873,x1874))
% 162.26/162.09 [188]~E(x1881,x1882)+E(f455(x1883,x1881,x1884),f455(x1883,x1882,x1884))
% 162.26/162.09 [189]~E(x1891,x1892)+E(f455(x1893,x1894,x1891),f455(x1893,x1894,x1892))
% 162.26/162.09 [190]~E(x1901,x1902)+E(f289(x1901),f289(x1902))
% 162.26/162.09 [191]~E(x1911,x1912)+E(f244(x1911),f244(x1912))
% 162.26/162.09 [192]~E(x1921,x1922)+E(f184(x1921,x1923),f184(x1922,x1923))
% 162.26/162.09 [193]~E(x1931,x1932)+E(f184(x1933,x1931),f184(x1933,x1932))
% 162.26/162.09 [194]~E(x1941,x1942)+E(f301(x1941,x1943),f301(x1942,x1943))
% 162.26/162.09 [195]~E(x1951,x1952)+E(f301(x1953,x1951),f301(x1953,x1952))
% 162.26/162.09 [196]~E(x1961,x1962)+E(f824(x1961,x1963,x1964),f824(x1962,x1963,x1964))
% 162.26/162.09 [197]~E(x1971,x1972)+E(f824(x1973,x1971,x1974),f824(x1973,x1972,x1974))
% 162.26/162.09 [198]~E(x1981,x1982)+E(f824(x1983,x1984,x1981),f824(x1983,x1984,x1982))
% 162.26/162.09 [199]~E(x1991,x1992)+E(f18(x1991,x1993,x1994),f18(x1992,x1993,x1994))
% 162.26/162.09 [200]~E(x2001,x2002)+E(f18(x2003,x2001,x2004),f18(x2003,x2002,x2004))
% 162.26/162.09 [201]~E(x2011,x2012)+E(f18(x2013,x2014,x2011),f18(x2013,x2014,x2012))
% 162.26/162.09 [202]~E(x2021,x2022)+E(f309(x2021),f309(x2022))
% 162.26/162.09 [203]~E(x2031,x2032)+E(f302(x2031,x2033,x2034),f302(x2032,x2033,x2034))
% 162.26/162.09 [204]~E(x2041,x2042)+E(f302(x2043,x2041,x2044),f302(x2043,x2042,x2044))
% 162.26/162.09 [205]~E(x2051,x2052)+E(f302(x2053,x2054,x2051),f302(x2053,x2054,x2052))
% 162.26/162.09 [206]~E(x2061,x2062)+E(f262(x2061),f262(x2062))
% 162.26/162.09 [207]~E(x2071,x2072)+E(f813(x2071,x2073,x2074),f813(x2072,x2073,x2074))
% 162.26/162.09 [208]~E(x2081,x2082)+E(f813(x2083,x2081,x2084),f813(x2083,x2082,x2084))
% 162.26/162.09 [209]~E(x2091,x2092)+E(f813(x2093,x2094,x2091),f813(x2093,x2094,x2092))
% 162.26/162.09 [210]~E(x2101,x2102)+E(f138(x2101),f138(x2102))
% 162.26/162.09 [211]~E(x2111,x2112)+E(f823(x2111,x2113,x2114),f823(x2112,x2113,x2114))
% 162.26/162.09 [212]~E(x2121,x2122)+E(f823(x2123,x2121,x2124),f823(x2123,x2122,x2124))
% 162.26/162.09 [213]~E(x2131,x2132)+E(f823(x2133,x2134,x2131),f823(x2133,x2134,x2132))
% 162.26/162.09 [214]~E(x2141,x2142)+E(f506(x2141,x2143,x2144,x2145),f506(x2142,x2143,x2144,x2145))
% 162.26/162.09 [215]~E(x2151,x2152)+E(f506(x2153,x2151,x2154,x2155),f506(x2153,x2152,x2154,x2155))
% 162.26/162.09 [216]~E(x2161,x2162)+E(f506(x2163,x2164,x2161,x2165),f506(x2163,x2164,x2162,x2165))
% 162.26/162.09 [217]~E(x2171,x2172)+E(f506(x2173,x2174,x2175,x2171),f506(x2173,x2174,x2175,x2172))
% 162.26/162.09 [218]~E(x2181,x2182)+E(f635(x2181,x2183),f635(x2182,x2183))
% 162.26/162.09 [219]~E(x2191,x2192)+E(f635(x2193,x2191),f635(x2193,x2192))
% 162.26/162.09 [220]~E(x2201,x2202)+E(f76(x2201),f76(x2202))
% 162.26/162.09 [221]~E(x2211,x2212)+E(f186(x2211,x2213,x2214),f186(x2212,x2213,x2214))
% 162.26/162.09 [222]~E(x2221,x2222)+E(f186(x2223,x2221,x2224),f186(x2223,x2222,x2224))
% 162.26/162.09 [223]~E(x2231,x2232)+E(f186(x2233,x2234,x2231),f186(x2233,x2234,x2232))
% 162.26/162.09 [224]~E(x2241,x2242)+E(f102(x2241),f102(x2242))
% 162.26/162.09 [225]~E(x2251,x2252)+E(f67(x2251,x2253,x2254,x2255,x2256),f67(x2252,x2253,x2254,x2255,x2256))
% 162.26/162.09 [226]~E(x2261,x2262)+E(f67(x2263,x2261,x2264,x2265,x2266),f67(x2263,x2262,x2264,x2265,x2266))
% 162.26/162.09 [227]~E(x2271,x2272)+E(f67(x2273,x2274,x2271,x2275,x2276),f67(x2273,x2274,x2272,x2275,x2276))
% 162.26/162.09 [228]~E(x2281,x2282)+E(f67(x2283,x2284,x2285,x2281,x2286),f67(x2283,x2284,x2285,x2282,x2286))
% 162.26/162.09 [229]~E(x2291,x2292)+E(f67(x2293,x2294,x2295,x2296,x2291),f67(x2293,x2294,x2295,x2296,x2292))
% 162.26/162.09 [230]~E(x2301,x2302)+E(f203(x2301),f203(x2302))
% 162.26/162.09 [231]~E(x2311,x2312)+E(f64(x2311,x2313),f64(x2312,x2313))
% 162.26/162.09 [232]~E(x2321,x2322)+E(f64(x2323,x2321),f64(x2323,x2322))
% 162.26/162.09 [233]~E(x2331,x2332)+E(f180(x2331,x2333),f180(x2332,x2333))
% 162.26/162.09 [234]~E(x2341,x2342)+E(f180(x2343,x2341),f180(x2343,x2342))
% 162.26/162.09 [235]~E(x2351,x2352)+E(f93(x2351),f93(x2352))
% 162.26/162.09 [236]~E(x2361,x2362)+E(f632(x2361,x2363,x2364),f632(x2362,x2363,x2364))
% 162.26/162.09 [237]~E(x2371,x2372)+E(f632(x2373,x2371,x2374),f632(x2373,x2372,x2374))
% 162.26/162.09 [238]~E(x2381,x2382)+E(f632(x2383,x2384,x2381),f632(x2383,x2384,x2382))
% 162.26/162.09 [239]~E(x2391,x2392)+E(f56(x2391),f56(x2392))
% 162.26/162.09 [240]~E(x2401,x2402)+E(f836(x2401,x2403,x2404,x2405,x2406),f836(x2402,x2403,x2404,x2405,x2406))
% 162.26/162.09 [241]~E(x2411,x2412)+E(f836(x2413,x2411,x2414,x2415,x2416),f836(x2413,x2412,x2414,x2415,x2416))
% 162.26/162.09 [242]~E(x2421,x2422)+E(f836(x2423,x2424,x2421,x2425,x2426),f836(x2423,x2424,x2422,x2425,x2426))
% 162.26/162.09 [243]~E(x2431,x2432)+E(f836(x2433,x2434,x2435,x2431,x2436),f836(x2433,x2434,x2435,x2432,x2436))
% 162.26/162.09 [244]~E(x2441,x2442)+E(f836(x2443,x2444,x2445,x2446,x2441),f836(x2443,x2444,x2445,x2446,x2442))
% 162.26/162.09 [245]~E(x2451,x2452)+E(f141(x2451),f141(x2452))
% 162.26/162.09 [246]~E(x2461,x2462)+E(f34(x2461,x2463),f34(x2462,x2463))
% 162.26/162.09 [247]~E(x2471,x2472)+E(f34(x2473,x2471),f34(x2473,x2472))
% 162.26/162.09 [248]~E(x2481,x2482)+E(f120(x2481,x2483),f120(x2482,x2483))
% 162.26/162.09 [249]~E(x2491,x2492)+E(f120(x2493,x2491),f120(x2493,x2492))
% 162.26/162.09 [250]~E(x2501,x2502)+E(f590(x2501,x2503,x2504,x2505),f590(x2502,x2503,x2504,x2505))
% 162.26/162.09 [251]~E(x2511,x2512)+E(f590(x2513,x2511,x2514,x2515),f590(x2513,x2512,x2514,x2515))
% 162.26/162.09 [252]~E(x2521,x2522)+E(f590(x2523,x2524,x2521,x2525),f590(x2523,x2524,x2522,x2525))
% 162.26/162.09 [253]~E(x2531,x2532)+E(f590(x2533,x2534,x2535,x2531),f590(x2533,x2534,x2535,x2532))
% 162.26/162.09 [254]~E(x2541,x2542)+E(f311(x2541,x2543,x2544),f311(x2542,x2543,x2544))
% 162.26/162.09 [255]~E(x2551,x2552)+E(f311(x2553,x2551,x2554),f311(x2553,x2552,x2554))
% 162.26/162.09 [256]~E(x2561,x2562)+E(f311(x2563,x2564,x2561),f311(x2563,x2564,x2562))
% 162.26/162.09 [257]~E(x2571,x2572)+E(f155(x2571,x2573),f155(x2572,x2573))
% 162.26/162.09 [258]~E(x2581,x2582)+E(f155(x2583,x2581),f155(x2583,x2582))
% 162.26/162.09 [259]~E(x2591,x2592)+E(f33(x2591,x2593),f33(x2592,x2593))
% 162.26/162.09 [260]~E(x2601,x2602)+E(f33(x2603,x2601),f33(x2603,x2602))
% 162.26/162.09 [261]~E(x2611,x2612)+E(f200(x2611),f200(x2612))
% 162.26/162.09 [262]~E(x2621,x2622)+E(f176(x2621),f176(x2622))
% 162.26/162.09 [263]~E(x2631,x2632)+E(f46(x2631,x2633),f46(x2632,x2633))
% 162.26/162.09 [264]~E(x2641,x2642)+E(f46(x2643,x2641),f46(x2643,x2642))
% 162.26/162.09 [265]~E(x2651,x2652)+E(f711(x2651,x2653,x2654,x2655),f711(x2652,x2653,x2654,x2655))
% 162.26/162.09 [266]~E(x2661,x2662)+E(f711(x2663,x2661,x2664,x2665),f711(x2663,x2662,x2664,x2665))
% 162.26/162.09 [267]~E(x2671,x2672)+E(f711(x2673,x2674,x2671,x2675),f711(x2673,x2674,x2672,x2675))
% 162.26/162.09 [268]~E(x2681,x2682)+E(f711(x2683,x2684,x2685,x2681),f711(x2683,x2684,x2685,x2682))
% 162.26/162.09 [269]~E(x2691,x2692)+E(f173(x2691,x2693,x2694),f173(x2692,x2693,x2694))
% 162.26/162.09 [270]~E(x2701,x2702)+E(f173(x2703,x2701,x2704),f173(x2703,x2702,x2704))
% 162.26/162.09 [271]~E(x2711,x2712)+E(f173(x2713,x2714,x2711),f173(x2713,x2714,x2712))
% 162.26/162.09 [272]~E(x2721,x2722)+E(f352(x2721,x2723,x2724,x2725,x2726),f352(x2722,x2723,x2724,x2725,x2726))
% 162.26/162.09 [273]~E(x2731,x2732)+E(f352(x2733,x2731,x2734,x2735,x2736),f352(x2733,x2732,x2734,x2735,x2736))
% 162.26/162.09 [274]~E(x2741,x2742)+E(f352(x2743,x2744,x2741,x2745,x2746),f352(x2743,x2744,x2742,x2745,x2746))
% 162.26/162.09 [275]~E(x2751,x2752)+E(f352(x2753,x2754,x2755,x2751,x2756),f352(x2753,x2754,x2755,x2752,x2756))
% 162.26/162.09 [276]~E(x2761,x2762)+E(f352(x2763,x2764,x2765,x2766,x2761),f352(x2763,x2764,x2765,x2766,x2762))
% 162.26/162.09 [277]~E(x2771,x2772)+E(f15(x2771,x2773),f15(x2772,x2773))
% 162.26/162.09 [278]~E(x2781,x2782)+E(f15(x2783,x2781),f15(x2783,x2782))
% 162.26/162.09 [279]~E(x2791,x2792)+E(f191(x2791,x2793),f191(x2792,x2793))
% 162.26/162.09 [280]~E(x2801,x2802)+E(f191(x2803,x2801),f191(x2803,x2802))
% 162.26/162.09 [281]~E(x2811,x2812)+E(f551(x2811,x2813,x2814,x2815),f551(x2812,x2813,x2814,x2815))
% 162.26/162.09 [282]~E(x2821,x2822)+E(f551(x2823,x2821,x2824,x2825),f551(x2823,x2822,x2824,x2825))
% 162.26/162.09 [283]~E(x2831,x2832)+E(f551(x2833,x2834,x2831,x2835),f551(x2833,x2834,x2832,x2835))
% 162.26/162.09 [284]~E(x2841,x2842)+E(f551(x2843,x2844,x2845,x2841),f551(x2843,x2844,x2845,x2842))
% 162.26/162.09 [285]~E(x2851,x2852)+E(f179(x2851,x2853,x2854),f179(x2852,x2853,x2854))
% 162.26/162.09 [286]~E(x2861,x2862)+E(f179(x2863,x2861,x2864),f179(x2863,x2862,x2864))
% 162.26/162.09 [287]~E(x2871,x2872)+E(f179(x2873,x2874,x2871),f179(x2873,x2874,x2872))
% 162.26/162.09 [288]~E(x2881,x2882)+E(f288(x2881,x2883,x2884),f288(x2882,x2883,x2884))
% 162.26/162.09 [289]~E(x2891,x2892)+E(f288(x2893,x2891,x2894),f288(x2893,x2892,x2894))
% 162.26/162.09 [290]~E(x2901,x2902)+E(f288(x2903,x2904,x2901),f288(x2903,x2904,x2902))
% 162.26/162.09 [291]~E(x2911,x2912)+E(f392(x2911,x2913,x2914),f392(x2912,x2913,x2914))
% 162.26/162.09 [292]~E(x2921,x2922)+E(f392(x2923,x2921,x2924),f392(x2923,x2922,x2924))
% 162.26/162.09 [293]~E(x2931,x2932)+E(f392(x2933,x2934,x2931),f392(x2933,x2934,x2932))
% 162.26/162.09 [294]~E(x2941,x2942)+E(f889(x2941,x2943),f889(x2942,x2943))
% 162.26/162.09 [295]~E(x2951,x2952)+E(f889(x2953,x2951),f889(x2953,x2952))
% 162.26/162.09 [296]~E(x2961,x2962)+E(f421(x2961,x2963,x2964,x2965),f421(x2962,x2963,x2964,x2965))
% 162.26/162.09 [297]~E(x2971,x2972)+E(f421(x2973,x2971,x2974,x2975),f421(x2973,x2972,x2974,x2975))
% 162.26/162.09 [298]~E(x2981,x2982)+E(f421(x2983,x2984,x2981,x2985),f421(x2983,x2984,x2982,x2985))
% 162.26/162.09 [299]~E(x2991,x2992)+E(f421(x2993,x2994,x2995,x2991),f421(x2993,x2994,x2995,x2992))
% 162.26/162.09 [300]~E(x3001,x3002)+E(f254(x3001),f254(x3002))
% 162.26/162.09 [301]~E(x3011,x3012)+E(f857(x3011,x3013,x3014),f857(x3012,x3013,x3014))
% 162.26/162.09 [302]~E(x3021,x3022)+E(f857(x3023,x3021,x3024),f857(x3023,x3022,x3024))
% 162.26/162.09 [303]~E(x3031,x3032)+E(f857(x3033,x3034,x3031),f857(x3033,x3034,x3032))
% 162.26/162.09 [304]~E(x3041,x3042)+E(f171(x3041),f171(x3042))
% 162.26/162.09 [305]~E(x3051,x3052)+E(f150(x3051,x3053),f150(x3052,x3053))
% 162.26/162.09 [306]~E(x3061,x3062)+E(f150(x3063,x3061),f150(x3063,x3062))
% 162.26/162.09 [307]~E(x3071,x3072)+E(f304(x3071,x3073,x3074),f304(x3072,x3073,x3074))
% 162.26/162.09 [308]~E(x3081,x3082)+E(f304(x3083,x3081,x3084),f304(x3083,x3082,x3084))
% 162.26/162.09 [309]~E(x3091,x3092)+E(f304(x3093,x3094,x3091),f304(x3093,x3094,x3092))
% 162.26/162.09 [310]~E(x3101,x3102)+E(f65(x3101,x3103,x3104),f65(x3102,x3103,x3104))
% 162.26/162.09 [311]~E(x3111,x3112)+E(f65(x3113,x3111,x3114),f65(x3113,x3112,x3114))
% 162.26/162.09 [312]~E(x3121,x3122)+E(f65(x3123,x3124,x3121),f65(x3123,x3124,x3122))
% 162.26/162.09 [313]~E(x3131,x3132)+E(f174(x3131),f174(x3132))
% 162.26/162.09 [314]~E(x3141,x3142)+E(f795(x3141,x3143,x3144),f795(x3142,x3143,x3144))
% 162.26/162.09 [315]~E(x3151,x3152)+E(f795(x3153,x3151,x3154),f795(x3153,x3152,x3154))
% 162.26/162.09 [316]~E(x3161,x3162)+E(f795(x3163,x3164,x3161),f795(x3163,x3164,x3162))
% 162.26/162.09 [317]~E(x3171,x3172)+E(f814(x3171,x3173,x3174),f814(x3172,x3173,x3174))
% 162.26/162.09 [318]~E(x3181,x3182)+E(f814(x3183,x3181,x3184),f814(x3183,x3182,x3184))
% 162.26/162.09 [319]~E(x3191,x3192)+E(f814(x3193,x3194,x3191),f814(x3193,x3194,x3192))
% 162.26/162.09 [320]~E(x3201,x3202)+E(f344(x3201,x3203,x3204),f344(x3202,x3203,x3204))
% 162.26/162.09 [321]~E(x3211,x3212)+E(f344(x3213,x3211,x3214),f344(x3213,x3212,x3214))
% 162.26/162.09 [322]~E(x3221,x3222)+E(f344(x3223,x3224,x3221),f344(x3223,x3224,x3222))
% 162.26/162.09 [323]~E(x3231,x3232)+E(f286(x3231,x3233),f286(x3232,x3233))
% 162.26/162.09 [324]~E(x3241,x3242)+E(f286(x3243,x3241),f286(x3243,x3242))
% 162.26/162.09 [325]~E(x3251,x3252)+E(f148(x3251,x3253),f148(x3252,x3253))
% 162.26/162.09 [326]~E(x3261,x3262)+E(f148(x3263,x3261),f148(x3263,x3262))
% 162.26/162.09 [327]~E(x3271,x3272)+E(f459(x3271,x3273,x3274,x3275,x3276),f459(x3272,x3273,x3274,x3275,x3276))
% 162.26/162.09 [328]~E(x3281,x3282)+E(f459(x3283,x3281,x3284,x3285,x3286),f459(x3283,x3282,x3284,x3285,x3286))
% 162.26/162.09 [329]~E(x3291,x3292)+E(f459(x3293,x3294,x3291,x3295,x3296),f459(x3293,x3294,x3292,x3295,x3296))
% 162.26/162.09 [330]~E(x3301,x3302)+E(f459(x3303,x3304,x3305,x3301,x3306),f459(x3303,x3304,x3305,x3302,x3306))
% 162.26/162.09 [331]~E(x3311,x3312)+E(f459(x3313,x3314,x3315,x3316,x3311),f459(x3313,x3314,x3315,x3316,x3312))
% 162.26/162.09 [332]~E(x3321,x3322)+E(f272(x3321,x3323,x3324,x3325),f272(x3322,x3323,x3324,x3325))
% 162.26/162.09 [333]~E(x3331,x3332)+E(f272(x3333,x3331,x3334,x3335),f272(x3333,x3332,x3334,x3335))
% 162.26/162.09 [334]~E(x3341,x3342)+E(f272(x3343,x3344,x3341,x3345),f272(x3343,x3344,x3342,x3345))
% 162.26/162.09 [335]~E(x3351,x3352)+E(f272(x3353,x3354,x3355,x3351),f272(x3353,x3354,x3355,x3352))
% 162.26/162.09 [336]~E(x3361,x3362)+E(f319(x3361,x3363),f319(x3362,x3363))
% 162.26/162.09 [337]~E(x3371,x3372)+E(f319(x3373,x3371),f319(x3373,x3372))
% 162.26/162.09 [338]~E(x3381,x3382)+E(f147(x3381,x3383),f147(x3382,x3383))
% 162.26/162.09 [339]~E(x3391,x3392)+E(f147(x3393,x3391),f147(x3393,x3392))
% 162.26/162.09 [340]~E(x3401,x3402)+E(f162(x3401,x3403),f162(x3402,x3403))
% 162.26/162.09 [341]~E(x3411,x3412)+E(f162(x3413,x3411),f162(x3413,x3412))
% 162.26/162.09 [342]~E(x3421,x3422)+E(f255(x3421),f255(x3422))
% 162.26/162.09 [343]~E(x3431,x3432)+E(f270(x3431,x3433,x3434),f270(x3432,x3433,x3434))
% 162.26/162.09 [344]~E(x3441,x3442)+E(f270(x3443,x3441,x3444),f270(x3443,x3442,x3444))
% 162.26/162.09 [345]~E(x3451,x3452)+E(f270(x3453,x3454,x3451),f270(x3453,x3454,x3452))
% 162.26/162.09 [346]~E(x3461,x3462)+E(f58(x3461),f58(x3462))
% 162.26/162.09 [347]~E(x3471,x3472)+E(f668(x3471,x3473,x3474),f668(x3472,x3473,x3474))
% 162.26/162.09 [348]~E(x3481,x3482)+E(f668(x3483,x3481,x3484),f668(x3483,x3482,x3484))
% 162.26/162.09 [349]~E(x3491,x3492)+E(f668(x3493,x3494,x3491),f668(x3493,x3494,x3492))
% 162.26/162.09 [350]~E(x3501,x3502)+E(f322(x3501,x3503),f322(x3502,x3503))
% 162.26/162.09 [351]~E(x3511,x3512)+E(f322(x3513,x3511),f322(x3513,x3512))
% 162.26/162.09 [352]~E(x3521,x3522)+E(f10(x3521,x3523),f10(x3522,x3523))
% 162.26/162.09 [353]~E(x3531,x3532)+E(f10(x3533,x3531),f10(x3533,x3532))
% 162.26/162.09 [354]~E(x3541,x3542)+E(f324(x3541,x3543),f324(x3542,x3543))
% 162.26/162.09 [355]~E(x3551,x3552)+E(f324(x3553,x3551),f324(x3553,x3552))
% 162.26/162.09 [356]~E(x3561,x3562)+E(f190(x3561,x3563,x3564,x3565),f190(x3562,x3563,x3564,x3565))
% 162.26/162.09 [357]~E(x3571,x3572)+E(f190(x3573,x3571,x3574,x3575),f190(x3573,x3572,x3574,x3575))
% 162.26/162.09 [358]~E(x3581,x3582)+E(f190(x3583,x3584,x3581,x3585),f190(x3583,x3584,x3582,x3585))
% 162.26/162.09 [359]~E(x3591,x3592)+E(f190(x3593,x3594,x3595,x3591),f190(x3593,x3594,x3595,x3592))
% 162.26/162.09 [360]~E(x3601,x3602)+E(f611(x3601,x3603,x3604,x3605,x3606,x3607),f611(x3602,x3603,x3604,x3605,x3606,x3607))
% 162.26/162.09 [361]~E(x3611,x3612)+E(f611(x3613,x3611,x3614,x3615,x3616,x3617),f611(x3613,x3612,x3614,x3615,x3616,x3617))
% 162.26/162.09 [362]~E(x3621,x3622)+E(f611(x3623,x3624,x3621,x3625,x3626,x3627),f611(x3623,x3624,x3622,x3625,x3626,x3627))
% 162.26/162.09 [363]~E(x3631,x3632)+E(f611(x3633,x3634,x3635,x3631,x3636,x3637),f611(x3633,x3634,x3635,x3632,x3636,x3637))
% 162.26/162.09 [364]~E(x3641,x3642)+E(f611(x3643,x3644,x3645,x3646,x3641,x3647),f611(x3643,x3644,x3645,x3646,x3642,x3647))
% 162.26/162.09 [365]~E(x3651,x3652)+E(f611(x3653,x3654,x3655,x3656,x3657,x3651),f611(x3653,x3654,x3655,x3656,x3657,x3652))
% 162.26/162.09 [366]~E(x3661,x3662)+E(f381(x3661,x3663,x3664,x3665),f381(x3662,x3663,x3664,x3665))
% 162.26/162.09 [367]~E(x3671,x3672)+E(f381(x3673,x3671,x3674,x3675),f381(x3673,x3672,x3674,x3675))
% 162.26/162.09 [368]~E(x3681,x3682)+E(f381(x3683,x3684,x3681,x3685),f381(x3683,x3684,x3682,x3685))
% 162.26/162.09 [369]~E(x3691,x3692)+E(f381(x3693,x3694,x3695,x3691),f381(x3693,x3694,x3695,x3692))
% 162.26/162.09 [370]~E(x3701,x3702)+E(f587(x3701,x3703,x3704),f587(x3702,x3703,x3704))
% 162.26/162.09 [371]~E(x3711,x3712)+E(f587(x3713,x3711,x3714),f587(x3713,x3712,x3714))
% 162.26/162.09 [372]~E(x3721,x3722)+E(f587(x3723,x3724,x3721),f587(x3723,x3724,x3722))
% 162.26/162.09 [373]~E(x3731,x3732)+E(f187(x3731,x3733,x3734,x3735),f187(x3732,x3733,x3734,x3735))
% 162.26/162.09 [374]~E(x3741,x3742)+E(f187(x3743,x3741,x3744,x3745),f187(x3743,x3742,x3744,x3745))
% 162.26/162.09 [375]~E(x3751,x3752)+E(f187(x3753,x3754,x3751,x3755),f187(x3753,x3754,x3752,x3755))
% 162.26/162.09 [376]~E(x3761,x3762)+E(f187(x3763,x3764,x3765,x3761),f187(x3763,x3764,x3765,x3762))
% 162.26/162.09 [377]~E(x3771,x3772)+E(f815(x3771,x3773,x3774),f815(x3772,x3773,x3774))
% 162.26/162.09 [378]~E(x3781,x3782)+E(f815(x3783,x3781,x3784),f815(x3783,x3782,x3784))
% 162.26/162.09 [379]~E(x3791,x3792)+E(f815(x3793,x3794,x3791),f815(x3793,x3794,x3792))
% 162.26/162.09 [380]~E(x3801,x3802)+E(f86(x3801,x3803),f86(x3802,x3803))
% 162.26/162.09 [381]~E(x3811,x3812)+E(f86(x3813,x3811),f86(x3813,x3812))
% 162.26/162.09 [382]~E(x3821,x3822)+E(f87(x3821),f87(x3822))
% 162.26/162.09 [383]~E(x3831,x3832)+E(f144(x3831),f144(x3832))
% 162.26/162.09 [384]~E(x3841,x3842)+E(f336(x3841),f336(x3842))
% 162.26/162.09 [385]~E(x3851,x3852)+E(f161(x3851,x3853),f161(x3852,x3853))
% 162.26/162.09 [386]~E(x3861,x3862)+E(f161(x3863,x3861),f161(x3863,x3862))
% 162.26/162.09 [387]~E(x3871,x3872)+E(f539(x3871,x3873,x3874),f539(x3872,x3873,x3874))
% 162.26/162.09 [388]~E(x3881,x3882)+E(f539(x3883,x3881,x3884),f539(x3883,x3882,x3884))
% 162.26/162.09 [389]~E(x3891,x3892)+E(f539(x3893,x3894,x3891),f539(x3893,x3894,x3892))
% 162.26/162.09 [390]~E(x3901,x3902)+E(f164(x3901,x3903),f164(x3902,x3903))
% 162.26/162.09 [391]~E(x3911,x3912)+E(f164(x3913,x3911),f164(x3913,x3912))
% 162.26/162.09 [392]~E(x3921,x3922)+E(f865(x3921,x3923),f865(x3922,x3923))
% 162.26/162.09 [393]~E(x3931,x3932)+E(f865(x3933,x3931),f865(x3933,x3932))
% 162.26/162.09 [394]~E(x3941,x3942)+E(f91(x3941,x3943),f91(x3942,x3943))
% 162.26/162.09 [395]~E(x3951,x3952)+E(f91(x3953,x3951),f91(x3953,x3952))
% 162.26/162.09 [396]~E(x3961,x3962)+E(f129(x3961),f129(x3962))
% 162.26/162.09 [397]~E(x3971,x3972)+E(f287(x3971,x3973),f287(x3972,x3973))
% 162.26/162.09 [398]~E(x3981,x3982)+E(f287(x3983,x3981),f287(x3983,x3982))
% 162.26/162.09 [399]~E(x3991,x3992)+E(f424(x3991,x3993,x3994,x3995),f424(x3992,x3993,x3994,x3995))
% 162.26/162.09 [400]~E(x4001,x4002)+E(f424(x4003,x4001,x4004,x4005),f424(x4003,x4002,x4004,x4005))
% 162.26/162.09 [401]~E(x4011,x4012)+E(f424(x4013,x4014,x4011,x4015),f424(x4013,x4014,x4012,x4015))
% 162.26/162.09 [402]~E(x4021,x4022)+E(f424(x4023,x4024,x4025,x4021),f424(x4023,x4024,x4025,x4022))
% 162.26/162.09 [403]~E(x4031,x4032)+E(f48(x4031,x4033),f48(x4032,x4033))
% 162.26/162.09 [404]~E(x4041,x4042)+E(f48(x4043,x4041),f48(x4043,x4042))
% 162.26/162.09 [405]~E(x4051,x4052)+E(f181(x4051,x4053),f181(x4052,x4053))
% 162.26/162.09 [406]~E(x4061,x4062)+E(f181(x4063,x4061),f181(x4063,x4062))
% 162.26/162.09 [407]~E(x4071,x4072)+E(f156(x4071,x4073),f156(x4072,x4073))
% 162.26/162.09 [408]~E(x4081,x4082)+E(f156(x4083,x4081),f156(x4083,x4082))
% 162.26/162.09 [409]~E(x4091,x4092)+E(f646(x4091,x4093,x4094,x4095,x4096),f646(x4092,x4093,x4094,x4095,x4096))
% 162.26/162.09 [410]~E(x4101,x4102)+E(f646(x4103,x4101,x4104,x4105,x4106),f646(x4103,x4102,x4104,x4105,x4106))
% 162.26/162.09 [411]~E(x4111,x4112)+E(f646(x4113,x4114,x4111,x4115,x4116),f646(x4113,x4114,x4112,x4115,x4116))
% 162.26/162.09 [412]~E(x4121,x4122)+E(f646(x4123,x4124,x4125,x4121,x4126),f646(x4123,x4124,x4125,x4122,x4126))
% 162.26/162.09 [413]~E(x4131,x4132)+E(f646(x4133,x4134,x4135,x4136,x4131),f646(x4133,x4134,x4135,x4136,x4132))
% 162.26/162.09 [414]~E(x4141,x4142)+E(f386(x4141,x4143,x4144),f386(x4142,x4143,x4144))
% 162.26/162.09 [415]~E(x4151,x4152)+E(f386(x4153,x4151,x4154),f386(x4153,x4152,x4154))
% 162.26/162.09 [416]~E(x4161,x4162)+E(f386(x4163,x4164,x4161),f386(x4163,x4164,x4162))
% 162.26/162.09 [417]~E(x4171,x4172)+E(f318(x4171,x4173,x4174,x4175),f318(x4172,x4173,x4174,x4175))
% 162.26/162.09 [418]~E(x4181,x4182)+E(f318(x4183,x4181,x4184,x4185),f318(x4183,x4182,x4184,x4185))
% 162.26/162.09 [419]~E(x4191,x4192)+E(f318(x4193,x4194,x4191,x4195),f318(x4193,x4194,x4192,x4195))
% 162.26/162.09 [420]~E(x4201,x4202)+E(f318(x4203,x4204,x4205,x4201),f318(x4203,x4204,x4205,x4202))
% 162.26/162.09 [421]~E(x4211,x4212)+E(f755(x4211,x4213,x4214,x4215),f755(x4212,x4213,x4214,x4215))
% 162.26/162.09 [422]~E(x4221,x4222)+E(f755(x4223,x4221,x4224,x4225),f755(x4223,x4222,x4224,x4225))
% 162.26/162.09 [423]~E(x4231,x4232)+E(f755(x4233,x4234,x4231,x4235),f755(x4233,x4234,x4232,x4235))
% 162.26/162.09 [424]~E(x4241,x4242)+E(f755(x4243,x4244,x4245,x4241),f755(x4243,x4244,x4245,x4242))
% 162.26/162.09 [425]~E(x4251,x4252)+E(f409(x4251,x4253,x4254,x4255),f409(x4252,x4253,x4254,x4255))
% 162.26/162.09 [426]~E(x4261,x4262)+E(f409(x4263,x4261,x4264,x4265),f409(x4263,x4262,x4264,x4265))
% 162.26/162.09 [427]~E(x4271,x4272)+E(f409(x4273,x4274,x4271,x4275),f409(x4273,x4274,x4272,x4275))
% 162.26/162.09 [428]~E(x4281,x4282)+E(f409(x4283,x4284,x4285,x4281),f409(x4283,x4284,x4285,x4282))
% 162.26/162.09 [429]~E(x4291,x4292)+E(f548(x4291,x4293,x4294,x4295,x4296,x4297),f548(x4292,x4293,x4294,x4295,x4296,x4297))
% 162.26/162.09 [430]~E(x4301,x4302)+E(f548(x4303,x4301,x4304,x4305,x4306,x4307),f548(x4303,x4302,x4304,x4305,x4306,x4307))
% 162.26/162.09 [431]~E(x4311,x4312)+E(f548(x4313,x4314,x4311,x4315,x4316,x4317),f548(x4313,x4314,x4312,x4315,x4316,x4317))
% 162.26/162.09 [432]~E(x4321,x4322)+E(f548(x4323,x4324,x4325,x4321,x4326,x4327),f548(x4323,x4324,x4325,x4322,x4326,x4327))
% 162.26/162.09 [433]~E(x4331,x4332)+E(f548(x4333,x4334,x4335,x4336,x4331,x4337),f548(x4333,x4334,x4335,x4336,x4332,x4337))
% 162.26/162.09 [434]~E(x4341,x4342)+E(f548(x4343,x4344,x4345,x4346,x4347,x4341),f548(x4343,x4344,x4345,x4346,x4347,x4342))
% 162.26/162.09 [435]~E(x4351,x4352)+E(f308(x4351),f308(x4352))
% 162.26/162.09 [436]~E(x4361,x4362)+E(f267(x4361,x4363,x4364),f267(x4362,x4363,x4364))
% 162.26/162.09 [437]~E(x4371,x4372)+E(f267(x4373,x4371,x4374),f267(x4373,x4372,x4374))
% 162.26/162.09 [438]~E(x4381,x4382)+E(f267(x4383,x4384,x4381),f267(x4383,x4384,x4382))
% 162.26/162.09 [439]~E(x4391,x4392)+E(f376(x4391,x4393,x4394),f376(x4392,x4393,x4394))
% 162.26/162.09 [440]~E(x4401,x4402)+E(f376(x4403,x4401,x4404),f376(x4403,x4402,x4404))
% 162.26/162.09 [441]~E(x4411,x4412)+E(f376(x4413,x4414,x4411),f376(x4413,x4414,x4412))
% 162.26/162.09 [442]~E(x4421,x4422)+E(f499(x4421,x4423,x4424),f499(x4422,x4423,x4424))
% 162.26/162.09 [443]~E(x4431,x4432)+E(f499(x4433,x4431,x4434),f499(x4433,x4432,x4434))
% 162.26/162.09 [444]~E(x4441,x4442)+E(f499(x4443,x4444,x4441),f499(x4443,x4444,x4442))
% 162.26/162.09 [445]~E(x4451,x4452)+E(f122(x4451,x4453,x4454),f122(x4452,x4453,x4454))
% 162.26/162.09 [446]~E(x4461,x4462)+E(f122(x4463,x4461,x4464),f122(x4463,x4462,x4464))
% 162.26/162.09 [447]~E(x4471,x4472)+E(f122(x4473,x4474,x4471),f122(x4473,x4474,x4472))
% 162.26/162.09 [448]~E(x4481,x4482)+E(f316(x4481),f316(x4482))
% 162.26/162.09 [449]~E(x4491,x4492)+E(f44(x4491),f44(x4492))
% 162.26/162.09 [450]~E(x4501,x4502)+E(f734(x4501,x4503,x4504,x4505,x4506),f734(x4502,x4503,x4504,x4505,x4506))
% 162.26/162.09 [451]~E(x4511,x4512)+E(f734(x4513,x4511,x4514,x4515,x4516),f734(x4513,x4512,x4514,x4515,x4516))
% 162.26/162.09 [452]~E(x4521,x4522)+E(f734(x4523,x4524,x4521,x4525,x4526),f734(x4523,x4524,x4522,x4525,x4526))
% 162.26/162.09 [453]~E(x4531,x4532)+E(f734(x4533,x4534,x4535,x4531,x4536),f734(x4533,x4534,x4535,x4532,x4536))
% 162.26/162.09 [454]~E(x4541,x4542)+E(f734(x4543,x4544,x4545,x4546,x4541),f734(x4543,x4544,x4545,x4546,x4542))
% 162.26/162.09 [455]~E(x4551,x4552)+E(f754(x4551,x4553,x4554,x4555),f754(x4552,x4553,x4554,x4555))
% 162.26/162.09 [456]~E(x4561,x4562)+E(f754(x4563,x4561,x4564,x4565),f754(x4563,x4562,x4564,x4565))
% 162.26/162.09 [457]~E(x4571,x4572)+E(f754(x4573,x4574,x4571,x4575),f754(x4573,x4574,x4572,x4575))
% 162.26/162.09 [458]~E(x4581,x4582)+E(f754(x4583,x4584,x4585,x4581),f754(x4583,x4584,x4585,x4582))
% 162.26/162.09 [459]~E(x4591,x4592)+E(f295(x4591,x4593,x4594,x4595),f295(x4592,x4593,x4594,x4595))
% 162.26/162.09 [460]~E(x4601,x4602)+E(f295(x4603,x4601,x4604,x4605),f295(x4603,x4602,x4604,x4605))
% 162.26/162.09 [461]~E(x4611,x4612)+E(f295(x4613,x4614,x4611,x4615),f295(x4613,x4614,x4612,x4615))
% 162.26/162.09 [462]~E(x4621,x4622)+E(f295(x4623,x4624,x4625,x4621),f295(x4623,x4624,x4625,x4622))
% 162.26/162.09 [463]~E(x4631,x4632)+E(f50(x4631,x4633),f50(x4632,x4633))
% 162.26/162.09 [464]~E(x4641,x4642)+E(f50(x4643,x4641),f50(x4643,x4642))
% 162.26/162.09 [465]~E(x4651,x4652)+E(f53(x4651,x4653),f53(x4652,x4653))
% 162.26/162.09 [466]~E(x4661,x4662)+E(f53(x4663,x4661),f53(x4663,x4662))
% 162.26/162.09 [467]~E(x4671,x4672)+E(f182(x4671,x4673),f182(x4672,x4673))
% 162.26/162.09 [468]~E(x4681,x4682)+E(f182(x4683,x4681),f182(x4683,x4682))
% 162.26/162.09 [469]~E(x4691,x4692)+E(f495(x4691,x4693,x4694,x4695,x4696),f495(x4692,x4693,x4694,x4695,x4696))
% 162.26/162.09 [470]~E(x4701,x4702)+E(f495(x4703,x4701,x4704,x4705,x4706),f495(x4703,x4702,x4704,x4705,x4706))
% 162.26/162.09 [471]~E(x4711,x4712)+E(f495(x4713,x4714,x4711,x4715,x4716),f495(x4713,x4714,x4712,x4715,x4716))
% 162.26/162.09 [472]~E(x4721,x4722)+E(f495(x4723,x4724,x4725,x4721,x4726),f495(x4723,x4724,x4725,x4722,x4726))
% 162.26/162.09 [473]~E(x4731,x4732)+E(f495(x4733,x4734,x4735,x4736,x4731),f495(x4733,x4734,x4735,x4736,x4732))
% 162.26/162.09 [474]~E(x4741,x4742)+E(f361(x4741,x4743,x4744,x4745,x4746),f361(x4742,x4743,x4744,x4745,x4746))
% 162.26/162.09 [475]~E(x4751,x4752)+E(f361(x4753,x4751,x4754,x4755,x4756),f361(x4753,x4752,x4754,x4755,x4756))
% 162.26/162.09 [476]~E(x4761,x4762)+E(f361(x4763,x4764,x4761,x4765,x4766),f361(x4763,x4764,x4762,x4765,x4766))
% 162.26/162.09 [477]~E(x4771,x4772)+E(f361(x4773,x4774,x4775,x4771,x4776),f361(x4773,x4774,x4775,x4772,x4776))
% 162.26/162.09 [478]~E(x4781,x4782)+E(f361(x4783,x4784,x4785,x4786,x4781),f361(x4783,x4784,x4785,x4786,x4782))
% 162.26/162.09 [479]~E(x4791,x4792)+E(f617(x4791,x4793,x4794,x4795,x4796),f617(x4792,x4793,x4794,x4795,x4796))
% 162.26/162.09 [480]~E(x4801,x4802)+E(f617(x4803,x4801,x4804,x4805,x4806),f617(x4803,x4802,x4804,x4805,x4806))
% 162.26/162.09 [481]~E(x4811,x4812)+E(f617(x4813,x4814,x4811,x4815,x4816),f617(x4813,x4814,x4812,x4815,x4816))
% 162.26/162.09 [482]~E(x4821,x4822)+E(f617(x4823,x4824,x4825,x4821,x4826),f617(x4823,x4824,x4825,x4822,x4826))
% 162.26/162.09 [483]~E(x4831,x4832)+E(f617(x4833,x4834,x4835,x4836,x4831),f617(x4833,x4834,x4835,x4836,x4832))
% 162.26/162.09 [484]~E(x4841,x4842)+E(f259(x4841,x4843),f259(x4842,x4843))
% 162.26/162.09 [485]~E(x4851,x4852)+E(f259(x4853,x4851),f259(x4853,x4852))
% 162.26/162.09 [486]~E(x4861,x4862)+E(f827(x4861,x4863,x4864),f827(x4862,x4863,x4864))
% 162.26/162.09 [487]~E(x4871,x4872)+E(f827(x4873,x4871,x4874),f827(x4873,x4872,x4874))
% 162.26/162.09 [488]~E(x4881,x4882)+E(f827(x4883,x4884,x4881),f827(x4883,x4884,x4882))
% 162.26/162.09 [489]~E(x4891,x4892)+E(f790(x4891,x4893,x4894),f790(x4892,x4893,x4894))
% 162.26/162.09 [490]~E(x4901,x4902)+E(f790(x4903,x4901,x4904),f790(x4903,x4902,x4904))
% 162.26/162.09 [491]~E(x4911,x4912)+E(f790(x4913,x4914,x4911),f790(x4913,x4914,x4912))
% 162.26/162.09 [492]~E(x4921,x4922)+E(f783(x4921,x4923),f783(x4922,x4923))
% 162.26/162.09 [493]~E(x4931,x4932)+E(f783(x4933,x4931),f783(x4933,x4932))
% 162.26/162.09 [494]~E(x4941,x4942)+E(f306(x4941),f306(x4942))
% 162.26/162.09 [495]~E(x4951,x4952)+E(f55(x4951,x4953,x4954),f55(x4952,x4953,x4954))
% 162.26/162.09 [496]~E(x4961,x4962)+E(f55(x4963,x4961,x4964),f55(x4963,x4962,x4964))
% 162.26/162.09 [497]~E(x4971,x4972)+E(f55(x4973,x4974,x4971),f55(x4973,x4974,x4972))
% 162.26/162.09 [498]~E(x4981,x4982)+E(f193(x4981,x4983,x4984,x4985),f193(x4982,x4983,x4984,x4985))
% 162.26/162.09 [499]~E(x4991,x4992)+E(f193(x4993,x4991,x4994,x4995),f193(x4993,x4992,x4994,x4995))
% 162.26/162.09 [500]~E(x5001,x5002)+E(f193(x5003,x5004,x5001,x5005),f193(x5003,x5004,x5002,x5005))
% 162.26/162.09 [501]~E(x5011,x5012)+E(f193(x5013,x5014,x5015,x5011),f193(x5013,x5014,x5015,x5012))
% 162.26/162.09 [502]~E(x5021,x5022)+E(f284(x5021),f284(x5022))
% 162.26/162.09 [503]~E(x5031,x5032)+E(f759(x5031,x5033,x5034,x5035,x5036,x5037,x5038,x5039),f759(x5032,x5033,x5034,x5035,x5036,x5037,x5038,x5039))
% 162.26/162.09 [504]~E(x5041,x5042)+E(f759(x5043,x5041,x5044,x5045,x5046,x5047,x5048,x5049),f759(x5043,x5042,x5044,x5045,x5046,x5047,x5048,x5049))
% 162.26/162.09 [505]~E(x5051,x5052)+E(f759(x5053,x5054,x5051,x5055,x5056,x5057,x5058,x5059),f759(x5053,x5054,x5052,x5055,x5056,x5057,x5058,x5059))
% 162.26/162.09 [506]~E(x5061,x5062)+E(f759(x5063,x5064,x5065,x5061,x5066,x5067,x5068,x5069),f759(x5063,x5064,x5065,x5062,x5066,x5067,x5068,x5069))
% 162.26/162.09 [507]~E(x5071,x5072)+E(f759(x5073,x5074,x5075,x5076,x5071,x5077,x5078,x5079),f759(x5073,x5074,x5075,x5076,x5072,x5077,x5078,x5079))
% 162.26/162.09 [508]~E(x5081,x5082)+E(f759(x5083,x5084,x5085,x5086,x5087,x5081,x5088,x5089),f759(x5083,x5084,x5085,x5086,x5087,x5082,x5088,x5089))
% 162.26/162.09 [509]~E(x5091,x5092)+E(f759(x5093,x5094,x5095,x5096,x5097,x5098,x5091,x5099),f759(x5093,x5094,x5095,x5096,x5097,x5098,x5092,x5099))
% 162.26/162.09 [510]~E(x5101,x5102)+E(f759(x5103,x5104,x5105,x5106,x5107,x5108,x5109,x5101),f759(x5103,x5104,x5105,x5106,x5107,x5108,x5109,x5102))
% 162.26/162.09 [511]~E(x5111,x5112)+E(f257(x5111,x5113),f257(x5112,x5113))
% 162.26/162.09 [512]~E(x5121,x5122)+E(f257(x5123,x5121),f257(x5123,x5122))
% 162.26/162.09 [513]~E(x5131,x5132)+E(f579(x5131,x5133,x5134),f579(x5132,x5133,x5134))
% 162.26/162.09 [514]~E(x5141,x5142)+E(f579(x5143,x5141,x5144),f579(x5143,x5142,x5144))
% 162.26/162.09 [515]~E(x5151,x5152)+E(f579(x5153,x5154,x5151),f579(x5153,x5154,x5152))
% 162.26/162.09 [516]~E(x5161,x5162)+E(f158(x5161,x5163,x5164),f158(x5162,x5163,x5164))
% 162.26/162.09 [517]~E(x5171,x5172)+E(f158(x5173,x5171,x5174),f158(x5173,x5172,x5174))
% 162.26/162.09 [518]~E(x5181,x5182)+E(f158(x5183,x5184,x5181),f158(x5183,x5184,x5182))
% 162.26/162.09 [519]~E(x5191,x5192)+E(f29(x5191,x5193,x5194),f29(x5192,x5193,x5194))
% 162.26/162.09 [520]~E(x5201,x5202)+E(f29(x5203,x5201,x5204),f29(x5203,x5202,x5204))
% 162.26/162.09 [521]~E(x5211,x5212)+E(f29(x5213,x5214,x5211),f29(x5213,x5214,x5212))
% 162.26/162.09 [522]~E(x5221,x5222)+E(f159(x5221,x5223,x5224,x5225),f159(x5222,x5223,x5224,x5225))
% 162.26/162.09 [523]~E(x5231,x5232)+E(f159(x5233,x5231,x5234,x5235),f159(x5233,x5232,x5234,x5235))
% 162.26/162.09 [524]~E(x5241,x5242)+E(f159(x5243,x5244,x5241,x5245),f159(x5243,x5244,x5242,x5245))
% 162.26/162.09 [525]~E(x5251,x5252)+E(f159(x5253,x5254,x5255,x5251),f159(x5253,x5254,x5255,x5252))
% 162.26/162.09 [526]~E(x5261,x5262)+E(f727(x5261,x5263),f727(x5262,x5263))
% 162.26/162.09 [527]~E(x5271,x5272)+E(f727(x5273,x5271),f727(x5273,x5272))
% 162.26/162.09 [528]~E(x5281,x5282)+E(f14(x5281,x5283),f14(x5282,x5283))
% 162.26/162.09 [529]~E(x5291,x5292)+E(f14(x5293,x5291),f14(x5293,x5292))
% 162.26/162.09 [530]~E(x5301,x5302)+E(f713(x5301,x5303,x5304,x5305),f713(x5302,x5303,x5304,x5305))
% 162.26/162.09 [531]~E(x5311,x5312)+E(f713(x5313,x5311,x5314,x5315),f713(x5313,x5312,x5314,x5315))
% 162.26/162.09 [532]~E(x5321,x5322)+E(f713(x5323,x5324,x5321,x5325),f713(x5323,x5324,x5322,x5325))
% 162.26/162.09 [533]~E(x5331,x5332)+E(f713(x5333,x5334,x5335,x5331),f713(x5333,x5334,x5335,x5332))
% 162.26/162.09 [534]~E(x5341,x5342)+E(f305(x5341,x5343,x5344),f305(x5342,x5343,x5344))
% 162.26/162.09 [535]~E(x5351,x5352)+E(f305(x5353,x5351,x5354),f305(x5353,x5352,x5354))
% 162.26/162.09 [536]~E(x5361,x5362)+E(f305(x5363,x5364,x5361),f305(x5363,x5364,x5362))
% 162.26/162.09 [537]~E(x5371,x5372)+E(f750(x5371,x5373,x5374),f750(x5372,x5373,x5374))
% 162.26/162.09 [538]~E(x5381,x5382)+E(f750(x5383,x5381,x5384),f750(x5383,x5382,x5384))
% 162.26/162.09 [539]~E(x5391,x5392)+E(f750(x5393,x5394,x5391),f750(x5393,x5394,x5392))
% 162.26/162.09 [540]~E(x5401,x5402)+E(f224(x5401),f224(x5402))
% 162.26/162.09 [541]~E(x5411,x5412)+E(f799(x5411,x5413,x5414),f799(x5412,x5413,x5414))
% 162.26/162.09 [542]~E(x5421,x5422)+E(f799(x5423,x5421,x5424),f799(x5423,x5422,x5424))
% 162.26/162.09 [543]~E(x5431,x5432)+E(f799(x5433,x5434,x5431),f799(x5433,x5434,x5432))
% 162.26/162.09 [544]~E(x5441,x5442)+E(f692(x5441,x5443,x5444,x5445,x5446),f692(x5442,x5443,x5444,x5445,x5446))
% 162.26/162.09 [545]~E(x5451,x5452)+E(f692(x5453,x5451,x5454,x5455,x5456),f692(x5453,x5452,x5454,x5455,x5456))
% 162.26/162.09 [546]~E(x5461,x5462)+E(f692(x5463,x5464,x5461,x5465,x5466),f692(x5463,x5464,x5462,x5465,x5466))
% 162.26/162.09 [547]~E(x5471,x5472)+E(f692(x5473,x5474,x5475,x5471,x5476),f692(x5473,x5474,x5475,x5472,x5476))
% 162.26/162.09 [548]~E(x5481,x5482)+E(f692(x5483,x5484,x5485,x5486,x5481),f692(x5483,x5484,x5485,x5486,x5482))
% 162.26/162.09 [549]~E(x5491,x5492)+E(f523(x5491,x5493,x5494,x5495,x5496),f523(x5492,x5493,x5494,x5495,x5496))
% 162.26/162.09 [550]~E(x5501,x5502)+E(f523(x5503,x5501,x5504,x5505,x5506),f523(x5503,x5502,x5504,x5505,x5506))
% 162.26/162.09 [551]~E(x5511,x5512)+E(f523(x5513,x5514,x5511,x5515,x5516),f523(x5513,x5514,x5512,x5515,x5516))
% 162.26/162.09 [552]~E(x5521,x5522)+E(f523(x5523,x5524,x5525,x5521,x5526),f523(x5523,x5524,x5525,x5522,x5526))
% 162.26/162.09 [553]~E(x5531,x5532)+E(f523(x5533,x5534,x5535,x5536,x5531),f523(x5533,x5534,x5535,x5536,x5532))
% 162.26/162.09 [554]~E(x5541,x5542)+E(f78(x5541,x5543,x5544,x5545),f78(x5542,x5543,x5544,x5545))
% 162.26/162.09 [555]~E(x5551,x5552)+E(f78(x5553,x5551,x5554,x5555),f78(x5553,x5552,x5554,x5555))
% 162.26/162.09 [556]~E(x5561,x5562)+E(f78(x5563,x5564,x5561,x5565),f78(x5563,x5564,x5562,x5565))
% 162.26/162.09 [557]~E(x5571,x5572)+E(f78(x5573,x5574,x5575,x5571),f78(x5573,x5574,x5575,x5572))
% 162.26/162.09 [558]~E(x5581,x5582)+E(f772(x5581,x5583,x5584,x5585),f772(x5582,x5583,x5584,x5585))
% 162.26/162.09 [559]~E(x5591,x5592)+E(f772(x5593,x5591,x5594,x5595),f772(x5593,x5592,x5594,x5595))
% 162.26/162.09 [560]~E(x5601,x5602)+E(f772(x5603,x5604,x5601,x5605),f772(x5603,x5604,x5602,x5605))
% 162.26/162.09 [561]~E(x5611,x5612)+E(f772(x5613,x5614,x5615,x5611),f772(x5613,x5614,x5615,x5612))
% 162.26/162.09 [562]~E(x5621,x5622)+E(f844(x5621,x5623),f844(x5622,x5623))
% 162.26/162.09 [563]~E(x5631,x5632)+E(f844(x5633,x5631),f844(x5633,x5632))
% 162.26/162.09 [564]~E(x5641,x5642)+E(f92(x5641),f92(x5642))
% 162.26/162.09 [565]~E(x5651,x5652)+E(f534(x5651,x5653,x5654),f534(x5652,x5653,x5654))
% 162.26/162.09 [566]~E(x5661,x5662)+E(f534(x5663,x5661,x5664),f534(x5663,x5662,x5664))
% 162.26/162.09 [567]~E(x5671,x5672)+E(f534(x5673,x5674,x5671),f534(x5673,x5674,x5672))
% 162.26/162.09 [568]~E(x5681,x5682)+E(f585(x5681,x5683,x5684,x5685),f585(x5682,x5683,x5684,x5685))
% 162.26/162.09 [569]~E(x5691,x5692)+E(f585(x5693,x5691,x5694,x5695),f585(x5693,x5692,x5694,x5695))
% 162.26/162.09 [570]~E(x5701,x5702)+E(f585(x5703,x5704,x5701,x5705),f585(x5703,x5704,x5702,x5705))
% 162.26/162.09 [571]~E(x5711,x5712)+E(f585(x5713,x5714,x5715,x5711),f585(x5713,x5714,x5715,x5712))
% 162.26/162.09 [572]~E(x5721,x5722)+E(f237(x5721,x5723,x5724),f237(x5722,x5723,x5724))
% 162.26/162.09 [573]~E(x5731,x5732)+E(f237(x5733,x5731,x5734),f237(x5733,x5732,x5734))
% 162.26/162.09 [574]~E(x5741,x5742)+E(f237(x5743,x5744,x5741),f237(x5743,x5744,x5742))
% 162.26/162.09 [575]~E(x5751,x5752)+E(f258(x5751,x5753),f258(x5752,x5753))
% 162.26/162.09 [576]~E(x5761,x5762)+E(f258(x5763,x5761),f258(x5763,x5762))
% 162.26/162.09 [577]~E(x5771,x5772)+E(f240(x5771,x5773),f240(x5772,x5773))
% 162.26/162.09 [578]~E(x5781,x5782)+E(f240(x5783,x5781),f240(x5783,x5782))
% 162.26/162.09 [579]~E(x5791,x5792)+E(f562(x5791,x5793,x5794,x5795,x5796,x5797,x5798),f562(x5792,x5793,x5794,x5795,x5796,x5797,x5798))
% 162.26/162.09 [580]~E(x5801,x5802)+E(f562(x5803,x5801,x5804,x5805,x5806,x5807,x5808),f562(x5803,x5802,x5804,x5805,x5806,x5807,x5808))
% 162.26/162.09 [581]~E(x5811,x5812)+E(f562(x5813,x5814,x5811,x5815,x5816,x5817,x5818),f562(x5813,x5814,x5812,x5815,x5816,x5817,x5818))
% 162.26/162.09 [582]~E(x5821,x5822)+E(f562(x5823,x5824,x5825,x5821,x5826,x5827,x5828),f562(x5823,x5824,x5825,x5822,x5826,x5827,x5828))
% 162.26/162.09 [583]~E(x5831,x5832)+E(f562(x5833,x5834,x5835,x5836,x5831,x5837,x5838),f562(x5833,x5834,x5835,x5836,x5832,x5837,x5838))
% 162.26/162.09 [584]~E(x5841,x5842)+E(f562(x5843,x5844,x5845,x5846,x5847,x5841,x5848),f562(x5843,x5844,x5845,x5846,x5847,x5842,x5848))
% 162.26/162.09 [585]~E(x5851,x5852)+E(f562(x5853,x5854,x5855,x5856,x5857,x5858,x5851),f562(x5853,x5854,x5855,x5856,x5857,x5858,x5852))
% 162.26/162.09 [586]~E(x5861,x5862)+E(f41(x5861,x5863),f41(x5862,x5863))
% 162.26/162.09 [587]~E(x5871,x5872)+E(f41(x5873,x5871),f41(x5873,x5872))
% 162.26/162.09 [588]~E(x5881,x5882)+E(f496(x5881,x5883,x5884,x5885,x5886),f496(x5882,x5883,x5884,x5885,x5886))
% 162.26/162.09 [589]~E(x5891,x5892)+E(f496(x5893,x5891,x5894,x5895,x5896),f496(x5893,x5892,x5894,x5895,x5896))
% 162.26/162.09 [590]~E(x5901,x5902)+E(f496(x5903,x5904,x5901,x5905,x5906),f496(x5903,x5904,x5902,x5905,x5906))
% 162.26/162.09 [591]~E(x5911,x5912)+E(f496(x5913,x5914,x5915,x5911,x5916),f496(x5913,x5914,x5915,x5912,x5916))
% 162.26/162.09 [592]~E(x5921,x5922)+E(f496(x5923,x5924,x5925,x5926,x5921),f496(x5923,x5924,x5925,x5926,x5922))
% 162.26/162.09 [593]~E(x5931,x5932)+E(f89(x5931,x5933),f89(x5932,x5933))
% 162.26/162.09 [594]~E(x5941,x5942)+E(f89(x5943,x5941),f89(x5943,x5942))
% 162.26/162.09 [595]~E(x5951,x5952)+E(f850(x5951,x5953,x5954,x5955,x5956,x5957,x5958,x5959,x59510),f850(x5952,x5953,x5954,x5955,x5956,x5957,x5958,x5959,x59510))
% 162.26/162.09 [596]~E(x5961,x5962)+E(f850(x5963,x5961,x5964,x5965,x5966,x5967,x5968,x5969,x59610),f850(x5963,x5962,x5964,x5965,x5966,x5967,x5968,x5969,x59610))
% 162.26/162.09 [597]~E(x5971,x5972)+E(f850(x5973,x5974,x5971,x5975,x5976,x5977,x5978,x5979,x59710),f850(x5973,x5974,x5972,x5975,x5976,x5977,x5978,x5979,x59710))
% 162.26/162.09 [598]~E(x5981,x5982)+E(f850(x5983,x5984,x5985,x5981,x5986,x5987,x5988,x5989,x59810),f850(x5983,x5984,x5985,x5982,x5986,x5987,x5988,x5989,x59810))
% 162.26/162.09 [599]~E(x5991,x5992)+E(f850(x5993,x5994,x5995,x5996,x5991,x5997,x5998,x5999,x59910),f850(x5993,x5994,x5995,x5996,x5992,x5997,x5998,x5999,x59910))
% 162.26/162.09 [600]~E(x6001,x6002)+E(f850(x6003,x6004,x6005,x6006,x6007,x6001,x6008,x6009,x60010),f850(x6003,x6004,x6005,x6006,x6007,x6002,x6008,x6009,x60010))
% 162.26/162.09 [601]~E(x6011,x6012)+E(f850(x6013,x6014,x6015,x6016,x6017,x6018,x6011,x6019,x60110),f850(x6013,x6014,x6015,x6016,x6017,x6018,x6012,x6019,x60110))
% 162.26/162.09 [602]~E(x6021,x6022)+E(f850(x6023,x6024,x6025,x6026,x6027,x6028,x6029,x6021,x60210),f850(x6023,x6024,x6025,x6026,x6027,x6028,x6029,x6022,x60210))
% 162.26/162.09 [603]~E(x6031,x6032)+E(f850(x6033,x6034,x6035,x6036,x6037,x6038,x6039,x60310,x6031),f850(x6033,x6034,x6035,x6036,x6037,x6038,x6039,x60310,x6032))
% 162.26/162.09 [604]~E(x6041,x6042)+E(f503(x6041,x6043,x6044,x6045,x6046),f503(x6042,x6043,x6044,x6045,x6046))
% 162.26/162.09 [605]~E(x6051,x6052)+E(f503(x6053,x6051,x6054,x6055,x6056),f503(x6053,x6052,x6054,x6055,x6056))
% 162.26/162.09 [606]~E(x6061,x6062)+E(f503(x6063,x6064,x6061,x6065,x6066),f503(x6063,x6064,x6062,x6065,x6066))
% 162.26/162.09 [607]~E(x6071,x6072)+E(f503(x6073,x6074,x6075,x6071,x6076),f503(x6073,x6074,x6075,x6072,x6076))
% 162.26/162.09 [608]~E(x6081,x6082)+E(f503(x6083,x6084,x6085,x6086,x6081),f503(x6083,x6084,x6085,x6086,x6082))
% 162.26/162.09 [609]~E(x6091,x6092)+E(f835(x6091,x6093,x6094,x6095,x6096),f835(x6092,x6093,x6094,x6095,x6096))
% 162.26/162.09 [610]~E(x6101,x6102)+E(f835(x6103,x6101,x6104,x6105,x6106),f835(x6103,x6102,x6104,x6105,x6106))
% 162.26/162.09 [611]~E(x6111,x6112)+E(f835(x6113,x6114,x6111,x6115,x6116),f835(x6113,x6114,x6112,x6115,x6116))
% 162.26/162.09 [612]~E(x6121,x6122)+E(f835(x6123,x6124,x6125,x6121,x6126),f835(x6123,x6124,x6125,x6122,x6126))
% 162.26/162.09 [613]~E(x6131,x6132)+E(f835(x6133,x6134,x6135,x6136,x6131),f835(x6133,x6134,x6135,x6136,x6132))
% 162.26/162.09 [614]~E(x6141,x6142)+E(f597(x6141,x6143,x6144,x6145,x6146),f597(x6142,x6143,x6144,x6145,x6146))
% 162.26/162.09 [615]~E(x6151,x6152)+E(f597(x6153,x6151,x6154,x6155,x6156),f597(x6153,x6152,x6154,x6155,x6156))
% 162.26/162.09 [616]~E(x6161,x6162)+E(f597(x6163,x6164,x6161,x6165,x6166),f597(x6163,x6164,x6162,x6165,x6166))
% 162.26/162.09 [617]~E(x6171,x6172)+E(f597(x6173,x6174,x6175,x6171,x6176),f597(x6173,x6174,x6175,x6172,x6176))
% 162.26/162.09 [618]~E(x6181,x6182)+E(f597(x6183,x6184,x6185,x6186,x6181),f597(x6183,x6184,x6185,x6186,x6182))
% 162.26/162.09 [619]~E(x6191,x6192)+E(f460(x6191,x6193,x6194,x6195,x6196),f460(x6192,x6193,x6194,x6195,x6196))
% 162.26/162.09 [620]~E(x6201,x6202)+E(f460(x6203,x6201,x6204,x6205,x6206),f460(x6203,x6202,x6204,x6205,x6206))
% 162.26/162.09 [621]~E(x6211,x6212)+E(f460(x6213,x6214,x6211,x6215,x6216),f460(x6213,x6214,x6212,x6215,x6216))
% 162.26/162.09 [622]~E(x6221,x6222)+E(f460(x6223,x6224,x6225,x6221,x6226),f460(x6223,x6224,x6225,x6222,x6226))
% 162.26/162.09 [623]~E(x6231,x6232)+E(f460(x6233,x6234,x6235,x6236,x6231),f460(x6233,x6234,x6235,x6236,x6232))
% 162.26/162.09 [624]~E(x6241,x6242)+E(f776(x6241,x6243,x6244,x6245,x6246),f776(x6242,x6243,x6244,x6245,x6246))
% 162.26/162.09 [625]~E(x6251,x6252)+E(f776(x6253,x6251,x6254,x6255,x6256),f776(x6253,x6252,x6254,x6255,x6256))
% 162.26/162.09 [626]~E(x6261,x6262)+E(f776(x6263,x6264,x6261,x6265,x6266),f776(x6263,x6264,x6262,x6265,x6266))
% 162.26/162.09 [627]~E(x6271,x6272)+E(f776(x6273,x6274,x6275,x6271,x6276),f776(x6273,x6274,x6275,x6272,x6276))
% 162.26/162.09 [628]~E(x6281,x6282)+E(f776(x6283,x6284,x6285,x6286,x6281),f776(x6283,x6284,x6285,x6286,x6282))
% 162.26/162.09 [629]~E(x6291,x6292)+E(f689(x6291,x6293,x6294,x6295),f689(x6292,x6293,x6294,x6295))
% 162.26/162.09 [630]~E(x6301,x6302)+E(f689(x6303,x6301,x6304,x6305),f689(x6303,x6302,x6304,x6305))
% 162.26/162.09 [631]~E(x6311,x6312)+E(f689(x6313,x6314,x6311,x6315),f689(x6313,x6314,x6312,x6315))
% 162.26/162.09 [632]~E(x6321,x6322)+E(f689(x6323,x6324,x6325,x6321),f689(x6323,x6324,x6325,x6322))
% 162.26/162.09 [633]~E(x6331,x6332)+E(f837(x6331,x6333,x6334,x6335),f837(x6332,x6333,x6334,x6335))
% 162.26/162.09 [634]~E(x6341,x6342)+E(f837(x6343,x6341,x6344,x6345),f837(x6343,x6342,x6344,x6345))
% 162.26/162.09 [635]~E(x6351,x6352)+E(f837(x6353,x6354,x6351,x6355),f837(x6353,x6354,x6352,x6355))
% 162.26/162.09 [636]~E(x6361,x6362)+E(f837(x6363,x6364,x6365,x6361),f837(x6363,x6364,x6365,x6362))
% 162.26/162.09 [637]~E(x6371,x6372)+E(f747(x6371,x6373,x6374),f747(x6372,x6373,x6374))
% 162.26/162.09 [638]~E(x6381,x6382)+E(f747(x6383,x6381,x6384),f747(x6383,x6382,x6384))
% 162.26/162.09 [639]~E(x6391,x6392)+E(f747(x6393,x6394,x6391),f747(x6393,x6394,x6392))
% 162.26/162.09 [640]~E(x6401,x6402)+E(f708(x6401,x6403,x6404),f708(x6402,x6403,x6404))
% 162.26/162.09 [641]~E(x6411,x6412)+E(f708(x6413,x6411,x6414),f708(x6413,x6412,x6414))
% 162.26/162.09 [642]~E(x6421,x6422)+E(f708(x6423,x6424,x6421),f708(x6423,x6424,x6422))
% 162.26/162.09 [643]~E(x6431,x6432)+E(f518(x6431,x6433,x6434),f518(x6432,x6433,x6434))
% 162.26/162.09 [644]~E(x6441,x6442)+E(f518(x6443,x6441,x6444),f518(x6443,x6442,x6444))
% 162.26/162.09 [645]~E(x6451,x6452)+E(f518(x6453,x6454,x6451),f518(x6453,x6454,x6452))
% 162.26/162.09 [646]~E(x6461,x6462)+E(f703(x6461,x6463,x6464),f703(x6462,x6463,x6464))
% 162.26/162.09 [647]~E(x6471,x6472)+E(f703(x6473,x6471,x6474),f703(x6473,x6472,x6474))
% 162.26/162.09 [648]~E(x6481,x6482)+E(f703(x6483,x6484,x6481),f703(x6483,x6484,x6482))
% 162.26/162.09 [649]~E(x6491,x6492)+E(f300(x6491),f300(x6492))
% 162.26/162.09 [650]~E(x6501,x6502)+E(f530(x6501,x6503,x6504,x6505),f530(x6502,x6503,x6504,x6505))
% 162.26/162.09 [651]~E(x6511,x6512)+E(f530(x6513,x6511,x6514,x6515),f530(x6513,x6512,x6514,x6515))
% 162.26/162.09 [652]~E(x6521,x6522)+E(f530(x6523,x6524,x6521,x6525),f530(x6523,x6524,x6522,x6525))
% 162.26/162.09 [653]~E(x6531,x6532)+E(f530(x6533,x6534,x6535,x6531),f530(x6533,x6534,x6535,x6532))
% 162.26/162.09 [654]~E(x6541,x6542)+E(f116(x6541),f116(x6542))
% 162.26/162.09 [655]~E(x6551,x6552)+E(f677(x6551,x6553,x6554),f677(x6552,x6553,x6554))
% 162.26/162.09 [656]~E(x6561,x6562)+E(f677(x6563,x6561,x6564),f677(x6563,x6562,x6564))
% 162.26/162.09 [657]~E(x6571,x6572)+E(f677(x6573,x6574,x6571),f677(x6573,x6574,x6572))
% 162.26/162.09 [658]~E(x6581,x6582)+E(f588(x6581,x6583,x6584),f588(x6582,x6583,x6584))
% 162.26/162.09 [659]~E(x6591,x6592)+E(f588(x6593,x6591,x6594),f588(x6593,x6592,x6594))
% 162.26/162.09 [660]~E(x6601,x6602)+E(f588(x6603,x6604,x6601),f588(x6603,x6604,x6602))
% 162.26/162.09 [661]~E(x6611,x6612)+E(f152(x6611,x6613,x6614,x6615,x6616),f152(x6612,x6613,x6614,x6615,x6616))
% 162.26/162.09 [662]~E(x6621,x6622)+E(f152(x6623,x6621,x6624,x6625,x6626),f152(x6623,x6622,x6624,x6625,x6626))
% 162.26/162.09 [663]~E(x6631,x6632)+E(f152(x6633,x6634,x6631,x6635,x6636),f152(x6633,x6634,x6632,x6635,x6636))
% 162.26/162.09 [664]~E(x6641,x6642)+E(f152(x6643,x6644,x6645,x6641,x6646),f152(x6643,x6644,x6645,x6642,x6646))
% 162.26/162.09 [665]~E(x6651,x6652)+E(f152(x6653,x6654,x6655,x6656,x6651),f152(x6653,x6654,x6655,x6656,x6652))
% 162.26/162.09 [666]~E(x6661,x6662)+E(f784(x6661,x6663,x6664),f784(x6662,x6663,x6664))
% 162.26/162.09 [667]~E(x6671,x6672)+E(f784(x6673,x6671,x6674),f784(x6673,x6672,x6674))
% 162.26/162.09 [668]~E(x6681,x6682)+E(f784(x6683,x6684,x6681),f784(x6683,x6684,x6682))
% 162.26/162.09 [669]~E(x6691,x6692)+E(f153(x6691,x6693,x6694,x6695),f153(x6692,x6693,x6694,x6695))
% 162.26/162.09 [670]~E(x6701,x6702)+E(f153(x6703,x6701,x6704,x6705),f153(x6703,x6702,x6704,x6705))
% 162.26/162.09 [671]~E(x6711,x6712)+E(f153(x6713,x6714,x6711,x6715),f153(x6713,x6714,x6712,x6715))
% 162.26/162.09 [672]~E(x6721,x6722)+E(f153(x6723,x6724,x6725,x6721),f153(x6723,x6724,x6725,x6722))
% 162.26/162.09 [673]~E(x6731,x6732)+E(f686(x6731,x6733,x6734),f686(x6732,x6733,x6734))
% 162.26/162.09 [674]~E(x6741,x6742)+E(f686(x6743,x6741,x6744),f686(x6743,x6742,x6744))
% 162.26/162.09 [675]~E(x6751,x6752)+E(f686(x6753,x6754,x6751),f686(x6753,x6754,x6752))
% 162.26/162.09 [676]~E(x6761,x6762)+E(f59(x6761),f59(x6762))
% 162.26/162.09 [677]~E(x6771,x6772)+E(f471(x6771,x6773,x6774,x6775),f471(x6772,x6773,x6774,x6775))
% 162.26/162.09 [678]~E(x6781,x6782)+E(f471(x6783,x6781,x6784,x6785),f471(x6783,x6782,x6784,x6785))
% 162.26/162.09 [679]~E(x6791,x6792)+E(f471(x6793,x6794,x6791,x6795),f471(x6793,x6794,x6792,x6795))
% 162.26/162.09 [680]~E(x6801,x6802)+E(f471(x6803,x6804,x6805,x6801),f471(x6803,x6804,x6805,x6802))
% 162.26/162.09 [681]~E(x6811,x6812)+E(f483(x6811,x6813,x6814,x6815),f483(x6812,x6813,x6814,x6815))
% 162.26/162.09 [682]~E(x6821,x6822)+E(f483(x6823,x6821,x6824,x6825),f483(x6823,x6822,x6824,x6825))
% 162.26/162.09 [683]~E(x6831,x6832)+E(f483(x6833,x6834,x6831,x6835),f483(x6833,x6834,x6832,x6835))
% 162.26/162.09 [684]~E(x6841,x6842)+E(f483(x6843,x6844,x6845,x6841),f483(x6843,x6844,x6845,x6842))
% 162.26/162.09 [685]~E(x6851,x6852)+E(f520(x6851,x6853,x6854),f520(x6852,x6853,x6854))
% 162.26/162.09 [686]~E(x6861,x6862)+E(f520(x6863,x6861,x6864),f520(x6863,x6862,x6864))
% 162.26/162.09 [687]~E(x6871,x6872)+E(f520(x6873,x6874,x6871),f520(x6873,x6874,x6872))
% 162.26/162.09 [688]~E(x6881,x6882)+E(f266(x6881,x6883,x6884),f266(x6882,x6883,x6884))
% 162.26/162.09 [689]~E(x6891,x6892)+E(f266(x6893,x6891,x6894),f266(x6893,x6892,x6894))
% 162.26/162.09 [690]~E(x6901,x6902)+E(f266(x6903,x6904,x6901),f266(x6903,x6904,x6902))
% 162.26/162.09 [691]~E(x6911,x6912)+E(f265(x6911,x6913),f265(x6912,x6913))
% 162.26/162.09 [692]~E(x6921,x6922)+E(f265(x6923,x6921),f265(x6923,x6922))
% 162.26/162.09 [693]~E(x6931,x6932)+E(f217(x6931),f217(x6932))
% 162.26/162.09 [694]~E(x6941,x6942)+E(f492(x6941,x6943,x6944,x6945,x6946),f492(x6942,x6943,x6944,x6945,x6946))
% 162.26/162.09 [695]~E(x6951,x6952)+E(f492(x6953,x6951,x6954,x6955,x6956),f492(x6953,x6952,x6954,x6955,x6956))
% 162.26/162.09 [696]~E(x6961,x6962)+E(f492(x6963,x6964,x6961,x6965,x6966),f492(x6963,x6964,x6962,x6965,x6966))
% 162.26/162.09 [697]~E(x6971,x6972)+E(f492(x6973,x6974,x6975,x6971,x6976),f492(x6973,x6974,x6975,x6972,x6976))
% 162.26/162.09 [698]~E(x6981,x6982)+E(f492(x6983,x6984,x6985,x6986,x6981),f492(x6983,x6984,x6985,x6986,x6982))
% 162.26/162.09 [699]~E(x6991,x6992)+E(f800(x6991,x6993),f800(x6992,x6993))
% 162.26/162.09 [700]~E(x7001,x7002)+E(f800(x7003,x7001),f800(x7003,x7002))
% 162.26/162.09 [701]~E(x7011,x7012)+E(f487(x7011,x7013,x7014,x7015,x7016),f487(x7012,x7013,x7014,x7015,x7016))
% 162.26/162.09 [702]~E(x7021,x7022)+E(f487(x7023,x7021,x7024,x7025,x7026),f487(x7023,x7022,x7024,x7025,x7026))
% 162.26/162.09 [703]~E(x7031,x7032)+E(f487(x7033,x7034,x7031,x7035,x7036),f487(x7033,x7034,x7032,x7035,x7036))
% 162.26/162.09 [704]~E(x7041,x7042)+E(f487(x7043,x7044,x7045,x7041,x7046),f487(x7043,x7044,x7045,x7042,x7046))
% 162.26/162.09 [705]~E(x7051,x7052)+E(f487(x7053,x7054,x7055,x7056,x7051),f487(x7053,x7054,x7055,x7056,x7052))
% 162.26/162.09 [706]~E(x7061,x7062)+E(f643(x7061,x7063,x7064,x7065),f643(x7062,x7063,x7064,x7065))
% 162.26/162.09 [707]~E(x7071,x7072)+E(f643(x7073,x7071,x7074,x7075),f643(x7073,x7072,x7074,x7075))
% 162.26/162.09 [708]~E(x7081,x7082)+E(f643(x7083,x7084,x7081,x7085),f643(x7083,x7084,x7082,x7085))
% 162.26/162.09 [709]~E(x7091,x7092)+E(f643(x7093,x7094,x7095,x7091),f643(x7093,x7094,x7095,x7092))
% 162.26/162.09 [710]~E(x7101,x7102)+E(f228(x7101,x7103),f228(x7102,x7103))
% 162.26/162.09 [711]~E(x7111,x7112)+E(f228(x7113,x7111),f228(x7113,x7112))
% 162.26/162.09 [712]~E(x7121,x7122)+E(f615(x7121,x7123,x7124,x7125),f615(x7122,x7123,x7124,x7125))
% 162.26/162.09 [713]~E(x7131,x7132)+E(f615(x7133,x7131,x7134,x7135),f615(x7133,x7132,x7134,x7135))
% 162.26/162.09 [714]~E(x7141,x7142)+E(f615(x7143,x7144,x7141,x7145),f615(x7143,x7144,x7142,x7145))
% 162.26/162.09 [715]~E(x7151,x7152)+E(f615(x7153,x7154,x7155,x7151),f615(x7153,x7154,x7155,x7152))
% 162.26/162.09 [716]~E(x7161,x7162)+E(f652(x7161,x7163,x7164,x7165),f652(x7162,x7163,x7164,x7165))
% 162.26/162.09 [717]~E(x7171,x7172)+E(f652(x7173,x7171,x7174,x7175),f652(x7173,x7172,x7174,x7175))
% 162.26/162.09 [718]~E(x7181,x7182)+E(f652(x7183,x7184,x7181,x7185),f652(x7183,x7184,x7182,x7185))
% 162.26/162.09 [719]~E(x7191,x7192)+E(f652(x7193,x7194,x7195,x7191),f652(x7193,x7194,x7195,x7192))
% 162.26/162.09 [720]~E(x7201,x7202)+E(f99(x7201,x7203,x7204),f99(x7202,x7203,x7204))
% 162.26/162.09 [721]~E(x7211,x7212)+E(f99(x7213,x7211,x7214),f99(x7213,x7212,x7214))
% 162.26/162.09 [722]~E(x7221,x7222)+E(f99(x7223,x7224,x7221),f99(x7223,x7224,x7222))
% 162.26/162.09 [723]~E(x7231,x7232)+E(f215(x7231,x7233,x7234),f215(x7232,x7233,x7234))
% 162.26/162.09 [724]~E(x7241,x7242)+E(f215(x7243,x7241,x7244),f215(x7243,x7242,x7244))
% 162.26/162.09 [725]~E(x7251,x7252)+E(f215(x7253,x7254,x7251),f215(x7253,x7254,x7252))
% 162.26/162.09 [726]~E(x7261,x7262)+E(f630(x7261,x7263,x7264,x7265),f630(x7262,x7263,x7264,x7265))
% 162.26/162.09 [727]~E(x7271,x7272)+E(f630(x7273,x7271,x7274,x7275),f630(x7273,x7272,x7274,x7275))
% 162.26/162.09 [728]~E(x7281,x7282)+E(f630(x7283,x7284,x7281,x7285),f630(x7283,x7284,x7282,x7285))
% 162.26/162.09 [729]~E(x7291,x7292)+E(f630(x7293,x7294,x7295,x7291),f630(x7293,x7294,x7295,x7292))
% 162.26/162.09 [730]~E(x7301,x7302)+E(f396(x7301,x7303,x7304),f396(x7302,x7303,x7304))
% 162.26/162.09 [731]~E(x7311,x7312)+E(f396(x7313,x7311,x7314),f396(x7313,x7312,x7314))
% 162.26/162.09 [732]~E(x7321,x7322)+E(f396(x7323,x7324,x7321),f396(x7323,x7324,x7322))
% 162.26/162.09 [733]~E(x7331,x7332)+E(f582(x7331,x7333,x7334,x7335),f582(x7332,x7333,x7334,x7335))
% 162.26/162.09 [734]~E(x7341,x7342)+E(f582(x7343,x7341,x7344,x7345),f582(x7343,x7342,x7344,x7345))
% 162.26/162.09 [735]~E(x7351,x7352)+E(f582(x7353,x7354,x7351,x7355),f582(x7353,x7354,x7352,x7355))
% 162.26/162.09 [736]~E(x7361,x7362)+E(f582(x7363,x7364,x7365,x7361),f582(x7363,x7364,x7365,x7362))
% 162.26/162.09 [737]~E(x7371,x7372)+E(f360(x7371,x7373,x7374,x7375,x7376),f360(x7372,x7373,x7374,x7375,x7376))
% 162.26/162.09 [738]~E(x7381,x7382)+E(f360(x7383,x7381,x7384,x7385,x7386),f360(x7383,x7382,x7384,x7385,x7386))
% 162.26/162.09 [739]~E(x7391,x7392)+E(f360(x7393,x7394,x7391,x7395,x7396),f360(x7393,x7394,x7392,x7395,x7396))
% 162.26/162.09 [740]~E(x7401,x7402)+E(f360(x7403,x7404,x7405,x7401,x7406),f360(x7403,x7404,x7405,x7402,x7406))
% 162.26/162.09 [741]~E(x7411,x7412)+E(f360(x7413,x7414,x7415,x7416,x7411),f360(x7413,x7414,x7415,x7416,x7412))
% 162.26/162.09 [742]~E(x7421,x7422)+E(f345(x7421,x7423,x7424,x7425),f345(x7422,x7423,x7424,x7425))
% 162.26/162.09 [743]~E(x7431,x7432)+E(f345(x7433,x7431,x7434,x7435),f345(x7433,x7432,x7434,x7435))
% 162.26/162.09 [744]~E(x7441,x7442)+E(f345(x7443,x7444,x7441,x7445),f345(x7443,x7444,x7442,x7445))
% 162.26/162.09 [745]~E(x7451,x7452)+E(f345(x7453,x7454,x7455,x7451),f345(x7453,x7454,x7455,x7452))
% 162.26/162.09 [746]~E(x7461,x7462)+E(f448(x7461,x7463),f448(x7462,x7463))
% 162.26/162.09 [747]~E(x7471,x7472)+E(f448(x7473,x7471),f448(x7473,x7472))
% 162.26/162.09 [748]~E(x7481,x7482)+E(f751(x7481,x7483,x7484,x7485,x7486,x7487),f751(x7482,x7483,x7484,x7485,x7486,x7487))
% 162.26/162.09 [749]~E(x7491,x7492)+E(f751(x7493,x7491,x7494,x7495,x7496,x7497),f751(x7493,x7492,x7494,x7495,x7496,x7497))
% 162.26/162.09 [750]~E(x7501,x7502)+E(f751(x7503,x7504,x7501,x7505,x7506,x7507),f751(x7503,x7504,x7502,x7505,x7506,x7507))
% 162.26/162.09 [751]~E(x7511,x7512)+E(f751(x7513,x7514,x7515,x7511,x7516,x7517),f751(x7513,x7514,x7515,x7512,x7516,x7517))
% 162.26/162.09 [752]~E(x7521,x7522)+E(f751(x7523,x7524,x7525,x7526,x7521,x7527),f751(x7523,x7524,x7525,x7526,x7522,x7527))
% 162.26/162.09 [753]~E(x7531,x7532)+E(f751(x7533,x7534,x7535,x7536,x7537,x7531),f751(x7533,x7534,x7535,x7536,x7537,x7532))
% 162.26/162.09 [754]~E(x7541,x7542)+E(f695(x7541,x7543),f695(x7542,x7543))
% 162.26/162.09 [755]~E(x7551,x7552)+E(f695(x7553,x7551),f695(x7553,x7552))
% 162.26/162.09 [756]~E(x7561,x7562)+E(f607(x7561,x7563,x7564),f607(x7562,x7563,x7564))
% 162.26/162.09 [757]~E(x7571,x7572)+E(f607(x7573,x7571,x7574),f607(x7573,x7572,x7574))
% 162.26/162.09 [758]~E(x7581,x7582)+E(f607(x7583,x7584,x7581),f607(x7583,x7584,x7582))
% 162.26/162.09 [759]~E(x7591,x7592)+E(f405(x7591,x7593,x7594),f405(x7592,x7593,x7594))
% 162.26/162.09 [760]~E(x7601,x7602)+E(f405(x7603,x7601,x7604),f405(x7603,x7602,x7604))
% 162.26/162.09 [761]~E(x7611,x7612)+E(f405(x7613,x7614,x7611),f405(x7613,x7614,x7612))
% 162.26/162.09 [762]~E(x7621,x7622)+E(f654(x7621,x7623,x7624,x7625,x7626),f654(x7622,x7623,x7624,x7625,x7626))
% 162.26/162.09 [763]~E(x7631,x7632)+E(f654(x7633,x7631,x7634,x7635,x7636),f654(x7633,x7632,x7634,x7635,x7636))
% 162.26/162.09 [764]~E(x7641,x7642)+E(f654(x7643,x7644,x7641,x7645,x7646),f654(x7643,x7644,x7642,x7645,x7646))
% 162.26/162.09 [765]~E(x7651,x7652)+E(f654(x7653,x7654,x7655,x7651,x7656),f654(x7653,x7654,x7655,x7652,x7656))
% 162.26/162.09 [766]~E(x7661,x7662)+E(f654(x7663,x7664,x7665,x7666,x7661),f654(x7663,x7664,x7665,x7666,x7662))
% 162.26/162.09 [767]~E(x7671,x7672)+E(f351(x7671,x7673,x7674,x7675,x7676),f351(x7672,x7673,x7674,x7675,x7676))
% 162.26/162.09 [768]~E(x7681,x7682)+E(f351(x7683,x7681,x7684,x7685,x7686),f351(x7683,x7682,x7684,x7685,x7686))
% 162.26/162.09 [769]~E(x7691,x7692)+E(f351(x7693,x7694,x7691,x7695,x7696),f351(x7693,x7694,x7692,x7695,x7696))
% 162.26/162.09 [770]~E(x7701,x7702)+E(f351(x7703,x7704,x7705,x7701,x7706),f351(x7703,x7704,x7705,x7702,x7706))
% 162.26/162.09 [771]~E(x7711,x7712)+E(f351(x7713,x7714,x7715,x7716,x7711),f351(x7713,x7714,x7715,x7716,x7712))
% 162.26/162.09 [772]~E(x7721,x7722)+E(f406(x7721,x7723,x7724),f406(x7722,x7723,x7724))
% 162.26/162.09 [773]~E(x7731,x7732)+E(f406(x7733,x7731,x7734),f406(x7733,x7732,x7734))
% 162.26/162.09 [774]~E(x7741,x7742)+E(f406(x7743,x7744,x7741),f406(x7743,x7744,x7742))
% 162.26/162.09 [775]~E(x7751,x7752)+E(f566(x7751,x7753),f566(x7752,x7753))
% 162.26/162.09 [776]~E(x7761,x7762)+E(f566(x7763,x7761),f566(x7763,x7762))
% 162.26/162.09 [777]~E(x7771,x7772)+E(f454(x7771,x7773,x7774,x7775),f454(x7772,x7773,x7774,x7775))
% 162.26/162.09 [778]~E(x7781,x7782)+E(f454(x7783,x7781,x7784,x7785),f454(x7783,x7782,x7784,x7785))
% 162.26/162.09 [779]~E(x7791,x7792)+E(f454(x7793,x7794,x7791,x7795),f454(x7793,x7794,x7792,x7795))
% 162.26/162.09 [780]~E(x7801,x7802)+E(f454(x7803,x7804,x7805,x7801),f454(x7803,x7804,x7805,x7802))
% 162.26/162.09 [781]~E(x7811,x7812)+E(f649(x7811,x7813,x7814,x7815,x7816),f649(x7812,x7813,x7814,x7815,x7816))
% 162.26/162.09 [782]~E(x7821,x7822)+E(f649(x7823,x7821,x7824,x7825,x7826),f649(x7823,x7822,x7824,x7825,x7826))
% 162.26/162.09 [783]~E(x7831,x7832)+E(f649(x7833,x7834,x7831,x7835,x7836),f649(x7833,x7834,x7832,x7835,x7836))
% 162.26/162.09 [784]~E(x7841,x7842)+E(f649(x7843,x7844,x7845,x7841,x7846),f649(x7843,x7844,x7845,x7842,x7846))
% 162.26/162.09 [785]~E(x7851,x7852)+E(f649(x7853,x7854,x7855,x7856,x7851),f649(x7853,x7854,x7855,x7856,x7852))
% 162.26/162.09 [786]~E(x7861,x7862)+E(f765(x7861,x7863),f765(x7862,x7863))
% 162.26/162.09 [787]~E(x7871,x7872)+E(f765(x7873,x7871),f765(x7873,x7872))
% 162.26/162.09 [788]~E(x7881,x7882)+E(f501(x7881,x7883,x7884,x7885,x7886),f501(x7882,x7883,x7884,x7885,x7886))
% 162.26/162.09 [789]~E(x7891,x7892)+E(f501(x7893,x7891,x7894,x7895,x7896),f501(x7893,x7892,x7894,x7895,x7896))
% 162.26/162.09 [790]~E(x7901,x7902)+E(f501(x7903,x7904,x7901,x7905,x7906),f501(x7903,x7904,x7902,x7905,x7906))
% 162.26/162.09 [791]~E(x7911,x7912)+E(f501(x7913,x7914,x7915,x7911,x7916),f501(x7913,x7914,x7915,x7912,x7916))
% 162.26/162.09 [792]~E(x7921,x7922)+E(f501(x7923,x7924,x7925,x7926,x7921),f501(x7923,x7924,x7925,x7926,x7922))
% 162.26/162.09 [793]~E(x7931,x7932)+E(f856(x7931,x7933,x7934),f856(x7932,x7933,x7934))
% 162.26/162.09 [794]~E(x7941,x7942)+E(f856(x7943,x7941,x7944),f856(x7943,x7942,x7944))
% 162.26/162.09 [795]~E(x7951,x7952)+E(f856(x7953,x7954,x7951),f856(x7953,x7954,x7952))
% 162.26/162.09 [796]~E(x7961,x7962)+E(f60(x7961,x7963,x7964,x7965),f60(x7962,x7963,x7964,x7965))
% 162.26/162.09 [797]~E(x7971,x7972)+E(f60(x7973,x7971,x7974,x7975),f60(x7973,x7972,x7974,x7975))
% 162.26/162.09 [798]~E(x7981,x7982)+E(f60(x7983,x7984,x7981,x7985),f60(x7983,x7984,x7982,x7985))
% 162.26/162.09 [799]~E(x7991,x7992)+E(f60(x7993,x7994,x7995,x7991),f60(x7993,x7994,x7995,x7992))
% 162.26/162.09 [800]~E(x8001,x8002)+E(f77(x8001,x8003,x8004,x8005,x8006),f77(x8002,x8003,x8004,x8005,x8006))
% 162.26/162.09 [801]~E(x8011,x8012)+E(f77(x8013,x8011,x8014,x8015,x8016),f77(x8013,x8012,x8014,x8015,x8016))
% 162.26/162.09 [802]~E(x8021,x8022)+E(f77(x8023,x8024,x8021,x8025,x8026),f77(x8023,x8024,x8022,x8025,x8026))
% 162.26/162.09 [803]~E(x8031,x8032)+E(f77(x8033,x8034,x8035,x8031,x8036),f77(x8033,x8034,x8035,x8032,x8036))
% 162.26/162.09 [804]~E(x8041,x8042)+E(f77(x8043,x8044,x8045,x8046,x8041),f77(x8043,x8044,x8045,x8046,x8042))
% 162.26/162.09 [805]~E(x8051,x8052)+E(f739(x8051,x8053,x8054),f739(x8052,x8053,x8054))
% 162.26/162.09 [806]~E(x8061,x8062)+E(f739(x8063,x8061,x8064),f739(x8063,x8062,x8064))
% 162.26/162.09 [807]~E(x8071,x8072)+E(f739(x8073,x8074,x8071),f739(x8073,x8074,x8072))
% 162.26/162.09 [808]~E(x8081,x8082)+E(f629(x8081,x8083,x8084,x8085),f629(x8082,x8083,x8084,x8085))
% 162.26/162.09 [809]~E(x8091,x8092)+E(f629(x8093,x8091,x8094,x8095),f629(x8093,x8092,x8094,x8095))
% 162.26/162.09 [810]~E(x8101,x8102)+E(f629(x8103,x8104,x8101,x8105),f629(x8103,x8104,x8102,x8105))
% 162.26/162.09 [811]~E(x8111,x8112)+E(f629(x8113,x8114,x8115,x8111),f629(x8113,x8114,x8115,x8112))
% 162.26/162.09 [812]~E(x8121,x8122)+E(f550(x8121,x8123,x8124),f550(x8122,x8123,x8124))
% 162.26/162.09 [813]~E(x8131,x8132)+E(f550(x8133,x8131,x8134),f550(x8133,x8132,x8134))
% 162.26/162.09 [814]~E(x8141,x8142)+E(f550(x8143,x8144,x8141),f550(x8143,x8144,x8142))
% 162.26/162.09 [815]~E(x8151,x8152)+E(f842(x8151,x8153,x8154,x8155),f842(x8152,x8153,x8154,x8155))
% 162.26/162.09 [816]~E(x8161,x8162)+E(f842(x8163,x8161,x8164,x8165),f842(x8163,x8162,x8164,x8165))
% 162.26/162.09 [817]~E(x8171,x8172)+E(f842(x8173,x8174,x8171,x8175),f842(x8173,x8174,x8172,x8175))
% 162.26/162.09 [818]~E(x8181,x8182)+E(f842(x8183,x8184,x8185,x8181),f842(x8183,x8184,x8185,x8182))
% 162.26/162.09 [819]~E(x8191,x8192)+E(f524(x8191,x8193),f524(x8192,x8193))
% 162.26/162.09 [820]~E(x8201,x8202)+E(f524(x8203,x8201),f524(x8203,x8202))
% 162.26/162.09 [821]~E(x8211,x8212)+E(f860(x8211,x8213,x8214),f860(x8212,x8213,x8214))
% 162.26/162.09 [822]~E(x8221,x8222)+E(f860(x8223,x8221,x8224),f860(x8223,x8222,x8224))
% 162.26/162.09 [823]~E(x8231,x8232)+E(f860(x8233,x8234,x8231),f860(x8233,x8234,x8232))
% 162.26/162.09 [824]~E(x8241,x8242)+E(f100(x8241,x8243,x8244,x8245),f100(x8242,x8243,x8244,x8245))
% 162.26/162.09 [825]~E(x8251,x8252)+E(f100(x8253,x8251,x8254,x8255),f100(x8253,x8252,x8254,x8255))
% 162.26/162.09 [826]~E(x8261,x8262)+E(f100(x8263,x8264,x8261,x8265),f100(x8263,x8264,x8262,x8265))
% 162.26/162.09 [827]~E(x8271,x8272)+E(f100(x8273,x8274,x8275,x8271),f100(x8273,x8274,x8275,x8272))
% 162.26/162.09 [828]~E(x8281,x8282)+E(f516(x8281,x8283,x8284,x8285,x8286,x8287,x8288,x8289),f516(x8282,x8283,x8284,x8285,x8286,x8287,x8288,x8289))
% 162.26/162.09 [829]~E(x8291,x8292)+E(f516(x8293,x8291,x8294,x8295,x8296,x8297,x8298,x8299),f516(x8293,x8292,x8294,x8295,x8296,x8297,x8298,x8299))
% 162.26/162.09 [830]~E(x8301,x8302)+E(f516(x8303,x8304,x8301,x8305,x8306,x8307,x8308,x8309),f516(x8303,x8304,x8302,x8305,x8306,x8307,x8308,x8309))
% 162.26/162.09 [831]~E(x8311,x8312)+E(f516(x8313,x8314,x8315,x8311,x8316,x8317,x8318,x8319),f516(x8313,x8314,x8315,x8312,x8316,x8317,x8318,x8319))
% 162.26/162.09 [832]~E(x8321,x8322)+E(f516(x8323,x8324,x8325,x8326,x8321,x8327,x8328,x8329),f516(x8323,x8324,x8325,x8326,x8322,x8327,x8328,x8329))
% 162.26/162.09 [833]~E(x8331,x8332)+E(f516(x8333,x8334,x8335,x8336,x8337,x8331,x8338,x8339),f516(x8333,x8334,x8335,x8336,x8337,x8332,x8338,x8339))
% 162.26/162.09 [834]~E(x8341,x8342)+E(f516(x8343,x8344,x8345,x8346,x8347,x8348,x8341,x8349),f516(x8343,x8344,x8345,x8346,x8347,x8348,x8342,x8349))
% 162.26/162.09 [835]~E(x8351,x8352)+E(f516(x8353,x8354,x8355,x8356,x8357,x8358,x8359,x8351),f516(x8353,x8354,x8355,x8356,x8357,x8358,x8359,x8352))
% 162.26/162.09 [836]~E(x8361,x8362)+E(f817(x8361,x8363),f817(x8362,x8363))
% 162.26/162.09 [837]~E(x8371,x8372)+E(f817(x8373,x8371),f817(x8373,x8372))
% 162.26/162.09 [838]~E(x8381,x8382)+E(f531(x8381,x8383,x8384),f531(x8382,x8383,x8384))
% 162.26/162.09 [839]~E(x8391,x8392)+E(f531(x8393,x8391,x8394),f531(x8393,x8392,x8394))
% 162.26/162.09 [840]~E(x8401,x8402)+E(f531(x8403,x8404,x8401),f531(x8403,x8404,x8402))
% 162.26/162.09 [841]~E(x8411,x8412)+E(f476(x8411,x8413,x8414,x8415,x8416),f476(x8412,x8413,x8414,x8415,x8416))
% 162.26/162.09 [842]~E(x8421,x8422)+E(f476(x8423,x8421,x8424,x8425,x8426),f476(x8423,x8422,x8424,x8425,x8426))
% 162.26/162.09 [843]~E(x8431,x8432)+E(f476(x8433,x8434,x8431,x8435,x8436),f476(x8433,x8434,x8432,x8435,x8436))
% 162.26/162.09 [844]~E(x8441,x8442)+E(f476(x8443,x8444,x8445,x8441,x8446),f476(x8443,x8444,x8445,x8442,x8446))
% 162.26/162.09 [845]~E(x8451,x8452)+E(f476(x8453,x8454,x8455,x8456,x8451),f476(x8453,x8454,x8455,x8456,x8452))
% 162.26/162.09 [846]~E(x8461,x8462)+E(f274(x8461,x8463,x8464,x8465,x8466),f274(x8462,x8463,x8464,x8465,x8466))
% 162.26/162.09 [847]~E(x8471,x8472)+E(f274(x8473,x8471,x8474,x8475,x8476),f274(x8473,x8472,x8474,x8475,x8476))
% 162.26/162.09 [848]~E(x8481,x8482)+E(f274(x8483,x8484,x8481,x8485,x8486),f274(x8483,x8484,x8482,x8485,x8486))
% 162.26/162.09 [849]~E(x8491,x8492)+E(f274(x8493,x8494,x8495,x8491,x8496),f274(x8493,x8494,x8495,x8492,x8496))
% 162.26/162.09 [850]~E(x8501,x8502)+E(f274(x8503,x8504,x8505,x8506,x8501),f274(x8503,x8504,x8505,x8506,x8502))
% 162.26/162.09 [851]~E(x8511,x8512)+E(f651(x8511,x8513,x8514,x8515),f651(x8512,x8513,x8514,x8515))
% 162.26/162.09 [852]~E(x8521,x8522)+E(f651(x8523,x8521,x8524,x8525),f651(x8523,x8522,x8524,x8525))
% 162.26/162.09 [853]~E(x8531,x8532)+E(f651(x8533,x8534,x8531,x8535),f651(x8533,x8534,x8532,x8535))
% 162.26/162.09 [854]~E(x8541,x8542)+E(f651(x8543,x8544,x8545,x8541),f651(x8543,x8544,x8545,x8542))
% 162.26/162.09 [855]~E(x8551,x8552)+E(f96(x8551),f96(x8552))
% 162.26/162.09 [856]~E(x8561,x8562)+E(f312(x8561,x8563),f312(x8562,x8563))
% 162.26/162.10 [857]~E(x8571,x8572)+E(f312(x8573,x8571),f312(x8573,x8572))
% 162.26/162.10 [858]~E(x8581,x8582)+E(f642(x8581,x8583,x8584),f642(x8582,x8583,x8584))
% 162.26/162.10 [859]~E(x8591,x8592)+E(f642(x8593,x8591,x8594),f642(x8593,x8592,x8594))
% 162.26/162.10 [860]~E(x8601,x8602)+E(f642(x8603,x8604,x8601),f642(x8603,x8604,x8602))
% 162.26/162.10 [861]~E(x8611,x8612)+E(f30(x8611,x8613,x8614),f30(x8612,x8613,x8614))
% 162.26/162.10 [862]~E(x8621,x8622)+E(f30(x8623,x8621,x8624),f30(x8623,x8622,x8624))
% 162.26/162.10 [863]~E(x8631,x8632)+E(f30(x8633,x8634,x8631),f30(x8633,x8634,x8632))
% 162.26/162.10 [864]~E(x8641,x8642)+E(f280(x8641,x8643,x8644,x8645),f280(x8642,x8643,x8644,x8645))
% 162.26/162.10 [865]~E(x8651,x8652)+E(f280(x8653,x8651,x8654,x8655),f280(x8653,x8652,x8654,x8655))
% 162.26/162.10 [866]~E(x8661,x8662)+E(f280(x8663,x8664,x8661,x8665),f280(x8663,x8664,x8662,x8665))
% 162.26/162.10 [867]~E(x8671,x8672)+E(f280(x8673,x8674,x8675,x8671),f280(x8673,x8674,x8675,x8672))
% 162.26/162.10 [868]~E(x8681,x8682)+E(f88(x8681),f88(x8682))
% 162.26/162.10 [869]~E(x8691,x8692)+E(f430(x8691,x8693,x8694,x8695),f430(x8692,x8693,x8694,x8695))
% 162.26/162.10 [870]~E(x8701,x8702)+E(f430(x8703,x8701,x8704,x8705),f430(x8703,x8702,x8704,x8705))
% 162.26/162.10 [871]~E(x8711,x8712)+E(f430(x8713,x8714,x8711,x8715),f430(x8713,x8714,x8712,x8715))
% 162.26/162.10 [872]~E(x8721,x8722)+E(f430(x8723,x8724,x8725,x8721),f430(x8723,x8724,x8725,x8722))
% 162.26/162.10 [873]~E(x8731,x8732)+E(f537(x8731,x8733,x8734),f537(x8732,x8733,x8734))
% 162.26/162.10 [874]~E(x8741,x8742)+E(f537(x8743,x8741,x8744),f537(x8743,x8742,x8744))
% 162.26/162.10 [875]~E(x8751,x8752)+E(f537(x8753,x8754,x8751),f537(x8753,x8754,x8752))
% 162.26/162.10 [876]~E(x8761,x8762)+E(f250(x8761,x8763),f250(x8762,x8763))
% 162.26/162.10 [877]~E(x8771,x8772)+E(f250(x8773,x8771),f250(x8773,x8772))
% 162.26/162.10 [878]~E(x8781,x8782)+E(f131(x8781),f131(x8782))
% 162.26/162.10 [879]~E(x8791,x8792)+E(f810(x8791,x8793,x8794),f810(x8792,x8793,x8794))
% 162.26/162.10 [880]~E(x8801,x8802)+E(f810(x8803,x8801,x8804),f810(x8803,x8802,x8804))
% 162.26/162.10 [881]~E(x8811,x8812)+E(f810(x8813,x8814,x8811),f810(x8813,x8814,x8812))
% 162.26/162.10 [882]~E(x8821,x8822)+E(f625(x8821,x8823,x8824),f625(x8822,x8823,x8824))
% 162.26/162.10 [883]~E(x8831,x8832)+E(f625(x8833,x8831,x8834),f625(x8833,x8832,x8834))
% 162.26/162.10 [884]~E(x8841,x8842)+E(f625(x8843,x8844,x8841),f625(x8843,x8844,x8842))
% 162.26/162.10 [885]~E(x8851,x8852)+E(f628(x8851,x8853,x8854,x8855),f628(x8852,x8853,x8854,x8855))
% 162.26/162.10 [886]~E(x8861,x8862)+E(f628(x8863,x8861,x8864,x8865),f628(x8863,x8862,x8864,x8865))
% 162.26/162.10 [887]~E(x8871,x8872)+E(f628(x8873,x8874,x8871,x8875),f628(x8873,x8874,x8872,x8875))
% 162.26/162.10 [888]~E(x8881,x8882)+E(f628(x8883,x8884,x8885,x8881),f628(x8883,x8884,x8885,x8882))
% 162.26/162.10 [889]~E(x8891,x8892)+E(f210(x8891,x8893),f210(x8892,x8893))
% 162.26/162.10 [890]~E(x8901,x8902)+E(f210(x8903,x8901),f210(x8903,x8902))
% 162.26/162.10 [891]~E(x8911,x8912)+E(f293(x8911,x8913,x8914),f293(x8912,x8913,x8914))
% 162.26/162.10 [892]~E(x8921,x8922)+E(f293(x8923,x8921,x8924),f293(x8923,x8922,x8924))
% 162.26/162.10 [893]~E(x8931,x8932)+E(f293(x8933,x8934,x8931),f293(x8933,x8934,x8932))
% 162.26/162.10 [894]~E(x8941,x8942)+E(f789(x8941,x8943,x8944,x8945),f789(x8942,x8943,x8944,x8945))
% 162.26/162.10 [895]~E(x8951,x8952)+E(f789(x8953,x8951,x8954,x8955),f789(x8953,x8952,x8954,x8955))
% 162.26/162.10 [896]~E(x8961,x8962)+E(f789(x8963,x8964,x8961,x8965),f789(x8963,x8964,x8962,x8965))
% 162.26/162.10 [897]~E(x8971,x8972)+E(f789(x8973,x8974,x8975,x8971),f789(x8973,x8974,x8975,x8972))
% 162.26/162.10 [898]~E(x8981,x8982)+E(f502(x8981,x8983,x8984,x8985,x8986),f502(x8982,x8983,x8984,x8985,x8986))
% 162.26/162.10 [899]~E(x8991,x8992)+E(f502(x8993,x8991,x8994,x8995,x8996),f502(x8993,x8992,x8994,x8995,x8996))
% 162.26/162.10 [900]~E(x9001,x9002)+E(f502(x9003,x9004,x9001,x9005,x9006),f502(x9003,x9004,x9002,x9005,x9006))
% 162.26/162.10 [901]~E(x9011,x9012)+E(f502(x9013,x9014,x9015,x9011,x9016),f502(x9013,x9014,x9015,x9012,x9016))
% 162.26/162.10 [902]~E(x9021,x9022)+E(f502(x9023,x9024,x9025,x9026,x9021),f502(x9023,x9024,x9025,x9026,x9022))
% 162.26/162.10 [903]~E(x9031,x9032)+E(f359(x9031,x9033,x9034,x9035,x9036),f359(x9032,x9033,x9034,x9035,x9036))
% 162.26/162.10 [904]~E(x9041,x9042)+E(f359(x9043,x9041,x9044,x9045,x9046),f359(x9043,x9042,x9044,x9045,x9046))
% 162.26/162.10 [905]~E(x9051,x9052)+E(f359(x9053,x9054,x9051,x9055,x9056),f359(x9053,x9054,x9052,x9055,x9056))
% 162.26/162.10 [906]~E(x9061,x9062)+E(f359(x9063,x9064,x9065,x9061,x9066),f359(x9063,x9064,x9065,x9062,x9066))
% 162.26/162.10 [907]~E(x9071,x9072)+E(f359(x9073,x9074,x9075,x9076,x9071),f359(x9073,x9074,x9075,x9076,x9072))
% 162.26/162.10 [908]~E(x9081,x9082)+E(f768(x9081,x9083,x9084,x9085,x9086),f768(x9082,x9083,x9084,x9085,x9086))
% 162.26/162.10 [909]~E(x9091,x9092)+E(f768(x9093,x9091,x9094,x9095,x9096),f768(x9093,x9092,x9094,x9095,x9096))
% 162.26/162.10 [910]~E(x9101,x9102)+E(f768(x9103,x9104,x9101,x9105,x9106),f768(x9103,x9104,x9102,x9105,x9106))
% 162.26/162.10 [911]~E(x9111,x9112)+E(f768(x9113,x9114,x9115,x9111,x9116),f768(x9113,x9114,x9115,x9112,x9116))
% 162.26/162.10 [912]~E(x9121,x9122)+E(f768(x9123,x9124,x9125,x9126,x9121),f768(x9123,x9124,x9125,x9126,x9122))
% 162.26/162.10 [913]~E(x9131,x9132)+E(f235(x9131,x9133,x9134),f235(x9132,x9133,x9134))
% 162.26/162.10 [914]~E(x9141,x9142)+E(f235(x9143,x9141,x9144),f235(x9143,x9142,x9144))
% 162.26/162.10 [915]~E(x9151,x9152)+E(f235(x9153,x9154,x9151),f235(x9153,x9154,x9152))
% 162.26/162.10 [916]~E(x9161,x9162)+E(f201(x9161,x9163),f201(x9162,x9163))
% 162.26/162.10 [917]~E(x9171,x9172)+E(f201(x9173,x9171),f201(x9173,x9172))
% 162.26/162.10 [918]~E(x9181,x9182)+E(f415(x9181,x9183),f415(x9182,x9183))
% 162.26/162.10 [919]~E(x9191,x9192)+E(f415(x9193,x9191),f415(x9193,x9192))
% 162.26/162.10 [920]~E(x9201,x9202)+E(f125(x9201,x9203),f125(x9202,x9203))
% 162.26/162.10 [921]~E(x9211,x9212)+E(f125(x9213,x9211),f125(x9213,x9212))
% 162.26/162.10 [922]~E(x9221,x9222)+E(f732(x9221,x9223,x9224,x9225,x9226),f732(x9222,x9223,x9224,x9225,x9226))
% 162.26/162.10 [923]~E(x9231,x9232)+E(f732(x9233,x9231,x9234,x9235,x9236),f732(x9233,x9232,x9234,x9235,x9236))
% 162.26/162.10 [924]~E(x9241,x9242)+E(f732(x9243,x9244,x9241,x9245,x9246),f732(x9243,x9244,x9242,x9245,x9246))
% 162.26/162.10 [925]~E(x9251,x9252)+E(f732(x9253,x9254,x9255,x9251,x9256),f732(x9253,x9254,x9255,x9252,x9256))
% 162.26/162.10 [926]~E(x9261,x9262)+E(f732(x9263,x9264,x9265,x9266,x9261),f732(x9263,x9264,x9265,x9266,x9262))
% 162.26/162.10 [927]~E(x9271,x9272)+E(f208(x9271,x9273,x9274,x9275),f208(x9272,x9273,x9274,x9275))
% 162.26/162.10 [928]~E(x9281,x9282)+E(f208(x9283,x9281,x9284,x9285),f208(x9283,x9282,x9284,x9285))
% 162.26/162.10 [929]~E(x9291,x9292)+E(f208(x9293,x9294,x9291,x9295),f208(x9293,x9294,x9292,x9295))
% 162.26/162.10 [930]~E(x9301,x9302)+E(f208(x9303,x9304,x9305,x9301),f208(x9303,x9304,x9305,x9302))
% 162.26/162.10 [931]~E(x9311,x9312)+E(f462(x9311,x9313,x9314,x9315),f462(x9312,x9313,x9314,x9315))
% 162.26/162.10 [932]~E(x9321,x9322)+E(f462(x9323,x9321,x9324,x9325),f462(x9323,x9322,x9324,x9325))
% 162.26/162.10 [933]~E(x9331,x9332)+E(f462(x9333,x9334,x9331,x9335),f462(x9333,x9334,x9332,x9335))
% 162.26/162.10 [934]~E(x9341,x9342)+E(f462(x9343,x9344,x9345,x9341),f462(x9343,x9344,x9345,x9342))
% 162.26/162.10 [935]~E(x9351,x9352)+E(f596(x9351,x9353,x9354,x9355),f596(x9352,x9353,x9354,x9355))
% 162.26/162.10 [936]~E(x9361,x9362)+E(f596(x9363,x9361,x9364,x9365),f596(x9363,x9362,x9364,x9365))
% 162.26/162.10 [937]~E(x9371,x9372)+E(f596(x9373,x9374,x9371,x9375),f596(x9373,x9374,x9372,x9375))
% 162.26/162.10 [938]~E(x9381,x9382)+E(f596(x9383,x9384,x9385,x9381),f596(x9383,x9384,x9385,x9382))
% 162.26/162.10 [939]~E(x9391,x9392)+E(f63(x9391,x9393,x9394),f63(x9392,x9393,x9394))
% 162.26/162.10 [940]~E(x9401,x9402)+E(f63(x9403,x9401,x9404),f63(x9403,x9402,x9404))
% 162.26/162.10 [941]~E(x9411,x9412)+E(f63(x9413,x9414,x9411),f63(x9413,x9414,x9412))
% 162.26/162.10 [942]~E(x9421,x9422)+E(f473(x9421,x9423,x9424,x9425,x9426,x9427,x9428),f473(x9422,x9423,x9424,x9425,x9426,x9427,x9428))
% 162.26/162.10 [943]~E(x9431,x9432)+E(f473(x9433,x9431,x9434,x9435,x9436,x9437,x9438),f473(x9433,x9432,x9434,x9435,x9436,x9437,x9438))
% 162.26/162.10 [944]~E(x9441,x9442)+E(f473(x9443,x9444,x9441,x9445,x9446,x9447,x9448),f473(x9443,x9444,x9442,x9445,x9446,x9447,x9448))
% 162.26/162.10 [945]~E(x9451,x9452)+E(f473(x9453,x9454,x9455,x9451,x9456,x9457,x9458),f473(x9453,x9454,x9455,x9452,x9456,x9457,x9458))
% 162.26/162.10 [946]~E(x9461,x9462)+E(f473(x9463,x9464,x9465,x9466,x9461,x9467,x9468),f473(x9463,x9464,x9465,x9466,x9462,x9467,x9468))
% 162.26/162.10 [947]~E(x9471,x9472)+E(f473(x9473,x9474,x9475,x9476,x9477,x9471,x9478),f473(x9473,x9474,x9475,x9476,x9477,x9472,x9478))
% 162.26/162.10 [948]~E(x9481,x9482)+E(f473(x9483,x9484,x9485,x9486,x9487,x9488,x9481),f473(x9483,x9484,x9485,x9486,x9487,x9488,x9482))
% 162.26/162.10 [949]~E(x9491,x9492)+E(f479(x9491,x9493,x9494,x9495,x9496),f479(x9492,x9493,x9494,x9495,x9496))
% 162.26/162.10 [950]~E(x9501,x9502)+E(f479(x9503,x9501,x9504,x9505,x9506),f479(x9503,x9502,x9504,x9505,x9506))
% 162.26/162.10 [951]~E(x9511,x9512)+E(f479(x9513,x9514,x9511,x9515,x9516),f479(x9513,x9514,x9512,x9515,x9516))
% 162.26/162.10 [952]~E(x9521,x9522)+E(f479(x9523,x9524,x9525,x9521,x9526),f479(x9523,x9524,x9525,x9522,x9526))
% 162.26/162.10 [953]~E(x9531,x9532)+E(f479(x9533,x9534,x9535,x9536,x9531),f479(x9533,x9534,x9535,x9536,x9532))
% 162.26/162.10 [954]~E(x9541,x9542)+E(f429(x9541,x9543,x9544,x9545),f429(x9542,x9543,x9544,x9545))
% 162.26/162.10 [955]~E(x9551,x9552)+E(f429(x9553,x9551,x9554,x9555),f429(x9553,x9552,x9554,x9555))
% 162.26/162.10 [956]~E(x9561,x9562)+E(f429(x9563,x9564,x9561,x9565),f429(x9563,x9564,x9562,x9565))
% 162.26/162.10 [957]~E(x9571,x9572)+E(f429(x9573,x9574,x9575,x9571),f429(x9573,x9574,x9575,x9572))
% 162.26/162.10 [958]~E(x9581,x9582)+E(f788(x9581,x9583,x9584,x9585),f788(x9582,x9583,x9584,x9585))
% 162.26/162.10 [959]~E(x9591,x9592)+E(f788(x9593,x9591,x9594,x9595),f788(x9593,x9592,x9594,x9595))
% 162.26/162.10 [960]~E(x9601,x9602)+E(f788(x9603,x9604,x9601,x9605),f788(x9603,x9604,x9602,x9605))
% 162.26/162.10 [961]~E(x9611,x9612)+E(f788(x9613,x9614,x9615,x9611),f788(x9613,x9614,x9615,x9612))
% 162.26/162.10 [962]~E(x9621,x9622)+E(f631(x9621,x9623,x9624,x9625),f631(x9622,x9623,x9624,x9625))
% 162.26/162.10 [963]~E(x9631,x9632)+E(f631(x9633,x9631,x9634,x9635),f631(x9633,x9632,x9634,x9635))
% 162.26/162.10 [964]~E(x9641,x9642)+E(f631(x9643,x9644,x9641,x9645),f631(x9643,x9644,x9642,x9645))
% 162.26/162.10 [965]~E(x9651,x9652)+E(f631(x9653,x9654,x9655,x9651),f631(x9653,x9654,x9655,x9652))
% 162.26/162.10 [966]~E(x9661,x9662)+E(f572(x9661,x9663,x9664,x9665,x9666,x9667),f572(x9662,x9663,x9664,x9665,x9666,x9667))
% 162.26/162.10 [967]~E(x9671,x9672)+E(f572(x9673,x9671,x9674,x9675,x9676,x9677),f572(x9673,x9672,x9674,x9675,x9676,x9677))
% 162.26/162.10 [968]~E(x9681,x9682)+E(f572(x9683,x9684,x9681,x9685,x9686,x9687),f572(x9683,x9684,x9682,x9685,x9686,x9687))
% 162.26/162.10 [969]~E(x9691,x9692)+E(f572(x9693,x9694,x9695,x9691,x9696,x9697),f572(x9693,x9694,x9695,x9692,x9696,x9697))
% 162.26/162.10 [970]~E(x9701,x9702)+E(f572(x9703,x9704,x9705,x9706,x9701,x9707),f572(x9703,x9704,x9705,x9706,x9702,x9707))
% 162.26/162.10 [971]~E(x9711,x9712)+E(f572(x9713,x9714,x9715,x9716,x9717,x9711),f572(x9713,x9714,x9715,x9716,x9717,x9712))
% 162.26/162.10 [972]~E(x9721,x9722)+E(f742(x9721,x9723,x9724,x9725),f742(x9722,x9723,x9724,x9725))
% 162.26/162.10 [973]~E(x9731,x9732)+E(f742(x9733,x9731,x9734,x9735),f742(x9733,x9732,x9734,x9735))
% 162.26/162.10 [974]~E(x9741,x9742)+E(f742(x9743,x9744,x9741,x9745),f742(x9743,x9744,x9742,x9745))
% 162.26/162.10 [975]~E(x9751,x9752)+E(f742(x9753,x9754,x9755,x9751),f742(x9753,x9754,x9755,x9752))
% 162.26/162.10 [976]~E(x9761,x9762)+E(f143(x9761,x9763,x9764),f143(x9762,x9763,x9764))
% 162.26/162.10 [977]~E(x9771,x9772)+E(f143(x9773,x9771,x9774),f143(x9773,x9772,x9774))
% 162.26/162.10 [978]~E(x9781,x9782)+E(f143(x9783,x9784,x9781),f143(x9783,x9784,x9782))
% 162.26/162.10 [979]~E(x9791,x9792)+E(f227(x9791,x9793),f227(x9792,x9793))
% 162.26/162.10 [980]~E(x9801,x9802)+E(f227(x9803,x9801),f227(x9803,x9802))
% 162.26/162.10 [981]~E(x9811,x9812)+E(f97(x9811,x9813,x9814,x9815),f97(x9812,x9813,x9814,x9815))
% 162.26/162.10 [982]~E(x9821,x9822)+E(f97(x9823,x9821,x9824,x9825),f97(x9823,x9822,x9824,x9825))
% 162.26/162.10 [983]~E(x9831,x9832)+E(f97(x9833,x9834,x9831,x9835),f97(x9833,x9834,x9832,x9835))
% 162.26/162.10 [984]~E(x9841,x9842)+E(f97(x9843,x9844,x9845,x9841),f97(x9843,x9844,x9845,x9842))
% 162.26/162.10 [985]~E(x9851,x9852)+E(f398(x9851,x9853,x9854,x9855),f398(x9852,x9853,x9854,x9855))
% 162.26/162.10 [986]~E(x9861,x9862)+E(f398(x9863,x9861,x9864,x9865),f398(x9863,x9862,x9864,x9865))
% 162.26/162.10 [987]~E(x9871,x9872)+E(f398(x9873,x9874,x9871,x9875),f398(x9873,x9874,x9872,x9875))
% 162.26/162.10 [988]~E(x9881,x9882)+E(f398(x9883,x9884,x9885,x9881),f398(x9883,x9884,x9885,x9882))
% 162.26/162.10 [989]~E(x9891,x9892)+E(f660(x9891,x9893),f660(x9892,x9893))
% 162.26/162.10 [990]~E(x9901,x9902)+E(f660(x9903,x9901),f660(x9903,x9902))
% 162.26/162.10 [991]~E(x9911,x9912)+E(f192(x9911,x9913,x9914),f192(x9912,x9913,x9914))
% 162.26/162.10 [992]~E(x9921,x9922)+E(f192(x9923,x9921,x9924),f192(x9923,x9922,x9924))
% 162.26/162.10 [993]~E(x9931,x9932)+E(f192(x9933,x9934,x9931),f192(x9933,x9934,x9932))
% 162.26/162.10 [994]~E(x9941,x9942)+E(f722(x9941,x9943,x9944),f722(x9942,x9943,x9944))
% 162.26/162.10 [995]~E(x9951,x9952)+E(f722(x9953,x9951,x9954),f722(x9953,x9952,x9954))
% 162.26/162.10 [996]~E(x9961,x9962)+E(f722(x9963,x9964,x9961),f722(x9963,x9964,x9962))
% 162.26/162.10 [997]~E(x9971,x9972)+E(f680(x9971,x9973),f680(x9972,x9973))
% 162.26/162.10 [998]~E(x9981,x9982)+E(f680(x9983,x9981),f680(x9983,x9982))
% 162.26/162.10 [999]~E(x9991,x9992)+E(f355(x9991,x9993,x9994,x9995,x9996),f355(x9992,x9993,x9994,x9995,x9996))
% 162.26/162.10 [1000]~E(x10001,x10002)+E(f355(x10003,x10001,x10004,x10005,x10006),f355(x10003,x10002,x10004,x10005,x10006))
% 162.26/162.10 [1001]~E(x10011,x10012)+E(f355(x10013,x10014,x10011,x10015,x10016),f355(x10013,x10014,x10012,x10015,x10016))
% 162.26/162.10 [1002]~E(x10021,x10022)+E(f355(x10023,x10024,x10025,x10021,x10026),f355(x10023,x10024,x10025,x10022,x10026))
% 162.26/162.10 [1003]~E(x10031,x10032)+E(f355(x10033,x10034,x10035,x10036,x10031),f355(x10033,x10034,x10035,x10036,x10032))
% 162.26/162.10 [1004]~E(x10041,x10042)+E(f637(x10041,x10043),f637(x10042,x10043))
% 162.26/162.10 [1005]~E(x10051,x10052)+E(f637(x10053,x10051),f637(x10053,x10052))
% 162.26/162.10 [1006]~E(x10061,x10062)+E(f645(x10061,x10063,x10064,x10065,x10066),f645(x10062,x10063,x10064,x10065,x10066))
% 162.26/162.10 [1007]~E(x10071,x10072)+E(f645(x10073,x10071,x10074,x10075,x10076),f645(x10073,x10072,x10074,x10075,x10076))
% 162.26/162.10 [1008]~E(x10081,x10082)+E(f645(x10083,x10084,x10081,x10085,x10086),f645(x10083,x10084,x10082,x10085,x10086))
% 162.26/162.10 [1009]~E(x10091,x10092)+E(f645(x10093,x10094,x10095,x10091,x10096),f645(x10093,x10094,x10095,x10092,x10096))
% 162.26/162.10 [1010]~E(x10101,x10102)+E(f645(x10103,x10104,x10105,x10106,x10101),f645(x10103,x10104,x10105,x10106,x10102))
% 162.26/162.10 [1011]~E(x10111,x10112)+E(f735(x10111,x10113,x10114,x10115,x10116),f735(x10112,x10113,x10114,x10115,x10116))
% 162.26/162.10 [1012]~E(x10121,x10122)+E(f735(x10123,x10121,x10124,x10125,x10126),f735(x10123,x10122,x10124,x10125,x10126))
% 162.26/162.10 [1013]~E(x10131,x10132)+E(f735(x10133,x10134,x10131,x10135,x10136),f735(x10133,x10134,x10132,x10135,x10136))
% 162.26/162.10 [1014]~E(x10141,x10142)+E(f735(x10143,x10144,x10145,x10141,x10146),f735(x10143,x10144,x10145,x10142,x10146))
% 162.26/162.10 [1015]~E(x10151,x10152)+E(f735(x10153,x10154,x10155,x10156,x10151),f735(x10153,x10154,x10155,x10156,x10152))
% 162.26/162.10 [1016]~E(x10161,x10162)+E(f855(x10161,x10163,x10164),f855(x10162,x10163,x10164))
% 162.26/162.10 [1017]~E(x10171,x10172)+E(f855(x10173,x10171,x10174),f855(x10173,x10172,x10174))
% 162.26/162.10 [1018]~E(x10181,x10182)+E(f855(x10183,x10184,x10181),f855(x10183,x10184,x10182))
% 162.26/162.10 [1019]~E(x10191,x10192)+E(f684(x10191,x10193),f684(x10192,x10193))
% 162.26/162.10 [1020]~E(x10201,x10202)+E(f684(x10203,x10201),f684(x10203,x10202))
% 162.26/162.10 [1021]~E(x10211,x10212)+E(f232(x10211,x10213),f232(x10212,x10213))
% 162.26/162.10 [1022]~E(x10221,x10222)+E(f232(x10223,x10221),f232(x10223,x10222))
% 162.26/162.10 [1023]~E(x10231,x10232)+E(f565(x10231,x10233),f565(x10232,x10233))
% 162.26/162.10 [1024]~E(x10241,x10242)+E(f565(x10243,x10241),f565(x10243,x10242))
% 162.26/162.10 [1025]~E(x10251,x10252)+E(f238(x10251,x10253,x10254,x10255),f238(x10252,x10253,x10254,x10255))
% 162.26/162.10 [1026]~E(x10261,x10262)+E(f238(x10263,x10261,x10264,x10265),f238(x10263,x10262,x10264,x10265))
% 162.26/162.10 [1027]~E(x10271,x10272)+E(f238(x10273,x10274,x10271,x10275),f238(x10273,x10274,x10272,x10275))
% 162.26/162.10 [1028]~E(x10281,x10282)+E(f238(x10283,x10284,x10285,x10281),f238(x10283,x10284,x10285,x10282))
% 162.26/162.10 [1029]~E(x10291,x10292)+E(f435(x10291,x10293,x10294,x10295),f435(x10292,x10293,x10294,x10295))
% 162.26/162.10 [1030]~E(x10301,x10302)+E(f435(x10303,x10301,x10304,x10305),f435(x10303,x10302,x10304,x10305))
% 162.26/162.10 [1031]~E(x10311,x10312)+E(f435(x10313,x10314,x10311,x10315),f435(x10313,x10314,x10312,x10315))
% 162.26/162.10 [1032]~E(x10321,x10322)+E(f435(x10323,x10324,x10325,x10321),f435(x10323,x10324,x10325,x10322))
% 162.26/162.10 [1033]~E(x10331,x10332)+E(f276(x10331),f276(x10332))
% 162.26/162.10 [1034]~E(x10341,x10342)+E(f589(x10341),f589(x10342))
% 162.26/162.10 [1035]~E(x10351,x10352)+E(f273(x10351,x10353,x10354,x10355,x10356),f273(x10352,x10353,x10354,x10355,x10356))
% 162.26/162.10 [1036]~E(x10361,x10362)+E(f273(x10363,x10361,x10364,x10365,x10366),f273(x10363,x10362,x10364,x10365,x10366))
% 162.26/162.10 [1037]~E(x10371,x10372)+E(f273(x10373,x10374,x10371,x10375,x10376),f273(x10373,x10374,x10372,x10375,x10376))
% 162.26/162.10 [1038]~E(x10381,x10382)+E(f273(x10383,x10384,x10385,x10381,x10386),f273(x10383,x10384,x10385,x10382,x10386))
% 162.26/162.10 [1039]~E(x10391,x10392)+E(f273(x10393,x10394,x10395,x10396,x10391),f273(x10393,x10394,x10395,x10396,x10392))
% 162.26/162.10 [1040]~E(x10401,x10402)+E(f669(x10401,x10403),f669(x10402,x10403))
% 162.26/162.10 [1041]~E(x10411,x10412)+E(f669(x10413,x10411),f669(x10413,x10412))
% 162.26/162.10 [1042]~E(x10421,x10422)+E(f748(x10421,x10423,x10424),f748(x10422,x10423,x10424))
% 162.26/162.10 [1043]~E(x10431,x10432)+E(f748(x10433,x10431,x10434),f748(x10433,x10432,x10434))
% 162.26/162.10 [1044]~E(x10441,x10442)+E(f748(x10443,x10444,x10441),f748(x10443,x10444,x10442))
% 162.26/162.10 [1045]~E(x10451,x10452)+E(f170(x10451,x10453,x10454),f170(x10452,x10453,x10454))
% 162.26/162.10 [1046]~E(x10461,x10462)+E(f170(x10463,x10461,x10464),f170(x10463,x10462,x10464))
% 162.26/162.10 [1047]~E(x10471,x10472)+E(f170(x10473,x10474,x10471),f170(x10473,x10474,x10472))
% 162.26/162.10 [1048]~E(x10481,x10482)+E(f701(x10481,x10483),f701(x10482,x10483))
% 162.26/162.10 [1049]~E(x10491,x10492)+E(f701(x10493,x10491),f701(x10493,x10492))
% 162.26/162.10 [1050]~E(x10501,x10502)+E(f467(x10501,x10503,x10504,x10505,x10506,x10507,x10508),f467(x10502,x10503,x10504,x10505,x10506,x10507,x10508))
% 162.26/162.10 [1051]~E(x10511,x10512)+E(f467(x10513,x10511,x10514,x10515,x10516,x10517,x10518),f467(x10513,x10512,x10514,x10515,x10516,x10517,x10518))
% 162.26/162.10 [1052]~E(x10521,x10522)+E(f467(x10523,x10524,x10521,x10525,x10526,x10527,x10528),f467(x10523,x10524,x10522,x10525,x10526,x10527,x10528))
% 162.26/162.10 [1053]~E(x10531,x10532)+E(f467(x10533,x10534,x10535,x10531,x10536,x10537,x10538),f467(x10533,x10534,x10535,x10532,x10536,x10537,x10538))
% 162.26/162.10 [1054]~E(x10541,x10542)+E(f467(x10543,x10544,x10545,x10546,x10541,x10547,x10548),f467(x10543,x10544,x10545,x10546,x10542,x10547,x10548))
% 162.26/162.10 [1055]~E(x10551,x10552)+E(f467(x10553,x10554,x10555,x10556,x10557,x10551,x10558),f467(x10553,x10554,x10555,x10556,x10557,x10552,x10558))
% 162.26/162.10 [1056]~E(x10561,x10562)+E(f467(x10563,x10564,x10565,x10566,x10567,x10568,x10561),f467(x10563,x10564,x10565,x10566,x10567,x10568,x10562))
% 162.26/162.10 [1057]~E(x10571,x10572)+E(f436(x10571,x10573,x10574,x10575),f436(x10572,x10573,x10574,x10575))
% 162.26/162.10 [1058]~E(x10581,x10582)+E(f436(x10583,x10581,x10584,x10585),f436(x10583,x10582,x10584,x10585))
% 162.26/162.10 [1059]~E(x10591,x10592)+E(f436(x10593,x10594,x10591,x10595),f436(x10593,x10594,x10592,x10595))
% 162.26/162.10 [1060]~E(x10601,x10602)+E(f436(x10603,x10604,x10605,x10601),f436(x10603,x10604,x10605,x10602))
% 162.26/162.10 [1061]~E(x10611,x10612)+E(f862(x10611,x10613),f862(x10612,x10613))
% 162.26/162.10 [1062]~E(x10621,x10622)+E(f862(x10623,x10621),f862(x10623,x10622))
% 162.26/162.10 [1063]~E(x10631,x10632)+E(f688(x10631,x10633,x10634),f688(x10632,x10633,x10634))
% 162.26/162.10 [1064]~E(x10641,x10642)+E(f688(x10643,x10641,x10644),f688(x10643,x10642,x10644))
% 162.26/162.10 [1065]~E(x10651,x10652)+E(f688(x10653,x10654,x10651),f688(x10653,x10654,x10652))
% 162.26/162.10 [1066]~E(x10661,x10662)+E(f664(x10661,x10663),f664(x10662,x10663))
% 162.26/162.10 [1067]~E(x10671,x10672)+E(f664(x10673,x10671),f664(x10673,x10672))
% 162.26/162.10 [1068]~E(x10681,x10682)+E(f515(x10681,x10683,x10684,x10685,x10686,x10687,x10688),f515(x10682,x10683,x10684,x10685,x10686,x10687,x10688))
% 162.26/162.10 [1069]~E(x10691,x10692)+E(f515(x10693,x10691,x10694,x10695,x10696,x10697,x10698),f515(x10693,x10692,x10694,x10695,x10696,x10697,x10698))
% 162.26/162.10 [1070]~E(x10701,x10702)+E(f515(x10703,x10704,x10701,x10705,x10706,x10707,x10708),f515(x10703,x10704,x10702,x10705,x10706,x10707,x10708))
% 162.26/162.10 [1071]~E(x10711,x10712)+E(f515(x10713,x10714,x10715,x10711,x10716,x10717,x10718),f515(x10713,x10714,x10715,x10712,x10716,x10717,x10718))
% 162.26/162.10 [1072]~E(x10721,x10722)+E(f515(x10723,x10724,x10725,x10726,x10721,x10727,x10728),f515(x10723,x10724,x10725,x10726,x10722,x10727,x10728))
% 162.26/162.10 [1073]~E(x10731,x10732)+E(f515(x10733,x10734,x10735,x10736,x10737,x10731,x10738),f515(x10733,x10734,x10735,x10736,x10737,x10732,x10738))
% 162.26/162.10 [1074]~E(x10741,x10742)+E(f515(x10743,x10744,x10745,x10746,x10747,x10748,x10741),f515(x10743,x10744,x10745,x10746,x10747,x10748,x10742))
% 162.26/162.10 [1075]~E(x10751,x10752)+E(f198(x10751,x10753,x10754,x10755),f198(x10752,x10753,x10754,x10755))
% 162.26/162.10 [1076]~E(x10761,x10762)+E(f198(x10763,x10761,x10764,x10765),f198(x10763,x10762,x10764,x10765))
% 162.26/162.10 [1077]~E(x10771,x10772)+E(f198(x10773,x10774,x10771,x10775),f198(x10773,x10774,x10772,x10775))
% 162.26/162.10 [1078]~E(x10781,x10782)+E(f198(x10783,x10784,x10785,x10781),f198(x10783,x10784,x10785,x10782))
% 162.26/162.10 [1079]~E(x10791,x10792)+E(f571(x10791,x10793,x10794,x10795),f571(x10792,x10793,x10794,x10795))
% 162.26/162.10 [1080]~E(x10801,x10802)+E(f571(x10803,x10801,x10804,x10805),f571(x10803,x10802,x10804,x10805))
% 162.26/162.10 [1081]~E(x10811,x10812)+E(f571(x10813,x10814,x10811,x10815),f571(x10813,x10814,x10812,x10815))
% 162.26/162.10 [1082]~E(x10821,x10822)+E(f571(x10823,x10824,x10825,x10821),f571(x10823,x10824,x10825,x10822))
% 162.26/162.10 [1083]~E(x10831,x10832)+E(f875(x10831,x10833,x10834),f875(x10832,x10833,x10834))
% 162.26/162.10 [1084]~E(x10841,x10842)+E(f875(x10843,x10841,x10844),f875(x10843,x10842,x10844))
% 162.26/162.10 [1085]~E(x10851,x10852)+E(f875(x10853,x10854,x10851),f875(x10853,x10854,x10852))
% 162.26/162.10 [1086]~E(x10861,x10862)+E(f442(x10861,x10863),f442(x10862,x10863))
% 162.26/162.10 [1087]~E(x10871,x10872)+E(f442(x10873,x10871),f442(x10873,x10872))
% 162.26/162.10 [1088]~E(x10881,x10882)+E(f594(x10881,x10883,x10884,x10885),f594(x10882,x10883,x10884,x10885))
% 162.26/162.10 [1089]~E(x10891,x10892)+E(f594(x10893,x10891,x10894,x10895),f594(x10893,x10892,x10894,x10895))
% 162.26/162.10 [1090]~E(x10901,x10902)+E(f594(x10903,x10904,x10901,x10905),f594(x10903,x10904,x10902,x10905))
% 162.26/162.10 [1091]~E(x10911,x10912)+E(f594(x10913,x10914,x10915,x10911),f594(x10913,x10914,x10915,x10912))
% 162.26/162.10 [1092]~E(x10921,x10922)+E(f234(x10921,x10923,x10924,x10925),f234(x10922,x10923,x10924,x10925))
% 162.26/162.10 [1093]~E(x10931,x10932)+E(f234(x10933,x10931,x10934,x10935),f234(x10933,x10932,x10934,x10935))
% 162.26/162.10 [1094]~E(x10941,x10942)+E(f234(x10943,x10944,x10941,x10945),f234(x10943,x10944,x10942,x10945))
% 162.26/162.10 [1095]~E(x10951,x10952)+E(f234(x10953,x10954,x10955,x10951),f234(x10953,x10954,x10955,x10952))
% 162.26/162.10 [1096]~E(x10961,x10962)+E(f710(x10961,x10963,x10964),f710(x10962,x10963,x10964))
% 162.26/162.10 [1097]~E(x10971,x10972)+E(f710(x10973,x10971,x10974),f710(x10973,x10972,x10974))
% 162.26/162.10 [1098]~E(x10981,x10982)+E(f710(x10983,x10984,x10981),f710(x10983,x10984,x10982))
% 162.26/162.10 [1099]~E(x10991,x10992)+E(f663(x10991,x10993),f663(x10992,x10993))
% 162.26/162.10 [1100]~E(x11001,x11002)+E(f663(x11003,x11001),f663(x11003,x11002))
% 162.26/162.10 [1101]~E(x11011,x11012)+E(f853(x11011,x11013,x11014),f853(x11012,x11013,x11014))
% 162.26/162.10 [1102]~E(x11021,x11022)+E(f853(x11023,x11021,x11024),f853(x11023,x11022,x11024))
% 162.26/162.10 [1103]~E(x11031,x11032)+E(f853(x11033,x11034,x11031),f853(x11033,x11034,x11032))
% 162.26/162.10 [1104]~E(x11041,x11042)+E(f242(x11041,x11043,x11044,x11045),f242(x11042,x11043,x11044,x11045))
% 162.26/162.10 [1105]~E(x11051,x11052)+E(f242(x11053,x11051,x11054,x11055),f242(x11053,x11052,x11054,x11055))
% 162.26/162.10 [1106]~E(x11061,x11062)+E(f242(x11063,x11064,x11061,x11065),f242(x11063,x11064,x11062,x11065))
% 162.26/162.10 [1107]~E(x11071,x11072)+E(f242(x11073,x11074,x11075,x11071),f242(x11073,x11074,x11075,x11072))
% 162.26/162.10 [1108]~E(x11081,x11082)+E(f681(x11081,x11083,x11084),f681(x11082,x11083,x11084))
% 162.26/162.10 [1109]~E(x11091,x11092)+E(f681(x11093,x11091,x11094),f681(x11093,x11092,x11094))
% 162.26/162.10 [1110]~E(x11101,x11102)+E(f681(x11103,x11104,x11101),f681(x11103,x11104,x11102))
% 162.26/162.10 [1111]~E(x11111,x11112)+E(f770(x11111,x11113,x11114,x11115,x11116),f770(x11112,x11113,x11114,x11115,x11116))
% 162.26/162.10 [1112]~E(x11121,x11122)+E(f770(x11123,x11121,x11124,x11125,x11126),f770(x11123,x11122,x11124,x11125,x11126))
% 162.26/162.10 [1113]~E(x11131,x11132)+E(f770(x11133,x11134,x11131,x11135,x11136),f770(x11133,x11134,x11132,x11135,x11136))
% 162.26/162.10 [1114]~E(x11141,x11142)+E(f770(x11143,x11144,x11145,x11141,x11146),f770(x11143,x11144,x11145,x11142,x11146))
% 162.26/162.10 [1115]~E(x11151,x11152)+E(f770(x11153,x11154,x11155,x11156,x11151),f770(x11153,x11154,x11155,x11156,x11152))
% 162.26/162.10 [1116]~E(x11161,x11162)+E(f809(x11161,x11163,x11164),f809(x11162,x11163,x11164))
% 162.26/162.10 [1117]~E(x11171,x11172)+E(f809(x11173,x11171,x11174),f809(x11173,x11172,x11174))
% 162.26/162.10 [1118]~E(x11181,x11182)+E(f809(x11183,x11184,x11181),f809(x11183,x11184,x11182))
% 162.26/162.10 [1119]~E(x11191,x11192)+E(f705(x11191,x11193),f705(x11192,x11193))
% 162.26/162.10 [1120]~E(x11201,x11202)+E(f705(x11203,x11201),f705(x11203,x11202))
% 162.26/162.10 [1121]~E(x11211,x11212)+E(f559(x11211,x11213,x11214),f559(x11212,x11213,x11214))
% 162.26/162.10 [1122]~E(x11221,x11222)+E(f559(x11223,x11221,x11224),f559(x11223,x11222,x11224))
% 162.26/162.10 [1123]~E(x11231,x11232)+E(f559(x11233,x11234,x11231),f559(x11233,x11234,x11232))
% 162.26/162.10 [1124]~E(x11241,x11242)+E(f489(x11241,x11243,x11244),f489(x11242,x11243,x11244))
% 162.26/162.10 [1125]~E(x11251,x11252)+E(f489(x11253,x11251,x11254),f489(x11253,x11252,x11254))
% 162.26/162.10 [1126]~E(x11261,x11262)+E(f489(x11263,x11264,x11261),f489(x11263,x11264,x11262))
% 162.26/162.10 [1127]~E(x11271,x11272)+E(f177(x11271,x11273,x11274),f177(x11272,x11273,x11274))
% 162.26/162.10 [1128]~E(x11281,x11282)+E(f177(x11283,x11281,x11284),f177(x11283,x11282,x11284))
% 162.26/162.10 [1129]~E(x11291,x11292)+E(f177(x11293,x11294,x11291),f177(x11293,x11294,x11292))
% 162.26/162.10 [1130]~E(x11301,x11302)+E(f194(x11301),f194(x11302))
% 162.26/162.10 [1131]~E(x11311,x11312)+E(f829(x11311,x11313,x11314),f829(x11312,x11313,x11314))
% 162.26/162.10 [1132]~E(x11321,x11322)+E(f829(x11323,x11321,x11324),f829(x11323,x11322,x11324))
% 162.26/162.10 [1133]~E(x11331,x11332)+E(f829(x11333,x11334,x11331),f829(x11333,x11334,x11332))
% 162.26/162.10 [1134]~E(x11341,x11342)+E(f412(x11341,x11343),f412(x11342,x11343))
% 162.26/162.10 [1135]~E(x11351,x11352)+E(f412(x11353,x11351),f412(x11353,x11352))
% 162.26/162.10 [1136]~E(x11361,x11362)+E(f249(x11361,x11363),f249(x11362,x11363))
% 162.26/162.10 [1137]~E(x11371,x11372)+E(f249(x11373,x11371),f249(x11373,x11372))
% 162.26/162.10 [1138]~E(x11381,x11382)+E(f679(x11381,x11383,x11384,x11385,x11386),f679(x11382,x11383,x11384,x11385,x11386))
% 162.26/162.10 [1139]~E(x11391,x11392)+E(f679(x11393,x11391,x11394,x11395,x11396),f679(x11393,x11392,x11394,x11395,x11396))
% 162.26/162.10 [1140]~E(x11401,x11402)+E(f679(x11403,x11404,x11401,x11405,x11406),f679(x11403,x11404,x11402,x11405,x11406))
% 162.26/162.10 [1141]~E(x11411,x11412)+E(f679(x11413,x11414,x11415,x11411,x11416),f679(x11413,x11414,x11415,x11412,x11416))
% 162.26/162.10 [1142]~E(x11421,x11422)+E(f679(x11423,x11424,x11425,x11426,x11421),f679(x11423,x11424,x11425,x11426,x11422))
% 162.26/162.10 [1143]~E(x11431,x11432)+E(f769(x11431,x11433,x11434),f769(x11432,x11433,x11434))
% 162.26/162.10 [1144]~E(x11441,x11442)+E(f769(x11443,x11441,x11444),f769(x11443,x11442,x11444))
% 162.26/162.10 [1145]~E(x11451,x11452)+E(f769(x11453,x11454,x11451),f769(x11453,x11454,x11452))
% 162.26/162.10 [1146]~E(x11461,x11462)+E(f130(x11461,x11463,x11464),f130(x11462,x11463,x11464))
% 162.26/162.10 [1147]~E(x11471,x11472)+E(f130(x11473,x11471,x11474),f130(x11473,x11472,x11474))
% 162.26/162.10 [1148]~E(x11481,x11482)+E(f130(x11483,x11484,x11481),f130(x11483,x11484,x11482))
% 162.26/162.10 [1149]~E(x11491,x11492)+E(f188(x11491,x11493,x11494),f188(x11492,x11493,x11494))
% 162.26/162.10 [1150]~E(x11501,x11502)+E(f188(x11503,x11501,x11504),f188(x11503,x11502,x11504))
% 162.26/162.10 [1151]~E(x11511,x11512)+E(f188(x11513,x11514,x11511),f188(x11513,x11514,x11512))
% 162.26/162.10 [1152]~E(x11521,x11522)+E(f165(x11521,x11523),f165(x11522,x11523))
% 162.26/162.10 [1153]~E(x11531,x11532)+E(f165(x11533,x11531),f165(x11533,x11532))
% 162.26/162.10 [1154]~E(x11541,x11542)+E(f586(x11541,x11543,x11544),f586(x11542,x11543,x11544))
% 162.26/162.10 [1155]~E(x11551,x11552)+E(f586(x11553,x11551,x11554),f586(x11553,x11552,x11554))
% 162.26/162.10 [1156]~E(x11561,x11562)+E(f586(x11563,x11564,x11561),f586(x11563,x11564,x11562))
% 162.26/162.10 [1157]~E(x11571,x11572)+E(f871(x11571,x11573,x11574,x11575,x11576,x11577),f871(x11572,x11573,x11574,x11575,x11576,x11577))
% 162.26/162.10 [1158]~E(x11581,x11582)+E(f871(x11583,x11581,x11584,x11585,x11586,x11587),f871(x11583,x11582,x11584,x11585,x11586,x11587))
% 162.26/162.10 [1159]~E(x11591,x11592)+E(f871(x11593,x11594,x11591,x11595,x11596,x11597),f871(x11593,x11594,x11592,x11595,x11596,x11597))
% 162.26/162.10 [1160]~E(x11601,x11602)+E(f871(x11603,x11604,x11605,x11601,x11606,x11607),f871(x11603,x11604,x11605,x11602,x11606,x11607))
% 162.26/162.10 [1161]~E(x11611,x11612)+E(f871(x11613,x11614,x11615,x11616,x11611,x11617),f871(x11613,x11614,x11615,x11616,x11612,x11617))
% 162.26/162.10 [1162]~E(x11621,x11622)+E(f871(x11623,x11624,x11625,x11626,x11627,x11621),f871(x11623,x11624,x11625,x11626,x11627,x11622))
% 162.26/162.10 [1163]~E(x11631,x11632)+E(f785(x11631,x11633,x11634),f785(x11632,x11633,x11634))
% 162.26/162.10 [1164]~E(x11641,x11642)+E(f785(x11643,x11641,x11644),f785(x11643,x11642,x11644))
% 162.26/162.10 [1165]~E(x11651,x11652)+E(f785(x11653,x11654,x11651),f785(x11653,x11654,x11652))
% 162.26/162.10 [1166]~E(x11661,x11662)+E(f432(x11661,x11663),f432(x11662,x11663))
% 162.26/162.10 [1167]~E(x11671,x11672)+E(f432(x11673,x11671),f432(x11673,x11672))
% 162.26/162.10 [1168]~E(x11681,x11682)+E(f554(x11681,x11683,x11684,x11685,x11686),f554(x11682,x11683,x11684,x11685,x11686))
% 162.26/162.10 [1169]~E(x11691,x11692)+E(f554(x11693,x11691,x11694,x11695,x11696),f554(x11693,x11692,x11694,x11695,x11696))
% 162.26/162.10 [1170]~E(x11701,x11702)+E(f554(x11703,x11704,x11701,x11705,x11706),f554(x11703,x11704,x11702,x11705,x11706))
% 162.26/162.10 [1171]~E(x11711,x11712)+E(f554(x11713,x11714,x11715,x11711,x11716),f554(x11713,x11714,x11715,x11712,x11716))
% 162.26/162.10 [1172]~E(x11721,x11722)+E(f554(x11723,x11724,x11725,x11726,x11721),f554(x11723,x11724,x11725,x11726,x11722))
% 162.26/162.10 [1173]~E(x11731,x11732)+E(f135(x11731,x11733),f135(x11732,x11733))
% 162.26/162.10 [1174]~E(x11741,x11742)+E(f135(x11743,x11741),f135(x11743,x11742))
% 162.26/162.10 [1175]~E(x11751,x11752)+E(f779(x11751,x11753,x11754,x11755,x11756),f779(x11752,x11753,x11754,x11755,x11756))
% 162.26/162.10 [1176]~E(x11761,x11762)+E(f779(x11763,x11761,x11764,x11765,x11766),f779(x11763,x11762,x11764,x11765,x11766))
% 162.26/162.10 [1177]~E(x11771,x11772)+E(f779(x11773,x11774,x11771,x11775,x11776),f779(x11773,x11774,x11772,x11775,x11776))
% 162.26/162.10 [1178]~E(x11781,x11782)+E(f779(x11783,x11784,x11785,x11781,x11786),f779(x11783,x11784,x11785,x11782,x11786))
% 162.26/162.10 [1179]~E(x11791,x11792)+E(f779(x11793,x11794,x11795,x11796,x11791),f779(x11793,x11794,x11795,x11796,x11792))
% 162.26/162.10 [1180]~E(x11801,x11802)+E(f511(x11801,x11803,x11804,x11805,x11806),f511(x11802,x11803,x11804,x11805,x11806))
% 162.26/162.10 [1181]~E(x11811,x11812)+E(f511(x11813,x11811,x11814,x11815,x11816),f511(x11813,x11812,x11814,x11815,x11816))
% 162.26/162.10 [1182]~E(x11821,x11822)+E(f511(x11823,x11824,x11821,x11825,x11826),f511(x11823,x11824,x11822,x11825,x11826))
% 162.26/162.10 [1183]~E(x11831,x11832)+E(f511(x11833,x11834,x11835,x11831,x11836),f511(x11833,x11834,x11835,x11832,x11836))
% 162.26/162.10 [1184]~E(x11841,x11842)+E(f511(x11843,x11844,x11845,x11846,x11841),f511(x11843,x11844,x11845,x11846,x11842))
% 162.26/162.10 [1185]~E(x11851,x11852)+E(f540(x11851,x11853,x11854),f540(x11852,x11853,x11854))
% 162.26/162.10 [1186]~E(x11861,x11862)+E(f540(x11863,x11861,x11864),f540(x11863,x11862,x11864))
% 162.26/162.10 [1187]~E(x11871,x11872)+E(f540(x11873,x11874,x11871),f540(x11873,x11874,x11872))
% 162.26/162.10 [1188]~E(x11881,x11882)+E(f780(x11881,x11883),f780(x11882,x11883))
% 162.26/162.10 [1189]~E(x11891,x11892)+E(f780(x11893,x11891),f780(x11893,x11892))
% 162.26/162.10 [1190]~E(x11901,x11902)+E(f737(x11901,x11903,x11904,x11905,x11906,x11907),f737(x11902,x11903,x11904,x11905,x11906,x11907))
% 162.26/162.10 [1191]~E(x11911,x11912)+E(f737(x11913,x11911,x11914,x11915,x11916,x11917),f737(x11913,x11912,x11914,x11915,x11916,x11917))
% 162.26/162.10 [1192]~E(x11921,x11922)+E(f737(x11923,x11924,x11921,x11925,x11926,x11927),f737(x11923,x11924,x11922,x11925,x11926,x11927))
% 162.26/162.10 [1193]~E(x11931,x11932)+E(f737(x11933,x11934,x11935,x11931,x11936,x11937),f737(x11933,x11934,x11935,x11932,x11936,x11937))
% 162.26/162.10 [1194]~E(x11941,x11942)+E(f737(x11943,x11944,x11945,x11946,x11941,x11947),f737(x11943,x11944,x11945,x11946,x11942,x11947))
% 162.26/162.10 [1195]~E(x11951,x11952)+E(f737(x11953,x11954,x11955,x11956,x11957,x11951),f737(x11953,x11954,x11955,x11956,x11957,x11952))
% 162.26/162.10 [1196]~E(x11961,x11962)+E(f447(x11961),f447(x11962))
% 162.26/162.10 [1197]~E(x11971,x11972)+E(f561(x11971,x11973,x11974,x11975,x11976,x11977,x11978),f561(x11972,x11973,x11974,x11975,x11976,x11977,x11978))
% 162.26/162.10 [1198]~E(x11981,x11982)+E(f561(x11983,x11981,x11984,x11985,x11986,x11987,x11988),f561(x11983,x11982,x11984,x11985,x11986,x11987,x11988))
% 162.26/162.10 [1199]~E(x11991,x11992)+E(f561(x11993,x11994,x11991,x11995,x11996,x11997,x11998),f561(x11993,x11994,x11992,x11995,x11996,x11997,x11998))
% 162.26/162.10 [1200]~E(x12001,x12002)+E(f561(x12003,x12004,x12005,x12001,x12006,x12007,x12008),f561(x12003,x12004,x12005,x12002,x12006,x12007,x12008))
% 162.26/162.10 [1201]~E(x12011,x12012)+E(f561(x12013,x12014,x12015,x12016,x12011,x12017,x12018),f561(x12013,x12014,x12015,x12016,x12012,x12017,x12018))
% 162.26/162.10 [1202]~E(x12021,x12022)+E(f561(x12023,x12024,x12025,x12026,x12027,x12021,x12028),f561(x12023,x12024,x12025,x12026,x12027,x12022,x12028))
% 162.26/162.10 [1203]~E(x12031,x12032)+E(f561(x12033,x12034,x12035,x12036,x12037,x12038,x12031),f561(x12033,x12034,x12035,x12036,x12037,x12038,x12032))
% 162.26/162.10 [1204]~E(x12041,x12042)+E(f504(x12041,x12043,x12044),f504(x12042,x12043,x12044))
% 162.26/162.10 [1205]~E(x12051,x12052)+E(f504(x12053,x12051,x12054),f504(x12053,x12052,x12054))
% 162.26/162.10 [1206]~E(x12061,x12062)+E(f504(x12063,x12064,x12061),f504(x12063,x12064,x12062))
% 162.26/162.10 [1207]~E(x12071,x12072)+E(f699(x12071,x12073,x12074,x12075,x12076),f699(x12072,x12073,x12074,x12075,x12076))
% 162.26/162.10 [1208]~E(x12081,x12082)+E(f699(x12083,x12081,x12084,x12085,x12086),f699(x12083,x12082,x12084,x12085,x12086))
% 162.26/162.10 [1209]~E(x12091,x12092)+E(f699(x12093,x12094,x12091,x12095,x12096),f699(x12093,x12094,x12092,x12095,x12096))
% 162.26/162.10 [1210]~E(x12101,x12102)+E(f699(x12103,x12104,x12105,x12101,x12106),f699(x12103,x12104,x12105,x12102,x12106))
% 162.26/162.10 [1211]~E(x12111,x12112)+E(f699(x12113,x12114,x12115,x12116,x12111),f699(x12113,x12114,x12115,x12116,x12112))
% 162.26/162.10 [1212]~E(x12121,x12122)+E(f676(x12121,x12123,x12124),f676(x12122,x12123,x12124))
% 162.26/162.10 [1213]~E(x12131,x12132)+E(f676(x12133,x12131,x12134),f676(x12133,x12132,x12134))
% 162.26/162.10 [1214]~E(x12141,x12142)+E(f676(x12143,x12144,x12141),f676(x12143,x12144,x12142))
% 162.26/162.10 [1215]~E(x12151,x12152)+E(f514(x12151,x12153,x12154,x12155,x12156),f514(x12152,x12153,x12154,x12155,x12156))
% 162.26/162.10 [1216]~E(x12161,x12162)+E(f514(x12163,x12161,x12164,x12165,x12166),f514(x12163,x12162,x12164,x12165,x12166))
% 162.26/162.10 [1217]~E(x12171,x12172)+E(f514(x12173,x12174,x12171,x12175,x12176),f514(x12173,x12174,x12172,x12175,x12176))
% 162.26/162.10 [1218]~E(x12181,x12182)+E(f514(x12183,x12184,x12185,x12181,x12186),f514(x12183,x12184,x12185,x12182,x12186))
% 162.26/162.10 [1219]~E(x12191,x12192)+E(f514(x12193,x12194,x12195,x12196,x12191),f514(x12193,x12194,x12195,x12196,x12192))
% 162.26/162.10 [1220]~E(x12201,x12202)+E(f773(x12201,x12203,x12204,x12205,x12206),f773(x12202,x12203,x12204,x12205,x12206))
% 162.26/162.10 [1221]~E(x12211,x12212)+E(f773(x12213,x12211,x12214,x12215,x12216),f773(x12213,x12212,x12214,x12215,x12216))
% 162.26/162.10 [1222]~E(x12221,x12222)+E(f773(x12223,x12224,x12221,x12225,x12226),f773(x12223,x12224,x12222,x12225,x12226))
% 162.26/162.10 [1223]~E(x12231,x12232)+E(f773(x12233,x12234,x12235,x12231,x12236),f773(x12233,x12234,x12235,x12232,x12236))
% 162.26/162.10 [1224]~E(x12241,x12242)+E(f773(x12243,x12244,x12245,x12246,x12241),f773(x12243,x12244,x12245,x12246,x12242))
% 162.26/162.10 [1225]~E(x12251,x12252)+E(f542(x12251,x12253,x12254),f542(x12252,x12253,x12254))
% 162.26/162.10 [1226]~E(x12261,x12262)+E(f542(x12263,x12261,x12264),f542(x12263,x12262,x12264))
% 162.26/162.10 [1227]~E(x12271,x12272)+E(f542(x12273,x12274,x12271),f542(x12273,x12274,x12272))
% 162.26/162.10 [1228]~E(x12281,x12282)+E(f876(x12281,x12283,x12284,x12285,x12286,x12287),f876(x12282,x12283,x12284,x12285,x12286,x12287))
% 162.26/162.10 [1229]~E(x12291,x12292)+E(f876(x12293,x12291,x12294,x12295,x12296,x12297),f876(x12293,x12292,x12294,x12295,x12296,x12297))
% 162.26/162.10 [1230]~E(x12301,x12302)+E(f876(x12303,x12304,x12301,x12305,x12306,x12307),f876(x12303,x12304,x12302,x12305,x12306,x12307))
% 162.26/162.10 [1231]~E(x12311,x12312)+E(f876(x12313,x12314,x12315,x12311,x12316,x12317),f876(x12313,x12314,x12315,x12312,x12316,x12317))
% 162.26/162.10 [1232]~E(x12321,x12322)+E(f876(x12323,x12324,x12325,x12326,x12321,x12327),f876(x12323,x12324,x12325,x12326,x12322,x12327))
% 162.26/162.10 [1233]~E(x12331,x12332)+E(f876(x12333,x12334,x12335,x12336,x12337,x12331),f876(x12333,x12334,x12335,x12336,x12337,x12332))
% 162.26/162.10 [1234]~E(x12341,x12342)+E(f806(x12341,x12343,x12344,x12345,x12346,x12347),f806(x12342,x12343,x12344,x12345,x12346,x12347))
% 162.26/162.10 [1235]~E(x12351,x12352)+E(f806(x12353,x12351,x12354,x12355,x12356,x12357),f806(x12353,x12352,x12354,x12355,x12356,x12357))
% 162.26/162.10 [1236]~E(x12361,x12362)+E(f806(x12363,x12364,x12361,x12365,x12366,x12367),f806(x12363,x12364,x12362,x12365,x12366,x12367))
% 162.26/162.10 [1237]~E(x12371,x12372)+E(f806(x12373,x12374,x12375,x12371,x12376,x12377),f806(x12373,x12374,x12375,x12372,x12376,x12377))
% 162.26/162.10 [1238]~E(x12381,x12382)+E(f806(x12383,x12384,x12385,x12386,x12381,x12387),f806(x12383,x12384,x12385,x12386,x12382,x12387))
% 162.26/162.10 [1239]~E(x12391,x12392)+E(f806(x12393,x12394,x12395,x12396,x12397,x12391),f806(x12393,x12394,x12395,x12396,x12397,x12392))
% 162.26/162.10 [1240]~E(x12401,x12402)+E(f627(x12401,x12403,x12404,x12405),f627(x12402,x12403,x12404,x12405))
% 162.26/162.10 [1241]~E(x12411,x12412)+E(f627(x12413,x12411,x12414,x12415),f627(x12413,x12412,x12414,x12415))
% 162.26/162.10 [1242]~E(x12421,x12422)+E(f627(x12423,x12424,x12421,x12425),f627(x12423,x12424,x12422,x12425))
% 162.26/162.10 [1243]~E(x12431,x12432)+E(f627(x12433,x12434,x12435,x12431),f627(x12433,x12434,x12435,x12432))
% 162.26/162.10 [1244]~E(x12441,x12442)+E(f211(x12441,x12443),f211(x12442,x12443))
% 162.26/162.10 [1245]~E(x12451,x12452)+E(f211(x12453,x12451),f211(x12453,x12452))
% 162.26/162.10 [1246]~E(x12461,x12462)+E(f453(x12461,x12463,x12464,x12465),f453(x12462,x12463,x12464,x12465))
% 162.26/162.10 [1247]~E(x12471,x12472)+E(f453(x12473,x12471,x12474,x12475),f453(x12473,x12472,x12474,x12475))
% 162.26/162.10 [1248]~E(x12481,x12482)+E(f453(x12483,x12484,x12481,x12485),f453(x12483,x12484,x12482,x12485))
% 162.26/162.10 [1249]~E(x12491,x12492)+E(f453(x12493,x12494,x12495,x12491),f453(x12493,x12494,x12495,x12492))
% 162.26/162.10 [1250]~E(x12501,x12502)+E(f869(x12501,x12503),f869(x12502,x12503))
% 162.26/162.10 [1251]~E(x12511,x12512)+E(f869(x12513,x12511),f869(x12513,x12512))
% 162.26/162.10 [1252]~E(x12521,x12522)+E(f741(x12521,x12523,x12524,x12525),f741(x12522,x12523,x12524,x12525))
% 162.26/162.10 [1253]~E(x12531,x12532)+E(f741(x12533,x12531,x12534,x12535),f741(x12533,x12532,x12534,x12535))
% 162.26/162.10 [1254]~E(x12541,x12542)+E(f741(x12543,x12544,x12541,x12545),f741(x12543,x12544,x12542,x12545))
% 162.26/162.10 [1255]~E(x12551,x12552)+E(f741(x12553,x12554,x12555,x12551),f741(x12553,x12554,x12555,x12552))
% 162.26/162.10 [1256]~E(x12561,x12562)+E(f446(x12561,x12563,x12564,x12565,x12566,x12567,x12568),f446(x12562,x12563,x12564,x12565,x12566,x12567,x12568))
% 162.26/162.10 [1257]~E(x12571,x12572)+E(f446(x12573,x12571,x12574,x12575,x12576,x12577,x12578),f446(x12573,x12572,x12574,x12575,x12576,x12577,x12578))
% 162.26/162.10 [1258]~E(x12581,x12582)+E(f446(x12583,x12584,x12581,x12585,x12586,x12587,x12588),f446(x12583,x12584,x12582,x12585,x12586,x12587,x12588))
% 162.26/162.10 [1259]~E(x12591,x12592)+E(f446(x12593,x12594,x12595,x12591,x12596,x12597,x12598),f446(x12593,x12594,x12595,x12592,x12596,x12597,x12598))
% 162.26/162.10 [1260]~E(x12601,x12602)+E(f446(x12603,x12604,x12605,x12606,x12601,x12607,x12608),f446(x12603,x12604,x12605,x12606,x12602,x12607,x12608))
% 162.26/162.10 [1261]~E(x12611,x12612)+E(f446(x12613,x12614,x12615,x12616,x12617,x12611,x12618),f446(x12613,x12614,x12615,x12616,x12617,x12612,x12618))
% 162.26/162.10 [1262]~E(x12621,x12622)+E(f446(x12623,x12624,x12625,x12626,x12627,x12628,x12621),f446(x12623,x12624,x12625,x12626,x12627,x12628,x12622))
% 162.26/162.10 [1263]~E(x12631,x12632)+E(f538(x12631,x12633,x12634),f538(x12632,x12633,x12634))
% 162.26/162.10 [1264]~E(x12641,x12642)+E(f538(x12643,x12641,x12644),f538(x12643,x12642,x12644))
% 162.26/162.10 [1265]~E(x12651,x12652)+E(f538(x12653,x12654,x12651),f538(x12653,x12654,x12652))
% 162.26/162.10 [1266]~E(x12661,x12662)+E(f522(x12661,x12663,x12664,x12665),f522(x12662,x12663,x12664,x12665))
% 162.26/162.10 [1267]~E(x12671,x12672)+E(f522(x12673,x12671,x12674,x12675),f522(x12673,x12672,x12674,x12675))
% 162.26/162.10 [1268]~E(x12681,x12682)+E(f522(x12683,x12684,x12681,x12685),f522(x12683,x12684,x12682,x12685))
% 162.26/162.10 [1269]~E(x12691,x12692)+E(f522(x12693,x12694,x12695,x12691),f522(x12693,x12694,x12695,x12692))
% 162.26/162.10 [1270]~E(x12701,x12702)+E(f375(x12701,x12703,x12704),f375(x12702,x12703,x12704))
% 162.26/162.10 [1271]~E(x12711,x12712)+E(f375(x12713,x12711,x12714),f375(x12713,x12712,x12714))
% 162.26/162.10 [1272]~E(x12721,x12722)+E(f375(x12723,x12724,x12721),f375(x12723,x12724,x12722))
% 162.26/162.10 [1273]~E(x12731,x12732)+E(f544(x12731),f544(x12732))
% 162.26/162.10 [1274]~E(x12741,x12742)+E(f494(x12741,x12743,x12744,x12745,x12746),f494(x12742,x12743,x12744,x12745,x12746))
% 162.26/162.10 [1275]~E(x12751,x12752)+E(f494(x12753,x12751,x12754,x12755,x12756),f494(x12753,x12752,x12754,x12755,x12756))
% 162.26/162.10 [1276]~E(x12761,x12762)+E(f494(x12763,x12764,x12761,x12765,x12766),f494(x12763,x12764,x12762,x12765,x12766))
% 162.26/162.10 [1277]~E(x12771,x12772)+E(f494(x12773,x12774,x12775,x12771,x12776),f494(x12773,x12774,x12775,x12772,x12776))
% 162.26/162.10 [1278]~E(x12781,x12782)+E(f494(x12783,x12784,x12785,x12786,x12781),f494(x12783,x12784,x12785,x12786,x12782))
% 162.26/162.10 [1279]~E(x12791,x12792)+E(f320(x12791,x12793),f320(x12792,x12793))
% 162.26/162.10 [1280]~E(x12801,x12802)+E(f320(x12803,x12801),f320(x12803,x12802))
% 162.26/162.10 [1281]~E(x12811,x12812)+E(f346(x12811,x12813),f346(x12812,x12813))
% 162.26/162.10 [1282]~E(x12821,x12822)+E(f346(x12823,x12821),f346(x12823,x12822))
% 162.26/162.10 [1283]~E(x12831,x12832)+E(f477(x12831,x12833,x12834,x12835,x12836),f477(x12832,x12833,x12834,x12835,x12836))
% 162.26/162.10 [1284]~E(x12841,x12842)+E(f477(x12843,x12841,x12844,x12845,x12846),f477(x12843,x12842,x12844,x12845,x12846))
% 162.26/162.10 [1285]~E(x12851,x12852)+E(f477(x12853,x12854,x12851,x12855,x12856),f477(x12853,x12854,x12852,x12855,x12856))
% 162.26/162.10 [1286]~E(x12861,x12862)+E(f477(x12863,x12864,x12865,x12861,x12866),f477(x12863,x12864,x12865,x12862,x12866))
% 162.26/162.10 [1287]~E(x12871,x12872)+E(f477(x12873,x12874,x12875,x12876,x12871),f477(x12873,x12874,x12875,x12876,x12872))
% 162.26/162.10 [1288]~E(x12881,x12882)+E(f715(x12881,x12883,x12884,x12885,x12886,x12887),f715(x12882,x12883,x12884,x12885,x12886,x12887))
% 162.26/162.10 [1289]~E(x12891,x12892)+E(f715(x12893,x12891,x12894,x12895,x12896,x12897),f715(x12893,x12892,x12894,x12895,x12896,x12897))
% 162.26/162.10 [1290]~E(x12901,x12902)+E(f715(x12903,x12904,x12901,x12905,x12906,x12907),f715(x12903,x12904,x12902,x12905,x12906,x12907))
% 162.26/162.10 [1291]~E(x12911,x12912)+E(f715(x12913,x12914,x12915,x12911,x12916,x12917),f715(x12913,x12914,x12915,x12912,x12916,x12917))
% 162.26/162.10 [1292]~E(x12921,x12922)+E(f715(x12923,x12924,x12925,x12926,x12921,x12927),f715(x12923,x12924,x12925,x12926,x12922,x12927))
% 162.26/162.10 [1293]~E(x12931,x12932)+E(f715(x12933,x12934,x12935,x12936,x12937,x12931),f715(x12933,x12934,x12935,x12936,x12937,x12932))
% 162.26/162.10 [1294]~E(x12941,x12942)+E(f54(x12941,x12943),f54(x12942,x12943))
% 162.26/162.10 [1295]~E(x12951,x12952)+E(f54(x12953,x12951),f54(x12953,x12952))
% 162.26/162.10 [1296]~E(x12961,x12962)+E(f616(x12961,x12963,x12964,x12965,x12966),f616(x12962,x12963,x12964,x12965,x12966))
% 162.26/162.10 [1297]~E(x12971,x12972)+E(f616(x12973,x12971,x12974,x12975,x12976),f616(x12973,x12972,x12974,x12975,x12976))
% 162.26/162.10 [1298]~E(x12981,x12982)+E(f616(x12983,x12984,x12981,x12985,x12986),f616(x12983,x12984,x12982,x12985,x12986))
% 162.26/162.10 [1299]~E(x12991,x12992)+E(f616(x12993,x12994,x12995,x12991,x12996),f616(x12993,x12994,x12995,x12992,x12996))
% 162.26/162.10 [1300]~E(x13001,x13002)+E(f616(x13003,x13004,x13005,x13006,x13001),f616(x13003,x13004,x13005,x13006,x13002))
% 162.26/162.10 [1301]~E(x13011,x13012)+E(f633(x13011,x13013,x13014,x13015),f633(x13012,x13013,x13014,x13015))
% 162.26/162.10 [1302]~E(x13021,x13022)+E(f633(x13023,x13021,x13024,x13025),f633(x13023,x13022,x13024,x13025))
% 162.26/162.10 [1303]~E(x13031,x13032)+E(f633(x13033,x13034,x13031,x13035),f633(x13033,x13034,x13032,x13035))
% 162.26/162.10 [1304]~E(x13041,x13042)+E(f633(x13043,x13044,x13045,x13041),f633(x13043,x13044,x13045,x13042))
% 162.26/162.10 [1305]~E(x13051,x13052)+E(f490(x13051,x13053,x13054,x13055,x13056),f490(x13052,x13053,x13054,x13055,x13056))
% 162.26/162.10 [1306]~E(x13061,x13062)+E(f490(x13063,x13061,x13064,x13065,x13066),f490(x13063,x13062,x13064,x13065,x13066))
% 162.26/162.10 [1307]~E(x13071,x13072)+E(f490(x13073,x13074,x13071,x13075,x13076),f490(x13073,x13074,x13072,x13075,x13076))
% 162.26/162.10 [1308]~E(x13081,x13082)+E(f490(x13083,x13084,x13085,x13081,x13086),f490(x13083,x13084,x13085,x13082,x13086))
% 162.26/162.10 [1309]~E(x13091,x13092)+E(f490(x13093,x13094,x13095,x13096,x13091),f490(x13093,x13094,x13095,x13096,x13092))
% 162.26/162.10 [1310]~E(x13101,x13102)+E(f440(x13101,x13103),f440(x13102,x13103))
% 162.26/162.10 [1311]~E(x13111,x13112)+E(f440(x13113,x13111),f440(x13113,x13112))
% 162.26/162.10 [1312]~E(x13121,x13122)+E(f868(x13121,x13123),f868(x13122,x13123))
% 162.26/162.10 [1313]~E(x13131,x13132)+E(f868(x13133,x13131),f868(x13133,x13132))
% 162.26/162.10 [1314]~E(x13141,x13142)+E(f337(x13141,x13143),f337(x13142,x13143))
% 162.26/162.10 [1315]~E(x13151,x13152)+E(f337(x13153,x13151),f337(x13153,x13152))
% 162.26/162.10 [1316]~E(x13161,x13162)+E(f690(x13161,x13163,x13164,x13165),f690(x13162,x13163,x13164,x13165))
% 162.26/162.10 [1317]~E(x13171,x13172)+E(f690(x13173,x13171,x13174,x13175),f690(x13173,x13172,x13174,x13175))
% 162.26/162.10 [1318]~E(x13181,x13182)+E(f690(x13183,x13184,x13181,x13185),f690(x13183,x13184,x13182,x13185))
% 162.26/162.10 [1319]~E(x13191,x13192)+E(f690(x13193,x13194,x13195,x13191),f690(x13193,x13194,x13195,x13192))
% 162.26/162.10 [1320]~E(x13201,x13202)+E(f756(x13201,x13203,x13204),f756(x13202,x13203,x13204))
% 162.26/162.10 [1321]~E(x13211,x13212)+E(f756(x13213,x13211,x13214),f756(x13213,x13212,x13214))
% 162.26/162.10 [1322]~E(x13221,x13222)+E(f756(x13223,x13224,x13221),f756(x13223,x13224,x13222))
% 162.26/162.10 [1323]~E(x13231,x13232)+E(f729(x13231,x13233,x13234),f729(x13232,x13233,x13234))
% 162.26/162.10 [1324]~E(x13241,x13242)+E(f729(x13243,x13241,x13244),f729(x13243,x13242,x13244))
% 162.26/162.10 [1325]~E(x13251,x13252)+E(f729(x13253,x13254,x13251),f729(x13253,x13254,x13252))
% 162.26/162.10 [1326]~E(x13261,x13262)+E(f816(x13261,x13263,x13264,x13265),f816(x13262,x13263,x13264,x13265))
% 162.26/162.10 [1327]~E(x13271,x13272)+E(f816(x13273,x13271,x13274,x13275),f816(x13273,x13272,x13274,x13275))
% 162.26/162.10 [1328]~E(x13281,x13282)+E(f816(x13283,x13284,x13281,x13285),f816(x13283,x13284,x13282,x13285))
% 162.26/162.10 [1329]~E(x13291,x13292)+E(f816(x13293,x13294,x13295,x13291),f816(x13293,x13294,x13295,x13292))
% 162.26/162.10 [1330]~E(x13301,x13302)+E(f752(x13301,x13303,x13304),f752(x13302,x13303,x13304))
% 162.26/162.10 [1331]~E(x13311,x13312)+E(f752(x13313,x13311,x13314),f752(x13313,x13312,x13314))
% 162.26/162.10 [1332]~E(x13321,x13322)+E(f752(x13323,x13324,x13321),f752(x13323,x13324,x13322))
% 162.26/162.10 [1333]~E(x13331,x13332)+E(f204(x13331,x13333),f204(x13332,x13333))
% 162.26/162.10 [1334]~E(x13341,x13342)+E(f204(x13343,x13341),f204(x13343,x13342))
% 162.26/162.10 [1335]~E(x13351,x13352)+E(f347(x13351,x13353),f347(x13352,x13353))
% 162.26/162.10 [1336]~E(x13361,x13362)+E(f347(x13363,x13361),f347(x13363,x13362))
% 162.26/162.10 [1337]~E(x13371,x13372)+E(f819(x13371,x13373,x13374,x13375),f819(x13372,x13373,x13374,x13375))
% 162.26/162.10 [1338]~E(x13381,x13382)+E(f819(x13383,x13381,x13384,x13385),f819(x13383,x13382,x13384,x13385))
% 162.26/162.10 [1339]~E(x13391,x13392)+E(f819(x13393,x13394,x13391,x13395),f819(x13393,x13394,x13392,x13395))
% 162.26/162.10 [1340]~E(x13401,x13402)+E(f819(x13403,x13404,x13405,x13401),f819(x13403,x13404,x13405,x13402))
% 162.26/162.10 [1341]~E(x13411,x13412)+E(f393(x13411),f393(x13412))
% 162.26/162.10 [1342]~E(x13421,x13422)+E(f263(x13421,x13423,x13424),f263(x13422,x13423,x13424))
% 162.26/162.10 [1343]~E(x13431,x13432)+E(f263(x13433,x13431,x13434),f263(x13433,x13432,x13434))
% 162.26/162.10 [1344]~E(x13441,x13442)+E(f263(x13443,x13444,x13441),f263(x13443,x13444,x13442))
% 162.26/162.10 [1345]~E(x13451,x13452)+E(f528(x13451,x13453,x13454),f528(x13452,x13453,x13454))
% 162.26/162.10 [1346]~E(x13461,x13462)+E(f528(x13463,x13461,x13464),f528(x13463,x13462,x13464))
% 162.26/162.10 [1347]~E(x13471,x13472)+E(f528(x13473,x13474,x13471),f528(x13473,x13474,x13472))
% 162.26/162.10 [1348]~E(x13481,x13482)+E(f626(x13481,x13483,x13484,x13485),f626(x13482,x13483,x13484,x13485))
% 162.26/162.10 [1349]~E(x13491,x13492)+E(f626(x13493,x13491,x13494,x13495),f626(x13493,x13492,x13494,x13495))
% 162.26/162.10 [1350]~E(x13501,x13502)+E(f626(x13503,x13504,x13501,x13505),f626(x13503,x13504,x13502,x13505))
% 162.26/162.10 [1351]~E(x13511,x13512)+E(f626(x13513,x13514,x13515,x13511),f626(x13513,x13514,x13515,x13512))
% 162.26/162.10 [1352]~E(x13521,x13522)+E(f546(x13521,x13523,x13524,x13525),f546(x13522,x13523,x13524,x13525))
% 162.26/162.10 [1353]~E(x13531,x13532)+E(f546(x13533,x13531,x13534,x13535),f546(x13533,x13532,x13534,x13535))
% 162.26/162.10 [1354]~E(x13541,x13542)+E(f546(x13543,x13544,x13541,x13545),f546(x13543,x13544,x13542,x13545))
% 162.26/162.10 [1355]~E(x13551,x13552)+E(f546(x13553,x13554,x13555,x13551),f546(x13553,x13554,x13555,x13552))
% 162.26/162.10 [1356]~E(x13561,x13562)+E(f456(x13561,x13563,x13564,x13565),f456(x13562,x13563,x13564,x13565))
% 162.26/162.10 [1357]~E(x13571,x13572)+E(f456(x13573,x13571,x13574,x13575),f456(x13573,x13572,x13574,x13575))
% 162.26/162.10 [1358]~E(x13581,x13582)+E(f456(x13583,x13584,x13581,x13585),f456(x13583,x13584,x13582,x13585))
% 162.26/162.10 [1359]~E(x13591,x13592)+E(f456(x13593,x13594,x13595,x13591),f456(x13593,x13594,x13595,x13592))
% 162.26/162.10 [1360]~E(x13601,x13602)+E(f618(x13601,x13603,x13604,x13605,x13606),f618(x13602,x13603,x13604,x13605,x13606))
% 162.26/162.10 [1361]~E(x13611,x13612)+E(f618(x13613,x13611,x13614,x13615,x13616),f618(x13613,x13612,x13614,x13615,x13616))
% 162.26/162.10 [1362]~E(x13621,x13622)+E(f618(x13623,x13624,x13621,x13625,x13626),f618(x13623,x13624,x13622,x13625,x13626))
% 162.26/162.10 [1363]~E(x13631,x13632)+E(f618(x13633,x13634,x13635,x13631,x13636),f618(x13633,x13634,x13635,x13632,x13636))
% 162.26/162.10 [1364]~E(x13641,x13642)+E(f618(x13643,x13644,x13645,x13646,x13641),f618(x13643,x13644,x13645,x13646,x13642))
% 162.26/162.10 [1365]~E(x13651,x13652)+E(f758(x13651,x13653,x13654,x13655,x13656,x13657,x13658,x13659),f758(x13652,x13653,x13654,x13655,x13656,x13657,x13658,x13659))
% 162.26/162.10 [1366]~E(x13661,x13662)+E(f758(x13663,x13661,x13664,x13665,x13666,x13667,x13668,x13669),f758(x13663,x13662,x13664,x13665,x13666,x13667,x13668,x13669))
% 162.26/162.10 [1367]~E(x13671,x13672)+E(f758(x13673,x13674,x13671,x13675,x13676,x13677,x13678,x13679),f758(x13673,x13674,x13672,x13675,x13676,x13677,x13678,x13679))
% 162.26/162.10 [1368]~E(x13681,x13682)+E(f758(x13683,x13684,x13685,x13681,x13686,x13687,x13688,x13689),f758(x13683,x13684,x13685,x13682,x13686,x13687,x13688,x13689))
% 162.26/162.10 [1369]~E(x13691,x13692)+E(f758(x13693,x13694,x13695,x13696,x13691,x13697,x13698,x13699),f758(x13693,x13694,x13695,x13696,x13692,x13697,x13698,x13699))
% 162.26/162.10 [1370]~E(x13701,x13702)+E(f758(x13703,x13704,x13705,x13706,x13707,x13701,x13708,x13709),f758(x13703,x13704,x13705,x13706,x13707,x13702,x13708,x13709))
% 162.26/162.10 [1371]~E(x13711,x13712)+E(f758(x13713,x13714,x13715,x13716,x13717,x13718,x13711,x13719),f758(x13713,x13714,x13715,x13716,x13717,x13718,x13712,x13719))
% 162.26/162.10 [1372]~E(x13721,x13722)+E(f758(x13723,x13724,x13725,x13726,x13727,x13728,x13729,x13721),f758(x13723,x13724,x13725,x13726,x13727,x13728,x13729,x13722))
% 162.26/162.10 [1373]~E(x13731,x13732)+E(f560(x13731,x13733,x13734,x13735,x13736,x13737),f560(x13732,x13733,x13734,x13735,x13736,x13737))
% 162.26/162.10 [1374]~E(x13741,x13742)+E(f560(x13743,x13741,x13744,x13745,x13746,x13747),f560(x13743,x13742,x13744,x13745,x13746,x13747))
% 162.26/162.10 [1375]~E(x13751,x13752)+E(f560(x13753,x13754,x13751,x13755,x13756,x13757),f560(x13753,x13754,x13752,x13755,x13756,x13757))
% 162.26/162.10 [1376]~E(x13761,x13762)+E(f560(x13763,x13764,x13765,x13761,x13766,x13767),f560(x13763,x13764,x13765,x13762,x13766,x13767))
% 162.26/162.10 [1377]~E(x13771,x13772)+E(f560(x13773,x13774,x13775,x13776,x13771,x13777),f560(x13773,x13774,x13775,x13776,x13772,x13777))
% 162.26/162.10 [1378]~E(x13781,x13782)+E(f560(x13783,x13784,x13785,x13786,x13787,x13781),f560(x13783,x13784,x13785,x13786,x13787,x13782))
% 162.26/162.10 [1379]~E(x13791,x13792)+E(f678(x13791,x13793,x13794),f678(x13792,x13793,x13794))
% 162.26/162.10 [1380]~E(x13801,x13802)+E(f678(x13803,x13801,x13804),f678(x13803,x13802,x13804))
% 162.26/162.10 [1381]~E(x13811,x13812)+E(f678(x13813,x13814,x13811),f678(x13813,x13814,x13812))
% 162.26/162.10 [1382]~E(x13821,x13822)+E(f178(x13821,x13823,x13824),f178(x13822,x13823,x13824))
% 162.26/162.10 [1383]~E(x13831,x13832)+E(f178(x13833,x13831,x13834),f178(x13833,x13832,x13834))
% 162.26/162.10 [1384]~E(x13841,x13842)+E(f178(x13843,x13844,x13841),f178(x13843,x13844,x13842))
% 162.26/162.10 [1385]~E(x13851,x13852)+E(f416(x13851,x13853,x13854),f416(x13852,x13853,x13854))
% 162.26/162.10 [1386]~E(x13861,x13862)+E(f416(x13863,x13861,x13864),f416(x13863,x13862,x13864))
% 162.26/162.10 [1387]~E(x13871,x13872)+E(f416(x13873,x13874,x13871),f416(x13873,x13874,x13872))
% 162.26/162.10 [1388]~E(x13881,x13882)+E(f767(x13881,x13883,x13884,x13885,x13886),f767(x13882,x13883,x13884,x13885,x13886))
% 162.26/162.10 [1389]~E(x13891,x13892)+E(f767(x13893,x13891,x13894,x13895,x13896),f767(x13893,x13892,x13894,x13895,x13896))
% 162.26/162.10 [1390]~E(x13901,x13902)+E(f767(x13903,x13904,x13901,x13905,x13906),f767(x13903,x13904,x13902,x13905,x13906))
% 162.26/162.10 [1391]~E(x13911,x13912)+E(f767(x13913,x13914,x13915,x13911,x13916),f767(x13913,x13914,x13915,x13912,x13916))
% 162.26/162.10 [1392]~E(x13921,x13922)+E(f767(x13923,x13924,x13925,x13926,x13921),f767(x13923,x13924,x13925,x13926,x13922))
% 162.26/162.10 [1393]~E(x13931,x13932)+E(f576(x13931,x13933,x13934,x13935),f576(x13932,x13933,x13934,x13935))
% 162.26/162.10 [1394]~E(x13941,x13942)+E(f576(x13943,x13941,x13944,x13945),f576(x13943,x13942,x13944,x13945))
% 162.26/162.10 [1395]~E(x13951,x13952)+E(f576(x13953,x13954,x13951,x13955),f576(x13953,x13954,x13952,x13955))
% 162.26/162.10 [1396]~E(x13961,x13962)+E(f576(x13963,x13964,x13965,x13961),f576(x13963,x13964,x13965,x13962))
% 162.26/162.10 [1397]~E(x13971,x13972)+E(f724(x13971),f724(x13972))
% 162.26/162.10 [1398]~E(x13981,x13982)+E(f648(x13981,x13983,x13984,x13985,x13986),f648(x13982,x13983,x13984,x13985,x13986))
% 162.26/162.10 [1399]~E(x13991,x13992)+E(f648(x13993,x13991,x13994,x13995,x13996),f648(x13993,x13992,x13994,x13995,x13996))
% 162.26/162.10 [1400]~E(x14001,x14002)+E(f648(x14003,x14004,x14001,x14005,x14006),f648(x14003,x14004,x14002,x14005,x14006))
% 162.26/162.10 [1401]~E(x14011,x14012)+E(f648(x14013,x14014,x14015,x14011,x14016),f648(x14013,x14014,x14015,x14012,x14016))
% 162.26/162.10 [1402]~E(x14021,x14022)+E(f648(x14023,x14024,x14025,x14026,x14021),f648(x14023,x14024,x14025,x14026,x14022))
% 162.26/162.10 [1403]~E(x14031,x14032)+E(f702(x14031,x14033),f702(x14032,x14033))
% 162.26/162.10 [1404]~E(x14041,x14042)+E(f702(x14043,x14041),f702(x14043,x14042))
% 162.26/162.10 [1405]~E(x14051,x14052)+E(f466(x14051,x14053,x14054,x14055,x14056,x14057,x14058),f466(x14052,x14053,x14054,x14055,x14056,x14057,x14058))
% 162.26/162.10 [1406]~E(x14061,x14062)+E(f466(x14063,x14061,x14064,x14065,x14066,x14067,x14068),f466(x14063,x14062,x14064,x14065,x14066,x14067,x14068))
% 162.26/162.10 [1407]~E(x14071,x14072)+E(f466(x14073,x14074,x14071,x14075,x14076,x14077,x14078),f466(x14073,x14074,x14072,x14075,x14076,x14077,x14078))
% 162.26/162.10 [1408]~E(x14081,x14082)+E(f466(x14083,x14084,x14085,x14081,x14086,x14087,x14088),f466(x14083,x14084,x14085,x14082,x14086,x14087,x14088))
% 162.26/162.10 [1409]~E(x14091,x14092)+E(f466(x14093,x14094,x14095,x14096,x14091,x14097,x14098),f466(x14093,x14094,x14095,x14096,x14092,x14097,x14098))
% 162.26/162.10 [1410]~E(x14101,x14102)+E(f466(x14103,x14104,x14105,x14106,x14107,x14101,x14108),f466(x14103,x14104,x14105,x14106,x14107,x14102,x14108))
% 162.26/162.10 [1411]~E(x14111,x14112)+E(f466(x14113,x14114,x14115,x14116,x14117,x14118,x14111),f466(x14113,x14114,x14115,x14116,x14117,x14118,x14112))
% 162.26/162.10 [1412]~E(x14121,x14122)+E(f478(x14121,x14123,x14124,x14125,x14126),f478(x14122,x14123,x14124,x14125,x14126))
% 162.26/162.10 [1413]~E(x14131,x14132)+E(f478(x14133,x14131,x14134,x14135,x14136),f478(x14133,x14132,x14134,x14135,x14136))
% 162.26/162.10 [1414]~E(x14141,x14142)+E(f478(x14143,x14144,x14141,x14145,x14146),f478(x14143,x14144,x14142,x14145,x14146))
% 162.26/162.10 [1415]~E(x14151,x14152)+E(f478(x14153,x14154,x14155,x14151,x14156),f478(x14153,x14154,x14155,x14152,x14156))
% 162.26/162.10 [1416]~E(x14161,x14162)+E(f478(x14163,x14164,x14165,x14166,x14161),f478(x14163,x14164,x14165,x14166,x14162))
% 162.26/162.10 [1417]~E(x14171,x14172)+E(f283(x14171,x14173,x14174,x14175),f283(x14172,x14173,x14174,x14175))
% 162.26/162.10 [1418]~E(x14181,x14182)+E(f283(x14183,x14181,x14184,x14185),f283(x14183,x14182,x14184,x14185))
% 162.26/162.10 [1419]~E(x14191,x14192)+E(f283(x14193,x14194,x14191,x14195),f283(x14193,x14194,x14192,x14195))
% 162.26/162.10 [1420]~E(x14201,x14202)+E(f283(x14203,x14204,x14205,x14201),f283(x14203,x14204,x14205,x14202))
% 162.26/162.10 [1421]~E(x14211,x14212)+E(f600(x14211,x14213,x14214,x14215,x14216),f600(x14212,x14213,x14214,x14215,x14216))
% 162.26/162.10 [1422]~E(x14221,x14222)+E(f600(x14223,x14221,x14224,x14225,x14226),f600(x14223,x14222,x14224,x14225,x14226))
% 162.26/162.10 [1423]~E(x14231,x14232)+E(f600(x14233,x14234,x14231,x14235,x14236),f600(x14233,x14234,x14232,x14235,x14236))
% 162.26/162.10 [1424]~E(x14241,x14242)+E(f600(x14243,x14244,x14245,x14241,x14246),f600(x14243,x14244,x14245,x14242,x14246))
% 162.26/162.10 [1425]~E(x14251,x14252)+E(f600(x14253,x14254,x14255,x14256,x14251),f600(x14253,x14254,x14255,x14256,x14252))
% 162.26/162.10 [1426]~E(x14261,x14262)+E(f313(x14261,x14263,x14264),f313(x14262,x14263,x14264))
% 162.26/162.10 [1427]~E(x14271,x14272)+E(f313(x14273,x14271,x14274),f313(x14273,x14272,x14274))
% 162.26/162.10 [1428]~E(x14281,x14282)+E(f313(x14283,x14284,x14281),f313(x14283,x14284,x14282))
% 162.26/162.10 [1429]~E(x14291,x14292)+E(f731(x14291,x14293,x14294,x14295),f731(x14292,x14293,x14294,x14295))
% 162.26/162.10 [1430]~E(x14301,x14302)+E(f731(x14303,x14301,x14304,x14305),f731(x14303,x14302,x14304,x14305))
% 162.26/162.10 [1431]~E(x14311,x14312)+E(f731(x14313,x14314,x14311,x14315),f731(x14313,x14314,x14312,x14315))
% 162.26/162.10 [1432]~E(x14321,x14322)+E(f731(x14323,x14324,x14325,x14321),f731(x14323,x14324,x14325,x14322))
% 162.26/162.10 [1433]~E(x14331,x14332)+E(f791(x14331,x14333,x14334),f791(x14332,x14333,x14334))
% 162.26/162.10 [1434]~E(x14341,x14342)+E(f791(x14343,x14341,x14344),f791(x14343,x14342,x14344))
% 162.26/162.10 [1435]~E(x14351,x14352)+E(f791(x14353,x14354,x14351),f791(x14353,x14354,x14352))
% 162.26/162.10 [1436]~E(x14361,x14362)+E(f323(x14361,x14363,x14364,x14365),f323(x14362,x14363,x14364,x14365))
% 162.26/162.10 [1437]~E(x14371,x14372)+E(f323(x14373,x14371,x14374,x14375),f323(x14373,x14372,x14374,x14375))
% 162.26/162.10 [1438]~E(x14381,x14382)+E(f323(x14383,x14384,x14381,x14385),f323(x14383,x14384,x14382,x14385))
% 162.26/162.10 [1439]~E(x14391,x14392)+E(f323(x14393,x14394,x14395,x14391),f323(x14393,x14394,x14395,x14392))
% 162.26/162.10 [1440]~E(x14401,x14402)+E(f852(x14401),f852(x14402))
% 162.26/162.10 [1441]~E(x14411,x14412)+E(f529(x14411,x14413,x14414),f529(x14412,x14413,x14414))
% 162.26/162.10 [1442]~E(x14421,x14422)+E(f529(x14423,x14421,x14424),f529(x14423,x14422,x14424))
% 162.26/162.10 [1443]~E(x14431,x14432)+E(f529(x14433,x14434,x14431),f529(x14433,x14434,x14432))
% 162.26/162.10 [1444]~E(x14441,x14442)+E(f241(x14441,x14443,x14444),f241(x14442,x14443,x14444))
% 162.26/162.10 [1445]~E(x14451,x14452)+E(f241(x14453,x14451,x14454),f241(x14453,x14452,x14454))
% 162.26/162.10 [1446]~E(x14461,x14462)+E(f241(x14463,x14464,x14461),f241(x14463,x14464,x14462))
% 162.26/162.10 [1447]~E(x14471,x14472)+E(f354(x14471,x14473,x14474,x14475,x14476,x14477,x14478),f354(x14472,x14473,x14474,x14475,x14476,x14477,x14478))
% 162.26/162.10 [1448]~E(x14481,x14482)+E(f354(x14483,x14481,x14484,x14485,x14486,x14487,x14488),f354(x14483,x14482,x14484,x14485,x14486,x14487,x14488))
% 162.26/162.10 [1449]~E(x14491,x14492)+E(f354(x14493,x14494,x14491,x14495,x14496,x14497,x14498),f354(x14493,x14494,x14492,x14495,x14496,x14497,x14498))
% 162.26/162.10 [1450]~E(x14501,x14502)+E(f354(x14503,x14504,x14505,x14501,x14506,x14507,x14508),f354(x14503,x14504,x14505,x14502,x14506,x14507,x14508))
% 162.26/162.10 [1451]~E(x14511,x14512)+E(f354(x14513,x14514,x14515,x14516,x14511,x14517,x14518),f354(x14513,x14514,x14515,x14516,x14512,x14517,x14518))
% 162.26/162.10 [1452]~E(x14521,x14522)+E(f354(x14523,x14524,x14525,x14526,x14527,x14521,x14528),f354(x14523,x14524,x14525,x14526,x14527,x14522,x14528))
% 162.26/162.10 [1453]~E(x14531,x14532)+E(f354(x14533,x14534,x14535,x14536,x14537,x14538,x14531),f354(x14533,x14534,x14535,x14536,x14537,x14538,x14532))
% 162.26/162.10 [1454]~E(x14541,x14542)+E(f209(x14541,x14543,x14544,x14545),f209(x14542,x14543,x14544,x14545))
% 162.26/162.10 [1455]~E(x14551,x14552)+E(f209(x14553,x14551,x14554,x14555),f209(x14553,x14552,x14554,x14555))
% 162.26/162.10 [1456]~E(x14561,x14562)+E(f209(x14563,x14564,x14561,x14565),f209(x14563,x14564,x14562,x14565))
% 162.26/162.10 [1457]~E(x14571,x14572)+E(f209(x14573,x14574,x14575,x14571),f209(x14573,x14574,x14575,x14572))
% 162.26/162.10 [1458]~E(x14581,x14582)+E(f771(x14581,x14583,x14584,x14585,x14586),f771(x14582,x14583,x14584,x14585,x14586))
% 162.26/162.10 [1459]~E(x14591,x14592)+E(f771(x14593,x14591,x14594,x14595,x14596),f771(x14593,x14592,x14594,x14595,x14596))
% 162.26/162.10 [1460]~E(x14601,x14602)+E(f771(x14603,x14604,x14601,x14605,x14606),f771(x14603,x14604,x14602,x14605,x14606))
% 162.26/162.10 [1461]~E(x14611,x14612)+E(f771(x14613,x14614,x14615,x14611,x14616),f771(x14613,x14614,x14615,x14612,x14616))
% 162.26/162.10 [1462]~E(x14621,x14622)+E(f771(x14623,x14624,x14625,x14626,x14621),f771(x14623,x14624,x14625,x14626,x14622))
% 162.26/162.10 [1463]~E(x14631,x14632)+E(f395(x14631,x14633,x14634),f395(x14632,x14633,x14634))
% 162.26/162.10 [1464]~E(x14641,x14642)+E(f395(x14643,x14641,x14644),f395(x14643,x14642,x14644))
% 162.26/162.10 [1465]~E(x14651,x14652)+E(f395(x14653,x14654,x14651),f395(x14653,x14654,x14652))
% 162.26/162.10 [1466]~E(x14661,x14662)+E(f357(x14661,x14663,x14664,x14665,x14666),f357(x14662,x14663,x14664,x14665,x14666))
% 162.26/162.10 [1467]~E(x14671,x14672)+E(f357(x14673,x14671,x14674,x14675,x14676),f357(x14673,x14672,x14674,x14675,x14676))
% 162.26/162.10 [1468]~E(x14681,x14682)+E(f357(x14683,x14684,x14681,x14685,x14686),f357(x14683,x14684,x14682,x14685,x14686))
% 162.26/162.10 [1469]~E(x14691,x14692)+E(f357(x14693,x14694,x14695,x14691,x14696),f357(x14693,x14694,x14695,x14692,x14696))
% 162.26/162.10 [1470]~E(x14701,x14702)+E(f357(x14703,x14704,x14705,x14706,x14701),f357(x14703,x14704,x14705,x14706,x14702))
% 162.26/162.10 [1471]~E(x14711,x14712)+E(f508(x14711,x14713,x14714,x14715,x14716),f508(x14712,x14713,x14714,x14715,x14716))
% 162.26/162.10 [1472]~E(x14721,x14722)+E(f508(x14723,x14721,x14724,x14725,x14726),f508(x14723,x14722,x14724,x14725,x14726))
% 162.26/162.10 [1473]~E(x14731,x14732)+E(f508(x14733,x14734,x14731,x14735,x14736),f508(x14733,x14734,x14732,x14735,x14736))
% 162.26/162.10 [1474]~E(x14741,x14742)+E(f508(x14743,x14744,x14745,x14741,x14746),f508(x14743,x14744,x14745,x14742,x14746))
% 162.26/162.10 [1475]~E(x14751,x14752)+E(f508(x14753,x14754,x14755,x14756,x14751),f508(x14753,x14754,x14755,x14756,x14752))
% 162.26/162.10 [1476]~E(x14761,x14762)+E(f519(x14761,x14763,x14764),f519(x14762,x14763,x14764))
% 162.26/162.10 [1477]~E(x14771,x14772)+E(f519(x14773,x14771,x14774),f519(x14773,x14772,x14774))
% 162.26/162.10 [1478]~E(x14781,x14782)+E(f519(x14783,x14784,x14781),f519(x14783,x14784,x14782))
% 162.26/162.10 [1479]~E(x14791,x14792)+E(f644(x14791,x14793,x14794),f644(x14792,x14793,x14794))
% 162.26/162.10 [1480]~E(x14801,x14802)+E(f644(x14803,x14801,x14804),f644(x14803,x14802,x14804))
% 162.26/162.10 [1481]~E(x14811,x14812)+E(f644(x14813,x14814,x14811),f644(x14813,x14814,x14812))
% 162.26/162.10 [1482]~E(x14821,x14822)+E(f385(x14821,x14823),f385(x14822,x14823))
% 162.26/162.10 [1483]~E(x14831,x14832)+E(f385(x14833,x14831),f385(x14833,x14832))
% 162.26/162.10 [1484]~E(x14841,x14842)+E(f439(x14841,x14843,x14844,x14845,x14846,x14847,x14848),f439(x14842,x14843,x14844,x14845,x14846,x14847,x14848))
% 162.26/162.10 [1485]~E(x14851,x14852)+E(f439(x14853,x14851,x14854,x14855,x14856,x14857,x14858),f439(x14853,x14852,x14854,x14855,x14856,x14857,x14858))
% 162.26/162.10 [1486]~E(x14861,x14862)+E(f439(x14863,x14864,x14861,x14865,x14866,x14867,x14868),f439(x14863,x14864,x14862,x14865,x14866,x14867,x14868))
% 162.26/162.10 [1487]~E(x14871,x14872)+E(f439(x14873,x14874,x14875,x14871,x14876,x14877,x14878),f439(x14873,x14874,x14875,x14872,x14876,x14877,x14878))
% 162.26/162.10 [1488]~E(x14881,x14882)+E(f439(x14883,x14884,x14885,x14886,x14881,x14887,x14888),f439(x14883,x14884,x14885,x14886,x14882,x14887,x14888))
% 162.26/162.10 [1489]~E(x14891,x14892)+E(f439(x14893,x14894,x14895,x14896,x14897,x14891,x14898),f439(x14893,x14894,x14895,x14896,x14897,x14892,x14898))
% 162.26/162.10 [1490]~E(x14901,x14902)+E(f439(x14903,x14904,x14905,x14906,x14907,x14908,x14901),f439(x14903,x14904,x14905,x14906,x14907,x14908,x14902))
% 162.26/162.10 [1491]~E(x14911,x14912)+E(f98(x14911,x14913,x14914),f98(x14912,x14913,x14914))
% 162.26/162.10 [1492]~E(x14921,x14922)+E(f98(x14923,x14921,x14924),f98(x14923,x14922,x14924))
% 162.26/162.10 [1493]~E(x14931,x14932)+E(f98(x14933,x14934,x14931),f98(x14933,x14934,x14932))
% 162.26/162.10 [1494]~E(x14941,x14942)+E(f541(x14941,x14943,x14944),f541(x14942,x14943,x14944))
% 162.26/162.10 [1495]~E(x14951,x14952)+E(f541(x14953,x14951,x14954),f541(x14953,x14952,x14954))
% 162.26/162.10 [1496]~E(x14961,x14962)+E(f541(x14963,x14964,x14961),f541(x14963,x14964,x14962))
% 162.26/162.10 [1497]~E(x14971,x14972)+E(f563(x14971),f563(x14972))
% 162.26/162.10 [1498]~E(x14981,x14982)+E(f620(x14981,x14983,x14984),f620(x14982,x14983,x14984))
% 162.26/162.10 [1499]~E(x14991,x14992)+E(f620(x14993,x14991,x14994),f620(x14993,x14992,x14994))
% 162.26/162.10 [1500]~E(x15001,x15002)+E(f620(x15003,x15004,x15001),f620(x15003,x15004,x15002))
% 162.26/162.10 [1501]~E(x15011,x15012)+E(f394(x15011,x15013,x15014),f394(x15012,x15013,x15014))
% 162.26/162.10 [1502]~E(x15021,x15022)+E(f394(x15023,x15021,x15024),f394(x15023,x15022,x15024))
% 162.26/162.10 [1503]~E(x15031,x15032)+E(f394(x15033,x15034,x15031),f394(x15033,x15034,x15032))
% 162.26/162.10 [1504]~E(x15041,x15042)+E(f841(x15041,x15043,x15044,x15045),f841(x15042,x15043,x15044,x15045))
% 162.26/162.10 [1505]~E(x15051,x15052)+E(f841(x15053,x15051,x15054,x15055),f841(x15053,x15052,x15054,x15055))
% 162.26/162.10 [1506]~E(x15061,x15062)+E(f841(x15063,x15064,x15061,x15065),f841(x15063,x15064,x15062,x15065))
% 162.26/162.10 [1507]~E(x15071,x15072)+E(f841(x15073,x15074,x15075,x15071),f841(x15073,x15074,x15075,x15072))
% 162.26/162.10 [1508]~E(x15081,x15082)+E(f723(x15081),f723(x15082))
% 162.26/162.10 [1509]~E(x15091,x15092)+E(f746(x15091,x15093,x15094,x15095,x15096),f746(x15092,x15093,x15094,x15095,x15096))
% 162.26/162.10 [1510]~E(x15101,x15102)+E(f746(x15103,x15101,x15104,x15105,x15106),f746(x15103,x15102,x15104,x15105,x15106))
% 162.26/162.10 [1511]~E(x15111,x15112)+E(f746(x15113,x15114,x15111,x15115,x15116),f746(x15113,x15114,x15112,x15115,x15116))
% 162.26/162.10 [1512]~E(x15121,x15122)+E(f746(x15123,x15124,x15125,x15121,x15126),f746(x15123,x15124,x15125,x15122,x15126))
% 162.26/162.10 [1513]~E(x15131,x15132)+E(f746(x15133,x15134,x15135,x15136,x15131),f746(x15133,x15134,x15135,x15136,x15132))
% 162.26/162.10 [1514]~E(x15141,x15142)+E(f574(x15141,x15143,x15144,x15145),f574(x15142,x15143,x15144,x15145))
% 162.26/162.10 [1515]~E(x15151,x15152)+E(f574(x15153,x15151,x15154,x15155),f574(x15153,x15152,x15154,x15155))
% 162.26/162.10 [1516]~E(x15161,x15162)+E(f574(x15163,x15164,x15161,x15165),f574(x15163,x15164,x15162,x15165))
% 162.26/162.10 [1517]~E(x15171,x15172)+E(f574(x15173,x15174,x15175,x15171),f574(x15173,x15174,x15175,x15172))
% 162.26/162.10 [1518]~E(x15181,x15182)+E(f822(x15181,x15183,x15184),f822(x15182,x15183,x15184))
% 162.26/162.10 [1519]~E(x15191,x15192)+E(f822(x15193,x15191,x15194),f822(x15193,x15192,x15194))
% 162.26/162.10 [1520]~E(x15201,x15202)+E(f822(x15203,x15204,x15201),f822(x15203,x15204,x15202))
% 162.26/162.10 [1521]~E(x15211,x15212)+E(f826(x15211,x15213,x15214),f826(x15212,x15213,x15214))
% 162.26/162.10 [1522]~E(x15221,x15222)+E(f826(x15223,x15221,x15224),f826(x15223,x15222,x15224))
% 162.26/162.10 [1523]~E(x15231,x15232)+E(f826(x15233,x15234,x15231),f826(x15233,x15234,x15232))
% 162.26/162.10 [1524]~E(x15241,x15242)+E(f441(x15241,x15243),f441(x15242,x15243))
% 162.26/162.10 [1525]~E(x15251,x15252)+E(f441(x15253,x15251),f441(x15253,x15252))
% 162.26/162.10 [1526]~E(x15261,x15262)+E(f403(x15261,x15263),f403(x15262,x15263))
% 162.26/162.10 [1527]~E(x15271,x15272)+E(f403(x15273,x15271),f403(x15273,x15272))
% 162.26/162.10 [1528]~E(x15281,x15282)+E(f481(x15281,x15283,x15284),f481(x15282,x15283,x15284))
% 162.26/162.10 [1529]~E(x15291,x15292)+E(f481(x15293,x15291,x15294),f481(x15293,x15292,x15294))
% 162.26/162.10 [1530]~E(x15301,x15302)+E(f481(x15303,x15304,x15301),f481(x15303,x15304,x15302))
% 162.26/162.10 [1531]~E(x15311,x15312)+E(f213(x15311),f213(x15312))
% 162.26/162.10 [1532]~E(x15321,x15322)+E(f510(x15321,x15323,x15324,x15325,x15326),f510(x15322,x15323,x15324,x15325,x15326))
% 162.26/162.10 [1533]~E(x15331,x15332)+E(f510(x15333,x15331,x15334,x15335,x15336),f510(x15333,x15332,x15334,x15335,x15336))
% 162.26/162.10 [1534]~E(x15341,x15342)+E(f510(x15343,x15344,x15341,x15345,x15346),f510(x15343,x15344,x15342,x15345,x15346))
% 162.26/162.10 [1535]~E(x15351,x15352)+E(f510(x15353,x15354,x15355,x15351,x15356),f510(x15353,x15354,x15355,x15352,x15356))
% 162.26/162.10 [1536]~E(x15361,x15362)+E(f510(x15363,x15364,x15365,x15366,x15361),f510(x15363,x15364,x15365,x15366,x15362))
% 162.26/162.10 [1537]~E(x15371,x15372)+E(f621(x15371,x15373,x15374),f621(x15372,x15373,x15374))
% 162.26/162.10 [1538]~E(x15381,x15382)+E(f621(x15383,x15381,x15384),f621(x15383,x15382,x15384))
% 162.26/162.10 [1539]~E(x15391,x15392)+E(f621(x15393,x15394,x15391),f621(x15393,x15394,x15392))
% 162.26/162.10 [1540]~E(x15401,x15402)+E(f533(x15401,x15403,x15404),f533(x15402,x15403,x15404))
% 162.26/162.10 [1541]~E(x15411,x15412)+E(f533(x15413,x15411,x15414),f533(x15413,x15412,x15414))
% 162.26/162.10 [1542]~E(x15421,x15422)+E(f533(x15423,x15424,x15421),f533(x15423,x15424,x15422))
% 162.26/162.10 [1543]~E(x15431,x15432)+E(f461(x15431,x15433,x15434,x15435,x15436,x15437),f461(x15432,x15433,x15434,x15435,x15436,x15437))
% 162.26/162.10 [1544]~E(x15441,x15442)+E(f461(x15443,x15441,x15444,x15445,x15446,x15447),f461(x15443,x15442,x15444,x15445,x15446,x15447))
% 162.26/162.10 [1545]~E(x15451,x15452)+E(f461(x15453,x15454,x15451,x15455,x15456,x15457),f461(x15453,x15454,x15452,x15455,x15456,x15457))
% 162.26/162.10 [1546]~E(x15461,x15462)+E(f461(x15463,x15464,x15465,x15461,x15466,x15467),f461(x15463,x15464,x15465,x15462,x15466,x15467))
% 162.26/162.10 [1547]~E(x15471,x15472)+E(f461(x15473,x15474,x15475,x15476,x15471,x15477),f461(x15473,x15474,x15475,x15476,x15472,x15477))
% 162.26/162.10 [1548]~E(x15481,x15482)+E(f461(x15483,x15484,x15485,x15486,x15487,x15481),f461(x15483,x15484,x15485,x15486,x15487,x15482))
% 162.26/162.10 [1549]~E(x15491,x15492)+E(f216(x15491),f216(x15492))
% 162.26/162.10 [1550]~E(x15501,x15502)+E(f221(x15501,x15503,x15504,x15505),f221(x15502,x15503,x15504,x15505))
% 162.26/162.10 [1551]~E(x15511,x15512)+E(f221(x15513,x15511,x15514,x15515),f221(x15513,x15512,x15514,x15515))
% 162.26/162.10 [1552]~E(x15521,x15522)+E(f221(x15523,x15524,x15521,x15525),f221(x15523,x15524,x15522,x15525))
% 162.26/162.10 [1553]~E(x15531,x15532)+E(f221(x15533,x15534,x15535,x15531),f221(x15533,x15534,x15535,x15532))
% 162.26/162.10 [1554]~E(x15541,x15542)+E(f794(x15541,x15543,x15544),f794(x15542,x15543,x15544))
% 162.26/162.10 [1555]~E(x15551,x15552)+E(f794(x15553,x15551,x15554),f794(x15553,x15552,x15554))
% 162.26/162.10 [1556]~E(x15561,x15562)+E(f794(x15563,x15564,x15561),f794(x15563,x15564,x15562))
% 162.26/162.10 [1557]~E(x15571,x15572)+E(f400(x15571,x15573,x15574),f400(x15572,x15573,x15574))
% 162.26/162.10 [1558]~E(x15581,x15582)+E(f400(x15583,x15581,x15584),f400(x15583,x15582,x15584))
% 162.26/162.10 [1559]~E(x15591,x15592)+E(f400(x15593,x15594,x15591),f400(x15593,x15594,x15592))
% 162.26/162.10 [1560]~E(x15601,x15602)+E(f464(x15601,x15603,x15604),f464(x15602,x15603,x15604))
% 162.26/162.10 [1561]~E(x15611,x15612)+E(f464(x15613,x15611,x15614),f464(x15613,x15612,x15614))
% 162.26/162.10 [1562]~E(x15621,x15622)+E(f464(x15623,x15624,x15621),f464(x15623,x15624,x15622))
% 162.26/162.10 [1563]~E(x15631,x15632)+E(f744(x15631,x15633,x15634,x15635),f744(x15632,x15633,x15634,x15635))
% 162.26/162.10 [1564]~E(x15641,x15642)+E(f744(x15643,x15641,x15644,x15645),f744(x15643,x15642,x15644,x15645))
% 162.26/162.10 [1565]~E(x15651,x15652)+E(f744(x15653,x15654,x15651,x15655),f744(x15653,x15654,x15652,x15655))
% 162.26/162.10 [1566]~E(x15661,x15662)+E(f744(x15663,x15664,x15665,x15661),f744(x15663,x15664,x15665,x15662))
% 162.26/162.10 [1567]~E(x15671,x15672)+E(f124(x15671,x15673,x15674),f124(x15672,x15673,x15674))
% 162.26/162.10 [1568]~E(x15681,x15682)+E(f124(x15683,x15681,x15684),f124(x15683,x15682,x15684))
% 162.26/162.10 [1569]~E(x15691,x15692)+E(f124(x15693,x15694,x15691),f124(x15693,x15694,x15692))
% 162.26/162.10 [1570]~E(x15701,x15702)+E(f474(x15701,x15703),f474(x15702,x15703))
% 162.26/162.10 [1571]~E(x15711,x15712)+E(f474(x15713,x15711),f474(x15713,x15712))
% 162.26/162.10 [1572]~E(x15721,x15722)+E(f833(x15721,x15723),f833(x15722,x15723))
% 162.26/162.10 [1573]~E(x15731,x15732)+E(f833(x15733,x15731),f833(x15733,x15732))
% 162.26/162.10 [1574]~E(x15741,x15742)+E(f146(x15741,x15743),f146(x15742,x15743))
% 162.26/162.10 [1575]~E(x15751,x15752)+E(f146(x15753,x15751),f146(x15753,x15752))
% 162.26/162.10 [1576]~E(x15761,x15762)+E(f655(x15761,x15763,x15764),f655(x15762,x15763,x15764))
% 162.26/162.10 [1577]~E(x15771,x15772)+E(f655(x15773,x15771,x15774),f655(x15773,x15772,x15774))
% 162.26/162.10 [1578]~E(x15781,x15782)+E(f655(x15783,x15784,x15781),f655(x15783,x15784,x15782))
% 162.26/162.10 [1579]~E(x15791,x15792)+E(f811(x15791,x15793,x15794),f811(x15792,x15793,x15794))
% 162.26/162.10 [1580]~E(x15801,x15802)+E(f811(x15803,x15801,x15804),f811(x15803,x15802,x15804))
% 162.26/162.10 [1581]~E(x15811,x15812)+E(f811(x15813,x15814,x15811),f811(x15813,x15814,x15812))
% 162.26/162.10 [1582]~E(x15821,x15822)+E(f458(x15821,x15823,x15824,x15825,x15826),f458(x15822,x15823,x15824,x15825,x15826))
% 162.26/162.10 [1583]~E(x15831,x15832)+E(f458(x15833,x15831,x15834,x15835,x15836),f458(x15833,x15832,x15834,x15835,x15836))
% 162.26/162.10 [1584]~E(x15841,x15842)+E(f458(x15843,x15844,x15841,x15845,x15846),f458(x15843,x15844,x15842,x15845,x15846))
% 162.26/162.10 [1585]~E(x15851,x15852)+E(f458(x15853,x15854,x15855,x15851,x15856),f458(x15853,x15854,x15855,x15852,x15856))
% 162.26/162.10 [1586]~E(x15861,x15862)+E(f458(x15863,x15864,x15865,x15866,x15861),f458(x15863,x15864,x15865,x15866,x15862))
% 162.26/162.10 [1587]~E(x15871,x15872)+E(f363(x15871,x15873,x15874),f363(x15872,x15873,x15874))
% 162.26/162.10 [1588]~E(x15881,x15882)+E(f363(x15883,x15881,x15884),f363(x15883,x15882,x15884))
% 162.26/162.10 [1589]~E(x15891,x15892)+E(f363(x15893,x15894,x15891),f363(x15893,x15894,x15892))
% 162.26/162.10 [1590]~E(x15901,x15902)+E(f480(x15901,x15903),f480(x15902,x15903))
% 162.26/162.10 [1591]~E(x15911,x15912)+E(f480(x15913,x15911),f480(x15913,x15912))
% 162.26/162.10 [1592]~E(x15921,x15922)+E(f377(x15921,x15923,x15924),f377(x15922,x15923,x15924))
% 162.26/162.10 [1593]~E(x15931,x15932)+E(f377(x15933,x15931,x15934),f377(x15933,x15932,x15934))
% 162.26/162.10 [1594]~E(x15941,x15942)+E(f377(x15943,x15944,x15941),f377(x15943,x15944,x15942))
% 162.26/162.10 [1595]~E(x15951,x15952)+E(f656(x15951,x15953,x15954),f656(x15952,x15953,x15954))
% 162.26/162.10 [1596]~E(x15961,x15962)+E(f656(x15963,x15961,x15964),f656(x15963,x15962,x15964))
% 162.26/162.10 [1597]~E(x15971,x15972)+E(f656(x15973,x15974,x15971),f656(x15973,x15974,x15972))
% 162.26/162.10 [1598]~E(x15981,x15982)+E(f726(x15981,x15983,x15984),f726(x15982,x15983,x15984))
% 162.26/162.10 [1599]~E(x15991,x15992)+E(f726(x15993,x15991,x15994),f726(x15993,x15992,x15994))
% 162.26/162.10 [1600]~E(x16001,x16002)+E(f726(x16003,x16004,x16001),f726(x16003,x16004,x16002))
% 162.26/162.10 [1601]~E(x16011,x16012)+E(f843(x16011,x16013,x16014,x16015),f843(x16012,x16013,x16014,x16015))
% 162.26/162.10 [1602]~E(x16021,x16022)+E(f843(x16023,x16021,x16024,x16025),f843(x16023,x16022,x16024,x16025))
% 162.26/162.10 [1603]~E(x16031,x16032)+E(f843(x16033,x16034,x16031,x16035),f843(x16033,x16034,x16032,x16035))
% 162.26/162.10 [1604]~E(x16041,x16042)+E(f843(x16043,x16044,x16045,x16041),f843(x16043,x16044,x16045,x16042))
% 162.26/162.10 [1605]~E(x16051,x16052)+E(f507(x16051,x16053,x16054,x16055),f507(x16052,x16053,x16054,x16055))
% 162.26/162.10 [1606]~E(x16061,x16062)+E(f507(x16063,x16061,x16064,x16065),f507(x16063,x16062,x16064,x16065))
% 162.26/162.10 [1607]~E(x16071,x16072)+E(f507(x16073,x16074,x16071,x16075),f507(x16073,x16074,x16072,x16075))
% 162.26/162.10 [1608]~E(x16081,x16082)+E(f507(x16083,x16084,x16085,x16081),f507(x16083,x16084,x16085,x16082))
% 162.26/162.10 [1609]~E(x16091,x16092)+E(f450(x16091,x16093,x16094),f450(x16092,x16093,x16094))
% 162.26/162.10 [1610]~E(x16101,x16102)+E(f450(x16103,x16101,x16104),f450(x16103,x16102,x16104))
% 162.26/162.10 [1611]~E(x16111,x16112)+E(f450(x16113,x16114,x16111),f450(x16113,x16114,x16112))
% 162.26/162.10 [1612]~E(x16121,x16122)+E(f728(x16121,x16123,x16124),f728(x16122,x16123,x16124))
% 162.26/162.10 [1613]~E(x16131,x16132)+E(f728(x16133,x16131,x16134),f728(x16133,x16132,x16134))
% 162.26/162.10 [1614]~E(x16141,x16142)+E(f728(x16143,x16144,x16141),f728(x16143,x16144,x16142))
% 162.26/162.10 [1615]~E(x16151,x16152)+E(f438(x16151,x16153,x16154,x16155),f438(x16152,x16153,x16154,x16155))
% 162.26/162.10 [1616]~E(x16161,x16162)+E(f438(x16163,x16161,x16164,x16165),f438(x16163,x16162,x16164,x16165))
% 162.26/162.10 [1617]~E(x16171,x16172)+E(f438(x16173,x16174,x16171,x16175),f438(x16173,x16174,x16172,x16175))
% 162.26/162.10 [1618]~E(x16181,x16182)+E(f438(x16183,x16184,x16185,x16181),f438(x16183,x16184,x16185,x16182))
% 162.26/162.10 [1619]~E(x16191,x16192)+E(f183(x16191),f183(x16192))
% 162.26/162.10 [1620]~E(x16201,x16202)+E(f598(x16201,x16203,x16204,x16205),f598(x16202,x16203,x16204,x16205))
% 162.26/162.10 [1621]~E(x16211,x16212)+E(f598(x16213,x16211,x16214,x16215),f598(x16213,x16212,x16214,x16215))
% 162.26/162.10 [1622]~E(x16221,x16222)+E(f598(x16223,x16224,x16221,x16225),f598(x16223,x16224,x16222,x16225))
% 162.26/162.10 [1623]~E(x16231,x16232)+E(f598(x16233,x16234,x16235,x16231),f598(x16233,x16234,x16235,x16232))
% 162.26/162.10 [1624]~E(x16241,x16242)+E(f132(x16241,x16243),f132(x16242,x16243))
% 162.26/162.10 [1625]~E(x16251,x16252)+E(f132(x16253,x16251),f132(x16253,x16252))
% 162.26/162.10 [1626]~E(x16261,x16262)+E(f212(x16261),f212(x16262))
% 162.26/162.10 [1627]~E(x16271,x16272)+E(f647(x16271,x16273,x16274,x16275,x16276),f647(x16272,x16273,x16274,x16275,x16276))
% 162.26/162.10 [1628]~E(x16281,x16282)+E(f647(x16283,x16281,x16284,x16285,x16286),f647(x16283,x16282,x16284,x16285,x16286))
% 162.26/162.10 [1629]~E(x16291,x16292)+E(f647(x16293,x16294,x16291,x16295,x16296),f647(x16293,x16294,x16292,x16295,x16296))
% 162.26/162.10 [1630]~E(x16301,x16302)+E(f647(x16303,x16304,x16305,x16301,x16306),f647(x16303,x16304,x16305,x16302,x16306))
% 162.26/162.10 [1631]~E(x16311,x16312)+E(f647(x16313,x16314,x16315,x16316,x16311),f647(x16313,x16314,x16315,x16316,x16312))
% 162.26/162.10 [1632]~E(x16321,x16322)+E(f830(x16321,x16323,x16324,x16325,x16326,x16327,x16328),f830(x16322,x16323,x16324,x16325,x16326,x16327,x16328))
% 162.26/162.10 [1633]~E(x16331,x16332)+E(f830(x16333,x16331,x16334,x16335,x16336,x16337,x16338),f830(x16333,x16332,x16334,x16335,x16336,x16337,x16338))
% 162.26/162.10 [1634]~E(x16341,x16342)+E(f830(x16343,x16344,x16341,x16345,x16346,x16347,x16348),f830(x16343,x16344,x16342,x16345,x16346,x16347,x16348))
% 162.26/162.10 [1635]~E(x16351,x16352)+E(f830(x16353,x16354,x16355,x16351,x16356,x16357,x16358),f830(x16353,x16354,x16355,x16352,x16356,x16357,x16358))
% 162.26/162.10 [1636]~E(x16361,x16362)+E(f830(x16363,x16364,x16365,x16366,x16361,x16367,x16368),f830(x16363,x16364,x16365,x16366,x16362,x16367,x16368))
% 162.26/162.10 [1637]~E(x16371,x16372)+E(f830(x16373,x16374,x16375,x16376,x16377,x16371,x16378),f830(x16373,x16374,x16375,x16376,x16377,x16372,x16378))
% 162.26/162.10 [1638]~E(x16381,x16382)+E(f830(x16383,x16384,x16385,x16386,x16387,x16388,x16381),f830(x16383,x16384,x16385,x16386,x16387,x16388,x16382))
% 162.26/162.10 [1639]~E(x16391,x16392)+E(f567(x16391,x16393),f567(x16392,x16393))
% 162.26/162.10 [1640]~E(x16401,x16402)+E(f567(x16403,x16401),f567(x16403,x16402))
% 162.26/162.10 [1641]~E(x16411,x16412)+E(f557(x16411,x16413,x16414,x16415,x16416,x16417,x16418,x16419),f557(x16412,x16413,x16414,x16415,x16416,x16417,x16418,x16419))
% 162.26/162.10 [1642]~E(x16421,x16422)+E(f557(x16423,x16421,x16424,x16425,x16426,x16427,x16428,x16429),f557(x16423,x16422,x16424,x16425,x16426,x16427,x16428,x16429))
% 162.26/162.10 [1643]~E(x16431,x16432)+E(f557(x16433,x16434,x16431,x16435,x16436,x16437,x16438,x16439),f557(x16433,x16434,x16432,x16435,x16436,x16437,x16438,x16439))
% 162.26/162.10 [1644]~E(x16441,x16442)+E(f557(x16443,x16444,x16445,x16441,x16446,x16447,x16448,x16449),f557(x16443,x16444,x16445,x16442,x16446,x16447,x16448,x16449))
% 162.26/162.10 [1645]~E(x16451,x16452)+E(f557(x16453,x16454,x16455,x16456,x16451,x16457,x16458,x16459),f557(x16453,x16454,x16455,x16456,x16452,x16457,x16458,x16459))
% 162.26/162.10 [1646]~E(x16461,x16462)+E(f557(x16463,x16464,x16465,x16466,x16467,x16461,x16468,x16469),f557(x16463,x16464,x16465,x16466,x16467,x16462,x16468,x16469))
% 162.26/162.10 [1647]~E(x16471,x16472)+E(f557(x16473,x16474,x16475,x16476,x16477,x16478,x16471,x16479),f557(x16473,x16474,x16475,x16476,x16477,x16478,x16472,x16479))
% 162.26/162.10 [1648]~E(x16481,x16482)+E(f557(x16483,x16484,x16485,x16486,x16487,x16488,x16489,x16481),f557(x16483,x16484,x16485,x16486,x16487,x16488,x16489,x16482))
% 162.26/162.10 [1649]~E(x16491,x16492)+E(f414(x16491,x16493),f414(x16492,x16493))
% 162.26/162.10 [1650]~E(x16501,x16502)+E(f414(x16503,x16501),f414(x16503,x16502))
% 162.26/162.10 [1651]~E(x16511,x16512)+E(f808(x16511,x16513,x16514,x16515,x16516,x16517),f808(x16512,x16513,x16514,x16515,x16516,x16517))
% 162.26/162.10 [1652]~E(x16521,x16522)+E(f808(x16523,x16521,x16524,x16525,x16526,x16527),f808(x16523,x16522,x16524,x16525,x16526,x16527))
% 162.26/162.10 [1653]~E(x16531,x16532)+E(f808(x16533,x16534,x16531,x16535,x16536,x16537),f808(x16533,x16534,x16532,x16535,x16536,x16537))
% 162.26/162.10 [1654]~E(x16541,x16542)+E(f808(x16543,x16544,x16545,x16541,x16546,x16547),f808(x16543,x16544,x16545,x16542,x16546,x16547))
% 162.26/162.10 [1655]~E(x16551,x16552)+E(f808(x16553,x16554,x16555,x16556,x16551,x16557),f808(x16553,x16554,x16555,x16556,x16552,x16557))
% 162.26/162.10 [1656]~E(x16561,x16562)+E(f808(x16563,x16564,x16565,x16566,x16567,x16561),f808(x16563,x16564,x16565,x16566,x16567,x16562))
% 162.26/162.10 [1657]~E(x16571,x16572)+E(f863(x16571,x16573),f863(x16572,x16573))
% 162.26/162.10 [1658]~E(x16581,x16582)+E(f863(x16583,x16581),f863(x16583,x16582))
% 162.26/162.10 [1659]~E(x16591,x16592)+E(f840(x16591,x16593,x16594,x16595),f840(x16592,x16593,x16594,x16595))
% 162.26/162.10 [1660]~E(x16601,x16602)+E(f840(x16603,x16601,x16604,x16605),f840(x16603,x16602,x16604,x16605))
% 162.26/162.10 [1661]~E(x16611,x16612)+E(f840(x16613,x16614,x16611,x16615),f840(x16613,x16614,x16612,x16615))
% 162.26/162.10 [1662]~E(x16621,x16622)+E(f840(x16623,x16624,x16625,x16621),f840(x16623,x16624,x16625,x16622))
% 162.26/162.10 [1663]~E(x16631,x16632)+E(f602(x16631,x16633),f602(x16632,x16633))
% 162.26/162.10 [1664]~E(x16641,x16642)+E(f602(x16643,x16641),f602(x16643,x16642))
% 162.26/162.10 [1665]~E(x16651,x16652)+E(f641(x16651,x16653),f641(x16652,x16653))
% 162.26/162.10 [1666]~E(x16661,x16662)+E(f641(x16663,x16661),f641(x16663,x16662))
% 162.26/162.10 [1667]~E(x16671,x16672)+E(f472(x16671,x16673,x16674),f472(x16672,x16673,x16674))
% 162.26/162.10 [1668]~E(x16681,x16682)+E(f472(x16683,x16681,x16684),f472(x16683,x16682,x16684))
% 162.26/162.10 [1669]~E(x16691,x16692)+E(f472(x16693,x16694,x16691),f472(x16693,x16694,x16692))
% 162.26/162.10 [1670]~E(x16701,x16702)+E(f805(x16701,x16703),f805(x16702,x16703))
% 162.26/162.10 [1671]~E(x16711,x16712)+E(f805(x16713,x16711),f805(x16713,x16712))
% 162.26/162.10 [1672]~E(x16721,x16722)+E(f774(x16721,x16723,x16724,x16725,x16726),f774(x16722,x16723,x16724,x16725,x16726))
% 162.26/162.10 [1673]~E(x16731,x16732)+E(f774(x16733,x16731,x16734,x16735,x16736),f774(x16733,x16732,x16734,x16735,x16736))
% 162.26/162.10 [1674]~E(x16741,x16742)+E(f774(x16743,x16744,x16741,x16745,x16746),f774(x16743,x16744,x16742,x16745,x16746))
% 162.26/162.10 [1675]~E(x16751,x16752)+E(f774(x16753,x16754,x16755,x16751,x16756),f774(x16753,x16754,x16755,x16752,x16756))
% 162.26/162.10 [1676]~E(x16761,x16762)+E(f774(x16763,x16764,x16765,x16766,x16761),f774(x16763,x16764,x16765,x16766,x16762))
% 162.26/162.10 [1677]~E(x16771,x16772)+E(f356(x16771,x16773,x16774,x16775,x16776),f356(x16772,x16773,x16774,x16775,x16776))
% 162.26/162.10 [1678]~E(x16781,x16782)+E(f356(x16783,x16781,x16784,x16785,x16786),f356(x16783,x16782,x16784,x16785,x16786))
% 162.26/162.10 [1679]~E(x16791,x16792)+E(f356(x16793,x16794,x16791,x16795,x16796),f356(x16793,x16794,x16792,x16795,x16796))
% 162.26/162.10 [1680]~E(x16801,x16802)+E(f356(x16803,x16804,x16805,x16801,x16806),f356(x16803,x16804,x16805,x16802,x16806))
% 162.26/162.10 [1681]~E(x16811,x16812)+E(f356(x16813,x16814,x16815,x16816,x16811),f356(x16813,x16814,x16815,x16816,x16812))
% 162.26/162.10 [1682]~E(x16821,x16822)+E(f606(x16821,x16823,x16824,x16825,x16826),f606(x16822,x16823,x16824,x16825,x16826))
% 162.26/162.10 [1683]~E(x16831,x16832)+E(f606(x16833,x16831,x16834,x16835,x16836),f606(x16833,x16832,x16834,x16835,x16836))
% 162.26/162.10 [1684]~E(x16841,x16842)+E(f606(x16843,x16844,x16841,x16845,x16846),f606(x16843,x16844,x16842,x16845,x16846))
% 162.26/162.10 [1685]~E(x16851,x16852)+E(f606(x16853,x16854,x16855,x16851,x16856),f606(x16853,x16854,x16855,x16852,x16856))
% 162.26/162.10 [1686]~E(x16861,x16862)+E(f606(x16863,x16864,x16865,x16866,x16861),f606(x16863,x16864,x16865,x16866,x16862))
% 162.26/162.10 [1687]~E(x16871,x16872)+E(f465(x16871,x16873,x16874),f465(x16872,x16873,x16874))
% 162.26/162.10 [1688]~E(x16881,x16882)+E(f465(x16883,x16881,x16884),f465(x16883,x16882,x16884))
% 162.26/162.10 [1689]~E(x16891,x16892)+E(f465(x16893,x16894,x16891),f465(x16893,x16894,x16892))
% 162.26/162.10 [1690]~E(x16901,x16902)+E(f299(x16901,x16903,x16904,x16905,x16906),f299(x16902,x16903,x16904,x16905,x16906))
% 162.26/162.10 [1691]~E(x16911,x16912)+E(f299(x16913,x16911,x16914,x16915,x16916),f299(x16913,x16912,x16914,x16915,x16916))
% 162.26/162.10 [1692]~E(x16921,x16922)+E(f299(x16923,x16924,x16921,x16925,x16926),f299(x16923,x16924,x16922,x16925,x16926))
% 162.26/162.10 [1693]~E(x16931,x16932)+E(f299(x16933,x16934,x16935,x16931,x16936),f299(x16933,x16934,x16935,x16932,x16936))
% 162.26/162.10 [1694]~E(x16941,x16942)+E(f299(x16943,x16944,x16945,x16946,x16941),f299(x16943,x16944,x16945,x16946,x16942))
% 162.26/162.10 [1695]~E(x16951,x16952)+E(f675(x16951,x16953,x16954),f675(x16952,x16953,x16954))
% 162.26/162.10 [1696]~E(x16961,x16962)+E(f675(x16963,x16961,x16964),f675(x16963,x16962,x16964))
% 162.26/162.10 [1697]~E(x16971,x16972)+E(f675(x16973,x16974,x16971),f675(x16973,x16974,x16972))
% 162.26/162.10 [1698]~E(x16981,x16982)+E(f397(x16981,x16983,x16984,x16985),f397(x16982,x16983,x16984,x16985))
% 162.26/162.10 [1699]~E(x16991,x16992)+E(f397(x16993,x16991,x16994,x16995),f397(x16993,x16992,x16994,x16995))
% 162.26/162.10 [1700]~E(x17001,x17002)+E(f397(x17003,x17004,x17001,x17005),f397(x17003,x17004,x17002,x17005))
% 162.26/162.10 [1701]~E(x17011,x17012)+E(f397(x17013,x17014,x17015,x17011),f397(x17013,x17014,x17015,x17012))
% 162.26/162.10 [1702]~E(x17021,x17022)+E(f838(x17021,x17023,x17024,x17025),f838(x17022,x17023,x17024,x17025))
% 162.26/162.10 [1703]~E(x17031,x17032)+E(f838(x17033,x17031,x17034,x17035),f838(x17033,x17032,x17034,x17035))
% 162.26/162.10 [1704]~E(x17041,x17042)+E(f838(x17043,x17044,x17041,x17045),f838(x17043,x17044,x17042,x17045))
% 162.26/162.10 [1705]~E(x17051,x17052)+E(f838(x17053,x17054,x17055,x17051),f838(x17053,x17054,x17055,x17052))
% 162.26/162.10 [1706]~E(x17061,x17062)+E(f475(x17061,x17063,x17064,x17065,x17066),f475(x17062,x17063,x17064,x17065,x17066))
% 162.26/162.10 [1707]~E(x17071,x17072)+E(f475(x17073,x17071,x17074,x17075,x17076),f475(x17073,x17072,x17074,x17075,x17076))
% 162.26/162.10 [1708]~E(x17081,x17082)+E(f475(x17083,x17084,x17081,x17085,x17086),f475(x17083,x17084,x17082,x17085,x17086))
% 162.26/162.10 [1709]~E(x17091,x17092)+E(f475(x17093,x17094,x17095,x17091,x17096),f475(x17093,x17094,x17095,x17092,x17096))
% 162.26/162.10 [1710]~E(x17101,x17102)+E(f475(x17103,x17104,x17105,x17106,x17101),f475(x17103,x17104,x17105,x17106,x17102))
% 162.26/162.10 [1711]~E(x17111,x17112)+E(f399(x17111,x17113,x17114,x17115),f399(x17112,x17113,x17114,x17115))
% 162.26/162.10 [1712]~E(x17121,x17122)+E(f399(x17123,x17121,x17124,x17125),f399(x17123,x17122,x17124,x17125))
% 162.26/162.10 [1713]~E(x17131,x17132)+E(f399(x17133,x17134,x17131,x17135),f399(x17133,x17134,x17132,x17135))
% 162.26/162.10 [1714]~E(x17141,x17142)+E(f399(x17143,x17144,x17145,x17141),f399(x17143,x17144,x17145,x17142))
% 162.26/162.10 [1715]~E(x17151,x17152)+E(f803(x17151,x17153,x17154,x17155),f803(x17152,x17153,x17154,x17155))
% 162.26/162.10 [1716]~E(x17161,x17162)+E(f803(x17163,x17161,x17164,x17165),f803(x17163,x17162,x17164,x17165))
% 162.26/162.10 [1717]~E(x17171,x17172)+E(f803(x17173,x17174,x17171,x17175),f803(x17173,x17174,x17172,x17175))
% 162.26/162.10 [1718]~E(x17181,x17182)+E(f803(x17183,x17184,x17185,x17181),f803(x17183,x17184,x17185,x17182))
% 162.26/162.10 [1719]~E(x17191,x17192)+E(f509(x17191,x17193,x17194,x17195,x17196),f509(x17192,x17193,x17194,x17195,x17196))
% 162.26/162.10 [1720]~E(x17201,x17202)+E(f509(x17203,x17201,x17204,x17205,x17206),f509(x17203,x17202,x17204,x17205,x17206))
% 162.26/162.10 [1721]~E(x17211,x17212)+E(f509(x17213,x17214,x17211,x17215,x17216),f509(x17213,x17214,x17212,x17215,x17216))
% 162.26/162.10 [1722]~E(x17221,x17222)+E(f509(x17223,x17224,x17225,x17221,x17226),f509(x17223,x17224,x17225,x17222,x17226))
% 162.26/162.10 [1723]~E(x17231,x17232)+E(f509(x17233,x17234,x17235,x17236,x17231),f509(x17233,x17234,x17235,x17236,x17232))
% 162.26/162.10 [1724]~E(x17241,x17242)+E(f378(x17241,x17243,x17244),f378(x17242,x17243,x17244))
% 162.26/162.10 [1725]~E(x17251,x17252)+E(f378(x17253,x17251,x17254),f378(x17253,x17252,x17254))
% 162.26/162.10 [1726]~E(x17261,x17262)+E(f378(x17263,x17264,x17261),f378(x17263,x17264,x17262))
% 162.26/162.10 [1727]~E(x17271,x17272)+E(f614(x17271,x17273,x17274,x17275,x17276),f614(x17272,x17273,x17274,x17275,x17276))
% 162.26/162.10 [1728]~E(x17281,x17282)+E(f614(x17283,x17281,x17284,x17285,x17286),f614(x17283,x17282,x17284,x17285,x17286))
% 162.26/162.10 [1729]~E(x17291,x17292)+E(f614(x17293,x17294,x17291,x17295,x17296),f614(x17293,x17294,x17292,x17295,x17296))
% 162.26/162.10 [1730]~E(x17301,x17302)+E(f614(x17303,x17304,x17305,x17301,x17306),f614(x17303,x17304,x17305,x17302,x17306))
% 162.26/162.10 [1731]~E(x17311,x17312)+E(f614(x17313,x17314,x17315,x17316,x17311),f614(x17313,x17314,x17315,x17316,x17312))
% 162.26/162.10 [1732]~E(x17321,x17322)+E(f17(x17321,x17323,x17324,x17325),f17(x17322,x17323,x17324,x17325))
% 162.26/162.10 [1733]~E(x17331,x17332)+E(f17(x17333,x17331,x17334,x17335),f17(x17333,x17332,x17334,x17335))
% 162.26/162.10 [1734]~E(x17341,x17342)+E(f17(x17343,x17344,x17341,x17345),f17(x17343,x17344,x17342,x17345))
% 162.26/162.10 [1735]~E(x17351,x17352)+E(f17(x17353,x17354,x17355,x17351),f17(x17353,x17354,x17355,x17352))
% 162.26/162.10 [1736]~E(x17361,x17362)+E(f849(x17361,x17363,x17364,x17365,x17366,x17367,x17368),f849(x17362,x17363,x17364,x17365,x17366,x17367,x17368))
% 162.26/162.10 [1737]~E(x17371,x17372)+E(f849(x17373,x17371,x17374,x17375,x17376,x17377,x17378),f849(x17373,x17372,x17374,x17375,x17376,x17377,x17378))
% 162.26/162.10 [1738]~E(x17381,x17382)+E(f849(x17383,x17384,x17381,x17385,x17386,x17387,x17388),f849(x17383,x17384,x17382,x17385,x17386,x17387,x17388))
% 162.26/162.10 [1739]~E(x17391,x17392)+E(f849(x17393,x17394,x17395,x17391,x17396,x17397,x17398),f849(x17393,x17394,x17395,x17392,x17396,x17397,x17398))
% 162.26/162.10 [1740]~E(x17401,x17402)+E(f849(x17403,x17404,x17405,x17406,x17401,x17407,x17408),f849(x17403,x17404,x17405,x17406,x17402,x17407,x17408))
% 162.26/162.10 [1741]~E(x17411,x17412)+E(f849(x17413,x17414,x17415,x17416,x17417,x17411,x17418),f849(x17413,x17414,x17415,x17416,x17417,x17412,x17418))
% 162.26/162.10 [1742]~E(x17421,x17422)+E(f849(x17423,x17424,x17425,x17426,x17427,x17428,x17421),f849(x17423,x17424,x17425,x17426,x17427,x17428,x17422))
% 162.26/162.10 [1743]~E(x17431,x17432)+E(f292(x17431,x17433,x17434),f292(x17432,x17433,x17434))
% 162.26/162.10 [1744]~E(x17441,x17442)+E(f292(x17443,x17441,x17444),f292(x17443,x17442,x17444))
% 162.26/162.10 [1745]~E(x17451,x17452)+E(f292(x17453,x17454,x17451),f292(x17453,x17454,x17452))
% 162.26/162.10 [1746]~E(x17461,x17462)+E(f434(x17461,x17463),f434(x17462,x17463))
% 162.26/162.10 [1747]~E(x17471,x17472)+E(f434(x17473,x17471),f434(x17473,x17472))
% 162.26/162.10 [1748]~E(x17481,x17482)+E(f388(x17481,x17483,x17484),f388(x17482,x17483,x17484))
% 162.26/162.10 [1749]~E(x17491,x17492)+E(f388(x17493,x17491,x17494),f388(x17493,x17492,x17494))
% 162.26/162.10 [1750]~E(x17501,x17502)+E(f388(x17503,x17504,x17501),f388(x17503,x17504,x17502))
% 162.26/162.10 [1751]~E(x17511,x17512)+E(f832(x17511,x17513,x17514),f832(x17512,x17513,x17514))
% 162.26/162.10 [1752]~E(x17521,x17522)+E(f832(x17523,x17521,x17524),f832(x17523,x17522,x17524))
% 162.26/162.10 [1753]~E(x17531,x17532)+E(f832(x17533,x17534,x17531),f832(x17533,x17534,x17532))
% 162.26/162.10 [1754]~E(x17541,x17542)+E(f848(x17541,x17543),f848(x17542,x17543))
% 162.26/162.10 [1755]~E(x17551,x17552)+E(f848(x17553,x17551),f848(x17553,x17552))
% 162.26/162.10 [1756]~E(x17561,x17562)+E(f372(x17561,x17563,x17564,x17565,x17566,x17567),f372(x17562,x17563,x17564,x17565,x17566,x17567))
% 162.26/162.10 [1757]~E(x17571,x17572)+E(f372(x17573,x17571,x17574,x17575,x17576,x17577),f372(x17573,x17572,x17574,x17575,x17576,x17577))
% 162.26/162.10 [1758]~E(x17581,x17582)+E(f372(x17583,x17584,x17581,x17585,x17586,x17587),f372(x17583,x17584,x17582,x17585,x17586,x17587))
% 162.26/162.10 [1759]~E(x17591,x17592)+E(f372(x17593,x17594,x17595,x17591,x17596,x17597),f372(x17593,x17594,x17595,x17592,x17596,x17597))
% 162.26/162.10 [1760]~E(x17601,x17602)+E(f372(x17603,x17604,x17605,x17606,x17601,x17607),f372(x17603,x17604,x17605,x17606,x17602,x17607))
% 162.26/162.10 [1761]~E(x17611,x17612)+E(f372(x17613,x17614,x17615,x17616,x17617,x17611),f372(x17613,x17614,x17615,x17616,x17617,x17612))
% 162.26/162.10 [1762]~E(x17621,x17622)+E(f553(x17621,x17623,x17624,x17625,x17626,x17627),f553(x17622,x17623,x17624,x17625,x17626,x17627))
% 162.26/162.10 [1763]~E(x17631,x17632)+E(f553(x17633,x17631,x17634,x17635,x17636,x17637),f553(x17633,x17632,x17634,x17635,x17636,x17637))
% 162.26/162.10 [1764]~E(x17641,x17642)+E(f553(x17643,x17644,x17641,x17645,x17646,x17647),f553(x17643,x17644,x17642,x17645,x17646,x17647))
% 162.26/162.10 [1765]~E(x17651,x17652)+E(f553(x17653,x17654,x17655,x17651,x17656,x17657),f553(x17653,x17654,x17655,x17652,x17656,x17657))
% 162.26/162.10 [1766]~E(x17661,x17662)+E(f553(x17663,x17664,x17665,x17666,x17661,x17667),f553(x17663,x17664,x17665,x17666,x17662,x17667))
% 162.26/162.10 [1767]~E(x17671,x17672)+E(f553(x17673,x17674,x17675,x17676,x17677,x17671),f553(x17673,x17674,x17675,x17676,x17677,x17672))
% 162.26/162.10 [1768]~E(x17681,x17682)+E(f864(x17681,x17683),f864(x17682,x17683))
% 162.26/162.10 [1769]~E(x17691,x17692)+E(f864(x17693,x17691),f864(x17693,x17692))
% 162.26/162.10 [1770]~E(x17701,x17702)+E(f500(x17701,x17703,x17704,x17705),f500(x17702,x17703,x17704,x17705))
% 162.26/162.10 [1771]~E(x17711,x17712)+E(f500(x17713,x17711,x17714,x17715),f500(x17713,x17712,x17714,x17715))
% 162.26/162.10 [1772]~E(x17721,x17722)+E(f500(x17723,x17724,x17721,x17725),f500(x17723,x17724,x17722,x17725))
% 162.26/162.10 [1773]~E(x17731,x17732)+E(f500(x17733,x17734,x17735,x17731),f500(x17733,x17734,x17735,x17732))
% 162.26/162.10 [1774]~E(x17741,x17742)+E(f369(x17741),f369(x17742))
% 162.26/162.10 [1775]~E(x17751,x17752)+E(f831(x17751,x17753,x17754,x17755,x17756,x17757,x17758),f831(x17752,x17753,x17754,x17755,x17756,x17757,x17758))
% 162.26/162.10 [1776]~E(x17761,x17762)+E(f831(x17763,x17761,x17764,x17765,x17766,x17767,x17768),f831(x17763,x17762,x17764,x17765,x17766,x17767,x17768))
% 162.26/162.10 [1777]~E(x17771,x17772)+E(f831(x17773,x17774,x17771,x17775,x17776,x17777,x17778),f831(x17773,x17774,x17772,x17775,x17776,x17777,x17778))
% 162.26/162.10 [1778]~E(x17781,x17782)+E(f831(x17783,x17784,x17785,x17781,x17786,x17787,x17788),f831(x17783,x17784,x17785,x17782,x17786,x17787,x17788))
% 162.26/162.10 [1779]~E(x17791,x17792)+E(f831(x17793,x17794,x17795,x17796,x17791,x17797,x17798),f831(x17793,x17794,x17795,x17796,x17792,x17797,x17798))
% 162.26/162.10 [1780]~E(x17801,x17802)+E(f831(x17803,x17804,x17805,x17806,x17807,x17801,x17808),f831(x17803,x17804,x17805,x17806,x17807,x17802,x17808))
% 162.26/162.10 [1781]~E(x17811,x17812)+E(f831(x17813,x17814,x17815,x17816,x17817,x17818,x17811),f831(x17813,x17814,x17815,x17816,x17817,x17818,x17812))
% 162.26/162.10 [1782]~E(x17821,x17822)+E(f764(x17821,x17823,x17824),f764(x17822,x17823,x17824))
% 162.26/162.10 [1783]~E(x17831,x17832)+E(f764(x17833,x17831,x17834),f764(x17833,x17832,x17834))
% 162.26/162.10 [1784]~E(x17841,x17842)+E(f764(x17843,x17844,x17841),f764(x17843,x17844,x17842))
% 162.26/162.10 [1785]~E(x17851,x17852)+E(f797(x17851,x17853,x17854),f797(x17852,x17853,x17854))
% 162.26/162.10 [1786]~E(x17861,x17862)+E(f797(x17863,x17861,x17864),f797(x17863,x17862,x17864))
% 162.26/162.10 [1787]~E(x17871,x17872)+E(f797(x17873,x17874,x17871),f797(x17873,x17874,x17872))
% 162.26/162.10 [1788]~E(x17881,x17882)+E(f659(x17881,x17883,x17884,x17885,x17886),f659(x17882,x17883,x17884,x17885,x17886))
% 162.26/162.10 [1789]~E(x17891,x17892)+E(f659(x17893,x17891,x17894,x17895,x17896),f659(x17893,x17892,x17894,x17895,x17896))
% 162.26/162.10 [1790]~E(x17901,x17902)+E(f659(x17903,x17904,x17901,x17905,x17906),f659(x17903,x17904,x17902,x17905,x17906))
% 162.26/162.10 [1791]~E(x17911,x17912)+E(f659(x17913,x17914,x17915,x17911,x17916),f659(x17913,x17914,x17915,x17912,x17916))
% 162.26/162.10 [1792]~E(x17921,x17922)+E(f659(x17923,x17924,x17925,x17926,x17921),f659(x17923,x17924,x17925,x17926,x17922))
% 162.26/162.10 [1793]~E(x17931,x17932)+E(f613(x17931,x17933,x17934,x17935,x17936),f613(x17932,x17933,x17934,x17935,x17936))
% 162.26/162.10 [1794]~E(x17941,x17942)+E(f613(x17943,x17941,x17944,x17945,x17946),f613(x17943,x17942,x17944,x17945,x17946))
% 162.26/162.10 [1795]~E(x17951,x17952)+E(f613(x17953,x17954,x17951,x17955,x17956),f613(x17953,x17954,x17952,x17955,x17956))
% 162.26/162.10 [1796]~E(x17961,x17962)+E(f613(x17963,x17964,x17965,x17961,x17966),f613(x17963,x17964,x17965,x17962,x17966))
% 162.26/162.10 [1797]~E(x17971,x17972)+E(f613(x17973,x17974,x17975,x17976,x17971),f613(x17973,x17974,x17975,x17976,x17972))
% 162.26/162.10 [1798]~E(x17981,x17982)+E(f423(x17981,x17983,x17984,x17985),f423(x17982,x17983,x17984,x17985))
% 162.26/162.10 [1799]~E(x17991,x17992)+E(f423(x17993,x17991,x17994,x17995),f423(x17993,x17992,x17994,x17995))
% 162.26/162.10 [1800]~E(x18001,x18002)+E(f423(x18003,x18004,x18001,x18005),f423(x18003,x18004,x18002,x18005))
% 162.26/162.10 [1801]~E(x18011,x18012)+E(f423(x18013,x18014,x18015,x18011),f423(x18013,x18014,x18015,x18012))
% 162.26/162.10 [1802]~E(x18021,x18022)+E(f687(x18021,x18023,x18024,x18025),f687(x18022,x18023,x18024,x18025))
% 162.26/162.10 [1803]~E(x18031,x18032)+E(f687(x18033,x18031,x18034,x18035),f687(x18033,x18032,x18034,x18035))
% 162.26/162.10 [1804]~E(x18041,x18042)+E(f687(x18043,x18044,x18041,x18045),f687(x18043,x18044,x18042,x18045))
% 162.26/162.10 [1805]~E(x18051,x18052)+E(f687(x18053,x18054,x18055,x18051),f687(x18053,x18054,x18055,x18052))
% 162.26/162.10 [1806]~E(x18061,x18062)+E(f389(x18061,x18063,x18064),f389(x18062,x18063,x18064))
% 162.26/162.10 [1807]~E(x18071,x18072)+E(f389(x18073,x18071,x18074),f389(x18073,x18072,x18074))
% 162.26/162.10 [1808]~E(x18081,x18082)+E(f389(x18083,x18084,x18081),f389(x18083,x18084,x18082))
% 162.26/162.10 [1809]~E(x18091,x18092)+E(f834(x18091,x18093,x18094,x18095),f834(x18092,x18093,x18094,x18095))
% 162.26/162.10 [1810]~E(x18101,x18102)+E(f834(x18103,x18101,x18104,x18105),f834(x18103,x18102,x18104,x18105))
% 162.26/162.10 [1811]~E(x18111,x18112)+E(f834(x18113,x18114,x18111,x18115),f834(x18113,x18114,x18112,x18115))
% 162.26/162.10 [1812]~E(x18121,x18122)+E(f834(x18123,x18124,x18125,x18121),f834(x18123,x18124,x18125,x18122))
% 162.26/162.10 [1813]~E(x18131,x18132)+E(f404(x18131,x18133),f404(x18132,x18133))
% 162.26/162.10 [1814]~E(x18141,x18142)+E(f404(x18143,x18141),f404(x18143,x18142))
% 162.26/162.10 [1815]~E(x18151,x18152)+E(f691(x18151,x18153,x18154,x18155),f691(x18152,x18153,x18154,x18155))
% 162.26/162.10 [1816]~E(x18161,x18162)+E(f691(x18163,x18161,x18164,x18165),f691(x18163,x18162,x18164,x18165))
% 162.26/162.10 [1817]~E(x18171,x18172)+E(f691(x18173,x18174,x18171,x18175),f691(x18173,x18174,x18172,x18175))
% 162.26/162.10 [1818]~E(x18181,x18182)+E(f691(x18183,x18184,x18185,x18181),f691(x18183,x18184,x18185,x18182))
% 162.26/162.10 [1819]~E(x18191,x18192)+E(f379(x18191,x18193,x18194),f379(x18192,x18193,x18194))
% 162.26/162.10 [1820]~E(x18201,x18202)+E(f379(x18203,x18201,x18204),f379(x18203,x18202,x18204))
% 162.26/162.10 [1821]~E(x18211,x18212)+E(f379(x18213,x18214,x18211),f379(x18213,x18214,x18212))
% 162.26/162.10 [1822]~E(x18221,x18222)+E(f547(x18221,x18223,x18224,x18225,x18226),f547(x18222,x18223,x18224,x18225,x18226))
% 162.26/162.10 [1823]~E(x18231,x18232)+E(f547(x18233,x18231,x18234,x18235,x18236),f547(x18233,x18232,x18234,x18235,x18236))
% 162.26/162.10 [1824]~E(x18241,x18242)+E(f547(x18243,x18244,x18241,x18245,x18246),f547(x18243,x18244,x18242,x18245,x18246))
% 162.26/162.10 [1825]~E(x18251,x18252)+E(f547(x18253,x18254,x18255,x18251,x18256),f547(x18253,x18254,x18255,x18252,x18256))
% 162.26/162.10 [1826]~E(x18261,x18262)+E(f547(x18263,x18264,x18265,x18266,x18261),f547(x18263,x18264,x18265,x18266,x18262))
% 162.26/162.10 [1827]~E(x18271,x18272)+E(f281(x18271,x18273,x18274),f281(x18272,x18273,x18274))
% 162.26/162.10 [1828]~E(x18281,x18282)+E(f281(x18283,x18281,x18284),f281(x18283,x18282,x18284))
% 162.26/162.10 [1829]~E(x18291,x18292)+E(f281(x18293,x18294,x18291),f281(x18293,x18294,x18292))
% 162.26/162.10 [1830]~E(x18301,x18302)+E(f709(x18301,x18303,x18304),f709(x18302,x18303,x18304))
% 162.26/162.10 [1831]~E(x18311,x18312)+E(f709(x18313,x18311,x18314),f709(x18313,x18312,x18314))
% 162.26/162.10 [1832]~E(x18321,x18322)+E(f709(x18323,x18324,x18321),f709(x18323,x18324,x18322))
% 162.26/162.10 [1833]~E(x18331,x18332)+E(f712(x18331,x18333,x18334,x18335,x18336),f712(x18332,x18333,x18334,x18335,x18336))
% 162.26/162.10 [1834]~E(x18341,x18342)+E(f712(x18343,x18341,x18344,x18345,x18346),f712(x18343,x18342,x18344,x18345,x18346))
% 162.26/162.10 [1835]~E(x18351,x18352)+E(f712(x18353,x18354,x18351,x18355,x18356),f712(x18353,x18354,x18352,x18355,x18356))
% 162.26/162.10 [1836]~E(x18361,x18362)+E(f712(x18363,x18364,x18365,x18361,x18366),f712(x18363,x18364,x18365,x18362,x18366))
% 162.26/162.10 [1837]~E(x18371,x18372)+E(f712(x18373,x18374,x18375,x18376,x18371),f712(x18373,x18374,x18375,x18376,x18372))
% 162.26/162.10 [1838]~E(x18381,x18382)+E(f867(x18381,x18383,x18384),f867(x18382,x18383,x18384))
% 162.26/162.10 [1839]~E(x18391,x18392)+E(f867(x18393,x18391,x18394),f867(x18393,x18392,x18394))
% 162.26/162.10 [1840]~E(x18401,x18402)+E(f867(x18403,x18404,x18401),f867(x18403,x18404,x18402))
% 162.26/162.10 [1841]~E(x18411,x18412)+E(f431(x18411,x18413,x18414,x18415),f431(x18412,x18413,x18414,x18415))
% 162.26/162.10 [1842]~E(x18421,x18422)+E(f431(x18423,x18421,x18424,x18425),f431(x18423,x18422,x18424,x18425))
% 162.26/162.10 [1843]~E(x18431,x18432)+E(f431(x18433,x18434,x18431,x18435),f431(x18433,x18434,x18432,x18435))
% 162.26/162.10 [1844]~E(x18441,x18442)+E(f431(x18443,x18444,x18445,x18441),f431(x18443,x18444,x18445,x18442))
% 162.26/162.10 [1845]~E(x18451,x18452)+E(f278(x18451,x18453),f278(x18452,x18453))
% 162.26/162.10 [1846]~E(x18461,x18462)+E(f278(x18463,x18461),f278(x18463,x18462))
% 162.26/162.10 [1847]~E(x18471,x18472)+E(f127(x18471),f127(x18472))
% 162.26/162.10 [1848]~E(x18481,x18482)+E(f513(x18481,x18483,x18484,x18485),f513(x18482,x18483,x18484,x18485))
% 162.26/162.10 [1849]~E(x18491,x18492)+E(f513(x18493,x18491,x18494,x18495),f513(x18493,x18492,x18494,x18495))
% 162.26/162.10 [1850]~E(x18501,x18502)+E(f513(x18503,x18504,x18501,x18505),f513(x18503,x18504,x18502,x18505))
% 162.26/162.10 [1851]~E(x18511,x18512)+E(f513(x18513,x18514,x18515,x18511),f513(x18513,x18514,x18515,x18512))
% 162.26/162.10 [1852]~E(x18521,x18522)+E(f612(x18521,x18523,x18524,x18525,x18526,x18527,x18528,x18529),f612(x18522,x18523,x18524,x18525,x18526,x18527,x18528,x18529))
% 162.26/162.10 [1853]~E(x18531,x18532)+E(f612(x18533,x18531,x18534,x18535,x18536,x18537,x18538,x18539),f612(x18533,x18532,x18534,x18535,x18536,x18537,x18538,x18539))
% 162.26/162.10 [1854]~E(x18541,x18542)+E(f612(x18543,x18544,x18541,x18545,x18546,x18547,x18548,x18549),f612(x18543,x18544,x18542,x18545,x18546,x18547,x18548,x18549))
% 162.26/162.10 [1855]~E(x18551,x18552)+E(f612(x18553,x18554,x18555,x18551,x18556,x18557,x18558,x18559),f612(x18553,x18554,x18555,x18552,x18556,x18557,x18558,x18559))
% 162.26/162.10 [1856]~E(x18561,x18562)+E(f612(x18563,x18564,x18565,x18566,x18561,x18567,x18568,x18569),f612(x18563,x18564,x18565,x18566,x18562,x18567,x18568,x18569))
% 162.26/162.10 [1857]~E(x18571,x18572)+E(f612(x18573,x18574,x18575,x18576,x18577,x18571,x18578,x18579),f612(x18573,x18574,x18575,x18576,x18577,x18572,x18578,x18579))
% 162.26/162.10 [1858]~E(x18581,x18582)+E(f612(x18583,x18584,x18585,x18586,x18587,x18588,x18581,x18589),f612(x18583,x18584,x18585,x18586,x18587,x18588,x18582,x18589))
% 162.26/162.10 [1859]~E(x18591,x18592)+E(f612(x18593,x18594,x18595,x18596,x18597,x18598,x18599,x18591),f612(x18593,x18594,x18595,x18596,x18597,x18598,x18599,x18592))
% 162.26/162.10 [1860]~E(x18601,x18602)+E(f706(x18601,x18603,x18604,x18605),f706(x18602,x18603,x18604,x18605))
% 162.26/162.10 [1861]~E(x18611,x18612)+E(f706(x18613,x18611,x18614,x18615),f706(x18613,x18612,x18614,x18615))
% 162.26/162.10 [1862]~E(x18621,x18622)+E(f706(x18623,x18624,x18621,x18625),f706(x18623,x18624,x18622,x18625))
% 162.26/162.10 [1863]~E(x18631,x18632)+E(f706(x18633,x18634,x18635,x18631),f706(x18633,x18634,x18635,x18632))
% 162.26/162.10 [1864]~E(x18641,x18642)+E(f581(x18641,x18643,x18644,x18645),f581(x18642,x18643,x18644,x18645))
% 162.26/162.10 [1865]~E(x18651,x18652)+E(f581(x18653,x18651,x18654,x18655),f581(x18653,x18652,x18654,x18655))
% 162.26/162.10 [1866]~E(x18661,x18662)+E(f581(x18663,x18664,x18661,x18665),f581(x18663,x18664,x18662,x18665))
% 162.26/162.10 [1867]~E(x18671,x18672)+E(f581(x18673,x18674,x18675,x18671),f581(x18673,x18674,x18675,x18672))
% 162.26/162.10 [1868]~E(x18681,x18682)+E(f366(x18681,x18683,x18684),f366(x18682,x18683,x18684))
% 162.26/162.10 [1869]~E(x18691,x18692)+E(f366(x18693,x18691,x18694),f366(x18693,x18692,x18694))
% 162.26/162.10 [1870]~E(x18701,x18702)+E(f366(x18703,x18704,x18701),f366(x18703,x18704,x18702))
% 162.26/162.10 [1871]~E(x18711,x18712)+E(f730(x18711,x18713,x18714),f730(x18712,x18713,x18714))
% 162.26/162.10 [1872]~E(x18721,x18722)+E(f730(x18723,x18721,x18724),f730(x18723,x18722,x18724))
% 162.26/162.10 [1873]~E(x18731,x18732)+E(f730(x18733,x18734,x18731),f730(x18733,x18734,x18732))
% 162.26/162.10 [1874]~E(x18741,x18742)+E(f126(x18741,x18743,x18744,x18745),f126(x18742,x18743,x18744,x18745))
% 162.26/162.10 [1875]~E(x18751,x18752)+E(f126(x18753,x18751,x18754,x18755),f126(x18753,x18752,x18754,x18755))
% 162.26/162.10 [1876]~E(x18761,x18762)+E(f126(x18763,x18764,x18761,x18765),f126(x18763,x18764,x18762,x18765))
% 162.26/162.10 [1877]~E(x18771,x18772)+E(f126(x18773,x18774,x18775,x18771),f126(x18773,x18774,x18775,x18772))
% 162.26/162.10 [1878]~E(x18781,x18782)+E(f75(x18781,x18783),f75(x18782,x18783))
% 162.26/162.10 [1879]~E(x18791,x18792)+E(f75(x18793,x18791),f75(x18793,x18792))
% 162.26/162.10 [1880]~E(x18801,x18802)+E(f296(x18801,x18803,x18804,x18805,x18806),f296(x18802,x18803,x18804,x18805,x18806))
% 162.26/162.10 [1881]~E(x18811,x18812)+E(f296(x18813,x18811,x18814,x18815,x18816),f296(x18813,x18812,x18814,x18815,x18816))
% 162.26/162.10 [1882]~E(x18821,x18822)+E(f296(x18823,x18824,x18821,x18825,x18826),f296(x18823,x18824,x18822,x18825,x18826))
% 162.26/162.10 [1883]~E(x18831,x18832)+E(f296(x18833,x18834,x18835,x18831,x18836),f296(x18833,x18834,x18835,x18832,x18836))
% 162.26/162.10 [1884]~E(x18841,x18842)+E(f296(x18843,x18844,x18845,x18846,x18841),f296(x18843,x18844,x18845,x18846,x18842))
% 162.26/162.10 [1885]~E(x18851,x18852)+E(f297(x18851,x18853,x18854),f297(x18852,x18853,x18854))
% 162.26/162.10 [1886]~E(x18861,x18862)+E(f297(x18863,x18861,x18864),f297(x18863,x18862,x18864))
% 162.26/162.10 [1887]~E(x18871,x18872)+E(f297(x18873,x18874,x18871),f297(x18873,x18874,x18872))
% 162.26/162.10 [1888]~E(x18881,x18882)+E(f552(x18881,x18883,x18884,x18885,x18886,x18887),f552(x18882,x18883,x18884,x18885,x18886,x18887))
% 162.26/162.10 [1889]~E(x18891,x18892)+E(f552(x18893,x18891,x18894,x18895,x18896,x18897),f552(x18893,x18892,x18894,x18895,x18896,x18897))
% 162.26/162.10 [1890]~E(x18901,x18902)+E(f552(x18903,x18904,x18901,x18905,x18906,x18907),f552(x18903,x18904,x18902,x18905,x18906,x18907))
% 162.26/162.10 [1891]~E(x18911,x18912)+E(f552(x18913,x18914,x18915,x18911,x18916,x18917),f552(x18913,x18914,x18915,x18912,x18916,x18917))
% 162.26/162.10 [1892]~E(x18921,x18922)+E(f552(x18923,x18924,x18925,x18926,x18921,x18927),f552(x18923,x18924,x18925,x18926,x18922,x18927))
% 162.26/162.10 [1893]~E(x18931,x18932)+E(f552(x18933,x18934,x18935,x18936,x18937,x18931),f552(x18933,x18934,x18935,x18936,x18937,x18932))
% 162.26/162.10 [1894]~E(x18941,x18942)+E(f383(x18941,x18943,x18944),f383(x18942,x18943,x18944))
% 162.26/162.10 [1895]~E(x18951,x18952)+E(f383(x18953,x18951,x18954),f383(x18953,x18952,x18954))
% 162.26/162.10 [1896]~E(x18961,x18962)+E(f383(x18963,x18964,x18961),f383(x18963,x18964,x18962))
% 162.26/162.10 [1897]~E(x18971,x18972)+E(f338(x18971),f338(x18972))
% 162.26/162.10 [1898]~E(x18981,x18982)+E(f584(x18981,x18983,x18984,x18985),f584(x18982,x18983,x18984,x18985))
% 162.26/162.10 [1899]~E(x18991,x18992)+E(f584(x18993,x18991,x18994,x18995),f584(x18993,x18992,x18994,x18995))
% 162.26/162.10 [1900]~E(x19001,x19002)+E(f584(x19003,x19004,x19001,x19005),f584(x19003,x19004,x19002,x19005))
% 162.26/162.10 [1901]~E(x19011,x19012)+E(f584(x19013,x19014,x19015,x19011),f584(x19013,x19014,x19015,x19012))
% 162.26/162.10 [1902]~E(x19021,x19022)+E(f373(x19021,x19023),f373(x19022,x19023))
% 162.26/162.10 [1903]~E(x19031,x19032)+E(f373(x19033,x19031),f373(x19033,x19032))
% 162.26/162.10 [1904]~E(x19041,x19042)+E(f410(x19041,x19043,x19044,x19045),f410(x19042,x19043,x19044,x19045))
% 162.26/162.10 [1905]~E(x19051,x19052)+E(f410(x19053,x19051,x19054,x19055),f410(x19053,x19052,x19054,x19055))
% 162.26/162.10 [1906]~E(x19061,x19062)+E(f410(x19063,x19064,x19061,x19065),f410(x19063,x19064,x19062,x19065))
% 162.26/162.10 [1907]~E(x19071,x19072)+E(f410(x19073,x19074,x19075,x19071),f410(x19073,x19074,x19075,x19072))
% 162.26/162.10 [1908]~E(x19081,x19082)+E(f449(x19081,x19083,x19084),f449(x19082,x19083,x19084))
% 162.26/162.10 [1909]~E(x19091,x19092)+E(f449(x19093,x19091,x19094),f449(x19093,x19092,x19094))
% 162.26/162.10 [1910]~E(x19101,x19102)+E(f449(x19103,x19104,x19101),f449(x19103,x19104,x19102))
% 162.26/162.10 [1911]~E(x19111,x19112)+E(f743(x19111,x19113,x19114,x19115),f743(x19112,x19113,x19114,x19115))
% 162.26/162.10 [1912]~E(x19121,x19122)+E(f743(x19123,x19121,x19124,x19125),f743(x19123,x19122,x19124,x19125))
% 162.26/162.10 [1913]~E(x19131,x19132)+E(f743(x19133,x19134,x19131,x19135),f743(x19133,x19134,x19132,x19135))
% 162.26/162.10 [1914]~E(x19141,x19142)+E(f743(x19143,x19144,x19145,x19141),f743(x19143,x19144,x19145,x19142))
% 162.26/162.10 [1915]~E(x19151,x19152)+E(f707(x19151,x19153,x19154,x19155,x19156,x19157,x19158,x19159),f707(x19152,x19153,x19154,x19155,x19156,x19157,x19158,x19159))
% 162.26/162.10 [1916]~E(x19161,x19162)+E(f707(x19163,x19161,x19164,x19165,x19166,x19167,x19168,x19169),f707(x19163,x19162,x19164,x19165,x19166,x19167,x19168,x19169))
% 162.26/162.10 [1917]~E(x19171,x19172)+E(f707(x19173,x19174,x19171,x19175,x19176,x19177,x19178,x19179),f707(x19173,x19174,x19172,x19175,x19176,x19177,x19178,x19179))
% 162.26/162.10 [1918]~E(x19181,x19182)+E(f707(x19183,x19184,x19185,x19181,x19186,x19187,x19188,x19189),f707(x19183,x19184,x19185,x19182,x19186,x19187,x19188,x19189))
% 162.26/162.10 [1919]~E(x19191,x19192)+E(f707(x19193,x19194,x19195,x19196,x19191,x19197,x19198,x19199),f707(x19193,x19194,x19195,x19196,x19192,x19197,x19198,x19199))
% 162.26/162.10 [1920]~E(x19201,x19202)+E(f707(x19203,x19204,x19205,x19206,x19207,x19201,x19208,x19209),f707(x19203,x19204,x19205,x19206,x19207,x19202,x19208,x19209))
% 162.26/162.10 [1921]~E(x19211,x19212)+E(f707(x19213,x19214,x19215,x19216,x19217,x19218,x19211,x19219),f707(x19213,x19214,x19215,x19216,x19217,x19218,x19212,x19219))
% 162.26/162.10 [1922]~E(x19221,x19222)+E(f707(x19223,x19224,x19225,x19226,x19227,x19228,x19229,x19221),f707(x19223,x19224,x19225,x19226,x19227,x19228,x19229,x19222))
% 162.26/162.10 [1923]~E(x19231,x19232)+E(f874(x19231,x19233,x19234),f874(x19232,x19233,x19234))
% 162.26/162.10 [1924]~E(x19241,x19242)+E(f874(x19243,x19241,x19244),f874(x19243,x19242,x19244))
% 162.26/162.10 [1925]~E(x19251,x19252)+E(f874(x19253,x19254,x19251),f874(x19253,x19254,x19252))
% 162.26/162.10 [1926]~E(x19261,x19262)+E(f671(x19261,x19263),f671(x19262,x19263))
% 162.26/162.10 [1927]~E(x19271,x19272)+E(f671(x19273,x19271),f671(x19273,x19272))
% 162.26/162.10 [1928]~E(x19281,x19282)+E(f166(x19281,x19283,x19284,x19285),f166(x19282,x19283,x19284,x19285))
% 162.26/162.10 [1929]~E(x19291,x19292)+E(f166(x19293,x19291,x19294,x19295),f166(x19293,x19292,x19294,x19295))
% 162.26/162.10 [1930]~E(x19301,x19302)+E(f166(x19303,x19304,x19301,x19305),f166(x19303,x19304,x19302,x19305))
% 162.26/162.10 [1931]~E(x19311,x19312)+E(f166(x19313,x19314,x19315,x19311),f166(x19313,x19314,x19315,x19312))
% 162.26/162.10 [1932]~E(x19321,x19322)+E(f350(x19321,x19323,x19324,x19325),f350(x19322,x19323,x19324,x19325))
% 162.26/162.10 [1933]~E(x19331,x19332)+E(f350(x19333,x19331,x19334,x19335),f350(x19333,x19332,x19334,x19335))
% 162.26/162.10 [1934]~E(x19341,x19342)+E(f350(x19343,x19344,x19341,x19345),f350(x19343,x19344,x19342,x19345))
% 162.26/162.10 [1935]~E(x19351,x19352)+E(f350(x19353,x19354,x19355,x19351),f350(x19353,x19354,x19355,x19352))
% 162.26/162.10 [1936]~E(x19361,x19362)+E(f802(x19361,x19363,x19364,x19365),f802(x19362,x19363,x19364,x19365))
% 162.26/162.10 [1937]~E(x19371,x19372)+E(f802(x19373,x19371,x19374,x19375),f802(x19373,x19372,x19374,x19375))
% 162.26/162.10 [1938]~E(x19381,x19382)+E(f802(x19383,x19384,x19381,x19385),f802(x19383,x19384,x19382,x19385))
% 162.26/162.10 [1939]~E(x19391,x19392)+E(f802(x19393,x19394,x19395,x19391),f802(x19393,x19394,x19395,x19392))
% 162.26/162.10 [1940]~E(x19401,x19402)+E(f666(x19401,x19403,x19404),f666(x19402,x19403,x19404))
% 162.26/162.10 [1941]~E(x19411,x19412)+E(f666(x19413,x19411,x19414),f666(x19413,x19412,x19414))
% 162.26/162.10 [1942]~E(x19421,x19422)+E(f666(x19423,x19424,x19421),f666(x19423,x19424,x19422))
% 162.26/162.10 [1943]~E(x19431,x19432)+E(f368(x19431,x19433),f368(x19432,x19433))
% 162.26/162.10 [1944]~E(x19441,x19442)+E(f368(x19443,x19441),f368(x19443,x19442))
% 162.26/162.10 [1945]~E(x19451,x19452)+E(f491(x19451,x19453,x19454,x19455,x19456),f491(x19452,x19453,x19454,x19455,x19456))
% 162.26/162.10 [1946]~E(x19461,x19462)+E(f491(x19463,x19461,x19464,x19465,x19466),f491(x19463,x19462,x19464,x19465,x19466))
% 162.26/162.10 [1947]~E(x19471,x19472)+E(f491(x19473,x19474,x19471,x19475,x19476),f491(x19473,x19474,x19472,x19475,x19476))
% 162.26/162.10 [1948]~E(x19481,x19482)+E(f491(x19483,x19484,x19485,x19481,x19486),f491(x19483,x19484,x19485,x19482,x19486))
% 162.26/162.10 [1949]~E(x19491,x19492)+E(f491(x19493,x19494,x19495,x19496,x19491),f491(x19493,x19494,x19495,x19496,x19492))
% 162.26/162.10 [1950]~E(x19501,x19502)+E(f505(x19501,x19503,x19504,x19505),f505(x19502,x19503,x19504,x19505))
% 162.26/162.10 [1951]~E(x19511,x19512)+E(f505(x19513,x19511,x19514,x19515),f505(x19513,x19512,x19514,x19515))
% 162.26/162.10 [1952]~E(x19521,x19522)+E(f505(x19523,x19524,x19521,x19525),f505(x19523,x19524,x19522,x19525))
% 162.26/162.10 [1953]~E(x19531,x19532)+E(f505(x19533,x19534,x19535,x19531),f505(x19533,x19534,x19535,x19532))
% 162.26/162.10 [1954]~E(x19541,x19542)+E(f444(x19541),f444(x19542))
% 162.26/162.10 [1955]~E(x19551,x19552)+E(f599(x19551,x19553,x19554),f599(x19552,x19553,x19554))
% 162.26/162.10 [1956]~E(x19561,x19562)+E(f599(x19563,x19561,x19564),f599(x19563,x19562,x19564))
% 162.26/162.10 [1957]~E(x19571,x19572)+E(f599(x19573,x19574,x19571),f599(x19573,x19574,x19572))
% 162.26/162.10 [1958]~E(x19581,x19582)+E(f443(x19581,x19583,x19584,x19585,x19586),f443(x19582,x19583,x19584,x19585,x19586))
% 162.26/162.10 [1959]~E(x19591,x19592)+E(f443(x19593,x19591,x19594,x19595,x19596),f443(x19593,x19592,x19594,x19595,x19596))
% 162.26/162.10 [1960]~E(x19601,x19602)+E(f443(x19603,x19604,x19601,x19605,x19606),f443(x19603,x19604,x19602,x19605,x19606))
% 162.26/162.10 [1961]~E(x19611,x19612)+E(f443(x19613,x19614,x19615,x19611,x19616),f443(x19613,x19614,x19615,x19612,x19616))
% 162.26/162.10 [1962]~E(x19621,x19622)+E(f443(x19623,x19624,x19625,x19626,x19621),f443(x19623,x19624,x19625,x19626,x19622))
% 162.26/162.10 [1963]~E(x19631,x19632)+E(f619(x19631,x19633,x19634,x19635,x19636),f619(x19632,x19633,x19634,x19635,x19636))
% 162.26/162.10 [1964]~E(x19641,x19642)+E(f619(x19643,x19641,x19644,x19645,x19646),f619(x19643,x19642,x19644,x19645,x19646))
% 162.26/162.10 [1965]~E(x19651,x19652)+E(f619(x19653,x19654,x19651,x19655,x19656),f619(x19653,x19654,x19652,x19655,x19656))
% 162.26/162.10 [1966]~E(x19661,x19662)+E(f619(x19663,x19664,x19665,x19661,x19666),f619(x19663,x19664,x19665,x19662,x19666))
% 162.26/162.10 [1967]~E(x19671,x19672)+E(f619(x19673,x19674,x19675,x19676,x19671),f619(x19673,x19674,x19675,x19676,x19672))
% 162.26/162.10 [1968]~E(x19681,x19682)+E(f408(x19681,x19683,x19684,x19685),f408(x19682,x19683,x19684,x19685))
% 162.26/162.10 [1969]~E(x19691,x19692)+E(f408(x19693,x19691,x19694,x19695),f408(x19693,x19692,x19694,x19695))
% 162.26/162.10 [1970]~E(x19701,x19702)+E(f408(x19703,x19704,x19701,x19705),f408(x19703,x19704,x19702,x19705))
% 162.26/162.10 [1971]~E(x19711,x19712)+E(f408(x19713,x19714,x19715,x19711),f408(x19713,x19714,x19715,x19712))
% 162.26/162.10 [1972]~E(x19721,x19722)+E(f700(x19721,x19723,x19724,x19725,x19726),f700(x19722,x19723,x19724,x19725,x19726))
% 162.26/162.10 [1973]~E(x19731,x19732)+E(f700(x19733,x19731,x19734,x19735,x19736),f700(x19733,x19732,x19734,x19735,x19736))
% 162.26/162.10 [1974]~E(x19741,x19742)+E(f700(x19743,x19744,x19741,x19745,x19746),f700(x19743,x19744,x19742,x19745,x19746))
% 162.26/162.10 [1975]~E(x19751,x19752)+E(f700(x19753,x19754,x19755,x19751,x19756),f700(x19753,x19754,x19755,x19752,x19756))
% 162.26/162.10 [1976]~E(x19761,x19762)+E(f700(x19763,x19764,x19765,x19766,x19761),f700(x19763,x19764,x19765,x19766,x19762))
% 162.26/162.10 [1977]~E(x19771,x19772)+E(f601(x19771),f601(x19772))
% 162.26/162.10 [1978]~E(x19781,x19782)+E(f264(x19781,x19783,x19784),f264(x19782,x19783,x19784))
% 162.26/162.10 [1979]~E(x19791,x19792)+E(f264(x19793,x19791,x19794),f264(x19793,x19792,x19794))
% 162.26/162.10 [1980]~E(x19801,x19802)+E(f264(x19803,x19804,x19801),f264(x19803,x19804,x19802))
% 162.26/162.10 [1981]~E(x19811,x19812)+E(f167(x19811,x19813,x19814,x19815),f167(x19812,x19813,x19814,x19815))
% 162.26/162.10 [1982]~E(x19821,x19822)+E(f167(x19823,x19821,x19824,x19825),f167(x19823,x19822,x19824,x19825))
% 162.26/162.10 [1983]~E(x19831,x19832)+E(f167(x19833,x19834,x19831,x19835),f167(x19833,x19834,x19832,x19835))
% 162.26/162.10 [1984]~E(x19841,x19842)+E(f167(x19843,x19844,x19845,x19841),f167(x19843,x19844,x19845,x19842))
% 162.26/162.10 [1985]~E(x19851,x19852)+E(f777(x19851,x19853,x19854,x19855,x19856),f777(x19852,x19853,x19854,x19855,x19856))
% 162.26/162.10 [1986]~E(x19861,x19862)+E(f777(x19863,x19861,x19864,x19865,x19866),f777(x19863,x19862,x19864,x19865,x19866))
% 162.26/162.10 [1987]~E(x19871,x19872)+E(f777(x19873,x19874,x19871,x19875,x19876),f777(x19873,x19874,x19872,x19875,x19876))
% 162.26/162.10 [1988]~E(x19881,x19882)+E(f777(x19883,x19884,x19885,x19881,x19886),f777(x19883,x19884,x19885,x19882,x19886))
% 162.26/162.10 [1989]~E(x19891,x19892)+E(f777(x19893,x19894,x19895,x19896,x19891),f777(x19893,x19894,x19895,x19896,x19892))
% 162.26/162.10 [1990]~E(x19901,x19902)+E(f470(x19901,x19903),f470(x19902,x19903))
% 162.26/162.10 [1991]~E(x19911,x19912)+E(f470(x19913,x19911),f470(x19913,x19912))
% 162.26/162.10 [1992]~E(x19921,x19922)+E(f870(x19921,x19923),f870(x19922,x19923))
% 162.26/162.10 [1993]~E(x19931,x19932)+E(f870(x19933,x19931),f870(x19933,x19932))
% 162.26/162.10 [1994]~E(x19941,x19942)+E(f358(x19941,x19943,x19944,x19945),f358(x19942,x19943,x19944,x19945))
% 162.26/162.10 [1995]~E(x19951,x19952)+E(f358(x19953,x19951,x19954,x19955),f358(x19953,x19952,x19954,x19955))
% 162.26/162.10 [1996]~E(x19961,x19962)+E(f358(x19963,x19964,x19961,x19965),f358(x19963,x19964,x19962,x19965))
% 162.26/162.10 [1997]~E(x19971,x19972)+E(f358(x19973,x19974,x19975,x19971),f358(x19973,x19974,x19975,x19972))
% 162.26/162.10 [1998]~E(x19981,x19982)+E(f674(x19981,x19983,x19984),f674(x19982,x19983,x19984))
% 162.26/162.10 [1999]~E(x19991,x19992)+E(f674(x19993,x19991,x19994),f674(x19993,x19992,x19994))
% 162.26/162.10 [2000]~E(x20001,x20002)+E(f674(x20003,x20004,x20001),f674(x20003,x20004,x20002))
% 162.26/162.10 [2001]~E(x20011,x20012)+E(f214(x20011,x20013),f214(x20012,x20013))
% 162.26/162.10 [2002]~E(x20021,x20022)+E(f214(x20023,x20021),f214(x20023,x20022))
% 162.26/162.10 [2003]~E(x20031,x20032)+E(f411(x20031,x20033,x20034,x20035),f411(x20032,x20033,x20034,x20035))
% 162.26/162.10 [2004]~E(x20041,x20042)+E(f411(x20043,x20041,x20044,x20045),f411(x20043,x20042,x20044,x20045))
% 162.26/162.10 [2005]~E(x20051,x20052)+E(f411(x20053,x20054,x20051,x20055),f411(x20053,x20054,x20052,x20055))
% 162.26/162.10 [2006]~E(x20061,x20062)+E(f411(x20063,x20064,x20065,x20061),f411(x20063,x20064,x20065,x20062))
% 162.26/162.10 [2007]~E(x20071,x20072)+E(f873(x20071,x20073,x20074),f873(x20072,x20073,x20074))
% 162.26/162.10 [2008]~E(x20081,x20082)+E(f873(x20083,x20081,x20084),f873(x20083,x20082,x20084))
% 162.26/162.10 [2009]~E(x20091,x20092)+E(f873(x20093,x20094,x20091),f873(x20093,x20094,x20092))
% 162.26/162.10 [2010]~E(x20101,x20102)+E(f353(x20101,x20103,x20104,x20105,x20106,x20107),f353(x20102,x20103,x20104,x20105,x20106,x20107))
% 162.26/162.10 [2011]~E(x20111,x20112)+E(f353(x20113,x20111,x20114,x20115,x20116,x20117),f353(x20113,x20112,x20114,x20115,x20116,x20117))
% 162.26/162.10 [2012]~E(x20121,x20122)+E(f353(x20123,x20124,x20121,x20125,x20126,x20127),f353(x20123,x20124,x20122,x20125,x20126,x20127))
% 162.26/162.10 [2013]~E(x20131,x20132)+E(f353(x20133,x20134,x20135,x20131,x20136,x20137),f353(x20133,x20134,x20135,x20132,x20136,x20137))
% 162.26/162.10 [2014]~E(x20141,x20142)+E(f353(x20143,x20144,x20145,x20146,x20141,x20147),f353(x20143,x20144,x20145,x20146,x20142,x20147))
% 162.26/162.10 [2015]~E(x20151,x20152)+E(f353(x20153,x20154,x20155,x20156,x20157,x20151),f353(x20153,x20154,x20155,x20156,x20157,x20152))
% 162.26/162.10 [2016]~E(x20161,x20162)+E(f775(x20161,x20163,x20164,x20165,x20166),f775(x20162,x20163,x20164,x20165,x20166))
% 162.26/162.10 [2017]~E(x20171,x20172)+E(f775(x20173,x20171,x20174,x20175,x20176),f775(x20173,x20172,x20174,x20175,x20176))
% 162.26/162.10 [2018]~E(x20181,x20182)+E(f775(x20183,x20184,x20181,x20185,x20186),f775(x20183,x20184,x20182,x20185,x20186))
% 162.26/162.10 [2019]~E(x20191,x20192)+E(f775(x20193,x20194,x20195,x20191,x20196),f775(x20193,x20194,x20195,x20192,x20196))
% 162.26/162.10 [2020]~E(x20201,x20202)+E(f775(x20203,x20204,x20205,x20206,x20201),f775(x20203,x20204,x20205,x20206,x20202))
% 162.26/162.10 [2021]~E(x20211,x20212)+E(f719(x20211,x20213,x20214,x20215),f719(x20212,x20213,x20214,x20215))
% 162.26/162.10 [2022]~E(x20221,x20222)+E(f719(x20223,x20221,x20224,x20225),f719(x20223,x20222,x20224,x20225))
% 162.26/162.10 [2023]~E(x20231,x20232)+E(f719(x20233,x20234,x20231,x20235),f719(x20233,x20234,x20232,x20235))
% 162.26/162.10 [2024]~E(x20241,x20242)+E(f719(x20243,x20244,x20245,x20241),f719(x20243,x20244,x20245,x20242))
% 162.26/162.10 [2025]~E(x20251,x20252)+E(f452(x20251,x20253,x20254),f452(x20252,x20253,x20254))
% 162.26/162.10 [2026]~E(x20261,x20262)+E(f452(x20263,x20261,x20264),f452(x20263,x20262,x20264))
% 162.26/162.10 [2027]~E(x20271,x20272)+E(f452(x20273,x20274,x20271),f452(x20273,x20274,x20272))
% 162.26/162.10 [2028]~E(x20281,x20282)+E(f340(x20281),f340(x20282))
% 162.26/162.10 [2029]~E(x20291,x20292)+E(f123(x20291,x20293,x20294),f123(x20292,x20293,x20294))
% 162.26/162.10 [2030]~E(x20301,x20302)+E(f123(x20303,x20301,x20304),f123(x20303,x20302,x20304))
% 162.26/162.10 [2031]~E(x20311,x20312)+E(f123(x20313,x20314,x20311),f123(x20313,x20314,x20312))
% 162.26/162.10 [2032]~E(x20321,x20322)+E(f636(x20321,x20323),f636(x20322,x20323))
% 162.26/162.10 [2033]~E(x20331,x20332)+E(f636(x20333,x20331),f636(x20333,x20332))
% 162.26/162.10 [2034]~E(x20341,x20342)+E(f290(x20341,x20343),f290(x20342,x20343))
% 162.26/162.10 [2035]~E(x20351,x20352)+E(f290(x20353,x20351),f290(x20353,x20352))
% 162.26/162.10 [2036]~E(x20361,x20362)+E(f555(x20361,x20363,x20364,x20365,x20366),f555(x20362,x20363,x20364,x20365,x20366))
% 162.26/162.10 [2037]~E(x20371,x20372)+E(f555(x20373,x20371,x20374,x20375,x20376),f555(x20373,x20372,x20374,x20375,x20376))
% 162.26/162.10 [2038]~E(x20381,x20382)+E(f555(x20383,x20384,x20381,x20385,x20386),f555(x20383,x20384,x20382,x20385,x20386))
% 162.26/162.10 [2039]~E(x20391,x20392)+E(f555(x20393,x20394,x20395,x20391,x20396),f555(x20393,x20394,x20395,x20392,x20396))
% 162.26/162.10 [2040]~E(x20401,x20402)+E(f555(x20403,x20404,x20405,x20406,x20401),f555(x20403,x20404,x20405,x20406,x20402))
% 162.26/162.10 [2041]~E(x20411,x20412)+E(f603(x20411,x20413),f603(x20412,x20413))
% 162.26/162.10 [2042]~E(x20421,x20422)+E(f603(x20423,x20421),f603(x20423,x20422))
% 162.26/162.10 [2043]~E(x20431,x20432)+E(f275(x20431,x20433),f275(x20432,x20433))
% 162.26/162.10 [2044]~E(x20441,x20442)+E(f275(x20443,x20441),f275(x20443,x20442))
% 162.26/162.10 [2045]~E(x20451,x20452)+E(f325(x20451,x20453,x20454),f325(x20452,x20453,x20454))
% 162.26/162.10 [2046]~E(x20461,x20462)+E(f325(x20463,x20461,x20464),f325(x20463,x20462,x20464))
% 162.26/162.10 [2047]~E(x20471,x20472)+E(f325(x20473,x20474,x20471),f325(x20473,x20474,x20472))
% 162.26/162.10 [2048]~E(x20481,x20482)+E(f517(x20481),f517(x20482))
% 162.26/162.10 [2049]~E(x20491,x20492)+E(f536(x20491,x20493,x20494),f536(x20492,x20493,x20494))
% 162.26/162.10 [2050]~E(x20501,x20502)+E(f536(x20503,x20501,x20504),f536(x20503,x20502,x20504))
% 162.26/162.10 [2051]~E(x20511,x20512)+E(f536(x20513,x20514,x20511),f536(x20513,x20514,x20512))
% 162.26/162.10 [2052]~E(x20521,x20522)+E(f335(x20521,x20523,x20524,x20525),f335(x20522,x20523,x20524,x20525))
% 162.26/162.10 [2053]~E(x20531,x20532)+E(f335(x20533,x20531,x20534,x20535),f335(x20533,x20532,x20534,x20535))
% 162.26/162.10 [2054]~E(x20541,x20542)+E(f335(x20543,x20544,x20541,x20545),f335(x20543,x20544,x20542,x20545))
% 162.26/162.10 [2055]~E(x20551,x20552)+E(f335(x20553,x20554,x20555,x20551),f335(x20553,x20554,x20555,x20552))
% 162.26/162.10 [2056]~E(x20561,x20562)+E(f583(x20561,x20563,x20564,x20565),f583(x20562,x20563,x20564,x20565))
% 162.26/162.10 [2057]~E(x20571,x20572)+E(f583(x20573,x20571,x20574,x20575),f583(x20573,x20572,x20574,x20575))
% 162.26/162.10 [2058]~E(x20581,x20582)+E(f583(x20583,x20584,x20581,x20585),f583(x20583,x20584,x20582,x20585))
% 162.26/162.10 [2059]~E(x20591,x20592)+E(f583(x20593,x20594,x20595,x20591),f583(x20593,x20594,x20595,x20592))
% 162.26/162.10 [2060]~E(x20601,x20602)+E(f532(x20601,x20603,x20604),f532(x20602,x20603,x20604))
% 162.26/162.10 [2061]~E(x20611,x20612)+E(f532(x20613,x20611,x20614),f532(x20613,x20612,x20614))
% 162.26/162.10 [2062]~E(x20621,x20622)+E(f532(x20623,x20624,x20621),f532(x20623,x20624,x20622))
% 162.26/162.10 [2063]~E(x20631,x20632)+E(f219(x20631,x20633,x20634,x20635),f219(x20632,x20633,x20634,x20635))
% 162.26/162.10 [2064]~E(x20641,x20642)+E(f219(x20643,x20641,x20644,x20645),f219(x20643,x20642,x20644,x20645))
% 162.26/162.10 [2065]~E(x20651,x20652)+E(f219(x20653,x20654,x20651,x20655),f219(x20653,x20654,x20652,x20655))
% 162.26/162.10 [2066]~E(x20661,x20662)+E(f219(x20663,x20664,x20665,x20661),f219(x20663,x20664,x20665,x20662))
% 162.26/162.10 [2067]~E(x20671,x20672)+E(f314(x20671,x20673,x20674),f314(x20672,x20673,x20674))
% 162.26/162.10 [2068]~E(x20681,x20682)+E(f314(x20683,x20681,x20684),f314(x20683,x20682,x20684))
% 162.26/162.10 [2069]~E(x20691,x20692)+E(f314(x20693,x20694,x20691),f314(x20693,x20694,x20692))
% 162.26/162.10 [2070]~E(x20701,x20702)+E(f796(x20701,x20703,x20704),f796(x20702,x20703,x20704))
% 162.26/162.10 [2071]~E(x20711,x20712)+E(f796(x20713,x20711,x20714),f796(x20713,x20712,x20714))
% 162.26/162.10 [2072]~E(x20721,x20722)+E(f796(x20723,x20724,x20721),f796(x20723,x20724,x20722))
% 162.26/162.10 [2073]~E(x20731,x20732)+E(f535(x20731),f535(x20732))
% 162.26/162.10 [2074]~E(x20741,x20742)+E(f243(x20741,x20743,x20744,x20745,x20746),f243(x20742,x20743,x20744,x20745,x20746))
% 162.26/162.10 [2075]~E(x20751,x20752)+E(f243(x20753,x20751,x20754,x20755,x20756),f243(x20753,x20752,x20754,x20755,x20756))
% 162.26/162.10 [2076]~E(x20761,x20762)+E(f243(x20763,x20764,x20761,x20765,x20766),f243(x20763,x20764,x20762,x20765,x20766))
% 162.26/162.10 [2077]~E(x20771,x20772)+E(f243(x20773,x20774,x20775,x20771,x20776),f243(x20773,x20774,x20775,x20772,x20776))
% 162.26/162.10 [2078]~E(x20781,x20782)+E(f243(x20783,x20784,x20785,x20786,x20781),f243(x20783,x20784,x20785,x20786,x20782))
% 162.26/162.10 [2079]~E(x20791,x20792)+E(f279(x20791,x20793),f279(x20792,x20793))
% 162.26/162.10 [2080]~E(x20801,x20802)+E(f279(x20803,x20801),f279(x20803,x20802))
% 162.26/162.10 [2081]~E(x20811,x20812)+E(f640(x20811,x20813,x20814),f640(x20812,x20813,x20814))
% 162.26/162.10 [2082]~E(x20821,x20822)+E(f640(x20823,x20821,x20824),f640(x20823,x20822,x20824))
% 162.26/162.10 [2083]~E(x20831,x20832)+E(f640(x20833,x20834,x20831),f640(x20833,x20834,x20832))
% 162.26/162.10 [2084]~E(x20841,x20842)+E(f362(x20841,x20843,x20844,x20845,x20846,x20847),f362(x20842,x20843,x20844,x20845,x20846,x20847))
% 162.26/162.10 [2085]~E(x20851,x20852)+E(f362(x20853,x20851,x20854,x20855,x20856,x20857),f362(x20853,x20852,x20854,x20855,x20856,x20857))
% 162.26/162.10 [2086]~E(x20861,x20862)+E(f362(x20863,x20864,x20861,x20865,x20866,x20867),f362(x20863,x20864,x20862,x20865,x20866,x20867))
% 162.26/162.10 [2087]~E(x20871,x20872)+E(f362(x20873,x20874,x20875,x20871,x20876,x20877),f362(x20873,x20874,x20875,x20872,x20876,x20877))
% 162.26/162.10 [2088]~E(x20881,x20882)+E(f362(x20883,x20884,x20885,x20886,x20881,x20887),f362(x20883,x20884,x20885,x20886,x20882,x20887))
% 162.26/162.10 [2089]~E(x20891,x20892)+E(f362(x20893,x20894,x20895,x20896,x20897,x20891),f362(x20893,x20894,x20895,x20896,x20897,x20892))
% 162.26/162.10 [2090]~E(x20901,x20902)+E(f558(x20901,x20903),f558(x20902,x20903))
% 162.26/162.10 [2091]~E(x20911,x20912)+E(f558(x20913,x20911),f558(x20913,x20912))
% 162.26/162.10 [2092]~E(x20921,x20922)+E(f578(x20921,x20923),f578(x20922,x20923))
% 162.26/162.10 [2093]~E(x20931,x20932)+E(f578(x20933,x20931),f578(x20933,x20932))
% 162.26/162.10 [2094]~E(x20941,x20942)+E(f343(x20941,x20943,x20944),f343(x20942,x20943,x20944))
% 162.26/162.10 [2095]~E(x20951,x20952)+E(f343(x20953,x20951,x20954),f343(x20953,x20952,x20954))
% 162.26/162.10 [2096]~E(x20961,x20962)+E(f343(x20963,x20964,x20961),f343(x20963,x20964,x20962))
% 162.26/162.10 [2097]~E(x20971,x20972)+E(f736(x20971,x20973,x20974,x20975,x20976,x20977,x20978),f736(x20972,x20973,x20974,x20975,x20976,x20977,x20978))
% 162.26/162.10 [2098]~E(x20981,x20982)+E(f736(x20983,x20981,x20984,x20985,x20986,x20987,x20988),f736(x20983,x20982,x20984,x20985,x20986,x20987,x20988))
% 162.26/162.10 [2099]~E(x20991,x20992)+E(f736(x20993,x20994,x20991,x20995,x20996,x20997,x20998),f736(x20993,x20994,x20992,x20995,x20996,x20997,x20998))
% 162.26/162.10 [2100]~E(x21001,x21002)+E(f736(x21003,x21004,x21005,x21001,x21006,x21007,x21008),f736(x21003,x21004,x21005,x21002,x21006,x21007,x21008))
% 162.26/162.10 [2101]~E(x21011,x21012)+E(f736(x21013,x21014,x21015,x21016,x21011,x21017,x21018),f736(x21013,x21014,x21015,x21016,x21012,x21017,x21018))
% 162.26/162.10 [2102]~E(x21021,x21022)+E(f736(x21023,x21024,x21025,x21026,x21027,x21021,x21028),f736(x21023,x21024,x21025,x21026,x21027,x21022,x21028))
% 162.26/162.10 [2103]~E(x21031,x21032)+E(f736(x21033,x21034,x21035,x21036,x21037,x21038,x21031),f736(x21033,x21034,x21035,x21036,x21037,x21038,x21032))
% 162.26/162.10 [2104]~E(x21041,x21042)+E(f222(x21041,x21043,x21044,x21045),f222(x21042,x21043,x21044,x21045))
% 162.26/162.10 [2105]~E(x21051,x21052)+E(f222(x21053,x21051,x21054,x21055),f222(x21053,x21052,x21054,x21055))
% 162.26/162.10 [2106]~E(x21061,x21062)+E(f222(x21063,x21064,x21061,x21065),f222(x21063,x21064,x21062,x21065))
% 162.26/162.10 [2107]~E(x21071,x21072)+E(f222(x21073,x21074,x21075,x21071),f222(x21073,x21074,x21075,x21072))
% 162.26/162.10 [2108]~E(x21081,x21082)+E(f786(x21081,x21083),f786(x21082,x21083))
% 162.26/162.10 [2109]~E(x21091,x21092)+E(f786(x21093,x21091),f786(x21093,x21092))
% 162.26/162.10 [2110]~E(x21101,x21102)+E(f650(x21101,x21103,x21104,x21105),f650(x21102,x21103,x21104,x21105))
% 162.26/162.10 [2111]~E(x21111,x21112)+E(f650(x21113,x21111,x21114,x21115),f650(x21113,x21112,x21114,x21115))
% 162.26/162.10 [2112]~E(x21121,x21122)+E(f650(x21123,x21124,x21121,x21125),f650(x21123,x21124,x21122,x21125))
% 162.26/162.10 [2113]~E(x21131,x21132)+E(f650(x21133,x21134,x21135,x21131),f650(x21133,x21134,x21135,x21132))
% 162.26/162.10 [2114]~E(x21141,x21142)+E(f291(x21141,x21143),f291(x21142,x21143))
% 162.26/162.10 [2115]~E(x21151,x21152)+E(f291(x21153,x21151),f291(x21153,x21152))
% 162.26/162.10 [2116]~E(x21161,x21162)+E(f206(x21161,x21163,x21164,x21165),f206(x21162,x21163,x21164,x21165))
% 162.26/162.10 [2117]~E(x21171,x21172)+E(f206(x21173,x21171,x21174,x21175),f206(x21173,x21172,x21174,x21175))
% 162.26/162.10 [2118]~E(x21181,x21182)+E(f206(x21183,x21184,x21181,x21185),f206(x21183,x21184,x21182,x21185))
% 162.26/162.10 [2119]~E(x21191,x21192)+E(f206(x21193,x21194,x21195,x21191),f206(x21193,x21194,x21195,x21192))
% 162.26/162.10 [2120]~E(x21201,x21202)+E(f570(x21201,x21203,x21204,x21205),f570(x21202,x21203,x21204,x21205))
% 162.26/162.10 [2121]~E(x21211,x21212)+E(f570(x21213,x21211,x21214,x21215),f570(x21213,x21212,x21214,x21215))
% 162.26/162.10 [2122]~E(x21221,x21222)+E(f570(x21223,x21224,x21221,x21225),f570(x21223,x21224,x21222,x21225))
% 162.26/162.10 [2123]~E(x21231,x21232)+E(f570(x21233,x21234,x21235,x21231),f570(x21233,x21234,x21235,x21232))
% 162.26/162.10 [2124]~E(x21241,x21242)+E(f854(x21241,x21243,x21244),f854(x21242,x21243,x21244))
% 162.26/162.10 [2125]~E(x21251,x21252)+E(f854(x21253,x21251,x21254),f854(x21253,x21252,x21254))
% 162.26/162.10 [2126]~E(x21261,x21262)+E(f854(x21263,x21264,x21261),f854(x21263,x21264,x21262))
% 162.26/162.10 [2127]~E(x21271,x21272)+E(f207(x21271,x21273,x21274,x21275),f207(x21272,x21273,x21274,x21275))
% 162.26/162.10 [2128]~E(x21281,x21282)+E(f207(x21283,x21281,x21284,x21285),f207(x21283,x21282,x21284,x21285))
% 162.26/162.10 [2129]~E(x21291,x21292)+E(f207(x21293,x21294,x21291,x21295),f207(x21293,x21294,x21292,x21295))
% 162.26/162.10 [2130]~E(x21301,x21302)+E(f207(x21303,x21304,x21305,x21301),f207(x21303,x21304,x21305,x21302))
% 162.26/162.10 [2131]~E(x21311,x21312)+E(f818(x21311,x21313,x21314,x21315),f818(x21312,x21313,x21314,x21315))
% 162.26/162.10 [2132]~E(x21321,x21322)+E(f818(x21323,x21321,x21324,x21325),f818(x21323,x21322,x21324,x21325))
% 162.26/162.10 [2133]~E(x21331,x21332)+E(f818(x21333,x21334,x21331,x21335),f818(x21333,x21334,x21332,x21335))
% 162.26/162.10 [2134]~E(x21341,x21342)+E(f818(x21343,x21344,x21345,x21341),f818(x21343,x21344,x21345,x21342))
% 162.26/162.10 [2135]~E(x21351,x21352)+E(f638(x21351,x21353,x21354,x21355,x21356),f638(x21352,x21353,x21354,x21355,x21356))
% 162.26/162.10 [2136]~E(x21361,x21362)+E(f638(x21363,x21361,x21364,x21365,x21366),f638(x21363,x21362,x21364,x21365,x21366))
% 162.26/162.10 [2137]~E(x21371,x21372)+E(f638(x21373,x21374,x21371,x21375,x21376),f638(x21373,x21374,x21372,x21375,x21376))
% 162.26/162.10 [2138]~E(x21381,x21382)+E(f638(x21383,x21384,x21385,x21381,x21386),f638(x21383,x21384,x21385,x21382,x21386))
% 162.26/162.10 [2139]~E(x21391,x21392)+E(f638(x21393,x21394,x21395,x21396,x21391),f638(x21393,x21394,x21395,x21396,x21392))
% 162.26/162.10 [2140]~E(x21401,x21402)+E(f575(x21401,x21403,x21404,x21405),f575(x21402,x21403,x21404,x21405))
% 162.26/162.10 [2141]~E(x21411,x21412)+E(f575(x21413,x21411,x21414,x21415),f575(x21413,x21412,x21414,x21415))
% 162.26/162.10 [2142]~E(x21421,x21422)+E(f575(x21423,x21424,x21421,x21425),f575(x21423,x21424,x21422,x21425))
% 162.26/162.10 [2143]~E(x21431,x21432)+E(f575(x21433,x21434,x21435,x21431),f575(x21433,x21434,x21435,x21432))
% 162.26/162.10 [2144]~E(x21441,x21442)+E(f498(x21441,x21443,x21444,x21445),f498(x21442,x21443,x21444,x21445))
% 162.26/162.10 [2145]~E(x21451,x21452)+E(f498(x21453,x21451,x21454,x21455),f498(x21453,x21452,x21454,x21455))
% 162.26/162.10 [2146]~E(x21461,x21462)+E(f498(x21463,x21464,x21461,x21465),f498(x21463,x21464,x21462,x21465))
% 162.26/162.10 [2147]~E(x21471,x21472)+E(f498(x21473,x21474,x21475,x21471),f498(x21473,x21474,x21475,x21472))
% 162.26/162.10 [2148]~E(x21481,x21482)+E(f223(x21481,x21483,x21484,x21485,x21486,x21487,x21488),f223(x21482,x21483,x21484,x21485,x21486,x21487,x21488))
% 162.26/162.10 [2149]~E(x21491,x21492)+E(f223(x21493,x21491,x21494,x21495,x21496,x21497,x21498),f223(x21493,x21492,x21494,x21495,x21496,x21497,x21498))
% 162.26/162.10 [2150]~E(x21501,x21502)+E(f223(x21503,x21504,x21501,x21505,x21506,x21507,x21508),f223(x21503,x21504,x21502,x21505,x21506,x21507,x21508))
% 162.26/162.10 [2151]~E(x21511,x21512)+E(f223(x21513,x21514,x21515,x21511,x21516,x21517,x21518),f223(x21513,x21514,x21515,x21512,x21516,x21517,x21518))
% 162.26/162.10 [2152]~E(x21521,x21522)+E(f223(x21523,x21524,x21525,x21526,x21521,x21527,x21528),f223(x21523,x21524,x21525,x21526,x21522,x21527,x21528))
% 162.26/162.10 [2153]~E(x21531,x21532)+E(f223(x21533,x21534,x21535,x21536,x21537,x21531,x21538),f223(x21533,x21534,x21535,x21536,x21537,x21532,x21538))
% 162.26/162.10 [2154]~E(x21541,x21542)+E(f223(x21543,x21544,x21545,x21546,x21547,x21548,x21541),f223(x21543,x21544,x21545,x21546,x21547,x21548,x21542))
% 162.26/162.10 [2155]~E(x21551,x21552)+E(f445(x21551,x21553),f445(x21552,x21553))
% 162.26/162.10 [2156]~E(x21561,x21562)+E(f445(x21563,x21561),f445(x21563,x21562))
% 162.26/162.10 [2157]~E(x21571,x21572)+E(f282(x21571,x21573),f282(x21572,x21573))
% 162.26/162.10 [2158]~E(x21581,x21582)+E(f282(x21583,x21581),f282(x21583,x21582))
% 162.26/162.10 [2159]~E(x21591,x21592)+E(f673(x21591,x21593),f673(x21592,x21593))
% 162.26/162.10 [2160]~E(x21601,x21602)+E(f673(x21603,x21601),f673(x21603,x21602))
% 162.26/162.10 [2161]~E(x21611,x21612)+E(f634(x21611,x21613,x21614,x21615,x21616),f634(x21612,x21613,x21614,x21615,x21616))
% 162.26/162.10 [2162]~E(x21621,x21622)+E(f634(x21623,x21621,x21624,x21625,x21626),f634(x21623,x21622,x21624,x21625,x21626))
% 162.26/162.10 [2163]~E(x21631,x21632)+E(f634(x21633,x21634,x21631,x21635,x21636),f634(x21633,x21634,x21632,x21635,x21636))
% 162.26/162.10 [2164]~E(x21641,x21642)+E(f634(x21643,x21644,x21645,x21641,x21646),f634(x21643,x21644,x21645,x21642,x21646))
% 162.26/162.10 [2165]~E(x21651,x21652)+E(f634(x21653,x21654,x21655,x21656,x21651),f634(x21653,x21654,x21655,x21656,x21652))
% 162.26/162.10 [2166]~E(x21661,x21662)+E(f760(x21661,x21663,x21664,x21665,x21666),f760(x21662,x21663,x21664,x21665,x21666))
% 162.26/162.10 [2167]~E(x21671,x21672)+E(f760(x21673,x21671,x21674,x21675,x21676),f760(x21673,x21672,x21674,x21675,x21676))
% 162.26/162.10 [2168]~E(x21681,x21682)+E(f760(x21683,x21684,x21681,x21685,x21686),f760(x21683,x21684,x21682,x21685,x21686))
% 162.26/162.10 [2169]~E(x21691,x21692)+E(f760(x21693,x21694,x21695,x21691,x21696),f760(x21693,x21694,x21695,x21692,x21696))
% 162.26/162.10 [2170]~E(x21701,x21702)+E(f760(x21703,x21704,x21705,x21706,x21701),f760(x21703,x21704,x21705,x21706,x21702))
% 162.26/162.10 [2171]~E(x21711,x21712)+E(f527(x21711,x21713,x21714),f527(x21712,x21713,x21714))
% 162.26/162.10 [2172]~E(x21721,x21722)+E(f527(x21723,x21721,x21724),f527(x21723,x21722,x21724))
% 162.26/162.10 [2173]~E(x21731,x21732)+E(f527(x21733,x21734,x21731),f527(x21733,x21734,x21732))
% 162.26/162.10 [2174]~E(x21741,x21742)+E(f658(x21741,x21743,x21744),f658(x21742,x21743,x21744))
% 162.26/162.10 [2175]~E(x21751,x21752)+E(f658(x21753,x21751,x21754),f658(x21753,x21752,x21754))
% 162.26/162.10 [2176]~E(x21761,x21762)+E(f658(x21763,x21764,x21761),f658(x21763,x21764,x21762))
% 162.26/162.10 [2177]~E(x21771,x21772)+E(f428(x21771,x21773,x21774,x21775),f428(x21772,x21773,x21774,x21775))
% 162.26/162.10 [2178]~E(x21781,x21782)+E(f428(x21783,x21781,x21784,x21785),f428(x21783,x21782,x21784,x21785))
% 162.26/162.10 [2179]~E(x21791,x21792)+E(f428(x21793,x21794,x21791,x21795),f428(x21793,x21794,x21792,x21795))
% 162.26/162.10 [2180]~E(x21801,x21802)+E(f428(x21803,x21804,x21805,x21801),f428(x21803,x21804,x21805,x21802))
% 162.26/162.10 [2181]~E(x21811,x21812)+E(f488(x21811,x21813,x21814),f488(x21812,x21813,x21814))
% 162.26/162.10 [2182]~E(x21821,x21822)+E(f488(x21823,x21821,x21824),f488(x21823,x21822,x21824))
% 162.26/162.10 [2183]~E(x21831,x21832)+E(f488(x21833,x21834,x21831),f488(x21833,x21834,x21832))
% 162.26/162.10 [2184]~E(x21841,x21842)+E(f698(x21841,x21843,x21844,x21845),f698(x21842,x21843,x21844,x21845))
% 162.26/162.10 [2185]~E(x21851,x21852)+E(f698(x21853,x21851,x21854,x21855),f698(x21853,x21852,x21854,x21855))
% 162.26/162.10 [2186]~E(x21861,x21862)+E(f698(x21863,x21864,x21861,x21865),f698(x21863,x21864,x21862,x21865))
% 162.26/162.10 [2187]~E(x21871,x21872)+E(f698(x21873,x21874,x21875,x21871),f698(x21873,x21874,x21875,x21872))
% 162.26/162.10 [2188]~E(x21881,x21882)+E(f364(x21881,x21883,x21884),f364(x21882,x21883,x21884))
% 162.26/162.10 [2189]~E(x21891,x21892)+E(f364(x21893,x21891,x21894),f364(x21893,x21892,x21894))
% 162.26/162.10 [2190]~E(x21901,x21902)+E(f364(x21903,x21904,x21901),f364(x21903,x21904,x21902))
% 162.26/162.10 [2191]~E(x21911,x21912)+E(f693(x21911,x21913),f693(x21912,x21913))
% 162.26/162.10 [2192]~E(x21921,x21922)+E(f693(x21923,x21921),f693(x21923,x21922))
% 162.26/162.10 [2193]~E(x21931,x21932)+E(f653(x21931,x21933,x21934,x21935),f653(x21932,x21933,x21934,x21935))
% 162.26/162.10 [2194]~E(x21941,x21942)+E(f653(x21943,x21941,x21944,x21945),f653(x21943,x21942,x21944,x21945))
% 162.26/162.10 [2195]~E(x21951,x21952)+E(f653(x21953,x21954,x21951,x21955),f653(x21953,x21954,x21952,x21955))
% 162.26/162.10 [2196]~E(x21961,x21962)+E(f653(x21963,x21964,x21965,x21961),f653(x21963,x21964,x21965,x21962))
% 162.26/162.10 [2197]~E(x21971,x21972)+E(f391(x21971,x21973,x21974),f391(x21972,x21973,x21974))
% 162.26/162.10 [2198]~E(x21981,x21982)+E(f391(x21983,x21981,x21984),f391(x21983,x21982,x21984))
% 162.26/162.10 [2199]~E(x21991,x21992)+E(f391(x21993,x21994,x21991),f391(x21993,x21994,x21992))
% 162.26/162.10 [2200]~E(x22001,x22002)+E(f401(x22001,x22003,x22004,x22005,x22006),f401(x22002,x22003,x22004,x22005,x22006))
% 162.26/162.10 [2201]~E(x22011,x22012)+E(f401(x22013,x22011,x22014,x22015,x22016),f401(x22013,x22012,x22014,x22015,x22016))
% 162.26/162.10 [2202]~E(x22021,x22022)+E(f401(x22023,x22024,x22021,x22025,x22026),f401(x22023,x22024,x22022,x22025,x22026))
% 162.26/162.10 [2203]~E(x22031,x22032)+E(f401(x22033,x22034,x22035,x22031,x22036),f401(x22033,x22034,x22035,x22032,x22036))
% 162.26/162.10 [2204]~E(x22041,x22042)+E(f401(x22043,x22044,x22045,x22046,x22041),f401(x22043,x22044,x22045,x22046,x22042))
% 162.26/162.10 [2205]~E(x22051,x22052)+E(f762(x22051,x22053,x22054),f762(x22052,x22053,x22054))
% 162.26/162.10 [2206]~E(x22061,x22062)+E(f762(x22063,x22061,x22064),f762(x22063,x22062,x22064))
% 162.26/162.10 [2207]~E(x22071,x22072)+E(f762(x22073,x22074,x22071),f762(x22073,x22074,x22072))
% 162.26/162.10 [2208]~E(x22081,x22082)+E(f861(x22081,x22083,x22084),f861(x22082,x22083,x22084))
% 162.26/162.10 [2209]~E(x22091,x22092)+E(f861(x22093,x22091,x22094),f861(x22093,x22092,x22094))
% 162.26/162.10 [2210]~E(x22101,x22102)+E(f861(x22103,x22104,x22101),f861(x22103,x22104,x22102))
% 162.26/162.10 [2211]~E(x22111,x22112)+E(f298(x22111,x22113,x22114,x22115),f298(x22112,x22113,x22114,x22115))
% 162.26/162.10 [2212]~E(x22121,x22122)+E(f298(x22123,x22121,x22124,x22125),f298(x22123,x22122,x22124,x22125))
% 162.26/162.10 [2213]~E(x22131,x22132)+E(f298(x22133,x22134,x22131,x22135),f298(x22133,x22134,x22132,x22135))
% 162.26/162.10 [2214]~E(x22141,x22142)+E(f298(x22143,x22144,x22145,x22141),f298(x22143,x22144,x22145,x22142))
% 162.26/162.10 [2215]~E(x22151,x22152)+E(f433(x22151,x22153),f433(x22152,x22153))
% 162.26/162.10 [2216]~E(x22161,x22162)+E(f433(x22163,x22161),f433(x22163,x22162))
% 162.26/162.10 [2217]~E(x22171,x22172)+E(f493(x22171,x22173,x22174,x22175),f493(x22172,x22173,x22174,x22175))
% 162.26/162.10 [2218]~E(x22181,x22182)+E(f493(x22183,x22181,x22184,x22185),f493(x22183,x22182,x22184,x22185))
% 162.26/162.10 [2219]~E(x22191,x22192)+E(f493(x22193,x22194,x22191,x22195),f493(x22193,x22194,x22192,x22195))
% 162.26/162.10 [2220]~E(x22201,x22202)+E(f493(x22203,x22204,x22205,x22201),f493(x22203,x22204,x22205,x22202))
% 162.26/162.10 [2221]~E(x22211,x22212)+E(f426(x22211,x22213,x22214,x22215),f426(x22212,x22213,x22214,x22215))
% 162.26/162.10 [2222]~E(x22221,x22222)+E(f426(x22223,x22221,x22224,x22225),f426(x22223,x22222,x22224,x22225))
% 162.26/162.10 [2223]~E(x22231,x22232)+E(f426(x22233,x22234,x22231,x22235),f426(x22233,x22234,x22232,x22235))
% 162.26/162.10 [2224]~E(x22241,x22242)+E(f426(x22243,x22244,x22245,x22241),f426(x22243,x22244,x22245,x22242))
% 162.26/162.10 [2225]~E(x22251,x22252)+E(f402(x22251,x22253,x22254,x22255,x22256),f402(x22252,x22253,x22254,x22255,x22256))
% 162.26/162.10 [2226]~E(x22261,x22262)+E(f402(x22263,x22261,x22264,x22265,x22266),f402(x22263,x22262,x22264,x22265,x22266))
% 162.26/162.10 [2227]~E(x22271,x22272)+E(f402(x22273,x22274,x22271,x22275,x22276),f402(x22273,x22274,x22272,x22275,x22276))
% 162.26/162.10 [2228]~E(x22281,x22282)+E(f402(x22283,x22284,x22285,x22281,x22286),f402(x22283,x22284,x22285,x22282,x22286))
% 162.26/162.10 [2229]~E(x22291,x22292)+E(f402(x22293,x22294,x22295,x22296,x22291),f402(x22293,x22294,x22295,x22296,x22292))
% 162.26/162.10 [2230]~E(x22301,x22302)+E(f763(x22301,x22303,x22304),f763(x22302,x22303,x22304))
% 162.26/162.10 [2231]~E(x22311,x22312)+E(f763(x22313,x22311,x22314),f763(x22313,x22312,x22314))
% 162.26/162.10 [2232]~E(x22321,x22322)+E(f763(x22323,x22324,x22321),f763(x22323,x22324,x22322))
% 162.26/162.10 [2233]~E(x22331,x22332)+E(f683(x22331,x22333,x22334),f683(x22332,x22333,x22334))
% 162.26/162.10 [2234]~E(x22341,x22342)+E(f683(x22343,x22341,x22344),f683(x22343,x22342,x22344))
% 162.26/162.10 [2235]~E(x22351,x22352)+E(f683(x22353,x22354,x22351),f683(x22353,x22354,x22352))
% 162.26/162.10 [2236]~E(x22361,x22362)+E(f624(x22361,x22363,x22364),f624(x22362,x22363,x22364))
% 162.26/162.10 [2237]~E(x22371,x22372)+E(f624(x22373,x22371,x22374),f624(x22373,x22372,x22374))
% 162.26/162.10 [2238]~E(x22381,x22382)+E(f624(x22383,x22384,x22381),f624(x22383,x22384,x22382))
% 162.26/162.10 [2239]~E(x22391,x22392)+E(f682(x22391,x22393,x22394),f682(x22392,x22393,x22394))
% 162.26/162.10 [2240]~E(x22401,x22402)+E(f682(x22403,x22401,x22404),f682(x22403,x22402,x22404))
% 162.26/162.10 [2241]~E(x22411,x22412)+E(f682(x22413,x22414,x22411),f682(x22413,x22414,x22412))
% 162.26/162.10 [2242]~E(x22421,x22422)+E(f526(x22421,x22423,x22424,x22425),f526(x22422,x22423,x22424,x22425))
% 162.26/162.10 [2243]~E(x22431,x22432)+E(f526(x22433,x22431,x22434,x22435),f526(x22433,x22432,x22434,x22435))
% 162.26/162.10 [2244]~E(x22441,x22442)+E(f526(x22443,x22444,x22441,x22445),f526(x22443,x22444,x22442,x22445))
% 162.26/162.10 [2245]~E(x22451,x22452)+E(f526(x22453,x22454,x22455,x22451),f526(x22453,x22454,x22455,x22452))
% 162.26/162.10 [2246]~E(x22461,x22462)+E(f463(x22461,x22463,x22464,x22465,x22466),f463(x22462,x22463,x22464,x22465,x22466))
% 162.26/162.10 [2247]~E(x22471,x22472)+E(f463(x22473,x22471,x22474,x22475,x22476),f463(x22473,x22472,x22474,x22475,x22476))
% 162.26/162.10 [2248]~E(x22481,x22482)+E(f463(x22483,x22484,x22481,x22485,x22486),f463(x22483,x22484,x22482,x22485,x22486))
% 162.26/162.10 [2249]~E(x22491,x22492)+E(f463(x22493,x22494,x22495,x22491,x22496),f463(x22493,x22494,x22495,x22492,x22496))
% 162.26/162.10 [2250]~E(x22501,x22502)+E(f463(x22503,x22504,x22505,x22506,x22501),f463(x22503,x22504,x22505,x22506,x22502))
% 162.26/162.10 [2251]~E(x22511,x22512)+E(f622(x22511,x22513),f622(x22512,x22513))
% 162.26/162.10 [2252]~E(x22521,x22522)+E(f622(x22523,x22521),f622(x22523,x22522))
% 162.26/162.10 [2253]~E(x22531,x22532)+E(f639(x22531,x22533,x22534),f639(x22532,x22533,x22534))
% 162.26/162.10 [2254]~E(x22541,x22542)+E(f639(x22543,x22541,x22544),f639(x22543,x22542,x22544))
% 162.26/162.10 [2255]~E(x22551,x22552)+E(f639(x22553,x22554,x22551),f639(x22553,x22554,x22552))
% 162.26/162.10 [2256]~E(x22561,x22562)+E(f413(x22561,x22563),f413(x22562,x22563))
% 162.26/162.10 [2257]~E(x22571,x22572)+E(f413(x22573,x22571),f413(x22573,x22572))
% 162.26/162.10 [2258]~E(x22581,x22582)+E(f437(x22581,x22583,x22584,x22585),f437(x22582,x22583,x22584,x22585))
% 162.26/162.10 [2259]~E(x22591,x22592)+E(f437(x22593,x22591,x22594,x22595),f437(x22593,x22592,x22594,x22595))
% 162.26/162.10 [2260]~E(x22601,x22602)+E(f437(x22603,x22604,x22601,x22605),f437(x22603,x22604,x22602,x22605))
% 162.26/162.10 [2261]~E(x22611,x22612)+E(f437(x22613,x22614,x22615,x22611),f437(x22613,x22614,x22615,x22612))
% 162.26/162.10 [2262]~E(x22621,x22622)+E(f315(x22621,x22623,x22624),f315(x22622,x22623,x22624))
% 162.26/162.10 [2263]~E(x22631,x22632)+E(f315(x22633,x22631,x22634),f315(x22633,x22632,x22634))
% 162.26/162.10 [2264]~E(x22641,x22642)+E(f315(x22643,x22644,x22641),f315(x22643,x22644,x22642))
% 162.26/162.10 [2265]~E(x22651,x22652)+E(f672(x22651,x22653),f672(x22652,x22653))
% 162.26/162.10 [2266]~E(x22661,x22662)+E(f672(x22663,x22661),f672(x22663,x22662))
% 162.26/162.10 [2267]~E(x22671,x22672)+E(f665(x22671,x22673,x22674),f665(x22672,x22673,x22674))
% 162.26/162.10 [2268]~E(x22681,x22682)+E(f665(x22683,x22681,x22684),f665(x22683,x22682,x22684))
% 162.26/162.10 [2269]~E(x22691,x22692)+E(f665(x22693,x22694,x22691),f665(x22693,x22694,x22692))
% 162.26/162.10 [2270]~E(x22701,x22702)+E(f419(x22701,x22703,x22704,x22705),f419(x22702,x22703,x22704,x22705))
% 162.26/162.10 [2271]~E(x22711,x22712)+E(f419(x22713,x22711,x22714,x22715),f419(x22713,x22712,x22714,x22715))
% 162.26/162.10 [2272]~E(x22721,x22722)+E(f419(x22723,x22724,x22721,x22725),f419(x22723,x22724,x22722,x22725))
% 162.26/162.10 [2273]~E(x22731,x22732)+E(f419(x22733,x22734,x22735,x22731),f419(x22733,x22734,x22735,x22732))
% 162.26/162.10 [2274]~E(x22741,x22742)+E(f694(x22741,x22743),f694(x22742,x22743))
% 162.26/162.10 [2275]~E(x22751,x22752)+E(f694(x22753,x22751),f694(x22753,x22752))
% 162.26/162.10 [2276]~E(x22761,x22762)+E(f781(x22761,x22763,x22764),f781(x22762,x22763,x22764))
% 162.26/162.10 [2277]~E(x22771,x22772)+E(f781(x22773,x22771,x22774),f781(x22773,x22772,x22774))
% 162.26/162.10 [2278]~E(x22781,x22782)+E(f781(x22783,x22784,x22781),f781(x22783,x22784,x22782))
% 162.26/162.10 [2279]~E(x22791,x22792)+E(f486(x22791,x22793,x22794),f486(x22792,x22793,x22794))
% 162.26/162.10 [2280]~E(x22801,x22802)+E(f486(x22803,x22801,x22804),f486(x22803,x22802,x22804))
% 162.26/162.10 [2281]~E(x22811,x22812)+E(f486(x22813,x22814,x22811),f486(x22813,x22814,x22812))
% 162.26/162.10 [2282]~E(x22821,x22822)+E(f95(x22821,x22823,x22824),f95(x22822,x22823,x22824))
% 162.26/162.10 [2283]~E(x22831,x22832)+E(f95(x22833,x22831,x22834),f95(x22833,x22832,x22834))
% 162.26/162.10 [2284]~E(x22841,x22842)+E(f95(x22843,x22844,x22841),f95(x22843,x22844,x22842))
% 162.26/162.10 [2285]~E(x22851,x22852)+E(f757(x22851,x22853),f757(x22852,x22853))
% 162.26/162.10 [2286]~E(x22861,x22862)+E(f757(x22863,x22861),f757(x22863,x22862))
% 162.26/162.10 [2287]~E(x22871,x22872)+E(f845(x22871),f845(x22872))
% 162.26/162.10 [2288]~E(x22881,x22882)+E(f573(x22881,x22883,x22884,x22885,x22886,x22887),f573(x22882,x22883,x22884,x22885,x22886,x22887))
% 162.26/162.10 [2289]~E(x22891,x22892)+E(f573(x22893,x22891,x22894,x22895,x22896,x22897),f573(x22893,x22892,x22894,x22895,x22896,x22897))
% 162.26/162.10 [2290]~E(x22901,x22902)+E(f573(x22903,x22904,x22901,x22905,x22906,x22907),f573(x22903,x22904,x22902,x22905,x22906,x22907))
% 162.26/162.10 [2291]~E(x22911,x22912)+E(f573(x22913,x22914,x22915,x22911,x22916,x22917),f573(x22913,x22914,x22915,x22912,x22916,x22917))
% 162.26/162.10 [2292]~E(x22921,x22922)+E(f573(x22923,x22924,x22925,x22926,x22921,x22927),f573(x22923,x22924,x22925,x22926,x22922,x22927))
% 162.26/162.10 [2293]~E(x22931,x22932)+E(f573(x22933,x22934,x22935,x22936,x22937,x22931),f573(x22933,x22934,x22935,x22936,x22937,x22932))
% 162.26/162.10 [2294]~E(x22941,x22942)+E(f390(x22941,x22943,x22944),f390(x22942,x22943,x22944))
% 162.26/162.10 [2295]~E(x22951,x22952)+E(f390(x22953,x22951,x22954),f390(x22953,x22952,x22954))
% 162.26/162.10 [2296]~E(x22961,x22962)+E(f390(x22963,x22964,x22961),f390(x22963,x22964,x22962))
% 162.26/162.10 [2297]~E(x22971,x22972)+E(f720(x22971,x22973,x22974,x22975),f720(x22972,x22973,x22974,x22975))
% 162.26/162.10 [2298]~E(x22981,x22982)+E(f720(x22983,x22981,x22984,x22985),f720(x22983,x22982,x22984,x22985))
% 162.26/162.10 [2299]~E(x22991,x22992)+E(f720(x22993,x22994,x22991,x22995),f720(x22993,x22994,x22992,x22995))
% 162.26/162.10 [2300]~E(x23001,x23002)+E(f720(x23003,x23004,x23005,x23001),f720(x23003,x23004,x23005,x23002))
% 162.26/162.10 [2301]~E(x23011,x23012)+E(f341(x23011),f341(x23012))
% 162.26/162.10 [2302]~E(x23021,x23022)+E(f580(x23021,x23023,x23024,x23025),f580(x23022,x23023,x23024,x23025))
% 162.26/162.10 [2303]~E(x23031,x23032)+E(f580(x23033,x23031,x23034,x23035),f580(x23033,x23032,x23034,x23035))
% 162.26/162.10 [2304]~E(x23041,x23042)+E(f580(x23043,x23044,x23041,x23045),f580(x23043,x23044,x23042,x23045))
% 162.26/162.10 [2305]~E(x23051,x23052)+E(f580(x23053,x23054,x23055,x23051),f580(x23053,x23054,x23055,x23052))
% 162.26/162.10 [2306]~E(x23061,x23062)+E(f761(x23061,x23063,x23064),f761(x23062,x23063,x23064))
% 162.26/162.10 [2307]~E(x23071,x23072)+E(f761(x23073,x23071,x23074),f761(x23073,x23072,x23074))
% 162.26/162.10 [2308]~E(x23081,x23082)+E(f761(x23083,x23084,x23081),f761(x23083,x23084,x23082))
% 162.26/162.10 [2309]~E(x23091,x23092)+E(f753(x23091,x23093,x23094,x23095,x23096),f753(x23092,x23093,x23094,x23095,x23096))
% 162.26/162.10 [2310]~E(x23101,x23102)+E(f753(x23103,x23101,x23104,x23105,x23106),f753(x23103,x23102,x23104,x23105,x23106))
% 162.26/162.10 [2311]~E(x23111,x23112)+E(f753(x23113,x23114,x23111,x23115,x23116),f753(x23113,x23114,x23112,x23115,x23116))
% 162.26/162.10 [2312]~E(x23121,x23122)+E(f753(x23123,x23124,x23125,x23121,x23126),f753(x23123,x23124,x23125,x23122,x23126))
% 162.26/162.10 [2313]~E(x23131,x23132)+E(f753(x23133,x23134,x23135,x23136,x23131),f753(x23133,x23134,x23135,x23136,x23132))
% 162.26/162.10 [2314]~E(x23141,x23142)+E(f792(x23141,x23143,x23144),f792(x23142,x23143,x23144))
% 162.26/162.10 [2315]~E(x23151,x23152)+E(f792(x23153,x23151,x23154),f792(x23153,x23152,x23154))
% 162.26/162.10 [2316]~E(x23161,x23162)+E(f792(x23163,x23164,x23161),f792(x23163,x23164,x23162))
% 162.26/162.10 [2317]~E(x23171,x23172)+E(f858(x23171,x23173,x23174),f858(x23172,x23173,x23174))
% 162.26/162.10 [2318]~E(x23181,x23182)+E(f858(x23183,x23181,x23184),f858(x23183,x23182,x23184))
% 162.26/162.10 [2319]~E(x23191,x23192)+E(f858(x23193,x23194,x23191),f858(x23193,x23194,x23192))
% 162.26/162.10 [2320]~E(x23201,x23202)+E(f766(x23201,x23203,x23204),f766(x23202,x23203,x23204))
% 162.26/162.10 [2321]~E(x23211,x23212)+E(f766(x23213,x23211,x23214),f766(x23213,x23212,x23214))
% 162.26/162.10 [2322]~E(x23221,x23222)+E(f766(x23223,x23224,x23221),f766(x23223,x23224,x23222))
% 162.26/162.10 [2323]~E(x23231,x23232)+E(f859(x23231,x23233,x23234),f859(x23232,x23233,x23234))
% 162.26/162.10 [2324]~E(x23241,x23242)+E(f859(x23243,x23241,x23244),f859(x23243,x23242,x23244))
% 162.26/162.10 [2325]~E(x23251,x23252)+E(f859(x23253,x23254,x23251),f859(x23253,x23254,x23252))
% 162.26/162.10 [2326]~E(x23261,x23262)+E(f714(x23261,x23263,x23264,x23265,x23266,x23267),f714(x23262,x23263,x23264,x23265,x23266,x23267))
% 162.26/162.10 [2327]~E(x23271,x23272)+E(f714(x23273,x23271,x23274,x23275,x23276,x23277),f714(x23273,x23272,x23274,x23275,x23276,x23277))
% 162.26/162.10 [2328]~E(x23281,x23282)+E(f714(x23283,x23284,x23281,x23285,x23286,x23287),f714(x23283,x23284,x23282,x23285,x23286,x23287))
% 162.26/162.10 [2329]~E(x23291,x23292)+E(f714(x23293,x23294,x23295,x23291,x23296,x23297),f714(x23293,x23294,x23295,x23292,x23296,x23297))
% 162.26/162.10 [2330]~E(x23301,x23302)+E(f714(x23303,x23304,x23305,x23306,x23301,x23307),f714(x23303,x23304,x23305,x23306,x23302,x23307))
% 162.26/162.10 [2331]~E(x23311,x23312)+E(f714(x23313,x23314,x23315,x23316,x23317,x23311),f714(x23313,x23314,x23315,x23316,x23317,x23312))
% 162.26/162.10 [2332]~E(x23321,x23322)+E(f733(x23321,x23323,x23324,x23325,x23326),f733(x23322,x23323,x23324,x23325,x23326))
% 162.26/162.10 [2333]~E(x23331,x23332)+E(f733(x23333,x23331,x23334,x23335,x23336),f733(x23333,x23332,x23334,x23335,x23336))
% 162.26/162.10 [2334]~E(x23341,x23342)+E(f733(x23343,x23344,x23341,x23345,x23346),f733(x23343,x23344,x23342,x23345,x23346))
% 162.26/162.10 [2335]~E(x23351,x23352)+E(f733(x23353,x23354,x23355,x23351,x23356),f733(x23353,x23354,x23355,x23352,x23356))
% 162.26/162.10 [2336]~E(x23361,x23362)+E(f733(x23363,x23364,x23365,x23366,x23361),f733(x23363,x23364,x23365,x23366,x23362))
% 162.26/162.10 [2337]~E(x23371,x23372)+E(f226(x23371,x23373),f226(x23372,x23373))
% 162.26/162.10 [2338]~E(x23381,x23382)+E(f226(x23383,x23381),f226(x23383,x23382))
% 162.26/162.10 [2339]~E(x23391,x23392)+E(f149(x23391,x23393),f149(x23392,x23393))
% 162.26/162.10 [2340]~E(x23401,x23402)+E(f149(x23403,x23401),f149(x23403,x23402))
% 162.26/162.10 [2341]~E(x23411,x23412)+E(f851(x23411,x23413),f851(x23412,x23413))
% 162.26/162.10 [2342]~E(x23421,x23422)+E(f851(x23423,x23421),f851(x23423,x23422))
% 162.26/162.10 [2343]~E(x23431,x23432)+E(f497(x23431,x23433,x23434),f497(x23432,x23433,x23434))
% 162.26/162.10 [2344]~E(x23441,x23442)+E(f497(x23443,x23441,x23444),f497(x23443,x23442,x23444))
% 162.26/162.10 [2345]~E(x23451,x23452)+E(f497(x23453,x23454,x23451),f497(x23453,x23454,x23452))
% 162.26/162.10 [2346]~E(x23461,x23462)+E(f807(x23461,x23463,x23464,x23465,x23466,x23467),f807(x23462,x23463,x23464,x23465,x23466,x23467))
% 162.26/162.10 [2347]~E(x23471,x23472)+E(f807(x23473,x23471,x23474,x23475,x23476,x23477),f807(x23473,x23472,x23474,x23475,x23476,x23477))
% 162.26/162.10 [2348]~E(x23481,x23482)+E(f807(x23483,x23484,x23481,x23485,x23486,x23487),f807(x23483,x23484,x23482,x23485,x23486,x23487))
% 162.26/162.10 [2349]~E(x23491,x23492)+E(f807(x23493,x23494,x23495,x23491,x23496,x23497),f807(x23493,x23494,x23495,x23492,x23496,x23497))
% 162.26/162.10 [2350]~E(x23501,x23502)+E(f807(x23503,x23504,x23505,x23506,x23501,x23507),f807(x23503,x23504,x23505,x23506,x23502,x23507))
% 162.26/162.10 [2351]~E(x23511,x23512)+E(f807(x23513,x23514,x23515,x23516,x23517,x23511),f807(x23513,x23514,x23515,x23516,x23517,x23512))
% 162.26/162.10 [2352]~E(x23521,x23522)+E(f348(x23521),f348(x23522))
% 162.26/162.10 [2353]~E(x23531,x23532)+E(f812(x23531,x23533,x23534),f812(x23532,x23533,x23534))
% 162.26/162.10 [2354]~E(x23541,x23542)+E(f812(x23543,x23541,x23544),f812(x23543,x23542,x23544))
% 162.26/162.10 [2355]~E(x23551,x23552)+E(f812(x23553,x23554,x23551),f812(x23553,x23554,x23552))
% 162.26/162.10 [2356]~E(x23561,x23562)+E(f68(x23561,x23563,x23564),f68(x23562,x23563,x23564))
% 162.26/162.10 [2357]~E(x23571,x23572)+E(f68(x23573,x23571,x23574),f68(x23573,x23572,x23574))
% 162.26/162.10 [2358]~E(x23581,x23582)+E(f68(x23583,x23584,x23581),f68(x23583,x23584,x23582))
% 162.26/162.10 [2359]~E(x23591,x23592)+E(f427(x23591,x23593,x23594,x23595,x23596,x23597,x23598),f427(x23592,x23593,x23594,x23595,x23596,x23597,x23598))
% 162.26/162.10 [2360]~E(x23601,x23602)+E(f427(x23603,x23601,x23604,x23605,x23606,x23607,x23608),f427(x23603,x23602,x23604,x23605,x23606,x23607,x23608))
% 162.26/162.10 [2361]~E(x23611,x23612)+E(f427(x23613,x23614,x23611,x23615,x23616,x23617,x23618),f427(x23613,x23614,x23612,x23615,x23616,x23617,x23618))
% 162.26/162.10 [2362]~E(x23621,x23622)+E(f427(x23623,x23624,x23625,x23621,x23626,x23627,x23628),f427(x23623,x23624,x23625,x23622,x23626,x23627,x23628))
% 162.26/162.10 [2363]~E(x23631,x23632)+E(f427(x23633,x23634,x23635,x23636,x23631,x23637,x23638),f427(x23633,x23634,x23635,x23636,x23632,x23637,x23638))
% 162.26/162.10 [2364]~E(x23641,x23642)+E(f427(x23643,x23644,x23645,x23646,x23647,x23641,x23648),f427(x23643,x23644,x23645,x23646,x23647,x23642,x23648))
% 162.26/162.10 [2365]~E(x23651,x23652)+E(f427(x23653,x23654,x23655,x23656,x23657,x23658,x23651),f427(x23653,x23654,x23655,x23656,x23657,x23658,x23652))
% 162.26/162.10 [2366]~E(x23661,x23662)+E(f512(x23661,x23663,x23664),f512(x23662,x23663,x23664))
% 162.26/162.10 [2367]~E(x23671,x23672)+E(f512(x23673,x23671,x23674),f512(x23673,x23672,x23674))
% 162.26/162.10 [2368]~E(x23681,x23682)+E(f512(x23683,x23684,x23681),f512(x23683,x23684,x23682))
% 162.26/162.10 [2369]~E(x23691,x23692)+E(f342(x23691),f342(x23692))
% 162.26/162.10 [2370]~E(x23701,x23702)+E(f798(x23701,x23703,x23704),f798(x23702,x23703,x23704))
% 162.26/162.10 [2371]~E(x23711,x23712)+E(f798(x23713,x23711,x23714),f798(x23713,x23712,x23714))
% 162.26/162.10 [2372]~E(x23721,x23722)+E(f798(x23723,x23724,x23721),f798(x23723,x23724,x23722))
% 162.26/162.10 [2373]~E(x23731,x23732)+E(f697(x23731,x23733,x23734,x23735),f697(x23732,x23733,x23734,x23735))
% 162.26/162.10 [2374]~E(x23741,x23742)+E(f697(x23743,x23741,x23744,x23745),f697(x23743,x23742,x23744,x23745))
% 162.26/162.10 [2375]~E(x23751,x23752)+E(f697(x23753,x23754,x23751,x23755),f697(x23753,x23754,x23752,x23755))
% 162.26/162.10 [2376]~E(x23761,x23762)+E(f697(x23763,x23764,x23765,x23761),f697(x23763,x23764,x23765,x23762))
% 162.26/162.10 [2377]~E(x23771,x23772)+E(f564(x23771,x23773),f564(x23772,x23773))
% 162.26/162.10 [2378]~E(x23781,x23782)+E(f564(x23783,x23781),f564(x23783,x23782))
% 162.26/162.10 [2379]~E(x23791,x23792)+E(f484(x23791,x23793,x23794,x23795),f484(x23792,x23793,x23794,x23795))
% 162.26/162.10 [2380]~E(x23801,x23802)+E(f484(x23803,x23801,x23804,x23805),f484(x23803,x23802,x23804,x23805))
% 162.26/162.10 [2381]~E(x23811,x23812)+E(f484(x23813,x23814,x23811,x23815),f484(x23813,x23814,x23812,x23815))
% 162.26/162.10 [2382]~E(x23821,x23822)+E(f484(x23823,x23824,x23825,x23821),f484(x23823,x23824,x23825,x23822))
% 162.26/162.10 [2383]~E(x23831,x23832)+E(f716(x23831,x23833,x23834,x23835,x23836,x23837),f716(x23832,x23833,x23834,x23835,x23836,x23837))
% 162.26/162.10 [2384]~E(x23841,x23842)+E(f716(x23843,x23841,x23844,x23845,x23846,x23847),f716(x23843,x23842,x23844,x23845,x23846,x23847))
% 162.26/162.10 [2385]~E(x23851,x23852)+E(f716(x23853,x23854,x23851,x23855,x23856,x23857),f716(x23853,x23854,x23852,x23855,x23856,x23857))
% 162.26/162.10 [2386]~E(x23861,x23862)+E(f716(x23863,x23864,x23865,x23861,x23866,x23867),f716(x23863,x23864,x23865,x23862,x23866,x23867))
% 162.26/162.10 [2387]~E(x23871,x23872)+E(f716(x23873,x23874,x23875,x23876,x23871,x23877),f716(x23873,x23874,x23875,x23876,x23872,x23877))
% 162.26/162.10 [2388]~E(x23881,x23882)+E(f716(x23883,x23884,x23885,x23886,x23887,x23881),f716(x23883,x23884,x23885,x23886,x23887,x23882))
% 162.26/162.10 [2389]~E(x23891,x23892)+E(f670(x23891,x23893,x23894),f670(x23892,x23893,x23894))
% 162.26/162.10 [2390]~E(x23901,x23902)+E(f670(x23903,x23901,x23904),f670(x23903,x23902,x23904))
% 162.26/162.10 [2391]~E(x23911,x23912)+E(f670(x23913,x23914,x23911),f670(x23913,x23914,x23912))
% 162.26/162.10 [2392]~E(x23921,x23922)+E(f738(x23921,x23923,x23924,x23925,x23926,x23927,x23928),f738(x23922,x23923,x23924,x23925,x23926,x23927,x23928))
% 162.26/162.10 [2393]~E(x23931,x23932)+E(f738(x23933,x23931,x23934,x23935,x23936,x23937,x23938),f738(x23933,x23932,x23934,x23935,x23936,x23937,x23938))
% 162.26/162.10 [2394]~E(x23941,x23942)+E(f738(x23943,x23944,x23941,x23945,x23946,x23947,x23948),f738(x23943,x23944,x23942,x23945,x23946,x23947,x23948))
% 162.26/162.10 [2395]~E(x23951,x23952)+E(f738(x23953,x23954,x23955,x23951,x23956,x23957,x23958),f738(x23953,x23954,x23955,x23952,x23956,x23957,x23958))
% 162.26/162.10 [2396]~E(x23961,x23962)+E(f738(x23963,x23964,x23965,x23966,x23961,x23967,x23968),f738(x23963,x23964,x23965,x23966,x23962,x23967,x23968))
% 162.26/162.10 [2397]~E(x23971,x23972)+E(f738(x23973,x23974,x23975,x23976,x23977,x23971,x23978),f738(x23973,x23974,x23975,x23976,x23977,x23972,x23978))
% 162.26/162.10 [2398]~E(x23981,x23982)+E(f738(x23983,x23984,x23985,x23986,x23987,x23988,x23981),f738(x23983,x23984,x23985,x23986,x23987,x23988,x23982))
% 162.26/162.10 [2399]~E(x23991,x23992)+E(f685(x23991,x23993),f685(x23992,x23993))
% 162.26/162.10 [2400]~E(x24001,x24002)+E(f685(x24003,x24001),f685(x24003,x24002))
% 162.26/162.10 [2401]~E(x24011,x24012)+E(f339(x24011,x24013),f339(x24012,x24013))
% 162.26/162.10 [2402]~E(x24021,x24022)+E(f339(x24023,x24021),f339(x24023,x24022))
% 162.26/162.10 [2403]~E(x24031,x24032)+E(f721(x24031,x24033,x24034,x24035,x24036),f721(x24032,x24033,x24034,x24035,x24036))
% 162.26/162.10 [2404]~E(x24041,x24042)+E(f721(x24043,x24041,x24044,x24045,x24046),f721(x24043,x24042,x24044,x24045,x24046))
% 162.26/162.10 [2405]~E(x24051,x24052)+E(f721(x24053,x24054,x24051,x24055,x24056),f721(x24053,x24054,x24052,x24055,x24056))
% 162.26/162.10 [2406]~E(x24061,x24062)+E(f721(x24063,x24064,x24065,x24061,x24066),f721(x24063,x24064,x24065,x24062,x24066))
% 162.26/162.10 [2407]~E(x24071,x24072)+E(f721(x24073,x24074,x24075,x24076,x24071),f721(x24073,x24074,x24075,x24076,x24072))
% 162.26/162.10 [2408]~E(x24081,x24082)+E(f365(x24081,x24083,x24084),f365(x24082,x24083,x24084))
% 162.26/162.10 [2409]~E(x24091,x24092)+E(f365(x24093,x24091,x24094),f365(x24093,x24092,x24094))
% 162.26/162.10 [2410]~E(x24101,x24102)+E(f365(x24103,x24104,x24101),f365(x24103,x24104,x24102))
% 162.26/162.10 [2411]~E(x24111,x24112)+E(f740(x24111,x24113,x24114,x24115),f740(x24112,x24113,x24114,x24115))
% 162.26/162.10 [2412]~E(x24121,x24122)+E(f740(x24123,x24121,x24124,x24125),f740(x24123,x24122,x24124,x24125))
% 162.26/162.10 [2413]~E(x24131,x24132)+E(f740(x24133,x24134,x24131,x24135),f740(x24133,x24134,x24132,x24135))
% 162.26/162.10 [2414]~E(x24141,x24142)+E(f740(x24143,x24144,x24145,x24141),f740(x24143,x24144,x24145,x24142))
% 162.26/162.10 [2415]~E(x24151,x24152)+E(f545(x24151),f545(x24152))
% 162.26/162.10 [2416]~E(x24161,x24162)+E(f218(x24161,x24163,x24164,x24165),f218(x24162,x24163,x24164,x24165))
% 162.26/162.10 [2417]~E(x24171,x24172)+E(f218(x24173,x24171,x24174,x24175),f218(x24173,x24172,x24174,x24175))
% 162.26/162.10 [2418]~E(x24181,x24182)+E(f218(x24183,x24184,x24181,x24185),f218(x24183,x24184,x24182,x24185))
% 162.26/162.10 [2419]~E(x24191,x24192)+E(f218(x24193,x24194,x24195,x24191),f218(x24193,x24194,x24195,x24192))
% 162.26/162.10 [2420]~E(x24201,x24202)+E(f787(x24201,x24203,x24204,x24205),f787(x24202,x24203,x24204,x24205))
% 162.26/162.10 [2421]~E(x24211,x24212)+E(f787(x24213,x24211,x24214,x24215),f787(x24213,x24212,x24214,x24215))
% 162.26/162.10 [2422]~E(x24221,x24222)+E(f787(x24223,x24224,x24221,x24225),f787(x24223,x24224,x24222,x24225))
% 162.26/162.10 [2423]~E(x24231,x24232)+E(f787(x24233,x24234,x24235,x24231),f787(x24233,x24234,x24235,x24232))
% 162.26/162.10 [2424]~E(x24241,x24242)+E(f485(x24241,x24243,x24244,x24245),f485(x24242,x24243,x24244,x24245))
% 162.26/162.10 [2425]~E(x24251,x24252)+E(f485(x24253,x24251,x24254,x24255),f485(x24253,x24252,x24254,x24255))
% 162.26/162.10 [2426]~E(x24261,x24262)+E(f485(x24263,x24264,x24261,x24265),f485(x24263,x24264,x24262,x24265))
% 162.26/162.10 [2427]~E(x24271,x24272)+E(f485(x24273,x24274,x24275,x24271),f485(x24273,x24274,x24275,x24272))
% 162.26/162.10 [2428]~E(x24281,x24282)+E(f422(x24281,x24283,x24284,x24285),f422(x24282,x24283,x24284,x24285))
% 162.26/162.10 [2429]~E(x24291,x24292)+E(f422(x24293,x24291,x24294,x24295),f422(x24293,x24292,x24294,x24295))
% 162.26/162.10 [2430]~E(x24301,x24302)+E(f422(x24303,x24304,x24301,x24305),f422(x24303,x24304,x24302,x24305))
% 162.26/162.10 [2431]~E(x24311,x24312)+E(f422(x24313,x24314,x24315,x24311),f422(x24313,x24314,x24315,x24312))
% 162.26/162.10 [2432]~E(x24321,x24322)+E(f793(x24321,x24323,x24324),f793(x24322,x24323,x24324))
% 162.26/162.10 [2433]~E(x24331,x24332)+E(f793(x24333,x24331,x24334),f793(x24333,x24332,x24334))
% 162.26/162.10 [2434]~E(x24341,x24342)+E(f793(x24343,x24344,x24341),f793(x24343,x24344,x24342))
% 162.26/162.10 [2435]~E(x24351,x24352)+E(f220(x24351,x24353,x24354,x24355,x24356,x24357,x24358),f220(x24352,x24353,x24354,x24355,x24356,x24357,x24358))
% 162.26/162.10 [2436]~E(x24361,x24362)+E(f220(x24363,x24361,x24364,x24365,x24366,x24367,x24368),f220(x24363,x24362,x24364,x24365,x24366,x24367,x24368))
% 162.26/162.10 [2437]~E(x24371,x24372)+E(f220(x24373,x24374,x24371,x24375,x24376,x24377,x24378),f220(x24373,x24374,x24372,x24375,x24376,x24377,x24378))
% 162.26/162.10 [2438]~E(x24381,x24382)+E(f220(x24383,x24384,x24385,x24381,x24386,x24387,x24388),f220(x24383,x24384,x24385,x24382,x24386,x24387,x24388))
% 162.26/162.10 [2439]~E(x24391,x24392)+E(f220(x24393,x24394,x24395,x24396,x24391,x24397,x24398),f220(x24393,x24394,x24395,x24396,x24392,x24397,x24398))
% 162.26/162.10 [2440]~E(x24401,x24402)+E(f220(x24403,x24404,x24405,x24406,x24407,x24401,x24408),f220(x24403,x24404,x24405,x24406,x24407,x24402,x24408))
% 162.26/162.10 [2441]~E(x24411,x24412)+E(f220(x24413,x24414,x24415,x24416,x24417,x24418,x24411),f220(x24413,x24414,x24415,x24416,x24417,x24418,x24412))
% 162.26/162.10 [2442]~E(x24421,x24422)+E(f370(x24421,x24423),f370(x24422,x24423))
% 162.26/162.10 [2443]~E(x24431,x24432)+E(f370(x24433,x24431),f370(x24433,x24432))
% 162.26/162.10 [2444]~E(x24441,x24442)+E(f418(x24441,x24443,x24444,x24445),f418(x24442,x24443,x24444,x24445))
% 162.26/162.10 [2445]~E(x24451,x24452)+E(f418(x24453,x24451,x24454,x24455),f418(x24453,x24452,x24454,x24455))
% 162.26/162.10 [2446]~E(x24461,x24462)+E(f418(x24463,x24464,x24461,x24465),f418(x24463,x24464,x24462,x24465))
% 162.26/162.10 [2447]~E(x24471,x24472)+E(f418(x24473,x24474,x24475,x24471),f418(x24473,x24474,x24475,x24472))
% 162.26/162.10 [2448]~E(x24481,x24482)+E(f662(x24481,x24483),f662(x24482,x24483))
% 162.26/162.10 [2449]~E(x24491,x24492)+E(f662(x24493,x24491),f662(x24493,x24492))
% 162.26/162.10 [2450]~E(x24501,x24502)+E(f846(x24501),f846(x24502))
% 162.26/162.10 [2451]~E(x24511,x24512)+E(f778(x24511,x24513,x24514,x24515,x24516),f778(x24512,x24513,x24514,x24515,x24516))
% 162.26/162.10 [2452]~E(x24521,x24522)+E(f778(x24523,x24521,x24524,x24525,x24526),f778(x24523,x24522,x24524,x24525,x24526))
% 162.26/162.10 [2453]~E(x24531,x24532)+E(f778(x24533,x24534,x24531,x24535,x24536),f778(x24533,x24534,x24532,x24535,x24536))
% 162.26/162.10 [2454]~E(x24541,x24542)+E(f778(x24543,x24544,x24545,x24541,x24546),f778(x24543,x24544,x24545,x24542,x24546))
% 162.26/162.10 [2455]~E(x24551,x24552)+E(f778(x24553,x24554,x24555,x24556,x24551),f778(x24553,x24554,x24555,x24556,x24552))
% 162.26/162.10 [2456]~E(x24561,x24562)+E(f371(x24561),f371(x24562))
% 162.26/162.10 [2457]~E(x24571,x24572)+E(f521(x24571,x24573,x24574),f521(x24572,x24573,x24574))
% 162.26/162.10 [2458]~E(x24581,x24582)+E(f521(x24583,x24581,x24584),f521(x24583,x24582,x24584))
% 162.26/162.10 [2459]~E(x24591,x24592)+E(f521(x24593,x24594,x24591),f521(x24593,x24594,x24592))
% 162.26/162.10 [2460]~E(x24601,x24602)+E(f294(x24601,x24603,x24604),f294(x24602,x24603,x24604))
% 162.26/162.10 [2461]~E(x24611,x24612)+E(f294(x24613,x24611,x24614),f294(x24613,x24612,x24614))
% 162.26/162.10 [2462]~E(x24621,x24622)+E(f294(x24623,x24624,x24621),f294(x24623,x24624,x24622))
% 162.26/162.10 [2463]~E(x24631,x24632)+E(f101(x24631,x24633,x24634,x24635),f101(x24632,x24633,x24634,x24635))
% 162.26/162.10 [2464]~E(x24641,x24642)+E(f101(x24643,x24641,x24644,x24645),f101(x24643,x24642,x24644,x24645))
% 162.26/162.10 [2465]~E(x24651,x24652)+E(f101(x24653,x24654,x24651,x24655),f101(x24653,x24654,x24652,x24655))
% 162.26/162.10 [2466]~E(x24661,x24662)+E(f101(x24663,x24664,x24665,x24661),f101(x24663,x24664,x24665,x24662))
% 162.26/162.10 [2467]~E(x24671,x24672)+E(f661(x24671,x24673),f661(x24672,x24673))
% 162.26/162.10 [2468]~E(x24681,x24682)+E(f661(x24683,x24681),f661(x24683,x24682))
% 162.26/162.10 [2469]~E(x24691,x24692)+E(f872(x24691,x24693),f872(x24692,x24693))
% 162.26/162.10 [2470]~E(x24701,x24702)+E(f872(x24703,x24701),f872(x24703,x24702))
% 162.26/162.10 [2471]~E(x24711,x24712)+E(f610(x24711,x24713,x24714,x24715,x24716,x24717),f610(x24712,x24713,x24714,x24715,x24716,x24717))
% 162.26/162.10 [2472]~E(x24721,x24722)+E(f610(x24723,x24721,x24724,x24725,x24726,x24727),f610(x24723,x24722,x24724,x24725,x24726,x24727))
% 162.26/162.10 [2473]~E(x24731,x24732)+E(f610(x24733,x24734,x24731,x24735,x24736,x24737),f610(x24733,x24734,x24732,x24735,x24736,x24737))
% 162.26/162.10 [2474]~E(x24741,x24742)+E(f610(x24743,x24744,x24745,x24741,x24746,x24747),f610(x24743,x24744,x24745,x24742,x24746,x24747))
% 162.26/162.10 [2475]~E(x24751,x24752)+E(f610(x24753,x24754,x24755,x24756,x24751,x24757),f610(x24753,x24754,x24755,x24756,x24752,x24757))
% 162.26/162.10 [2476]~E(x24761,x24762)+E(f610(x24763,x24764,x24765,x24766,x24767,x24761),f610(x24763,x24764,x24765,x24766,x24767,x24762))
% 162.26/162.10 [2477]~E(x24771,x24772)+E(f134(x24771,x24773,x24774,x24775),f134(x24772,x24773,x24774,x24775))
% 162.26/162.10 [2478]~E(x24781,x24782)+E(f134(x24783,x24781,x24784,x24785),f134(x24783,x24782,x24784,x24785))
% 162.26/162.10 [2479]~E(x24791,x24792)+E(f134(x24793,x24794,x24791,x24795),f134(x24793,x24794,x24792,x24795))
% 162.26/162.10 [2480]~E(x24801,x24802)+E(f134(x24803,x24804,x24805,x24801),f134(x24803,x24804,x24805,x24802))
% 162.26/162.10 [2481]~E(x24811,x24812)+E(f801(x24811,x24813,x24814,x24815,x24816),f801(x24812,x24813,x24814,x24815,x24816))
% 162.26/162.10 [2482]~E(x24821,x24822)+E(f801(x24823,x24821,x24824,x24825,x24826),f801(x24823,x24822,x24824,x24825,x24826))
% 162.26/162.10 [2483]~E(x24831,x24832)+E(f801(x24833,x24834,x24831,x24835,x24836),f801(x24833,x24834,x24832,x24835,x24836))
% 162.26/162.10 [2484]~E(x24841,x24842)+E(f801(x24843,x24844,x24845,x24841,x24846),f801(x24843,x24844,x24845,x24842,x24846))
% 162.26/162.10 [2485]~E(x24851,x24852)+E(f801(x24853,x24854,x24855,x24856,x24851),f801(x24853,x24854,x24855,x24856,x24852))
% 162.26/162.10 [2486]~E(x24861,x24862)+E(f725(x24861,x24863,x24864),f725(x24862,x24863,x24864))
% 162.26/162.10 [2487]~E(x24871,x24872)+E(f725(x24873,x24871,x24874),f725(x24873,x24872,x24874))
% 162.26/162.10 [2488]~E(x24881,x24882)+E(f725(x24883,x24884,x24881),f725(x24883,x24884,x24882))
% 162.26/162.10 [2489]~E(x24891,x24892)+E(f866(x24891,x24893,x24894),f866(x24892,x24893,x24894))
% 162.26/162.10 [2490]~E(x24901,x24902)+E(f866(x24903,x24901,x24904),f866(x24903,x24902,x24904))
% 162.26/162.10 [2491]~E(x24911,x24912)+E(f866(x24913,x24914,x24911),f866(x24913,x24914,x24912))
% 162.26/162.10 [2492]~E(x24921,x24922)+E(f417(x24921,x24923,x24924),f417(x24922,x24923,x24924))
% 162.26/162.10 [2493]~E(x24931,x24932)+E(f417(x24933,x24931,x24934),f417(x24933,x24932,x24934))
% 162.26/162.10 [2494]~E(x24941,x24942)+E(f417(x24943,x24944,x24941),f417(x24943,x24944,x24942))
% 162.26/162.10 [2495]~E(x24951,x24952)+E(f704(x24951,x24953),f704(x24952,x24953))
% 162.26/162.10 [2496]~E(x24961,x24962)+E(f704(x24963,x24961),f704(x24963,x24962))
% 162.26/162.10 [2497]~E(x24971,x24972)+E(f133(x24971,x24973,x24974,x24975,x24976),f133(x24972,x24973,x24974,x24975,x24976))
% 162.26/162.10 [2498]~E(x24981,x24982)+E(f133(x24983,x24981,x24984,x24985,x24986),f133(x24983,x24982,x24984,x24985,x24986))
% 162.26/162.10 [2499]~E(x24991,x24992)+E(f133(x24993,x24994,x24991,x24995,x24996),f133(x24993,x24994,x24992,x24995,x24996))
% 162.26/162.10 [2500]~E(x25001,x25002)+E(f133(x25003,x25004,x25005,x25001,x25006),f133(x25003,x25004,x25005,x25002,x25006))
% 162.26/162.10 [2501]~E(x25011,x25012)+E(f133(x25013,x25014,x25015,x25016,x25011),f133(x25013,x25014,x25015,x25016,x25012))
% 162.26/162.10 [2502]~E(x25021,x25022)+E(f451(x25021,x25023,x25024),f451(x25022,x25023,x25024))
% 162.26/162.10 [2503]~E(x25031,x25032)+E(f451(x25033,x25031,x25034),f451(x25033,x25032,x25034))
% 162.26/162.10 [2504]~E(x25041,x25042)+E(f451(x25043,x25044,x25041),f451(x25043,x25044,x25042))
% 162.26/162.10 [2505]~E(x25051,x25052)+E(f696(x25051,x25053),f696(x25052,x25053))
% 162.26/162.10 [2506]~E(x25061,x25062)+E(f696(x25063,x25061),f696(x25063,x25062))
% 162.26/162.10 [2507]~E(x25071,x25072)+E(f457(x25071,x25073,x25074),f457(x25072,x25073,x25074))
% 162.26/162.10 [2508]~E(x25081,x25082)+E(f457(x25083,x25081,x25084),f457(x25083,x25082,x25084))
% 162.26/162.10 [2509]~E(x25091,x25092)+E(f457(x25093,x25094,x25091),f457(x25093,x25094,x25092))
% 162.26/162.10 [2510]~E(x25101,x25102)+E(f592(x25101,x25103,x25104),f592(x25102,x25103,x25104))
% 162.26/162.10 [2511]~E(x25111,x25112)+E(f592(x25113,x25111,x25114),f592(x25113,x25112,x25114))
% 162.26/162.10 [2512]~E(x25121,x25122)+E(f592(x25123,x25124,x25121),f592(x25123,x25124,x25122))
% 162.26/162.10 [2513]~E(x25131,x25132)+E(f717(x25131,x25133,x25134,x25135,x25136,x25137),f717(x25132,x25133,x25134,x25135,x25136,x25137))
% 162.26/162.10 [2514]~E(x25141,x25142)+E(f717(x25143,x25141,x25144,x25145,x25146,x25147),f717(x25143,x25142,x25144,x25145,x25146,x25147))
% 162.26/162.10 [2515]~E(x25151,x25152)+E(f717(x25153,x25154,x25151,x25155,x25156,x25157),f717(x25153,x25154,x25152,x25155,x25156,x25157))
% 162.26/162.10 [2516]~E(x25161,x25162)+E(f717(x25163,x25164,x25165,x25161,x25166,x25167),f717(x25163,x25164,x25165,x25162,x25166,x25167))
% 162.26/162.10 [2517]~E(x25171,x25172)+E(f717(x25173,x25174,x25175,x25176,x25171,x25177),f717(x25173,x25174,x25175,x25176,x25172,x25177))
% 162.26/162.10 [2518]~E(x25181,x25182)+E(f717(x25183,x25184,x25185,x25186,x25187,x25181),f717(x25183,x25184,x25185,x25186,x25187,x25182))
% 162.26/162.10 [2519]~E(x25191,x25192)+E(f525(x25191,x25193,x25194),f525(x25192,x25193,x25194))
% 162.26/162.10 [2520]~E(x25201,x25202)+E(f525(x25203,x25201,x25204),f525(x25203,x25202,x25204))
% 162.26/162.10 [2521]~E(x25211,x25212)+E(f525(x25213,x25214,x25211),f525(x25213,x25214,x25212))
% 162.26/162.10 [2522]~E(x25221,x25222)+E(f380(x25221,x25223,x25224),f380(x25222,x25223,x25224))
% 162.26/162.10 [2523]~E(x25231,x25232)+E(f380(x25233,x25231,x25234),f380(x25233,x25232,x25234))
% 162.26/162.10 [2524]~E(x25241,x25242)+E(f380(x25243,x25244,x25241),f380(x25243,x25244,x25242))
% 162.26/162.10 [2525]~E(x25251,x25252)+E(f349(x25251,x25253),f349(x25252,x25253))
% 162.26/162.10 [2526]~E(x25261,x25262)+E(f349(x25263,x25261),f349(x25263,x25262))
% 162.26/162.10 [2527]~E(x25271,x25272)+E(f745(x25271,x25273,x25274,x25275),f745(x25272,x25273,x25274,x25275))
% 162.26/162.10 [2528]~E(x25281,x25282)+E(f745(x25283,x25281,x25284,x25285),f745(x25283,x25282,x25284,x25285))
% 162.26/162.10 [2529]~E(x25291,x25292)+E(f745(x25293,x25294,x25291,x25295),f745(x25293,x25294,x25292,x25295))
% 162.26/162.10 [2530]~E(x25301,x25302)+E(f745(x25303,x25304,x25305,x25301),f745(x25303,x25304,x25305,x25302))
% 162.26/162.10 [2531]~E(x25311,x25312)+E(f549(x25311,x25313,x25314,x25315),f549(x25312,x25313,x25314,x25315))
% 162.26/162.10 [2532]~E(x25321,x25322)+E(f549(x25323,x25321,x25324,x25325),f549(x25323,x25322,x25324,x25325))
% 162.26/162.10 [2533]~E(x25331,x25332)+E(f549(x25333,x25334,x25331,x25335),f549(x25333,x25334,x25332,x25335))
% 162.26/162.10 [2534]~E(x25341,x25342)+E(f549(x25343,x25344,x25345,x25341),f549(x25343,x25344,x25345,x25342))
% 162.26/162.10 [2535]~E(x25351,x25352)+E(f568(x25351,x25353),f568(x25352,x25353))
% 162.26/162.10 [2536]~E(x25361,x25362)+E(f568(x25363,x25361),f568(x25363,x25362))
% 162.26/162.10 [2537]~E(x25371,x25372)+E(f821(x25371,x25373,x25374),f821(x25372,x25373,x25374))
% 162.26/162.10 [2538]~E(x25381,x25382)+E(f821(x25383,x25381,x25384),f821(x25383,x25382,x25384))
% 162.26/162.10 [2539]~E(x25391,x25392)+E(f821(x25393,x25394,x25391),f821(x25393,x25394,x25392))
% 162.26/162.10 [2540]~E(x25401,x25402)+E(f407(x25401,x25403),f407(x25402,x25403))
% 162.26/162.10 [2541]~E(x25411,x25412)+E(f407(x25413,x25411),f407(x25413,x25412))
% 162.26/162.10 [2542]~E(x25421,x25422)+E(f233(x25421,x25423,x25424),f233(x25422,x25423,x25424))
% 162.26/162.10 [2543]~E(x25431,x25432)+E(f233(x25433,x25431,x25434),f233(x25433,x25432,x25434))
% 162.26/162.10 [2544]~E(x25441,x25442)+E(f233(x25443,x25444,x25441),f233(x25443,x25444,x25442))
% 162.26/162.10 [2545]~E(x25451,x25452)+E(f608(x25451,x25453,x25454),f608(x25452,x25453,x25454))
% 162.26/162.10 [2546]~E(x25461,x25462)+E(f608(x25463,x25461,x25464),f608(x25463,x25462,x25464))
% 162.26/162.10 [2547]~E(x25471,x25472)+E(f608(x25473,x25474,x25471),f608(x25473,x25474,x25472))
% 162.26/162.10 [2548]~E(x25481,x25482)+E(f384(x25481,x25483,x25484,x25485,x25486,x25487,x25488),f384(x25482,x25483,x25484,x25485,x25486,x25487,x25488))
% 162.26/162.10 [2549]~E(x25491,x25492)+E(f384(x25493,x25491,x25494,x25495,x25496,x25497,x25498),f384(x25493,x25492,x25494,x25495,x25496,x25497,x25498))
% 162.26/162.10 [2550]~E(x25501,x25502)+E(f384(x25503,x25504,x25501,x25505,x25506,x25507,x25508),f384(x25503,x25504,x25502,x25505,x25506,x25507,x25508))
% 162.26/162.10 [2551]~E(x25511,x25512)+E(f384(x25513,x25514,x25515,x25511,x25516,x25517,x25518),f384(x25513,x25514,x25515,x25512,x25516,x25517,x25518))
% 162.26/162.10 [2552]~E(x25521,x25522)+E(f384(x25523,x25524,x25525,x25526,x25521,x25527,x25528),f384(x25523,x25524,x25525,x25526,x25522,x25527,x25528))
% 162.26/162.10 [2553]~E(x25531,x25532)+E(f384(x25533,x25534,x25535,x25536,x25537,x25531,x25538),f384(x25533,x25534,x25535,x25536,x25537,x25532,x25538))
% 162.26/162.10 [2554]~E(x25541,x25542)+E(f384(x25543,x25544,x25545,x25546,x25547,x25548,x25541),f384(x25543,x25544,x25545,x25546,x25547,x25548,x25542))
% 162.26/162.10 [2555]~E(x25551,x25552)+E(f367(x25551,x25553),f367(x25552,x25553))
% 162.26/162.10 [2556]~E(x25561,x25562)+E(f367(x25563,x25561),f367(x25563,x25562))
% 162.26/162.10 [2557]~E(x25571,x25572)+E(f387(x25571,x25573,x25574),f387(x25572,x25573,x25574))
% 162.26/162.10 [2558]~E(x25581,x25582)+E(f387(x25583,x25581,x25584),f387(x25583,x25582,x25584))
% 162.26/162.10 [2559]~E(x25591,x25592)+E(f387(x25593,x25594,x25591),f387(x25593,x25594,x25592))
% 162.26/162.10 [2560]~E(x25601,x25602)+E(f482(x25601,x25603,x25604,x25605),f482(x25602,x25603,x25604,x25605))
% 162.26/162.10 [2561]~E(x25611,x25612)+E(f482(x25613,x25611,x25614,x25615),f482(x25613,x25612,x25614,x25615))
% 162.26/162.10 [2562]~E(x25621,x25622)+E(f482(x25623,x25624,x25621,x25625),f482(x25623,x25624,x25622,x25625))
% 162.26/162.10 [2563]~E(x25631,x25632)+E(f482(x25633,x25634,x25635,x25631),f482(x25633,x25634,x25635,x25632))
% 162.26/162.10 [2564]~E(x25641,x25642)+E(f605(x25641,x25643,x25644,x25645),f605(x25642,x25643,x25644,x25645))
% 162.26/162.10 [2565]~E(x25651,x25652)+E(f605(x25653,x25651,x25654,x25655),f605(x25653,x25652,x25654,x25655))
% 162.26/162.10 [2566]~E(x25661,x25662)+E(f605(x25663,x25664,x25661,x25665),f605(x25663,x25664,x25662,x25665))
% 162.26/162.10 [2567]~E(x25671,x25672)+E(f605(x25673,x25674,x25675,x25671),f605(x25673,x25674,x25675,x25672))
% 162.26/162.10 [2568]~E(x25681,x25682)+E(f374(x25681),f374(x25682))
% 162.26/162.10 [2569]~E(x25691,x25692)+E(f591(x25691,x25693,x25694),f591(x25692,x25693,x25694))
% 162.26/162.10 [2570]~E(x25701,x25702)+E(f591(x25703,x25701,x25704),f591(x25703,x25702,x25704))
% 162.26/162.10 [2571]~E(x25711,x25712)+E(f591(x25713,x25714,x25711),f591(x25713,x25714,x25712))
% 162.26/162.10 [2572]~E(x25721,x25722)+E(f828(x25721,x25723),f828(x25722,x25723))
% 162.26/162.10 [2573]~E(x25731,x25732)+E(f828(x25733,x25731),f828(x25733,x25732))
% 162.26/162.10 [2574]~E(x25741,x25742)+E(f749(x25741,x25743,x25744),f749(x25742,x25743,x25744))
% 162.26/162.10 [2575]~E(x25751,x25752)+E(f749(x25753,x25751,x25754),f749(x25753,x25752,x25754))
% 162.26/162.10 [2576]~E(x25761,x25762)+E(f749(x25763,x25764,x25761),f749(x25763,x25764,x25762))
% 162.26/162.10 [2577]~E(x25771,x25772)+E(f556(x25771,x25773,x25774,x25775,x25776,x25777,x25778,x25779),f556(x25772,x25773,x25774,x25775,x25776,x25777,x25778,x25779))
% 162.26/162.10 [2578]~E(x25781,x25782)+E(f556(x25783,x25781,x25784,x25785,x25786,x25787,x25788,x25789),f556(x25783,x25782,x25784,x25785,x25786,x25787,x25788,x25789))
% 162.26/162.10 [2579]~E(x25791,x25792)+E(f556(x25793,x25794,x25791,x25795,x25796,x25797,x25798,x25799),f556(x25793,x25794,x25792,x25795,x25796,x25797,x25798,x25799))
% 162.26/162.10 [2580]~E(x25801,x25802)+E(f556(x25803,x25804,x25805,x25801,x25806,x25807,x25808,x25809),f556(x25803,x25804,x25805,x25802,x25806,x25807,x25808,x25809))
% 162.26/162.10 [2581]~E(x25811,x25812)+E(f556(x25813,x25814,x25815,x25816,x25811,x25817,x25818,x25819),f556(x25813,x25814,x25815,x25816,x25812,x25817,x25818,x25819))
% 162.26/162.10 [2582]~E(x25821,x25822)+E(f556(x25823,x25824,x25825,x25826,x25827,x25821,x25828,x25829),f556(x25823,x25824,x25825,x25826,x25827,x25822,x25828,x25829))
% 162.26/162.10 [2583]~E(x25831,x25832)+E(f556(x25833,x25834,x25835,x25836,x25837,x25838,x25831,x25839),f556(x25833,x25834,x25835,x25836,x25837,x25838,x25832,x25839))
% 162.26/162.10 [2584]~E(x25841,x25842)+E(f556(x25843,x25844,x25845,x25846,x25847,x25848,x25849,x25841),f556(x25843,x25844,x25845,x25846,x25847,x25848,x25849,x25842))
% 162.26/162.10 [2585]~E(x25851,x25852)+E(f425(x25851,x25853,x25854,x25855),f425(x25852,x25853,x25854,x25855))
% 162.26/162.10 [2586]~E(x25861,x25862)+E(f425(x25863,x25861,x25864,x25865),f425(x25863,x25862,x25864,x25865))
% 162.26/162.10 [2587]~E(x25871,x25872)+E(f425(x25873,x25874,x25871,x25875),f425(x25873,x25874,x25872,x25875))
% 162.26/162.10 [2588]~E(x25881,x25882)+E(f425(x25883,x25884,x25885,x25881),f425(x25883,x25884,x25885,x25882))
% 162.26/162.10 [2589]~E(x25891,x25892)+E(f230(x25891,x25893),f230(x25892,x25893))
% 162.26/162.10 [2590]~E(x25901,x25902)+E(f230(x25903,x25901),f230(x25903,x25902))
% 162.26/162.10 [2591]~E(x25911,x25912)+E(f839(x25911,x25913,x25914,x25915),f839(x25912,x25913,x25914,x25915))
% 162.26/162.10 [2592]~E(x25921,x25922)+E(f839(x25923,x25921,x25924,x25925),f839(x25923,x25922,x25924,x25925))
% 162.26/162.10 [2593]~E(x25931,x25932)+E(f839(x25933,x25934,x25931,x25935),f839(x25933,x25934,x25932,x25935))
% 162.26/162.10 [2594]~E(x25941,x25942)+E(f839(x25943,x25944,x25945,x25941),f839(x25943,x25944,x25945,x25942))
% 162.26/162.10 [2595]~E(x25951,x25952)+E(f21(x25951,x25953),f21(x25952,x25953))
% 162.26/162.10 [2596]~E(x25961,x25962)+E(f21(x25963,x25961),f21(x25963,x25962))
% 162.26/162.10 [2597]~E(x25971,x25972)+E(f804(x25971,x25973,x25974,x25975),f804(x25972,x25973,x25974,x25975))
% 162.26/162.10 [2598]~E(x25981,x25982)+E(f804(x25983,x25981,x25984,x25985),f804(x25983,x25982,x25984,x25985))
% 162.26/162.10 [2599]~E(x25991,x25992)+E(f804(x25993,x25994,x25991,x25995),f804(x25993,x25994,x25992,x25995))
% 162.26/162.10 [2600]~E(x26001,x26002)+E(f804(x26003,x26004,x26005,x26001),f804(x26003,x26004,x26005,x26002))
% 162.26/162.10 [2601]~E(x26011,x26012)+E(f667(x26011,x26013,x26014),f667(x26012,x26013,x26014))
% 162.26/162.10 [2602]~E(x26021,x26022)+E(f667(x26023,x26021,x26024),f667(x26023,x26022,x26024))
% 162.26/162.10 [2603]~E(x26031,x26032)+E(f667(x26033,x26034,x26031),f667(x26033,x26034,x26032))
% 162.26/162.10 [2604]~E(x26041,x26042)+E(f820(x26041,x26043),f820(x26042,x26043))
% 162.26/162.10 [2605]~E(x26051,x26052)+E(f820(x26053,x26051),f820(x26053,x26052))
% 162.26/162.10 [2606]~E(x26061,x26062)+E(f847(x26061),f847(x26062))
% 162.26/162.10 [2607]~E(x26071,x26072)+E(f595(x26071,x26073,x26074,x26075),f595(x26072,x26073,x26074,x26075))
% 162.26/162.10 [2608]~E(x26081,x26082)+E(f595(x26083,x26081,x26084,x26085),f595(x26083,x26082,x26084,x26085))
% 162.26/162.10 [2609]~E(x26091,x26092)+E(f595(x26093,x26094,x26091,x26095),f595(x26093,x26094,x26092,x26095))
% 162.26/162.10 [2610]~E(x26101,x26102)+E(f595(x26103,x26104,x26105,x26101),f595(x26103,x26104,x26105,x26102))
% 162.26/162.10 [2611]~E(x26111,x26112)+E(f609(x26111,x26113,x26114,x26115,x26116),f609(x26112,x26113,x26114,x26115,x26116))
% 162.26/162.10 [2612]~E(x26121,x26122)+E(f609(x26123,x26121,x26124,x26125,x26126),f609(x26123,x26122,x26124,x26125,x26126))
% 162.26/162.10 [2613]~E(x26131,x26132)+E(f609(x26133,x26134,x26131,x26135,x26136),f609(x26133,x26134,x26132,x26135,x26136))
% 162.26/162.10 [2614]~E(x26141,x26142)+E(f609(x26143,x26144,x26145,x26141,x26146),f609(x26143,x26144,x26145,x26142,x26146))
% 162.26/162.10 [2615]~E(x26151,x26152)+E(f609(x26153,x26154,x26155,x26156,x26151),f609(x26153,x26154,x26155,x26156,x26152))
% 162.26/162.10 [2616]~E(x26161,x26162)+E(f718(x26161,x26163,x26164),f718(x26162,x26163,x26164))
% 162.26/162.10 [2617]~E(x26171,x26172)+E(f718(x26173,x26171,x26174),f718(x26173,x26172,x26174))
% 162.26/162.10 [2618]~E(x26181,x26182)+E(f718(x26183,x26184,x26181),f718(x26183,x26184,x26182))
% 162.26/162.10 [2619]~E(x26191,x26192)+E(f543(x26191,x26193,x26194,x26195,x26196),f543(x26192,x26193,x26194,x26195,x26196))
% 162.26/162.10 [2620]~E(x26201,x26202)+E(f543(x26203,x26201,x26204,x26205,x26206),f543(x26203,x26202,x26204,x26205,x26206))
% 162.26/162.10 [2621]~E(x26211,x26212)+E(f543(x26213,x26214,x26211,x26215,x26216),f543(x26213,x26214,x26212,x26215,x26216))
% 162.26/162.10 [2622]~E(x26221,x26222)+E(f543(x26223,x26224,x26225,x26221,x26226),f543(x26223,x26224,x26225,x26222,x26226))
% 162.26/162.10 [2623]~E(x26231,x26232)+E(f543(x26233,x26234,x26235,x26236,x26231),f543(x26233,x26234,x26235,x26236,x26232))
% 162.26/162.10 [2624]~E(x26241,x26242)+E(f577(x26241,x26243),f577(x26242,x26243))
% 162.26/162.10 [2625]~E(x26251,x26252)+E(f577(x26253,x26251),f577(x26253,x26252))
% 162.26/162.10 [2626]~E(x26261,x26262)+E(f623(x26261,x26263),f623(x26262,x26263))
% 162.26/162.10 [2627]~E(x26271,x26272)+E(f623(x26273,x26271),f623(x26273,x26272))
% 162.26/162.10 [2628]~E(x26281,x26282)+E(f569(x26281,x26283),f569(x26282,x26283))
% 162.26/162.10 [2629]~E(x26291,x26292)+E(f569(x26293,x26291),f569(x26293,x26292))
% 162.26/162.10 [2630]~E(x26301,x26302)+E(f657(x26301,x26303,x26304),f657(x26302,x26303,x26304))
% 162.26/162.10 [2631]~E(x26311,x26312)+E(f657(x26313,x26311,x26314),f657(x26313,x26312,x26314))
% 162.26/162.10 [2632]~E(x26321,x26322)+E(f657(x26323,x26324,x26321),f657(x26323,x26324,x26322))
% 162.26/162.10 [2633]~E(x26331,x26332)+E(f782(x26331,x26333),f782(x26332,x26333))
% 162.26/162.10 [2634]~E(x26341,x26342)+E(f782(x26343,x26341),f782(x26343,x26342))
% 162.26/162.10 [2635]~P1(x26351)+P1(x26352)+~E(x26351,x26352)
% 162.26/162.10 [2636]~P2(x26361)+P2(x26362)+~E(x26361,x26362)
% 162.26/162.10 [2637]~P24(x26371)+P24(x26372)+~E(x26371,x26372)
% 162.26/162.10 [2638]~P25(x26381)+P25(x26382)+~E(x26381,x26382)
% 162.26/162.10 [2639]P147(x26392,x26393,x26394)+~E(x26391,x26392)+~P147(x26391,x26393,x26394)
% 162.26/162.10 [2640]P147(x26403,x26402,x26404)+~E(x26401,x26402)+~P147(x26403,x26401,x26404)
% 162.26/162.10 [2641]P147(x26413,x26414,x26412)+~E(x26411,x26412)+~P147(x26413,x26414,x26411)
% 162.26/162.10 [2642]~P26(x26421)+P26(x26422)+~E(x26421,x26422)
% 162.26/162.10 [2643]~P107(x26431)+P107(x26432)+~E(x26431,x26432)
% 162.26/162.10 [2644]~P65(x26441)+P65(x26442)+~E(x26441,x26442)
% 162.26/162.10 [2645]~P77(x26451)+P77(x26452)+~E(x26451,x26452)
% 162.26/162.10 [2646]~P40(x26461)+P40(x26462)+~E(x26461,x26462)
% 162.26/162.10 [2647]~P27(x26471)+P27(x26472)+~E(x26471,x26472)
% 162.26/162.10 [2648]~P106(x26481)+P106(x26482)+~E(x26481,x26482)
% 162.26/162.10 [2649]~P61(x26491)+P61(x26492)+~E(x26491,x26492)
% 162.26/162.10 [2650]~P125(x26501)+P125(x26502)+~E(x26501,x26502)
% 162.26/162.10 [2651]~P92(x26511)+P92(x26512)+~E(x26511,x26512)
% 162.26/162.10 [2652]P38(x26522,x26523)+~E(x26521,x26522)+~P38(x26521,x26523)
% 162.26/162.10 [2653]P38(x26533,x26532)+~E(x26531,x26532)+~P38(x26533,x26531)
% 162.26/162.10 [2654]P29(x26542,x26543)+~E(x26541,x26542)+~P29(x26541,x26543)
% 162.26/162.10 [2655]P29(x26553,x26552)+~E(x26551,x26552)+~P29(x26553,x26551)
% 162.26/162.10 [2656]P12(x26562,x26563,x26564)+~E(x26561,x26562)+~P12(x26561,x26563,x26564)
% 162.26/162.10 [2657]P12(x26573,x26572,x26574)+~E(x26571,x26572)+~P12(x26573,x26571,x26574)
% 162.26/162.10 [2658]P12(x26583,x26584,x26582)+~E(x26581,x26582)+~P12(x26583,x26584,x26581)
% 162.26/162.10 [2659]~P108(x26591)+P108(x26592)+~E(x26591,x26592)
% 162.26/162.10 [2660]~P110(x26601)+P110(x26602)+~E(x26601,x26602)
% 162.26/162.10 [2661]P21(x26612,x26613,x26614,x26615)+~E(x26611,x26612)+~P21(x26611,x26613,x26614,x26615)
% 162.26/162.10 [2662]P21(x26623,x26622,x26624,x26625)+~E(x26621,x26622)+~P21(x26623,x26621,x26624,x26625)
% 162.26/162.10 [2663]P21(x26633,x26634,x26632,x26635)+~E(x26631,x26632)+~P21(x26633,x26634,x26631,x26635)
% 162.26/162.10 [2664]P21(x26643,x26644,x26645,x26642)+~E(x26641,x26642)+~P21(x26643,x26644,x26645,x26641)
% 162.26/162.10 [2665]~P64(x26651)+P64(x26652)+~E(x26651,x26652)
% 162.26/162.10 [2666]~P109(x26661)+P109(x26662)+~E(x26661,x26662)
% 162.26/162.10 [2667]P57(x26672,x26673)+~E(x26671,x26672)+~P57(x26671,x26673)
% 162.26/162.10 [2668]P57(x26683,x26682)+~E(x26681,x26682)+~P57(x26683,x26681)
% 162.26/162.10 [2669]~P63(x26691)+P63(x26692)+~E(x26691,x26692)
% 162.26/162.10 [2670]~P91(x26701)+P91(x26702)+~E(x26701,x26702)
% 162.26/162.10 [2671]~P94(x26711)+P94(x26712)+~E(x26711,x26712)
% 162.26/162.10 [2672]~P143(x26721)+P143(x26722)+~E(x26721,x26722)
% 162.26/162.10 [2673]~P58(x26731)+P58(x26732)+~E(x26731,x26732)
% 162.26/162.10 [2674]~P66(x26741)+P66(x26742)+~E(x26741,x26742)
% 162.26/162.10 [2675]P20(x26752,x26753,x26754)+~E(x26751,x26752)+~P20(x26751,x26753,x26754)
% 162.26/162.10 [2676]P20(x26763,x26762,x26764)+~E(x26761,x26762)+~P20(x26763,x26761,x26764)
% 162.26/162.10 [2677]P20(x26773,x26774,x26772)+~E(x26771,x26772)+~P20(x26773,x26774,x26771)
% 162.26/162.10 [2678]~P81(x26781)+P81(x26782)+~E(x26781,x26782)
% 162.26/162.10 [2679]P146(x26792,x26793,x26794)+~E(x26791,x26792)+~P146(x26791,x26793,x26794)
% 162.26/162.10 [2680]P146(x26803,x26802,x26804)+~E(x26801,x26802)+~P146(x26803,x26801,x26804)
% 162.26/162.10 [2681]P146(x26813,x26814,x26812)+~E(x26811,x26812)+~P146(x26813,x26814,x26811)
% 162.26/162.10 [2682]~P73(x26821)+P73(x26822)+~E(x26821,x26822)
% 162.26/162.10 [2683]~P84(x26831)+P84(x26832)+~E(x26831,x26832)
% 162.26/162.10 [2684]P48(x26842,x26843,x26844)+~E(x26841,x26842)+~P48(x26841,x26843,x26844)
% 162.26/162.10 [2685]P48(x26853,x26852,x26854)+~E(x26851,x26852)+~P48(x26853,x26851,x26854)
% 162.26/162.10 [2686]P48(x26863,x26864,x26862)+~E(x26861,x26862)+~P48(x26863,x26864,x26861)
% 162.26/162.10 [2687]~P96(x26871)+P96(x26872)+~E(x26871,x26872)
% 162.26/162.10 [2688]~P111(x26881)+P111(x26882)+~E(x26881,x26882)
% 162.26/162.10 [2689]~P67(x26891)+P67(x26892)+~E(x26891,x26892)
% 162.26/162.10 [2690]~P115(x26901)+P115(x26902)+~E(x26901,x26902)
% 162.26/162.10 [2691]~P144(x26911)+P144(x26912)+~E(x26911,x26912)
% 162.26/162.10 [2692]~P68(x26921)+P68(x26922)+~E(x26921,x26922)
% 162.26/162.10 [2693]~P60(x26931)+P60(x26932)+~E(x26931,x26932)
% 162.26/162.10 [2694]P7(x26942,x26943,x26944)+~E(x26941,x26942)+~P7(x26941,x26943,x26944)
% 162.26/162.10 [2695]P7(x26953,x26952,x26954)+~E(x26951,x26952)+~P7(x26953,x26951,x26954)
% 162.26/162.10 [2696]P7(x26963,x26964,x26962)+~E(x26961,x26962)+~P7(x26963,x26964,x26961)
% 162.26/162.10 [2697]~P69(x26971)+P69(x26972)+~E(x26971,x26972)
% 162.26/162.10 [2698]P35(x26982,x26983,x26984,x26985,x26986)+~E(x26981,x26982)+~P35(x26981,x26983,x26984,x26985,x26986)
% 162.26/162.10 [2699]P35(x26993,x26992,x26994,x26995,x26996)+~E(x26991,x26992)+~P35(x26993,x26991,x26994,x26995,x26996)
% 162.26/162.10 [2700]P35(x27003,x27004,x27002,x27005,x27006)+~E(x27001,x27002)+~P35(x27003,x27004,x27001,x27005,x27006)
% 162.26/162.10 [2701]P35(x27013,x27014,x27015,x27012,x27016)+~E(x27011,x27012)+~P35(x27013,x27014,x27015,x27011,x27016)
% 162.26/162.10 [2702]P35(x27023,x27024,x27025,x27026,x27022)+~E(x27021,x27022)+~P35(x27023,x27024,x27025,x27026,x27021)
% 162.26/162.10 [2703]~P71(x27031)+P71(x27032)+~E(x27031,x27032)
% 162.26/162.10 [2704]~P70(x27041)+P70(x27042)+~E(x27041,x27042)
% 162.26/162.10 [2705]~P78(x27051)+P78(x27052)+~E(x27051,x27052)
% 162.26/162.10 [2706]~P101(x27061)+P101(x27062)+~E(x27061,x27062)
% 162.26/162.10 [2707]~P87(x27071)+P87(x27072)+~E(x27071,x27072)
% 162.26/162.10 [2708]P30(x27082,x27083,x27084)+~E(x27081,x27082)+~P30(x27081,x27083,x27084)
% 162.26/162.10 [2709]P30(x27093,x27092,x27094)+~E(x27091,x27092)+~P30(x27093,x27091,x27094)
% 162.26/162.10 [2710]P30(x27103,x27104,x27102)+~E(x27101,x27102)+~P30(x27103,x27104,x27101)
% 162.26/162.10 [2711]P32(x27112,x27113,x27114)+~E(x27111,x27112)+~P32(x27111,x27113,x27114)
% 162.26/162.10 [2712]P32(x27123,x27122,x27124)+~E(x27121,x27122)+~P32(x27123,x27121,x27124)
% 162.26/162.10 [2713]P32(x27133,x27134,x27132)+~E(x27131,x27132)+~P32(x27133,x27134,x27131)
% 162.26/162.10 [2714]P16(x27142,x27143,x27144,x27145)+~E(x27141,x27142)+~P16(x27141,x27143,x27144,x27145)
% 162.26/162.10 [2715]P16(x27153,x27152,x27154,x27155)+~E(x27151,x27152)+~P16(x27153,x27151,x27154,x27155)
% 162.26/162.10 [2716]P16(x27163,x27164,x27162,x27165)+~E(x27161,x27162)+~P16(x27163,x27164,x27161,x27165)
% 162.26/162.10 [2717]P16(x27173,x27174,x27175,x27172)+~E(x27171,x27172)+~P16(x27173,x27174,x27175,x27171)
% 162.26/162.10 [2718]~P112(x27181)+P112(x27182)+~E(x27181,x27182)
% 162.26/162.10 [2719]P36(x27192,x27193,x27194)+~E(x27191,x27192)+~P36(x27191,x27193,x27194)
% 162.26/162.10 [2720]P36(x27203,x27202,x27204)+~E(x27201,x27202)+~P36(x27203,x27201,x27204)
% 162.26/162.10 [2721]P36(x27213,x27214,x27212)+~E(x27211,x27212)+~P36(x27213,x27214,x27211)
% 162.26/162.10 [2722]~P137(x27221)+P137(x27222)+~E(x27221,x27222)
% 162.26/162.10 [2723]~P85(x27231)+P85(x27232)+~E(x27231,x27232)
% 162.26/162.10 [2724]~P86(x27241)+P86(x27242)+~E(x27241,x27242)
% 162.26/162.10 [2725]~P123(x27251)+P123(x27252)+~E(x27251,x27252)
% 162.26/162.10 [2726]~P126(x27261)+P126(x27262)+~E(x27261,x27262)
% 162.26/162.10 [2727]~P113(x27271)+P113(x27272)+~E(x27271,x27272)
% 162.26/162.10 [2728]~P102(x27281)+P102(x27282)+~E(x27281,x27282)
% 162.26/162.10 [2729]~P138(x27291)+P138(x27292)+~E(x27291,x27292)
% 162.26/162.10 [2730]~P139(x27301)+P139(x27302)+~E(x27301,x27302)
% 162.26/162.10 [2731]~P62(x27311)+P62(x27312)+~E(x27311,x27312)
% 162.26/162.10 [2732]~P74(x27321)+P74(x27322)+~E(x27321,x27322)
% 162.26/162.10 [2733]~P82(x27331)+P82(x27332)+~E(x27331,x27332)
% 162.26/162.10 [2734]P55(x27342,x27343)+~E(x27341,x27342)+~P55(x27341,x27343)
% 162.26/162.10 [2735]P55(x27353,x27352)+~E(x27351,x27352)+~P55(x27353,x27351)
% 162.26/162.10 [2736]P51(x27362,x27363,x27364,x27365,x27366,x27367,x27368)+~E(x27361,x27362)+~P51(x27361,x27363,x27364,x27365,x27366,x27367,x27368)
% 162.26/162.10 [2737]P51(x27373,x27372,x27374,x27375,x27376,x27377,x27378)+~E(x27371,x27372)+~P51(x27373,x27371,x27374,x27375,x27376,x27377,x27378)
% 162.26/162.10 [2738]P51(x27383,x27384,x27382,x27385,x27386,x27387,x27388)+~E(x27381,x27382)+~P51(x27383,x27384,x27381,x27385,x27386,x27387,x27388)
% 162.26/162.10 [2739]P51(x27393,x27394,x27395,x27392,x27396,x27397,x27398)+~E(x27391,x27392)+~P51(x27393,x27394,x27395,x27391,x27396,x27397,x27398)
% 162.26/162.10 [2740]P51(x27403,x27404,x27405,x27406,x27402,x27407,x27408)+~E(x27401,x27402)+~P51(x27403,x27404,x27405,x27406,x27401,x27407,x27408)
% 162.26/162.10 [2741]P51(x27413,x27414,x27415,x27416,x27417,x27412,x27418)+~E(x27411,x27412)+~P51(x27413,x27414,x27415,x27416,x27417,x27411,x27418)
% 162.26/162.10 [2742]P51(x27423,x27424,x27425,x27426,x27427,x27428,x27422)+~E(x27421,x27422)+~P51(x27423,x27424,x27425,x27426,x27427,x27428,x27421)
% 162.26/162.10 [2743]~P79(x27431)+P79(x27432)+~E(x27431,x27432)
% 162.26/162.10 [2744]~P118(x27441)+P118(x27442)+~E(x27441,x27442)
% 162.26/162.10 [2745]~P135(x27451)+P135(x27452)+~E(x27451,x27452)
% 162.26/162.10 [2746]P6(x27462,x27463,x27464)+~E(x27461,x27462)+~P6(x27461,x27463,x27464)
% 162.26/162.10 [2747]P6(x27473,x27472,x27474)+~E(x27471,x27472)+~P6(x27473,x27471,x27474)
% 162.26/162.10 [2748]P6(x27483,x27484,x27482)+~E(x27481,x27482)+~P6(x27483,x27484,x27481)
% 162.26/162.10 [2749]P13(x27492,x27493,x27494)+~E(x27491,x27492)+~P13(x27491,x27493,x27494)
% 162.26/162.10 [2750]P13(x27503,x27502,x27504)+~E(x27501,x27502)+~P13(x27503,x27501,x27504)
% 162.26/162.10 [2751]P13(x27513,x27514,x27512)+~E(x27511,x27512)+~P13(x27513,x27514,x27511)
% 162.26/162.10 [2752]~P83(x27521)+P83(x27522)+~E(x27521,x27522)
% 162.26/162.10 [2753]~P114(x27531)+P114(x27532)+~E(x27531,x27532)
% 162.26/162.10 [2754]~P119(x27541)+P119(x27542)+~E(x27541,x27542)
% 162.26/162.10 [2755]P5(x27552,x27553)+~E(x27551,x27552)+~P5(x27551,x27553)
% 162.26/162.10 [2756]P5(x27563,x27562)+~E(x27561,x27562)+~P5(x27563,x27561)
% 162.26/162.10 [2757]~P100(x27571)+P100(x27572)+~E(x27571,x27572)
% 162.26/162.10 [2758]~P141(x27581)+P141(x27582)+~E(x27581,x27582)
% 162.26/162.10 [2759]P31(x27592,x27593)+~E(x27591,x27592)+~P31(x27591,x27593)
% 162.26/162.10 [2760]P31(x27603,x27602)+~E(x27601,x27602)+~P31(x27603,x27601)
% 162.26/162.10 [2761]~P127(x27611)+P127(x27612)+~E(x27611,x27612)
% 162.26/162.10 [2762]~P90(x27621)+P90(x27622)+~E(x27621,x27622)
% 162.26/162.10 [2763]P11(x27632,x27633,x27634)+~E(x27631,x27632)+~P11(x27631,x27633,x27634)
% 162.26/162.10 [2764]P11(x27643,x27642,x27644)+~E(x27641,x27642)+~P11(x27643,x27641,x27644)
% 162.26/162.10 [2765]P11(x27653,x27654,x27652)+~E(x27651,x27652)+~P11(x27653,x27654,x27651)
% 162.26/162.10 [2766]P15(x27662,x27663,x27664,x27665)+~E(x27661,x27662)+~P15(x27661,x27663,x27664,x27665)
% 162.26/162.10 [2767]P15(x27673,x27672,x27674,x27675)+~E(x27671,x27672)+~P15(x27673,x27671,x27674,x27675)
% 162.26/162.10 [2768]P15(x27683,x27684,x27682,x27685)+~E(x27681,x27682)+~P15(x27683,x27684,x27681,x27685)
% 162.26/162.10 [2769]P15(x27693,x27694,x27695,x27692)+~E(x27691,x27692)+~P15(x27693,x27694,x27695,x27691)
% 162.26/162.10 [2770]~P80(x27701)+P80(x27702)+~E(x27701,x27702)
% 162.26/162.10 [2771]~P75(x27711)+P75(x27712)+~E(x27711,x27712)
% 162.26/162.10 [2772]~P145(x27721)+P145(x27722)+~E(x27721,x27722)
% 162.26/162.10 [2773]P54(x27732,x27733,x27734,x27735,x27736)+~E(x27731,x27732)+~P54(x27731,x27733,x27734,x27735,x27736)
% 162.26/162.10 [2774]P54(x27743,x27742,x27744,x27745,x27746)+~E(x27741,x27742)+~P54(x27743,x27741,x27744,x27745,x27746)
% 162.26/162.10 [2775]P54(x27753,x27754,x27752,x27755,x27756)+~E(x27751,x27752)+~P54(x27753,x27754,x27751,x27755,x27756)
% 162.26/162.10 [2776]P54(x27763,x27764,x27765,x27762,x27766)+~E(x27761,x27762)+~P54(x27763,x27764,x27765,x27761,x27766)
% 162.26/162.10 [2777]P54(x27773,x27774,x27775,x27776,x27772)+~E(x27771,x27772)+~P54(x27773,x27774,x27775,x27776,x27771)
% 162.26/162.10 [2778]P53(x27782,x27783,x27784)+~E(x27781,x27782)+~P53(x27781,x27783,x27784)
% 162.26/162.10 [2779]P53(x27793,x27792,x27794)+~E(x27791,x27792)+~P53(x27793,x27791,x27794)
% 162.26/162.10 [2780]P53(x27803,x27804,x27802)+~E(x27801,x27802)+~P53(x27803,x27804,x27801)
% 162.26/162.10 [2781]~P131(x27811)+P131(x27812)+~E(x27811,x27812)
% 162.26/162.10 [2782]P23(x27822,x27823,x27824)+~E(x27821,x27822)+~P23(x27821,x27823,x27824)
% 162.26/162.10 [2783]P23(x27833,x27832,x27834)+~E(x27831,x27832)+~P23(x27833,x27831,x27834)
% 162.26/162.10 [2784]P23(x27843,x27844,x27842)+~E(x27841,x27842)+~P23(x27843,x27844,x27841)
% 162.26/162.10 [2785]~P130(x27851)+P130(x27852)+~E(x27851,x27852)
% 162.26/162.10 [2786]P43(x27862,x27863)+~E(x27861,x27862)+~P43(x27861,x27863)
% 162.26/162.10 [2787]P43(x27873,x27872)+~E(x27871,x27872)+~P43(x27873,x27871)
% 162.26/162.10 [2788]~P44(x27881)+P44(x27882)+~E(x27881,x27882)
% 162.26/162.10 [2789]~P140(x27891)+P140(x27892)+~E(x27891,x27892)
% 162.26/162.10 [2790]~P95(x27901)+P95(x27902)+~E(x27901,x27902)
% 162.26/162.10 [2791]~P37(x27911)+P37(x27912)+~E(x27911,x27912)
% 162.26/162.10 [2792]~P132(x27921)+P132(x27922)+~E(x27921,x27922)
% 162.26/162.10 [2793]~P142(x27931)+P142(x27932)+~E(x27931,x27932)
% 162.26/162.10 [2794]~P88(x27941)+P88(x27942)+~E(x27941,x27942)
% 162.26/162.10 [2795]P8(x27952,x27953,x27954)+~E(x27951,x27952)+~P8(x27951,x27953,x27954)
% 162.26/162.10 [2796]P8(x27963,x27962,x27964)+~E(x27961,x27962)+~P8(x27963,x27961,x27964)
% 162.26/162.10 [2797]P8(x27973,x27974,x27972)+~E(x27971,x27972)+~P8(x27973,x27974,x27971)
% 162.26/162.10 [2798]P17(x27982,x27983,x27984,x27985,x27986)+~E(x27981,x27982)+~P17(x27981,x27983,x27984,x27985,x27986)
% 162.26/162.10 [2799]P17(x27993,x27992,x27994,x27995,x27996)+~E(x27991,x27992)+~P17(x27993,x27991,x27994,x27995,x27996)
% 162.26/162.10 [2800]P17(x28003,x28004,x28002,x28005,x28006)+~E(x28001,x28002)+~P17(x28003,x28004,x28001,x28005,x28006)
% 162.26/162.10 [2801]P17(x28013,x28014,x28015,x28012,x28016)+~E(x28011,x28012)+~P17(x28013,x28014,x28015,x28011,x28016)
% 162.26/162.10 [2802]P17(x28023,x28024,x28025,x28026,x28022)+~E(x28021,x28022)+~P17(x28023,x28024,x28025,x28026,x28021)
% 162.26/162.10 [2803]~P28(x28031)+P28(x28032)+~E(x28031,x28032)
% 162.26/162.10 [2804]P10(x28042,x28043,x28044,x28045,x28046,x28047)+~E(x28041,x28042)+~P10(x28041,x28043,x28044,x28045,x28046,x28047)
% 162.26/162.10 [2805]P10(x28053,x28052,x28054,x28055,x28056,x28057)+~E(x28051,x28052)+~P10(x28053,x28051,x28054,x28055,x28056,x28057)
% 162.26/162.10 [2806]P10(x28063,x28064,x28062,x28065,x28066,x28067)+~E(x28061,x28062)+~P10(x28063,x28064,x28061,x28065,x28066,x28067)
% 162.26/162.10 [2807]P10(x28073,x28074,x28075,x28072,x28076,x28077)+~E(x28071,x28072)+~P10(x28073,x28074,x28075,x28071,x28076,x28077)
% 162.26/162.10 [2808]P10(x28083,x28084,x28085,x28086,x28082,x28087)+~E(x28081,x28082)+~P10(x28083,x28084,x28085,x28086,x28081,x28087)
% 162.26/162.10 [2809]P10(x28093,x28094,x28095,x28096,x28097,x28092)+~E(x28091,x28092)+~P10(x28093,x28094,x28095,x28096,x28097,x28091)
% 162.26/162.10 [2810]~P133(x28101)+P133(x28102)+~E(x28101,x28102)
% 162.26/162.10 [2811]P22(x28112,x28113)+~E(x28111,x28112)+~P22(x28111,x28113)
% 162.26/162.10 [2812]P22(x28123,x28122)+~E(x28121,x28122)+~P22(x28123,x28121)
% 162.26/162.10 [2813]~P93(x28131)+P93(x28132)+~E(x28131,x28132)
% 162.26/162.10 [2814]~P99(x28141)+P99(x28142)+~E(x28141,x28142)
% 162.26/162.10 [2815]P18(x28152,x28153,x28154,x28155,x28156,x28157)+~E(x28151,x28152)+~P18(x28151,x28153,x28154,x28155,x28156,x28157)
% 162.26/162.10 [2816]P18(x28163,x28162,x28164,x28165,x28166,x28167)+~E(x28161,x28162)+~P18(x28163,x28161,x28164,x28165,x28166,x28167)
% 162.26/162.10 [2817]P18(x28173,x28174,x28172,x28175,x28176,x28177)+~E(x28171,x28172)+~P18(x28173,x28174,x28171,x28175,x28176,x28177)
% 162.26/162.10 [2818]P18(x28183,x28184,x28185,x28182,x28186,x28187)+~E(x28181,x28182)+~P18(x28183,x28184,x28185,x28181,x28186,x28187)
% 162.26/162.10 [2819]P18(x28193,x28194,x28195,x28196,x28192,x28197)+~E(x28191,x28192)+~P18(x28193,x28194,x28195,x28196,x28191,x28197)
% 162.26/162.10 [2820]P18(x28203,x28204,x28205,x28206,x28207,x28202)+~E(x28201,x28202)+~P18(x28203,x28204,x28205,x28206,x28207,x28201)
% 162.26/162.10 [2821]~P104(x28211)+P104(x28212)+~E(x28211,x28212)
% 162.26/162.10 [2822]~P134(x28221)+P134(x28222)+~E(x28221,x28222)
% 162.26/162.10 [2823]P42(x28232,x28233,x28234,x28235,x28236,x28237)+~E(x28231,x28232)+~P42(x28231,x28233,x28234,x28235,x28236,x28237)
% 162.26/162.10 [2824]P42(x28243,x28242,x28244,x28245,x28246,x28247)+~E(x28241,x28242)+~P42(x28243,x28241,x28244,x28245,x28246,x28247)
% 162.26/162.10 [2825]P42(x28253,x28254,x28252,x28255,x28256,x28257)+~E(x28251,x28252)+~P42(x28253,x28254,x28251,x28255,x28256,x28257)
% 162.26/162.10 [2826]P42(x28263,x28264,x28265,x28262,x28266,x28267)+~E(x28261,x28262)+~P42(x28263,x28264,x28265,x28261,x28266,x28267)
% 162.26/162.10 [2827]P42(x28273,x28274,x28275,x28276,x28272,x28277)+~E(x28271,x28272)+~P42(x28273,x28274,x28275,x28276,x28271,x28277)
% 162.26/162.10 [2828]P42(x28283,x28284,x28285,x28286,x28287,x28282)+~E(x28281,x28282)+~P42(x28283,x28284,x28285,x28286,x28287,x28281)
% 162.26/162.10 [2829]~P116(x28291)+P116(x28292)+~E(x28291,x28292)
% 162.26/162.10 [2830]P34(x28302,x28303,x28304)+~E(x28301,x28302)+~P34(x28301,x28303,x28304)
% 162.26/162.10 [2831]P34(x28313,x28312,x28314)+~E(x28311,x28312)+~P34(x28313,x28311,x28314)
% 162.26/162.10 [2832]P34(x28323,x28324,x28322)+~E(x28321,x28322)+~P34(x28323,x28324,x28321)
% 162.26/162.10 [2833]~P124(x28331)+P124(x28332)+~E(x28331,x28332)
% 162.26/162.10 [2834]P39(x28342,x28343)+~E(x28341,x28342)+~P39(x28341,x28343)
% 162.26/162.10 [2835]P39(x28353,x28352)+~E(x28351,x28352)+~P39(x28353,x28351)
% 162.26/162.10 [2836]P47(x28362,x28363,x28364)+~E(x28361,x28362)+~P47(x28361,x28363,x28364)
% 162.26/162.10 [2837]P47(x28373,x28372,x28374)+~E(x28371,x28372)+~P47(x28373,x28371,x28374)
% 162.26/162.10 [2838]P47(x28383,x28384,x28382)+~E(x28381,x28382)+~P47(x28383,x28384,x28381)
% 162.26/162.10 [2839]P14(x28392,x28393,x28394)+~E(x28391,x28392)+~P14(x28391,x28393,x28394)
% 162.26/162.10 [2840]P14(x28403,x28402,x28404)+~E(x28401,x28402)+~P14(x28403,x28401,x28404)
% 162.26/162.10 [2841]P14(x28413,x28414,x28412)+~E(x28411,x28412)+~P14(x28413,x28414,x28411)
% 162.26/162.10 [2842]~P121(x28421)+P121(x28422)+~E(x28421,x28422)
% 162.26/162.10 [2843]P9(x28432,x28433,x28434,x28435)+~E(x28431,x28432)+~P9(x28431,x28433,x28434,x28435)
% 162.26/162.10 [2844]P9(x28443,x28442,x28444,x28445)+~E(x28441,x28442)+~P9(x28443,x28441,x28444,x28445)
% 162.26/162.10 [2845]P9(x28453,x28454,x28452,x28455)+~E(x28451,x28452)+~P9(x28453,x28454,x28451,x28455)
% 162.26/162.10 [2846]P9(x28463,x28464,x28465,x28462)+~E(x28461,x28462)+~P9(x28463,x28464,x28465,x28461)
% 162.26/162.10 [2847]P52(x28472,x28473,x28474)+~E(x28471,x28472)+~P52(x28471,x28473,x28474)
% 162.26/162.10 [2848]P52(x28483,x28482,x28484)+~E(x28481,x28482)+~P52(x28483,x28481,x28484)
% 162.26/162.10 [2849]P52(x28493,x28494,x28492)+~E(x28491,x28492)+~P52(x28493,x28494,x28491)
% 162.26/162.10 [2850]~P128(x28501)+P128(x28502)+~E(x28501,x28502)
% 162.26/162.10 [2851]P49(x28512,x28513)+~E(x28511,x28512)+~P49(x28511,x28513)
% 162.26/162.10 [2852]P49(x28523,x28522)+~E(x28521,x28522)+~P49(x28523,x28521)
% 162.26/162.10 [2853]P19(x28532,x28533,x28534,x28535,x28536,x28537)+~E(x28531,x28532)+~P19(x28531,x28533,x28534,x28535,x28536,x28537)
% 162.26/162.10 [2854]P19(x28543,x28542,x28544,x28545,x28546,x28547)+~E(x28541,x28542)+~P19(x28543,x28541,x28544,x28545,x28546,x28547)
% 162.26/162.10 [2855]P19(x28553,x28554,x28552,x28555,x28556,x28557)+~E(x28551,x28552)+~P19(x28553,x28554,x28551,x28555,x28556,x28557)
% 162.26/162.10 [2856]P19(x28563,x28564,x28565,x28562,x28566,x28567)+~E(x28561,x28562)+~P19(x28563,x28564,x28565,x28561,x28566,x28567)
% 162.26/162.10 [2857]P19(x28573,x28574,x28575,x28576,x28572,x28577)+~E(x28571,x28572)+~P19(x28573,x28574,x28575,x28576,x28571,x28577)
% 162.26/162.10 [2858]P19(x28583,x28584,x28585,x28586,x28587,x28582)+~E(x28581,x28582)+~P19(x28583,x28584,x28585,x28586,x28587,x28581)
% 162.26/162.10 [2859]~P129(x28591)+P129(x28592)+~E(x28591,x28592)
% 162.26/162.10 [2860]~P59(x28601)+P59(x28602)+~E(x28601,x28602)
% 162.26/162.10 [2861]~P98(x28611)+P98(x28612)+~E(x28611,x28612)
% 162.26/162.10 [2862]P33(x28622,x28623,x28624,x28625)+~E(x28621,x28622)+~P33(x28621,x28623,x28624,x28625)
% 162.26/162.10 [2863]P33(x28633,x28632,x28634,x28635)+~E(x28631,x28632)+~P33(x28633,x28631,x28634,x28635)
% 162.26/162.10 [2864]P33(x28643,x28644,x28642,x28645)+~E(x28641,x28642)+~P33(x28643,x28644,x28641,x28645)
% 162.26/162.10 [2865]P33(x28653,x28654,x28655,x28652)+~E(x28651,x28652)+~P33(x28653,x28654,x28655,x28651)
% 162.26/162.10 [2866]~P120(x28661)+P120(x28662)+~E(x28661,x28662)
% 162.26/162.10 [2867]~P97(x28671)+P97(x28672)+~E(x28671,x28672)
% 162.26/162.10 [2868]~P103(x28681)+P103(x28682)+~E(x28681,x28682)
% 162.26/162.10 [2869]P46(x28692,x28693,x28694)+~E(x28691,x28692)+~P46(x28691,x28693,x28694)
% 162.26/162.10 [2870]P46(x28703,x28702,x28704)+~E(x28701,x28702)+~P46(x28703,x28701,x28704)
% 162.26/162.10 [2871]P46(x28713,x28714,x28712)+~E(x28711,x28712)+~P46(x28713,x28714,x28711)
% 162.26/162.10 [2872]P56(x28722,x28723,x28724,x28725)+~E(x28721,x28722)+~P56(x28721,x28723,x28724,x28725)
% 162.26/162.10 [2873]P56(x28733,x28732,x28734,x28735)+~E(x28731,x28732)+~P56(x28733,x28731,x28734,x28735)
% 162.26/162.10 [2874]P56(x28743,x28744,x28742,x28745)+~E(x28741,x28742)+~P56(x28743,x28744,x28741,x28745)
% 162.26/162.10 [2875]P56(x28753,x28754,x28755,x28752)+~E(x28751,x28752)+~P56(x28753,x28754,x28755,x28751)
% 162.26/162.10 [2876]~P72(x28761)+P72(x28762)+~E(x28761,x28762)
% 162.26/162.10 [2877]P3(x28772,x28773,x28774)+~E(x28771,x28772)+~P3(x28771,x28773,x28774)
% 162.26/162.10 [2878]P3(x28783,x28782,x28784)+~E(x28781,x28782)+~P3(x28783,x28781,x28784)
% 162.26/162.10 [2879]P3(x28793,x28794,x28792)+~E(x28791,x28792)+~P3(x28793,x28794,x28791)
% 162.26/162.10 [2880]P50(x28802,x28803)+~E(x28801,x28802)+~P50(x28801,x28803)
% 162.26/162.10 [2881]P50(x28813,x28812)+~E(x28811,x28812)+~P50(x28813,x28811)
% 162.26/162.10 [2882]P4(x28822,x28823,x28824,x28825,x28826)+~E(x28821,x28822)+~P4(x28821,x28823,x28824,x28825,x28826)
% 162.26/162.10 [2883]P4(x28833,x28832,x28834,x28835,x28836)+~E(x28831,x28832)+~P4(x28833,x28831,x28834,x28835,x28836)
% 162.26/162.10 [2884]P4(x28843,x28844,x28842,x28845,x28846)+~E(x28841,x28842)+~P4(x28843,x28844,x28841,x28845,x28846)
% 162.26/162.10 [2885]P4(x28853,x28854,x28855,x28852,x28856)+~E(x28851,x28852)+~P4(x28853,x28854,x28855,x28851,x28856)
% 162.26/162.10 [2886]P4(x28863,x28864,x28865,x28866,x28862)+~E(x28861,x28862)+~P4(x28863,x28864,x28865,x28866,x28861)
% 162.26/162.10 [2887]P41(x28872,x28873,x28874,x28875)+~E(x28871,x28872)+~P41(x28871,x28873,x28874,x28875)
% 162.26/162.10 [2888]P41(x28883,x28882,x28884,x28885)+~E(x28881,x28882)+~P41(x28883,x28881,x28884,x28885)
% 162.26/162.10 [2889]P41(x28893,x28894,x28892,x28895)+~E(x28891,x28892)+~P41(x28893,x28894,x28891,x28895)
% 162.26/162.10 [2890]P41(x28903,x28904,x28905,x28902)+~E(x28901,x28902)+~P41(x28903,x28904,x28905,x28901)
% 162.26/162.10 [2891]P45(x28912,x28913)+~E(x28911,x28912)+~P45(x28911,x28913)
% 162.26/162.10 [2892]P45(x28923,x28922)+~E(x28921,x28922)+~P45(x28923,x28921)
% 162.26/162.10 [2893]~P89(x28931)+P89(x28932)+~E(x28931,x28932)
% 162.26/162.10 [2894]~P117(x28941)+P117(x28942)+~E(x28941,x28942)
% 162.26/162.10 [2895]~P105(x28951)+P105(x28952)+~E(x28951,x28952)
% 162.26/162.10 [2896]~P76(x28961)+P76(x28962)+~E(x28961,x28962)
% 162.26/162.10 [2897]~P136(x28971)+P136(x28972)+~E(x28971,x28972)
% 162.26/162.10 [2898]~P122(x28981)+P122(x28982)+~E(x28981,x28982)
% 162.26/162.10
% 162.26/162.10 %-------------------------------------------
% 162.46/162.13 cnf(10243,plain,
% 162.46/162.13 (E(f331(f257(x102431,x102431),f258(x102431,x102432)),x102432)),
% 162.46/162.13 inference(rename_variables,[],[3270])).
% 162.46/162.13 cnf(10246,plain,
% 162.46/162.13 (~E(f331(a118,x102461),x102461)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(10249,plain,
% 162.46/162.13 (~E(f331(a118,x102491),x102491)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(10252,plain,
% 162.46/162.13 (E(f331(f257(x102521,x102521),f258(x102521,x102522)),x102522)),
% 162.46/162.13 inference(rename_variables,[],[3270])).
% 162.46/162.13 cnf(10259,plain,
% 162.46/162.13 (~E(f331(a118,x102591),x102591)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(10270,plain,
% 162.46/162.13 (~E(f331(a118,x102701),x102701)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(10275,plain,
% 162.46/162.13 (~P24(f331(f63(x102751,x102752,f196(f891(x102751,a877))),x102753))),
% 162.46/162.13 inference(rename_variables,[],[4578])).
% 162.46/162.13 cnf(10278,plain,
% 162.46/162.13 (~P24(f331(f63(x102781,x102782,f196(f891(x102781,a877))),x102783))),
% 162.46/162.13 inference(rename_variables,[],[4578])).
% 162.46/162.13 cnf(10281,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x102811),f2(a883)))),
% 162.46/162.13 inference(rename_variables,[],[4557])).
% 162.46/162.13 cnf(10284,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x102841),f2(a883)))),
% 162.46/162.13 inference(rename_variables,[],[4557])).
% 162.46/162.13 cnf(10301,plain,
% 162.46/162.13 (~P24(f331(f331(f247(a883),f331(a118,x103011)),x103011))),
% 162.46/162.13 inference(rename_variables,[],[4566])).
% 162.46/162.13 cnf(10304,plain,
% 162.46/162.13 (~E(f331(f331(f154(x103041),x103042),x103043),x103043)),
% 162.46/162.13 inference(rename_variables,[],[4509])).
% 162.46/162.13 cnf(10310,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x103101),f2(a883)))),
% 162.46/162.13 inference(rename_variables,[],[4557])).
% 162.46/162.13 cnf(10313,plain,
% 162.46/162.13 (E(f331(f257(x103131,x103131),f258(x103131,x103132)),x103132)),
% 162.46/162.13 inference(rename_variables,[],[3270])).
% 162.46/162.13 cnf(10316,plain,
% 162.46/162.13 (E(f331(f257(x103161,x103161),f258(x103161,x103162)),x103162)),
% 162.46/162.13 inference(rename_variables,[],[3270])).
% 162.46/162.13 cnf(10320,plain,
% 162.46/162.13 (~P24(f331(a202,a84))),
% 162.46/162.13 inference(scs_inference,[],[4485,10246,10249,10259,3102,3270,10243,10252,10313,3146,3210,3176,3154,4509,3296,4557,10281,10284,4554,4505,4566,4564,3287,4547,4578,10275,4581,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131])).
% 162.46/162.13 cnf(10323,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),f331(f331(f81(a883),x103231),x103232)),x103232))),
% 162.46/162.13 inference(rename_variables,[],[4579])).
% 162.46/162.13 cnf(10326,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),f331(f331(f81(a883),x103261),x103262)),x103262))),
% 162.46/162.13 inference(rename_variables,[],[4579])).
% 162.46/162.13 cnf(10330,plain,
% 162.46/162.13 (~E(x103301,f331(a118,x103301))),
% 162.46/162.13 inference(scs_inference,[],[4485,10246,10249,10259,3102,3270,10243,10252,10313,3146,3210,3176,3154,4509,3385,3296,4557,10281,10284,4554,4505,4566,4564,3287,4547,4578,10275,4581,4579,10323,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197])).
% 162.46/162.13 cnf(10344,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x103441),x103441))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(10347,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),f45(a883,x103471,x103472)),x103471))),
% 162.46/162.13 inference(rename_variables,[],[3767])).
% 162.46/162.13 cnf(10370,plain,
% 162.46/162.13 (E(f331(f38(a883),f331(f254(a883),x103701)),x103701)),
% 162.46/162.13 inference(rename_variables,[],[3205])).
% 162.46/162.13 cnf(10378,plain,
% 162.46/162.13 (~E(f331(a118,x103781),x103781)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(10381,plain,
% 162.46/162.13 (~E(f331(a118,x103811),x103811)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(10384,plain,
% 162.46/162.13 (~E(f331(a118,x103841),x103841)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(10389,plain,
% 162.46/162.13 (P24(f331(f331(f248(a883),x103891),f331(a118,x103891)))),
% 162.46/162.13 inference(rename_variables,[],[3385])).
% 162.46/162.13 cnf(10398,plain,
% 162.46/162.13 (P24(f331(f331(f203(a24),x103981),x103981))),
% 162.46/162.13 inference(rename_variables,[],[3313])).
% 162.46/162.13 cnf(10405,plain,
% 162.46/162.13 (E(f331(f257(x104051,x104051),f258(x104051,x104052)),x104052)),
% 162.46/162.13 inference(rename_variables,[],[3270])).
% 162.46/162.13 cnf(10408,plain,
% 162.46/162.13 (E(f331(f257(x104081,x104081),f258(x104081,x104082)),x104082)),
% 162.46/162.13 inference(rename_variables,[],[3270])).
% 162.46/162.13 cnf(10427,plain,
% 162.46/162.13 (P24(f331(f331(f247(a1),x104271),x104271))),
% 162.46/162.13 inference(rename_variables,[],[3315])).
% 162.46/162.13 cnf(10436,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x104361),x104361))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(10441,plain,
% 162.46/162.13 (~E(f331(f331(f331(f73(x104411,f887(x104412)),x104413),x104414),f331(f239(x104412),x104415)),f331(f16(f887(x104412),x104411),f199(x104412)))),
% 162.46/162.13 inference(rename_variables,[],[4575])).
% 162.46/162.13 cnf(10445,plain,
% 162.46/162.13 (E(f331(f331(f81(a883),x104451),f696(x104451,x104451)),x104451)),
% 162.46/162.13 inference(scs_inference,[],[4485,10246,10249,10259,10270,10378,10381,3102,3270,10243,10252,10313,10316,10405,3146,3210,3176,3154,3243,4575,4509,3205,4080,4590,3225,3385,10389,3296,4557,10281,10284,3745,3889,3342,3317,4554,4505,4035,3313,3314,3315,3316,4553,10344,3410,3828,3767,10347,4566,10301,4564,4543,3287,4547,4548,4578,10275,4581,3788,4579,10323,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488])).
% 162.46/162.13 cnf(10468,plain,
% 162.46/162.13 (~E(f331(f331(f154(x104681),x104682),x104683),x104683)),
% 162.46/162.13 inference(rename_variables,[],[4509])).
% 162.46/162.13 cnf(10471,plain,
% 162.46/162.13 (~E(f331(a28,x104711),f34(x104712,x104713))),
% 162.46/162.13 inference(rename_variables,[],[4500])).
% 162.46/162.13 cnf(10482,plain,
% 162.46/162.13 (P24(f331(f331(f247(a1),x104821),x104821))),
% 162.46/162.13 inference(rename_variables,[],[3315])).
% 162.46/162.13 cnf(10487,plain,
% 162.46/162.13 (~E(f331(a118,x104871),x104871)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(10494,plain,
% 162.46/162.13 (P24(f331(f331(f203(a24),x104941),x104941))),
% 162.46/162.13 inference(rename_variables,[],[3313])).
% 162.46/162.13 cnf(10507,plain,
% 162.46/162.13 (P24(f331(f331(f248(a883),x105071),f331(a118,x105071)))),
% 162.46/162.13 inference(rename_variables,[],[3385])).
% 162.46/162.13 cnf(10512,plain,
% 162.46/162.13 (E(f331(f331(f137(x105121),f119(x105121)),x105122),x105122)),
% 162.46/162.13 inference(rename_variables,[],[3265])).
% 162.46/162.13 cnf(10515,plain,
% 162.46/162.13 (E(f331(f331(f137(x105151),f119(x105151)),x105152),x105152)),
% 162.46/162.13 inference(rename_variables,[],[3265])).
% 162.46/162.13 cnf(10530,plain,
% 162.46/162.13 (~P24(f331(f63(x105301,x105302,f196(f891(x105301,a877))),x105303))),
% 162.46/162.13 inference(rename_variables,[],[4578])).
% 162.46/162.13 cnf(10549,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x105491),x105491))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(10561,plain,
% 162.46/162.13 (E(f331(f331(f262(a883),f331(f110(a883),a103)),x105611),f331(f331(f262(a883),f2(a883)),x105611))),
% 162.46/162.13 inference(scs_inference,[],[4485,10246,10249,10259,10270,10378,10381,10384,4500,3102,3270,10243,10252,10313,10316,10405,3146,3210,3176,3154,3243,3265,10512,4575,4509,10304,3205,4080,4590,3225,3677,3385,10389,10507,3296,4557,10281,10284,10310,4571,3745,3889,3342,3343,3317,4554,4505,4035,3313,10398,3314,3315,10427,3316,4553,10344,10436,3410,3828,3767,10347,4566,10301,4564,4543,3287,3288,4544,4547,4548,4578,10275,10278,4581,3788,4579,10323,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848])).
% 162.46/162.13 cnf(10564,plain,
% 162.46/162.13 (~E(f331(a28,x105641),f34(x105642,x105643))),
% 162.46/162.13 inference(rename_variables,[],[4500])).
% 162.46/162.13 cnf(10573,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x105731),x105731))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(10578,plain,
% 162.46/162.13 (P24(f331(f331(f248(a883),x105781),f331(a118,x105781)))),
% 162.46/162.13 inference(rename_variables,[],[3385])).
% 162.46/162.13 cnf(10581,plain,
% 162.46/162.13 (~P24(f331(f63(x105811,x105812,f196(f891(x105811,a877))),x105813))),
% 162.46/162.13 inference(rename_variables,[],[4578])).
% 162.46/162.13 cnf(10584,plain,
% 162.46/162.13 (~P24(f331(f63(x105841,x105842,f196(f891(x105841,a877))),x105843))),
% 162.46/162.13 inference(rename_variables,[],[4578])).
% 162.46/162.13 cnf(10589,plain,
% 162.46/162.13 (~P24(f331(f63(x105891,x105892,f196(f891(x105891,a877))),x105893))),
% 162.46/162.13 inference(rename_variables,[],[4578])).
% 162.46/162.13 cnf(10599,plain,
% 162.46/162.13 (~E(f331(f172(x105991),f331(a118,f331(f331(f137(x105991),f331(f172(x105991),x105992)),f331(f331(f154(x105991),x105993),f119(x105991))))),f331(f331(f154(x105991),x105993),x105992))),
% 162.46/162.13 inference(scs_inference,[],[4485,10246,10249,10259,10270,10378,10381,10384,10487,4500,10471,3102,3270,10243,10252,10313,10316,10405,3146,3210,3176,3154,3243,3265,10512,4575,4509,10304,3205,4080,4590,3225,3677,3385,10389,10507,10578,3296,4557,10281,10284,10310,4571,3745,3889,3342,3343,3317,4554,4505,4035,3313,10398,3314,3315,10427,3316,4553,10344,10436,10549,3410,3828,3767,10347,4566,10301,4564,4543,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,4581,3788,4579,10323,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024])).
% 162.46/162.13 cnf(10600,plain,
% 162.46/162.13 (~E(f331(a118,x106001),x106001)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(10614,plain,
% 162.46/162.13 (P24(f331(f331(f248(a105),f331(a3,x106141)),f331(a3,f331(a118,x106141))))),
% 162.46/162.13 inference(scs_inference,[],[4485,10246,10249,10259,10270,10378,10381,10384,10487,4500,10471,3102,3270,10243,10252,10313,10316,10405,3146,3210,3176,3154,3243,3265,10512,4575,4509,10304,3205,4080,4590,3225,3677,3385,10389,10507,10578,3758,3296,4557,10281,10284,10310,4571,3745,3889,3342,3343,3317,4554,4505,4035,3313,10398,3314,3315,10427,3316,4553,10344,10436,10549,3410,3828,3767,10347,4566,10301,4564,4543,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,4581,3788,4579,10323,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104])).
% 162.46/162.13 cnf(10625,plain,
% 162.46/162.13 (P24(f331(f331(f203(a24),x106251),x106251))),
% 162.46/162.13 inference(rename_variables,[],[3313])).
% 162.46/162.13 cnf(10628,plain,
% 162.46/162.13 (P24(f331(f331(f248(a883),x106281),f331(a118,f331(f331(f81(a883),x106282),x106281))))),
% 162.46/162.13 inference(rename_variables,[],[3756])).
% 162.46/162.13 cnf(10630,plain,
% 162.46/162.13 (P24(f331(f331(f248(a883),x106301),f331(f331(f82(a883),f331(a118,x106301)),f331(a118,x106301))))),
% 162.46/162.13 inference(scs_inference,[],[4485,10246,10249,10259,10270,10378,10381,10384,10487,4500,10471,3102,3270,10243,10252,10313,10316,10405,3146,3210,3176,3154,3243,3265,10512,4575,4509,10304,3205,4080,4590,3225,3677,3385,10389,10507,10578,3758,3296,4557,10281,10284,10310,4571,3745,3889,3342,3343,3317,4554,4505,4035,3313,10398,10494,3314,3315,10427,3316,4553,10344,10436,10549,3410,3828,3767,10347,4566,10301,4564,4543,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,3582,4581,3788,4579,10323,3756,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129])).
% 162.46/162.13 cnf(10631,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x106311),f331(f331(f82(a883),x106311),x106311)))),
% 162.46/162.13 inference(rename_variables,[],[3582])).
% 162.46/162.13 cnf(10634,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x106341),f331(f331(f82(a883),x106341),x106341)))),
% 162.46/162.13 inference(rename_variables,[],[3582])).
% 162.46/162.13 cnf(10639,plain,
% 162.46/162.13 (P24(f331(f331(f248(a883),x106391),f331(a118,x106391)))),
% 162.46/162.13 inference(rename_variables,[],[3385])).
% 162.46/162.13 cnf(10642,plain,
% 162.46/162.13 (P24(f331(f331(f248(a883),x106421),f331(a118,x106421)))),
% 162.46/162.13 inference(rename_variables,[],[3385])).
% 162.46/162.13 cnf(10645,plain,
% 162.46/162.13 (P24(f331(f331(f333(x106451),x106452),f256(f891(x106451,a877))))),
% 162.46/162.13 inference(rename_variables,[],[3472])).
% 162.46/162.13 cnf(10662,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),f331(f331(f81(a883),x106621),x106622)),x106622))),
% 162.46/162.13 inference(rename_variables,[],[4579])).
% 162.46/162.13 cnf(10665,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),f331(f331(f81(a883),x106651),x106652)),x106652))),
% 162.46/162.13 inference(rename_variables,[],[4579])).
% 162.46/162.13 cnf(10668,plain,
% 162.46/162.13 (~P24(f331(f331(f247(a883),f331(a118,x106681)),x106681))),
% 162.46/162.13 inference(rename_variables,[],[4566])).
% 162.46/162.13 cnf(10671,plain,
% 162.46/162.13 (~P24(f331(f331(f247(a883),f331(a118,x106711)),x106711))),
% 162.46/162.13 inference(rename_variables,[],[4566])).
% 162.46/162.13 cnf(10674,plain,
% 162.46/162.13 (P24(f331(f256(f891(x106741,a877)),x106742))),
% 162.46/162.13 inference(rename_variables,[],[3379])).
% 162.46/162.13 cnf(10677,plain,
% 162.46/162.13 (E(f331(f38(a883),f331(f254(a883),x106771)),x106771)),
% 162.46/162.13 inference(rename_variables,[],[3205])).
% 162.46/162.13 cnf(10680,plain,
% 162.46/162.13 (P24(f331(f331(f248(a883),x106801),f331(a118,x106801)))),
% 162.46/162.13 inference(rename_variables,[],[3385])).
% 162.46/162.13 cnf(10687,plain,
% 162.46/162.13 (P24(f331(f331(f203(a24),x106871),x106871))),
% 162.46/162.13 inference(rename_variables,[],[3313])).
% 162.46/162.13 cnf(10692,plain,
% 162.46/162.13 (P24(f331(f331(f247(a1),x106921),x106921))),
% 162.46/162.13 inference(rename_variables,[],[3315])).
% 162.46/162.13 cnf(10701,plain,
% 162.46/162.13 (E(f331(f257(x107011,x107011),f258(x107011,x107012)),x107012)),
% 162.46/162.13 inference(rename_variables,[],[3270])).
% 162.46/162.13 cnf(10704,plain,
% 162.46/162.13 (P24(f331(f256(f891(x107041,a877)),x107042))),
% 162.46/162.13 inference(rename_variables,[],[3379])).
% 162.46/162.13 cnf(10707,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),f2(a883)),x107071))),
% 162.46/162.13 inference(rename_variables,[],[3336])).
% 162.46/162.13 cnf(10710,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x107101,a877)),f196(f891(x107101,a877))),x107102))),
% 162.46/162.13 inference(rename_variables,[],[3754])).
% 162.46/162.13 cnf(10713,plain,
% 162.46/162.13 (P24(f331(f256(f891(x107131,a877)),x107132))),
% 162.46/162.13 inference(rename_variables,[],[3379])).
% 162.46/162.13 cnf(10715,plain,
% 162.46/162.13 (~P24(f331(f331(f247(a883),f331(f331(f82(a883),f331(a118,x107151)),f331(a118,x107151))),x107151))),
% 162.46/162.13 inference(scs_inference,[],[4485,10246,10249,10259,10270,10378,10381,10384,10487,4500,10471,3102,3270,10243,10252,10313,10316,10405,10408,3146,3210,3176,3154,3243,3265,10512,4575,4509,10304,3205,10370,4080,4590,3225,3677,3617,3385,10389,10507,10578,10639,10642,3758,3296,4557,10281,10284,10310,4571,3745,3525,3889,3342,3343,3317,4554,4505,4035,3313,10398,10494,10625,3314,3315,10427,10482,3316,4553,10344,10436,10549,3472,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,3336,4564,4543,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,4589,3754,3582,10631,10634,4581,3788,4579,10323,10326,10662,3756,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337])).
% 162.46/162.13 cnf(10716,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x107161),f331(f331(f82(a883),x107161),x107161)))),
% 162.46/162.13 inference(rename_variables,[],[3582])).
% 162.46/162.13 cnf(10720,plain,
% 162.46/162.13 (E(f331(f172(x107201),f243(x107202,x107203,f331(f331(f137(x107201),f331(f172(x107201),x107204)),f331(f331(f154(x107201),x107205),f119(x107201))),x107206,f199(x107203))),f331(f331(f154(x107201),x107205),x107204))),
% 162.46/162.13 inference(scs_inference,[],[4485,10246,10249,10259,10270,10378,10381,10384,10487,4500,10471,3102,3270,10243,10252,10313,10316,10405,10408,3146,3966,3210,3176,3154,3243,3265,10512,4575,4509,10304,3205,10370,4080,4590,3225,3677,3617,3385,10389,10507,10578,10639,10642,3758,3296,4557,10281,10284,10310,4571,3745,3525,3889,3342,3343,3317,4554,4505,4035,3313,10398,10494,10625,3314,3315,10427,10482,3316,4553,10344,10436,10549,3472,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,3336,4564,4543,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,4589,3754,3582,10631,10634,4581,3788,4579,10323,10326,10662,3756,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376])).
% 162.46/162.13 cnf(10733,plain,
% 162.46/162.13 (~P24(f331(f331(f247(a883),f331(a118,f331(a118,f331(f331(f81(a883),x107331),x107332)))),f331(a118,x107332)))),
% 162.46/162.13 inference(scs_inference,[],[4485,10246,10249,10259,10270,10378,10381,10384,10487,4500,10471,3102,3270,10243,10252,10313,10316,10405,10408,3146,3966,3210,3176,3154,3243,3265,10512,4575,4509,10304,3205,10370,4080,4590,3225,3677,3617,3385,10389,10507,10578,10639,10642,10680,3758,3296,4557,10281,10284,10310,4571,3745,3525,3889,3342,3343,3317,4554,4505,4035,3313,10398,10494,10625,3314,3315,10427,10482,3316,4553,10344,10436,10549,3472,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,3336,4564,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,4589,3754,3582,10631,10634,4581,3788,4579,10323,10326,10662,3756,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384])).
% 162.46/162.13 cnf(10756,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x107561),x107561))),
% 162.46/162.13 inference(rename_variables,[],[3314])).
% 162.46/162.13 cnf(10767,plain,
% 162.46/162.13 (~P24(f331(f331(f196(f891(x107671,f891(x107672,a877))),x107673),x107674))),
% 162.46/162.13 inference(rename_variables,[],[4583])).
% 162.46/162.13 cnf(10774,plain,
% 162.46/162.13 (P24(f331(f331(f248(a883),x107741),f331(a118,x107741)))),
% 162.46/162.13 inference(rename_variables,[],[3385])).
% 162.46/162.13 cnf(10776,plain,
% 162.46/162.13 (P24(f331(f331(f248(a1),f331(f331(f22(a1),x107761),f79(a1))),x107761))),
% 162.46/162.13 inference(scs_inference,[],[4485,10246,10249,10259,10270,10378,10381,10384,10487,4500,10471,3102,3270,10243,10252,10313,10316,10405,10408,3146,3966,3210,3176,3154,3243,3265,10512,4575,4509,10304,3205,10370,4080,3942,4590,3225,3677,3617,3385,10389,10507,10578,10639,10642,10680,3758,3296,4557,10281,10284,10310,4571,3745,3525,3889,3342,3343,3317,4554,4505,4035,3313,10398,10494,10625,3314,10756,3315,10427,10482,10692,3316,4553,10344,10436,10549,3472,4569,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,10671,3336,4564,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,4589,3754,3582,10631,10634,4581,4583,3788,4579,10323,10326,10662,3756,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636])).
% 162.46/162.13 cnf(10777,plain,
% 162.46/162.13 (P24(f331(f331(f247(a1),x107771),x107771))),
% 162.46/162.13 inference(rename_variables,[],[3315])).
% 162.46/162.13 cnf(10782,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x107821),f2(a883)))),
% 162.46/162.13 inference(rename_variables,[],[4557])).
% 162.46/162.13 cnf(10795,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x107951),f2(a883)))),
% 162.46/162.13 inference(rename_variables,[],[4557])).
% 162.46/162.13 cnf(10798,plain,
% 162.46/162.13 (~P24(f331(f331(f248(f891(x107981,a877)),x107982),f196(f891(x107981,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4576])).
% 162.46/162.13 cnf(10801,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x108011),x108011))),
% 162.46/162.13 inference(rename_variables,[],[3314])).
% 162.46/162.13 cnf(10804,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x108041),x108041))),
% 162.46/162.13 inference(rename_variables,[],[3314])).
% 162.46/162.13 cnf(10818,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x108181),f331(f331(f22(a883),x108181),x108182)))),
% 162.46/162.13 inference(scs_inference,[],[4485,10246,10249,10259,10270,10378,10381,10384,10487,4500,10471,3102,3270,10243,10252,10313,10316,10405,10408,3146,3966,3210,3176,3154,3243,3265,10512,4575,4509,10304,3205,10370,4080,3942,4590,3225,3677,3617,3385,10389,10507,10578,10639,10642,10680,3758,3296,4557,10281,10284,10310,10782,4571,3745,3525,3889,3342,3343,3317,4554,4505,4046,4035,4576,3313,10398,10494,10625,3314,10756,10801,10804,3315,10427,10482,10692,3316,4553,10344,10436,10549,10573,3472,4569,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,10671,3336,4564,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,4589,3754,3582,10631,10634,4581,4583,3788,4579,10323,10326,10662,3756,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793])).
% 162.46/162.13 cnf(10819,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x108191),x108191))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(10828,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x108281),x108282),f196(f891(x108281,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(10837,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x108371),x108371))),
% 162.46/162.13 inference(rename_variables,[],[3314])).
% 162.46/162.13 cnf(10840,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x108401),x108402),f196(f891(x108401,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(10843,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x108431,a877)),f331(f310(x108432,x108431,x108433),f331(f311(x108432,x108431,x108433),x108434))),x108434))),
% 162.46/162.13 inference(rename_variables,[],[4178])).
% 162.46/162.13 cnf(10850,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x108501,a877)),f331(f175(x108501),f331(f139(x108501,x108502),x108503))),f331(f175(x108501),x108503)))),
% 162.46/162.13 inference(rename_variables,[],[3951])).
% 162.46/162.13 cnf(10853,plain,
% 162.46/162.13 (E(f331(f310(x108531,x108531,f5(x108531)),x108532),x108532)),
% 162.46/162.13 inference(rename_variables,[],[3375])).
% 162.46/162.13 cnf(10860,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),f2(a883)),x108601))),
% 162.46/162.13 inference(rename_variables,[],[3336])).
% 162.46/162.13 cnf(10863,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x108631),x108631))),
% 162.46/162.13 inference(rename_variables,[],[3314])).
% 162.46/162.13 cnf(10866,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x108661),x108661))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(10869,plain,
% 162.46/162.13 (~P24(f331(f331(f196(f891(x108691,f891(x108692,a877))),x108693),x108694))),
% 162.46/162.13 inference(rename_variables,[],[4583])).
% 162.46/162.13 cnf(10876,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x108761),x108761))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(10887,plain,
% 162.46/162.13 (P24(f331(f331(f248(a883),x108871),f331(a118,f331(f331(f81(a883),x108872),x108871))))),
% 162.46/162.13 inference(rename_variables,[],[3756])).
% 162.46/162.13 cnf(10890,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x108901),f331(f331(f82(a883),x108901),x108901)))),
% 162.46/162.13 inference(rename_variables,[],[3582])).
% 162.46/162.13 cnf(10900,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x109001),x109001))),
% 162.46/162.13 inference(rename_variables,[],[3314])).
% 162.46/162.13 cnf(10903,plain,
% 162.46/162.13 (P24(f331(f331(f247(a1),x109031),x109031))),
% 162.46/162.13 inference(rename_variables,[],[3315])).
% 162.46/162.13 cnf(10906,plain,
% 162.46/162.13 (~E(f331(a118,x109061),x109061)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(10911,plain,
% 162.46/162.13 (P24(f331(f331(f333(x109111),x109112),f256(f891(x109111,a877))))),
% 162.46/162.13 inference(rename_variables,[],[3472])).
% 162.46/162.13 cnf(10916,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x109161),f2(a883)))),
% 162.46/162.13 inference(rename_variables,[],[4557])).
% 162.46/162.13 cnf(10918,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x109181,a877)),x109182),f40(f891(x109181,a877),f331(f308(x109181),x109182))))),
% 162.46/162.13 inference(scs_inference,[],[4582,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,4500,10471,3102,3270,10243,10252,10313,10316,10405,10408,3146,3966,3210,3176,3154,3375,3243,3265,10512,4575,4509,10304,3205,10370,4080,3942,4590,3225,3516,3677,3617,3385,10389,10507,10578,10639,10642,10680,10774,3758,3296,4557,10281,10284,10310,10782,10795,4571,3745,3525,3889,3342,3343,3317,4554,4505,4046,3951,10850,3678,4035,4576,3313,10398,10494,10625,3314,10756,10801,10804,10837,10863,3315,10427,10482,10692,10777,3316,4553,10344,10436,10549,10573,10819,10866,3472,10645,4569,10828,10840,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,10671,3336,10707,4564,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,4589,3754,3582,10631,10634,10716,10890,4581,4583,10767,4178,3788,4579,10323,10326,10662,3756,10628,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484])).
% 162.46/162.13 cnf(10931,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),f2(a883)),x109311))),
% 162.46/162.13 inference(rename_variables,[],[3336])).
% 162.46/162.13 cnf(10938,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x109381),x109381))),
% 162.46/162.13 inference(rename_variables,[],[3314])).
% 162.46/162.13 cnf(10947,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x109471),x109472),f196(f891(x109471,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(10951,plain,
% 162.46/162.13 (E(f331(f331(f108(f891(x109511,a877)),f331(f331(f108(f891(x109511,a877)),x109512),f331(f80(f891(x109511,a877)),x109513))),x109513),f196(f891(x109511,a877)))),
% 162.46/162.13 inference(scs_inference,[],[4582,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,4500,10471,3102,3270,10243,10252,10313,10316,10405,10408,3146,3966,3210,3176,3154,3375,3243,3265,10512,4575,4509,10304,3205,10370,4080,3942,4590,3225,3516,3677,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,3758,3296,4557,10281,10284,10310,10782,10795,4571,3745,3525,3889,3342,3343,3317,4554,4505,4046,3951,10850,3678,4035,4576,3313,10398,10494,10625,3314,10756,10801,10804,10837,10863,10900,3315,10427,10482,10692,10777,3316,4553,10344,10436,10549,10573,10819,10866,3472,10645,10911,4569,10828,10840,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,10671,3336,10707,10860,4564,3835,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,4589,3754,3582,10631,10634,10716,10890,4581,4583,10767,4178,3788,4579,10323,10326,10662,3756,10628,4020,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758])).
% 162.46/162.13 cnf(10954,plain,
% 162.46/162.13 (P24(f331(f331(f333(f884(x109541)),x109542),f164(x109541,f256(f891(x109541,a877)))))),
% 162.46/162.13 inference(scs_inference,[],[4582,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,4500,10471,3102,3270,10243,10252,10313,10316,10405,10408,3146,3966,3210,3176,3154,3375,3243,3265,10512,4575,4509,10304,3205,10370,4080,3942,4590,3225,3516,3677,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,3758,3296,4557,10281,10284,10310,10782,10795,4571,3745,3525,3889,3342,3343,3317,4554,4505,4046,3951,10850,3678,4035,4576,3313,10398,10494,10625,3314,10756,10801,10804,10837,10863,10900,3315,10427,10482,10692,10777,3316,4553,10344,10436,10549,10573,10819,10866,3472,10645,10911,4569,10828,10840,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,10671,3336,10707,10860,4564,3835,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,4589,3754,3582,10631,10634,10716,10890,4581,4583,10767,4178,3788,4579,10323,10326,10662,3756,10628,4020,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768])).
% 162.46/162.13 cnf(10955,plain,
% 162.46/162.13 (P24(f331(f331(f333(x109551),x109552),f256(f891(x109551,a877))))),
% 162.46/162.13 inference(rename_variables,[],[3472])).
% 162.46/162.13 cnf(10958,plain,
% 162.46/162.13 (~P24(f331(f331(f333(f890(f884(x109581),f884(x109581))),f331(f331(f261(f884(x109581),f884(x109581)),x109582),f119(x109581))),f148(x109581,x109583)))),
% 162.46/162.13 inference(rename_variables,[],[4590])).
% 162.46/162.13 cnf(10964,plain,
% 162.46/162.13 (~P24(f331(f331(f333(f890(x109641,x109641)),x109642),f258(x109641,f196(f891(x109641,a877)))))),
% 162.46/162.13 inference(scs_inference,[],[4582,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,4500,10471,3102,3270,10243,10252,10313,10316,10405,10408,3146,3966,3210,3176,3154,3375,3243,3265,10512,4575,4509,10304,3205,10370,4080,3942,4590,3225,3516,3677,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,3758,3296,4557,10281,10284,10310,10782,10795,4571,3745,3525,3889,3342,3343,3317,4554,4505,4046,3951,10850,3678,4035,4576,3313,10398,10494,10625,3314,10756,10801,10804,10837,10863,10900,3315,10427,10482,10692,10777,3316,4553,10344,10436,10549,10573,10819,10866,3472,10645,10911,4569,10828,10840,10947,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,10671,3336,10707,10860,4564,3835,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,4589,3754,3582,10631,10634,10716,10890,4581,4583,10767,4178,3788,4579,10323,10326,10662,3756,10628,4020,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896])).
% 162.46/162.13 cnf(10965,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x109651),x109652),f196(f891(x109651,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(10967,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x109671),x109672),f331(f311(x109671,x109673,x109674),f196(f891(x109673,a877)))))),
% 162.46/162.13 inference(scs_inference,[],[4582,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,4500,10471,3102,3270,10243,10252,10313,10316,10405,10408,3146,3966,3210,3176,3154,3375,3243,3265,10512,4575,4509,10304,3205,10370,4080,3942,4590,3225,3516,3677,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,3758,3296,4557,10281,10284,10310,10782,10795,4571,3745,3525,3889,3342,3343,3317,4554,4505,4046,3951,10850,3678,4035,4576,3313,10398,10494,10625,3314,10756,10801,10804,10837,10863,10900,3315,10427,10482,10692,10777,3316,4553,10344,10436,10549,10573,10819,10866,3472,10645,10911,4569,10828,10840,10947,10965,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,10671,3336,10707,10860,4564,3835,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,4589,3754,3582,10631,10634,10716,10890,4581,4583,10767,4178,3788,4579,10323,10326,10662,3756,10628,4020,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925])).
% 162.46/162.13 cnf(10968,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x109681),x109682),f196(f891(x109681,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(10971,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x109711,a877)),x109712),f331(f331(f309(x109711),x109713),x109712)))),
% 162.46/162.13 inference(rename_variables,[],[3752])).
% 162.46/162.13 cnf(10974,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x109741),x109741))),
% 162.46/162.13 inference(rename_variables,[],[3314])).
% 162.46/162.13 cnf(10977,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x109771,a877)),x109772),f331(f331(f309(x109771),x109773),x109772)))),
% 162.46/162.13 inference(rename_variables,[],[3752])).
% 162.46/162.13 cnf(10979,plain,
% 162.46/162.13 (P35(x109791,x109792,x109793,f120(x109791,f119(x109791)),f119(x109792))),
% 162.46/162.13 inference(scs_inference,[],[4582,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,4500,10471,3102,3156,3270,10243,10252,10313,10316,10405,10408,3146,3966,3210,3176,3154,3375,3243,3265,10512,4575,4509,10304,3205,10370,4080,3942,4590,3225,3516,3677,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,3758,3296,4557,10281,10284,10310,10782,10795,4571,3745,3525,3889,3342,3343,3317,4554,4505,4046,3951,10850,3678,4035,4576,3313,10398,10494,10625,3314,10756,10801,10804,10837,10863,10900,10938,3315,10427,10482,10692,10777,3316,4553,10344,10436,10549,10573,10819,10866,3472,10645,10911,4569,10828,10840,10947,10965,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,10671,3336,10707,10860,4564,3835,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,4589,3752,10971,3754,3582,10631,10634,10716,10890,4581,4583,10767,4178,3788,4579,10323,10326,10662,3756,10628,4020,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035])).
% 162.46/162.13 cnf(10992,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x109921,a877)),x109922),f331(f331(f309(x109921),x109923),x109922)))),
% 162.46/162.13 inference(rename_variables,[],[3752])).
% 162.46/162.13 cnf(10997,plain,
% 162.46/162.13 (~P24(f331(f63(x109971,x109972,f196(f891(x109971,a877))),x109973))),
% 162.46/162.13 inference(rename_variables,[],[4578])).
% 162.46/162.13 cnf(11001,plain,
% 162.46/162.13 (~P24(f331(f331(f333(f890(a883,a883)),f331(f331(f261(a883,a883),f331(a118,x110011)),x110011)),f307(a883,a321)))),
% 162.46/162.13 inference(scs_inference,[],[4582,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,4500,10471,3102,3156,3270,10243,10252,10313,10316,10405,10408,3146,3966,3210,3176,3154,3375,3243,3265,10512,4575,4509,10304,3205,10370,4080,3942,4590,3225,3516,3677,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,3758,3296,4557,10281,10284,10310,10782,10795,4571,3745,3525,3889,3342,3343,3317,4554,4505,4046,3951,10850,3678,4035,4576,3313,10398,10494,10625,3314,10756,10801,10804,10837,10863,10900,10938,3315,10427,10482,10692,10777,3316,4553,10344,10436,10549,10573,10819,10866,3472,10645,10911,10955,4569,10828,10840,10947,10965,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,10671,3336,10707,10860,4564,3835,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,10589,4589,3906,3752,10971,10977,3754,3582,10631,10634,10716,10890,4581,4583,10767,4178,3788,4579,10323,10326,10662,3756,10628,4020,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358])).
% 162.46/162.13 cnf(11010,plain,
% 162.46/162.13 (P24(f331(f331(f248(a883),x110101),f331(a118,x110101)))),
% 162.46/162.13 inference(rename_variables,[],[3385])).
% 162.46/162.13 cnf(11017,plain,
% 162.46/162.13 (E(f331(f74(x110171,x110172,x110171,x110173),f35(x110171)),x110173)),
% 162.46/162.13 inference(rename_variables,[],[3770])).
% 162.46/162.13 cnf(11020,plain,
% 162.46/162.13 (~E(f331(f310(x110201,f891(x110201,a877),x110202),x110203),f331(f308(x110201),x110203))),
% 162.46/162.13 inference(rename_variables,[],[4567])).
% 162.46/162.13 cnf(11023,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x110231),x110232),f196(f891(x110231,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(11026,plain,
% 162.46/162.13 (P24(f331(f331(f333(f890(x110261,x110261)),f331(f331(f261(x110261,x110261),x110262),x110262)),f307(x110261,x110263)))),
% 162.46/162.13 inference(rename_variables,[],[3942])).
% 162.46/162.13 cnf(11029,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x110291,a877)),f331(f175(x110291),f173(x110291,x110292,x110293))),f331(f175(x110291),x110293)))),
% 162.46/162.13 inference(rename_variables,[],[4001])).
% 162.46/162.13 cnf(11032,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x110321,a877)),x110322),f256(f891(x110321,a877))))),
% 162.46/162.13 inference(rename_variables,[],[3695])).
% 162.46/162.13 cnf(11048,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x110481,a877)),f196(f891(x110481,a877))),x110482))),
% 162.46/162.13 inference(rename_variables,[],[3754])).
% 162.46/162.13 cnf(11059,plain,
% 162.46/162.13 (~P24(f331(f331(f333(f890(f884(x110591),f884(x110591))),f331(f331(f261(f884(x110591),f884(x110591)),x110592),f119(x110591))),f150(x110591,x110593)))),
% 162.46/162.13 inference(rename_variables,[],[4591])).
% 162.46/162.13 cnf(11070,plain,
% 162.46/162.13 (~E(f331(a118,x110701),x110701)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(11073,plain,
% 162.46/162.13 (~E(f331(a118,x110731),x110731)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(11075,plain,
% 162.46/162.13 (P24(f331(f331(f333(f890(f884(x110751),f884(x110751))),f331(f331(f261(f884(x110751),f884(x110751)),f119(x110751)),f119(x110751))),f331(f331(f288(f884(x110751),f884(x110751),f884(x110751)),f161(x110751,x110752)),f307(f884(x110751),f161(x110751,x110752)))))),
% 162.46/162.13 inference(scs_inference,[],[4582,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,4500,10471,3102,3156,3270,10243,10252,10313,10316,10405,10408,3770,3146,3966,3210,3176,3154,3375,3243,3265,10512,4575,3939,4509,10304,4567,3205,10370,4080,3942,11026,4590,10958,4591,3225,3516,3677,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,3758,3296,4557,10281,10284,10310,10782,10795,10916,4571,3745,3525,3889,3342,3343,3317,4554,4505,4046,3951,10850,4001,3678,4035,3695,4576,3313,10398,10494,10625,3314,10756,10801,10804,10837,10863,10900,10938,3315,10427,10482,10692,10777,3316,4553,10344,10436,10549,10573,10819,10866,3472,10645,10911,10955,4569,10828,10840,10947,10965,10968,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,10671,3336,10707,10860,4564,3835,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,10589,4589,3906,3752,10971,10977,3754,10710,3582,10631,10634,10716,10890,4581,4583,10767,4178,3788,4579,10323,10326,10662,3756,10628,4020,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590])).
% 162.46/162.13 cnf(11085,plain,
% 162.46/162.13 (P21(x110851,x110851,f5(x110851),x110852)),
% 162.46/162.13 inference(rename_variables,[],[3553])).
% 162.46/162.13 cnf(11090,plain,
% 162.46/162.13 (~E(f331(f310(x110901,f891(x110901,a877),x110902),x110903),f331(f308(x110901),x110903))),
% 162.46/162.13 inference(rename_variables,[],[4567])).
% 162.46/162.13 cnf(11095,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x110951,a877)),x110952),f256(f891(x110951,a877))))),
% 162.46/162.13 inference(rename_variables,[],[3695])).
% 162.46/162.13 cnf(11109,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x111091),x111092),f196(f891(x111091,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(11112,plain,
% 162.46/162.13 (~P24(f331(f331(f247(a883),f331(a118,x111121)),x111121))),
% 162.46/162.13 inference(rename_variables,[],[4566])).
% 162.46/162.13 cnf(11117,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x111171),x111172),f196(f891(x111171,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(11129,plain,
% 162.46/162.13 (~P24(f331(f331(f333(a883),f331(a118,f331(f145(a883,a883,f81(a883),f2(a883)),x111291))),f331(f175(a883),x111291)))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,4500,10471,10564,3102,3156,3270,10243,10252,10313,10316,10405,10408,3770,3146,3966,3210,3176,3154,3375,3243,3265,10512,4575,3939,4509,10304,4567,11020,3421,3205,10370,4080,3942,11026,4590,10958,4591,3225,3516,3677,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,11010,3758,3296,4557,10281,10284,10310,10782,10795,10916,4571,3745,3525,3889,3342,3343,3317,4554,4505,4046,3951,10850,4001,3678,4035,3695,11032,4576,3313,10398,10494,10625,3314,10756,10801,10804,10837,10863,10900,10938,3315,10427,10482,10692,10777,3316,4553,10344,10436,10549,10573,10819,10866,3472,10645,10911,10955,4569,10828,10840,10947,10965,10968,11023,11109,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,10671,11112,3336,10707,10860,4564,3835,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,10589,4589,3906,3752,10971,10977,3754,10710,3582,10631,10634,10716,10890,4581,4583,10767,4178,3788,4579,10323,10326,10662,3756,10628,4020,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802])).
% 162.46/162.13 cnf(11130,plain,
% 162.46/162.13 (~P24(f331(f331(f247(a883),f331(a118,x111301)),x111301))),
% 162.46/162.13 inference(rename_variables,[],[4566])).
% 162.46/162.13 cnf(11133,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x111331),x111332),f196(f891(x111331,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(11141,plain,
% 162.46/162.13 (E(f331(f139(x111411,f256(f891(x111412,a877))),f732(x111413,x111414,f331(f331(f154(x111411),x111414),x111413),f256(f891(x111412,a877)),x111411)),x111413)),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,4500,10471,10564,3102,3156,3270,10243,10252,10313,10316,10405,10408,3770,3146,3966,3210,3176,3154,3375,3243,3265,10512,4575,3939,4509,10304,4567,11020,3421,3205,10370,4080,3942,11026,4590,10958,4591,3225,3516,3677,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,11010,3758,3296,4557,10281,10284,10310,10782,10795,10916,4571,3745,3525,3889,3342,3343,3317,4554,4505,4046,3951,10850,4001,3678,4035,3695,11032,4576,3313,10398,10494,10625,3314,10756,10801,10804,10837,10863,10900,10938,3315,10427,10482,10692,10777,3316,4553,10344,10436,10549,10573,10819,10866,3472,10645,10911,10955,4569,10828,10840,10947,10965,10968,11023,11109,11117,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,10671,11112,3336,10707,10860,4564,3835,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,10589,4589,3906,3752,10971,10977,3754,10710,3582,10631,10634,10716,10890,4581,4583,10767,4178,3788,4579,10323,10326,10662,3756,10628,4020,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878])).
% 162.46/162.13 cnf(11143,plain,
% 162.46/162.13 (E(f331(x111431,f543(f331(x111431,x111432),f331(f239(x111433),x111432),x111431,x111434,x111433)),f331(x111431,x111432))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,4500,10471,10564,3102,3156,3270,10243,10252,10313,10316,10405,10408,3770,3146,3966,3210,3176,3154,3375,3243,3265,10512,3420,4575,3939,4509,10304,4567,11020,3421,3205,10370,4080,3942,11026,4590,10958,4591,3225,3516,3677,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,11010,3758,3296,4557,10281,10284,10310,10782,10795,10916,4571,3745,3525,3889,3342,3343,3317,4554,4505,4046,3951,10850,4001,3678,4035,3695,11032,4576,3313,10398,10494,10625,3314,10756,10801,10804,10837,10863,10900,10938,3315,10427,10482,10692,10777,3316,4553,10344,10436,10549,10573,10819,10866,3472,10645,10911,10955,4569,10828,10840,10947,10965,10968,11023,11109,11117,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,10671,11112,3336,10707,10860,4564,3835,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,10589,4589,3906,3752,10971,10977,3754,10710,3582,10631,10634,10716,10890,4581,4583,10767,4178,3788,4579,10323,10326,10662,3756,10628,4020,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880])).
% 162.46/162.13 cnf(11152,plain,
% 162.46/162.13 (P24(f331(f331(f333(f890(x111521,x111521)),f331(f331(f261(x111521,x111521),x111522),x111522)),f307(x111521,x111523)))),
% 162.46/162.13 inference(rename_variables,[],[3942])).
% 162.46/162.13 cnf(11157,plain,
% 162.46/162.13 (~P24(f331(f331(f333(f890(f884(x111571),f884(x111571))),f331(f331(f261(f884(x111571),f884(x111571)),x111572),f119(x111571))),f148(x111571,x111573)))),
% 162.46/162.13 inference(rename_variables,[],[4590])).
% 162.46/162.13 cnf(11160,plain,
% 162.46/162.13 (~P24(f331(f331(f333(f890(f884(x111601),f884(x111601))),f331(f331(f261(f884(x111601),f884(x111601)),x111602),f119(x111601))),f150(x111601,x111603)))),
% 162.46/162.13 inference(rename_variables,[],[4591])).
% 162.46/162.13 cnf(11163,plain,
% 162.46/162.13 (~P24(f331(f331(f333(f890(f884(x111631),f884(x111631))),f331(f331(f261(f884(x111631),f884(x111631)),x111632),f119(x111631))),f160(x111631,x111633)))),
% 162.46/162.13 inference(rename_variables,[],[4592])).
% 162.46/162.13 cnf(11168,plain,
% 162.46/162.13 (~P24(f331(f331(f248(f891(x111681,a877)),x111682),f196(f891(x111681,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4576])).
% 162.46/162.13 cnf(11171,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x111711),x111712),f196(f891(x111711,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(11175,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x111751,a877)),x111752),f331(f331(f107(f891(x111751,a877)),x111753),f256(f891(x111751,a877)))))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,4500,10471,10564,3102,3156,3270,10243,10252,10313,10316,10405,10408,3770,3146,3966,3210,3176,3154,3375,3243,3265,10512,3420,4575,3939,4509,10304,4567,11020,3421,3205,10370,4080,3942,11026,4590,10958,11157,4591,11059,4592,3225,3516,3677,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,11010,3758,3296,4557,10281,10284,10310,10782,10795,10916,4571,3745,3525,3889,3342,3343,3317,4554,4505,4046,3951,10850,4001,3678,4035,3695,11032,11095,4576,10798,3313,10398,10494,10625,3314,10756,10801,10804,10837,10863,10900,10938,3315,10427,10482,10692,10777,3316,4553,10344,10436,10549,10573,10819,10866,3472,10645,10911,10955,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,10671,11112,3336,10707,10860,4564,3835,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,10589,4589,3906,3752,10971,10977,3754,10710,3582,10631,10634,10716,10890,4581,4583,10767,4178,3788,4579,10323,10326,10662,3756,10628,4020,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064])).
% 162.46/162.13 cnf(11176,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x111761,a877)),x111762),f256(f891(x111761,a877))))),
% 162.46/162.13 inference(rename_variables,[],[3695])).
% 162.46/162.13 cnf(11179,plain,
% 162.46/162.13 (~P24(f331(f331(f196(f891(x111791,f891(x111792,a877))),x111793),x111794))),
% 162.46/162.13 inference(rename_variables,[],[4583])).
% 162.46/162.13 cnf(11188,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x111881),x111882),f196(f891(x111881,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(11191,plain,
% 162.46/162.13 (~P24(f331(f331(f333(f890(x111911,x111911)),f331(f331(f261(x111911,x111911),x111912),x111913)),f156(x111911,f119(f891(x111911,a883)))))),
% 162.46/162.13 inference(rename_variables,[],[4589])).
% 162.46/162.13 cnf(11194,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x111941,a877)),x111942),x111942))),
% 162.46/162.13 inference(rename_variables,[],[3613])).
% 162.46/162.13 cnf(11197,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x111971),x111972),f196(f891(x111971,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(11199,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x111991,a877)),f331(f285(x111992,x111991,f196(f891(f890(x111992,x111991),a877))),x111993)),x111994))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,4500,10471,10564,3102,3156,3270,10243,10252,10313,10316,10405,10408,3770,3146,3966,3210,3176,3154,3375,3243,3265,10512,3420,4575,3939,4509,10304,4567,11020,3421,3205,10370,4080,3942,11026,4590,10958,11157,4591,11059,4592,3225,3516,3677,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,11010,3758,3296,4557,10281,10284,10310,10782,10795,10916,4571,3745,3525,3889,3342,3343,3317,4554,4505,4046,3951,10850,4001,3678,4035,3695,11032,11095,4576,10798,3313,10398,10494,10625,3314,10756,10801,10804,10837,10863,10900,10938,3315,10427,10482,10692,10777,3316,4553,10344,10436,10549,10573,10819,10866,3472,10645,10911,10955,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,10671,11112,3336,10707,10860,4564,3835,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,10589,4589,3906,3752,10971,10977,3613,3754,10710,11048,3582,10631,10634,10716,10890,4581,4583,10767,10869,4178,3788,4579,10323,10326,10662,3756,10628,4020,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246])).
% 162.46/162.13 cnf(11200,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x112001,a877)),f196(f891(x112001,a877))),x112002))),
% 162.46/162.13 inference(rename_variables,[],[3754])).
% 162.46/162.13 cnf(11203,plain,
% 162.46/162.13 (P24(f331(f331(f333(f890(x112031,x112031)),f331(f331(f261(x112031,x112031),x112032),x112032)),f307(x112031,x112033)))),
% 162.46/162.13 inference(rename_variables,[],[3942])).
% 162.46/162.13 cnf(11205,plain,
% 162.46/162.13 (~P35(x112051,x112052,x112053,f331(f331(f157(x112054,x112051),x112055),f331(a118,f119(x112054))),f119(x112052))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,4500,10471,10564,3102,3156,3270,10243,10252,10313,10316,10405,10408,3770,3146,3966,3210,3176,3154,3375,3243,3265,10512,3420,4575,3939,4509,10304,4567,11020,3421,3205,10370,4080,3942,11026,11152,4590,10958,11157,4591,11059,4592,3225,3516,3677,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,11010,3758,3296,4557,10281,10284,10310,10782,10795,10916,4571,3745,3525,3889,3342,3343,3317,4554,4505,4046,3951,10850,4001,3678,4035,3695,11032,11095,4576,10798,3313,10398,10494,10625,3314,10756,10801,10804,10837,10863,10900,10938,3315,10427,10482,10692,10777,3316,4553,10344,10436,10549,10573,10819,10866,3472,10645,10911,10955,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,10671,11112,3336,10707,10860,4564,3835,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,10589,4589,3906,3752,10971,10977,3613,3754,10710,11048,3582,10631,10634,10716,10890,4581,4583,10767,10869,4178,3788,4579,10323,10326,10662,3756,10628,4020,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255])).
% 162.46/162.13 cnf(11207,plain,
% 162.46/162.13 (~E(f331(f331(f108(f891(f890(f884(x112071),f884(x112071)),a877)),f331(f286(f884(x112071),f884(x112071)),f161(x112071,x112072))),f307(f884(x112071),f161(x112071,x112072))),f196(f891(f890(f884(x112071),f884(x112071)),a877)))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,4500,10471,10564,3102,3156,3270,10243,10252,10313,10316,10405,10408,3770,3146,3966,3210,3176,3154,3375,3243,3265,10512,3420,4575,3939,4509,10304,4567,11020,3421,3205,10370,4080,3942,11026,11152,4590,10958,11157,4591,11059,4592,3225,3516,3677,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,11010,3758,3296,4557,10281,10284,10310,10782,10795,10916,4571,3745,3525,3889,3342,3343,3317,4554,4505,4046,3951,10850,4001,3678,4035,3695,11032,11095,4576,10798,3313,10398,10494,10625,3314,10756,10801,10804,10837,10863,10900,10938,3315,10427,10482,10692,10777,3316,4553,10344,10436,10549,10573,10819,10866,3472,10645,10911,10955,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,10671,11112,3336,10707,10860,4564,3835,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,10589,4589,3906,3752,10971,10977,3613,3754,10710,11048,3582,10631,10634,10716,10890,4581,4583,10767,10869,4178,3788,4579,10323,10326,10662,3756,10628,4020,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280])).
% 162.46/162.13 cnf(11214,plain,
% 162.46/162.13 (~P24(f331(f331(f333(f890(f884(x112141),f884(x112141))),f331(f331(f261(f884(x112141),f884(x112141)),x112142),f119(x112141))),f160(x112141,x112143)))),
% 162.46/162.13 inference(rename_variables,[],[4592])).
% 162.46/162.13 cnf(11217,plain,
% 162.46/162.13 (~P24(f331(f331(f333(f890(f884(x112171),f884(x112171))),f331(f331(f261(f884(x112171),f884(x112171)),f119(x112171)),x112172)),f148(x112171,x112173)))),
% 162.46/162.13 inference(rename_variables,[],[4593])).
% 162.46/162.13 cnf(11225,plain,
% 162.46/162.13 (P24(f331(f331(f333(x112251),x112252),f256(f891(x112251,a877))))),
% 162.46/162.13 inference(rename_variables,[],[3472])).
% 162.46/162.13 cnf(11230,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x112301,a877)),f196(f891(x112301,a877))),x112302))),
% 162.46/162.13 inference(rename_variables,[],[3754])).
% 162.46/162.13 cnf(11233,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x112331),x112332),f196(f891(x112331,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(11236,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x112361,a877)),x112362),f256(f891(x112361,a877))))),
% 162.46/162.13 inference(rename_variables,[],[3695])).
% 162.46/162.13 cnf(11240,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x112401,a877)),f331(f285(x112402,x112401,x112403),f196(f891(x112402,a877)))),x112404))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,4500,10471,10564,3102,3156,3270,10243,10252,10313,10316,10405,10408,3770,3146,3966,3210,3176,3154,3375,3243,3265,10512,3420,4575,3939,4509,10304,4567,11020,3421,3205,10370,4080,3942,11026,11152,4590,10958,11157,4591,11059,4592,11163,4593,4594,3225,3516,3677,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,11010,3758,3296,4557,10281,10284,10310,10782,10795,10916,4571,3745,3525,3889,3342,3343,3317,4554,4505,4046,3951,10850,4001,3678,4035,3695,11032,11095,11176,4576,10798,11168,3313,10398,10494,10625,3314,10756,10801,10804,10837,10863,10900,10938,3315,10427,10482,10692,10777,3316,4553,10344,10436,10549,10573,10819,10866,3472,10645,10911,10955,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,3379,10674,10704,3410,3828,3767,10347,4566,10301,10668,10671,11112,3336,10707,10860,4564,3835,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,10589,4589,3906,3752,10971,10977,3613,3754,10710,11048,11200,11230,3582,10631,10634,10716,10890,4581,4583,10767,10869,4178,4086,3788,4579,10323,10326,10662,3756,10628,4020,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522])).
% 162.46/162.13 cnf(11241,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x112411,a877)),f196(f891(x112411,a877))),x112412))),
% 162.46/162.13 inference(rename_variables,[],[3754])).
% 162.46/162.13 cnf(11254,plain,
% 162.46/162.13 (P24(f331(f256(f891(x112541,a877)),x112542))),
% 162.46/162.13 inference(rename_variables,[],[3379])).
% 162.46/162.13 cnf(11262,plain,
% 162.46/162.13 (~P24(f331(f331(f333(f890(f884(x112621),f884(x112621))),f331(f331(f261(f884(x112621),f884(x112621)),x112622),f119(x112621))),f148(x112621,x112623)))),
% 162.46/162.13 inference(rename_variables,[],[4590])).
% 162.46/162.13 cnf(11265,plain,
% 162.46/162.13 (~P24(f331(f331(f333(f890(f884(x112651),f884(x112651))),f331(f331(f261(f884(x112651),f884(x112651)),x112652),f119(x112651))),f150(x112651,x112653)))),
% 162.46/162.13 inference(rename_variables,[],[4591])).
% 162.46/162.13 cnf(11268,plain,
% 162.46/162.13 (~E(f331(f331(f154(x112681),x112682),x112683),x112683)),
% 162.46/162.13 inference(rename_variables,[],[4509])).
% 162.46/162.13 cnf(11271,plain,
% 162.46/162.13 (~E(f331(a118,x112711),x112711)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(11274,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x112741),x112742),f196(f891(x112741,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(11279,plain,
% 162.46/162.13 (P24(f331(f331(f333(f890(f884(x112791),f884(x112791))),f331(f331(f261(f884(x112791),f884(x112791)),x112792),x112792)),f161(x112791,f307(x112791,x112793))))),
% 162.46/162.13 inference(rename_variables,[],[4074])).
% 162.46/162.13 cnf(11284,plain,
% 162.46/162.13 (~P24(f331(f331(f333(f890(f884(x112841),f884(x112841))),f331(f331(f261(f884(x112841),f884(x112841)),x112842),f119(x112841))),f148(x112841,x112843)))),
% 162.46/162.13 inference(rename_variables,[],[4590])).
% 162.46/162.13 cnf(11288,plain,
% 162.46/162.13 (E(f331(f331(f154(x112881),f618(f307(x112881,x112882),f331(f331(f154(x112881),x112883),x112884),x112884,x112883,x112881)),f619(f307(x112881,x112882),f331(f331(f154(x112881),x112883),x112884),x112884,x112883,x112881)),f331(f331(f154(x112881),x112883),x112884))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,4500,10471,10564,3102,3156,3270,10243,10252,10313,10316,10405,10408,3770,3146,3966,3210,3176,3154,3375,3243,3265,10512,3420,4575,3939,4509,10304,10468,4567,11020,3421,3205,10370,4080,3942,11026,11152,4590,10958,11157,11262,4591,11059,11160,4592,11163,4593,11217,4594,3225,3516,3677,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,11010,3758,3296,4557,10281,10284,10310,10782,10795,10916,4571,3745,3525,3889,3342,3343,3317,4554,4505,4074,11279,4046,3951,10850,4001,3678,4035,3695,11032,11095,11176,4576,10798,11168,3313,10398,10494,10625,3314,10756,10801,10804,10837,10863,10900,10938,3315,10427,10482,10692,10777,3316,4553,10344,10436,10549,10573,10819,10866,3472,10645,10911,10955,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,3379,10674,10704,10713,3410,3828,3767,10347,4566,10301,10668,10671,11112,3336,10707,10860,4564,3835,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,10589,4589,3906,3752,10971,10977,3613,3754,10710,11048,11200,11230,3582,10631,10634,10716,10890,4581,4583,10767,10869,4178,4086,3788,4579,10323,10326,10662,3756,10628,4020,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724])).
% 162.46/162.13 cnf(11294,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x112941),x112942),f196(f891(x112941,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(11297,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x112971),x112972),f196(f891(x112971,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(11300,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x113001),x113002),f196(f891(x113001,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(11303,plain,
% 162.46/162.13 (P24(f331(f331(f333(x113031),x113032),f256(f891(x113031,a877))))),
% 162.46/162.13 inference(rename_variables,[],[3472])).
% 162.46/162.13 cnf(11308,plain,
% 162.46/162.13 (~P24(f331(f331(f333(f890(x113081,x113081)),f331(f331(f261(x113081,x113081),x113082),x113083)),f156(x113081,f119(f891(x113081,a883)))))),
% 162.46/162.13 inference(rename_variables,[],[4589])).
% 162.46/162.13 cnf(11311,plain,
% 162.46/162.13 (~E(f331(f310(x113111,f891(x113111,a877),x113112),x113113),f331(f308(x113111),x113113))),
% 162.46/162.13 inference(rename_variables,[],[4567])).
% 162.46/162.13 cnf(11314,plain,
% 162.46/162.13 (~E(f331(f310(x113141,f891(x113141,a877),x113142),x113143),f331(f308(x113141),x113143))),
% 162.46/162.13 inference(rename_variables,[],[4567])).
% 162.46/162.13 cnf(11319,plain,
% 162.46/162.13 (~P24(f331(f331(f333(f890(f884(x113191),f884(x113191))),f331(f331(f261(f884(x113191),f884(x113191)),x113192),f119(x113191))),f148(x113191,x113193)))),
% 162.46/162.13 inference(rename_variables,[],[4590])).
% 162.46/162.13 cnf(11325,plain,
% 162.46/162.13 (~P24(f331(f331(f333(f890(f884(x113251),f884(x113251))),f331(f331(f261(f884(x113251),f884(x113251)),x113252),f119(x113251))),f148(x113251,x113253)))),
% 162.46/162.13 inference(rename_variables,[],[4590])).
% 162.46/162.13 cnf(11328,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x113281),x113282),f196(f891(x113281,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(11331,plain,
% 162.46/162.13 (~P24(f331(f331(f196(f891(x113311,f891(x113312,a877))),x113313),x113314))),
% 162.46/162.13 inference(rename_variables,[],[4583])).
% 162.46/162.13 cnf(11334,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x113341),f2(a883)))),
% 162.46/162.13 inference(rename_variables,[],[4557])).
% 162.46/162.13 cnf(11338,plain,
% 162.46/162.13 (P24(f331(f331(f333(f890(x113381,x113382)),f331(f331(f261(x113381,x113382),f331(x113383,x113384)),f331(x113385,x113384))),f331(f310(f890(x113386,x113386),f890(x113381,x113382),f271(x113386,x113381,x113386,x113382,x113383,x113385)),f307(x113386,x113387))))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,4500,10471,10564,3102,3156,3270,10243,10252,10313,10316,10405,10408,3770,3146,3966,3210,3176,3154,3375,3243,3265,10512,3420,4575,3939,4509,10304,10468,4567,11020,11090,11311,3421,3205,10370,4080,3942,11026,11152,11203,4590,10958,11157,11262,11284,11319,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,3677,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,11010,3758,3296,4557,10281,10284,10310,10782,10795,10916,4571,3745,3525,3889,3342,3343,3317,4554,4505,4074,11279,4046,3951,10850,4001,3678,4035,3695,11032,11095,11176,4576,10798,11168,3313,10398,10494,10625,3314,10756,10801,10804,10837,10863,10900,10938,3315,10427,10482,10692,10777,3316,4553,10344,10436,10549,10573,10819,10866,3472,10645,10911,10955,11225,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,3379,10674,10704,10713,3410,3828,3767,10347,4566,10301,10668,10671,11112,3336,10707,10860,4564,3835,4543,4545,3287,3288,4544,4547,4548,4578,10275,10278,10530,10581,10584,10589,4589,11191,3906,3752,10971,10977,3613,3754,10710,11048,11200,11230,3582,10631,10634,10716,10890,4581,4583,10767,10869,11179,4178,4086,3788,4579,10323,10326,10662,3756,10628,4020,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038])).
% 162.46/162.13 cnf(11341,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x113411),x113412),f196(f891(x113411,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(11344,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x113441),x113442),f196(f891(x113441,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(11347,plain,
% 162.46/162.13 (P24(f331(f331(f333(x113471),f331(x113472,x113473)),f331(f310(x113474,x113471,x113472),f256(f891(x113474,a877)))))),
% 162.46/162.13 inference(rename_variables,[],[3906])).
% 162.46/162.13 cnf(11350,plain,
% 162.46/162.13 (~P24(f331(f331(f333(f890(x113501,x113501)),f331(f331(f261(x113501,x113501),x113502),x113503)),f156(x113501,f119(f891(x113501,a883)))))),
% 162.46/162.13 inference(rename_variables,[],[4589])).
% 162.46/162.13 cnf(11358,plain,
% 162.46/162.13 (E(f120(x113581,f119(x113581)),f119(x113581))),
% 162.46/162.13 inference(rename_variables,[],[3156])).
% 162.46/162.13 cnf(11361,plain,
% 162.46/162.13 (~E(f331(a118,x113611),x113611)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(11368,plain,
% 162.46/162.13 (~E(f331(a118,x113681),x113681)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(11373,plain,
% 162.46/162.13 (E(f331(f257(x113731,x113731),f258(x113731,x113732)),x113732)),
% 162.46/162.13 inference(rename_variables,[],[3270])).
% 162.46/162.13 cnf(11376,plain,
% 162.46/162.13 (E(f331(f257(x113761,x113761),f258(x113761,x113762)),x113762)),
% 162.46/162.13 inference(rename_variables,[],[3270])).
% 162.46/162.13 cnf(11382,plain,
% 162.46/162.13 (~E(f331(a118,x113821),x113821)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(11398,plain,
% 162.46/162.13 (E(f331(f331(f22(a883),f2(a883)),x113981),f2(a883))),
% 162.46/162.13 inference(rename_variables,[],[3226])).
% 162.46/162.13 cnf(11401,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x114011),f2(a883)))),
% 162.46/162.13 inference(rename_variables,[],[4557])).
% 162.46/162.13 cnf(11408,plain,
% 162.46/162.13 (E(f331(f331(f81(a1),f331(f331(f82(a1),x114081),f331(f331(f39(a1),x114082),x114081))),f45(a1,x114082,x114081)),x114082)),
% 162.46/162.13 inference(rename_variables,[],[3857])).
% 162.46/162.13 cnf(11432,plain,
% 162.46/162.13 (~E(f331(a118,x114321),x114321)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(11435,plain,
% 162.46/162.13 (~E(f331(a118,x114351),x114351)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(11461,plain,
% 162.46/162.13 (~P24(f331(f63(x114611,x114612,f196(f891(x114611,a877))),x114613))),
% 162.46/162.13 inference(rename_variables,[],[4578])).
% 162.46/162.13 cnf(11464,plain,
% 162.46/162.13 (~P24(f331(f331(f196(f891(x114641,f891(x114642,a877))),x114643),x114644))),
% 162.46/162.13 inference(rename_variables,[],[4583])).
% 162.46/162.13 cnf(11467,plain,
% 162.46/162.13 (P24(f331(f331(f333(x114671),x114672),f256(f891(x114671,a877))))),
% 162.46/162.13 inference(rename_variables,[],[3472])).
% 162.46/162.13 cnf(11479,plain,
% 162.46/162.13 (P24(f331(f331(f203(a24),x114791),x114791))),
% 162.46/162.13 inference(rename_variables,[],[3313])).
% 162.46/162.13 cnf(11486,plain,
% 162.46/162.13 (P24(f331(f67(x114861,x114862,x114863,x114864,f196(f891(x114861,a877))),x114864))),
% 162.46/162.13 inference(rename_variables,[],[4224])).
% 162.46/162.13 cnf(11487,plain,
% 162.46/162.13 (E(f331(f257(x114871,x114871),f258(x114871,x114872)),x114872)),
% 162.46/162.13 inference(rename_variables,[],[3270])).
% 162.46/162.13 cnf(11492,plain,
% 162.46/162.13 (~P24(f331(f331(f196(f891(x114921,f891(x114922,a877))),x114923),x114924))),
% 162.46/162.13 inference(rename_variables,[],[4583])).
% 162.46/162.13 cnf(11503,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),f331(f331(f81(a883),x115031),x115032)),x115032))),
% 162.46/162.13 inference(rename_variables,[],[4579])).
% 162.46/162.13 cnf(11506,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a1),f331(f106(a1),x115061)),f2(a1)))),
% 162.46/162.13 inference(rename_variables,[],[4571])).
% 162.46/162.13 cnf(11524,plain,
% 162.46/162.13 (~E(f331(f331(f251(a883),f331(a118,x115241)),x115241),f331(a118,x115241))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,4500,10471,10564,3230,2915,2917,2921,2922,2931,2939,2940,2975,2982,2983,2991,2994,3029,3037,3040,3043,3044,3070,3080,3086,3102,4481,3156,11358,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,3770,3146,3966,3857,11408,3210,3176,3154,3375,3243,3265,10512,3420,4575,3939,4509,10304,10468,4567,11020,11090,11311,11314,3421,3205,10370,10677,3206,3124,3226,11398,4080,3942,11026,11152,11203,4590,10958,11157,11262,11284,11319,11325,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,3677,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,11010,3758,3296,4557,10281,10284,10310,10782,10795,10916,11334,11401,4571,3745,3525,3889,3342,3343,3317,4554,4505,3508,4574,4074,11279,3636,4046,3951,10850,4001,3678,4035,3695,11032,11095,11176,4576,10798,11168,3313,10398,10494,10625,10687,3314,10756,10801,10804,10837,10863,10900,10938,3315,10427,10482,10692,10777,3316,4553,10344,10436,10549,10573,10819,10866,3472,10645,10911,10955,11225,11303,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,3379,10674,10704,10713,3410,3828,3767,10347,4566,10301,10668,10671,11112,11130,3336,10707,10860,4564,3835,4543,4545,3287,3288,4544,4547,4548,4588,4224,4578,10275,10278,10530,10581,10584,10589,10997,4589,11191,11308,3906,3752,10971,10977,3613,3754,10710,11048,11200,11230,3582,10631,10634,10716,10890,4581,4583,10767,10869,11179,11331,11464,4178,4086,3788,4579,10323,10326,10662,10665,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390])).
% 162.46/162.13 cnf(11531,plain,
% 162.46/162.13 (E(f331(f257(x115311,x115311),f258(x115311,x115312)),x115312)),
% 162.46/162.13 inference(rename_variables,[],[3270])).
% 162.46/162.13 cnf(11536,plain,
% 162.46/162.13 (E(f331(f257(x115361,x115361),f258(x115361,x115362)),x115362)),
% 162.46/162.13 inference(rename_variables,[],[3270])).
% 162.46/162.13 cnf(11539,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a1),f331(f106(a1),x115391)),f2(a1)))),
% 162.46/162.13 inference(rename_variables,[],[4571])).
% 162.46/162.13 cnf(11544,plain,
% 162.46/162.13 (~E(f331(a118,x115441),x115441)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(11553,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x115531),x115531))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(11574,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a1),f331(f106(a1),x115741)),f2(a1)))),
% 162.46/162.13 inference(rename_variables,[],[4571])).
% 162.46/162.13 cnf(11587,plain,
% 162.46/162.13 (P24(f331(f331(f247(a1),x115871),x115871))),
% 162.46/162.13 inference(rename_variables,[],[3315])).
% 162.46/162.13 cnf(11590,plain,
% 162.46/162.13 (~P24(f331(f331(f247(a883),f331(a118,x115901)),x115901))),
% 162.46/162.13 inference(rename_variables,[],[4566])).
% 162.46/162.13 cnf(11591,plain,
% 162.46/162.13 (~E(f331(a118,x115911),x115911)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(11601,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),f331(f331(f81(a883),x116011),x116012)),x116011))),
% 162.46/162.13 inference(rename_variables,[],[4580])).
% 162.46/162.13 cnf(11604,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a1),f331(f106(a1),x116041)),f2(a1)))),
% 162.46/162.13 inference(rename_variables,[],[4571])).
% 162.46/162.13 cnf(11607,plain,
% 162.46/162.13 (~E(f331(a118,x116071),x116071)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(11620,plain,
% 162.46/162.13 (P24(f331(f331(f333(x116201),x116202),f331(f331(f309(x116201),x116202),x116203)))),
% 162.46/162.13 inference(rename_variables,[],[3626])).
% 162.46/162.13 cnf(11621,plain,
% 162.46/162.13 (~P24(f331(f331(f247(a1),f2(a1)),f331(f80(a1),f331(f106(a1),f331(a118,x116211)))))),
% 162.46/162.13 inference(rename_variables,[],[4581])).
% 162.46/162.13 cnf(11624,plain,
% 162.46/162.13 (P24(f331(f331(f248(a883),f331(f331(f22(a883),x116241),x116242)),f331(a118,x116241)))),
% 162.46/162.13 inference(rename_variables,[],[3758])).
% 162.46/162.13 cnf(11627,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),f45(a883,x116271,x116272)),x116271))),
% 162.46/162.13 inference(rename_variables,[],[3767])).
% 162.46/162.13 cnf(11633,plain,
% 162.46/162.13 (E(f331(f331(f137(x116331),x116332),f119(x116331)),x116332)),
% 162.46/162.13 inference(rename_variables,[],[3244])).
% 162.46/162.13 cnf(11636,plain,
% 162.46/162.13 (E(f331(f257(x116361,x116361),f258(x116361,x116362)),x116362)),
% 162.46/162.13 inference(rename_variables,[],[3270])).
% 162.46/162.13 cnf(11639,plain,
% 162.46/162.13 (E(f331(f74(x116391,x116392,x116391,x116393),f35(x116391)),x116393)),
% 162.46/162.13 inference(rename_variables,[],[3770])).
% 162.46/162.13 cnf(11645,plain,
% 162.46/162.13 (~P24(f331(f331(f247(a883),f331(a118,x116451)),x116451))),
% 162.46/162.13 inference(rename_variables,[],[4566])).
% 162.46/162.13 cnf(11654,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x116541),x116541))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(11657,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),f45(a883,x116571,x116572)),x116571))),
% 162.46/162.13 inference(rename_variables,[],[3767])).
% 162.46/162.13 cnf(11658,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),f2(a883)),x116581))),
% 162.46/162.13 inference(rename_variables,[],[3336])).
% 162.46/162.13 cnf(11660,plain,
% 162.46/162.13 (~P24(f331(f331(f247(a1),f79(a1)),f2(a1)))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,4500,10471,10564,3230,2914,2915,2917,2918,2921,2922,2931,2939,2940,2975,2982,2983,2991,2994,3029,3037,3040,3041,3043,3044,3063,3064,3068,3070,3080,3086,3102,4481,3156,11358,3358,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,3244,11633,3770,11017,11639,3146,3966,3857,11408,3210,3176,3171,3154,3155,3375,3243,3265,10512,3420,4575,3939,4509,10304,10468,4567,11020,11090,11311,11314,3421,3205,10370,10677,3206,3477,3124,3226,11398,4080,3942,11026,11152,11203,4590,10958,11157,11262,11284,11319,11325,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,3677,4367,4368,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,11010,3758,3296,4557,10281,10284,10310,10782,10795,10916,11334,11401,4571,11506,11539,11574,3745,3525,3889,3342,3343,3317,4554,4505,3508,4574,4074,11279,3636,4046,3951,10850,4001,3678,4035,3695,11032,11095,11176,4576,10798,11168,3313,10398,10494,10625,10687,3314,10756,10801,10804,10837,10863,10900,10938,3315,10427,10482,10692,10777,10903,3316,4553,10344,10436,10549,10573,10819,10866,10876,11553,3472,10645,10911,10955,11225,11303,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,3379,10674,10704,10713,3416,3410,3828,3767,10347,11627,4566,10301,10668,10671,11112,11130,11590,3336,10707,10860,10931,4564,3835,4543,4545,3287,3288,4544,4547,4548,4588,3626,4224,4578,10275,10278,10530,10581,10584,10589,10997,4589,11191,11308,3906,3752,10971,10977,3613,3754,10710,11048,11200,11230,3582,10631,10634,10716,10890,4581,4583,10767,10869,11179,11331,11464,4178,4086,3788,4579,10323,10326,10662,10665,4580,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827])).
% 162.46/162.13 cnf(11675,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x116751),x116751))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(11678,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x116781),x116781))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(11681,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x116811),x116811))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(11684,plain,
% 162.46/162.13 (P24(f331(f331(f333(x116841),f331(x116842,x116843)),f331(f310(x116844,x116841,x116842),f256(f891(x116844,a877)))))),
% 162.46/162.13 inference(rename_variables,[],[3906])).
% 162.46/162.13 cnf(11685,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),f331(f331(f81(a883),x116851),x116852)),x116852))),
% 162.46/162.13 inference(rename_variables,[],[4579])).
% 162.46/162.13 cnf(11688,plain,
% 162.46/162.13 (P24(f331(f331(f333(x116881),f331(x116882,x116883)),f331(f310(x116884,x116881,x116882),f256(f891(x116884,a877)))))),
% 162.46/162.13 inference(rename_variables,[],[3906])).
% 162.46/162.13 cnf(11689,plain,
% 162.46/162.13 (~P24(f331(f331(f247(a883),f331(a118,x116891)),x116891))),
% 162.46/162.13 inference(rename_variables,[],[4566])).
% 162.46/162.13 cnf(11694,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),f331(f331(f81(a883),x116941),x116942)),x116941))),
% 162.46/162.13 inference(rename_variables,[],[4580])).
% 162.46/162.13 cnf(11697,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x116971),x116971))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(11700,plain,
% 162.46/162.13 (P24(f331(f331(f203(a24),x117001),x117001))),
% 162.46/162.13 inference(rename_variables,[],[3313])).
% 162.46/162.13 cnf(11706,plain,
% 162.46/162.13 (~P36(x117061,x117062,f119(x117061))),
% 162.46/162.13 inference(rename_variables,[],[4520])).
% 162.46/162.13 cnf(11709,plain,
% 162.46/162.13 (P24(f331(f331(f333(x117091),x117092),f256(f891(x117091,a877))))),
% 162.46/162.13 inference(rename_variables,[],[3472])).
% 162.46/162.13 cnf(11710,plain,
% 162.46/162.13 (~P24(f331(f331(f247(a883),f331(a118,x117101)),x117101))),
% 162.46/162.13 inference(rename_variables,[],[4566])).
% 162.46/162.13 cnf(11713,plain,
% 162.46/162.13 (~P24(f331(f63(x117131,x117132,f196(f891(x117131,a877))),x117133))),
% 162.46/162.13 inference(rename_variables,[],[4578])).
% 162.46/162.13 cnf(11726,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x117261),x117262),f196(f891(x117261,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(11729,plain,
% 162.46/162.13 (E(f331(f331(f16(x117291,x117292),x117293),x117294),x117293)),
% 162.46/162.13 inference(rename_variables,[],[3303])).
% 162.46/162.13 cnf(11732,plain,
% 162.46/162.13 (E(f331(f331(f16(x117321,x117322),x117323),x117324),x117323)),
% 162.46/162.13 inference(rename_variables,[],[3303])).
% 162.46/162.13 cnf(11744,plain,
% 162.46/162.13 (P24(f331(f331(f248(a883),f2(a883)),f331(a118,x117441)))),
% 162.46/162.13 inference(rename_variables,[],[3397])).
% 162.46/162.13 cnf(11747,plain,
% 162.46/162.13 (P24(f331(f331(f203(a24),x117471),x117471))),
% 162.46/162.13 inference(rename_variables,[],[3313])).
% 162.46/162.13 cnf(11750,plain,
% 162.46/162.13 (P24(f331(f331(f333(x117501),f331(x117502,x117503)),f331(f310(x117504,x117501,x117502),f256(f891(x117504,a877)))))),
% 162.46/162.13 inference(rename_variables,[],[3906])).
% 162.46/162.13 cnf(11753,plain,
% 162.46/162.13 (P24(f331(f62(x117531),f331(f175(x117531),x117532)))),
% 162.46/162.13 inference(rename_variables,[],[3357])).
% 162.46/162.13 cnf(11756,plain,
% 162.46/162.13 (P24(f331(f62(x117561),f331(f175(x117561),x117562)))),
% 162.46/162.13 inference(rename_variables,[],[3357])).
% 162.46/162.13 cnf(11759,plain,
% 162.46/162.13 (P24(f331(f331(f247(a1),f331(f80(a1),f331(f106(a1),x117591))),f331(f106(a1),x117592)))),
% 162.46/162.13 inference(rename_variables,[],[3789])).
% 162.46/162.13 cnf(11762,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x117621),x117622),f196(f891(x117621,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(11774,plain,
% 162.46/162.13 (~P24(f331(f331(f333(a883),x117741),f331(f254(a883),f2(a883))))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,4519,4520,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,4500,10471,10564,3230,2914,2915,2917,2918,2921,2922,2925,2931,2939,2940,2975,2982,2983,2991,2994,3029,3037,3040,3041,3043,3044,3046,3063,3064,3068,3070,3080,3086,3102,4481,3156,11358,3358,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,3244,11633,3770,11017,11639,3146,3966,3857,11408,3210,3176,3171,3154,3155,3375,3243,3265,10512,3420,4575,3939,4509,10304,10468,3303,11729,4567,11020,11090,11311,11314,3421,3205,10370,10677,3206,3477,3124,3226,11398,4080,3942,11026,11152,11203,4590,10958,11157,11262,11284,11319,11325,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,3677,4367,4368,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,11010,3758,11624,3296,3397,4557,10281,10284,10310,10782,10795,10916,11334,11401,4571,11506,11539,11574,3745,3525,3889,3342,3343,3317,4554,4505,3508,4574,4074,11279,3636,3357,11753,4046,3951,10850,4001,3678,4035,3695,11032,11095,11176,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,3314,10756,10801,10804,10837,10863,10900,10938,3315,10427,10482,10692,10777,10903,3316,3393,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,3472,10645,10911,10955,11225,11303,11467,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,3379,10674,10704,10713,3416,3410,3828,3767,10347,11627,4566,10301,10668,10671,11112,11130,11590,11645,11689,3336,10707,10860,10931,3789,4564,3835,4543,4545,3287,3288,4544,4547,4548,4588,3626,4224,4578,10275,10278,10530,10581,10584,10589,10997,11461,4589,11191,11308,4013,3906,11347,11684,11688,3752,10971,10977,3613,3754,10710,11048,11200,11230,3582,10631,10634,10716,10890,4581,11621,4583,10767,10869,11179,11331,11464,4178,4086,3788,3733,4579,10323,10326,10662,10665,11503,4580,11601,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161])).
% 162.46/162.13 cnf(11781,plain,
% 162.46/162.13 (P24(f331(f331(f203(a24),x117811),x117811))),
% 162.46/162.13 inference(rename_variables,[],[3313])).
% 162.46/162.13 cnf(11784,plain,
% 162.46/162.13 (P24(f331(f331(f247(a1),x117841),x117841))),
% 162.46/162.13 inference(rename_variables,[],[3315])).
% 162.46/162.13 cnf(11793,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x117931),f2(a883)))),
% 162.46/162.13 inference(rename_variables,[],[4557])).
% 162.46/162.13 cnf(11796,plain,
% 162.46/162.13 (P24(f331(f331(f247(a1),x117961),x117961))),
% 162.46/162.13 inference(rename_variables,[],[3315])).
% 162.46/162.13 cnf(11801,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x118011),f2(a883)))),
% 162.46/162.13 inference(rename_variables,[],[4557])).
% 162.46/162.13 cnf(11808,plain,
% 162.46/162.13 (P24(f331(f256(f891(x118081,a877)),x118082))),
% 162.46/162.13 inference(rename_variables,[],[3379])).
% 162.46/162.13 cnf(11813,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),f2(a883)),x118131))),
% 162.46/162.13 inference(rename_variables,[],[3336])).
% 162.46/162.13 cnf(11814,plain,
% 162.46/162.13 (~P24(f331(f331(f247(a883),f331(a118,x118141)),x118141))),
% 162.46/162.13 inference(rename_variables,[],[4566])).
% 162.46/162.13 cnf(11817,plain,
% 162.46/162.13 (~P24(f331(f63(x118171,x118172,f196(f891(x118171,a877))),x118173))),
% 162.46/162.13 inference(rename_variables,[],[4578])).
% 162.46/162.13 cnf(11834,plain,
% 162.46/162.13 (P24(f331(f331(f248(a1),f331(f80(a1),f79(a1))),f2(a1)))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,4519,4520,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,4500,10471,10564,3230,2914,2915,2917,2918,2921,2922,2925,2928,2931,2932,2939,2940,2975,2982,2983,2991,2994,3029,3035,3037,3040,3041,3043,3044,3046,3063,3064,3068,3070,3080,3086,3102,4481,3156,11358,3358,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,3244,11633,3770,11017,11639,3146,3966,3857,11408,3210,3176,3171,3154,3155,3375,3243,3265,10512,3420,4575,3939,4509,10304,10468,3303,11729,4567,11020,11090,11311,11314,3421,3205,10370,10677,3206,3477,3124,3226,11398,4080,3942,11026,11152,11203,4590,10958,11157,11262,11284,11319,11325,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,3677,4367,4368,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,11010,3758,11624,3296,3397,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,4571,11506,11539,11574,11604,3745,3525,3889,3342,3343,3317,4554,4505,3508,4574,4074,11279,3636,3357,11753,4046,3951,10850,4001,3678,4035,3695,11032,11095,11176,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,11747,3314,10756,10801,10804,10837,10863,10900,10938,3315,10427,10482,10692,10777,10903,11587,11784,3316,3393,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,3472,10645,10911,10955,11225,11303,11467,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,3379,10674,10704,10713,11254,3416,3410,3828,3767,10347,11627,11657,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,3336,10707,10860,10931,11658,3789,4564,3835,4543,4545,3287,3288,4544,4547,4548,4588,3626,4224,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,4013,3906,11347,11684,11688,3752,10971,10977,3613,3754,10710,11048,11200,11230,3582,10631,10634,10716,10890,4581,11621,4583,10767,10869,11179,11331,11464,4178,4086,3788,3733,4579,10323,10326,10662,10665,11503,4580,11601,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462])).
% 162.46/162.13 cnf(11839,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x118391),x118391))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(11842,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x118421),x118421))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(11845,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x118451),x118451))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(11848,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x118481),x118481))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(11851,plain,
% 162.46/162.13 (~P24(f331(f331(f247(a883),f331(a118,x118511)),x118511))),
% 162.46/162.13 inference(rename_variables,[],[4566])).
% 162.46/162.13 cnf(11854,plain,
% 162.46/162.13 (~P24(f331(f331(f247(a883),f331(a118,x118541)),x118541))),
% 162.46/162.13 inference(rename_variables,[],[4566])).
% 162.46/162.13 cnf(11857,plain,
% 162.46/162.13 (~P24(f331(f331(f247(a883),f331(a118,x118571)),x118571))),
% 162.46/162.13 inference(rename_variables,[],[4566])).
% 162.46/162.13 cnf(11860,plain,
% 162.46/162.13 (~P24(f331(f331(f247(a883),f331(a118,x118601)),x118601))),
% 162.46/162.13 inference(rename_variables,[],[4566])).
% 162.46/162.13 cnf(11876,plain,
% 162.46/162.13 (P24(f331(f331(f203(a24),f331(f331(f22(a883),x118761),f331(a118,x118761))),f2(a883)))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,4519,4520,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,4500,10471,10564,3230,2914,2915,2917,2918,2921,2922,2925,2928,2931,2932,2939,2940,2975,2982,2983,2991,2994,3029,3035,3037,3040,3041,3043,3044,3046,3063,3064,3068,3070,3080,3086,3102,4481,3156,11358,3358,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,3244,11633,3770,11017,11639,3146,3966,3857,11408,3210,3176,3171,3154,3155,3375,3243,3265,10512,3420,4575,3939,4509,10304,10468,3303,11729,4567,11020,11090,11311,11314,3421,3205,10370,10677,3206,3477,3124,3226,11398,4080,3942,11026,11152,11203,4590,10958,11157,11262,11284,11319,11325,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,3677,4367,4368,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,11010,3758,11624,3296,3397,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,4571,11506,11539,11574,11604,3745,3525,3889,3342,3343,3317,4554,4505,3508,4574,4074,11279,3636,3357,11753,4046,3951,10850,4001,3678,4035,3695,11032,11095,11176,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,11747,11781,3314,10756,10801,10804,10837,10863,10900,10938,3315,10427,10482,10692,10777,10903,11587,11784,3316,3393,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,3472,10645,10911,10955,11225,11303,11467,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,3379,10674,10704,10713,11254,3416,3410,3828,3767,10347,11627,11657,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,3336,10707,10860,10931,11658,3789,4564,3835,4543,4545,3287,3288,4544,4547,4548,4588,3626,4224,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,4013,3906,11347,11684,11688,3752,10971,10977,3613,3754,10710,11048,11200,11230,3582,10631,10634,10716,10890,4581,11621,4583,10767,10869,11179,11331,11464,4178,4086,3788,3733,4579,10323,10326,10662,10665,11503,4580,11601,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462,6463,6465,6466,6468,6470,6471,6472,6474,6476,6479,6485,6486,6487,6488,6494,6496,6536])).
% 162.46/162.13 cnf(11877,plain,
% 162.46/162.13 (P24(f331(f331(f203(a24),x118771),x118771))),
% 162.46/162.13 inference(rename_variables,[],[3313])).
% 162.46/162.13 cnf(11883,plain,
% 162.46/162.13 (P24(f331(f331(f247(a1),x118831),x118831))),
% 162.46/162.13 inference(rename_variables,[],[3315])).
% 162.46/162.13 cnf(11894,plain,
% 162.46/162.13 (P24(f331(f331(f247(a1),x118941),x118941))),
% 162.46/162.13 inference(rename_variables,[],[3315])).
% 162.46/162.13 cnf(11897,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(f890(f884(x118971),f884(x118971)),a877)),f161(x118971,x118972)),f307(f884(x118971),f160(x118971,x118972))))),
% 162.46/162.13 inference(rename_variables,[],[4006])).
% 162.46/162.13 cnf(11904,plain,
% 162.46/162.13 (P24(f331(f331(f248(a883),x119041),f331(a118,x119041)))),
% 162.46/162.13 inference(rename_variables,[],[3385])).
% 162.46/162.13 cnf(11907,plain,
% 162.46/162.13 (P24(f331(f331(f333(f891(x119071,a877)),x119072),f331(f308(x119071),x119072)))),
% 162.46/162.13 inference(rename_variables,[],[3678])).
% 162.46/162.13 cnf(11908,plain,
% 162.46/162.13 (~E(f331(a118,x119081),x119081)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(11915,plain,
% 162.46/162.13 (P24(f331(f331(f247(a1),x119151),x119151))),
% 162.46/162.13 inference(rename_variables,[],[3315])).
% 162.46/162.13 cnf(11920,plain,
% 162.46/162.13 (P24(f331(f331(f247(a1),x119201),x119201))),
% 162.46/162.13 inference(rename_variables,[],[3315])).
% 162.46/162.13 cnf(11926,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a1),f331(f80(a1),a103)),f2(a1)))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,4519,4520,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,4500,10471,10564,3523,3230,2914,2915,2917,2918,2921,2922,2925,2928,2931,2932,2939,2940,2975,2982,2983,2991,2994,3029,3035,3037,3040,3041,3043,3044,3046,3063,3064,3068,3070,3080,3086,3102,4481,3156,11358,3358,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,3244,11633,3770,11017,11639,3146,3966,3857,11408,3210,3176,3171,3154,3155,3375,3243,3265,10512,3420,4575,3939,4509,10304,10468,3303,11729,4567,11020,11090,11311,11314,3421,3205,10370,10677,3206,3477,3124,3226,11398,4080,3942,11026,11152,11203,4590,10958,11157,11262,11284,11319,11325,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,3677,4367,4368,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,11010,3758,11624,3296,3397,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,4571,11506,11539,11574,11604,3745,3525,3889,3342,3343,3317,4554,4505,3508,4574,4074,11279,3636,3357,11753,4046,4006,3951,10850,4001,3678,4035,3695,11032,11095,11176,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,11747,11781,3314,10756,10801,10804,10837,10863,10900,10938,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,3316,3393,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,3472,10645,10911,10955,11225,11303,11467,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,3379,10674,10704,10713,11254,3416,3410,3828,3767,10347,11627,11657,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,3336,10707,10860,10931,11658,3789,4564,3835,4543,4545,3287,3288,4544,4547,4548,4588,3626,4224,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,4013,3906,11347,11684,11688,3752,10971,10977,3613,3754,10710,11048,11200,11230,3582,10631,10634,10716,10890,4581,11621,4583,10767,10869,11179,11331,11464,4178,4086,3788,3733,4579,10323,10326,10662,10665,11503,4580,11601,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462,6463,6465,6466,6468,6470,6471,6472,6474,6476,6479,6485,6486,6487,6488,6494,6496,6536,6541,6556,6557,6558,6559,6594,6599,6601,6606,6607,6615,6619,6632,6657,6658,6659,6660,6671,6676,6693])).
% 162.46/162.13 cnf(11929,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x119291,a877)),x119292),f331(f331(f309(x119291),x119293),x119292)))),
% 162.46/162.13 inference(rename_variables,[],[3752])).
% 162.46/162.13 cnf(11932,plain,
% 162.46/162.13 (P24(f331(f331(f203(a24),x119321),x119321))),
% 162.46/162.13 inference(rename_variables,[],[3313])).
% 162.46/162.13 cnf(11933,plain,
% 162.46/162.13 (~E(f331(a118,x119331),x119331)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(11944,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x119441),x119441))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(11945,plain,
% 162.46/162.13 (~E(f331(a118,x119451),x119451)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(11948,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x119481),x119481))),
% 162.46/162.13 inference(rename_variables,[],[3314])).
% 162.46/162.13 cnf(11951,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x119511),x119511))),
% 162.46/162.13 inference(rename_variables,[],[3314])).
% 162.46/162.13 cnf(11954,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x119541),x119541))),
% 162.46/162.13 inference(rename_variables,[],[3314])).
% 162.46/162.13 cnf(11957,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x119571),x119571))),
% 162.46/162.13 inference(rename_variables,[],[3314])).
% 162.46/162.13 cnf(11960,plain,
% 162.46/162.13 (P24(f331(f331(f247(a1),x119601),x119601))),
% 162.46/162.13 inference(rename_variables,[],[3315])).
% 162.46/162.13 cnf(11963,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x119631),x119631))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(11966,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x119661),x119661))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(11967,plain,
% 162.46/162.13 (P24(f331(f331(f248(a883),x119671),f331(a118,x119671)))),
% 162.46/162.13 inference(rename_variables,[],[3385])).
% 162.46/162.13 cnf(11976,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x119761),x119761))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(11977,plain,
% 162.46/162.13 (~E(f331(a118,x119771),x119771)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(11982,plain,
% 162.46/162.13 (P24(f331(f331(f247(a1),x119821),x119821))),
% 162.46/162.13 inference(rename_variables,[],[3315])).
% 162.46/162.13 cnf(11997,plain,
% 162.46/162.13 (P24(f331(f331(f247(a1),x119971),x119971))),
% 162.46/162.13 inference(rename_variables,[],[3315])).
% 162.46/162.13 cnf(12002,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),f2(a883)),x120021))),
% 162.46/162.13 inference(rename_variables,[],[3336])).
% 162.46/162.13 cnf(12019,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x120191),f2(a883)))),
% 162.46/162.13 inference(rename_variables,[],[4557])).
% 162.46/162.13 cnf(12022,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x120221),f2(a883)))),
% 162.46/162.13 inference(rename_variables,[],[4557])).
% 162.46/162.13 cnf(12025,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x120251),x120252),f196(f891(x120251,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(12028,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x120281),x120282),f196(f891(x120281,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(12031,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x120311),x120311))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(12033,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x120331),f331(f331(f251(a883),x120331),x120332)))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,4519,4520,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,4500,10471,10564,3523,3230,2914,2915,2917,2918,2921,2922,2925,2928,2931,2932,2939,2940,2975,2982,2983,2991,2994,3029,3035,3037,3040,3041,3043,3044,3046,3063,3064,3068,3070,3080,3086,3102,4481,3156,11358,3358,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,3244,11633,3255,3770,11017,11639,3999,3146,3966,3857,11408,3210,3176,3171,3154,3155,3375,3243,3265,10512,3420,4575,3939,4509,10304,10468,3303,11729,4567,11020,11090,11311,11314,3421,3205,10370,10677,3206,3477,3124,3226,11398,4080,3942,11026,11152,11203,4590,10958,11157,11262,11284,11319,11325,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,3677,4367,4368,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,3758,11624,3296,3397,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,4571,11506,11539,11574,11604,3745,3525,3889,3342,3343,3317,4554,4505,3508,4574,4074,11279,3636,3357,11753,4046,4006,3951,10850,4001,3678,4035,3695,11032,11095,11176,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,3316,3393,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,3472,10645,10911,10955,11225,11303,11467,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,3379,10674,10704,10713,11254,3416,3410,3828,3767,10347,11627,11657,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,3336,10707,10860,10931,11658,11813,3789,4564,3800,3835,4543,4545,3287,3288,4544,4547,4548,4588,3807,3626,4224,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,4013,3906,11347,11684,11688,3752,10971,10977,10992,3613,3754,10710,11048,11200,11230,3582,10631,10634,10716,10890,4581,11621,4583,10767,10869,11179,11331,11464,4178,4086,3788,3733,4579,10323,10326,10662,10665,11503,4580,11601,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462,6463,6465,6466,6468,6470,6471,6472,6474,6476,6479,6485,6486,6487,6488,6494,6496,6536,6541,6556,6557,6558,6559,6594,6599,6601,6606,6607,6615,6619,6632,6657,6658,6659,6660,6671,6676,6693,6697,6716,6749,6750,6751,6756,6764,6785,6787,6789,6791,6794,6800,6802,6815,6822,6857,6860,6861,6874,6875,6876,6877,6893,6894,6911,6937,6960,6971,6973,6974,6976,6978,6979,7014,7015,7020,7021,7023,7025])).
% 162.46/162.13 cnf(12034,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x120341),x120341))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(12037,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x120371),x120371))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(12039,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x120391),f331(f331(f108(a883),x120391),x120392)))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,4519,4520,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,4500,10471,10564,3523,3230,2914,2915,2917,2918,2921,2922,2925,2928,2931,2932,2939,2940,2975,2982,2983,2991,2994,3029,3035,3037,3040,3041,3043,3044,3046,3063,3064,3068,3070,3080,3086,3102,4481,3156,11358,3358,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,3244,11633,3255,3770,11017,11639,3999,3146,3966,3857,11408,3210,3176,3171,3154,3155,3375,3243,3265,10512,3420,4575,3939,4509,10304,10468,3303,11729,4567,11020,11090,11311,11314,3421,3205,10370,10677,3206,3477,3124,3226,11398,4080,3942,11026,11152,11203,4590,10958,11157,11262,11284,11319,11325,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,3677,4367,4368,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,3758,11624,3296,3397,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,4571,11506,11539,11574,11604,3745,3525,3889,3342,3343,3317,4554,4505,3508,4574,4074,11279,3636,3357,11753,4046,4006,3951,10850,4001,3678,4035,3695,11032,11095,11176,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,3316,3393,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,3472,10645,10911,10955,11225,11303,11467,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,3379,10674,10704,10713,11254,3416,3410,3828,3767,10347,11627,11657,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,3336,10707,10860,10931,11658,11813,3789,4564,3800,3835,4543,4545,3287,3288,4544,4547,4548,4588,3807,3626,4224,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,4013,3906,11347,11684,11688,3752,10971,10977,10992,3613,3754,10710,11048,11200,11230,3582,10631,10634,10716,10890,4581,11621,4583,10767,10869,11179,11331,11464,4178,4086,3788,3733,4579,10323,10326,10662,10665,11503,4580,11601,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462,6463,6465,6466,6468,6470,6471,6472,6474,6476,6479,6485,6486,6487,6488,6494,6496,6536,6541,6556,6557,6558,6559,6594,6599,6601,6606,6607,6615,6619,6632,6657,6658,6659,6660,6671,6676,6693,6697,6716,6749,6750,6751,6756,6764,6785,6787,6789,6791,6794,6800,6802,6815,6822,6857,6860,6861,6874,6875,6876,6877,6893,6894,6911,6937,6960,6971,6973,6974,6976,6978,6979,7014,7015,7020,7021,7023,7025,7026,7027])).
% 162.46/162.13 cnf(12040,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x120401),x120401))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(12043,plain,
% 162.46/162.13 (P24(f331(f331(f248(a883),x120431),f331(a118,x120431)))),
% 162.46/162.13 inference(rename_variables,[],[3385])).
% 162.46/162.13 cnf(12050,plain,
% 162.46/162.13 (P24(f331(f331(f333(f891(x120501,a877)),x120502),f331(f308(x120501),x120502)))),
% 162.46/162.13 inference(rename_variables,[],[3678])).
% 162.46/162.13 cnf(12054,plain,
% 162.46/162.13 (~P24(f331(f331(f333(a883),f331(a118,f331(f145(a883,a883,f81(a883),f2(a883)),x120541))),f331(f175(a883),f331(f139(a883,x120542),x120541))))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,4519,4520,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,4500,10471,10564,3523,3230,2914,2915,2917,2918,2921,2922,2925,2928,2931,2932,2939,2940,2975,2982,2983,2991,2994,3029,3035,3037,3040,3041,3043,3044,3046,3063,3064,3068,3070,3080,3086,3102,4481,3156,11358,3358,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,3244,11633,3255,3770,11017,11639,3999,3146,3966,3857,11408,3210,3176,3171,3154,3155,3375,3243,3265,10512,3420,4575,3939,4509,10304,10468,3303,11729,4567,11020,11090,11311,11314,3421,3205,10370,10677,3206,3477,3124,3226,11398,4080,3942,11026,11152,11203,4590,10958,11157,11262,11284,11319,11325,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,3677,4367,4368,3617,3824,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,3758,11624,3296,3397,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,4571,11506,11539,11574,11604,3745,3525,3889,3342,3343,3317,4554,4505,3508,4574,4074,11279,3636,3357,11753,4046,4006,3951,10850,4001,3678,11907,4035,3695,11032,11095,11176,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,3316,3393,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,3472,10645,10911,10955,11225,11303,11467,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,3379,10674,10704,10713,11254,3416,3410,3828,3767,10347,11627,11657,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,3336,10707,10860,10931,11658,11813,3789,4564,3800,3835,4543,4545,3287,3288,4544,4547,4548,4588,3807,3626,4224,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,4013,3906,11347,11684,11688,3752,10971,10977,10992,3613,3754,10710,11048,11200,11230,3582,10631,10634,10716,10890,4581,11621,4583,10767,10869,11179,11331,11464,4178,4086,3788,3733,4579,10323,10326,10662,10665,11503,4580,11601,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462,6463,6465,6466,6468,6470,6471,6472,6474,6476,6479,6485,6486,6487,6488,6494,6496,6536,6541,6556,6557,6558,6559,6594,6599,6601,6606,6607,6615,6619,6632,6657,6658,6659,6660,6671,6676,6693,6697,6716,6749,6750,6751,6756,6764,6785,6787,6789,6791,6794,6800,6802,6815,6822,6857,6860,6861,6874,6875,6876,6877,6893,6894,6911,6937,6960,6971,6973,6974,6976,6978,6979,7014,7015,7020,7021,7023,7025,7026,7027,7052,7061,7062,7073,7083,7122])).
% 162.46/162.13 cnf(12055,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x120551,a877)),f331(f175(x120551),f331(f139(x120551,x120552),x120553))),f331(f175(x120551),x120553)))),
% 162.46/162.13 inference(rename_variables,[],[3951])).
% 162.46/162.13 cnf(12062,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x120621),x120622),f196(f891(x120621,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(12067,plain,
% 162.46/162.13 (E(f331(f197(f884(x120671)),f331(f171(x120671),x120672)),f331(f197(f884(x120671)),x120672))),
% 162.46/162.13 inference(rename_variables,[],[3327])).
% 162.46/162.13 cnf(12074,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x120741,a877)),x120742),f256(f891(x120741,a877))))),
% 162.46/162.13 inference(rename_variables,[],[3695])).
% 162.46/162.13 cnf(12075,plain,
% 162.46/162.13 (~E(f331(a118,x120751),x120751)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(12078,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x120781,a877)),f331(f310(x120782,x120781,x120783),f331(f311(x120782,x120781,x120783),x120784))),x120784))),
% 162.46/162.13 inference(rename_variables,[],[4178])).
% 162.46/162.13 cnf(12081,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x120811,a877)),f331(f175(x120811),f331(f139(x120811,x120812),x120813))),f331(f175(x120811),x120813)))),
% 162.46/162.13 inference(rename_variables,[],[3951])).
% 162.46/162.13 cnf(12087,plain,
% 162.46/162.13 (P24(f331(f331(f248(a883),x120871),f331(a118,x120871)))),
% 162.46/162.13 inference(rename_variables,[],[3385])).
% 162.46/162.13 cnf(12096,plain,
% 162.46/162.13 (E(f331(f257(x120961,x120961),f258(x120961,x120962)),x120962)),
% 162.46/162.13 inference(rename_variables,[],[3270])).
% 162.46/162.13 cnf(12107,plain,
% 162.46/162.13 (P24(f331(f62(x121071),f196(f891(x121071,a877))))),
% 162.46/162.13 inference(rename_variables,[],[3393])).
% 162.46/162.13 cnf(12108,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x121081),x121082),f196(f891(x121081,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(12113,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x121131),f2(a883)))),
% 162.46/162.13 inference(rename_variables,[],[4557])).
% 162.46/162.13 cnf(12114,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x121141),x121141))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(12119,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x121191,a877)),f331(f175(x121191),f173(x121191,x121192,x121193))),f331(f175(x121191),x121193)))),
% 162.46/162.13 inference(rename_variables,[],[4001])).
% 162.46/162.13 cnf(12122,plain,
% 162.46/162.13 (P21(x121221,x121221,f5(x121221),x121222)),
% 162.46/162.13 inference(rename_variables,[],[3553])).
% 162.46/162.13 cnf(12127,plain,
% 162.46/162.13 (P24(f331(f331(f333(f891(x121271,a877)),x121272),f331(f308(x121271),x121272)))),
% 162.46/162.13 inference(rename_variables,[],[3678])).
% 162.46/162.13 cnf(12134,plain,
% 162.46/162.13 (P24(f331(f331(f203(a24),x121341),x121341))),
% 162.46/162.13 inference(rename_variables,[],[3313])).
% 162.46/162.13 cnf(12137,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x121371),x121372),f196(f891(x121371,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(12140,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x121401,a877)),x121402),f331(f331(f309(x121401),x121403),x121402)))),
% 162.46/162.13 inference(rename_variables,[],[3752])).
% 162.46/162.13 cnf(12141,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x121411,a877)),x121412),f256(f891(x121411,a877))))),
% 162.46/162.13 inference(rename_variables,[],[3695])).
% 162.46/162.13 cnf(12148,plain,
% 162.46/162.13 (P24(f331(f331(f248(a883),x121481),f331(a118,x121481)))),
% 162.46/162.13 inference(rename_variables,[],[3385])).
% 162.46/162.13 cnf(12151,plain,
% 162.46/162.13 (P24(f331(f331(f248(a883),x121511),f331(a118,x121511)))),
% 162.46/162.13 inference(rename_variables,[],[3385])).
% 162.46/162.13 cnf(12154,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x121541),x121541))),
% 162.46/162.13 inference(rename_variables,[],[3314])).
% 162.46/162.13 cnf(12157,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x121571),x121571))),
% 162.46/162.13 inference(rename_variables,[],[3314])).
% 162.46/162.13 cnf(12160,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x121601),x121601))),
% 162.46/162.13 inference(rename_variables,[],[3314])).
% 162.46/162.13 cnf(12163,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x121631),x121631))),
% 162.46/162.13 inference(rename_variables,[],[3314])).
% 162.46/162.13 cnf(12166,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x121661,a877)),x121662),x121662))),
% 162.46/162.13 inference(rename_variables,[],[3613])).
% 162.46/162.13 cnf(12170,plain,
% 162.46/162.13 (~P24(f331(f331(f247(a1),f331(f331(f22(a1),a84),a103)),f2(a1)))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,11085,4519,4520,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,4500,10471,10564,3523,3230,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2939,2940,2975,2982,2983,2991,2994,3029,3035,3037,3040,3041,3043,3044,3046,3063,3064,3068,3070,3080,3086,3102,4481,3156,11358,3358,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,3244,11633,3255,3770,11017,11639,3999,3146,3966,3857,11408,3210,3176,3171,3154,3155,3327,3375,3243,3265,10512,3420,4575,3939,4509,10304,10468,3303,11729,4567,11020,11090,11311,11314,3421,3205,10370,10677,3206,3477,3124,3226,11398,4080,3942,11026,11152,11203,4590,10958,11157,11262,11284,11319,11325,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,3677,4367,4368,3617,3824,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,3758,11624,3296,3397,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,4571,11506,11539,11574,11604,3745,3525,3889,3342,3343,3317,4554,4505,3508,4574,4074,11279,3636,3357,11753,11756,4046,4006,3951,10850,12055,4001,11029,3678,11907,12050,4035,3695,11032,11095,11176,11236,12074,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,3316,3393,12107,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,3472,10645,10911,10955,11225,11303,11467,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,3379,10674,10704,10713,11254,3416,3410,3828,3767,10347,11627,11657,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,3336,10707,10860,10931,11658,11813,3789,4564,3800,3835,4543,4545,3287,3288,4544,4547,4548,4588,3807,3626,4224,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,4013,3906,11347,11684,11688,3752,10971,10977,10992,11929,3613,11194,3754,10710,11048,11200,11230,3582,10631,10634,10716,10890,4581,11621,4583,10767,10869,11179,11331,11464,4178,10843,4086,3788,3733,4579,10323,10326,10662,10665,11503,4580,11601,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462,6463,6465,6466,6468,6470,6471,6472,6474,6476,6479,6485,6486,6487,6488,6494,6496,6536,6541,6556,6557,6558,6559,6594,6599,6601,6606,6607,6615,6619,6632,6657,6658,6659,6660,6671,6676,6693,6697,6716,6749,6750,6751,6756,6764,6785,6787,6789,6791,6794,6800,6802,6815,6822,6857,6860,6861,6874,6875,6876,6877,6893,6894,6911,6937,6960,6971,6973,6974,6976,6978,6979,7014,7015,7020,7021,7023,7025,7026,7027,7052,7061,7062,7073,7083,7122,7132,7136,7143,7154,7155,7160,7162,7168,7176,7177,7190,7207,7225,7227,7244,7288,7290,7291,7292,7299,7304,7320,7364,7398,7412,7429,7462,7465,7488,7512,7530,7533,7534,7544,7561,7562,7564,7566,7568,7570,7594,7619,7620])).
% 162.46/162.13 cnf(12173,plain,
% 162.46/162.13 (P24(f331(f331(f333(f891(x121731,a877)),x121732),f331(f308(x121731),x121732)))),
% 162.46/162.13 inference(rename_variables,[],[3678])).
% 162.46/162.13 cnf(12182,plain,
% 162.46/162.13 (~E(f331(a118,x121821),x121821)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(12183,plain,
% 162.46/162.13 (E(f331(f310(x121831,x121831,f5(x121831)),x121832),x121832)),
% 162.46/162.13 inference(rename_variables,[],[3375])).
% 162.46/162.13 cnf(12186,plain,
% 162.46/162.13 (P33(x121861,x121862,f119(x121861),f119(x121861))),
% 162.46/162.13 inference(rename_variables,[],[3563])).
% 162.46/162.13 cnf(12189,plain,
% 162.46/162.13 (~E(f331(a118,x121891),x121891)),
% 162.46/162.13 inference(rename_variables,[],[4485])).
% 162.46/162.13 cnf(12192,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x121921,a877)),f331(f175(x121921),f173(x121921,x121922,x121923))),f331(f175(x121921),x121923)))),
% 162.46/162.13 inference(rename_variables,[],[4001])).
% 162.46/162.13 cnf(12193,plain,
% 162.46/162.13 (P24(f331(f62(x121931),f331(f175(x121931),x121932)))),
% 162.46/162.13 inference(rename_variables,[],[3357])).
% 162.46/162.13 cnf(12204,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x122041),x122041))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(12207,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x122071),x122071))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(12212,plain,
% 162.46/162.13 (E(f331(f197(f884(x122121)),f331(f171(x122121),x122122)),f331(f197(f884(x122121)),x122122))),
% 162.46/162.13 inference(rename_variables,[],[3327])).
% 162.46/162.13 cnf(12219,plain,
% 162.46/162.13 (P29(a883,f331(f172(a883),f331(f331(f157(f884(x122191),a883),f197(f884(x122191))),f182(x122191,x122192))))),
% 162.46/162.13 inference(rename_variables,[],[3867])).
% 162.46/162.13 cnf(12222,plain,
% 162.46/162.13 (P21(x122221,x122221,f5(x122221),x122222)),
% 162.46/162.13 inference(rename_variables,[],[3553])).
% 162.46/162.13 cnf(12225,plain,
% 162.46/162.13 (P24(f331(f331(f333(f884(x122251)),f119(x122251)),f164(x122251,x122252)))),
% 162.46/162.13 inference(rename_variables,[],[3516])).
% 162.46/162.13 cnf(12228,plain,
% 162.46/162.13 (~P24(f331(f331(f196(f891(x122281,f891(x122282,a877))),x122283),x122284))),
% 162.46/162.13 inference(rename_variables,[],[4583])).
% 162.46/162.13 cnf(12230,plain,
% 162.46/162.13 (P24(f331(f331(f248(f891(x122301,a877)),f331(a118,f256(f891(x122301,a877)))),f331(f331(f309(x122301),x122302),f256(f891(x122301,a877)))))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,11085,12122,3563,4519,4520,4503,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,4500,10471,10564,3523,3230,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2939,2940,2975,2982,2983,2991,2994,3029,3035,3037,3040,3041,3043,3044,3046,3063,3064,3068,3070,3080,3086,3102,4481,3156,11358,3358,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,3244,11633,3255,3770,11017,11639,3999,3146,3966,3857,11408,3210,3176,3171,3154,3155,3160,3190,3327,12067,3375,10853,3243,3265,10512,3420,4575,3939,4509,10304,10468,3303,11729,4567,11020,11090,11311,11314,3421,3205,10370,10677,3206,3477,3124,3226,11398,4080,3942,11026,11152,11203,4590,10958,11157,11262,11284,11319,11325,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,3677,4367,4368,3617,3824,3867,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,3758,11624,3296,3397,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,4571,11506,11539,11574,11604,3745,3525,3889,3342,3343,3317,4554,4505,3508,4574,4074,11279,3636,3357,11753,11756,4046,4006,3951,10850,12055,4001,11029,12119,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,3316,3393,12107,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,3472,10645,10911,10955,11225,11303,11467,11709,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,3379,10674,10704,10713,11254,3416,3410,3828,3767,10347,11627,11657,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,3336,10707,10860,10931,11658,11813,3789,4564,3800,3835,4543,4545,3287,3288,4544,4547,4548,4588,3807,3626,4224,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,4013,3906,11347,11684,11688,3752,10971,10977,10992,11929,3613,11194,3754,10710,11048,11200,11230,3582,10631,10634,10716,10890,4581,11621,4583,10767,10869,11179,11331,11464,11492,4178,10843,4086,3788,3733,4579,10323,10326,10662,10665,11503,4580,11601,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462,6463,6465,6466,6468,6470,6471,6472,6474,6476,6479,6485,6486,6487,6488,6494,6496,6536,6541,6556,6557,6558,6559,6594,6599,6601,6606,6607,6615,6619,6632,6657,6658,6659,6660,6671,6676,6693,6697,6716,6749,6750,6751,6756,6764,6785,6787,6789,6791,6794,6800,6802,6815,6822,6857,6860,6861,6874,6875,6876,6877,6893,6894,6911,6937,6960,6971,6973,6974,6976,6978,6979,7014,7015,7020,7021,7023,7025,7026,7027,7052,7061,7062,7073,7083,7122,7132,7136,7143,7154,7155,7160,7162,7168,7176,7177,7190,7207,7225,7227,7244,7288,7290,7291,7292,7299,7304,7320,7364,7398,7412,7429,7462,7465,7488,7512,7530,7533,7534,7544,7561,7562,7564,7566,7568,7570,7594,7619,7620,7652,7654,7655,7656,7661,7681,7690,7701,7706,7712,7714,7720,7731,7732,7734,7755,7764,7789,7856,7857,7899,7907,7908])).
% 162.46/162.13 cnf(12233,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),x122331),x122331))),
% 162.46/162.13 inference(rename_variables,[],[3314])).
% 162.46/162.13 cnf(12234,plain,
% 162.46/162.13 (P24(f331(f331(f247(a883),f2(a883)),x122341))),
% 162.46/162.13 inference(rename_variables,[],[3336])).
% 162.46/162.13 cnf(12236,plain,
% 162.46/162.13 (P24(f331(f331(f247(a1),f2(a1)),f364(x122361,f196(f891(x122362,f891(x122363,a877))),f79(a1))))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,11085,12122,3563,4519,4520,4503,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,4500,10471,10564,3523,3230,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2939,2940,2975,2982,2983,2991,2994,3029,3035,3037,3040,3041,3043,3044,3046,3063,3064,3068,3070,3080,3086,3102,4481,3156,11358,3358,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,3244,11633,3255,3770,11017,11639,3999,3146,3966,3857,11408,3210,3176,3171,3154,3155,3160,3190,3327,12067,3375,10853,3243,3265,10512,3420,4575,3939,4509,10304,10468,3303,11729,4567,11020,11090,11311,11314,3421,3205,10370,10677,3206,3477,3124,3226,11398,4080,3942,11026,11152,11203,4590,10958,11157,11262,11284,11319,11325,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,3677,4367,4368,3617,3824,3867,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,3758,11624,3296,3397,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,4571,11506,11539,11574,11604,3745,3525,3889,3342,3343,3317,4554,4505,3508,4574,4074,11279,3636,3357,11753,11756,4046,4006,3951,10850,12055,4001,11029,12119,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,3316,3393,12107,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,3472,10645,10911,10955,11225,11303,11467,11709,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,3379,10674,10704,10713,11254,3416,3410,3828,3767,10347,11627,11657,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,3336,10707,10860,10931,11658,11813,12002,3789,4564,3800,3835,4543,4545,3287,3288,4544,4547,4548,4588,3807,3626,4224,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,4013,3906,11347,11684,11688,3752,10971,10977,10992,11929,3613,11194,3754,10710,11048,11200,11230,3582,10631,10634,10716,10890,4581,11621,4583,10767,10869,11179,11331,11464,11492,12228,4178,10843,4086,3788,3733,4579,10323,10326,10662,10665,11503,4580,11601,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462,6463,6465,6466,6468,6470,6471,6472,6474,6476,6479,6485,6486,6487,6488,6494,6496,6536,6541,6556,6557,6558,6559,6594,6599,6601,6606,6607,6615,6619,6632,6657,6658,6659,6660,6671,6676,6693,6697,6716,6749,6750,6751,6756,6764,6785,6787,6789,6791,6794,6800,6802,6815,6822,6857,6860,6861,6874,6875,6876,6877,6893,6894,6911,6937,6960,6971,6973,6974,6976,6978,6979,7014,7015,7020,7021,7023,7025,7026,7027,7052,7061,7062,7073,7083,7122,7132,7136,7143,7154,7155,7160,7162,7168,7176,7177,7190,7207,7225,7227,7244,7288,7290,7291,7292,7299,7304,7320,7364,7398,7412,7429,7462,7465,7488,7512,7530,7533,7534,7544,7561,7562,7564,7566,7568,7570,7594,7619,7620,7652,7654,7655,7656,7661,7681,7690,7701,7706,7712,7714,7720,7731,7732,7734,7755,7764,7789,7856,7857,7899,7907,7908,7927,7928])).
% 162.46/162.13 cnf(12237,plain,
% 162.46/162.13 (~P24(f331(f331(f196(f891(x122371,f891(x122372,a877))),x122373),x122374))),
% 162.46/162.13 inference(rename_variables,[],[4583])).
% 162.46/162.13 cnf(12240,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(f890(f884(x122401),f884(x122401)),a877)),f161(x122401,x122402)),f307(f884(x122401),f160(x122401,x122402))))),
% 162.46/162.13 inference(rename_variables,[],[4006])).
% 162.46/162.13 cnf(12245,plain,
% 162.46/162.13 (P24(f331(f331(f248(f891(x122451,a877)),f196(f891(x122451,a877))),f256(f891(x122451,a877))))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,11085,12122,3563,4519,4520,4503,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,4500,10471,10564,3523,3230,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2939,2940,2975,2982,2983,2991,2994,3029,3035,3037,3040,3041,3043,3044,3046,3063,3064,3068,3070,3080,3086,3102,4481,3156,11358,3358,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,3244,11633,3255,3770,11017,11639,3999,3146,3966,3857,11408,3210,3176,3171,3154,3155,3160,3190,3327,12067,3375,10853,3243,3265,10512,3420,4575,3939,4509,10304,10468,3303,11729,4567,11020,11090,11311,11314,3421,3205,10370,10677,3206,3477,3124,3226,11398,4080,3942,11026,11152,11203,4590,10958,11157,11262,11284,11319,11325,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,3677,4367,4368,3617,3824,3867,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,3758,11624,3296,3397,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,4571,11506,11539,11574,11604,3745,3525,3889,3342,3343,3317,4554,4505,3508,4574,4074,11279,3636,3357,11753,11756,4046,4006,11897,12240,3951,10850,12055,4001,11029,12119,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,3316,3393,12107,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,3472,10645,10911,10955,11225,11303,11467,11709,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,3379,10674,10704,10713,11254,3416,3410,3828,3767,10347,11627,11657,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,3336,10707,10860,10931,11658,11813,12002,3789,4564,3800,3835,4543,4545,3287,3288,4544,4547,4548,4588,3807,3626,4224,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,4013,3906,11347,11684,11688,3752,10971,10977,10992,11929,3613,11194,3754,10710,11048,11200,11230,11241,3582,10631,10634,10716,10890,4581,11621,4583,10767,10869,11179,11331,11464,11492,12228,4178,10843,4086,3788,3733,4579,10323,10326,10662,10665,11503,4580,11601,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,102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% 162.46/162.13 cnf(12246,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x122461,a877)),f196(f891(x122461,a877))),x122462))),
% 162.46/162.13 inference(rename_variables,[],[3754])).
% 162.46/162.13 cnf(12249,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x122491,a877)),f331(f310(x122492,x122491,x122493),f331(f311(x122492,x122491,x122493),x122494))),x122494))),
% 162.46/162.13 inference(rename_variables,[],[4178])).
% 162.46/162.13 cnf(12252,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x122521,a877)),f331(f175(x122521),f173(x122521,x122522,x122523))),f331(f175(x122521),x122523)))),
% 162.46/162.13 inference(rename_variables,[],[4001])).
% 162.46/162.13 cnf(12253,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x122531,a877)),f331(f175(x122531),f331(f139(x122531,x122532),x122533))),f331(f175(x122531),x122533)))),
% 162.46/162.13 inference(rename_variables,[],[3951])).
% 162.46/162.13 cnf(12256,plain,
% 162.46/162.13 (P21(x122561,f887(x122561),f239(x122561),x122562)),
% 162.46/162.13 inference(rename_variables,[],[3564])).
% 162.46/162.13 cnf(12261,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x122611,a877)),f331(f310(x122612,x122611,x122613),f331(f311(x122612,x122611,x122613),x122614))),x122614))),
% 162.46/162.13 inference(rename_variables,[],[4178])).
% 162.46/162.13 cnf(12264,plain,
% 162.46/162.13 (P24(f331(f62(f887(x122641)),f331(f310(x122642,f887(x122641),f331(f180(x122642,x122641),x122643)),f256(f891(x122642,a877)))))),
% 162.46/162.13 inference(rename_variables,[],[4013])).
% 162.46/162.13 cnf(12269,plain,
% 162.46/162.13 (P24(f331(f331(f333(f884(x122691)),f119(x122691)),f164(x122691,x122692)))),
% 162.46/162.13 inference(rename_variables,[],[3516])).
% 162.46/162.13 cnf(12272,plain,
% 162.46/162.13 (~P24(f331(f331(f333(f890(f884(x122721),f884(x122721))),f331(f331(f261(f884(x122721),f884(x122721)),x122722),f119(x122721))),f148(x122721,x122723)))),
% 162.46/162.13 inference(rename_variables,[],[4590])).
% 162.46/162.13 cnf(12275,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x122751),f2(a883)))),
% 162.46/162.13 inference(rename_variables,[],[4557])).
% 162.46/162.13 cnf(12277,plain,
% 162.46/162.13 (~P24(f331(f62(x122771),f256(f891(x122771,a877))))),
% 162.46/162.13 inference(scs_inference,[],[4582,3553,11085,12122,3563,3564,3281,4519,4520,3185,4503,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,4500,10471,10564,3523,3230,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2933,2939,2940,2975,2982,2983,2991,2994,3029,3035,3037,3040,3041,3043,3044,3046,3063,3064,3068,3070,3080,3086,3102,4481,3156,11358,3358,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,3244,11633,3255,3770,11017,11639,3999,3146,3966,3857,11408,3210,3176,3171,3154,3155,3160,3190,3327,12067,3375,10853,3243,3265,10512,3420,4575,3939,4509,10304,10468,3303,11729,4567,11020,11090,11311,11314,3421,3205,10370,10677,3206,3477,3124,3226,11398,4080,3942,11026,11152,11203,4590,10958,11157,11262,11284,11319,11325,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,12225,12269,3677,4367,4368,3617,3824,3867,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,3758,11624,3296,3397,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,4571,11506,11539,11574,11604,3745,3525,3889,3342,3343,3317,4554,4505,3508,4574,4074,11279,3636,3357,11753,11756,4046,4006,11897,12240,3951,10850,12055,12081,4001,11029,12119,12192,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,3316,3393,12107,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,3472,10645,10911,10955,11225,11303,11467,11709,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,3379,10674,10704,10713,11254,3416,3410,3828,3767,10347,11627,11657,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,3336,10707,10860,10931,11658,11813,12002,3789,4564,3800,3835,4543,4545,3287,3288,4544,4547,4548,4588,3807,3626,4224,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,4013,3906,11347,11684,11688,3752,10971,10977,10992,11929,3613,11194,12166,3754,10710,11048,11200,11230,11241,3582,10631,10634,10716,10890,4581,11621,4583,10767,10869,11179,11331,11464,11492,12228,4178,10843,12078,12249,4086,3788,3733,4579,10323,10326,10662,10665,11503,4580,11601,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462,6463,6465,6466,6468,6470,6471,6472,6474,6476,6479,6485,6486,6487,6488,6494,6496,6536,6541,6556,6557,6558,6559,6594,6599,6601,6606,6607,6615,6619,6632,6657,6658,6659,6660,6671,6676,6693,6697,6716,6749,6750,6751,6756,6764,6785,6787,6789,6791,6794,6800,6802,6815,6822,6857,6860,6861,6874,6875,6876,6877,6893,6894,6911,6937,6960,6971,6973,6974,6976,6978,6979,7014,7015,7020,7021,7023,7025,7026,7027,7052,7061,7062,7073,7083,7122,7132,7136,7143,7154,7155,7160,7162,7168,7176,7177,7190,7207,7225,7227,7244,7288,7290,7291,7292,7299,7304,7320,7364,7398,7412,7429,7462,7465,7488,7512,7530,7533,7534,7544,7561,7562,7564,7566,7568,7570,7594,7619,7620,7652,7654,7655,7656,7661,7681,7690,7701,7706,7712,7714,7720,7731,7732,7734,7755,7764,7789,7856,7857,7899,7907,7908,7927,7928,7945,7946,8011,8012,8013,8039,8075,8082,8085,8094,8106,8139,8145,8152])).
% 162.46/162.13 cnf(12278,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x122781,a877)),x122782),x122782))),
% 162.46/162.13 inference(rename_variables,[],[3613])).
% 162.46/162.13 cnf(12281,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x122811),x122812),f196(f891(x122811,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(12284,plain,
% 162.46/162.13 (~P24(f331(f331(f196(f891(x122841,f891(x122842,a877))),x122843),x122844))),
% 162.46/162.13 inference(rename_variables,[],[4583])).
% 162.46/162.13 cnf(12287,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x122871,a877)),f331(f310(x122872,x122871,x122873),f331(f311(x122872,x122871,x122873),x122874))),x122874))),
% 162.46/162.13 inference(rename_variables,[],[4178])).
% 162.46/162.13 cnf(12288,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x122881,a877)),x122882),x122882))),
% 162.46/162.13 inference(rename_variables,[],[3613])).
% 162.46/162.13 cnf(12293,plain,
% 162.46/162.13 (E(f331(f257(x122931,x122931),f258(x122931,x122932)),x122932)),
% 162.46/162.13 inference(rename_variables,[],[3270])).
% 162.46/162.13 cnf(12296,plain,
% 162.46/162.13 (P24(f331(f331(f247(f891(x122961,a877)),f331(f175(x122961),f173(x122961,x122962,x122963))),f331(f175(x122961),x122963)))),
% 162.46/162.13 inference(rename_variables,[],[4001])).
% 162.46/162.13 cnf(12297,plain,
% 162.46/162.13 (P24(f331(f62(x122971),f331(f175(x122971),x122972)))),
% 162.46/162.13 inference(rename_variables,[],[3357])).
% 162.46/162.13 cnf(12300,plain,
% 162.46/162.13 (P24(f331(f331(f203(a24),x123001),x123001))),
% 162.46/162.13 inference(rename_variables,[],[3313])).
% 162.46/162.13 cnf(12303,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x123031),x123031))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(12306,plain,
% 162.46/162.13 (~P24(f331(f331(f248(a883),x123061),x123061))),
% 162.46/162.13 inference(rename_variables,[],[4553])).
% 162.46/162.13 cnf(12317,plain,
% 162.46/162.13 (P21(x123171,x123171,f5(x123171),x123172)),
% 162.46/162.13 inference(rename_variables,[],[3553])).
% 162.46/162.13 cnf(12324,plain,
% 162.46/162.13 (~P24(f331(f331(f333(x123241),x123242),f196(f891(x123241,a877))))),
% 162.46/162.13 inference(rename_variables,[],[4569])).
% 162.46/162.13 cnf(12327,plain,
% 162.46/162.13 (P24(f331(f331(f333(f890(x123271,x123271)),f331(f331(f261(x123271,x123271),x123272),x123272)),f307(x123271,x123273)))),
% 162.46/162.13 inference(rename_variables,[],[3942])).
% 162.46/162.13 cnf(12330,plain,
% 162.46/162.14 (~P24(f331(f331(f333(x123301),x123302),f196(f891(x123301,a877))))),
% 162.46/162.14 inference(rename_variables,[],[4569])).
% 162.46/162.14 cnf(12333,plain,
% 162.46/162.14 (P24(f331(f331(f333(f890(x123331,x123331)),f331(f331(f261(x123331,x123331),x123332),x123332)),f307(x123331,x123333)))),
% 162.46/162.14 inference(rename_variables,[],[3942])).
% 162.46/162.14 cnf(12340,plain,
% 162.46/162.14 (~E(f331(f331(f154(x123401),x123402),x123403),x123403)),
% 162.46/162.14 inference(rename_variables,[],[4509])).
% 162.46/162.14 cnf(12343,plain,
% 162.46/162.14 (P24(f331(f331(f333(x123431),x123432),f256(f891(x123431,a877))))),
% 162.46/162.14 inference(rename_variables,[],[3472])).
% 162.46/162.14 cnf(12344,plain,
% 162.46/162.14 (~E(f331(a118,x123441),x123441)),
% 162.46/162.14 inference(rename_variables,[],[4485])).
% 162.46/162.14 cnf(12347,plain,
% 162.46/162.14 (P24(f331(f331(f333(f884(x123471)),f119(x123471)),f164(x123471,x123472)))),
% 162.46/162.14 inference(rename_variables,[],[3516])).
% 162.46/162.14 cnf(12348,plain,
% 162.46/162.14 (~E(f331(f331(f154(x123481),x123482),x123483),f119(x123481))),
% 162.46/162.14 inference(rename_variables,[],[4518])).
% 162.46/162.14 cnf(12351,plain,
% 162.46/162.14 (P24(f331(f331(f333(x123511),f331(x123512,x123513)),f331(f310(x123514,x123511,x123512),f256(f891(x123514,a877)))))),
% 162.46/162.14 inference(rename_variables,[],[3906])).
% 162.46/162.14 cnf(12352,plain,
% 162.46/162.14 (P21(x123521,x123521,f5(x123521),x123522)),
% 162.46/162.14 inference(rename_variables,[],[3553])).
% 162.46/162.14 cnf(12355,plain,
% 162.46/162.14 (P24(f331(f331(f247(f891(x123551,a877)),f196(f891(x123551,a877))),x123552))),
% 162.46/162.14 inference(rename_variables,[],[3754])).
% 162.46/162.14 cnf(12356,plain,
% 162.46/162.14 (P24(f331(f331(f247(f891(x123561,a877)),x123562),x123562))),
% 162.46/162.14 inference(rename_variables,[],[3613])).
% 162.46/162.14 cnf(12359,plain,
% 162.46/162.14 (P24(f331(f331(f333(x123591),f331(x123592,x123593)),f331(f310(x123594,x123591,x123592),f256(f891(x123594,a877)))))),
% 162.46/162.14 inference(rename_variables,[],[3906])).
% 162.46/162.14 cnf(12360,plain,
% 162.46/162.14 (P21(x123601,x123601,f5(x123601),x123602)),
% 162.46/162.14 inference(rename_variables,[],[3553])).
% 162.46/162.14 cnf(12363,plain,
% 162.46/162.14 (P24(f331(f331(f333(f890(f884(x123631),f884(x123631))),f331(f331(f261(f884(x123631),f884(x123631)),f119(x123631)),f119(x123631))),f161(x123631,x123632)))),
% 162.46/162.14 inference(rename_variables,[],[4080])).
% 162.46/162.14 cnf(12366,plain,
% 162.46/162.14 (~P24(f331(f331(f248(a883),x123661),x123661))),
% 162.46/162.14 inference(rename_variables,[],[4553])).
% 162.46/162.14 cnf(12367,plain,
% 162.46/162.14 (~P24(f331(f331(f248(a883),x123671),f2(a883)))),
% 162.46/162.14 inference(rename_variables,[],[4557])).
% 162.46/162.14 cnf(12373,plain,
% 162.46/162.14 (P21(x123731,x123731,f5(x123731),x123732)),
% 162.46/162.14 inference(rename_variables,[],[3553])).
% 162.46/162.14 cnf(12376,plain,
% 162.46/162.14 (E(f331(f331(f137(x123761),x123762),f119(x123761)),x123762)),
% 162.46/162.14 inference(rename_variables,[],[3244])).
% 162.46/162.14 cnf(12377,plain,
% 162.46/162.14 (~E(f331(f331(f154(x123771),x123772),x123773),x123773)),
% 162.46/162.14 inference(rename_variables,[],[4509])).
% 162.46/162.14 cnf(12380,plain,
% 162.46/162.14 (E(f331(f331(f137(x123801),x123802),f119(x123801)),x123802)),
% 162.46/162.14 inference(rename_variables,[],[3244])).
% 162.46/162.14 cnf(12381,plain,
% 162.46/162.14 (~E(f331(f331(f154(x123811),x123812),x123813),x123813)),
% 162.46/162.14 inference(rename_variables,[],[4509])).
% 162.46/162.14 cnf(12384,plain,
% 162.46/162.14 (E(f331(f331(f137(x123841),x123842),f119(x123841)),x123842)),
% 162.46/162.14 inference(rename_variables,[],[3244])).
% 162.46/162.14 cnf(12393,plain,
% 162.46/162.14 (P24(f331(f331(f247(f891(x123931,a877)),x123932),f256(f891(x123931,a877))))),
% 162.46/162.14 inference(rename_variables,[],[3695])).
% 162.46/162.14 cnf(12397,plain,
% 162.46/162.14 (~P24(f331(f331(f248(a883),x123971),x123971))),
% 162.46/162.14 inference(rename_variables,[],[4553])).
% 162.46/162.14 cnf(12398,plain,
% 162.46/162.14 (~E(f331(a118,x123981),x123981)),
% 162.46/162.14 inference(rename_variables,[],[4485])).
% 162.46/162.14 cnf(12401,plain,
% 162.46/162.14 (P24(f331(f331(f247(f891(x124011,a877)),f196(f891(x124011,a877))),x124012))),
% 162.46/162.14 inference(rename_variables,[],[3754])).
% 162.46/162.14 cnf(12404,plain,
% 162.46/162.14 (P24(f331(f331(f247(a883),x124041),x124041))),
% 162.46/162.14 inference(rename_variables,[],[3314])).
% 162.46/162.14 cnf(12407,plain,
% 162.46/162.14 (P24(f331(f331(f247(f891(x124071,a877)),x124072),x124072))),
% 162.46/162.14 inference(rename_variables,[],[3613])).
% 162.46/162.14 cnf(12412,plain,
% 162.46/162.14 (P24(f331(f331(f247(f891(x124121,a877)),x124122),f331(f331(f309(x124121),x124123),x124122)))),
% 162.46/162.14 inference(rename_variables,[],[3752])).
% 162.46/162.14 cnf(12415,plain,
% 162.46/162.14 (P24(f331(f331(f247(f891(x124151,a877)),x124152),x124152))),
% 162.46/162.14 inference(rename_variables,[],[3613])).
% 162.46/162.14 cnf(12416,plain,
% 162.46/162.14 (~P24(f331(f331(f333(x124161),x124162),f196(f891(x124161,a877))))),
% 162.46/162.14 inference(rename_variables,[],[4569])).
% 162.46/162.14 cnf(12419,plain,
% 162.46/162.14 (~P24(f331(f331(f333(x124191),x124192),f196(f891(x124191,a877))))),
% 162.46/162.14 inference(rename_variables,[],[4569])).
% 162.46/162.14 cnf(12428,plain,
% 162.46/162.14 (P21(x124281,x124281,f5(x124281),x124282)),
% 162.46/162.14 inference(rename_variables,[],[3553])).
% 162.46/162.14 cnf(12431,plain,
% 162.46/162.14 (E(f331(f197(f884(x124311)),f331(f171(x124311),x124312)),f331(f197(f884(x124311)),x124312))),
% 162.46/162.14 inference(rename_variables,[],[3327])).
% 162.46/162.14 cnf(12434,plain,
% 162.46/162.14 (~P24(f331(f331(f248(a883),x124341),x124341))),
% 162.46/162.14 inference(rename_variables,[],[4553])).
% 162.46/162.14 cnf(12435,plain,
% 162.46/162.14 (P24(f331(f256(f891(x124351,a877)),x124352))),
% 162.46/162.14 inference(rename_variables,[],[3379])).
% 162.46/162.14 cnf(12438,plain,
% 162.46/162.14 (~P24(f331(f331(f333(x124381),x124382),f196(f891(x124381,a877))))),
% 162.46/162.14 inference(rename_variables,[],[4569])).
% 162.46/162.14 cnf(12441,plain,
% 162.46/162.14 (P24(f331(f331(f333(x124411),f331(x124412,x124413)),f331(f310(x124414,x124411,x124412),f256(f891(x124414,a877)))))),
% 162.46/162.14 inference(rename_variables,[],[3906])).
% 162.46/162.14 cnf(12442,plain,
% 162.46/162.14 (P24(f331(f331(f333(f890(x124421,x124421)),f331(f331(f261(x124421,x124421),x124422),x124422)),f307(x124421,x124423)))),
% 162.46/162.14 inference(rename_variables,[],[3942])).
% 162.46/162.14 cnf(12445,plain,
% 162.46/162.14 (P24(f331(f331(f333(f890(x124451,x124451)),f331(f331(f261(x124451,x124451),x124452),x124452)),f307(x124451,x124453)))),
% 162.46/162.14 inference(rename_variables,[],[3942])).
% 162.46/162.14 cnf(12448,plain,
% 162.46/162.14 (P24(f331(f331(f247(a883),x124481),x124481))),
% 162.46/162.14 inference(rename_variables,[],[3314])).
% 162.46/162.14 cnf(12449,plain,
% 162.46/162.14 (P24(f331(f256(f891(x124491,a877)),x124492))),
% 162.46/162.14 inference(rename_variables,[],[3379])).
% 162.46/162.14 cnf(12452,plain,
% 162.46/162.14 (P24(f331(f62(x124521),f331(f175(x124521),x124522)))),
% 162.46/162.14 inference(rename_variables,[],[3357])).
% 162.46/162.14 cnf(12457,plain,
% 162.46/162.14 (P24(f331(f331(f333(f890(f884(x124571),f884(x124571))),f331(f331(f261(f884(x124571),f884(x124571)),f119(x124571)),f119(x124571))),f331(f331(f288(f884(x124571),f884(x124571),f884(x124571)),f161(x124571,x124572)),f161(x124571,x124572))))),
% 162.46/162.14 inference(scs_inference,[],[4582,3553,11085,12122,12222,12317,12352,12360,12373,3563,3564,3281,4519,4520,3185,4503,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,12189,12344,4500,10471,10564,3374,3523,3230,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2933,2939,2940,2975,2982,2983,2991,2994,3029,3035,3037,3040,3041,3043,3044,3046,3063,3064,3068,3070,3080,3086,3102,4481,3156,11358,3358,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,12096,3244,11633,12376,12380,12384,3255,3770,11017,11639,3999,3146,3966,4497,3857,11408,3210,3176,3171,3154,3155,3160,3190,3327,12067,12212,3375,10853,12183,3242,3243,3265,10512,3420,4575,3939,4509,10304,10468,11268,12340,12377,4518,12348,3303,11729,4567,11020,11090,11311,11314,3421,3205,10370,10677,3206,3477,3124,3226,11398,4080,12363,3942,11026,11152,11203,12327,12333,12442,4590,10958,11157,11262,11284,11319,11325,12272,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,12225,12269,12347,3677,4367,4368,3617,3824,3867,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,12151,3758,11624,3296,3397,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,12275,4571,11506,11539,11574,11604,3745,3525,3889,3342,3343,3317,4554,4505,3704,3508,4574,4074,11279,3636,3357,11753,11756,12193,12297,4046,4006,11897,12240,3951,10850,12055,12081,4001,11029,12119,12192,12252,12296,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,12141,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,12134,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,12233,12404,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,3316,3393,12107,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,12207,12303,12306,12366,12397,3472,10645,10911,10955,11225,11303,11467,11709,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,12137,12281,12324,12330,12416,12419,3379,10674,10704,10713,11254,11808,12435,3416,3410,3828,3767,10347,11627,11657,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,3336,10707,10860,10931,11658,11813,12002,3789,4564,3800,3835,4543,4545,3287,3288,4544,4547,4548,4588,3807,3626,4224,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,11350,4013,3906,11347,11684,11688,11750,12351,12359,3752,10971,10977,10992,11929,12140,3613,11194,12166,12278,12288,12356,12407,3754,10710,11048,11200,11230,11241,12246,12355,3582,10631,10634,10716,10890,4581,11621,4583,10767,10869,11179,11331,11464,11492,12228,12237,4178,10843,12078,12249,12261,4086,3788,3733,4579,10323,10326,10662,10665,11503,4580,11601,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8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% 162.46/162.14 cnf(12459,plain,
% 162.46/162.14 (P24(f331(f331(f333(f890(x124591,x124591)),f331(f331(f261(x124591,x124591),x124592),x124592)),f331(f331(f288(x124591,x124591,x124591),f307(x124591,x124593)),f307(x124591,f307(x124591,x124593)))))),
% 162.46/162.14 inference(scs_inference,[],[4582,3553,11085,12122,12222,12317,12352,12360,12373,3563,3564,3281,4519,4520,3185,4503,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,12189,12344,4500,10471,10564,3374,3523,3230,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2933,2939,2940,2975,2982,2983,2991,2994,3029,3035,3037,3040,3041,3043,3044,3046,3063,3064,3068,3070,3080,3086,3102,4481,3156,11358,3358,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,12096,3244,11633,12376,12380,12384,3255,3770,11017,11639,3999,3146,3966,4497,3857,11408,3210,3176,3171,3154,3155,3160,3190,3327,12067,12212,3375,10853,12183,3242,3243,3265,10512,3420,4575,3939,4509,10304,10468,11268,12340,12377,4518,12348,3303,11729,4567,11020,11090,11311,11314,3421,3205,10370,10677,3206,3477,3124,3226,11398,4080,12363,3942,11026,11152,11203,12327,12333,12442,12445,4590,10958,11157,11262,11284,11319,11325,12272,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,12225,12269,12347,3677,4367,4368,3617,3824,3867,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,12151,3758,11624,3296,3397,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,12275,4571,11506,11539,11574,11604,3745,3525,3889,3342,3343,3317,4554,4505,3704,3508,4574,4074,11279,3636,3357,11753,11756,12193,12297,4046,4006,11897,12240,3951,10850,12055,12081,4001,11029,12119,12192,12252,12296,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,12141,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,12134,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,12233,12404,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,3316,3393,12107,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,12207,12303,12306,12366,12397,3472,10645,10911,10955,11225,11303,11467,11709,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,12137,12281,12324,12330,12416,12419,3379,10674,10704,10713,11254,11808,12435,3416,3410,3828,3767,10347,11627,11657,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,3336,10707,10860,10931,11658,11813,12002,3789,4564,3800,3835,4543,4545,3287,3288,4544,4547,4548,4588,3807,3626,4224,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,11350,4013,3906,11347,11684,11688,11750,12351,12359,3752,10971,10977,10992,11929,12140,3613,11194,12166,12278,12288,12356,12407,3754,10710,11048,11200,11230,11241,12246,12355,3582,10631,10634,10716,10890,4581,11621,4583,10767,10869,11179,11331,11464,11492,12228,12237,4178,10843,12078,12249,12261,4086,3788,3733,4579,10323,10326,10662,10665,11503,4580,11601,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462,6463,6465,6466,6468,6470,6471,6472,6474,6476,6479,6485,6486,6487,6488,6494,6496,6536,6541,6556,6557,6558,6559,6594,6599,6601,6606,6607,6615,6619,6632,6657,6658,6659,6660,6671,6676,6693,6697,6716,6749,6750,6751,6756,6764,6785,6787,6789,6791,6794,6800,6802,6815,6822,6857,6860,6861,6874,6875,6876,6877,6893,6894,6911,6937,6960,6971,6973,6974,6976,6978,6979,7014,7015,7020,7021,7023,7025,7026,7027,7052,7061,7062,7073,7083,7122,7132,7136,7143,7154,7155,7160,7162,7168,7176,7177,7190,7207,7225,7227,7244,7288,7290,7291,7292,7299,7304,7320,7364,7398,7412,7429,7462,7465,7488,7512,7530,7533,7534,7544,7561,7562,7564,7566,7568,7570,7594,7619,7620,7652,7654,7655,7656,7661,7681,7690,7701,7706,7712,7714,7720,7731,7732,7734,7755,7764,7789,7856,7857,7899,7907,7908,7927,7928,7945,7946,8011,8012,8013,8039,8075,8082,8085,8094,8106,8139,8145,8152,8165,8184,8191,8211,8253,8283,8295,8313,8316,8343,8366,8427,8428,8432,8434,8454,8541,8542,8543,8544,8597,8627,8664,8681,8731,8781,8784,8799,8806,8844,8865,8894,8895,8911,8912,9044,9048,9061,9072,9101,9103,9106,9110,9113,9114,9129,9130,9153,9159,9171,9217,9236,9298,9299,9301,9366,9372,9400,9407])).
% 162.46/162.14 cnf(12462,plain,
% 162.46/162.14 (~P24(f331(f331(f196(f891(x124621,f891(x124622,a877))),x124623),x124624))),
% 162.46/162.14 inference(rename_variables,[],[4583])).
% 162.46/162.14 cnf(12465,plain,
% 162.46/162.14 (P24(f331(f331(f247(f891(x124651,a877)),x124652),f256(f891(x124651,a877))))),
% 162.46/162.14 inference(rename_variables,[],[3695])).
% 162.46/162.14 cnf(12468,plain,
% 162.46/162.14 (P24(f331(f331(f333(f890(x124681,x124681)),f331(f331(f261(x124681,x124681),x124682),x124682)),f307(x124681,x124683)))),
% 162.46/162.14 inference(rename_variables,[],[3942])).
% 162.46/162.14 cnf(12471,plain,
% 162.46/162.14 (~P24(f331(f331(f248(a883),f331(f331(f81(a883),x124711),x124712)),x124712))),
% 162.46/162.14 inference(rename_variables,[],[4579])).
% 162.46/162.14 cnf(12472,plain,
% 162.46/162.14 (P24(f331(f331(f248(a883),x124721),f331(a118,x124721)))),
% 162.46/162.14 inference(rename_variables,[],[3385])).
% 162.46/162.14 cnf(12475,plain,
% 162.46/162.14 (P24(f331(f331(f247(f891(x124751,a877)),f331(f175(x124751),f331(f139(x124751,x124752),x124753))),f331(f175(x124751),x124753)))),
% 162.46/162.14 inference(rename_variables,[],[3951])).
% 162.46/162.14 cnf(12478,plain,
% 162.46/162.14 (P24(f331(f331(f247(f891(x124781,a877)),x124782),f256(f891(x124781,a877))))),
% 162.46/162.14 inference(rename_variables,[],[3695])).
% 162.46/162.14 cnf(12481,plain,
% 162.46/162.14 (E(f331(f257(x124811,x124811),f258(x124811,x124812)),x124812)),
% 162.46/162.14 inference(rename_variables,[],[3270])).
% 162.46/162.14 cnf(12492,plain,
% 162.46/162.14 (~P24(f331(f331(f333(x124921),x124922),f196(f891(x124921,a877))))),
% 162.46/162.14 inference(rename_variables,[],[4569])).
% 162.46/162.14 cnf(12493,plain,
% 162.46/162.14 (P24(f331(f331(f333(f890(f884(x124931),f884(x124931))),f331(f331(f261(f884(x124931),f884(x124931)),f119(x124931)),f119(x124931))),f161(x124931,x124932)))),
% 162.46/162.14 inference(rename_variables,[],[4080])).
% 162.46/162.14 cnf(12495,plain,
% 162.46/162.14 (P24(f331(f331(f333(f890(a883,a883)),f331(f331(f261(a883,a883),f331(a118,x124951)),f331(a118,f331(a118,x124951)))),f331(f331(f288(a883,a883,a883),f307(a883,a321)),f307(a883,f307(a883,a321)))))),
% 162.46/162.14 inference(scs_inference,[],[4582,3553,11085,12122,12222,12317,12352,12360,12373,3563,3564,3281,4519,4520,3185,4503,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,12189,12344,4500,10471,10564,3374,3523,3230,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2933,2939,2940,2975,2982,2983,2991,2994,3029,3035,3037,3040,3041,3043,3044,3046,3063,3064,3068,3070,3080,3086,3102,4481,3652,3156,11358,3358,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,12096,12293,3244,11633,12376,12380,12384,3255,3770,11017,11639,3999,3146,3966,4497,3857,11408,3210,3176,3171,3154,3155,3160,3190,3327,12067,12212,3375,10853,12183,3242,3243,3265,10512,3420,4575,3939,4509,10304,10468,11268,12340,12377,4518,12348,3303,11729,4567,11020,11090,11311,11314,3421,3205,10370,10677,3206,3477,3124,3226,11398,4080,12363,3942,11026,11152,11203,12327,12333,12442,12445,12468,4590,10958,11157,11262,11284,11319,11325,12272,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,12225,12269,12347,3677,4367,4368,3617,3824,3867,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,12151,3758,11624,3296,3397,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,12275,4571,11506,11539,11574,11604,3745,3525,3889,3342,3343,3317,4554,4505,3704,4216,3508,4574,4074,11279,3636,3357,11753,11756,12193,12297,4046,4006,11897,12240,3951,10850,12055,12081,12253,4001,11029,12119,12192,12252,12296,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,12141,12393,12465,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,12134,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,12233,12404,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,3316,3393,12107,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,12207,12303,12306,12366,12397,3472,10645,10911,10955,11225,11303,11467,11709,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,12137,12281,12324,12330,12416,12419,12438,3379,10674,10704,10713,11254,11808,12435,3416,3410,3828,3767,10347,11627,11657,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,3336,10707,10860,10931,11658,11813,12002,3789,4564,3800,3835,4543,4545,3287,3288,4544,4547,4548,4588,3807,3626,4224,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,11350,4013,3906,11347,11684,11688,11750,12351,12359,3752,10971,10977,10992,11929,12140,3613,11194,12166,12278,12288,12356,12407,4078,3754,10710,11048,11200,11230,11241,12246,12355,3582,10631,10634,10716,10890,4581,11621,4583,10767,10869,11179,11331,11464,11492,12228,12237,12284,4178,10843,12078,12249,12261,4086,3788,3733,4579,10323,10326,10662,10665,11503,11685,4580,11601,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462,6463,6465,6466,6468,6470,6471,6472,6474,6476,6479,6485,6486,6487,6488,6494,6496,6536,6541,6556,6557,6558,6559,6594,6599,6601,6606,6607,6615,6619,6632,6657,6658,6659,6660,6671,6676,6693,6697,6716,6749,6750,6751,6756,6764,6785,6787,6789,6791,6794,6800,6802,6815,6822,6857,6860,6861,6874,6875,6876,6877,6893,6894,6911,6937,6960,6971,6973,6974,6976,6978,6979,7014,7015,7020,7021,7023,7025,7026,7027,7052,7061,7062,7073,7083,7122,7132,7136,7143,7154,7155,7160,7162,7168,7176,7177,7190,7207,7225,7227,7244,7288,7290,7291,7292,7299,7304,7320,7364,7398,7412,7429,7462,7465,7488,7512,7530,7533,7534,7544,7561,7562,7564,7566,7568,7570,7594,7619,7620,7652,7654,7655,7656,7661,7681,7690,7701,7706,7712,7714,7720,7731,7732,7734,7755,7764,7789,7856,7857,7899,7907,7908,7927,7928,7945,7946,8011,8012,8013,8039,8075,8082,8085,8094,8106,8139,8145,8152,8165,8184,8191,8211,8253,8283,8295,8313,8316,8343,8366,8427,8428,8432,8434,8454,8541,8542,8543,8544,8597,8627,8664,8681,8731,8781,8784,8799,8806,8844,8865,8894,8895,8911,8912,9044,9048,9061,9072,9101,9103,9106,9110,9113,9114,9129,9130,9153,9159,9171,9217,9236,9298,9299,9301,9366,9372,9400,9407,9408,9411,9412,9429,9443,9452,9464,9478,9479,9481,9483,9520])).
% 162.46/162.14 cnf(12498,plain,
% 162.46/162.14 (~P24(f331(f331(f333(x124981),x124982),f196(f891(x124981,a877))))),
% 162.46/162.14 inference(rename_variables,[],[4569])).
% 162.46/162.14 cnf(12501,plain,
% 162.46/162.14 (P32(x125011,x125012,f119(x125011))),
% 162.46/162.14 inference(rename_variables,[],[3249])).
% 162.46/162.14 cnf(12504,plain,
% 162.46/162.14 (E(f331(f197(f884(x125041)),f331(f171(x125041),x125042)),f331(f197(f884(x125041)),x125042))),
% 162.46/162.14 inference(rename_variables,[],[3327])).
% 162.46/162.14 cnf(12507,plain,
% 162.46/162.14 (~P24(f331(f331(f333(x125071),x125072),f196(f891(x125071,a877))))),
% 162.46/162.14 inference(rename_variables,[],[4569])).
% 162.46/162.14 cnf(12512,plain,
% 162.46/162.14 (P24(f331(f331(f203(a24),x125121),x125121))),
% 162.46/162.14 inference(rename_variables,[],[3313])).
% 162.46/162.14 cnf(12514,plain,
% 162.46/162.14 (~P24(f331(f331(f333(f890(f884(x125141),f884(x125141))),f331(f331(f261(f884(x125141),f884(x125141)),x125142),x125142)),f150(x125141,f156(x125141,f119(f891(x125141,a883))))))),
% 162.46/162.14 inference(scs_inference,[],[4582,3553,11085,12122,12222,12317,12352,12360,12373,3563,3564,3281,3249,4519,4520,3185,4503,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,12189,12344,4500,10471,10564,3374,3523,3230,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2933,2939,2940,2975,2982,2983,2991,2994,3029,3035,3037,3040,3041,3043,3044,3046,3063,3064,3068,3070,3080,3086,3102,4481,3652,3156,11358,3358,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,12096,12293,3244,11633,12376,12380,12384,3255,3770,11017,11639,3999,3146,3966,4497,3857,11408,3210,3176,3171,3154,3155,3160,3190,3327,12067,12212,12431,3375,10853,12183,3242,3243,3265,10512,3420,4575,3939,4509,10304,10468,11268,12340,12377,4518,12348,3303,11729,4567,11020,11090,11311,11314,3421,3205,10370,10677,3206,3477,3124,3226,11398,4080,12363,12493,3942,11026,11152,11203,12327,12333,12442,12445,12468,4590,10958,11157,11262,11284,11319,11325,12272,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,12225,12269,12347,3677,4367,4368,3617,3824,3867,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,12151,3758,11624,3296,3397,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,12275,4571,11506,11539,11574,11604,3745,3525,3889,3342,3343,3317,4554,4505,3704,4216,3508,4574,4074,11279,3636,3357,11753,11756,12193,12297,4046,4006,11897,12240,3951,10850,12055,12081,12253,4001,11029,12119,12192,12252,12296,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,12141,12393,12465,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,12134,12300,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,12233,12404,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,3316,3393,12107,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,12207,12303,12306,12366,12397,12434,3472,10645,10911,10955,11225,11303,11467,11709,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,12137,12281,12324,12330,12416,12419,12438,12492,12498,3379,10674,10704,10713,11254,11808,12435,3416,3410,3828,3767,10347,11627,11657,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,3336,10707,10860,10931,11658,11813,12002,3789,4564,3800,3835,4543,4545,3287,3288,4544,4547,4548,4588,3807,3626,4224,11486,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,11350,4013,3906,11347,11684,11688,11750,12351,12359,3752,10971,10977,10992,11929,12140,3613,11194,12166,12278,12288,12356,12407,4078,3754,10710,11048,11200,11230,11241,12246,12355,3582,10631,10634,10716,10890,4581,11621,4583,10767,10869,11179,11331,11464,11492,12228,12237,12284,4178,10843,12078,12249,12261,4086,3788,3733,4579,10323,10326,10662,10665,11503,11685,4580,11601,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462,6463,6465,6466,6468,6470,6471,6472,6474,6476,6479,6485,6486,6487,6488,6494,6496,6536,6541,6556,6557,6558,6559,6594,6599,6601,6606,6607,6615,6619,6632,6657,6658,6659,6660,6671,6676,6693,6697,6716,6749,6750,6751,6756,6764,6785,6787,6789,6791,6794,6800,6802,6815,6822,6857,6860,6861,6874,6875,6876,6877,6893,6894,6911,6937,6960,6971,6973,6974,6976,6978,6979,7014,7015,7020,7021,7023,7025,7026,7027,7052,7061,7062,7073,7083,7122,7132,7136,7143,7154,7155,7160,7162,7168,7176,7177,7190,7207,7225,7227,7244,7288,7290,7291,7292,7299,7304,7320,7364,7398,7412,7429,7462,7465,7488,7512,7530,7533,7534,7544,7561,7562,7564,7566,7568,7570,7594,7619,7620,7652,7654,7655,7656,7661,7681,7690,7701,7706,7712,7714,7720,7731,7732,7734,7755,7764,7789,7856,7857,7899,7907,7908,7927,7928,7945,7946,8011,8012,8013,8039,8075,8082,8085,8094,8106,8139,8145,8152,8165,8184,8191,8211,8253,8283,8295,8313,8316,8343,8366,8427,8428,8432,8434,8454,8541,8542,8543,8544,8597,8627,8664,8681,8731,8781,8784,8799,8806,8844,8865,8894,8895,8911,8912,9044,9048,9061,9072,9101,9103,9106,9110,9113,9114,9129,9130,9153,9159,9171,9217,9236,9298,9299,9301,9366,9372,9400,9407,9408,9411,9412,9429,9443,9452,9464,9478,9479,9481,9483,9520,9655,9697,9698,9745,9799,9907,9908])).
% 162.46/162.14 cnf(12516,plain,
% 162.46/162.14 (~P24(f331(f331(f248(a883),x125161),x125161))),
% 162.46/162.14 inference(rename_variables,[],[4553])).
% 162.46/162.14 cnf(12519,plain,
% 162.46/162.14 (P24(f331(f331(f333(x125191),x125192),f256(f891(x125191,a877))))),
% 162.46/162.14 inference(rename_variables,[],[3472])).
% 162.46/162.14 cnf(12526,plain,
% 162.46/162.14 (P24(f331(f331(f247(f891(x125261,a877)),x125262),x125262))),
% 162.46/162.14 inference(rename_variables,[],[3613])).
% 162.46/162.14 cnf(12529,plain,
% 162.46/162.14 (~P24(f331(f331(f333(x125291),x125292),f196(f891(x125291,a877))))),
% 162.46/162.14 inference(rename_variables,[],[4569])).
% 162.46/162.14 cnf(12532,plain,
% 162.46/162.14 (P24(f331(f331(f247(a1),f2(a1)),f331(f331(f262(a1),f331(f76(a1),x125321)),x125322)))),
% 162.46/162.14 inference(rename_variables,[],[3788])).
% 162.46/162.14 cnf(12535,plain,
% 162.46/162.14 (~E(f331(a118,x125351),x125351)),
% 162.46/162.14 inference(rename_variables,[],[4485])).
% 162.46/162.14 cnf(12537,plain,
% 162.46/162.14 (E(f331(f257(x125371,x125371),f258(x125371,x125372)),x125372)),
% 162.46/162.14 inference(rename_variables,[],[3270])).
% 162.46/162.14 cnf(12542,plain,
% 162.46/162.14 (E(f331(f257(x125421,x125421),f258(x125421,x125422)),x125422)),
% 162.46/162.14 inference(rename_variables,[],[3270])).
% 162.46/162.14 cnf(12544,plain,
% 162.46/162.14 (E(f331(f257(x125441,x125441),f258(x125441,x125442)),x125442)),
% 162.46/162.14 inference(rename_variables,[],[3270])).
% 162.46/162.14 cnf(12546,plain,
% 162.46/162.14 (E(f331(f257(x125461,x125461),f258(x125461,x125462)),x125462)),
% 162.46/162.14 inference(rename_variables,[],[3270])).
% 162.46/162.14 cnf(12548,plain,
% 162.46/162.14 (E(f331(f257(x125481,x125481),f258(x125481,x125482)),x125482)),
% 162.46/162.14 inference(rename_variables,[],[3270])).
% 162.46/162.14 cnf(12550,plain,
% 162.46/162.14 (P38(x125501,f156(x125501,x125502))),
% 162.46/162.14 inference(rename_variables,[],[3185])).
% 162.46/162.14 cnf(12556,plain,
% 162.46/162.14 (P21(x125561,x125561,f5(x125561),x125562)),
% 162.46/162.14 inference(rename_variables,[],[3553])).
% 162.46/162.14 cnf(12558,plain,
% 162.46/162.14 (P21(x125581,x125581,f5(x125581),x125582)),
% 162.46/162.14 inference(rename_variables,[],[3553])).
% 162.46/162.14 cnf(12566,plain,
% 162.46/162.14 (E(f331(f257(x125661,x125661),f258(x125661,x125662)),x125662)),
% 162.46/162.14 inference(rename_variables,[],[3270])).
% 162.46/162.14 cnf(12568,plain,
% 162.46/162.14 (P20(x125681,x125682,f196(f891(f882(x125681),a877)))),
% 162.46/162.14 inference(rename_variables,[],[3373])).
% 162.46/162.14 cnf(12577,plain,
% 162.46/162.14 (P48(x125771,x125772,f258(x125771,x125772))),
% 162.46/162.14 inference(rename_variables,[],[3280])).
% 162.46/162.14 cnf(12579,plain,
% 162.46/162.14 (P48(x125791,x125792,f258(x125791,x125792))),
% 162.46/162.14 inference(rename_variables,[],[3280])).
% 162.46/162.14 cnf(12583,plain,
% 162.46/162.14 (E(f331(f257(x125831,x125831),f258(x125831,x125832)),x125832)),
% 162.46/162.14 inference(rename_variables,[],[3270])).
% 162.46/162.14 cnf(12589,plain,
% 162.46/162.14 (E(f331(f257(x125891,x125891),f258(x125891,x125892)),x125892)),
% 162.46/162.14 inference(rename_variables,[],[3270])).
% 162.46/162.14 cnf(12591,plain,
% 162.46/162.14 (P30(x125911,f2(a883),f331(f331(f331(f93(x125911),x125912),f331(a28,x125913)),x125914))),
% 162.46/162.14 inference(rename_variables,[],[3688])).
% 162.46/162.14 cnf(12608,plain,
% 162.46/162.14 (E(f196(f891(f890(x126081,x126081),a877)),f258(x126081,f196(f891(x126081,a877))))),
% 162.46/162.14 inference(rename_variables,[],[3388])).
% 162.46/162.14 cnf(12613,plain,
% 162.46/162.14 (P11(x126131,f891(x126131,a877),f309(x126131))),
% 162.46/162.14 inference(rename_variables,[],[3284])).
% 162.46/162.14 cnf(12619,plain,
% 162.46/162.14 (P53(x126191,f196(f891(x126191,a877)),x126192)),
% 162.46/162.14 inference(rename_variables,[],[3334])).
% 162.46/162.14 cnf(12624,plain,
% 162.46/162.14 (E(f331(f257(x126241,x126241),f258(x126241,x126242)),x126242)),
% 162.46/162.14 inference(rename_variables,[],[3270])).
% 162.46/162.14 cnf(12626,plain,
% 162.46/162.14 (P42(x126261,x126262,x126263,x126264,f196(f891(x126261,a877)),x126264)),
% 162.46/162.14 inference(rename_variables,[],[4246])).
% 162.46/162.14 cnf(12629,plain,
% 162.46/162.14 (P42(x126291,x126292,x126293,x126294,f196(f891(x126291,a877)),x126294)),
% 162.46/162.14 inference(rename_variables,[],[4246])).
% 162.46/162.14 cnf(12633,plain,
% 162.46/162.14 (E(f331(f257(x126331,x126331),f258(x126331,x126332)),x126332)),
% 162.46/162.14 inference(rename_variables,[],[3270])).
% 162.46/162.14 cnf(12635,plain,
% 162.46/162.14 (P39(x126351,f199(x126351))),
% 162.46/162.14 inference(rename_variables,[],[3143])).
% 162.46/162.14 cnf(12641,plain,
% 162.46/162.14 (P52(x126411,x126411,f258(x126411,x126412))),
% 162.46/162.14 inference(rename_variables,[],[3281])).
% 162.46/162.14 cnf(12650,plain,
% 162.46/162.14 (P33(x126501,x126502,f119(x126501),f119(x126501))),
% 162.46/162.14 inference(rename_variables,[],[3563])).
% 162.46/162.14 cnf(12652,plain,
% 162.46/162.14 (P33(x126521,x126522,f119(x126521),f119(x126521))),
% 162.46/162.14 inference(rename_variables,[],[3563])).
% 162.46/162.14 cnf(12657,plain,
% 162.46/162.14 (P24(f331(f331(f248(a883),f2(a883)),f331(a118,x126571)))),
% 162.46/162.14 inference(rename_variables,[],[3397])).
% 162.46/162.14 cnf(12658,plain,
% 162.46/162.14 (~E(f331(a118,x126581),x126581)),
% 162.46/162.14 inference(rename_variables,[],[4485])).
% 162.46/162.14 cnf(12664,plain,
% 162.46/162.14 (P24(f331(f331(f248(a883),x126641),f331(a118,x126641)))),
% 162.46/162.14 inference(rename_variables,[],[3385])).
% 162.46/162.14 cnf(12669,plain,
% 162.46/162.14 (~P24(f331(f331(f248(a883),x126691),f2(a883)))),
% 162.46/162.14 inference(rename_variables,[],[4557])).
% 162.46/162.14 cnf(12672,plain,
% 162.46/162.14 (~P24(f331(f331(f248(a883),x126721),f2(a883)))),
% 162.46/162.14 inference(rename_variables,[],[4557])).
% 162.46/162.14 cnf(12679,plain,
% 162.46/162.14 (~P24(f331(f331(f248(a1),f331(f106(a1),x126791)),f331(f80(a1),f331(f106(a1),x126792))))),
% 162.46/162.14 inference(rename_variables,[],[4577])).
% 162.46/162.14 cnf(12689,plain,
% 162.46/162.14 (~P24(f331(f331(f248(a883),x126891),f2(a883)))),
% 162.46/162.14 inference(rename_variables,[],[4557])).
% 162.46/162.14 cnf(12692,plain,
% 162.46/162.14 (~P24(f331(f331(f248(a883),x126921),f2(a883)))),
% 162.46/162.14 inference(rename_variables,[],[4557])).
% 162.46/162.14 cnf(12695,plain,
% 162.46/162.14 (P24(f331(f62(a883),f304(a883,x126951,x126952)))),
% 162.46/162.14 inference(rename_variables,[],[3526])).
% 162.46/162.14 cnf(12698,plain,
% 162.46/162.14 (P24(f331(f62(a883),f304(a883,x126981,x126982)))),
% 162.46/162.14 inference(rename_variables,[],[3526])).
% 162.46/162.14 cnf(12701,plain,
% 162.46/162.14 (P24(f331(f62(a883),f304(a883,x127011,x127012)))),
% 162.46/162.14 inference(rename_variables,[],[3526])).
% 162.46/162.14 cnf(12704,plain,
% 162.46/162.14 (P24(f331(f62(a883),f304(a883,x127041,x127042)))),
% 162.46/162.14 inference(rename_variables,[],[3526])).
% 162.46/162.14 cnf(12711,plain,
% 162.46/162.14 (P24(f331(f331(f247(a1),f331(f80(a1),f331(f106(a1),x127111))),f331(f106(a1),x127112)))),
% 162.46/162.14 inference(rename_variables,[],[3789])).
% 162.46/162.14 cnf(12714,plain,
% 162.46/162.14 (~P24(f331(f331(f248(a883),x127141),f2(a883)))),
% 162.46/162.14 inference(rename_variables,[],[4557])).
% 162.46/162.14 cnf(12715,plain,
% 162.46/162.14 (P24(f331(f331(f247(a883),x127151),x127151))),
% 162.46/162.14 inference(rename_variables,[],[3314])).
% 162.46/162.14 cnf(12722,plain,
% 162.46/162.14 (P24(f331(f331(f248(a883),x127221),f331(a118,x127221)))),
% 162.46/162.14 inference(rename_variables,[],[3385])).
% 162.46/162.14 cnf(12725,plain,
% 162.46/162.14 (P24(f331(f331(f333(x127251),f331(x127252,x127253)),f331(f310(x127254,x127251,x127252),f256(f891(x127254,a877)))))),
% 162.46/162.14 inference(rename_variables,[],[3906])).
% 162.46/162.14 cnf(12726,plain,
% 162.46/162.14 (~E(f331(a118,x127261),f2(a883))),
% 162.46/162.14 inference(rename_variables,[],[4495])).
% 162.46/162.14 cnf(12730,plain,
% 162.46/162.14 (P24(f331(f331(f247(a1),f331(f110(a1),a84)),f2(a1)))),
% 162.46/162.14 inference(scs_inference,[],[4582,3553,11085,12122,12222,12317,12352,12360,12373,12428,12556,3563,12186,12650,12652,3564,12256,3280,12577,12579,3281,12641,3249,12501,4519,4520,11706,4246,12626,12629,3284,12613,3123,3143,12635,3185,12550,4503,3615,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,12189,12344,12398,12535,4500,10471,10564,3374,3334,12619,3523,3230,4495,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2933,2939,2940,2949,2975,2982,2983,2991,2994,3029,3031,3035,3037,3040,3041,3043,3044,3046,3063,3064,3068,3070,3080,3086,4480,3102,3184,4481,3652,3156,11358,3294,3358,3267,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,12096,12293,12481,12537,12542,12544,12546,12548,12566,12583,12589,12624,3244,11633,12376,12380,12384,3255,3770,11017,11639,3999,3146,3966,4497,4507,3857,11408,3373,12568,3210,3176,3350,3688,12591,3171,3974,3693,4464,3154,3155,3133,3160,3190,3327,12067,12212,12431,12504,3375,10853,12183,3242,3243,3265,10512,3420,4575,10441,3939,4509,10304,10468,11268,12340,12377,4518,12348,3303,11729,4567,11020,11090,11311,11314,3421,3637,3388,12608,3205,10370,10677,3206,3477,3198,3124,3226,11398,4080,12363,12493,3942,11026,11152,11203,12327,12333,12442,12445,12468,4590,10958,11157,11262,11284,11319,11325,12272,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,12225,12269,12347,3677,4367,4368,3617,3655,3824,3867,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,12151,12472,12664,3758,11624,3296,3397,11744,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,12275,12367,12669,12672,12689,12692,4571,11506,11539,11574,11604,3745,3525,3526,12695,12698,12701,3889,3342,3343,3317,4554,3204,4505,3704,4216,4007,3508,4574,4074,11279,3636,3357,11753,11756,12193,12297,4046,4006,11897,12240,3951,10850,12055,12081,12253,4001,11029,12119,12192,12252,12296,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,12141,12393,12465,12478,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,12134,12300,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,12233,12404,12448,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,11997,3316,3393,12107,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,12207,12303,12306,12366,12397,12434,3472,10645,10911,10955,11225,11303,11467,11709,12343,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,12137,12281,12324,12330,12416,12419,12438,12492,12498,12507,3379,10674,10704,10713,11254,11808,12435,3416,3410,3828,3767,10347,11627,11657,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,3336,10707,10860,10931,11658,11813,12002,3789,11759,3531,4564,3800,3835,4543,4545,4546,3287,3288,4544,4547,4548,4588,3807,3626,4224,11486,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,11350,4013,12264,3906,11347,11684,11688,11750,12351,12359,12441,3752,10971,10977,10992,11929,12140,3613,11194,12166,12278,12288,12356,12407,12415,4078,3754,10710,11048,11200,11230,11241,12246,12355,3582,10631,10634,10716,10890,3581,4581,11621,4577,12679,4583,10767,10869,11179,11331,11464,11492,12228,12237,12284,12462,4178,10843,12078,12249,12261,4086,3788,3733,3734,4579,10323,10326,10662,10665,11503,11685,4580,11601,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806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% 162.46/162.14 cnf(12731,plain,
% 162.46/162.14 (P24(f331(f331(f247(a1),x127311),x127311))),
% 162.46/162.14 inference(rename_variables,[],[3315])).
% 162.46/162.14 cnf(12734,plain,
% 162.46/162.14 (P24(f331(f62(a883),f304(a883,x127341,x127342)))),
% 162.46/162.14 inference(rename_variables,[],[3526])).
% 162.46/162.14 cnf(12737,plain,
% 162.46/162.14 (P24(f331(f62(a883),f304(a883,x127371,x127372)))),
% 162.46/162.14 inference(rename_variables,[],[3526])).
% 162.46/162.14 cnf(12740,plain,
% 162.46/162.14 (P24(f331(f331(f247(a883),x127401),x127401))),
% 162.46/162.14 inference(rename_variables,[],[3314])).
% 162.46/162.14 cnf(12753,plain,
% 162.46/162.14 (P24(f331(f331(f248(a883),x127531),f331(a118,x127531)))),
% 162.46/162.14 inference(rename_variables,[],[3385])).
% 162.46/162.14 cnf(12758,plain,
% 162.46/162.14 (P24(f331(f331(f247(a883),f45(a883,x127581,x127582)),x127581))),
% 162.46/162.14 inference(rename_variables,[],[3767])).
% 162.46/162.14 cnf(12765,plain,
% 162.46/162.14 (P24(f331(f331(f248(a883),x127651),f331(a118,x127651)))),
% 162.46/162.14 inference(rename_variables,[],[3385])).
% 162.46/162.14 cnf(12766,plain,
% 162.46/162.14 (~P24(f331(f331(f248(a883),x127661),f2(a883)))),
% 162.46/162.14 inference(rename_variables,[],[4557])).
% 162.46/162.14 cnf(12777,plain,
% 162.46/162.14 (~P24(f331(f331(f248(a1),f331(f106(a1),x127771)),f2(a1)))),
% 162.46/162.14 inference(rename_variables,[],[4571])).
% 162.46/162.14 cnf(12778,plain,
% 162.46/162.14 (P24(f331(f256(f891(x127781,a877)),x127782))),
% 162.46/162.14 inference(rename_variables,[],[3379])).
% 162.46/162.14 cnf(12781,plain,
% 162.46/162.14 (~P24(f331(f331(f248(a1),f331(f106(a1),x127811)),f2(a1)))),
% 162.46/162.14 inference(rename_variables,[],[4571])).
% 162.46/162.14 cnf(12782,plain,
% 162.46/162.14 (P24(f331(f256(f891(x127821,a877)),x127822))),
% 162.46/162.14 inference(rename_variables,[],[3379])).
% 162.46/162.14 cnf(12785,plain,
% 162.46/162.14 (P24(f331(f256(f891(x127851,a877)),x127852))),
% 162.46/162.14 inference(rename_variables,[],[3379])).
% 162.46/162.14 cnf(12796,plain,
% 162.46/162.14 (~P24(f331(f331(f333(x127961),x127962),f196(f891(x127961,a877))))),
% 162.46/162.14 inference(rename_variables,[],[4569])).
% 162.46/162.14 cnf(12797,plain,
% 162.46/162.14 (P24(f331(f62(x127971),f196(f891(x127971,a877))))),
% 162.46/162.14 inference(rename_variables,[],[3393])).
% 162.46/162.14 cnf(12806,plain,
% 162.46/162.14 (P24(f331(f331(f247(a883),f2(a883)),x128061))),
% 162.46/162.14 inference(rename_variables,[],[3336])).
% 162.46/162.14 cnf(12809,plain,
% 162.46/162.14 (P24(f331(f331(f248(a883),x128091),f331(a118,x128091)))),
% 162.46/162.14 inference(rename_variables,[],[3385])).
% 162.46/162.14 cnf(12810,plain,
% 162.46/162.14 (~E(f331(a118,x128101),x128101)),
% 162.46/162.14 inference(rename_variables,[],[4485])).
% 162.46/162.14 cnf(12813,plain,
% 162.46/162.14 (~P24(f331(f331(f333(x128131),x128132),f196(f891(x128131,a877))))),
% 162.46/162.14 inference(rename_variables,[],[4569])).
% 162.46/162.14 cnf(12816,plain,
% 162.46/162.14 (~P24(f331(f331(f333(x128161),x128162),f196(f891(x128161,a877))))),
% 162.46/162.14 inference(rename_variables,[],[4569])).
% 162.46/162.14 cnf(12819,plain,
% 162.46/162.14 (P24(f331(f331(f247(a883),x128191),x128191))),
% 162.46/162.14 inference(rename_variables,[],[3314])).
% 162.46/162.14 cnf(12826,plain,
% 162.46/162.14 (P24(f331(f331(f247(a883),x128261),x128261))),
% 162.46/162.14 inference(rename_variables,[],[3314])).
% 162.46/162.14 cnf(12830,plain,
% 162.46/162.14 (P24(f331(f331(f248(a883),x128301),f331(a118,x128301)))),
% 162.46/162.14 inference(rename_variables,[],[3385])).
% 162.46/162.14 cnf(12833,plain,
% 162.46/162.14 (P24(f331(f331(f247(a883),x128331),x128331))),
% 162.46/162.14 inference(rename_variables,[],[3314])).
% 162.46/162.14 cnf(12838,plain,
% 162.46/162.14 (P24(f331(f331(f247(a883),x128381),x128381))),
% 162.46/162.14 inference(rename_variables,[],[3314])).
% 162.46/162.14 cnf(12841,plain,
% 162.46/162.14 (P24(f331(f331(f247(a883),x128411),x128411))),
% 162.46/162.14 inference(rename_variables,[],[3314])).
% 162.46/162.14 cnf(12844,plain,
% 162.46/162.14 (P24(f331(f331(f247(a883),x128441),x128441))),
% 162.46/162.14 inference(rename_variables,[],[3314])).
% 162.46/162.14 cnf(12847,plain,
% 162.46/162.14 (E(f331(f331(f22(f891(x128471,a877)),f196(f891(x128471,a877))),x128472),f196(f891(x128471,a877)))),
% 162.46/162.14 inference(rename_variables,[],[3584])).
% 162.46/162.14 cnf(12848,plain,
% 162.46/162.14 (P24(f331(f62(x128481),f196(f891(x128481,a877))))),
% 162.46/162.14 inference(rename_variables,[],[3393])).
% 162.46/162.14 cnf(12851,plain,
% 162.46/162.14 (E(f331(f331(f22(f891(x128511,a877)),f196(f891(x128511,a877))),x128512),f196(f891(x128511,a877)))),
% 162.46/162.14 inference(rename_variables,[],[3584])).
% 162.46/162.14 cnf(12852,plain,
% 162.46/162.14 (P24(f331(f62(x128521),f196(f891(x128521,a877))))),
% 162.46/162.14 inference(rename_variables,[],[3393])).
% 162.46/162.14 cnf(12855,plain,
% 162.46/162.14 (E(f331(f331(f22(f891(x128551,a877)),f196(f891(x128551,a877))),x128552),f196(f891(x128551,a877)))),
% 162.46/162.14 inference(rename_variables,[],[3584])).
% 162.46/162.14 cnf(12856,plain,
% 162.46/162.14 (P24(f331(f62(x128561),f196(f891(x128561,a877))))),
% 162.46/162.14 inference(rename_variables,[],[3393])).
% 162.46/162.14 cnf(12859,plain,
% 162.46/162.14 (E(f331(f331(f22(f891(x128591,a877)),f196(f891(x128591,a877))),x128592),f196(f891(x128591,a877)))),
% 162.46/162.14 inference(rename_variables,[],[3584])).
% 162.46/162.14 cnf(12860,plain,
% 162.46/162.14 (P24(f331(f62(x128601),f196(f891(x128601,a877))))),
% 162.46/162.14 inference(rename_variables,[],[3393])).
% 162.46/162.14 cnf(12864,plain,
% 162.46/162.14 (E(f331(f257(x128641,x128641),f258(x128641,x128642)),x128642)),
% 162.46/162.14 inference(rename_variables,[],[3270])).
% 162.46/162.14 cnf(12869,plain,
% 162.46/162.14 (E(f331(f331(f22(f891(x128691,a877)),f196(f891(x128691,a877))),x128692),f196(f891(x128691,a877)))),
% 162.46/162.14 inference(rename_variables,[],[3584])).
% 162.46/162.14 cnf(12870,plain,
% 162.46/162.14 (P24(f331(f62(x128701),f196(f891(x128701,a877))))),
% 162.46/162.14 inference(rename_variables,[],[3393])).
% 162.46/162.14 cnf(12874,plain,
% 162.46/162.14 (P24(f331(f62(x128741),f196(f891(x128741,a877))))),
% 162.46/162.14 inference(rename_variables,[],[3393])).
% 162.46/162.14 cnf(12877,plain,
% 162.46/162.14 (P24(f331(f331(f247(a883),x128771),x128771))),
% 162.46/162.14 inference(rename_variables,[],[3314])).
% 162.46/162.14 cnf(12883,plain,
% 162.46/162.14 (P24(f331(f331(f247(a1),x128831),x128831))),
% 162.46/162.14 inference(rename_variables,[],[3315])).
% 162.46/162.14 cnf(12886,plain,
% 162.46/162.14 (P24(f331(f331(f248(a883),x128861),f331(a118,x128861)))),
% 162.46/162.14 inference(rename_variables,[],[3385])).
% 162.46/162.14 cnf(12889,plain,
% 162.46/162.14 (P24(f331(f331(f247(a883),x128891),x128891))),
% 162.46/162.14 inference(rename_variables,[],[3314])).
% 162.46/162.14 cnf(12892,plain,
% 162.46/162.14 (P24(f331(f331(f248(a883),x128921),f331(a118,x128921)))),
% 162.46/162.14 inference(rename_variables,[],[3385])).
% 162.46/162.14 cnf(12907,plain,
% 162.46/162.14 (P24(f331(f331(f247(a1),x129071),x129071))),
% 162.46/162.14 inference(rename_variables,[],[3315])).
% 162.46/162.14 cnf(12912,plain,
% 162.46/162.14 (~P24(f331(f331(f333(x129121),x129122),f196(f891(x129121,a877))))),
% 162.46/162.14 inference(rename_variables,[],[4569])).
% 162.46/162.14 cnf(12923,plain,
% 162.46/162.14 (P24(f331(f331(f333(x129231),x129232),f256(f891(x129231,a877))))),
% 162.46/162.14 inference(rename_variables,[],[3472])).
% 162.46/162.14 cnf(12929,plain,
% 162.46/162.14 (P24(f331(f331(f247(f891(x129291,a877)),f331(f175(x129291),f331(f139(x129291,x129292),x129293))),f331(f175(x129291),x129293)))),
% 162.46/162.14 inference(rename_variables,[],[3951])).
% 162.46/162.14 cnf(12935,plain,
% 162.46/162.14 (~P24(f331(f331(f248(a883),x129351),f2(a883)))),
% 162.46/162.14 inference(rename_variables,[],[4557])).
% 162.46/162.14 cnf(12936,plain,
% 162.46/162.14 (P24(f331(f331(f247(a1),x129361),x129361))),
% 162.46/162.14 inference(rename_variables,[],[3315])).
% 162.46/162.14 cnf(12940,plain,
% 162.46/162.14 (~P24(f331(f331(f248(a883),x129401),f2(a883)))),
% 162.46/162.14 inference(rename_variables,[],[4557])).
% 162.46/162.14 cnf(12941,plain,
% 162.46/162.14 (P24(f331(f331(f247(a1),x129411),x129411))),
% 162.46/162.14 inference(rename_variables,[],[3315])).
% 162.46/162.14 cnf(12950,plain,
% 162.46/162.14 (P24(f331(f331(f247(a883),x129501),x129501))),
% 162.46/162.14 inference(rename_variables,[],[3314])).
% 162.46/162.14 cnf(12957,plain,
% 162.46/162.14 (E(f331(f331(f16(x129571,x129572),x129573),x129574),x129573)),
% 162.46/162.14 inference(rename_variables,[],[3303])).
% 162.46/162.14 cnf(12960,plain,
% 162.46/162.14 (P24(f331(f331(f247(f891(x129601,a877)),f331(f175(x129601),f173(x129601,x129602,x129603))),f331(f175(x129601),x129603)))),
% 162.46/162.14 inference(rename_variables,[],[4001])).
% 162.46/162.14 cnf(12962,plain,
% 162.46/162.14 (P24(f331(f331(f247(a883),f539(f331(x129621,f2(a883)),x129621,f2(a883))),f2(a883)))),
% 162.46/162.14 inference(scs_inference,[],[4582,3553,11085,12122,12222,12317,12352,12360,12373,12428,12556,3563,12186,12650,12652,3564,12256,3280,12577,12579,3281,12641,3249,12501,4519,4520,11706,4246,12626,12629,3284,12613,3123,3143,12635,3185,12550,4503,3615,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,12189,12344,12398,12535,12658,4500,10471,10564,3374,3334,12619,3523,3230,4495,2899,2900,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2933,2936,2939,2940,2949,2953,2975,2982,2983,2991,2994,3005,3009,3017,3020,3029,3031,3032,3035,3036,3037,3040,3041,3043,3044,3046,3063,3064,3068,3069,3070,3080,3086,4480,3102,3184,4481,3652,3156,11358,3294,3358,3267,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,12096,12293,12481,12537,12542,12544,12546,12548,12566,12583,12589,12624,12633,3638,3881,3244,11633,12376,12380,12384,3255,3770,11017,11639,3999,3146,3966,4497,4507,3857,11408,3373,12568,3210,3176,3350,3688,12591,3171,3974,3693,4464,3154,3155,3133,3160,3190,3327,12067,12212,12431,12504,3375,10853,12183,3242,3243,3265,10512,3420,4575,10441,3939,4509,10304,10468,11268,12340,12377,4518,12348,3303,11729,11732,4567,11020,11090,11311,11314,3421,3637,3388,12608,3205,10370,10677,3206,3477,3198,3124,3226,11398,4080,12363,12493,3942,11026,11152,11203,12327,12333,12442,12445,12468,4590,10958,11157,11262,11284,11319,11325,12272,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,12225,12269,12347,3677,4367,4368,3617,3655,3824,3584,12847,12851,12855,12859,12869,3867,12219,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,12151,12472,12664,12722,12753,12765,12809,12830,12886,12892,3758,11624,3296,3397,11744,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,12275,12367,12669,12672,12689,12692,12714,12766,12935,12940,4571,11506,11539,11574,11604,12777,12781,3745,3525,3526,12695,12698,12701,12704,12734,3889,3342,3343,3317,4554,3204,4505,3704,4216,4007,3508,4574,4074,11279,3636,3357,11753,11756,12193,12297,12452,4046,4006,11897,12240,3951,10850,12055,12081,12253,12475,4001,11029,12119,12192,12252,12296,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,12141,12393,12465,12478,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,12134,12300,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,12233,12404,12448,12715,12740,12819,12826,12833,12838,12841,12844,12877,12889,12950,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,11997,12731,12883,12907,12936,12941,3316,3393,12107,12797,12848,12852,12856,12860,12870,12874,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,12207,12303,12306,12366,12397,12434,12516,3472,10645,10911,10955,11225,11303,11467,11709,12343,12519,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,12137,12281,12324,12330,12416,12419,12438,12492,12498,12507,12529,12796,12813,12816,3379,10674,10704,10713,11254,11808,12435,12449,12778,12782,12785,3416,3410,3828,3767,10347,11627,11657,12758,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,3336,10707,10860,10931,11658,11813,12002,12234,3789,11759,12711,3531,4564,3800,3835,4543,4545,4546,3287,3288,4544,4547,4548,4588,3807,3626,4224,11486,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,11350,4013,12264,3906,11347,11684,11688,11750,12351,12359,12441,3752,10971,10977,10992,11929,12140,3613,11194,12166,12278,12288,12356,12407,12415,3650,4078,3754,10710,11048,11200,11230,11241,12246,12355,3582,10631,10634,10716,10890,3581,4581,11621,4577,12679,4583,10767,10869,11179,11331,11464,11492,12228,12237,12284,12462,4178,10843,12078,12249,12261,4086,3788,12532,3733,3734,4579,10323,10326,10662,10665,11503,11685,12471,4580,11601,11694,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063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% 162.46/162.14 cnf(12964,plain,
% 162.46/162.14 (~P24(f331(f331(f248(a883),x129641),f2(a883)))),
% 162.46/162.14 inference(rename_variables,[],[4557])).
% 162.46/162.14 cnf(12965,plain,
% 162.46/162.14 (P24(f331(f331(f247(a1),x129651),x129651))),
% 162.46/162.14 inference(rename_variables,[],[3315])).
% 162.46/162.14 cnf(12969,plain,
% 162.46/162.14 (~P24(f331(f331(f248(a883),x129691),f2(a883)))),
% 162.46/162.14 inference(rename_variables,[],[4557])).
% 162.46/162.14 cnf(12974,plain,
% 162.46/162.14 (~P24(f331(f331(f248(f891(a883,a877)),f302(a883,f331(a118,x129741),f331(a118,x129741))),f302(a883,x129742,x129741)))),
% 162.46/162.14 inference(scs_inference,[],[4582,3553,11085,12122,12222,12317,12352,12360,12373,12428,12556,3563,12186,12650,12652,3564,12256,3280,12577,12579,3281,12641,3249,12501,4519,4520,11706,4246,12626,12629,3284,12613,3123,3143,12635,3185,12550,4503,3615,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,12189,12344,12398,12535,12658,4500,10471,10564,3374,3334,12619,3523,3230,4495,2899,2900,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2933,2936,2939,2940,2949,2953,2975,2982,2983,2991,2994,3005,3009,3017,3020,3029,3031,3032,3035,3036,3037,3040,3041,3043,3044,3046,3063,3064,3068,3069,3070,3080,3086,4480,3102,3184,4481,3652,3156,11358,3294,3358,3267,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,12096,12293,12481,12537,12542,12544,12546,12548,12566,12583,12589,12624,12633,3638,3881,3244,11633,12376,12380,12384,3255,3770,11017,11639,3999,3146,3966,4497,4507,3857,11408,3373,12568,3210,3176,3350,3688,12591,3171,3974,3693,4464,3154,3155,3133,3160,3190,3327,12067,12212,12431,12504,3375,10853,12183,3242,3243,3265,10512,3420,4575,10441,3939,4509,10304,10468,11268,12340,12377,4518,12348,3303,11729,11732,4567,11020,11090,11311,11314,3421,3637,3388,12608,3205,10370,10677,3206,3477,3198,3124,3226,11398,4080,12363,12493,3942,11026,11152,11203,12327,12333,12442,12445,12468,4590,10958,11157,11262,11284,11319,11325,12272,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,12225,12269,12347,3677,4367,4368,3617,3655,3824,3584,12847,12851,12855,12859,12869,3867,12219,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,12151,12472,12664,12722,12753,12765,12809,12830,12886,12892,3758,11624,3296,3397,11744,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,12275,12367,12669,12672,12689,12692,12714,12766,12935,12940,12964,4571,11506,11539,11574,11604,12777,12781,3745,3525,3526,12695,12698,12701,12704,12734,3889,3342,3343,3317,4554,3204,4505,3704,4216,4007,3508,4574,4074,11279,3636,3357,11753,11756,12193,12297,12452,4046,4006,11897,12240,3951,10850,12055,12081,12253,12475,4001,11029,12119,12192,12252,12296,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,12141,12393,12465,12478,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,12134,12300,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,12233,12404,12448,12715,12740,12819,12826,12833,12838,12841,12844,12877,12889,12950,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,11997,12731,12883,12907,12936,12941,12965,3316,3393,12107,12797,12848,12852,12856,12860,12870,12874,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,12207,12303,12306,12366,12397,12434,12516,3472,10645,10911,10955,11225,11303,11467,11709,12343,12519,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,12137,12281,12324,12330,12416,12419,12438,12492,12498,12507,12529,12796,12813,12816,3379,10674,10704,10713,11254,11808,12435,12449,12778,12782,12785,3416,3410,3828,3767,10347,11627,11657,12758,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,3336,10707,10860,10931,11658,11813,12002,12234,3789,11759,12711,3531,4564,3800,3835,4543,4545,4546,3287,3288,4544,4547,4548,4588,3807,3626,4224,11486,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,11350,4013,12264,3906,11347,11684,11688,11750,12351,12359,12441,3752,10971,10977,10992,11929,12140,3613,11194,12166,12278,12288,12356,12407,12415,3650,4078,3754,10710,11048,11200,11230,11241,12246,12355,3582,10631,10634,10716,10890,3581,4581,11621,4577,12679,4583,10767,10869,11179,11331,11464,11492,12228,12237,12284,12462,4178,10843,12078,12249,12261,4086,3788,12532,3733,3734,4579,10323,10326,10662,10665,11503,11685,12471,4580,11601,11694,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462,6463,6465,6466,6468,6470,6471,6472,6474,6476,6479,6485,6486,6487,6488,6494,6496,6536,6541,6556,6557,6558,6559,6594,6599,6601,6606,6607,6615,6619,6632,6657,6658,6659,6660,6671,6676,6693,6697,6716,6749,6750,6751,6756,6764,6785,6787,6789,6791,6794,6800,6802,6815,6822,6857,6860,6861,6874,6875,6876,6877,6893,6894,6911,6937,6960,6971,6973,6974,6976,6978,6979,7014,7015,7020,7021,7023,7025,7026,7027,7052,7061,7062,7073,7083,7122,7132,7136,7143,7154,7155,7160,7162,7168,7176,7177,7190,7207,7225,7227,7244,7288,7290,7291,7292,7299,7304,7320,7364,7398,7412,7429,7462,7465,7488,7512,7530,7533,7534,7544,7561,7562,7564,7566,7568,7570,7594,7619,7620,7652,7654,7655,7656,7661,7681,7690,7701,7706,7712,7714,7720,7731,7732,7734,7755,7764,7789,7856,7857,7899,7907,7908,7927,7928,7945,7946,8011,8012,8013,8039,8075,8082,8085,8094,8106,8139,8145,8152,8165,8184,8191,8211,8253,8283,8295,8313,8316,8343,8366,8427,8428,8432,8434,8454,8541,8542,8543,8544,8597,8627,8664,8681,8731,8781,8784,8799,8806,8844,8865,8894,8895,8911,8912,9044,9048,9061,9072,9101,9103,9106,9110,9113,9114,9129,9130,9153,9159,9171,9217,9236,9298,9299,9301,9366,9372,9400,9407,9408,9411,9412,9429,9443,9452,9464,9478,9479,9481,9483,9520,9655,9697,9698,9745,9799,9907,9908,9952,10014,10093,10107,10208,3,2637,2639,2640,2641,2642,2645,2646,2647,2652,2653,2655,2661,2662,2663,2664,2667,2674,2675,2676,2677,2679,2680,2681,2684,2685,2686,2688,2698,2699,2701,2702,2704,2708,2709,2710,2711,2712,2713,2719,2720,2721,2739,2746,2747,2748,2756,2760,2763,2765,2775,2776,2778,2779,2782,2803,2823,2826,2827,2828,2829,2834,2835,2843,2845,2847,2848,2849,2851,2852,2862,2864,2865,2891,5249,5311,5409,5495,5496,5497,5571,5669,5700,5733,5749,5751,5757,5820,5821,5822,5823,5829,5862,5994,6039,6062,6099,6139,6282,6289,6322,6323,6341,6344,6346,6353,6354,6355,6356,6357,6358,6359,6360,6441,6508,6509,6517,6592,6626,6627,6668,6669,6801,6814,6885,6886,6890,6912,6935,6943,6945,6993,7018,7019,7035,7036,7037,7072,7116,7117,7214,7270,7271,7272,7273,7287,7314,7369,7370,7379,7386,7388,7400,7432,7433,7434,7435,7574,7575,7582,7584,7585,7586,7797,7799,7800,7816,7854,7923,7964,8022,8044,8045,8063,8124,8224,8293,8294,8296,8328,8390,8391,8462,8481])).
% 162.46/162.14 cnf(12975,plain,
% 162.46/162.14 (P24(f331(f331(f247(a883),x129751),x129751))),
% 162.46/162.14 inference(rename_variables,[],[3314])).
% 162.46/162.14 cnf(12977,plain,
% 162.46/162.14 (~P24(f331(f331(f247(f891(a883,a877)),f302(a883,f331(a118,x129771),f331(a118,x129771))),f302(a883,x129772,x129771)))),
% 162.46/162.14 inference(scs_inference,[],[4582,3553,11085,12122,12222,12317,12352,12360,12373,12428,12556,3563,12186,12650,12652,3564,12256,3280,12577,12579,3281,12641,3249,12501,4519,4520,11706,4246,12626,12629,3284,12613,3123,3143,12635,3185,12550,4503,3615,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,12189,12344,12398,12535,12658,4500,10471,10564,3374,3334,12619,3523,3230,4495,2899,2900,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2933,2936,2939,2940,2949,2953,2975,2982,2983,2991,2994,3005,3009,3017,3020,3029,3031,3032,3035,3036,3037,3040,3041,3043,3044,3046,3063,3064,3068,3069,3070,3080,3086,4480,3102,3184,4481,3652,3156,11358,3294,3358,3267,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,12096,12293,12481,12537,12542,12544,12546,12548,12566,12583,12589,12624,12633,3638,3881,3244,11633,12376,12380,12384,3255,3770,11017,11639,3999,3146,3966,4497,4507,3857,11408,3373,12568,3210,3176,3350,3688,12591,3171,3974,3693,4464,3154,3155,3133,3160,3190,3327,12067,12212,12431,12504,3375,10853,12183,3242,3243,3265,10512,3420,4575,10441,3939,4509,10304,10468,11268,12340,12377,4518,12348,3303,11729,11732,4567,11020,11090,11311,11314,3421,3637,3388,12608,3205,10370,10677,3206,3477,3198,3124,3226,11398,4080,12363,12493,3942,11026,11152,11203,12327,12333,12442,12445,12468,4590,10958,11157,11262,11284,11319,11325,12272,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,12225,12269,12347,3677,4367,4368,3617,3655,3824,3584,12847,12851,12855,12859,12869,3867,12219,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,12151,12472,12664,12722,12753,12765,12809,12830,12886,12892,3758,11624,3296,3397,11744,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,12275,12367,12669,12672,12689,12692,12714,12766,12935,12940,12964,4571,11506,11539,11574,11604,12777,12781,3745,3525,3526,12695,12698,12701,12704,12734,3889,3342,3343,3317,4554,3204,4505,3704,4216,4007,3508,4574,4074,11279,3636,3357,11753,11756,12193,12297,12452,4046,4006,11897,12240,3951,10850,12055,12081,12253,12475,4001,11029,12119,12192,12252,12296,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,12141,12393,12465,12478,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,12134,12300,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,12233,12404,12448,12715,12740,12819,12826,12833,12838,12841,12844,12877,12889,12950,12975,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,11997,12731,12883,12907,12936,12941,12965,3316,3393,12107,12797,12848,12852,12856,12860,12870,12874,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,12207,12303,12306,12366,12397,12434,12516,3472,10645,10911,10955,11225,11303,11467,11709,12343,12519,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,12137,12281,12324,12330,12416,12419,12438,12492,12498,12507,12529,12796,12813,12816,3379,10674,10704,10713,11254,11808,12435,12449,12778,12782,12785,3416,3410,3828,3767,10347,11627,11657,12758,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,3336,10707,10860,10931,11658,11813,12002,12234,3789,11759,12711,3531,4564,3800,3835,4543,4545,4546,3287,3288,4544,4547,4548,4588,3807,3626,4224,11486,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,11350,4013,12264,3906,11347,11684,11688,11750,12351,12359,12441,3752,10971,10977,10992,11929,12140,3613,11194,12166,12278,12288,12356,12407,12415,3650,4078,3754,10710,11048,11200,11230,11241,12246,12355,3582,10631,10634,10716,10890,3581,4581,11621,4577,12679,4583,10767,10869,11179,11331,11464,11492,12228,12237,12284,12462,4178,10843,12078,12249,12261,4086,3788,12532,3733,3734,4579,10323,10326,10662,10665,11503,11685,12471,4580,11601,11694,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462,6463,6465,6466,6468,6470,6471,6472,6474,6476,6479,6485,6486,6487,6488,6494,6496,6536,6541,6556,6557,6558,6559,6594,6599,6601,6606,6607,6615,6619,6632,6657,6658,6659,6660,6671,6676,6693,6697,6716,6749,6750,6751,6756,6764,6785,6787,6789,6791,6794,6800,6802,6815,6822,6857,6860,6861,6874,6875,6876,6877,6893,6894,6911,6937,6960,6971,6973,6974,6976,6978,6979,7014,7015,7020,7021,7023,7025,7026,7027,7052,7061,7062,7073,7083,7122,7132,7136,7143,7154,7155,7160,7162,7168,7176,7177,7190,7207,7225,7227,7244,7288,7290,7291,7292,7299,7304,7320,7364,7398,7412,7429,7462,7465,7488,7512,7530,7533,7534,7544,7561,7562,7564,7566,7568,7570,7594,7619,7620,7652,7654,7655,7656,7661,7681,7690,7701,7706,7712,7714,7720,7731,7732,7734,7755,7764,7789,7856,7857,7899,7907,7908,7927,7928,7945,7946,8011,8012,8013,8039,8075,8082,8085,8094,8106,8139,8145,8152,8165,8184,8191,8211,8253,8283,8295,8313,8316,8343,8366,8427,8428,8432,8434,8454,8541,8542,8543,8544,8597,8627,8664,8681,8731,8781,8784,8799,8806,8844,8865,8894,8895,8911,8912,9044,9048,9061,9072,9101,9103,9106,9110,9113,9114,9129,9130,9153,9159,9171,9217,9236,9298,9299,9301,9366,9372,9400,9407,9408,9411,9412,9429,9443,9452,9464,9478,9479,9481,9483,9520,9655,9697,9698,9745,9799,9907,9908,9952,10014,10093,10107,10208,3,2637,2639,2640,2641,2642,2645,2646,2647,2652,2653,2655,2661,2662,2663,2664,2667,2674,2675,2676,2677,2679,2680,2681,2684,2685,2686,2688,2698,2699,2701,2702,2704,2708,2709,2710,2711,2712,2713,2719,2720,2721,2739,2746,2747,2748,2756,2760,2763,2765,2775,2776,2778,2779,2782,2803,2823,2826,2827,2828,2829,2834,2835,2843,2845,2847,2848,2849,2851,2852,2862,2864,2865,2891,5249,5311,5409,5495,5496,5497,5571,5669,5700,5733,5749,5751,5757,5820,5821,5822,5823,5829,5862,5994,6039,6062,6099,6139,6282,6289,6322,6323,6341,6344,6346,6353,6354,6355,6356,6357,6358,6359,6360,6441,6508,6509,6517,6592,6626,6627,6668,6669,6801,6814,6885,6886,6890,6912,6935,6943,6945,6993,7018,7019,7035,7036,7037,7072,7116,7117,7214,7270,7271,7272,7273,7287,7314,7369,7370,7379,7386,7388,7400,7432,7433,7434,7435,7574,7575,7582,7584,7585,7586,7797,7799,7800,7816,7854,7923,7964,8022,8044,8045,8063,8124,8224,8293,8294,8296,8328,8390,8391,8462,8481,8482])).
% 162.46/162.14 cnf(12978,plain,
% 162.46/162.14 (P24(f331(f331(f247(a883),x129781),x129781))),
% 162.46/162.14 inference(rename_variables,[],[3314])).
% 162.46/162.14 cnf(12981,plain,
% 162.46/162.14 (~P24(f331(f331(f247(a883),f331(a118,x129811)),x129811))),
% 162.46/162.14 inference(rename_variables,[],[4566])).
% 162.46/162.14 cnf(12986,plain,
% 162.46/162.14 (E(x129861,f500(f331(f5(x129862),f331(f5(x129862),x129861)),f5(x129862),x129862,x129862))),
% 162.46/162.14 inference(scs_inference,[],[4582,3553,11085,12122,12222,12317,12352,12360,12373,12428,12556,12558,3563,12186,12650,12652,3564,12256,3280,12577,12579,3281,12641,3249,12501,4519,4520,11706,4246,12626,12629,3284,12613,3123,3143,12635,3185,12550,4503,3615,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,12189,12344,12398,12535,12658,4500,10471,10564,3374,3334,12619,3523,3230,4495,2899,2900,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2933,2936,2939,2940,2949,2953,2975,2982,2983,2991,2994,3005,3009,3017,3020,3029,3031,3032,3035,3036,3037,3040,3041,3043,3044,3046,3063,3064,3068,3069,3070,3080,3086,4480,3102,3184,4481,3652,3156,11358,3294,3358,3267,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,12096,12293,12481,12537,12542,12544,12546,12548,12566,12583,12589,12624,12633,3638,3881,3244,11633,12376,12380,12384,3255,3770,11017,11639,3999,3145,3146,3966,4497,4507,3857,11408,3373,12568,3210,3176,3350,3688,12591,3171,3974,3693,4464,3154,3155,3133,3160,3190,3327,12067,12212,12431,12504,3375,10853,12183,3242,3243,3265,10512,3420,4575,10441,3939,4509,10304,10468,11268,12340,12377,4518,12348,3303,11729,11732,4567,11020,11090,11311,11314,3421,3637,3388,12608,3205,10370,10677,3206,3477,3198,3124,3226,11398,4080,12363,12493,3942,11026,11152,11203,12327,12333,12442,12445,12468,4590,10958,11157,11262,11284,11319,11325,12272,4591,11059,11160,11265,4592,11163,4593,11217,4594,3225,3516,12225,12269,12347,3677,4367,4368,3617,3655,3824,3584,12847,12851,12855,12859,12869,3867,12219,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,12151,12472,12664,12722,12753,12765,12809,12830,12886,12892,3758,11624,3296,3397,11744,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,12275,12367,12669,12672,12689,12692,12714,12766,12935,12940,12964,4571,11506,11539,11574,11604,12777,12781,3745,3525,3526,12695,12698,12701,12704,12734,3889,3342,3343,3317,4554,3204,4505,3704,4216,4007,3508,4574,4074,11279,3636,3357,11753,11756,12193,12297,12452,4046,4006,11897,12240,3951,10850,12055,12081,12253,12475,4001,11029,12119,12192,12252,12296,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,12141,12393,12465,12478,4576,10798,11168,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,12134,12300,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,12233,12404,12448,12715,12740,12819,12826,12833,12838,12841,12844,12877,12889,12950,12975,12978,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,11997,12731,12883,12907,12936,12941,12965,3316,3393,12107,12797,12848,12852,12856,12860,12870,12874,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,12207,12303,12306,12366,12397,12434,12516,3472,10645,10911,10955,11225,11303,11467,11709,12343,12519,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,12137,12281,12324,12330,12416,12419,12438,12492,12498,12507,12529,12796,12813,12816,3379,10674,10704,10713,11254,11808,12435,12449,12778,12782,12785,3416,3410,3828,3767,10347,11627,11657,12758,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,12981,3336,10707,10860,10931,11658,11813,12002,12234,3789,11759,12711,3531,4564,3800,3835,4543,4545,4546,3287,3288,4544,4547,4548,4588,3807,3626,4224,11486,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,11350,4013,12264,3906,11347,11684,11688,11750,12351,12359,12441,12725,3752,10971,10977,10992,11929,12140,3613,11194,12166,12278,12288,12356,12407,12415,3650,4078,3754,10710,11048,11200,11230,11241,12246,12355,3582,10631,10634,10716,10890,3581,4581,11621,4577,12679,4583,10767,10869,11179,11331,11464,11492,12228,12237,12284,12462,4178,10843,12078,12249,12261,4086,3788,12532,3733,3734,4579,10323,10326,10662,10665,11503,11685,12471,4580,11601,11694,3756,10628,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,59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% 162.46/162.14 cnf(12987,plain,
% 162.46/162.14 (P24(f331(f331(f333(x129871),f331(x129872,x129873)),f331(f310(x129874,x129871,x129872),f256(f891(x129874,a877)))))),
% 162.46/162.14 inference(rename_variables,[],[3906])).
% 162.46/162.14 cnf(12988,plain,
% 162.46/162.14 (P21(x129881,x129881,f5(x129881),x129882)),
% 162.46/162.14 inference(rename_variables,[],[3553])).
% 162.46/162.14 cnf(12992,plain,
% 162.46/162.14 (P24(f331(f331(f333(x129921),x129922),f256(f891(x129921,a877))))),
% 162.46/162.14 inference(rename_variables,[],[3472])).
% 162.46/162.14 cnf(12993,plain,
% 162.46/162.14 (~P24(f331(f331(f333(x129931),x129932),f196(f891(x129931,a877))))),
% 162.46/162.14 inference(rename_variables,[],[4569])).
% 162.46/162.14 cnf(12997,plain,
% 162.46/162.14 (P24(f331(f331(f247(f891(x129971,a877)),x129972),f256(f891(x129971,a877))))),
% 162.46/162.14 inference(rename_variables,[],[3695])).
% 162.46/162.14 cnf(12998,plain,
% 162.46/162.14 (P21(x129981,x129981,f5(x129981),x129982)),
% 162.46/162.14 inference(rename_variables,[],[3553])).
% 162.46/162.14 cnf(13002,plain,
% 162.46/162.14 (P24(f331(f331(f247(f891(x130021,a877)),x130022),f256(f891(x130021,a877))))),
% 162.46/162.14 inference(rename_variables,[],[3695])).
% 162.46/162.14 cnf(13003,plain,
% 162.46/162.14 (P21(x130031,x130031,f5(x130031),x130032)),
% 162.46/162.14 inference(rename_variables,[],[3553])).
% 162.46/162.14 cnf(13007,plain,
% 162.46/162.14 (P21(x130071,x130071,f5(x130071),x130072)),
% 162.46/162.14 inference(rename_variables,[],[3553])).
% 162.46/162.14 cnf(13010,plain,
% 162.46/162.14 (~P24(f331(f331(f248(f891(x130101,a877)),x130102),f196(f891(x130101,a877))))),
% 162.46/162.14 inference(rename_variables,[],[4576])).
% 162.46/162.14 cnf(13013,plain,
% 162.46/162.14 (P21(x130131,x130131,f5(x130131),x130132)),
% 162.46/162.14 inference(rename_variables,[],[3553])).
% 162.46/162.14 cnf(13016,plain,
% 162.46/162.14 (P21(x130161,x130161,f5(x130161),x130162)),
% 162.46/162.14 inference(rename_variables,[],[3553])).
% 162.46/162.14 cnf(13019,plain,
% 162.46/162.14 (P24(f331(f331(f333(x130191),x130192),f331(f331(f309(x130191),x130192),x130193)))),
% 162.46/162.14 inference(rename_variables,[],[3626])).
% 162.46/162.14 cnf(13027,plain,
% 162.46/162.14 (P24(f331(f331(f247(f891(x130271,a877)),f196(f891(x130271,a877))),x130272))),
% 162.46/162.14 inference(rename_variables,[],[3754])).
% 162.46/162.14 cnf(13031,plain,
% 162.46/162.14 (E(f331(f257(x130311,x130311),f258(x130311,x130312)),x130312)),
% 162.46/162.14 inference(rename_variables,[],[3270])).
% 162.46/162.14 cnf(13035,plain,
% 162.46/162.14 (~P24(f331(f331(f333(x130351),x130352),f196(f891(x130351,a877))))),
% 162.46/162.14 inference(rename_variables,[],[4569])).
% 162.46/162.14 cnf(13038,plain,
% 162.46/162.14 (P24(f331(f331(f247(f891(x130381,a877)),x130382),f331(f331(f309(x130381),x130383),x130382)))),
% 162.46/162.14 inference(rename_variables,[],[3752])).
% 162.46/162.14 cnf(13039,plain,
% 162.46/162.14 (P24(f331(f331(f333(x130391),f331(x130392,x130393)),f331(f310(x130394,x130391,x130392),f256(f891(x130394,a877)))))),
% 162.46/162.14 inference(rename_variables,[],[3906])).
% 162.46/162.14 cnf(13040,plain,
% 162.46/162.14 (P21(x130401,x130401,f5(x130401),x130402)),
% 162.46/162.14 inference(rename_variables,[],[3553])).
% 162.46/162.14 cnf(13043,plain,
% 162.46/162.14 (P24(f331(f331(f333(x130431),x130432),f256(f891(x130431,a877))))),
% 162.46/162.14 inference(rename_variables,[],[3472])).
% 162.46/162.14 cnf(13047,plain,
% 162.46/162.14 (P24(f331(f331(f247(f891(x130471,a877)),x130472),x130472))),
% 162.46/162.14 inference(rename_variables,[],[3613])).
% 162.46/162.14 cnf(13053,plain,
% 162.46/162.14 (~P24(f331(f331(f333(x130531),x130532),f196(f891(x130531,a877))))),
% 162.46/162.14 inference(rename_variables,[],[4569])).
% 162.46/162.14 cnf(13056,plain,
% 162.46/162.14 (~P24(f331(f331(f333(x130561),x130562),f196(f891(x130561,a877))))),
% 162.46/162.14 inference(rename_variables,[],[4569])).
% 162.46/162.14 cnf(13060,plain,
% 162.46/162.14 (E(f331(f331(f16(x130601,x130602),x130603),x130604),x130603)),
% 162.46/162.14 inference(rename_variables,[],[3303])).
% 162.46/162.14 cnf(13063,plain,
% 162.46/162.14 (P24(f331(f331(f248(a883),x130631),f331(a118,x130631)))),
% 162.46/162.14 inference(rename_variables,[],[3385])).
% 162.46/162.14 cnf(13064,plain,
% 162.46/162.14 (~E(f331(a118,x130641),x130641)),
% 162.46/162.14 inference(rename_variables,[],[4485])).
% 162.46/162.14 cnf(13067,plain,
% 162.46/162.14 (P24(f331(f331(f248(a883),x130671),f331(a118,f331(f331(f81(a883),x130672),x130671))))),
% 162.46/162.14 inference(rename_variables,[],[3756])).
% 162.46/162.14 cnf(13068,plain,
% 162.46/162.14 (P24(f331(f331(f248(a883),x130681),f331(a118,x130681)))),
% 162.46/162.14 inference(rename_variables,[],[3385])).
% 162.46/162.14 cnf(13070,plain,
% 162.46/162.14 (~E(f331(f331(f82(a883),f331(a118,f2(a883))),f34(x130701,x130702)),f331(f331(f82(a883),f331(a118,f2(a883))),f33(x130703,x130704)))),
% 162.46/162.14 inference(scs_inference,[],[4582,3553,11085,12122,12222,12317,12352,12360,12373,12428,12556,12558,12988,12998,13003,13007,13013,13016,3563,12186,12650,12652,3564,12256,3280,12577,12579,3281,12641,3249,12501,4519,4520,11706,4246,12626,12629,3284,12613,3123,3143,12635,3185,12550,4503,3615,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,12189,12344,12398,12535,12658,12810,13064,4500,10471,10564,3374,3334,12619,3523,3230,4495,2899,2900,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2933,2936,2939,2940,2949,2953,2975,2979,2982,2983,2991,2994,3005,3009,3017,3020,3029,3031,3032,3035,3036,3037,3040,3041,3043,3044,3046,3063,3064,3068,3069,3070,3080,3086,4480,3102,3184,4481,3652,3156,11358,3294,3358,3267,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,12096,12293,12481,12537,12542,12544,12546,12548,12566,12583,12589,12624,12633,12864,3638,3881,3244,11633,12376,12380,12384,3255,3770,11017,11639,3999,3145,3146,3966,4497,4507,3857,11408,3373,12568,3210,3176,3350,3688,12591,3171,3974,3191,3693,4464,3154,3155,3133,3160,3190,3327,12067,12212,12431,12504,3375,10853,12183,3242,3243,3265,10512,3420,4575,10441,3939,4509,10304,10468,11268,12340,12377,12381,4518,12348,3303,11729,11732,12957,4567,11020,11090,11311,11314,3298,3421,3637,3388,12608,3205,10370,10677,3206,4551,3477,3198,3124,3226,11398,4080,12363,12493,3942,11026,11152,11203,12327,12333,12442,12445,12468,4590,10958,11157,11262,11284,11319,11325,12272,4591,11059,11160,11265,4592,11163,11214,4593,11217,4594,3225,3516,12225,12269,12347,3677,4367,4368,3617,3655,3824,3584,12847,12851,12855,12859,12869,3867,12219,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,12151,12472,12664,12722,12753,12765,12809,12830,12886,12892,13063,3758,11624,3296,3397,11744,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,12275,12367,12669,12672,12689,12692,12714,12766,12935,12940,12964,4571,11506,11539,11574,11604,12777,12781,3745,3525,3526,12695,12698,12701,12704,12734,3889,3342,3343,3317,4554,3204,4505,3704,4216,4007,3508,4574,4074,11279,3636,3357,11753,11756,12193,12297,12452,4046,4006,11897,12240,3951,10850,12055,12081,12253,12475,4001,11029,12119,12192,12252,12296,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,12141,12393,12465,12478,12997,13002,4576,10798,11168,13010,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,12134,12300,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,12233,12404,12448,12715,12740,12819,12826,12833,12838,12841,12844,12877,12889,12950,12975,12978,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,11997,12731,12883,12907,12936,12941,12965,3316,3393,12107,12797,12848,12852,12856,12860,12870,12874,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,12207,12303,12306,12366,12397,12434,12516,3472,10645,10911,10955,11225,11303,11467,11709,12343,12519,12923,12992,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,12137,12281,12324,12330,12416,12419,12438,12492,12498,12507,12529,12796,12813,12816,12912,12993,13035,13053,3379,10674,10704,10713,11254,11808,12435,12449,12778,12782,12785,3416,3410,3828,3767,10347,11627,11657,12758,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,12981,3336,10707,10860,10931,11658,11813,12002,12234,3789,11759,12711,3531,4564,3800,3835,4543,4545,4546,3287,3288,4544,4547,4548,4588,3807,3626,11620,4224,11486,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,11350,4013,12264,3906,11347,11684,11688,11750,12351,12359,12441,12725,12987,13039,3752,10971,10977,10992,11929,12140,12412,3613,11194,12166,12278,12288,12356,12407,12415,12526,3650,4078,3754,10710,11048,11200,11230,11241,12246,12355,12401,3582,10631,10634,10716,10890,3581,4581,11621,4577,12679,4583,10767,10869,11179,11331,11464,11492,12228,12237,12284,12462,4178,10843,12078,12249,12261,12287,4086,3788,12532,3733,3734,4579,10323,10326,10662,10665,11503,11685,12471,4580,11601,11694,3756,10628,10887,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462,6463,6465,6466,6468,6470,6471,6472,6474,6476,6479,6485,6486,6487,6488,6494,6496,6536,6541,6556,6557,6558,6559,6594,6599,6601,6606,6607,6615,6619,6632,6657,6658,6659,6660,6671,6676,6693,6697,6716,6749,6750,6751,6756,6764,6785,6787,6789,6791,6794,6800,6802,6815,6822,6857,6860,6861,6874,6875,6876,6877,6893,6894,6911,6937,6960,6971,6973,6974,6976,6978,6979,7014,7015,7020,7021,7023,7025,7026,7027,7052,7061,7062,7073,7083,7122,7132,7136,7143,7154,7155,7160,7162,7168,7176,7177,7190,7207,7225,7227,7244,7288,7290,7291,7292,7299,7304,7320,7364,7398,7412,7429,7462,7465,7488,7512,7530,7533,7534,7544,7561,7562,7564,7566,7568,7570,7594,7619,7620,7652,7654,7655,7656,7661,7681,7690,7701,7706,7712,7714,7720,7731,7732,7734,7755,7764,7789,7856,7857,7899,7907,7908,7927,7928,7945,7946,8011,8012,8013,8039,8075,8082,8085,8094,8106,8139,8145,8152,8165,8184,8191,8211,8253,8283,8295,8313,8316,8343,8366,8427,8428,8432,8434,8454,8541,8542,8543,8544,8597,8627,8664,8681,8731,8781,8784,8799,8806,8844,8865,8894,8895,8911,8912,9044,9048,9061,9072,9101,9103,9106,9110,9113,9114,9129,9130,9153,9159,9171,9217,9236,9298,9299,9301,9366,9372,9400,9407,9408,9411,9412,9429,9443,9452,9464,9478,9479,9481,9483,9520,9655,9697,9698,9745,9799,9907,9908,9952,10014,10093,10107,10208,3,2637,2639,2640,2641,2642,2645,2646,2647,2652,2653,2655,2661,2662,2663,2664,2667,2674,2675,2676,2677,2679,2680,2681,2684,2685,2686,2688,2698,2699,2701,2702,2704,2708,2709,2710,2711,2712,2713,2719,2720,2721,2739,2746,2747,2748,2756,2760,2763,2765,2775,2776,2778,2779,2782,2803,2823,2826,2827,2828,2829,2834,2835,2843,2845,2847,2848,2849,2851,2852,2862,2864,2865,2891,5249,5311,5409,5495,5496,5497,5571,5669,5700,5733,5749,5751,5757,5820,5821,5822,5823,5829,5862,5994,6039,6062,6099,6139,6282,6289,6322,6323,6341,6344,6346,6353,6354,6355,6356,6357,6358,6359,6360,6441,6508,6509,6517,6592,6626,6627,6668,6669,6801,6814,6885,6886,6890,6912,6935,6943,6945,6993,7018,7019,7035,7036,7037,7072,7116,7117,7214,7270,7271,7272,7273,7287,7314,7369,7370,7379,7386,7388,7400,7432,7433,7434,7435,7574,7575,7582,7584,7585,7586,7797,7799,7800,7816,7854,7923,7964,8022,8044,8045,8063,8124,8224,8293,8294,8296,8328,8390,8391,8462,8481,8482,8483,8484,8631,8838,8862,8863,8943,8957,9012,9013,9118,9163,9186,9218,9260,9450,9734,9872,9929,9975,9977,6057,6424,6425,6511])).
% 162.46/162.14 cnf(13072,plain,
% 162.46/162.14 (~E(f331(a118,x130721),x130721)),
% 162.46/162.14 inference(rename_variables,[],[4485])).
% 162.46/162.15 cnf(13077,plain,
% 162.46/162.15 (P24(f331(f331(f247(a1),f2(a1)),f331(f106(a1),x130771)))),
% 162.46/162.15 inference(rename_variables,[],[3416])).
% 162.46/162.15 cnf(13080,plain,
% 162.46/162.15 (P24(f331(f331(f247(a883),f2(a883)),x130801))),
% 162.46/162.15 inference(rename_variables,[],[3336])).
% 162.46/162.15 cnf(13081,plain,
% 162.46/162.15 (P24(f331(f331(f247(a883),x130811),x130811))),
% 162.46/162.15 inference(rename_variables,[],[3314])).
% 162.46/162.15 cnf(13084,plain,
% 162.46/162.15 (~E(f331(a118,x130841),f2(a883))),
% 162.46/162.15 inference(rename_variables,[],[4495])).
% 162.46/162.15 cnf(13089,plain,
% 162.46/162.15 (P24(f331(f331(f333(x130891),x130892),f256(f891(x130891,a877))))),
% 162.46/162.15 inference(rename_variables,[],[3472])).
% 162.46/162.15 cnf(13093,plain,
% 162.46/162.15 (~P24(f331(f331(f333(x130931),x130932),f196(f891(x130931,a877))))),
% 162.46/162.15 inference(rename_variables,[],[4569])).
% 162.46/162.15 cnf(13096,plain,
% 162.46/162.15 (P24(f331(f62(a883),f304(a883,x130961,x130962)))),
% 162.46/162.15 inference(rename_variables,[],[3526])).
% 162.46/162.15 cnf(13097,plain,
% 162.46/162.15 (E(f331(f331(f251(a883),f331(a118,x130971)),f331(a118,x130972)),f331(a118,f331(f331(f251(a883),x130971),x130972)))),
% 162.46/162.15 inference(rename_variables,[],[3488])).
% 162.46/162.15 cnf(13100,plain,
% 162.46/162.15 (P24(f331(f62(a883),f304(a883,x131001,x131002)))),
% 162.46/162.15 inference(rename_variables,[],[3526])).
% 162.46/162.15 cnf(13101,plain,
% 162.46/162.15 (E(f331(f331(f246(a883),f331(a118,x131011)),f331(a118,x131012)),f331(a118,f331(f331(f246(a883),x131011),x131012)))),
% 162.46/162.15 inference(rename_variables,[],[3489])).
% 162.46/162.15 cnf(13104,plain,
% 162.46/162.15 (P24(f331(f62(a883),f304(a883,x131041,x131042)))),
% 162.46/162.15 inference(rename_variables,[],[3526])).
% 162.46/162.15 cnf(13108,plain,
% 162.46/162.15 (P24(f331(f62(a883),f304(a883,x131081,x131082)))),
% 162.46/162.15 inference(rename_variables,[],[3526])).
% 162.46/162.15 cnf(13112,plain,
% 162.46/162.15 (P24(f331(f331(f247(f891(x131121,a877)),f331(f175(x131121),f331(f139(x131121,x131122),x131123))),f331(f175(x131121),x131123)))),
% 162.46/162.15 inference(rename_variables,[],[3951])).
% 162.46/162.15 cnf(13113,plain,
% 162.46/162.15 (E(f331(f331(f16(x131131,x131132),x131133),x131134),x131133)),
% 162.46/162.15 inference(rename_variables,[],[3303])).
% 162.46/162.15 cnf(13116,plain,
% 162.46/162.15 (P24(f331(f331(f247(f891(x131161,a877)),f331(f175(x131161),f331(f331(f176(x131161),x131162),x131163))),f331(f175(x131161),x131163)))),
% 162.46/162.15 inference(rename_variables,[],[3996])).
% 162.46/162.15 cnf(13117,plain,
% 162.46/162.15 (E(f331(f331(f16(x131171,x131172),x131173),x131174),x131173)),
% 162.46/162.15 inference(rename_variables,[],[3303])).
% 162.46/162.15 cnf(13121,plain,
% 162.46/162.15 (E(f331(f331(f16(x131211,x131212),x131213),x131214),x131213)),
% 162.46/162.15 inference(rename_variables,[],[3303])).
% 162.46/162.15 cnf(13134,plain,
% 162.46/162.15 (P24(f331(f331(f247(a1),f2(a1)),f331(f106(a1),x131341)))),
% 162.46/162.15 inference(rename_variables,[],[3416])).
% 162.46/162.15 cnf(13137,plain,
% 162.46/162.15 (~P24(f331(f331(f333(x131371),x131372),f196(f891(x131371,a877))))),
% 162.46/162.15 inference(rename_variables,[],[4569])).
% 162.46/162.15 cnf(13140,plain,
% 162.46/162.15 (~P24(f331(f331(f333(x131401),x131402),f196(f891(x131401,a877))))),
% 162.46/162.15 inference(rename_variables,[],[4569])).
% 162.46/162.15 cnf(13141,plain,
% 162.46/162.15 (E(f331(f257(x131411,x131411),f258(x131411,x131412)),x131412)),
% 162.46/162.15 inference(rename_variables,[],[3270])).
% 162.46/162.15 cnf(13142,plain,
% 162.46/162.15 (P21(x131421,x131421,f5(x131421),x131422)),
% 162.46/162.15 inference(rename_variables,[],[3553])).
% 162.46/162.15 cnf(13146,plain,
% 162.46/162.15 (E(f331(f257(x131461,x131461),f258(x131461,x131462)),x131462)),
% 162.46/162.15 inference(rename_variables,[],[3270])).
% 162.46/162.15 cnf(13152,plain,
% 162.46/162.15 (P24(f331(f331(f248(a883),x131521),f331(a118,x131521)))),
% 162.46/162.15 inference(rename_variables,[],[3385])).
% 162.46/162.15 cnf(13154,plain,
% 162.46/162.15 (P24(f331(f331(f247(a883),x131541),x131541))),
% 162.46/162.15 inference(rename_variables,[],[3314])).
% 162.46/162.15 cnf(13155,plain,
% 162.46/162.15 (P24(f331(f331(f247(a883),f2(a883)),x131551))),
% 162.46/162.15 inference(rename_variables,[],[3336])).
% 162.46/162.15 cnf(13158,plain,
% 162.46/162.15 (P24(f331(f331(f248(a883),x131581),f331(a118,x131581)))),
% 162.46/162.15 inference(rename_variables,[],[3385])).
% 162.46/162.15 cnf(13160,plain,
% 162.46/162.15 (P24(f331(f331(f247(a883),x131601),x131601))),
% 162.46/162.15 inference(rename_variables,[],[3314])).
% 162.46/162.15 cnf(13161,plain,
% 162.46/162.15 (P24(f331(f331(f247(a883),f2(a883)),x131611))),
% 162.46/162.15 inference(rename_variables,[],[3336])).
% 162.46/162.15 cnf(13165,plain,
% 162.46/162.15 (P24(f331(f331(f247(a883),f2(a883)),x131651))),
% 162.46/162.15 inference(rename_variables,[],[3336])).
% 162.46/162.15 cnf(13166,plain,
% 162.46/162.15 (P24(f331(f331(f248(a883),f2(a883)),f331(a118,x131661)))),
% 162.46/162.15 inference(rename_variables,[],[3397])).
% 162.46/162.15 cnf(13167,plain,
% 162.46/162.15 (E(f331(f257(x131671,x131671),f258(x131671,x131672)),x131672)),
% 162.46/162.15 inference(rename_variables,[],[3270])).
% 162.46/162.15 cnf(13170,plain,
% 162.46/162.15 (P24(f331(f48(f331(f257(x131701,x131701),f258(x131701,f331(f331(f81(a883),f331(f331(f82(a883),f331(f260(a883,a883),f331(f331(f261(a883,a883),f2(a883)),x131702))),f331(a118,f331(f331(f81(a883),x131703),f331(f269(a883,a883),f331(f331(f261(a883,a883),f2(a883)),x131702)))))),f331(f269(a883,a883),f331(f331(f261(a883,a883),f2(a883)),x131702))))),f331(a118,f331(f331(f81(a883),x131703),f331(f269(a883,a883),f331(f331(f261(a883,a883),f2(a883)),x131702))))),f331(f331(f261(a883,a883),f2(a883)),x131702)))),
% 162.46/162.15 inference(scs_inference,[],[4582,3553,11085,12122,12222,12317,12352,12360,12373,12428,12556,12558,12988,12998,13003,13007,13013,13016,13040,13142,3563,12186,12650,12652,3564,12256,3280,12577,12579,3281,12641,3249,12501,4519,4520,11706,4246,12626,12629,3284,12613,3123,3143,12635,3185,12550,4503,3615,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,12189,12344,12398,12535,12658,12810,13064,4500,10471,10564,3374,3334,12619,3523,3230,4495,12726,13084,2899,2900,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2933,2936,2939,2940,2949,2953,2975,2979,2982,2983,2991,2994,2995,3005,3006,3009,3017,3020,3029,3031,3032,3035,3036,3037,3040,3041,3043,3044,3046,3063,3064,3068,3069,3070,3080,3086,4480,3102,3184,4481,3652,3156,11358,3294,3358,3267,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,12096,12293,12481,12537,12542,12544,12546,12548,12566,12583,12589,12624,12633,12864,13031,13141,13146,13167,3638,3881,3244,11633,12376,12380,12384,3255,3770,11017,11639,3999,3145,3146,3966,4497,4507,3857,11408,3373,12568,3210,3176,3350,3688,12591,3171,3974,3191,3693,4464,3154,3155,3133,3160,3190,3327,12067,12212,12431,12504,3375,10853,12183,3242,3243,3265,10512,3420,4575,10441,3939,4509,10304,10468,11268,12340,12377,12381,4518,12348,3303,11729,11732,12957,13060,13113,13117,13121,4567,11020,11090,11311,11314,3217,3298,3421,3637,3413,3388,12608,3205,10370,10677,3206,4551,3477,3198,3124,3226,11398,4080,12363,12493,3942,11026,11152,11203,12327,12333,12442,12445,12468,4590,10958,11157,11262,11284,11319,11325,12272,4591,11059,11160,11265,4592,11163,11214,4593,11217,4594,3225,3516,12225,12269,12347,3677,4367,4368,3498,3617,3655,3824,3584,12847,12851,12855,12859,12869,3867,12219,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,12151,12472,12664,12722,12753,12765,12809,12830,12886,12892,13063,13068,13152,13158,3758,11624,3296,3397,11744,12657,13166,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,12275,12367,12669,12672,12689,12692,12714,12766,12935,12940,12964,4571,11506,11539,11574,11604,12777,12781,3745,3525,3526,12695,12698,12701,12704,12734,12737,13096,13100,13104,3889,3488,13097,3489,13101,3342,3343,3317,4554,3204,4505,3704,4216,4007,3508,4574,4074,11279,3636,3357,11753,11756,12193,12297,12452,4046,4006,11897,12240,3951,10850,12055,12081,12253,12475,12929,13112,3996,13116,4001,11029,12119,12192,12252,12296,12960,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,12141,12393,12465,12478,12997,13002,4576,10798,11168,13010,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,12134,12300,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,12233,12404,12448,12715,12740,12819,12826,12833,12838,12841,12844,12877,12889,12950,12975,12978,13081,13154,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,11997,12731,12883,12907,12936,12941,12965,3316,3393,12107,12797,12848,12852,12856,12860,12870,12874,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,12207,12303,12306,12366,12397,12434,12516,3472,10645,10911,10955,11225,11303,11467,11709,12343,12519,12923,12992,13043,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,12137,12281,12324,12330,12416,12419,12438,12492,12498,12507,12529,12796,12813,12816,12912,12993,13035,13053,13056,13093,13137,13140,3379,10674,10704,10713,11254,11808,12435,12449,12778,12782,12785,3416,13077,3410,3828,3767,10347,11627,11657,12758,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,12981,3336,10707,10860,10931,11658,11813,12002,12234,12806,13080,13155,13161,13165,3789,11759,12711,3531,4564,3800,3835,4543,4545,4546,3287,3288,4544,4547,4548,4588,4301,3807,3626,11620,4224,11486,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,11350,4013,12264,3906,11347,11684,11688,11750,12351,12359,12441,12725,12987,13039,3752,10971,10977,10992,11929,12140,12412,3613,11194,12166,12278,12288,12356,12407,12415,12526,13047,3650,4078,3754,10710,11048,11200,11230,11241,12246,12355,12401,13027,3582,10631,10634,10716,10890,3581,4581,11621,4577,12679,4583,10767,10869,11179,11331,11464,11492,12228,12237,12284,12462,4178,10843,12078,12249,12261,12287,4086,3788,12532,3733,3734,4579,10323,10326,10662,10665,11503,11685,12471,4580,11601,11694,3756,10628,10887,13067,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260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72,7116,7117,7214,7270,7271,7272,7273,7287,7314,7369,7370,7379,7386,7388,7400,7432,7433,7434,7435,7574,7575,7582,7584,7585,7586,7797,7799,7800,7816,7854,7923,7964,8022,8044,8045,8063,8124,8224,8293,8294,8296,8328,8390,8391,8462,8481,8482,8483,8484,8631,8838,8862,8863,8943,8957,9012,9013,9118,9163,9186,9218,9260,9450,9734,9872,9929,9975,9977,6057,6424,6425,6511,6527,6528,6934,7152,8556,8587,8775,8968,8969,9035,9036,9311,9312,9313,9314,9523,9816,10103,10190,10191,6493,8381,8382,8827,8845])).
% 162.46/162.15 cnf(13186,plain,
% 162.46/162.15 (E(f331(f331(f81(a883),f2(a883)),f623(f331(a118,f2(a883)),f2(a883))),f2(a883))),
% 162.46/162.15 inference(scs_inference,[],[4582,3553,11085,12122,12222,12317,12352,12360,12373,12428,12556,12558,12988,12998,13003,13007,13013,13016,13040,13142,3563,12186,12650,12652,3564,12256,3280,12577,12579,3281,12641,3249,12501,4519,4520,11706,4246,12626,12629,3284,12613,3123,3143,12635,3185,12550,4503,3615,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,12189,12344,12398,12535,12658,12810,13064,4500,10471,10564,3374,3334,12619,3523,3230,4495,12726,13084,2899,2900,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2933,2936,2939,2940,2949,2953,2970,2975,2979,2982,2983,2991,2992,2994,2995,3005,3006,3009,3017,3020,3029,3031,3032,3035,3036,3037,3040,3041,3043,3044,3046,3063,3064,3068,3069,3070,3080,3086,4480,3102,3184,4481,3652,3156,11358,3294,3358,3267,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,12096,12293,12481,12537,12542,12544,12546,12548,12566,12583,12589,12624,12633,12864,13031,13141,13146,13167,3638,3881,3244,11633,12376,12380,12384,3255,3770,11017,11639,3999,3145,3146,3966,4497,4507,3857,11408,3373,12568,3210,3176,3350,3688,12591,3171,3974,3191,3693,4464,3154,3155,3133,3160,3190,3327,12067,12212,12431,12504,3375,10853,12183,3242,3243,3265,10512,3420,4575,10441,3939,4509,10304,10468,11268,12340,12377,12381,4518,12348,3303,11729,11732,12957,13060,13113,13117,13121,4567,11020,11090,11311,11314,3217,3298,3421,3637,3413,3388,12608,3205,10370,10677,3206,4551,3477,3198,3124,3226,11398,4080,12363,12493,3942,11026,11152,11203,12327,12333,12442,12445,12468,4590,10958,11157,11262,11284,11319,11325,12272,4591,11059,11160,11265,4592,11163,11214,4593,11217,4594,3225,3516,12225,12269,12347,3677,4367,4368,3498,3617,3655,3824,3584,12847,12851,12855,12859,12869,3867,12219,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,12151,12472,12664,12722,12753,12765,12809,12830,12886,12892,13063,13068,13152,13158,3758,11624,3296,3397,11744,12657,13166,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,12275,12367,12669,12672,12689,12692,12714,12766,12935,12940,12964,12969,4571,11506,11539,11574,11604,12777,12781,3745,3525,3526,12695,12698,12701,12704,12734,12737,13096,13100,13104,3889,3488,13097,3489,13101,3342,3343,3317,4554,3204,4505,3704,4216,4007,3508,4574,4074,11279,3636,3357,11753,11756,12193,12297,12452,4046,4006,11897,12240,3951,10850,12055,12081,12253,12475,12929,13112,3996,13116,4001,11029,12119,12192,12252,12296,12960,4002,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,12141,12393,12465,12478,12997,13002,4576,10798,11168,13010,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,12134,12300,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,12233,12404,12448,12715,12740,12819,12826,12833,12838,12841,12844,12877,12889,12950,12975,12978,13081,13154,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,11997,12731,12883,12907,12936,12941,12965,3316,3393,12107,12797,12848,12852,12856,12860,12870,12874,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,12207,12303,12306,12366,12397,12434,12516,3472,10645,10911,10955,11225,11303,11467,11709,12343,12519,12923,12992,13043,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,12137,12281,12324,12330,12416,12419,12438,12492,12498,12507,12529,12796,12813,12816,12912,12993,13035,13053,13056,13093,13137,13140,3379,10674,10704,10713,11254,11808,12435,12449,12778,12782,12785,3416,13077,13134,3410,3828,3767,10347,11627,11657,12758,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,12981,3336,10707,10860,10931,11658,11813,12002,12234,12806,13080,13155,13161,13165,3789,11759,12711,3531,4564,3800,3835,4543,4545,4546,3287,3288,4544,4547,4548,4588,4301,3807,3626,11620,4224,11486,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,11350,4013,12264,3906,11347,11684,11688,11750,12351,12359,12441,12725,12987,13039,3752,10971,10977,10992,11929,12140,12412,3613,11194,12166,12278,12288,12356,12407,12415,12526,13047,3650,4078,3754,10710,11048,11200,11230,11241,12246,12355,12401,13027,3582,10631,10634,10716,10890,3581,4581,11621,4577,12679,4583,10767,10869,11179,11331,11464,11492,12228,12237,12284,12462,4178,10843,12078,12249,12261,12287,4086,3788,12532,3733,3734,4579,10323,10326,10662,10665,11503,11685,12471,4580,11601,11694,3756,10628,10887,13067,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462,6463,6465,6466,6468,6470,6471,6472,6474,6476,6479,6485,6486,6487,6488,6494,6496,6536,6541,6556,6557,6558,6559,6594,6599,6601,6606,6607,6615,6619,6632,6657,6658,6659,6660,6671,6676,6693,6697,6716,6749,6750,6751,6756,6764,6785,6787,6789,6791,6794,6800,6802,6815,6822,6857,6860,6861,6874,6875,6876,6877,6893,6894,6911,6937,6960,6971,6973,6974,6976,6978,6979,7014,7015,7020,7021,7023,7025,7026,7027,7052,7061,7062,7073,7083,7122,7132,7136,7143,7154,7155,7160,7162,7168,7176,7177,7190,7207,7225,7227,7244,7288,7290,7291,7292,7299,7304,7320,7364,7398,7412,7429,7462,7465,7488,7512,7530,7533,7534,7544,7561,7562,7564,7566,7568,7570,7594,7619,7620,7652,7654,7655,7656,7661,7681,7690,7701,7706,7712,7714,7720,7731,7732,7734,7755,7764,7789,7856,7857,7899,7907,7908,7927,7928,7945,7946,8011,8012,8013,8039,8075,8082,8085,8094,8106,8139,8145,8152,8165,8184,8191,8211,8253,8283,8295,8313,8316,8343,8366,8427,8428,8432,8434,8454,8541,8542,8543,8544,8597,8627,8664,8681,8731,8781,8784,8799,8806,8844,8865,8894,8895,8911,8912,9044,9048,9061,9072,9101,9103,9106,9110,9113,9114,9129,9130,9153,9159,9171,9217,9236,9298,9299,9301,9366,9372,9400,9407,9408,9411,9412,9429,9443,9452,9464,9478,9479,9481,9483,9520,9655,9697,9698,9745,9799,9907,9908,9952,10014,10093,10107,10208,3,2637,2639,2640,2641,2642,2645,2646,2647,2652,2653,2655,2661,2662,2663,2664,2667,2674,2675,2676,2677,2679,2680,2681,2684,2685,2686,2688,2698,2699,2701,2702,2704,2708,2709,2710,2711,2712,2713,2719,2720,2721,2739,2746,2747,2748,2756,2760,2763,2765,2775,2776,2778,2779,2782,2803,2823,2826,2827,2828,2829,2834,2835,2843,2845,2847,2848,2849,2851,2852,2862,2864,2865,2891,5249,5311,5409,5495,5496,5497,5571,5669,5700,5733,5749,5751,5757,5820,5821,5822,5823,5829,5862,5994,6039,6062,6099,6139,6282,6289,6322,6323,6341,6344,6346,6353,6354,6355,6356,6357,6358,6359,6360,6441,6508,6509,6517,6592,6626,6627,6668,6669,6801,6814,6885,6886,6890,6912,6935,6943,6945,6993,7018,7019,7035,7036,7037,7072,7116,7117,7214,7270,7271,7272,7273,7287,7314,7369,7370,7379,7386,7388,7400,7432,7433,7434,7435,7574,7575,7582,7584,7585,7586,7797,7799,7800,7816,7854,7923,7964,8022,8044,8045,8063,8124,8224,8293,8294,8296,8328,8390,8391,8462,8481,8482,8483,8484,8631,8838,8862,8863,8943,8957,9012,9013,9118,9163,9186,9218,9260,9450,9734,9872,9929,9975,9977,6057,6424,6425,6511,6527,6528,6934,7152,8556,8587,8775,8968,8969,9035,9036,9311,9312,9313,9314,9523,9816,10103,10190,10191,6493,8381,8382,8827,8845,9817,10189,4677,4679])).
% 162.46/162.15 cnf(13246,plain,
% 162.46/162.15 (P24(f331(f331(f248(a1),f2(a1)),f331(f76(a1),f79(a1))))),
% 162.46/162.15 inference(scs_inference,[],[4582,3553,11085,12122,12222,12317,12352,12360,12373,12428,12556,12558,12988,12998,13003,13007,13013,13016,13040,13142,3563,12186,12650,12652,3564,12256,3280,12577,12579,3281,12641,3249,12501,4519,4520,11706,4246,12626,12629,3284,12613,3123,3143,12635,3185,12550,4503,3615,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,12189,12344,12398,12535,12658,12810,13064,4500,10471,10564,3374,3334,12619,3523,3230,4495,12726,13084,2899,2900,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2933,2936,2939,2940,2949,2953,2970,2975,2979,2982,2983,2991,2992,2994,2995,3005,3006,3009,3017,3020,3029,3031,3032,3035,3036,3037,3040,3041,3043,3044,3046,3063,3064,3068,3069,3070,3080,3086,4480,3102,3184,4481,3652,3156,11358,3294,3358,3267,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,12096,12293,12481,12537,12542,12544,12546,12548,12566,12583,12589,12624,12633,12864,13031,13141,13146,13167,3638,3881,3244,11633,12376,12380,12384,3255,3770,11017,11639,3999,3145,3146,3966,4497,4507,3857,11408,3373,12568,3210,3176,3350,3688,12591,3171,3974,3191,3693,4464,3154,3155,3133,3160,3190,3327,12067,12212,12431,12504,3375,10853,12183,3242,3243,3265,10512,3420,4575,10441,3939,4509,10304,10468,11268,12340,12377,12381,4518,12348,3303,11729,11732,12957,13060,13113,13117,13121,4567,11020,11090,11311,11314,3217,3298,3421,3637,3413,3388,12608,3205,10370,10677,3206,4551,3477,3198,3124,3226,11398,4080,12363,12493,3942,11026,11152,11203,12327,12333,12442,12445,12468,4590,10958,11157,11262,11284,11319,11325,12272,4591,11059,11160,11265,4592,11163,11214,4593,11217,4594,3225,3516,12225,12269,12347,3677,4367,4368,3498,3617,3655,3824,3584,12847,12851,12855,12859,12869,3867,12219,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,12151,12472,12664,12722,12753,12765,12809,12830,12886,12892,13063,13068,13152,13158,3758,11624,3296,3397,11744,12657,13166,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,12275,12367,12669,12672,12689,12692,12714,12766,12935,12940,12964,12969,4571,11506,11539,11574,11604,12777,12781,3745,3525,3526,12695,12698,12701,12704,12734,12737,13096,13100,13104,3889,3488,13097,3489,13101,3342,3343,3317,4554,3204,4505,3704,4216,4007,3508,4574,4074,11279,3636,3357,11753,11756,12193,12297,12452,4046,4006,11897,12240,3951,10850,12055,12081,12253,12475,12929,13112,3996,13116,4001,11029,12119,12192,12252,12296,12960,4002,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,12141,12393,12465,12478,12997,13002,4576,10798,11168,13010,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,12134,12300,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,12233,12404,12448,12715,12740,12819,12826,12833,12838,12841,12844,12877,12889,12950,12975,12978,13081,13154,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,11997,12731,12883,12907,12936,12941,12965,3316,3393,12107,12797,12848,12852,12856,12860,12870,12874,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,12207,12303,12306,12366,12397,12434,12516,3472,10645,10911,10955,11225,11303,11467,11709,12343,12519,12923,12992,13043,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,12137,12281,12324,12330,12416,12419,12438,12492,12498,12507,12529,12796,12813,12816,12912,12993,13035,13053,13056,13093,13137,13140,3379,10674,10704,10713,11254,11808,12435,12449,12778,12782,12785,3416,13077,13134,3410,3828,3767,10347,11627,11657,12758,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,12981,3336,10707,10860,10931,11658,11813,12002,12234,12806,13080,13155,13161,13165,3789,11759,12711,3531,4564,3800,3835,4543,4545,4546,3287,3288,4544,4547,4548,4588,4301,3807,3626,11620,4224,11486,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,11350,4013,12264,3906,11347,11684,11688,11750,12351,12359,12441,12725,12987,13039,3752,10971,10977,10992,11929,12140,12412,3613,11194,12166,12278,12288,12356,12407,12415,12526,13047,3650,4078,3754,10710,11048,11200,11230,11241,12246,12355,12401,13027,3582,10631,10634,10716,10890,3581,4581,11621,4577,12679,4583,10767,10869,11179,11331,11464,11492,12228,12237,12284,12462,4178,10843,12078,12249,12261,12287,4086,3788,12532,3733,3734,4579,10323,10326,10662,10665,11503,11685,12471,4580,11601,11694,3756,10628,10887,13067,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462,6463,6465,6466,6468,6470,6471,6472,6474,6476,6479,6485,6486,6487,6488,6494,6496,6536,6541,6556,6557,6558,6559,6594,6599,6601,6606,6607,6615,6619,6632,6657,6658,6659,6660,6671,6676,6693,6697,6716,6749,6750,6751,6756,6764,6785,6787,6789,6791,6794,6800,6802,6815,6822,6857,6860,6861,6874,6875,6876,6877,6893,6894,6911,6937,6960,6971,6973,6974,6976,6978,6979,7014,7015,7020,7021,7023,7025,7026,7027,7052,7061,7062,7073,7083,7122,7132,7136,7143,7154,7155,7160,7162,7168,7176,7177,7190,7207,7225,7227,7244,7288,7290,7291,7292,7299,7304,7320,7364,7398,7412,7429,7462,7465,7488,7512,7530,7533,7534,7544,7561,7562,7564,7566,7568,7570,7594,7619,7620,7652,7654,7655,7656,7661,7681,7690,7701,7706,7712,7714,7720,7731,7732,7734,7755,7764,7789,7856,7857,7899,7907,7908,7927,7928,7945,7946,8011,8012,8013,8039,8075,8082,8085,8094,8106,8139,8145,8152,8165,8184,8191,8211,8253,8283,8295,8313,8316,8343,8366,8427,8428,8432,8434,8454,8541,8542,8543,8544,8597,8627,8664,8681,8731,8781,8784,8799,8806,8844,8865,8894,8895,8911,8912,9044,9048,9061,9072,9101,9103,9106,9110,9113,9114,9129,9130,9153,9159,9171,9217,9236,9298,9299,9301,9366,9372,9400,9407,9408,9411,9412,9429,9443,9452,9464,9478,9479,9481,9483,9520,9655,9697,9698,9745,9799,9907,9908,9952,10014,10093,10107,10208,3,2637,2639,2640,2641,2642,2645,2646,2647,2652,2653,2655,2661,2662,2663,2664,2667,2674,2675,2676,2677,2679,2680,2681,2684,2685,2686,2688,2698,2699,2701,2702,2704,2708,2709,2710,2711,2712,2713,2719,2720,2721,2739,2746,2747,2748,2756,2760,2763,2765,2775,2776,2778,2779,2782,2803,2823,2826,2827,2828,2829,2834,2835,2843,2845,2847,2848,2849,2851,2852,2862,2864,2865,2891,5249,5311,5409,5495,5496,5497,5571,5669,5700,5733,5749,5751,5757,5820,5821,5822,5823,5829,5862,5994,6039,6062,6099,6139,6282,6289,6322,6323,6341,6344,6346,6353,6354,6355,6356,6357,6358,6359,6360,6441,6508,6509,6517,6592,6626,6627,6668,6669,6801,6814,6885,6886,6890,6912,6935,6943,6945,6993,7018,7019,7035,7036,7037,7072,7116,7117,7214,7270,7271,7272,7273,7287,7314,7369,7370,7379,7386,7388,7400,7432,7433,7434,7435,7574,7575,7582,7584,7585,7586,7797,7799,7800,7816,7854,7923,7964,8022,8044,8045,8063,8124,8224,8293,8294,8296,8328,8390,8391,8462,8481,8482,8483,8484,8631,8838,8862,8863,8943,8957,9012,9013,9118,9163,9186,9218,9260,9450,9734,9872,9929,9975,9977,6057,6424,6425,6511,6527,6528,6934,7152,8556,8587,8775,8968,8969,9035,9036,9311,9312,9313,9314,9523,9816,10103,10190,10191,6493,8381,8382,8827,8845,9817,10189,4677,4679,4680,4735,4743,4878,4894,4895,4917,4920,4924,4925,4954,5009,5051,5071,5128,5177,5205,5241,5244,5250,5252,5253,5279,5354,5377,5512,5576,5577,5578,5696])).
% 162.46/162.15 cnf(13266,plain,
% 162.46/162.15 (~P24(f331(f331(f248(a883),f331(a118,f331(f331(f81(a883),x132661),x132662))),f331(a118,x132662)))),
% 162.46/162.15 inference(scs_inference,[],[4582,3553,11085,12122,12222,12317,12352,12360,12373,12428,12556,12558,12988,12998,13003,13007,13013,13016,13040,13142,3563,12186,12650,12652,3564,12256,3280,12577,12579,3281,12641,3249,12501,4519,4520,11706,4246,12626,12629,3284,12613,3123,3143,12635,3185,12550,4503,3615,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,12189,12344,12398,12535,12658,12810,13064,4500,10471,10564,3374,3334,12619,3523,3230,4495,12726,13084,2899,2900,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2933,2936,2939,2940,2949,2953,2970,2975,2979,2982,2983,2991,2992,2994,2995,3005,3006,3009,3017,3020,3029,3031,3032,3035,3036,3037,3040,3041,3043,3044,3046,3063,3064,3068,3069,3070,3080,3086,4480,3102,3184,4481,3652,3156,11358,3294,3358,3267,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,12096,12293,12481,12537,12542,12544,12546,12548,12566,12583,12589,12624,12633,12864,13031,13141,13146,13167,3638,3881,3244,11633,12376,12380,12384,3255,3770,11017,11639,3999,3145,3146,3966,4497,4507,3857,11408,3373,12568,3210,3176,3350,3688,12591,3171,3974,3191,3693,4464,3154,3155,3133,3160,3190,3327,12067,12212,12431,12504,3375,10853,12183,3242,3243,3265,10512,3420,4575,10441,3939,4509,10304,10468,11268,12340,12377,12381,4518,12348,3303,11729,11732,12957,13060,13113,13117,13121,4567,11020,11090,11311,11314,3217,3298,3421,3637,3413,3388,12608,3205,10370,10677,3206,4551,3477,3198,3124,3226,11398,4080,12363,12493,3942,11026,11152,11203,12327,12333,12442,12445,12468,4590,10958,11157,11262,11284,11319,11325,12272,4591,11059,11160,11265,4592,11163,11214,4593,11217,4594,3225,3516,12225,12269,12347,3677,4367,4368,3498,3617,3655,3824,3584,12847,12851,12855,12859,12869,3867,12219,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,12151,12472,12664,12722,12753,12765,12809,12830,12886,12892,13063,13068,13152,13158,3758,11624,3296,3397,11744,12657,13166,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,12275,12367,12669,12672,12689,12692,12714,12766,12935,12940,12964,12969,4571,11506,11539,11574,11604,12777,12781,3745,3525,3526,12695,12698,12701,12704,12734,12737,13096,13100,13104,3889,3488,13097,3489,13101,3342,3343,3317,4554,3204,4505,3704,4216,4007,3508,4574,4074,11279,3636,3357,11753,11756,12193,12297,12452,4046,4006,11897,12240,3951,10850,12055,12081,12253,12475,12929,13112,3996,13116,4001,11029,12119,12192,12252,12296,12960,4002,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,12141,12393,12465,12478,12997,13002,4576,10798,11168,13010,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,12134,12300,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,12233,12404,12448,12715,12740,12819,12826,12833,12838,12841,12844,12877,12889,12950,12975,12978,13081,13154,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,11997,12731,12883,12907,12936,12941,12965,3316,3393,12107,12797,12848,12852,12856,12860,12870,12874,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,12207,12303,12306,12366,12397,12434,12516,3472,10645,10911,10955,11225,11303,11467,11709,12343,12519,12923,12992,13043,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,12137,12281,12324,12330,12416,12419,12438,12492,12498,12507,12529,12796,12813,12816,12912,12993,13035,13053,13056,13093,13137,13140,3379,10674,10704,10713,11254,11808,12435,12449,12778,12782,12785,3416,13077,13134,3410,3828,3767,10347,11627,11657,12758,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,12981,3336,10707,10860,10931,11658,11813,12002,12234,12806,13080,13155,13161,13165,3789,11759,12711,3531,4564,3800,3835,4543,4545,4546,3287,3288,4544,4547,4548,4588,4301,3807,3626,11620,4224,11486,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,11350,4013,12264,3906,11347,11684,11688,11750,12351,12359,12441,12725,12987,13039,3752,10971,10977,10992,11929,12140,12412,3613,11194,12166,12278,12288,12356,12407,12415,12526,13047,3650,4078,3754,10710,11048,11200,11230,11241,12246,12355,12401,13027,3582,10631,10634,10716,10890,3581,4581,11621,4577,12679,4583,10767,10869,11179,11331,11464,11492,12228,12237,12284,12462,4178,10843,12078,12249,12261,12287,4086,3788,12532,3733,3734,4579,10323,10326,10662,10665,11503,11685,12471,4580,11601,11694,3756,10628,10887,13067,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462,6463,6465,6466,6468,6470,6471,6472,6474,6476,6479,6485,6486,6487,6488,6494,6496,6536,6541,6556,6557,6558,6559,6594,6599,6601,6606,6607,6615,6619,6632,6657,6658,6659,6660,6671,6676,6693,6697,6716,6749,6750,6751,6756,6764,6785,6787,6789,6791,6794,6800,6802,6815,6822,6857,6860,6861,6874,6875,6876,6877,6893,6894,6911,6937,6960,6971,6973,6974,6976,6978,6979,7014,7015,7020,7021,7023,7025,7026,7027,7052,7061,7062,7073,7083,7122,7132,7136,7143,7154,7155,7160,7162,7168,7176,7177,7190,7207,7225,7227,7244,7288,7290,7291,7292,7299,7304,7320,7364,7398,7412,7429,7462,7465,7488,7512,7530,7533,7534,7544,7561,7562,7564,7566,7568,7570,7594,7619,7620,7652,7654,7655,7656,7661,7681,7690,7701,7706,7712,7714,7720,7731,7732,7734,7755,7764,7789,7856,7857,7899,7907,7908,7927,7928,7945,7946,8011,8012,8013,8039,8075,8082,8085,8094,8106,8139,8145,8152,8165,8184,8191,8211,8253,8283,8295,8313,8316,8343,8366,8427,8428,8432,8434,8454,8541,8542,8543,8544,8597,8627,8664,8681,8731,8781,8784,8799,8806,8844,8865,8894,8895,8911,8912,9044,9048,9061,9072,9101,9103,9106,9110,9113,9114,9129,9130,9153,9159,9171,9217,9236,9298,9299,9301,9366,9372,9400,9407,9408,9411,9412,9429,9443,9452,9464,9478,9479,9481,9483,9520,9655,9697,9698,9745,9799,9907,9908,9952,10014,10093,10107,10208,3,2637,2639,2640,2641,2642,2645,2646,2647,2652,2653,2655,2661,2662,2663,2664,2667,2674,2675,2676,2677,2679,2680,2681,2684,2685,2686,2688,2698,2699,2701,2702,2704,2708,2709,2710,2711,2712,2713,2719,2720,2721,2739,2746,2747,2748,2756,2760,2763,2765,2775,2776,2778,2779,2782,2803,2823,2826,2827,2828,2829,2834,2835,2843,2845,2847,2848,2849,2851,2852,2862,2864,2865,2891,5249,5311,5409,5495,5496,5497,5571,5669,5700,5733,5749,5751,5757,5820,5821,5822,5823,5829,5862,5994,6039,6062,6099,6139,6282,6289,6322,6323,6341,6344,6346,6353,6354,6355,6356,6357,6358,6359,6360,6441,6508,6509,6517,6592,6626,6627,6668,6669,6801,6814,6885,6886,6890,6912,6935,6943,6945,6993,7018,7019,7035,7036,7037,7072,7116,7117,7214,7270,7271,7272,7273,7287,7314,7369,7370,7379,7386,7388,7400,7432,7433,7434,7435,7574,7575,7582,7584,7585,7586,7797,7799,7800,7816,7854,7923,7964,8022,8044,8045,8063,8124,8224,8293,8294,8296,8328,8390,8391,8462,8481,8482,8483,8484,8631,8838,8862,8863,8943,8957,9012,9013,9118,9163,9186,9218,9260,9450,9734,9872,9929,9975,9977,6057,6424,6425,6511,6527,6528,6934,7152,8556,8587,8775,8968,8969,9035,9036,9311,9312,9313,9314,9523,9816,10103,10190,10191,6493,8381,8382,8827,8845,9817,10189,4677,4679,4680,4735,4743,4878,4894,4895,4917,4920,4924,4925,4954,5009,5051,5071,5128,5177,5205,5241,5244,5250,5252,5253,5279,5354,5377,5512,5576,5577,5578,5696,5697,5722,5723,5727,5780,5786,5788,5797,5803,5875])).
% 162.46/162.15 cnf(13276,plain,
% 162.46/162.15 (~P24(f331(f62(x132761),f40(f891(x132761,a877),f256(f891(f891(x132761,a877),a877)))))),
% 162.46/162.15 inference(scs_inference,[],[4582,3553,11085,12122,12222,12317,12352,12360,12373,12428,12556,12558,12988,12998,13003,13007,13013,13016,13040,13142,3563,12186,12650,12652,3564,12256,3280,12577,12579,3281,12641,3249,12501,4519,4520,11706,4246,12626,12629,3284,12613,3123,3143,12635,3185,12550,4503,3615,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,12189,12344,12398,12535,12658,12810,13064,4500,10471,10564,3374,3334,12619,3523,3230,4495,12726,13084,2899,2900,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2933,2936,2939,2940,2949,2953,2970,2975,2979,2982,2983,2991,2992,2994,2995,3005,3006,3009,3017,3020,3029,3031,3032,3035,3036,3037,3040,3041,3043,3044,3046,3063,3064,3068,3069,3070,3080,3086,4480,3102,3184,4481,3652,3156,11358,3294,3358,3267,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,12096,12293,12481,12537,12542,12544,12546,12548,12566,12583,12589,12624,12633,12864,13031,13141,13146,13167,3638,3881,3244,11633,12376,12380,12384,3255,3770,11017,11639,3999,3145,3146,3966,4497,4507,3857,11408,3373,12568,3210,3176,3350,3688,12591,3171,3974,3191,3693,4464,3154,3155,3133,3160,3190,3327,12067,12212,12431,12504,3375,10853,12183,3242,3243,3265,10512,3420,4575,10441,3939,4509,10304,10468,11268,12340,12377,12381,4518,12348,3303,11729,11732,12957,13060,13113,13117,13121,4567,11020,11090,11311,11314,3217,3298,3421,3637,3413,3388,12608,3205,10370,10677,3206,4551,3477,3198,3124,3226,11398,4080,12363,12493,3942,11026,11152,11203,12327,12333,12442,12445,12468,4590,10958,11157,11262,11284,11319,11325,12272,4591,11059,11160,11265,4592,11163,11214,4593,11217,4594,3225,3516,12225,12269,12347,3677,4367,4368,3498,3617,3655,3824,3584,12847,12851,12855,12859,12869,3867,12219,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,12151,12472,12664,12722,12753,12765,12809,12830,12886,12892,13063,13068,13152,13158,3758,11624,3296,3397,11744,12657,13166,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,12275,12367,12669,12672,12689,12692,12714,12766,12935,12940,12964,12969,4571,11506,11539,11574,11604,12777,12781,3745,3525,3526,12695,12698,12701,12704,12734,12737,13096,13100,13104,3889,3488,13097,3489,13101,3342,3343,3317,4554,3204,4505,3704,4216,4007,3508,4574,4074,11279,3636,3357,11753,11756,12193,12297,12452,4046,4006,11897,12240,3951,10850,12055,12081,12253,12475,12929,13112,3996,13116,4001,11029,12119,12192,12252,12296,12960,4002,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,12141,12393,12465,12478,12997,13002,4576,10798,11168,13010,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,12134,12300,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,12233,12404,12448,12715,12740,12819,12826,12833,12838,12841,12844,12877,12889,12950,12975,12978,13081,13154,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,11997,12731,12883,12907,12936,12941,12965,3316,3393,12107,12797,12848,12852,12856,12860,12870,12874,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,12207,12303,12306,12366,12397,12434,12516,3472,10645,10911,10955,11225,11303,11467,11709,12343,12519,12923,12992,13043,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,12137,12281,12324,12330,12416,12419,12438,12492,12498,12507,12529,12796,12813,12816,12912,12993,13035,13053,13056,13093,13137,13140,3379,10674,10704,10713,11254,11808,12435,12449,12778,12782,12785,3416,13077,13134,3410,3828,3767,10347,11627,11657,12758,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,12981,3336,10707,10860,10931,11658,11813,12002,12234,12806,13080,13155,13161,13165,3789,11759,12711,3531,4564,3800,3835,4543,4545,4546,3287,3288,4544,4547,4548,4588,4301,3807,3626,11620,4224,11486,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,11350,4013,12264,3906,11347,11684,11688,11750,12351,12359,12441,12725,12987,13039,3752,10971,10977,10992,11929,12140,12412,3613,11194,12166,12278,12288,12356,12407,12415,12526,13047,3650,4078,3754,10710,11048,11200,11230,11241,12246,12355,12401,13027,3582,10631,10634,10716,10890,3581,4581,11621,4577,12679,4583,10767,10869,11179,11331,11464,11492,12228,12237,12284,12462,4178,10843,12078,12249,12261,12287,4086,3788,12532,3733,3734,4579,10323,10326,10662,10665,11503,11685,12471,4580,11601,11694,3756,10628,10887,13067,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462,6463,6465,6466,6468,6470,6471,6472,6474,6476,6479,6485,6486,6487,6488,6494,6496,6536,6541,6556,6557,6558,6559,6594,6599,6601,6606,6607,6615,6619,6632,6657,6658,6659,6660,6671,6676,6693,6697,6716,6749,6750,6751,6756,6764,6785,6787,6789,6791,6794,6800,6802,6815,6822,6857,6860,6861,6874,6875,6876,6877,6893,6894,6911,6937,6960,6971,6973,6974,6976,6978,6979,7014,7015,7020,7021,7023,7025,7026,7027,7052,7061,7062,7073,7083,7122,7132,7136,7143,7154,7155,7160,7162,7168,7176,7177,7190,7207,7225,7227,7244,7288,7290,7291,7292,7299,7304,7320,7364,7398,7412,7429,7462,7465,7488,7512,7530,7533,7534,7544,7561,7562,7564,7566,7568,7570,7594,7619,7620,7652,7654,7655,7656,7661,7681,7690,7701,7706,7712,7714,7720,7731,7732,7734,7755,7764,7789,7856,7857,7899,7907,7908,7927,7928,7945,7946,8011,8012,8013,8039,8075,8082,8085,8094,8106,8139,8145,8152,8165,8184,8191,8211,8253,8283,8295,8313,8316,8343,8366,8427,8428,8432,8434,8454,8541,8542,8543,8544,8597,8627,8664,8681,8731,8781,8784,8799,8806,8844,8865,8894,8895,8911,8912,9044,9048,9061,9072,9101,9103,9106,9110,9113,9114,9129,9130,9153,9159,9171,9217,9236,9298,9299,9301,9366,9372,9400,9407,9408,9411,9412,9429,9443,9452,9464,9478,9479,9481,9483,9520,9655,9697,9698,9745,9799,9907,9908,9952,10014,10093,10107,10208,3,2637,2639,2640,2641,2642,2645,2646,2647,2652,2653,2655,2661,2662,2663,2664,2667,2674,2675,2676,2677,2679,2680,2681,2684,2685,2686,2688,2698,2699,2701,2702,2704,2708,2709,2710,2711,2712,2713,2719,2720,2721,2739,2746,2747,2748,2756,2760,2763,2765,2775,2776,2778,2779,2782,2803,2823,2826,2827,2828,2829,2834,2835,2843,2845,2847,2848,2849,2851,2852,2862,2864,2865,2891,5249,5311,5409,5495,5496,5497,5571,5669,5700,5733,5749,5751,5757,5820,5821,5822,5823,5829,5862,5994,6039,6062,6099,6139,6282,6289,6322,6323,6341,6344,6346,6353,6354,6355,6356,6357,6358,6359,6360,6441,6508,6509,6517,6592,6626,6627,6668,6669,6801,6814,6885,6886,6890,6912,6935,6943,6945,6993,7018,7019,7035,7036,7037,7072,7116,7117,7214,7270,7271,7272,7273,7287,7314,7369,7370,7379,7386,7388,7400,7432,7433,7434,7435,7574,7575,7582,7584,7585,7586,7797,7799,7800,7816,7854,7923,7964,8022,8044,8045,8063,8124,8224,8293,8294,8296,8328,8390,8391,8462,8481,8482,8483,8484,8631,8838,8862,8863,8943,8957,9012,9013,9118,9163,9186,9218,9260,9450,9734,9872,9929,9975,9977,6057,6424,6425,6511,6527,6528,6934,7152,8556,8587,8775,8968,8969,9035,9036,9311,9312,9313,9314,9523,9816,10103,10190,10191,6493,8381,8382,8827,8845,9817,10189,4677,4679,4680,4735,4743,4878,4894,4895,4917,4920,4924,4925,4954,5009,5051,5071,5128,5177,5205,5241,5244,5250,5252,5253,5279,5354,5377,5512,5576,5577,5578,5696,5697,5722,5723,5727,5780,5786,5788,5797,5803,5875,5952,6017,6080,6103,6269])).
% 162.46/162.15 cnf(13292,plain,
% 162.46/162.15 (~P24(f331(f331(f248(a883),f2(a883)),f196(a883)))),
% 162.46/162.15 inference(scs_inference,[],[4582,3553,11085,12122,12222,12317,12352,12360,12373,12428,12556,12558,12988,12998,13003,13007,13013,13016,13040,13142,3563,12186,12650,12652,3564,12256,3280,12577,12579,3281,12641,3249,12501,4519,4520,11706,4246,12626,12629,3284,12613,3123,3143,12635,3185,12550,4503,3615,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,12189,12344,12398,12535,12658,12810,13064,4500,10471,10564,3374,3334,12619,3523,3230,4495,12726,13084,2899,2900,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2933,2936,2939,2940,2949,2953,2970,2975,2979,2982,2983,2991,2992,2994,2995,3005,3006,3009,3017,3020,3029,3031,3032,3035,3036,3037,3040,3041,3043,3044,3046,3063,3064,3068,3069,3070,3080,3086,4480,3102,3184,4481,3652,3156,11358,3294,3358,3267,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,12096,12293,12481,12537,12542,12544,12546,12548,12566,12583,12589,12624,12633,12864,13031,13141,13146,13167,3638,3881,3244,11633,12376,12380,12384,3255,3770,11017,11639,3999,3145,3146,3966,4497,4507,3857,11408,3373,12568,3210,3176,3350,3688,12591,3171,3974,3191,3693,4464,3154,3155,3133,3160,3190,3327,12067,12212,12431,12504,3375,10853,12183,3242,3243,3265,10512,3420,4575,10441,3939,4509,10304,10468,11268,12340,12377,12381,4518,12348,3303,11729,11732,12957,13060,13113,13117,13121,4567,11020,11090,11311,11314,3217,3298,3421,3637,3413,3388,12608,3205,10370,10677,3206,4551,3477,3198,3124,3226,11398,4080,12363,12493,3942,11026,11152,11203,12327,12333,12442,12445,12468,4590,10958,11157,11262,11284,11319,11325,12272,4591,11059,11160,11265,4592,11163,11214,4593,11217,4594,3225,3516,12225,12269,12347,3677,4367,4368,3498,3617,3655,3824,3584,12847,12851,12855,12859,12869,3867,12219,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,12151,12472,12664,12722,12753,12765,12809,12830,12886,12892,13063,13068,13152,13158,3758,11624,3296,3397,11744,12657,13166,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,12275,12367,12669,12672,12689,12692,12714,12766,12935,12940,12964,12969,4571,11506,11539,11574,11604,12777,12781,3745,3525,3526,12695,12698,12701,12704,12734,12737,13096,13100,13104,3889,3488,13097,3489,13101,3342,3343,3317,4554,3204,4505,3704,4216,4007,3508,4574,4074,11279,3636,3357,11753,11756,12193,12297,12452,4046,4006,11897,12240,3951,10850,12055,12081,12253,12475,12929,13112,3996,13116,4001,11029,12119,12192,12252,12296,12960,4002,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,12141,12393,12465,12478,12997,13002,4576,10798,11168,13010,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,12134,12300,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,12233,12404,12448,12715,12740,12819,12826,12833,12838,12841,12844,12877,12889,12950,12975,12978,13081,13154,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,11997,12731,12883,12907,12936,12941,12965,3316,3393,12107,12797,12848,12852,12856,12860,12870,12874,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,12207,12303,12306,12366,12397,12434,12516,3472,10645,10911,10955,11225,11303,11467,11709,12343,12519,12923,12992,13043,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,12137,12281,12324,12330,12416,12419,12438,12492,12498,12507,12529,12796,12813,12816,12912,12993,13035,13053,13056,13093,13137,13140,3379,10674,10704,10713,11254,11808,12435,12449,12778,12782,12785,3416,13077,13134,3410,3828,3767,10347,11627,11657,12758,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,12981,3336,10707,10860,10931,11658,11813,12002,12234,12806,13080,13155,13161,13165,3789,11759,12711,3531,4564,3800,3835,4543,4545,4546,3287,3288,4544,4547,4548,4588,4301,3807,3626,11620,4224,11486,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,11350,4013,12264,3906,11347,11684,11688,11750,12351,12359,12441,12725,12987,13039,3752,10971,10977,10992,11929,12140,12412,3613,11194,12166,12278,12288,12356,12407,12415,12526,13047,3650,4078,3754,10710,11048,11200,11230,11241,12246,12355,12401,13027,3582,10631,10634,10716,10890,3581,4581,11621,4577,12679,4583,10767,10869,11179,11331,11464,11492,12228,12237,12284,12462,4178,10843,12078,12249,12261,12287,4086,3788,12532,3733,3734,4579,10323,10326,10662,10665,11503,11685,12471,4580,11601,11694,3756,10628,10887,13067,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5243,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5358,5359,5360,5367,5371,5372,5373,5382,5386,5387,5388,5393,5406,5415,5427,5429,5437,5438,5442,5446,5471,5477,5487,5488,5503,5514,5536,5542,5558,5559,5562,5581,5589,5590,5595,5596,5606,5607,5621,5625,5634,5635,5637,5652,5657,5667,5668,5680,5687,5701,5705,5708,5714,5715,5716,5719,5724,5761,5762,5765,5767,5770,5771,5772,5774,5776,5778,5783,5790,5805,5819,5824,5825,5838,5839,5844,5848,5850,5855,5896,5908,5917,5921,5932,5935,5936,5944,5958,5964,5982,5985,5997,6024,6038,6063,6083,6084,6087,6102,6104,6105,6107,6120,6121,6124,6126,6129,6130,6142,6148,6149,6150,6154,6156,6194,6195,6200,6203,6212,6248,6250,6252,6254,6263,6265,6267,6273,6275,6281,6284,6292,6299,6300,6301,6305,6327,6328,6329,6331,6337,6340,6376,6377,6380,6381,6382,6383,6384,6385,6386,6393,6426,6427,6436,6457,6458,6477,6480,6491,6492,6498,6524,6526,6542,6579,6582,6583,6636,6661,6703,6723,6732,6733,6734,6735,6754,6755,6761,6768,6771,6773,6775,6776,6777,6779,6793,6804,6806,6807,6818,6821,6871,6882,6884,6888,6902,6903,6939,6952,6983,7002,7017,7071,7098,7153,7174,7183,7186,7241,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7401,7411,7414,7430,7479,7480,7484,7528,7529,7547,7611,7630,7653,7675,7689,7705,7715,7723,7724,7753,7756,7758,7768,7806,7818,7843,7896,7925,7957,8003,8019,8035,8036,8117,8170,8189,8212,8231,8255,8350,8352,8358,8374,8378,8394,8413,8424,8426,8443,8449,8453,8476,8488,8489,8504,8505,8515,8516,8517,8518,8519,8537,8538,8539,8547,8561,8562,8574,8578,8580,8581,8582,8590,8594,8623,8624,8649,8662,8665,8682,8704,8705,8706,8719,8720,8721,8742,8753,8762,8763,8764,8765,8767,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8978,9009,9010,9011,9026,9038,9042,9063,9064,9112,9115,9144,9191,9192,9193,9206,9232,9246,9252,9255,9280,9281,9309,9375,9403,9404,9405,9430,9431,9447,9465,9471,9493,9522,9544,9552,9553,9554,9555,9568,9570,9575,9614,9615,9621,9622,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9881,9919,9920,9921,9930,9931,9936,9950,9969,9974,9986,10038,10116,10117,10206,10227,2,8,9,4623,4624,4642,4673,4674,4676,4704,4710,4711,4720,4770,4772,4802,4816,4846,4941,4942,4956,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5363,5364,5374,5378,5379,5380,5381,5383,5384,5389,5390,5391,5392,5423,5424,5425,5433,5434,5435,5436,5482,5484,5486,5521,5523,5524,5526,5527,5529,5530,5532,5541,5546,5548,5549,5550,5551,5552,5553,5560,5570,5573,5584,5600,5601,5604,5615,5617,5618,5619,5644,5654,5670,5671,5681,5682,5684,5686,5691,5726,5730,5732,5792,5826,5827,5831,5837,5840,5841,5842,5843,5849,5860,5861,5863,5864,5872,5893,5924,5939,5942,5943,5945,5954,5975,5976,5977,5980,5981,5999,6010,6011,6040,6041,6045,6065,6068,6072,6091,6096,6097,6122,6125,6133,6141,6147,6153,6160,6161,6162,6163,6197,6213,6266,6302,6303,6324,6325,6330,6333,6334,6338,6342,6351,6369,6388,6389,6394,6404,6419,6439,6445,6447,6462,6463,6465,6466,6468,6470,6471,6472,6474,6476,6479,6485,6486,6487,6488,6494,6496,6536,6541,6556,6557,6558,6559,6594,6599,6601,6606,6607,6615,6619,6632,6657,6658,6659,6660,6671,6676,6693,6697,6716,6749,6750,6751,6756,6764,6785,6787,6789,6791,6794,6800,6802,6815,6822,6857,6860,6861,6874,6875,6876,6877,6893,6894,6911,6937,6960,6971,6973,6974,6976,6978,6979,7014,7015,7020,7021,7023,7025,7026,7027,7052,7061,7062,7073,7083,7122,7132,7136,7143,7154,7155,7160,7162,7168,7176,7177,7190,7207,7225,7227,7244,7288,7290,7291,7292,7299,7304,7320,7364,7398,7412,7429,7462,7465,7488,7512,7530,7533,7534,7544,7561,7562,7564,7566,7568,7570,7594,7619,7620,7652,7654,7655,7656,7661,7681,7690,7701,7706,7712,7714,7720,7731,7732,7734,7755,7764,7789,7856,7857,7899,7907,7908,7927,7928,7945,7946,8011,8012,8013,8039,8075,8082,8085,8094,8106,8139,8145,8152,8165,8184,8191,8211,8253,8283,8295,8313,8316,8343,8366,8427,8428,8432,8434,8454,8541,8542,8543,8544,8597,8627,8664,8681,8731,8781,8784,8799,8806,8844,8865,8894,8895,8911,8912,9044,9048,9061,9072,9101,9103,9106,9110,9113,9114,9129,9130,9153,9159,9171,9217,9236,9298,9299,9301,9366,9372,9400,9407,9408,9411,9412,9429,9443,9452,9464,9478,9479,9481,9483,9520,9655,9697,9698,9745,9799,9907,9908,9952,10014,10093,10107,10208,3,2637,2639,2640,2641,2642,2645,2646,2647,2652,2653,2655,2661,2662,2663,2664,2667,2674,2675,2676,2677,2679,2680,2681,2684,2685,2686,2688,2698,2699,2701,2702,2704,2708,2709,2710,2711,2712,2713,2719,2720,2721,2739,2746,2747,2748,2756,2760,2763,2765,2775,2776,2778,2779,2782,2803,2823,2826,2827,2828,2829,2834,2835,2843,2845,2847,2848,2849,2851,2852,2862,2864,2865,2891,5249,5311,5409,5495,5496,5497,5571,5669,5700,5733,5749,5751,5757,5820,5821,5822,5823,5829,5862,5994,6039,6062,6099,6139,6282,6289,6322,6323,6341,6344,6346,6353,6354,6355,6356,6357,6358,6359,6360,6441,6508,6509,6517,6592,6626,6627,6668,6669,6801,6814,6885,6886,6890,6912,6935,6943,6945,6993,7018,7019,7035,7036,7037,7072,7116,7117,7214,7270,7271,7272,7273,7287,7314,7369,7370,7379,7386,7388,7400,7432,7433,7434,7435,7574,7575,7582,7584,7585,7586,7797,7799,7800,7816,7854,7923,7964,8022,8044,8045,8063,8124,8224,8293,8294,8296,8328,8390,8391,8462,8481,8482,8483,8484,8631,8838,8862,8863,8943,8957,9012,9013,9118,9163,9186,9218,9260,9450,9734,9872,9929,9975,9977,6057,6424,6425,6511,6527,6528,6934,7152,8556,8587,8775,8968,8969,9035,9036,9311,9312,9313,9314,9523,9816,10103,10190,10191,6493,8381,8382,8827,8845,9817,10189,4677,4679,4680,4735,4743,4878,4894,4895,4917,4920,4924,4925,4954,5009,5051,5071,5128,5177,5205,5241,5244,5250,5252,5253,5279,5354,5377,5512,5576,5577,5578,5696,5697,5722,5723,5727,5780,5786,5788,5797,5803,5875,5952,6017,6080,6103,6269,6367,6387,6539,6741,6742,6883,6946,6986])).
% 162.46/162.15 cnf(13322,plain,
% 162.46/162.15 (~E(f331(a26,x133221),f331(f239(a879),f331(a28,a893)))),
% 162.46/162.15 inference(scs_inference,[],[4582,3553,11085,12122,12222,12317,12352,12360,12373,12428,12556,12558,12988,12998,13003,13007,13013,13016,13040,13142,3563,12186,12650,12652,3564,12256,3280,12577,12579,3281,12641,3249,12501,4519,4520,11706,4246,12626,12629,3284,12613,3123,3143,12635,3185,12550,4503,3615,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,12189,12344,12398,12535,12658,12810,13064,4500,10471,10564,3374,3334,12619,3523,3230,4495,12726,13084,2899,2900,2914,2915,2917,2918,2920,2921,2922,2924,2925,2928,2931,2932,2933,2936,2939,2940,2949,2953,2970,2975,2979,2982,2983,2991,2992,2994,2995,3005,3006,3009,3017,3020,3029,3031,3032,3035,3036,3037,3040,3041,3043,3044,3046,3063,3064,3068,3069,3070,3080,3086,4480,3102,3184,4481,3652,3156,11358,3294,3358,3267,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,12096,12293,12481,12537,12542,12544,12546,12548,12566,12583,12589,12624,12633,12864,13031,13141,13146,13167,3638,3881,3244,11633,12376,12380,12384,3255,3770,11017,11639,3999,3145,3146,3966,4497,4507,3857,11408,3373,12568,3210,3176,3350,3688,12591,3171,3974,3191,3693,4464,3154,3155,3133,3160,3190,3327,12067,12212,12431,12504,3375,10853,12183,3242,3243,3265,10512,3420,4575,10441,3939,4509,10304,10468,11268,12340,12377,12381,4518,12348,3303,11729,11732,12957,13060,13113,13117,13121,4567,11020,11090,11311,11314,3217,3298,3421,3637,3413,3388,12608,3205,10370,10677,3206,4551,3477,3198,3124,3226,11398,4080,12363,12493,3942,11026,11152,11203,12327,12333,12442,12445,12468,4590,10958,11157,11262,11284,11319,11325,12272,4591,11059,11160,11265,4592,11163,11214,4593,11217,4594,3225,3516,12225,12269,12347,3677,4367,4368,3498,3617,3655,3824,3584,12847,12851,12855,12859,12869,3867,12219,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,12151,12472,12664,12722,12753,12765,12809,12830,12886,12892,13063,13068,13152,13158,3758,11624,3296,3397,11744,12657,13166,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,12275,12367,12669,12672,12689,12692,12714,12766,12935,12940,12964,12969,4571,11506,11539,11574,11604,12777,12781,3745,3525,3526,12695,12698,12701,12704,12734,12737,13096,13100,13104,3889,3488,13097,3489,13101,3342,3343,3317,4554,3204,4505,3704,4216,4007,3508,4574,4074,11279,3636,3357,11753,11756,12193,12297,12452,4046,4006,11897,12240,3951,10850,12055,12081,12253,12475,12929,13112,3996,13116,4001,11029,12119,12192,12252,12296,12960,4002,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,12141,12393,12465,12478,12997,13002,4576,10798,11168,13010,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,12134,12300,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,12233,12404,12448,12715,12740,12819,12826,12833,12838,12841,12844,12877,12889,12950,12975,12978,13081,13154,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,11997,12731,12883,12907,12936,12941,12965,3316,3393,12107,12797,12848,12852,12856,12860,12870,12874,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,12207,12303,12306,12366,12397,12434,12516,3472,10645,10911,10955,11225,11303,11467,11709,12343,12519,12923,12992,13043,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,12137,12281,12324,12330,12416,12419,12438,12492,12498,12507,12529,12796,12813,12816,12912,12993,13035,13053,13056,13093,13137,13140,3379,10674,10704,10713,11254,11808,12435,12449,12778,12782,12785,3416,13077,13134,3410,3828,3767,10347,11627,11657,12758,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,12981,3336,10707,10860,10931,11658,11813,12002,12234,12806,13080,13155,13161,13165,3789,11759,12711,3531,4564,3800,3835,4543,4545,4546,3287,3288,4544,4547,4548,4588,4301,3807,3626,11620,4224,11486,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,11350,4013,12264,3906,11347,11684,11688,11750,12351,12359,12441,12725,12987,13039,3752,10971,10977,10992,11929,12140,12412,3613,11194,12166,12278,12288,12356,12407,12415,12526,13047,3650,4078,3754,10710,11048,11200,11230,11241,12246,12355,12401,13027,3582,10631,10634,10716,10890,3581,4581,11621,4577,12679,4583,10767,10869,11179,11331,11464,11492,12228,12237,12284,12462,4178,10843,12078,12249,12261,12287,4086,3788,12532,3733,3734,4579,10323,10326,10662,10665,11503,11685,12471,4580,11601,11694,3756,10628,10887,13067,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,52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7018,7019,7035,7036,7037,7072,7116,7117,7214,7270,7271,7272,7273,7287,7314,7369,7370,7379,7386,7388,7400,7432,7433,7434,7435,7574,7575,7582,7584,7585,7586,7797,7799,7800,7816,7854,7923,7964,8022,8044,8045,8063,8124,8224,8293,8294,8296,8328,8390,8391,8462,8481,8482,8483,8484,8631,8838,8862,8863,8943,8957,9012,9013,9118,9163,9186,9218,9260,9450,9734,9872,9929,9975,9977,6057,6424,6425,6511,6527,6528,6934,7152,8556,8587,8775,8968,8969,9035,9036,9311,9312,9313,9314,9523,9816,10103,10190,10191,6493,8381,8382,8827,8845,9817,10189,4677,4679,4680,4735,4743,4878,4894,4895,4917,4920,4924,4925,4954,5009,5051,5071,5128,5177,5205,5241,5244,5250,5252,5253,5279,5354,5377,5512,5576,5577,5578,5696,5697,5722,5723,5727,5780,5786,5788,5797,5803,5875,5952,6017,6080,6103,6269,6367,6387,6539,6741,6742,6883,6946,6986,7158,7371,7441,7773,7775,7865,7936,7938,7939,8020,8782,9039,9277,9558,4859])).
% 162.46/162.15 cnf(13325,plain,
% 162.46/162.15 (~E(f331(a118,x133251),x133251)),
% 162.46/162.15 inference(rename_variables,[],[4485])).
% 162.46/162.15 cnf(13331,plain,
% 162.46/162.15 (P24(f331(f62(a883),f304(a883,x133311,x133312)))),
% 162.46/162.15 inference(rename_variables,[],[3526])).
% 162.46/162.15 cnf(13356,plain,
% 162.46/162.15 (~E(f331(a118,x133561),x133561)),
% 162.46/162.15 inference(rename_variables,[],[4485])).
% 162.46/162.15 cnf(13376,plain,
% 162.46/162.15 (~E(f331(a118,x133761),x133761)),
% 162.46/162.15 inference(rename_variables,[],[4485])).
% 162.46/162.15 cnf(13399,plain,
% 162.46/162.15 (P24(f331(f331(f248(a883),f2(a883)),f331(f331(f81(a883),f331(a118,f2(a883))),f2(a883))))),
% 162.46/162.15 inference(scs_inference,[],[4582,3553,11085,12122,12222,12317,12352,12360,12373,12428,12556,12558,12988,12998,13003,13007,13013,13016,13040,13142,3563,12186,12650,12652,3564,12256,3280,12577,12579,3281,12641,3249,12501,4519,4520,11706,4246,12626,12629,3284,12613,3123,3143,12635,3185,12550,4503,3615,4485,10246,10249,10259,10270,10378,10381,10384,10487,10600,10906,11070,11073,11271,11361,11368,11382,11432,11435,11544,11591,11607,11908,11933,11945,11977,12075,12182,12189,12344,12398,12535,12658,12810,13064,13072,13325,13356,13376,4500,10471,10564,3374,3334,12619,3523,3230,4495,12726,13084,2899,2900,2914,2915,2917,2918,2920,2921,2922,2924,2925,2926,2928,2931,2932,2933,2936,2939,2940,2949,2953,2970,2975,2979,2982,2983,2991,2992,2994,2995,3005,3006,3009,3017,3020,3029,3031,3032,3033,3035,3036,3037,3040,3041,3043,3044,3046,3063,3064,3068,3069,3070,3080,3086,4480,3102,3184,4481,3652,3156,11358,3294,3358,3267,3270,10243,10252,10313,10316,10405,10408,10701,11373,11376,11487,11531,11536,11636,12096,12293,12481,12537,12542,12544,12546,12548,12566,12583,12589,12624,12633,12864,13031,13141,13146,13167,3638,3881,3244,11633,12376,12380,12384,3255,3770,11017,11639,3999,3145,3146,3966,4497,4507,3857,11408,3373,12568,3208,3210,3681,3176,3350,3688,12591,3171,3974,3191,3693,4464,3154,3155,3133,3160,3190,3327,12067,12212,12431,12504,3375,10853,12183,3242,3243,3265,10512,10515,3420,4575,10441,3939,4509,10304,10468,11268,12340,12377,12381,4518,12348,3303,11729,11732,12957,13060,13113,13117,13121,4567,11020,11090,11311,11314,3217,3298,3421,3637,3413,3388,12608,3205,10370,10677,3206,4551,3477,3198,3124,3226,11398,4080,12363,12493,3942,11026,11152,11203,12327,12333,12442,12445,12468,4590,10958,11157,11262,11284,11319,11325,12272,4591,11059,11160,11265,4592,11163,11214,4593,11217,4594,3225,3516,12225,12269,12347,3677,4367,4368,3498,3617,3655,3824,3584,12847,12851,12855,12859,12869,3867,12219,3501,3747,3385,10389,10507,10578,10639,10642,10680,10774,11010,11904,11967,12043,12087,12148,12151,12472,12664,12722,12753,12765,12809,12830,12886,12892,13063,13068,13152,13158,3758,11624,3296,3397,11744,12657,13166,3579,4557,10281,10284,10310,10782,10795,10916,11334,11401,11793,11801,12019,12022,12113,12275,12367,12669,12672,12689,12692,12714,12766,12935,12940,12964,12969,4571,11506,11539,11574,11604,12777,12781,3745,3525,3526,12695,12698,12701,12704,12734,12737,13096,13100,13104,13108,13331,3527,3889,3488,13097,3489,13101,3342,3343,3317,4554,3204,4505,3704,4216,4007,3508,4574,4074,11279,3636,3357,11753,11756,12193,12297,12452,4046,4006,11897,12240,3951,10850,12055,12081,12253,12475,12929,13112,3996,13116,4001,11029,12119,12192,12252,12296,12960,4002,3678,11907,12050,12127,12173,4035,3695,11032,11095,11176,11236,12074,12141,12393,12465,12478,12997,13002,4576,10798,11168,13010,3313,10398,10494,10625,10687,11479,11700,11747,11781,11877,11932,12134,12300,12512,3314,10756,10801,10804,10837,10863,10900,10938,10974,11948,11951,11954,11957,12154,12157,12160,12163,12233,12404,12448,12715,12740,12819,12826,12833,12838,12841,12844,12877,12889,12950,12975,12978,13081,13154,13160,3315,10427,10482,10692,10777,10903,11587,11784,11796,11883,11894,11915,11920,11960,11982,11997,12731,12883,12907,12936,12941,12965,3316,3393,12107,12797,12848,12852,12856,12860,12870,12874,4553,10344,10436,10549,10573,10819,10866,10876,11553,11654,11675,11678,11681,11697,11839,11842,11845,11848,11944,11963,11966,11976,12031,12034,12037,12040,12114,12204,12207,12303,12306,12366,12397,12434,12516,3472,10645,10911,10955,11225,11303,11467,11709,12343,12519,12923,12992,13043,13089,4569,10828,10840,10947,10965,10968,11023,11109,11117,11133,11171,11188,11197,11233,11274,11294,11297,11300,11328,11341,11344,11726,11762,12025,12028,12062,12108,12137,12281,12324,12330,12416,12419,12438,12492,12498,12507,12529,12796,12813,12816,12912,12993,13035,13053,13056,13093,13137,13140,3379,10674,10704,10713,11254,11808,12435,12449,12778,12782,12785,3416,13077,13134,3410,3828,3767,10347,11627,11657,12758,4566,10301,10668,10671,11112,11130,11590,11645,11689,11710,11814,11851,11854,11857,11860,12981,3336,10707,10860,10931,11658,11813,12002,12234,12806,13080,13155,13161,13165,3789,11759,12711,3531,4564,3800,3835,4543,4545,4546,3287,3288,4544,4547,4548,4588,4301,3807,3626,11620,13019,4224,11486,4578,10275,10278,10530,10581,10584,10589,10997,11461,11713,11817,4589,11191,11308,11350,4013,12264,3906,11347,11684,11688,11750,12351,12359,12441,12725,12987,13039,3752,10971,10977,10992,11929,12140,12412,13038,3613,11194,12166,12278,12288,12356,12407,12415,12526,13047,3650,4078,3754,10710,11048,11200,11230,11241,12246,12355,12401,13027,3582,10631,10634,10716,10890,3580,3581,4581,11621,4577,12679,4583,10767,10869,11179,11331,11464,11492,12228,12237,12284,12462,4178,10843,12078,12249,12261,12287,4086,3788,12532,3733,3734,4579,10323,10326,10662,10665,11503,11685,12471,4580,11601,11694,3756,10628,10887,13067,4020,4586,4608,4613,4620,4636,4685,4687,4716,4734,4741,4742,4781,4811,4817,4900,4926,4927,4987,4988,5010,5011,5024,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9,6360,6441,6508,6509,6517,6592,6626,6627,6668,6669,6801,6814,6885,6886,6890,6912,6935,6943,6945,6993,7018,7019,7035,7036,7037,7072,7116,7117,7214,7270,7271,7272,7273,7287,7314,7369,7370,7379,7386,7388,7400,7432,7433,7434,7435,7574,7575,7582,7584,7585,7586,7797,7799,7800,7816,7854,7923,7964,8022,8044,8045,8063,8124,8224,8293,8294,8296,8328,8390,8391,8462,8481,8482,8483,8484,8631,8838,8862,8863,8943,8957,9012,9013,9118,9163,9186,9218,9260,9450,9734,9872,9929,9975,9977,6057,6424,6425,6511,6527,6528,6934,7152,8556,8587,8775,8968,8969,9035,9036,9311,9312,9313,9314,9523,9816,10103,10190,10191,6493,8381,8382,8827,8845,9817,10189,4677,4679,4680,4735,4743,4878,4894,4895,4917,4920,4924,4925,4954,5009,5051,5071,5128,5177,5205,5241,5244,5250,5252,5253,5279,5354,5377,5512,5576,5577,5578,5696,5697,5722,5723,5727,5780,5786,5788,5797,5803,5875,5952,6017,6080,6103,6269,6367,6387,6539,6741,6742,6883,6946,6986,7158,7371,7441,7773,7775,7865,7936,7938,7939,8020,8782,9039,9277,9558,4859,4908,4955,5095,5510,5689,5956,6019,6032,6053,6067,6321,6744,7133,7330,7397,7474,7759,7828,7862,9394,9395,2635,2636,2784,5859,5906,6049,6134,6609,6610,5594,7858])).
% 162.46/162.15 cnf(13415,plain,
% 162.46/162.15 (P24(f331(f331(f248(a1),f331(f331(f22(a1),x134151),f79(a1))),x134151))),
% 162.46/162.15 inference(rename_variables,[],[10776])).
% 162.46/162.15 cnf(13420,plain,
% 162.46/162.15 (~P24(f331(f331(f333(a883),x134201),f331(f254(a883),f2(a883))))),
% 162.46/162.15 inference(rename_variables,[],[11774])).
% 162.46/162.15 cnf(13423,plain,
% 162.46/162.15 (~P24(f331(f331(f333(f890(x134231,x134231)),x134232),f258(x134231,f196(f891(x134231,a877)))))),
% 162.46/162.15 inference(rename_variables,[],[10964])).
% 162.46/162.15 cnf(13426,plain,
% 162.46/162.15 (~P24(f331(f331(f247(a883),f331(f331(f82(a883),f331(a118,x134261)),f331(a118,x134261))),x134261))),
% 162.46/162.15 inference(rename_variables,[],[10715])).
% 162.46/162.15 cnf(13431,plain,
% 162.46/162.15 (~P24(f331(f331(f196(f891(x134311,f891(x134312,a877))),x134313),x134314))),
% 162.46/162.15 inference(rename_variables,[],[4583])).
% 162.46/162.15 cnf(13443,plain,
% 162.46/162.15 (E(f331(x134431,f543(f331(x134431,x134432),f331(f239(x134433),x134432),x134431,x134434,x134433)),f331(x134431,x134432))),
% 162.46/162.15 inference(rename_variables,[],[11143])).
% 162.46/162.15 cnf(13446,plain,
% 162.46/162.15 (P24(f331(f331(f247(f891(x134461,a877)),x134462),f331(f331(f107(f891(x134461,a877)),x134463),f256(f891(x134461,a877)))))),
% 162.46/162.15 inference(rename_variables,[],[11175])).
% 162.46/162.15 cnf(13457,plain,
% 162.46/162.15 (~E(f331(f331(f154(x134571),x134572),x134573),x134573)),
% 162.46/162.15 inference(rename_variables,[],[4509])).
% 162.46/162.15 cnf(13462,plain,
% 162.46/162.15 (~P24(f331(f331(f333(a883),x134621),f331(f254(a883),f2(a883))))),
% 162.46/162.15 inference(rename_variables,[],[11774])).
% 162.46/162.15 cnf(13472,plain,
% 162.46/162.15 (~E(f331(f331(f251(a883),f331(a118,x134721)),x134721),f331(a118,x134721))),
% 162.46/162.15 inference(rename_variables,[],[11524])).
% 162.46/162.15 cnf(13481,plain,
% 162.46/162.15 (~P35(x134811,x134812,x134813,f331(f331(f157(x134814,x134811),x134815),f331(a118,f119(x134814))),f119(x134812))),
% 162.46/162.15 inference(rename_variables,[],[11205])).
% 162.46/162.15 cnf(13488,plain,
% 162.46/162.15 (~P24(f331(f331(f247(a883),f331(a118,x134881)),x134881))),
% 162.46/162.15 inference(rename_variables,[],[4566])).
% 162.46/162.15 cnf(13491,plain,
% 162.46/162.15 (~P24(f331(f331(f333(x134911),x134912),f196(f891(x134911,a877))))),
% 162.46/162.15 inference(rename_variables,[],[4569])).
% 162.46/162.15 cnf(13500,plain,
% 162.46/162.15 (~P24(f331(f331(f333(x135001),x135002),f196(f891(x135001,a877))))),
% 162.46/162.15 inference(rename_variables,[],[4569])).
% 162.46/162.15 cnf(13504,plain,
% 162.46/162.15 (~P24(f331(f331(f196(f891(x135041,f891(x135042,a877))),x135043),x135044))),
% 162.46/162.15 inference(rename_variables,[],[4583])).
% 162.46/162.15 cnf(13522,plain,
% 162.46/162.15 (~P24(f331(f331(f333(a883),x135221),f331(f254(a883),f2(a883))))),
% 162.46/162.15 inference(rename_variables,[],[11774])).
% 162.46/162.15 cnf(13527,plain,
% 162.46/162.15 (~P24(f331(f331(f196(f891(x135271,f891(x135272,a877))),x135273),x135274))),
% 162.46/162.15 inference(rename_variables,[],[4583])).
% 162.46/162.15 cnf(13532,plain,
% 162.46/162.15 (P24(f331(f331(f333(x135321),f331(x135322,x135323)),f331(f310(x135324,x135321,x135322),f256(f891(x135324,a877)))))),
% 162.46/162.15 inference(rename_variables,[],[3906])).
% 162.46/162.15 cnf(13547,plain,
% 162.46/162.15 (P24(f331(f331(f333(x135471),f331(x135472,x135473)),f331(f310(x135474,x135471,x135472),f256(f891(x135474,a877)))))),
% 162.46/162.15 inference(rename_variables,[],[3906])).
% 162.46/162.15 cnf(13552,plain,
% 162.46/162.15 (~P24(f331(f331(f333(x135521),x135522),f196(f891(x135521,a877))))),
% 162.46/162.15 inference(rename_variables,[],[4569])).
% 162.46/162.15 cnf(13562,plain,
% 162.46/162.15 (~P24(f331(f331(f333(f890(x135621,x135621)),x135622),f258(x135621,f196(f891(x135621,a877)))))),
% 162.46/162.15 inference(rename_variables,[],[10964])).
% 162.46/162.15 cnf(13573,plain,
% 162.46/162.15 (E(f331(f257(x135731,x135731),f258(x135731,x135732)),x135732)),
% 162.46/162.15 inference(rename_variables,[],[3270])).
% 162.46/162.15 cnf(13576,plain,
% 162.46/162.15 (E(f331(f257(x135761,x135761),f258(x135761,x135762)),x135762)),
% 162.46/162.15 inference(rename_variables,[],[3270])).
% 162.46/162.15 cnf(13579,plain,
% 162.46/162.15 (E(f331(f331(f137(x135791),x135792),f119(x135791)),x135792)),
% 162.46/162.15 inference(rename_variables,[],[3244])).
% 162.46/162.15 cnf(13588,plain,
% 162.46/162.15 (~P24(f331(f331(f333(x135881),x135882),f196(f891(x135881,a877))))),
% 162.46/162.15 inference(rename_variables,[],[4569])).
% 162.46/162.15 cnf(13605,plain,
% 162.46/162.15 (~P24(f331(f331(f333(x136051),x136052),f196(f891(x136051,a877))))),
% 162.46/162.15 inference(rename_variables,[],[4569])).
% 162.46/162.15 cnf(13617,plain,
% 162.46/162.15 (~E(f331(f331(f154(x136171),x136172),x136173),x136173)),
% 162.46/162.15 inference(rename_variables,[],[4509])).
% 162.46/162.15 cnf(13640,plain,
% 162.46/162.15 (P24(f331(f331(f247(a883),x136401),x136401))),
% 162.46/162.15 inference(rename_variables,[],[3314])).
% 162.46/162.15 cnf(13643,plain,
% 162.46/162.15 (~P24(f331(f331(f333(a883),x136431),f331(f254(a883),f2(a883))))),
% 162.46/162.15 inference(rename_variables,[],[11774])).
% 162.46/162.15 cnf(13654,plain,
% 162.46/162.15 (P24(f331(f331(f247(a883),x136541),f331(f331(f82(a883),x136541),x136541)))),
% 162.46/162.15 inference(rename_variables,[],[3582])).
% 162.46/162.15 cnf(13662,plain,
% 162.46/162.15 (~P24(f331(f331(f333(x136621),x136622),f331(f311(x136621,x136623,x136624),f196(f891(x136623,a877)))))),
% 162.46/162.15 inference(rename_variables,[],[10967])).
% 162.46/162.15 cnf(13684,plain,
% 162.46/162.15 (~P24(f331(f331(f333(x136841),x136842),f196(f891(x136841,a877))))),
% 162.46/162.15 inference(rename_variables,[],[4569])).
% 162.46/162.15 cnf(13691,plain,
% 162.46/162.15 (E(f331(x136911,f543(f331(x136911,x136912),f331(f239(x136913),x136912),x136911,x136914,x136913)),f331(x136911,x136912))),
% 162.46/162.15 inference(rename_variables,[],[11143])).
% 162.46/162.15 cnf(13703,plain,
% 162.46/162.15 (P24(f331(f331(f247(f891(x137031,a877)),x137032),x137032))),
% 162.46/162.15 inference(rename_variables,[],[3613])).
% 162.46/162.15 cnf(13706,plain,
% 162.46/162.15 (~P24(f331(f331(f333(a883),x137061),f331(f254(a883),f2(a883))))),
% 162.46/162.15 inference(rename_variables,[],[11774])).
% 162.46/162.15 cnf(13711,plain,
% 162.46/162.15 (P24(f331(f331(f248(a883),x137111),f331(a118,f331(f331(f81(a883),x137112),x137111))))),
% 162.46/162.15 inference(rename_variables,[],[3756])).
% 162.46/162.15 cnf(13723,plain,
% 162.46/162.15 (~E(f331(f331(f154(x137231),x137232),x137233),x137233)),
% 162.46/162.15 inference(rename_variables,[],[4509])).
% 162.46/162.15 cnf(13730,plain,
% 162.46/162.15 (~E(f331(f331(f251(a883),f331(a118,x137301)),x137301),f331(a118,x137301))),
% 162.46/162.15 inference(rename_variables,[],[11524])).
% 162.46/162.15 cnf(13738,plain,
% 162.46/162.15 (~P24(f331(f331(f333(f890(x137381,x137381)),x137382),f258(x137381,f196(f891(x137381,a877)))))),
% 162.46/162.15 inference(rename_variables,[],[10964])).
% 162.46/162.15 cnf(13751,plain,
% 162.46/162.15 (~E(f331(f331(f154(x137511),x137512),x137513),x137513)),
% 162.46/162.15 inference(rename_variables,[],[4509])).
% 162.46/162.15 cnf(13758,plain,
% 162.46/162.15 (P24(f331(f331(f247(a883),f45(a883,x137581,x137582)),x137581))),
% 162.46/162.15 inference(rename_variables,[],[3767])).
% 162.46/162.15 cnf(13761,plain,
% 162.46/162.15 (~E(f331(f331(f154(x137611),x137612),x137613),x137613)),
% 162.46/162.15 inference(rename_variables,[],[4509])).
% 162.46/162.15 cnf(13768,plain,
% 162.46/162.15 (~P24(f331(f331(f333(f890(f884(x137681),f884(x137681))),f331(f331(f261(f884(x137681),f884(x137681)),x137682),f119(x137681))),f148(x137681,x137683)))),
% 162.46/162.15 inference(rename_variables,[],[4590])).
% 162.46/162.15 cnf(13779,plain,
% 162.46/162.15 (P24(f331(f331(f247(a883),x137791),f331(f331(f82(a883),x137791),x137791)))),
% 162.46/162.15 inference(rename_variables,[],[3582])).
% 162.46/162.15 cnf(13782,plain,
% 162.46/162.15 (~P24(f331(f331(f333(f890(x137821,x137821)),x137822),f258(x137821,f196(f891(x137821,a877)))))),
% 162.46/162.15 inference(rename_variables,[],[10964])).
% 162.46/162.15 cnf(13789,plain,
% 162.46/162.15 (~P24(f331(f331(f196(f891(x137891,f891(x137892,a877))),x137893),x137894))),
% 162.46/162.15 inference(rename_variables,[],[4583])).
% 162.46/162.15 cnf(13798,plain,
% 162.46/162.15 (~E(f331(f331(f154(x137981),x137982),x137983),x137983)),
% 162.46/162.15 inference(rename_variables,[],[4509])).
% 162.46/162.15 cnf(13801,plain,
% 162.46/162.15 (~P24(f331(f331(f333(f890(x138011,x138011)),x138012),f258(x138011,f196(f891(x138011,a877)))))),
% 162.46/162.15 inference(rename_variables,[],[10964])).
% 162.46/162.15 cnf(13808,plain,
% 162.46/162.15 (E(f331(f331(f137(x138081),x138082),f119(x138081)),x138082)),
% 162.46/162.15 inference(rename_variables,[],[3244])).
% 162.46/162.15 cnf(13813,plain,
% 162.46/162.15 (~P24(f331(f331(f247(a883),f331(a118,x138131)),x138131))),
% 162.46/162.15 inference(rename_variables,[],[4566])).
% 162.46/162.15 cnf(13829,plain,
% 162.46/162.15 (~P24(f331(f331(f333(x138291),x138292),f331(f311(x138291,x138293,x138294),f196(f891(x138293,a877)))))),
% 162.46/162.15 inference(rename_variables,[],[10967])).
% 162.46/162.15 cnf(13836,plain,
% 162.46/162.15 (P24(f331(f331(f248(a1),f331(f331(f22(a1),x138361),f79(a1))),x138361))),
% 162.46/162.15 inference(rename_variables,[],[10776])).
% 162.46/162.15 cnf(13839,plain,
% 162.46/162.15 (P24(f331(f331(f247(a883),f2(a883)),x138391))),
% 162.46/162.15 inference(rename_variables,[],[3336])).
% 162.46/162.15 cnf(13846,plain,
% 162.46/162.15 (~E(f331(f331(f154(x138461),x138462),x138463),x138463)),
% 162.46/162.15 inference(rename_variables,[],[4509])).
% 162.46/162.15 cnf(13854,plain,
% 162.46/162.15 (~P24(f331(f331(f333(x138541),x138542),f196(f891(x138541,a877))))),
% 162.46/162.15 inference(rename_variables,[],[4569])).
% 162.46/162.15 cnf(13861,plain,
% 162.46/162.15 (P24(f331(f331(f247(f891(x138611,a877)),f331(f175(x138611),f173(x138611,x138612,x138613))),f331(f175(x138611),x138613)))),
% 162.46/162.15 inference(rename_variables,[],[4001])).
% 162.46/162.15 cnf(13864,plain,
% 162.46/162.15 (E(f331(f331(f137(x138641),x138642),f119(x138641)),x138642)),
% 162.46/162.15 inference(rename_variables,[],[3244])).
% 162.46/162.15 cnf(13867,plain,
% 162.46/162.15 (P24(f331(f331(f247(a883),x138671),f331(f331(f82(a883),x138671),x138671)))),
% 162.46/162.15 inference(rename_variables,[],[3582])).
% 162.46/162.15 cnf(13870,plain,
% 162.46/162.15 (~P24(f331(f331(f248(a883),x138701),x138701))),
% 162.46/162.15 inference(rename_variables,[],[4553])).
% 162.46/162.15 cnf(13873,plain,
% 162.46/162.15 (~P24(f331(f331(f333(x138731),x138732),f196(f891(x138731,a877))))),
% 162.46/162.15 inference(rename_variables,[],[4569])).
% 162.46/162.15 cnf(13876,plain,
% 162.46/162.15 (~P24(f331(f331(f333(a883),x138761),f331(f254(a883),f2(a883))))),
% 162.46/162.15 inference(rename_variables,[],[11774])).
% 162.46/162.15 cnf(13892,plain,
% 162.46/162.15 (~P24(f331(f331(f333(a883),x138921),f331(f254(a883),f2(a883))))),
% 162.46/162.15 inference(rename_variables,[],[11774])).
% 162.46/162.15 cnf(13903,plain,
% 162.46/162.15 (~E(f331(a118,x139031),f2(a883))),
% 162.46/162.15 inference(rename_variables,[],[4495])).
% 162.46/162.15 cnf(13929,plain,
% 162.46/162.15 (~P24(f331(f331(f333(f890(f884(x139291),f884(x139291))),f331(f331(f261(f884(x139291),f884(x139291)),x139292),f119(x139291))),f150(x139291,x139293)))),
% 162.46/162.15 inference(rename_variables,[],[4591])).
% 162.46/162.15 cnf(13961,plain,
% 162.46/162.15 (P24(f331(f331(f333(x139611),f331(x139612,x139613)),f331(f310(x139614,x139611,x139612),f256(f891(x139614,a877)))))),
% 162.46/162.15 inference(rename_variables,[],[3906])).
% 162.46/162.15 cnf(13977,plain,
% 162.46/162.15 (~P24(f331(f331(f333(a883),x139771),f331(f254(a883),f2(a883))))),
% 162.46/162.15 inference(rename_variables,[],[11774])).
% 162.46/162.15 cnf(13989,plain,
% 162.46/162.15 (~P24(f331(f331(f333(f890(x139891,x139891)),x139892),f258(x139891,f196(f891(x139891,a877)))))),
% 162.46/162.15 inference(rename_variables,[],[10964])).
% 162.46/162.15 cnf(14001,plain,
% 162.46/162.15 (~E(f331(f331(f154(x140011),x140012),x140013),x140013)),
% 162.46/162.15 inference(rename_variables,[],[4509])).
% 162.46/162.15 cnf(14012,plain,
% 162.46/162.15 (P24(f331(f331(f247(a883),x140121),f331(f331(f81(a883),x140121),x140122)))),
% 162.46/162.15 inference(rename_variables,[],[3581])).
% 162.46/162.15 cnf(14071,plain,
% 162.46/162.15 (P24(f331(f331(f247(f891(x140711,a877)),f331(f175(x140711),f173(x140711,x140712,x140713))),f331(f175(x140711),x140713)))),
% 162.46/162.15 inference(rename_variables,[],[4001])).
% 162.46/162.15 cnf(14105,plain,
% 162.46/162.15 (P24(f331(f331(f247(f891(x141051,a877)),x141052),f331(f331(f309(x141051),x141053),x141052)))),
% 162.46/162.15 inference(rename_variables,[],[3752])).
% 162.46/162.15 cnf(14131,plain,
% 162.46/162.15 ($false),
% 162.46/162.15 inference(scs_inference,[],[3342,3745,4046,3889,4080,3102,4581,3314,13640,4554,3942,4590,13768,4544,3410,3758,4569,13491,13500,13552,13588,13605,13684,13854,13873,3397,4001,13861,14071,3906,13532,13547,13961,3788,3420,4500,4495,13903,4575,4509,13457,13617,13723,13751,13761,13798,13846,14001,4588,3296,4074,3951,3315,3767,13758,3336,13839,3626,3752,14105,3613,13703,3582,13654,13779,13867,3581,14012,3756,13711,3270,13573,13576,3244,13579,13808,13864,3677,4591,13929,4592,4553,13870,4566,13488,13813,4577,4583,13431,13504,13527,13789,4579,4580,11524,13472,13730,10330,13070,13322,10599,11207,12730,11834,11876,12962,12457,11338,13246,13399,12245,12236,10630,10614,11075,12459,12495,10954,13170,11175,13446,10918,12230,10776,13415,13836,11240,11199,4358,11143,13443,13691,13186,12986,10951,10445,11288,10720,10561,3348,3254,11141,10320,11001,12974,12977,13266,10733,13292,11660,12170,11926,12277,11774,13420,13462,13522,13643,13706,13876,13892,13977,11129,10964,13423,13562,13738,13782,13801,13989,10967,13662,13829,10715,13426,10818,12033,12039,12054,12514,13276,11205,13481,10979,2907,4540,3858,5536,6734,8764,10227,6252,8662,4926,5197,5985,9039,9827,5786,8019,6524,4894,8515,5276,4734,5790,8765,8424,6793,9553,9919,5908,7843,5011,9255,6203,5177,5819,6754,8117,5797,6148,9614,2,5770,8665,5050,5279,5487,5896,6806,7724,7896,9405,6755,6821,7756,8537,5429,5010,5079,5253,6380,7430,5558,4987,5371,8873,9622,10116,5621,9575,5313,6121,8504,6376,5373,6385,6779,7305,9974,8,5803,8853,8889,5272,8036,8547,9554,7158,7411,7939,5637,5234,5783,5776,5716,7441,6384,7925,5875,5245,5761,6124,6742,5350,9144,5342,5705,7098,6328,5559,6888,8580,5205,5077,8488,8519,9555,8516,6526,8682,6103,6083,4677,4685,5335,7303,6771,9447,9670,5719,6267,6871,7675,6733,7768,5340,5780,8374,8449,7183,8704,9465,10038,9920,5393,8020,8581,6387,7547,6491,4636,5437,6777,9950,5762,5944,6661,6776,6884,9762,5589,5590,5958,9026,8358,9309,5341,5577,6299,9921,5372,5388,5917,9493,5131,5503,6300,7313,8378,9192,5680,9,5838,6331,6377,6498,8582,8624,8878,9931,5326,7723,8562,5084,6768,7480,7806,6818,6105,8578,6200,6269,6903,6329,8742,9232,9930,5774,5850,9544,5701,5767,6882,9969,8443,5668,5715,6154,6773,6195,9721,6156,5367,5722,9063,5708,7818,8212,8350,6436,5406,8898,8231,7484,6340,6087,6305,10206,5206,6775,9752,8782,6254,5078,8763,5071,6038,6194,7241,4620,4781,5222,5057,8978,7325,5488,5825,6583,9711,8539,5009,4954,9881,6284,6458,7865,4988,5921,7017,7153,6102,6263,5260,6275,7689,8590,9986,6248,6150,8789,9277,4811,5358,5844,5778,5360,7321,9793,5765,5596,7479,8762,9430,9064,7705,6130,5438,8394,9471,5336,5353,4878,9010,4716]),
% 162.46/162.15 ['proof']).
% 162.46/162.15 % SZS output end Proof
% 162.46/162.15 % Total time :147.230000s
%------------------------------------------------------------------------------